Hidrodinamica e Propulsao.pdf

195
Hidrodin ˆ amica e Propuls ˜ ao Engenharia de M´aquinas Mar´ ıtimas Jorge Trindade ENIDH 2012

Transcript of Hidrodinamica e Propulsao.pdf

Page 1: Hidrodinamica e Propulsao.pdf

Hidrodinamica e PropulsaoEngenharia de Maquinas Marıtimas

Jorge Trindade

ENIDH

2012

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Indice

1 Introducao 1

1.1 Geometria do navio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Principais dimensoes dos navios . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.2 Coeficientes de forma do navio . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Comportamento hidrodinamico do navio . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Metodos empıricos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Metodos experimentais . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Simulacoes numericas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Resistencia 13

2.1 Analise dimensional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Leis da semelhanca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1 Semelhanca geometrica . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.2 Semelhanca cinematica . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.3 Semelhanca dinamica . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Decomposicao da resistencia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.1 Resistencia de onda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.2 Resistencia de atrito . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3.3 Resistencia viscosa de pressao . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4 Ensaios de resistencia em tanques de reboque . . . . . . . . . . . . . . . . . . . 26

2.5 Calculo da resistencia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.5.1 Metodos de extrapolacao . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.5.2 Resistencias adicionais . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.6 Previsao com dados sistematicos ou estatısticos . . . . . . . . . . . . . . . . . . 32

2.7 Ensaios a escala real . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3 Propulsao 35

3.1 Sistemas de propulsao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.1 Helices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.2 Outros meios de propulsao . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2 Helices propulsores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.2.1 Geometria do helice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.2.2 Valores caracterısticos . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.3 Teoria da quantidade de movimento . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3.1 Forca propulsiva . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

i

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ii INDICE

3.3.2 Coeficiente de carga . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.3.3 Rendimento ideal do helice . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.4 Ensaios com modelos reduzidos de helices . . . . . . . . . . . . . . . . . . . . . 453.4.1 Diagrama em aguas livres . . . . . . . . . . . . . . . . . . . . . . . . . . 463.4.2 Rendimento . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.4.3 Indice de qualidade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.5 Series sistematicas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.5.1 Serie sistematica de Wageningen . . . . . . . . . . . . . . . . . . . . . . 483.5.2 Outras series sistematicas . . . . . . . . . . . . . . . . . . . . . . . . . . 493.5.3 Diagrama de 4 quadrantes . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.6 Cavitacao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.6.1 Origem da cavitacao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.6.2 Controle da cavitacao . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.6.3 Consideracao da cavitacao na seleccao do helice . . . . . . . . . . . . . . 553.6.4 Ensaios experimentais . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.7 Seleccao do helice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.7.1 Variaveis de optimizacao . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.7.2 Tipos de problema . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.8 Interaccao entre casco e helice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.8.1 Ensaios de propulsao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.8.2 Potencia e velocidade . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.8.3 Extrapolacao dos resultados do ensaio de propulsao . . . . . . . . . . . 66

4 Instalacoes Propulsoras 674.1 Introducao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.2 Propulsao diesel-mecanica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.2.1 Accionamento de auxiliares . . . . . . . . . . . . . . . . . . . . . . . . . 704.2.2 Engrenagens redutoras . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.2.3 Configuracao ”pai-e-filho” . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.3 Propulsao diesel-electrica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.3.1 Propulsao por motor electrico . . . . . . . . . . . . . . . . . . . . . . . . 744.3.2 Propulsores azimutais . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.4 Seleccao do motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.4.1 Turbinas e motores electricos . . . . . . . . . . . . . . . . . . . . . . . . 794.4.2 Motores diesel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Indice Remissivo 83

A Previsao Baseada nos Ensaios de Propulsao 87

B Provas de velocidade e Potencia 121

C Condicoes das Provas de Velocidade e Potencia 133

D Seleccao de Motores Propulsores 141

E Derating 175

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Lista de Figuras

1.1 Plano de flutuacao, longitudinal e transversal de um navio. . . . . . . . . . . . 2

1.2 Plano geometrico de um navio. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Principais dimensoes dos navios. . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Marcacao no costado das linhas de carga do navio. . . . . . . . . . . . . . . . . 5

1.5 Tanque de provas utilizado por W. Froude. . . . . . . . . . . . . . . . . . . . . 7

1.6 Tanque de testes actual. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.7 Bacia para testes com ondulacao. . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.8 Bacia para testes com aguas geladas. . . . . . . . . . . . . . . . . . . . . . . . . 8

1.9 Escoamento num helice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.10 Malha colocada a esquerda e desfasada a direita. . . . . . . . . . . . . . . . . . 9

1.11 Representacao esquematica de um “PC-cluster”. . . . . . . . . . . . . . . . . . . 10

1.12 Um “PC-cluster” com 24 nos computacionais. . . . . . . . . . . . . . . . . . . . 10

1.13 Decomposicao 1D, 2D ou 3D do domınio espacial de um problema. . . . . . . . 11

1.14 Troca de valores nas fronteiras dos sub-domınios. . . . . . . . . . . . . . . . . . 11

2.1 Decomposicao da resistencia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2 Sistema de ondas gerado por um ponto de pressao em movimento. . . . . . . . 20

2.3 Sistemas de ondas da proa e da popa. . . . . . . . . . . . . . . . . . . . . . . . 21

2.4 Interaccao entre os dois sistemas de ondas. . . . . . . . . . . . . . . . . . . . . . 22

2.5 Curva da resistencia de onda. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.6 Variacao do coeficiente da resistencia de atrito com o numero de Reynolds ecom a rugosidade da superfıcie. . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.7 Distribuicao de pressao num escoamento ideal, invıscido. . . . . . . . . . . . . . 26

2.8 Modelo a escala reduzida para ensaios de resistencia. . . . . . . . . . . . . . . . 27

2.9 Representacao grafica da dependencia decTcF0

comFr4

cF0. . . . . . . . . . . . . . 29

2.10 Reducao de velocidade (%) em aguas pouco profundas. . . . . . . . . . . . . . . 33

3.1 Helice com tubeira. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2 Helices de passo fixo e de passo controlavel. . . . . . . . . . . . . . . . . . . . . 36

3.3 Helices em contra-rotacao. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4 Helices supercavitante. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.5 Propulsao por jacto de agua. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.6 Propulsores azimutais. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.7 Propulsores cicloidais. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

iii

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iv LISTA DE FIGURAS

3.8 Geometria do helice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.9 Distribuicao espacial de velocidade e pressao para a teoria da quantidade de

movimento. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.10 Diagrama de aguas livres. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.11 Aspecto geometrico das pas da serie B de Wageningen . . . . . . . . . . . . . . 483.12 Diagrama em aguas livres de um helice da serie sistematica de Wageningen. . . 503.13 Notacao do diagrama com 4 quadrantes. . . . . . . . . . . . . . . . . . . . . . . 513.14 Diagrama em aguas livres de 4 quadrantes para os helices Wageningen B-4.70. 533.15 Efeito da cavitacao no valor dos parametros relativos a aguas livres. . . . . . . 543.16 Pressao de vapor da agua em funcao da temperatura. . . . . . . . . . . . . . . 553.17 Diagrama de Burrill. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.18 Instalacoes de ensaio do RINA. . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.19 Imagem da cavitacao num helice. . . . . . . . . . . . . . . . . . . . . . . . . . . 583.20 Modelo para ensaios de propulsao. . . . . . . . . . . . . . . . . . . . . . . . . . 613.21 Resultados dos ensaios de propulsao. . . . . . . . . . . . . . . . . . . . . . . . . 66

4.1 Variantes de instalacoes propulsoras diesel-mecanicas lentas e de media veloci-dade. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.2 Instalacoes propulsoras diesel-mecanica (em cima) e diesel-electrica (em baixo). 694.3 Acoplamento com relacao variavel de velocidades. . . . . . . . . . . . . . . . . . 714.4 Conversao da frequencia da energia electrica. . . . . . . . . . . . . . . . . . . . 724.5 Instalacao propulsora com quatro motores, engrenagens redutoras e dois helices. 734.6 Instalacao com dois motores diesel diferentes, engrenagens redutoras, embrai-

agens e geradores acoplados aos veios. . . . . . . . . . . . . . . . . . . . . . . . 744.7 Motor electrico de propulsao. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754.8 Instalacao diesel-electrica. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.9 Representacao esquematica de uma instalacao diesel-electrica. . . . . . . . . . . 774.10 Propulsores azimutais. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.11 Diagrama de carga de um motor diesel . . . . . . . . . . . . . . . . . . . . . . . 80

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Lista de Tabelas

1.1 Valores de K na formula de Alexander. . . . . . . . . . . . . . . . . . . . . . . 6

2.1 Valores do coeficiente de correccao cA em funcao do comprimento do navio. . . 29

3.1 Series sistematicas de propulsores. . . . . . . . . . . . . . . . . . . . . . . . . . 483.2 Coeficiente para atribuicao do diametro maximo do helice pela Eq. (3.34). . . . 593.3 Constante para o calculo do diametro equivalente em agua livres pela Eq. (3.35). 59

v

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vi LISTA DE TABELAS

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Capıtulo 1Introducao

1.1 Geometria do navio

A variacao da proporcao relativa das dimensoes principais de um navio tem um importanteefeito nas suas caracterısticas operacionais. Afecta as suas caracterısticas hidrodinamicas, asua resistencia estrutural e, naturalmente a capacidade de carga.

Os navios existentes, em particular as unidades de construcao mais recente, constituemuma boa “fonte de inspiracao” para o pre-dimensionamento de um navio novo. No que dizrespeito a informacao mais detalhada, estas bases de dados sao, regra geral, bem resguardadaspelos gabinetes de estudo e projecto, bem como pelos estaleiros construtores. No entanto,alguns destes dados estao disponıveis nos registos publicados pelas sociedades classificadorase por alguns gabinetes de estudo.

Depois de um processo iterativo de dimensionamento do navio, durante o qual sao tidasem consideracao as variaveis de optimizacao seleccionadas, a solucao final da forma do navioconstitui o plano geometrico do navio. Na pratica, este plano geometrico e gerado por umadas seguintes vias:

- deformacao de um navio de referencia;

- modelo matematico para definicao de forma em funcao de parametros do navio;

- utilizacao das series sistematicas.

1.1.1 Principais dimensoes dos navios

O casco de um navio e uma forma tridimensional, na maior parte dos casos simetrica rela-tivamente a um plano vertical longitudinal do navio. O contorno do casco fica definido pelasua interseccao com tres planos ortogonais (Fig. 1.1):

- o plano de flutuacao de projecto;

- o plano longitudinal;

- o plano transversal.

1

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2 CAPITULO 1. INTRODUCAO

Figura 1.1: Plano de flutuacao, longitudinal e transversal de um navio.

O plano longitudinal, unico plano de simetria do navio, e o plano de referencia. A formado navio cortada por este plano e o perfil. O plano de flutuacao de projecto e um planoperpendicular ao plano longitudinal, escolhido como plano de referencia. Os planos paralelosao plano de flutuacao de projecto sao conhecidos como planos de agua, ou de flutuacao, e aslinhas de interseccao como linhas de agua. Os planos de flutuacao sao simetricos relativamenteao plano longitudinal. Os planos perpendiculares ao plano longitudinal e ao plano de flutuacaode projecto sao os planos transversais. As seccoes transversais exibem simetria relativamenteao plano longitudinal.

A seccao do navio equidistante das perpendiculares e normal aos planos de flutuacao deverao e longitudinal e designada por seccao de meio-navio, ou seccao mestra. Na Fig. 1.2esta representado um plano de linhas do navio, que inclui o plano do casco, no qual, porconvencao, sempre que o navio e simetrico, se exibem metades das seccoes. Do lado direitorepresentam-se metades das seccoes avante de meio-navio e do lado esquerdo metades dasseccoes a re. O plano de linhas do navio inclui ainda o plano da metade da boca, no qual saorepresentados os planos de flutuacao.

Figura 1.2: Plano geometrico de um navio.

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1.1. GEOMETRIA DO NAVIO 3

Na Fig. 1.3 estao representadas as dimensoes mais frequentemente utilizadas para definiro navio. Quanto ao comprimento do navio, sao tres as definicoes a considerar:

- o comprimento entre perpendiculares, Lpp, distancia medida ao longo do plano de flu-tuacao de verao entre a perpendicular da popa e a perpendicular da proa;

- o comprimento na linha de agua, Lwl, distancia na linha de flutuacao que se verifique, senada for referido devera entender-se a linha de flutuacao de verao, entre as interseccoesda proa e popa com a mesma linha de flutuacao;

- o comprimento fora a fora, Loa, distancia entre os pontos extremos a vante e a re donavio, medida numa direccao paralela a linha de flutuacao de verao.

Designa-se por boca, a maxima distancia entre as faces interiores das chapas de costadonos dois bordos do navio, na seccao mestra, se outra seccao nao for indicada. O pontal e adistancia na vertical, medida a meio navio, entre a face inferior do conves e a face superiorda chapa da quilha. O calado de um navio em qualquer ponto do seu comprimento e adistancia na vertical entre a quilha e a linha de agua. O calado varia nao so com o estado decarregamento do navio mas tambem com a densidade da agua em que este se encontra.

A altura desde a linha de flutuacao e o conves e designada por bordo livre. Pode sercalculado pela diferenca entre o pontal e o calado.

Um aspecto importante relativamente a seguranca de um navio mercante prende-se coma alocacao regulamentar de um valor mınimo do bordo livre, como forma de garantir umareserva de estabilidade suficiente para a seguranca da navegacao. Este valor mınimo do bordolivre depende do local de navegacao e da epoca do ano. No costado do navio estao marcadasas linhas de carga por forma a permitir verificar facilmente se as condicoes de seguranca saoverificadas. O valor de referencia e a linha de Verao que e marcada no centro de um cırculo,Fig. 1.4. Ao lado deste cırculo, sao marcadas na horizontal linhas adicionais que correspondemao:

- bordo livre de Inverno, superior em 1/48 avos do bordo livre de Verao;

- bordo livre de Inverno no Atlantico Norte, ainda superior em 50 mm;

- bordo livre tropical, inferior em 1/48 avos do bordo livre de Verao;

- bordo livre em agua doce, inferior em ∆ / (40 t) cm, sendo ∆ o deslocamento em ton et as ton por cm de imersao;

- bordo livre tropical em agua doce e inferior em 1/48 avos do bordo livre de Verao aobordo livre em agua doce.

1.1.2 Coeficientes de forma do navio

O deslocamento do navio e o peso do volume de agua que o navio desloca quando a flutuarem aguas tranquilas,

∆ = ρg∇ (1.1)

em que ρ e a massa volumica da agua em que o navio se encontra a flutuar, g e a aceleracaoda gravidade e ∇ o volume deslocado.

A partir das principais dimensoes da navio, definem-se os seguintes coeficientes de forma:

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4 CAPITULO 1. INTRODUCAO

Figura 1.3: Principais dimensoes dos navios.

- o coeficiente de finura total (“block coeficient”):

Cb =∇

LppBT(1.2)

onde:

- ∇ e o volume do deslocamento;

- Lpp o comprimento entre perpendiculares;

- B a boca (maxima abaixo da linha de agua);

- e T e o calado medio do navio.

- o coeficiente de finura da flutuacao:

Cwp =AwpLwpB

(1.3)

em que:

- Awp e a area do plano de flutuacao;

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1.1. GEOMETRIA DO NAVIO 5

Figura 1.4: Marcacao no costado das linhas de carga do navio.

- Lwp o comprimento na linha de flutuacao;

- e B a boca (maxima na linha de flutuacao).

- o coeficiente de finura da seccao mestra:

Cm =AmBT

(1.4)

representando por:

- Am a area imersa na seccao mestra;

- B a boca na seccao mestra;

- e T o calado a meio navio.

- o coeficiente prismatico longitudinal:

Cp =∇

AmLpp(1.5)

em que novamente:

- ∇ e o volume da querena;

- Am a area imersa a meio navio;

- e Lpp o comprimento entre perpendiculares.

Como exemplo da utilizacao dos coeficientes de forma no estabelecimento de relacoesempıricas para inıcio do projecto de um navio, pode-se indicar a formula de Alexander,

Cb = K − 0.5× V√L

(1.6)

em que K apresenta os valores da Tab. 1.1 de acordo com o tipo de navio. A formula deAlexander estabelece uma relacao empırica entre o coeficiente de finura total do navio, a suavelocidade e o comprimento. Pela especificidade de cada caso, o coeficiente de finura totalCb do navio podera depois desviar-se do valor inicialmente previsto durante o processo deoptimizacao das caracterısticas do navio.

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6 CAPITULO 1. INTRODUCAO

Tipo de Navio K

Petroleiro 1.13Graneleiro 1.11Carga geral 1.10

Navio de linha 1.05Ferry 1.08

Rebocador 1.18

Tabela 1.1: Valores de K na formula de Alexander.

1.2 Comportamento hidrodinamico do navio

A analise do comportamento hidrodinamico do navio pode ser decomposta em diversas areas,de entre as quais se pode salientar:

- a resistencia;

- a propulsao;

- o comportamento do navio no mar;

- a capacidade de manobra.

O calculo do escoamento e o projecto de helices pode ser considerado como um sub-topico dotema resistencia e propulsao.

As metodologias para o calculo ou para a previsao dos parametros relevantes do compor-tamento do navio podem ser classificadas como:

- empıricas e estatısticas;

- experimentais em modelos a escala reduzida, ou a escala real;

- numericas, atraves de solucoes analıticas ou com recurso a mecanica de fluidos compu-tacional.

Os princıpios fundamentais destas metodologias sao sumariamente descritos nas seccoesseguintes.

1.3 Metodos empıricos

Os metodos empıricos baseiam-se num modelo fısico relativamente simples e na analise porregressao para a determinacao dos coeficientes relevantes, a partir de um so navio ou de umaserie de navios. Os resultados assim obtidos sao depois expressos sob a forma de constantes,formulas, tabelas, graficos, etc.

Numerosos estudos realizados entre 1940 e 1960 permitiram criar series de “boas” formasde carenas. O efeito da variacao dos principais parametros do casco, como por exemplo ocoeficiente de bloco, foi determinado por alteracao sistematica daqueles parametros.

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1.4. METODOS EXPERIMENTAIS 7

Figura 1.5: Tanque de provas utilizadopor W. Froude. Figura 1.6: Tanque de testes actual.

1.4 Metodos experimentais

Esta abordagem baseia-se no teste de modelos em escala reduzida para extrair informacao quepossa ser extrapolada para a escala do navio. Apesar dos grandes esforcos de investigacao enormalizacao, a correlacao modelo-navio esta sujeita a algum grau de empirismo. Cada umadas principais instalacoes de teste (tuneis, bacias, etc.) tende a adoptar os metodos de ensaioe tratamento da informacao que melhor se adaptam a experiencia ja incorporada nas suasbases de dados. Esta nao uniformidade de processos dificulta, se nao mesmo em muitos casosimpossibilita, o aproveitamento estatıstico dos dados de uma forma agregada.

Embora a metodologia base para a avaliacao da resistencia de um modelo num tanque detestes se mantenha praticamente inalterada desde os tempos de Froude (1874), varios aspectostecnicos sofreram grande evolucao. De entre estes, podem-se salientar:

- as tecnicas experimentais nao-intrusivas, como a Laser-Doppler Velocimetry, que per-mitem a medicao do campo de velocidades na esteira do navio para melhorar o projectodo helice;

- a analise do padrao da formacao ondosa gerada pelo modelo para estimar a resistenciade onda;

- nos testes de modelos com propulsao autonoma, e possıvel agora medir grandezas rela-cionadas com o propulsor como o impulso, binario, rpm, etc.

Instalacoes com caracterısticas bem diferentes surgiram entretanto para possibilitar outrotipo de estudos. Trata-se de bacias equipadas com geradores de ondas, para ensaios de modeloscom o objectivo de estudar as questoes de manobrabilidade e de comportamento do navio nomar, Fig. 1.7.

Outro tipo de bacias para ensaios de modelos de navios, Fig. 1.8, dedica-se preferencial-mente a estudos e ensaios relacionados com a presenca de gelo no mar.

Por ultimo, um outro tipo de instalacao de teste nesta area dedica-se ao estudo do desem-penho de helices propulsores. Neste tipo de instalacao, que iremos abordar com um poucomais de detalhe no Cap. 3, para alem da determinacao de varias caracterısticas de desempenhodo helice, pode-se vizualizar o padrao de cavitacao no helice.

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8 CAPITULO 1. INTRODUCAO

Figura 1.7: Bacia para testescom ondulacao.

Figura 1.8: Bacia para testes comaguas geladas.

Figura 1.9: Escoamento num helice.

1.5 Simulacoes numericas

As simulacoes de escoamento obtidas pela mecanica de fluidos computacional sao ainda consi-deradas pela industria como pouco precisas para a previsao da resistencia de um casco ou daforca propulsiva de um helice. No entanto, o contributo da mecanica de fluidos computacionalesta a tornar-se cada vez mais importante em determinados passos do processo de projecto.Casos tıpicos de aplicacao sao, por exemplo:

- a simulacao de escoamento invıscido, com superfıcie livre, para analise do comporta-mento da proa, interaccao com o bolbo, formacao ondosa, etc.

- as simulacoes de escoamento viscoso na zona da popa, desprezando a formacao ondosapara avaliacao do comportamento de apendice ou analise do escoamento de aproximacaoao helice.

No caso mais geral, o escoamento de fluidos incompressıveis em regime nao-estacionario emodelado pelas seguintes equacoes:

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1.5. SIMULACOES NUMERICAS 9

- Equacao da continuidade,

∂ui∂xi

= 0 (1.7)

- Equacao de conservacao da quantidade de movimento,

∂ρui∂t

+∂

∂xj(ρuiuj) = − ∂p

∂xi+ µ

∂2ui∂xj∂xj

+ ρbi (1.8)

- Equacao de conservacao da energia (forma simplificada),

∂θ

∂t+∂ (θuj)

∂xj=

κ

ρc

∂2θ

∂xj∂xj(1.9)

em que xi e a coordenada na direccao i, ui e a componente da velocidade na direccao i, ρe µ sao a massa especıfica e a viscosidade do fluido, respectivamente, p e a pressao, κ e acondutividade termica, c e o calor especıfico, θ e a temperatura, b e a componente na direccaoi das forcas exteriores por unidade de massa e t e o tempo.

As equacoes sao discretizadas no espaco de acordo com uma malha colocada ou desfasada.Na Fig. 1.10 esta indicada a localizacao das variaveis, no caso bi-dimensional, para cadauma daqueles tipos de malhas. Cada um daqueles tipos de malha de discretizacao apresenta

Figura 1.10: Malha colocada a esquerda e desfasada a direita.

algumas vantagens e desvantagens. As mais importantes estao relacionadas com:

- a complexidade da programacao;

- o tratamento das fronteiras do problema;

- a solucao para o acoplamento pressao-velocidade (formato xadrez na solucao da pressao).

Selecionado o tipo de malha a utilizar, outras opcoes ha a tomar para desenvolver o metodode solucao. Algumas das mais comuns sao:

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10 CAPITULO 1. INTRODUCAO

Figura 1.11: Representacao esquematicade um “PC-cluster”.

Figura 1.12: Um “PC-cluster”com 24 nos computacionais.

- SIMPLE / metodo de projeccao;

- volume finito / diferencas finitas;

- aproximacao dos termos convectivos/difusivos das equacoes;

- “upwind”;

- diferencas centrais de ordem 2;

- diferencas centrais de ordem 4;

- o metodo de integracao para a evolucao temporal;

- Euler;

- Crank-Nicolson;

- Adams-Bashforth;

- Runge-Kutta.

Tratando-se de calculos complexos, o tempo de calculo podera ser reduzido, sem acrescimosignificativo de custos, com recurso de um “PC-cluster”, Fig. 1.11.

Este tipo de estruturas computacionais caracterizam-se por dispor de:

- 20 a 1000 CPU;

- 2 a 8 GB RAM por no;

- comunicacao em rede com velocidade superior a 1 Gbps;

- elevada capacidade para armazenamento de dados;

- sistema operativo estavel.

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1.5. SIMULACOES NUMERICAS 11

Para a solucao de um problema de mecanica de fluidos num “PC-cluster” e necessario pro-ceder a decomposicao do domınio espacial do problema (Fig. 1.13) e recorrer a rotinas de umadas varias bibliotecas disponıveis para efectuar a troca de dados entre os nos computacionais,como por exemplo a biblioteca Message Passing Interface, necessaria para a continuacao docalculo. Na Fig. 1.14 estao representados esquematicamente aquelas comunicacoes de dadosrelativos as fronteiras dos sub-domınios de calculo.

Figura 1.13: Decomposicao 1D, 2D ou 3D do domınio espacial de um pro-blema.

Figura 1.14: Troca de valores nas fronteiras dos sub-domınios.

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12 CAPITULO 1. INTRODUCAO

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Capıtulo 2Resistencia

2.1 Analise dimensional

A resistencia do navio a uma velocidade constante e a forca necessaria para rebocar o navioa essa velocidade em aguas tranquilas. Se a querena nao tiver apendices, a resistencia diz-seda querena simples. Designaremos por potencia efectiva, ou potencia de reboque, a potencianecessaria para vencer a resistencia do navio a uma dada velocidade,

Pe = V RT (2.1)

em que V e a velocidade do navio e RT a sua resistencia total.

A resistencia do navio RT = f (V,L, ρ, ν, g) depende:

- da velocidade do navio V ;

- das dimensoes do navio, representadas aqui por uma dimensao linear L;

- da massa especıfica do fluido ρ;

- da viscosidade cinematica do fluido ν;

- da aceleracao da gravidade g.

Assim, a resistencia do navio devera ser uma funcao da forma

RT = V aLbρcνdge (2.2)

Ao estudar a resistencia de um navio e importante calcular nao o seu valor absoluto, mastambem a sua relacao com outro valor, dimensionalmente semelhante, tomado como referen-cia. Vamos dar o nome de coeficientes especıficos a estas relacoes. No caso da resistenciatotal do navio, o valor do coeficiente e obtido por

cT =RT

1

2ρSV 2

(2.3)

em que ρ e a massa especıfica do fluido, S a superfıcie molhada do navio e V a sua velocidade.

13

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14 CAPITULO 2. RESISTENCIA

Resolvendo o sistema de equacoes gerado pela Eq. (2.2) em ordem a a, b e c, e considerandoa definicao do coeficiente em 2.3 dada pela Eq. (2.3), temos

RT = ρV 2L2f

(V L

ν,gL

V 2

)(2.4)

Ou seja, a analise dimensional mostra que o coeficiente de resistencia total do navio,

ct = f

(V L

ν,gL

V 2

)(2.5)

depende dos grupos adimensionais designados por numero de Froude,

Fr =V√gL

(2.6)

e por numero de Reynolds,

Re =V L

ν(2.7)

calculados para o navio.

2.2 Leis da semelhanca

No caso dos ensaios de modelos para avaliacao da resistencia de uma querena, podemosconsiderar tres formas de semelhanca:

- semelhanca geometrica;

- semelhanca cinematica;

- semelhanca dinamica.

2.2.1 Semelhanca geometrica

Verificar-se semelhanca geometrica significa a existencia de uma razao constante entre qual-quer dimensao linear na escala real do prototipo (comprimento, boca, calado do navio, etc.)Ls e o dimensao linear na escala do modelo Lm. Aquela razao e a escala geometrica do modeloλ,

Ls = λLm (2.8)

Consequentemente, temos para as areas,

As = λ2Am (2.9)

e para os volumes,

∇s = λ3∇m (2.10)

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2.2. LEIS DA SEMELHANCA 15

2.2.2 Semelhanca cinematica

A semelhanca cinematica significa a existencia de uma razao constante entre o “tempo” naescala real, ts e o “tempo” na escala do modelo tm, a escala cinematica τ :

ts = τ · tm (2.11)

A verificacao simultanea das condicoes de semelhanca geometrica e cinematica resulta nosseguintes factores de escala:

- para a velocidade:

Vs =λ

τVm (2.12)

- e para a aceleracao:

as =λ

τ2am (2.13)

2.2.3 Semelhanca dinamica

Obter semelhanca dinamica significa que a razao entre cada uma das forcas actuantes no navioa escala real e as correspondentes forcas actuantes no modelo e constante, escala dinamica domodelo κ,

Fs = κ ·Fm (2.14)

As forcas presentes, actuantes sobre o navio e sobre o modelo, podem ser classificadas deacordo com a sua natureza como:

- as forcas de inercia;

- as forcas gravıticas;

- as forcas de atrito.

Forcas de inerciaAs forcas de inercia regem-se pela lei de Newton, expressa por

F = m · a (2.15)

em que F e a forca de inercia, m a massa do corpo, e a a aceleracao a que ele e sujeito.Considerando o volume deslocado pelo navio ∇, a massa do navio e

m = ρ · ∇ (2.16)

sendo ρ a massa volumica da agua.Entao, a razao entre as forcas de inercia e uma equacao que incorpora os tres factores de

escala, lei da Semelhanca de Newton, e dada por

κ =FsFm

=ρs · ∇s · asρm · ∇m · am

=ρsρm· λ

4

τ2(2.17)

que pode ser re-escrita como

κ =FsFm

=ρsρm·λ2 ·

τ

)2

=ρsρm· AsAm·(VsVm

)2

(2.18)

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16 CAPITULO 2. RESISTENCIA

Forcas de origem hidrodinamicaAs forcas de origem hidrodinamica sao normalmente descritas recorrendo a um coeficiente

adimensional c na seguinte forma, semelhante a Eq. (2.3),

F = c · 12ρ ·V 2 ·A (2.19)

em que V e uma velocidade de referencia, por exemplo a velocidade do navio e A uma area dereferencia como, por exemplo, a area das obras vivas com mar calmo. Aplicando a Eq. (2.19)ao navio e ao modelo e combinando as duas equacoes, obtem-se

FsFm

=cs · ρs ·V 2

s ·Ascm · ρm ·V 2

m ·Am=

cscm

ρsρm· AsAm·(VsVm

)2

(2.20)

Daqui resulta que igualando o valor dos coeficientes no navio e no modelo, cs = cm, ficagarantida a verificacao da lei da semelhanca de Newton.

Forcas GravıticasAs forcas gravıticas podem ser descritas de forma semelhante as forcas de inercia, para o

navio

Gs = ρs · g · ∇s (2.21)

e para o modelo

Gs = ρs · g · ∇s Gm = ρm · g · ∇m (2.22)

daqui resultando uma nova escala,

κg =GsGm

=ρsρm· ∇s∇m

=ρsρm·λ3 (2.23)

Para que se possa verificar a semelhanca dinamica, os factores de escala devem apresentaro mesmo valor, ou seja, κ = κg. Se

κ =ρsρm· λ

4

τ2

e

κg =ρsρm·λ3

entao, para que κ = κg e necessario verificar-se

τ =√λ (2.24)

Esta nova relacao permite eliminar a escala temporal em todas as relacoes apresentadas,ficando a proporcionalidade apenas dependente de λ como, por exemplo, na Eq. (2.12), fazendo

VsVm

=√λ (2.25)

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2.2. LEIS DA SEMELHANCA 17

Numero de FroudeA Eq. (2.25) pode ainda assumir a forma de uma relacao entre a dimensao linear e a

velocidade do modelo e do navio,

Vs√Ls

=Vm√Lm

(2.26)

Adimensionalisando a razao entre a velocidade V e a raiz quadrada do comprimento Lcom a aceleracao da gravidade, g = 9.81 m/s2, obtemos o numero de Froude

Fr =V√g ·L

(2.27)

Na ausencia de forcas viscosas, igual numero de Froude assegura semelhanca dinamica.Para igual numero de Froude, as ondulacoes no modelo e a escala real, desde que de pequenaamplitude, podem considerar-se geometricamente semelhantes.

A lei de Froude e verificada em todos os ensaios de modelos de navios, ensaios de resis-tencia, propulsao, comportamento no mar e manobrabilidade. A aplicacao da lei de Froudeimpoe os seguintes factores de escala para a velocidade,

VsVm

=√λ (2.28)

forca,

FsFm

=ρsρm·λ3 (2.29)

e potencia,

PsPm

=Fs ·VsFm ·Vm

=ρsρm·λ3.5 (2.30)

Forcas de atritoAs forcas viscosas R, com origem no atrito entre camadas de fluido, sao modeladas por

R = µ · ∂u∂n·A (2.31)

em que µ e a viscosidade dinamica do fluido, A a area sujeita ao atrito e∂u

∂no gradiente de

velocidade, avaliado na direccao normal ao escoamento.A razao das forcas de atrito no navio e no modelo e dada por

κf =RsRm

=µs ·

∂us∂ns·As

µm ·∂um∂nm

·Am=

µsµm

λ2

τ(2.32)

Na presenca das forcas de atrito, para verificar a condicao de semelhanca dinamica, seranecessario que κf = κ, ou seja:

µsµm

λ2

τ=

ρsρm

λ4

τ2(2.33)

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18 CAPITULO 2. RESISTENCIA

Se introduzirmos a viscosidade cinematica, como ν = µ/ρ, obtem-se:

νsνm

=λ2

τ=

Vs ·LsVm ·Lm

ou seja,

Vs ·Lsνs

=Vm ·Lmνm

(2.34)

Numero de ReynoldsEntao, de acordo com a Eq. (2.34), se apenas estiverem presentes forcas de inercia e de

atrito, a igualdade do numero de Reynolds,

Re =V ·Lν

(2.35)

assegura semelhanca dinamica entre o modelo e o navio.Para o calculo do numero de Reynolds, a viscosidade cinematica da agua do mar (m2/s)

pode ser estimada, em funcao da temperatura θ (◦C) e da salinidade s (%), por

ν = (0.014 · s+ (0.000645 · θ − 0.0503) · θ + 1.75) · 10−6 (2.36)

Semelhanca dinamicaO numero de Froude e o numero de Reynolds estao relacionados por,

Re

Fr=V ·Lν

√gL

V=

√gL3

ν(2.37)

A semelhanca de Froude e facilmente obtida para testes em modelos porque para modelosmais pequenos a velocidade de teste diminui. A semelhanca de Reynolds e mais difıcil deobter pois modelos mais pequenos exigem superior velocidade de teste para igual viscosidadecinematica.

os navios de superfıcie estao sujeitos a forcas gravıticas e de atrito. Assim, nos testes demodelos a escala reduzida ambas as leis, de Froude e de Reynolds, deveriam ser satisfeitas;

ResRem

=νmνs·

√L3s

L3m

=νmνs·λ1.5 = 1 (2.38)

No entanto, nao existem, ou pelo menos nao sao economicamente viaveis, fluidos que permitamsatisfazer esta condicao. Para diminuir os erros de extrapolacao dos efeitos viscosos, a agua emque sao realizados os testes pode ser aquecida para aumentar a diferenca entre as viscosidades.

2.3 Decomposicao da resistencia

A resistencia do navio tem origem complexa e, para facilidade de analise, e tradicionalmentedecomposta em varios termos. No entanto, nao existe uniformidade nos diversos textos quantoa forma como realizar aquela decomposicao. Uma das abordagens a este assunto consisteem considerar as decomposicoes constantes na Fig. 2.1. De acordo com a figura, podemosconsiderar a seguinte decomposicao da resistencia total:

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2.3. DECOMPOSICAO DA RESISTENCIA 19

- a resistencia de onda;

- a resistencia de atrito;

- a resistencia viscosa de pressao.

Figura 2.1: Decomposicao da resistencia.

Para alem dos termos relativos a uma querena simples em aguas tranquilas, outras com-ponentes adicionais da resistencia deverao ser consideradas:

- a resistencia aerodinamica, resistencia ao avanco no ar da parte emersa do casco esuperestruturas do navio;

- a resistencia adicional em mar ondoso, resistencia resultante da accao de ondas inciden-tes sobre a estrutura do navio;

- a resistencia adicional devida aos apendices da querena.

2.3.1 Resistencia de onda

Quando o navio avanca na superfıcie tranquila do mar e rodeado e seguido por uma formacaoondosa. Esta formacao e quase imperceptıvel a baixa velocidade. No entanto, a partir deuma dada velocidade torna-se claramente visıvel e, a partir daı, tem dimensao crescentecom a velocidade. Para alem da dependencia com a velocidade, a formacao ondosa dependetambem da forma da querena.

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20 CAPITULO 2. RESISTENCIA

Nos estudos de resistencia de onda nao se pode afirmar que uma dada velocidade e elevadaou baixa sem conhecermos tambem a dimensao do navio. Assim, surge frequentemente areferencia ao conceito de velocidade relativa, como razao entre a velocidade do navio e umparametro representativo da dimensao do navio,

vrel =V√L

(2.39)

com V em nos e L em pes, em substituicao do adimensional numero de Froude.Numa perspectiva do estudo hidrodinamico do escoamanto, o navio pode ser considerado

como um campo de pressao em movimento. Kelvin resolveu analiticamente o caso simplificadodo sistema de ondas criado pelo movimento de um ponto de pressao. Demonstrou que o padraoda formacao ondosa inclui um sistemas de ondas divergentes e um outro sistema cujas cristasdas ondas se apresentam normais a direccao do movimento, como representado na Fig. 2.2.Ambos os sistemas de ondas viajam a velocidade do ponto de pressao.

Figura 2.2: Sistema de ondas gerado por um ponto de pressao em movi-mento.

O sistema de ondas associado ao movimento de um navio e bastante mais complicado.No entanto, como primeira aproximacao, o navio pode ser considerado com um campo depressao em movimento composto por uma sobrepressao considerada pontual na proa e umadepressao, tambem pontual, na popa. Assim, num navio que se desloque a uma velocidaderelativa elevada, a formacao ondosa provocada e constituıda por dois sistemas principais deondas, Fig. 2.3:

- o sistema da proa;

- o sistema da popa.

Cada um dos sistemas de ondas formados, com origem na proa e na popa do navio, econstituıdo por dois tipos de ondas:

- as ondas transversais;

- as ondas divergentes.

Geralmente, os dois sistemas de ondas divergentes sao detectaveis apesar de o sistema dapopa ser muito mais fraco. Nao e normalmente possıvel isolar o sistema transversal da popa,sendo apenas visıvel a re do navio a composicao dos dois sistemas, transversal e divergente.

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2.3. DECOMPOSICAO DA RESISTENCIA 21

Figura 2.3: Sistemas de ondas da proa e da popa.

A proa produz um sistema de ondas semelhante ao descrito por Kelvin para um ponto depressao em movimento e, pelo contrario, na popa forma-se um sistema de ondas semelhante,mas com uma depressao localizada na popa. Conforme representado na Fig. 2.3, se a linhaque une os pontos de maior elevacao das cristas das ondas divergentes fizer com a direccaolongitudinal do navio um angulo α, entao a direccao destas fara um angulo 2α com a mesmadireccao.

O comprimento de onda de ambos os sistemas transversais e igual e dado por:

λ =2πV 2

g(2.40)

Existe uma interaccao entre as formacoes ondosa transversais dos sistemas de ondas daproa e da popa. Se os sistemas estiverem “em fase”, de tal forma que as cristas das ondascoincidam, o sistema resultante tera maior altura e, consequentemente, maior energia. Se,pelo contrario, a cava de um dos sistemas de ondas ficar sobreposta com uma crista do outrosistema, a energia consumida para gerar o sistema de ondas sera reduzida. A velocidade Ve o comprimento do navio L sao muito importantes para a determinacao da energia total dosistema de ondas gerado e, consequentemente, para a resistencia de onda do navio.

Continuando a assumir o modelo fısico que aproxima o movimento do navio por umcampo de pressao em movimento, a distancia entre os dois pontos de pressao, proa e popa,e aproximada por 0, 9L. Sabendo que uma onda gravıtica com comprimento de onda λ sedesloca em aguas profundas a velocidade

C =

√λg

2π(2.41)

para que haja coincidencia de uma crista ou cava do sistema da proa com a primeira cavagerada na popa, devera verificar-se

V 2

0, 9L=

g

Nπ(2.42)

Tomando em consideracao a Fig. 2.4, verifica-se que as cavas vao coincidir para N =1, 3, 5, ... enquanto que para N par as cristas do sistema da proa coincidem com as cavas dosistema da popa. Se nao existisse esta interaccao entre os dois sistemas de ondas a resistenciade onda apresentaria uma evolucao “bem comportada” crescente com a velocidade do navio,

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22 CAPITULO 2. RESISTENCIA

Figura 2.4: Interaccao entre os dois sistemas de ondas.

conforme representado pela linha tracejada da Fig. 2.5. Na realidade, a partir de uma dadavelocidade a partir da qual esta interaccao se torna significativa, verifica-se a existencia deelevacoes e depressoes na curva correspondendo aos casos extremos de interaccao entre ossistemas de ondas. E de esperar que a maior elevacao se verifique para N = 1 porque avelocidade e mais elevada para esta condicao.

Como a curva de resistencia de onda exibe estes maximos e mınimos locais, o navio deveser projectado para operar num mınimo local da curva de resistencia de onda, a velocidadeeconomica.

Quando o comprimento de onda das ondas transversais e igual ao comprimento do na-vio, o numero de Froude e aproximadamente 0, 4. Ate este valor do numero de Froude, asondas transversais sao as principais responsaveis pelas elevacoes e depressoes na curva daresistencia de onda. Se o numero de Froude aumentar, aumentara tambem a resistencia deonda sobretudo a custa da influencia das ondas divergentes. O maximo da resistencia deonda verifica-se para Fr ≈ 0, 5. A velocidade correspondente designa-se por “velocidade daquerena”. Acima da “velocidade da querena” a resistencia de onda do navio decresce. Naviosrapidos que operem acima da velocidade de querena deverao naturalmente dispor de potenciainstalada suficiente para vencer aquele pico de resistencia.

Bolbo de proaA finalidade da instalacao dos bolbos de proa e a reducao da resistencia de onda. O

mecanismo de reducao consiste na interferencia dos sistemas de onda. O sistema de ondasgerado pela pressao elevada no bolbo interfere com o sistema de ondas da proa, reduzindo asua amplitude. A interferencia favoravel ocorre quando a cava do sistema transversal de ondas

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2.3. DECOMPOSICAO DA RESISTENCIA 23

Figura 2.5: Curva da resistencia de onda.

do bolbo surgir na crista do sistema de ondas da proa do navio. Esta situacao de interferenciafavoravel sendo optimizada para uma dada velocidade, pode no entanto ser considerada comotendo efeito favoravel num determinado intervalo de velocidades.

Efeito da profundidade restritaOs efeitos da profundidade finita comecam a fazer-se sentir quando a profundidade h e

menor que metade do comprimento de onda da formacao ondosa gerada pelo movimento donavio, h < λ/2. Doutra forma, podemos considerar profundidade infinita sempre que,

h >λ

2(2.43)

No caso de profundidades muito pequenas, h < 0, 05λ∞, a velocidade de propagacao deixade depender do comprimento de onda, Eq. (2.41) e passa a depender apenas da profundidade

C =√gh (2.44)

Neste caso, a velocidade de grupo e igual a velocidade de propagacao, a velocidade crıtica:

Cg = C =√gh (2.45)

Para caracterizar o efeito da profundidade e usado o numero de Froude baseado na pro-fundidade h:

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24 CAPITULO 2. RESISTENCIA

- se V/√gh < 0, 4, o padrao de ondas e semelhante ao caso de profundidade infinita;

- se V/√gh se aproximar de 1, o angulo da envolvente aproxima-se de 90◦;

- se V/√gh > 1, sinα =

√gh/V .

2.3.2 Resistencia de atrito

A resistencia de atrito do navio resulta do escoamento em torno da querena com numero deReynolds elevado. Quando um corpo se move num fluido em repouso, uma fina camada defluido adere ao corpo em movimento, ou seja, tem velocidade nula relativamente ao corpo.A variacao de velocidade e elevada nas proximidades da superfıcie do corpo e diminui como aumento da distancia ao mesmo. E pratica habitual convencionar-se para a definicao daespessura da camada limite, a distancia a partir da superfıcie do corpo ate que a velocidadedo fluido seja 1% da velocidade do corpo.

Desenvolve-se assim da proa para a popa do navio uma camada limite tridimensional. Estacamada limite inicia-se em escoamento laminar e sofre transicao para o regime turbulento.Normalmente, esta transicao ocorre junto a proa do navio. Esta transicao e controlada pelonumero de Reynolds do escoamento. Considerando o caso da placa lisa plana, a transicaoocorre para valores entre Re = 3×105 e Re = 106. Em regime turbulento os efeitos dissipativosde energia vao alem do atrito molecular. Com crescente numero de Reynolds, verificam-seintensas trocas de quantidade de movimento em camadas adjacentes do fluido, ou seja, maiortransporte de energia.

No caso de uma placa plana, a espessura da camada limite turbulenta pode ser aproximadapor:

δx

L= 0, 37 (ReL)−1/5 (2.46)

Num navio, o gradiente lontitudinal de pressao na regiao da proa e, em geral, favoravelao escoamento. Pelo contrario, este gradiente e adverso na regiao da popa e a camada limiteaumenta significativamente de espessura deixando de poder ser considerada pequena quandocomparada com o comprimento ou a boca do navio. Para todos os efeitos praticos, a camadalimite de um navio pode ser considerada completamente turbulenta.

A dependencia da resistencia de atrito com o numero de Reynolds e com a rugosidade dasuperfıcie e indicada pelo grafico da Fig. 2.6. Para uma superfıcie rugosa, a resistencia seguea linha da superfıcie lisa ate que, para um dado valor de Re, se separa e tem a partir daıum andamento quase horizontal, ou seja, o coeficiente torna-se independente do Re. Quantomais rugosa for a superfıcie mais cedo se evidencia este comportamento.

A resistencia de atrito de um navio e habitualmente dividida em duas componentes:

- a resistencia a que ficaria sujeita uma placa plana com area equivalente;

- o aumento de resistencia originado pela forma do navio.

A resistencia de atrito foi estimada durante decadas por expressoes empıricas como, porexemplo, a formula de Froude:

RF = 1− 0, 0043 (θ − 15) fSV 1,825 (2.47)

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2.3. DECOMPOSICAO DA RESISTENCIA 25

Figura 2.6: Variacao do coeficiente da resistencia de atrito com o numerode Reynolds e com a rugosidade da superfıcie.

em que θ e a temperatura do fluido, expressa em ◦C e

f = 0, 1392 +0, 258

2, 68 + L(2.48)

Outra formula empırica muito popular para a previsao do coeficiente da resistencia de atrito edevida a Schoenherr e conhecida como formula da ATTC (American Towing Tank Conference)

0, 242√cF

= log (Re · cF ) (2.49)

Esta correlacao preve coeficientes de atrito excessivos quando aplicada a modelos muitopequenos. Para ultrapassar este problema foi proposta na ITTC (International Towing TankConference) de 1957 uma nova formula,

cF =0, 075

(logRe− 2)2(2.50)

designada por linha de correlacao modelo-navio da ITTC 1957.

2.3.3 Resistencia viscosa de pressao

A componente da pressao originada pelas ondas formadas pelo movimento do navio ja foiconsiderada. Resta agora considerar a resistencia originada por diferencas de pressao a actuarno casco devida a efeitos viscosos do escoamento. Num escoamento ideal, ver Fig. 2.7, apressao exercida na popa do navio seria igual a exercida na proa, ou seja forca resultantenula. Na pratica, os efeitos viscosos vao reduzir a pressao exercida na popa do navio.

Parte desta resistencia sera devida a geracao de vortices nas descontinuidades do casco.Outra parte sera devida a um aumento de espessura da camada limite nalguns casos po-tenciada por fenomenos de separacao do escoamento. Estes aspectos sao fundamentalmentecondicionados pela forma do casco pelo que sao normalmente considerados como uma “resis-tencia de forma”.

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26 CAPITULO 2. RESISTENCIA

Figura 2.7: Distribuicao de pressao num escoamento ideal, invıscido.

2.4 Ensaios de resistencia em tanques de reboque

Apesar da crescente importancia dos metodos numericos, os ensaios com modelos a escalareduzida de navios em tanques de reboque sao ainda essenciais para a avaliacao hidrodinamicados novos projectos e para a validacao de novas solucoes.

Os testes devem ser realizados em condicoes que permitam considerar que o modelo e onavio tem comportamentos semelhantes por forma a que os resultados obtidos para o modelopossam ser extrapolados para a escala real do navio. Com este objectivo, os ensaios realizam-se respeitando a igualdade do numero de Froude.

Os testes sao realizados em tanques de reboque, com agua imovel e o modelo rebocado porum “carrinho” ou, em alternativa, os testes podem ser realizados em “tanques de circulacao”,em que o modelo esta imovel e a agua circula.

No primeiro caso, apos um percurso inicial de aceleracao, a velocidade do “carrinho” deveser mantida constante para obter um regime estacionario e garantir o rigor das observacoesefectuadas. A fase final e de desaceleracao e imobilizacao do modelo. Assim, os tanques dereboque apresentam frequentemente centenas de metros de extensao.

O comprimento do modelo, como o exemplo representado esquematicamente na Fig. 2.8,e escolhido de acordo com as condicoes experimentais no tanque de reboque. O modelo deveser tao grande quanto possıvel por forma a minimizar efeitos de escala relativos aos aspectosviscosos, nomeadamente as diferencas relativas a escoamentos laminares e turbulentos e asquestoes relacionadas com fenomenos de separacao do escoamento. Por outro lado, a dimensaodo modelo deve ainda permitir evitar deformacoes resultantes de esforcos no modelo e noequipamento de teste.

A dimensao do modelo deve ser suficientemente pequena para permitir que o “carrinho”de reboque do modelo atinja a velocidade correspondente e evitar os efeitos de aguas res-tritas nos testes efectuados. Estes constrangimentos conduzem naturalmente a um intervalopratico de comprimentos admissıveis. Os modelos para ensaios de resistencia e propulsaotem normalmente comprimentos entre 4 m < Lm < 10 m. A escala dos modelos esta entre15 < λ < 45.

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2.5. CALCULO DA RESISTENCIA 27

Figura 2.8: Modelo a escala reduzida para ensaios de resistencia.

Durante o movimento, o modelo mantem o rumo atraves de fios-guia, sendo livre paraadoptar o caimento que resultar do seu movimento. Ainda de acordo com a Fig. 2.8, aresistencia total de reboque do modelo e dada por,

RT = G1 + sinαG2 (2.51)

Com os ensaios de resistencia com o modelo a escala reduzida pretende-se obter dadosque permitam estimar a resistencia do navio sem o propulsor e apendices, ou seja, dita daquerena simples. Dos ensaios no tanque de reboque obtem-se a resistencia nas condicoes dotanque, ou seja:

- aguas suficientemente profundas;

- ausencia de correntes;

- ausencia de vento;

- agua doce a temperatura ambiente.

O numero de Reynolds e normalmente superior duas ordens de grandeza na escala do navioque na escala do modelo, tipicamente na ordem de 109 e 107, respectivamente. O modelo temfrequentemente uma fita rugosa para estimular artificialmente a transicao da camada limitelaminar para turbulenta mais perto da proa do modelo. Globalmente, o desvio originadopelo facto de nao se manter constante o numero de Reynolds no ensaio e depois compensadoatraves de correccoes empıricas.

2.5 Calculo da resistencia

2.5.1 Metodos de extrapolacao

A resistencia do modelo tem depois de ser convertida por forma a obter-se uma estimativada resistencia do navio na escala real. Para tal, estao disponıveis, entre outros, os seguintesmetodos:

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28 CAPITULO 2. RESISTENCIA

- o metodo ITTC 1957;

- o metodo de Hughes/Prohaska;

- o metodo ITTC 1978;

- o metodo Geosim de Telfer.

Actualmente, o metodo mais frequentemente utilizado na pratica e o metodo ITTC 1978.

Metodo ITTC 1957

Para a aplicacao deste metodo, a resistencia total da querena, RT , e considerada decompostanos seguintes termos,

RT = RF +RR (2.52)

a resistencia de atrito, RF , e a resistencia residual, RR.Os coeficientes de resistencia, adimensionais, sao genericamente calculados por,

ci =Ri

12ρV

2S(2.53)

Na aplicacao deste metodo de previsao e considerado igual para o modelo e para o navioo coeficiente de resistencia residual,

cR = cTm − cFm (2.54)

determinado a partir do coeficiente de resistencia total do modelo,

cTm =RTm

12ρmV

2mSm

(2.55)

e da formula “ITTC 1957” (Eq. (2.50)) para o calculo do coeficiente de resistencia de atritocF ,

cF =0.075

(log10Re− 2)2

O coeficiente de resistencia total para o navio e entao estimado por:

cTs = cFs + cR + cA = cFs + (cTm − cFm) + cA (2.56)

em que cA e um factor de correccao tradicionalmente associado a rugosidade do casco. Defacto, embora o modelo esteja construıdo a uma dada escala geometrica, a rugosidade dassuperfıcies do modelo e do navio nao respeitam esta escala. O valor de cA pode ser obtidopor correlacoes empıricas como, por exemplo,

cA = 0.35× 10−3 − 2× Lpp × 10−6 (2.57)

ou a partir de valores tabelados (Tab. 2.1).A previsao da resistencia total do navio e dada por

RTs = cTs ·1

2ρsV

2s Ss (2.58)

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2.5. CALCULO DA RESISTENCIA 29

Lpp(m) cA50 - 150 0,0004-0,00035150 - 210 0,0002210 - 260 0,0001260 - 300 0300 - 350 -0,0001350 - 400 0,00025

Tabela 2.1: Valores do coeficiente de correccao cA em funcao do compri-mento do navio.

Metodo de Hughes-Prohaska

O metodo de Hughes-Prohaska e normalmente classificado como um metodo de factor deforma. E considerada a decomposicao da resistencia total em duas componentes, uma asso-ciada a resistencia de onda e outra dependente da forma do casco. Considerando entao oscoeficientes adimensionais, fica

cT = (1 + k) · cF0 + cw (2.59)

Para a determinacao do factor de forma, presume-se aqui a relacao

cTcF0

= (1 + k) + αFr4

cF0(2.60)

que e particularmente valida para valores reduzidos de velocidade.Apos varios ensaios a diferentes velocidades, diferentes numeros de Froude, e possıvel

construir um grafico semelhante ao representado na Fig. 2.9 e, com base naqueles valores,obter o valor de k por regressao linear.

Figura 2.9: Representacao grafica da dependencia decTcF0

comFr4

cF0.

Este factor de forma, (1 + k),e assumido como independente dos valores de Fr e de Re eigual para o navio e modelo.

O procedimento de calculo do metodo de Hughes-Prohaska e o seguinte:

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30 CAPITULO 2. RESISTENCIA

- determinar o coeficiente de resistencia total,

cTm =RTm

1

2ρmV

2mSm

- determinar o coeficiente de resistencia de onda, o mesmo para o modelo e o navio,

cw = cTm − cF0m · (1 + k) (2.61)

- determinar o coeficiente de resistencia total para o navio,

cTs = cw + cF0s · (1 + k) + cA (2.62)

- determinar a resistencia total para o navio, novamente por

RTs = cTs ·1

2ρsV

2s Ss

O coeficiente da resistencia de atrito, cF0, e neste caso obtido pela correlacao de Hughes,

cF0 =0.067

(log10Re− 2)2(2.63)

Quanto ao coeficiente de correccao cA, a ITTC recomenda a aplicacao universal de

cA = 0.0004 (2.64)

na aplicacao deste metodo.

Metodo ITTC 1978

E uma modificacao do metodo de Hughes-Prohaska, geralmente mais preciso que os ante-riormente apresentados. Ao contrario dos metodos anteriormente descritos, este metodo deextrapolacao dos resultados obtidos nos ensaios com modelos a escala reduzida inclui o efeitoda resistencia do ar.

A previsao do coeficiente de resistencia total para o navio e, tambem aqui, descrita emtermos do factor de forma, ou seja,

cTs = (1 + k) cFs + cw + cA + cAA (2.65)

em que:

- cw e o coeficiente de resistencia de onda, igual para o navio e modelo;

- cA e o coeficiente de correccao;

- e cAA a resistencia do ar, cAA = 0.001 · ATS

.

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2.5. CALCULO DA RESISTENCIA 31

O coeficiente da resistencia de atrito e determinada de forma semelhante a preconizadapara o metodo ITTC 57, Eq. (2.50).

Para a determinacao da correccao devida pela variacao da rugosidade da querena, e acon-selhada aqui a seguinte formula:

cA · 103 = 105 3

√ksLoss

− 0.64 (2.66)

em que ks e a rugosidade do casco e Loss e o comprimento do navio no plano de flutuacao.Para navios novos ks/Loss = 10−6 e cA = 0.00041.

Os detalhes sugeridos pela ITTC na aplicacao deste metodo estao indicados no ApendiceA.

Metodo Geosim

Este metodo foi proposto por Telfer em 1927. Dos metodos aqui enunciados, e consideradocomo o metodo de extrapolacao com previsoes mais precisas da resistencia do navio. Agrande vantagem do metodo resulta de nao recorrer a qualquer decomposicao, teoricamentequestionavel, da resistencia total.

Sao realizados varios ensaios com modelos geometricamente semelhantes mas a diferentesescalas. Isto significa que os testes podem ser realizados, para a mesma velocidade equivalente,com igual numero de Froude e diferente numero de Reynolds. O coeficiente de resistencia total,obtido naqueles ensaios, e representado em funcao de logRe−1/3. Para cada um dos modelos,obtem-se uma curva da resistencia, em funcao do Fr, que permite fazer a extrapolacao paraa escala do navio.

Pela grande quantidade de modelos a construir e ensaios a realizar, trata-se de um metodomuito dispendioso, utilizado sobretudo apenas para fins de investigacao.

2.5.2 Resistencias adicionais

As condicoes de ensaio dos modelos sao substancialmente diferentes daquelas em que o navioira operar. As principais diferencas a considerar resultam de:

- a presenca de apendices na querena;

- a navegacao em aguas pouco profundas;

- o vento;

- a crescente rugosidade do casco durante a vida do navio;

- as condicoes de mar.

Para estimar as alteracoes causadas por estes itens no comportamento do navio, usam-secorreccoes empıricas, baseadas em pressupostos fısicos, para correlacionar os valores obtidosno modelo, ou no navio em provas de mar, com os estimados para as condicoes normais deservico do navio. A resistencia adicional devida a apendices e a resistencia do navio em aguaspouco profundas sao os topicos sucintamente abordados nos paragrafos seguintes.

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32 CAPITULO 2. RESISTENCIA

Resistencia adicional dos apendices

Os modelos de navios a escala reduzida podem ser testados com apendices a escala geome-trica apropriada. No entanto, nem sempre nesta altura do projecto estes estao completamentedefinidos. Por outro lado, o escoamento em torno dos apendices e predominantemente go-vernado pelas forcas de origem viscosa. Seria entao necessario, para obter resultados fiaveis,verificarem-se condicoes de semelhanca de Reynolds, o que, como ja referido, nao e viavelse, cumulativamente, pretendermos manter a igualdade do numero de Froude. Consequente-mente, a presenca dos apendices em condicoes de semelhanca de Froude tem pouca relevancia.

Em primeira analise, os apendices do casco contribuem para um aumento da superfıciemolhada do navio. Por outro lado, da sua presenca surgem tambem alteracoes no factor deforma do casco. Para a determinacao da resistencia de forma dos apendices pode recorrer-se adois ensaios, com e sem apendices, a uma velocidade superior. Se admitirmos que a resistenciade onda e igual nos dois casos, a diferenca de resistencia verificada, tendo descontado adiferenca de resistencia de atrito resultante da variacao da area molhada, da-nos a resistenciade forma dos apendices.

Os valores tıpicos de acrescimo de resistencia originados pela presenca de apendices saoos seguintes:

- robaletes: 1 a 2%;

- impulsores:

- de proa: 0 a 1%;

- transversais de popa: 1 a 6%;

- aranhas de veios: 5 a 12% (“twin-screw” pode chegar a 20%);

- leme: 1%.

Resistencia em aguas pouco profundas

Quando um navio navega em aguas pouco profundas verifica-se um aumento, quer da resis-tencia de atrito, quer da resistencia de onda. Em particular, a resistencia aumenta signifi-cativamente para valores proximos do numero de Froude crıtico, baseado na profundidade,Fnh = V/

√gH = 1.

O aumento da resistencia do navio quando a navegar em aguas pouco profundas foi es-tudado por Schlichting. A sua hipotese de trabalho foi a seguinte: a resistencia de onda e amesma se o comprimento de onda da ondulacao transversal for igual.

O grafico da Fig. 2.10 permite prever a perda de velocidade do navio em aguas poucoprofundas. Correccoes simples nao sao possıveis para aguas muito pouco profundas ja que osfenomenos envolvidos sao complexos. Nestes casos, so testes em modelos ou simulacoes porCFD poderao contribuir para uma melhor previsao.

2.6 Previsao da resistencia com dados sistematicos ou estatıs-ticos

Na fase preliminar do projecto de um navio podem ser utilizados metodos aproximados para aprevisao da resistencia baseados em ensaios de series sistematicas de navios ou, pela regressao

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2.6. PREVISAO COM DADOS SISTEMATICOS OU ESTATISTICOS 33

Figura 2.10: Reducao de velocidade (%) em aguas pouco profundas.

estatıstica de dados experimentais relativos a modelos e a navios a escala real.Series sistematicas sao conjuntos de formas de querena em que se provocou a variacao,

sistematica, de um ou mais dos seus parametros de forma. As variacoes sistematicas saofeitas em torno de uma “forma mae” (“parent form”). Os resultados dos ensaios de resistenciados modelos que constituem a serie permitem determinar um coeficiente adimensional deresistencia para uma forma de querena contida ou interpolada na serie.

Taylor mediu, entre 1907 e 1914, 80 modelos obtidos por variacao sistematica de:

- a razao entre o comprimento e a raiz cubica do deslocamento (5 valores de L/∆1/3);

- a razao entre a boca e o calado (B/T = 2, 25; 3, 75);

- o coeficiente prismatico (8 valores de 0,48 a 0,86);

a partir de uma “forma mae”: o cruzador “Leviathan”.Estes dados foram posteriormente re-trabalhados por Gertler em 1954, disponibilizando

diagramas de resistencia residual.Outra serie sistematica, com particular interesse para os navios mercantes, e a serie 60,

devida aos trabalhos de Todd. Consta de 5 “formas mae” com coeficientes de finura, 0,60,0,65, 0,70, 0,75 e 0,80. Para cada uma daquelas “formas mae” existem variacoes de L/B,B/T , etc.

Como exemplo de um metodo de previsao da resistencia de navios envolvendo dadosestatısticos pode-se indicar o metodo de Holtrop e Mennen. Este metodo pode ser aplicadopara efectuar uma analise qualitativa do projecto de um navio no que diz respeito a suaresistencia. O metodo baseia-se na regressao estatıstica de resultados de ensaios em modelose de resultados de provas de mar de navios. A base de dados e muito vasta cobrindo umagama muito alargada de tipos de navios. No entanto, para formas muito especıficas de navio,

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34 CAPITULO 2. RESISTENCIA

a precisao das previsoes pode reduzir-se pelo menor numero de elementos daquele tipo nabase.

2.7 Ensaios a escala real

Os resultados obtidos nas provas de mar de um navio sao talvez o mais importante requisitopara a aceitacao deste pelo armador. A especificacao detalhada destas provas deve estarclaramente contratualizada entre o armador e o estaleiro. Entre outros organismos, a ITTCrecomenda alguns procedimentos para a realizacao destas provas. As recomendacoes para asprovas de velocidade e de potencia estao incluıdas no Apendice B.

Os problemas surgem normalmente em consequencia de as provas se realizarem em condi-coes diferentes, quer das que foram consideradas como condicoes de projecto, quer daquelasque se verificaram nos ensaios com o modelo a escala reduzida.

O contrato de construcao deve especificar uma velocidade contratual do navio, a carga deprojecto, para uma dada percentagem da MCR do motor, em aguas tranquilas e profundas ena ausencia de vento. Sao raras as ocasioes em que e possıvel realizar as provas de mar emcondicoes proximas das condicoes contratuais. As condicoes em que se realizam as provas demar incluem, frequentemente:

- condicao de carga parcial ou em condicao de lastro;

- presenca de correntes e ondulacao;

- aguas pouco profundas;

Para prevenir maior diversidade de resultados, e habitual definir contratualmente valoreslimite para as condicoes ambientais em que as provas de mar se realizarao. As condicoesrecomendadas pela ITTC para a realizacao das provas de velocidade e potencia estao noApendice C. As diferencas entre as condicoes contratuais e verificadas durante a realizacaodas provas de mar impoem a utilizacao de correlacoes para corrigir os resultados obtidos paraas condicoes de contrato. Para alem de todas as incertezas experimentais, todo este processode correccao, com recurso a graficos e tabelas, oferece muitas duvidas de aplicacao.

A “prova da milha” pode ser avaliada com velocidade “over ground” ou velocidade “inwater”. A velocidade na agua exclui o efeito das correntes. A velocidade “over ground”era avaliada atraves de equipamentos de navegacao mas, a disponibilidade de sistemas deposicionamento por satelite (GPS) permitiu eliminar muitos problemas e incertezas destasprovas. Para reduzir os efeitos de ventos e correntes, as provas de velocidade, consumo, etc.devem ser realizadas repetidamente em sentidos opostos.

De notar que as provas de mar de um navio vao muito para alem das provas de veloci-dade e potencia. Todas as funcionalidades do navio, operacionais e de seguranca, deverao serdemonstradas. Para as restantes provas, nomeadamente as que dizem respeito a manobrabi-lidade do navio, existem tambem recomendacoes exaustivas da ITTC para a sua realizacao.

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Capıtulo 3Propulsao

3.1 Sistemas de propulsao

Em qualquer tipo de navio temos presente um propulsor cuja finalidade e a geracao de umaforca propulsiva. As solucoes propulsivas sao muito diversas mas predominantemente os navioscontinuam a utilizar helices simples como meio de propulsao. Outros meios de propulsao comexpressao significativa em aplicacoes especıficas sao:

- os helices “especiais”, com particular destaque para os helices com tubeira e os helicescontra-rotativos;

- os sistemas de jacto de agua (“water-jets” ou “pump-jets”);

- os propulsores azimutais (“AziPod’s)”;

- e os propulsores cicloidais (“Voith-Schneider”).

Na escolha da solucao propulsiva devera ser sempre considerado o seu rendimento e ainteraccao com a querena. Outro aspecto generico a considerar durante o projecto da solucaopropulsiva e o fenomeno da cavitacao originada pela velocidade elevada do movimento daspas do helice na agua.

3.1.1 Helices

O helice e colocado tradicionalmente a popa do navio para recuperar parte da energia dis-pendida para vencer a resistencia da querena. Na forma mais tradicional da popa dos navios,a esteira nominal e muito nao-uniforme. A uniformidade da esteira da querena e uma dascondicoes necessarias para o bom funcionamento do helice. A utilizacao da popa aberta oude um bolbo na popa permite melhorar a esteira.

As pas do helice, animadas de velocidade de rotacao e de avanco, funcionando comosuperfıcies sustentadoras, estao distribuıdas simetricamente em torno do cubo. As seccoesdas pas funcionam como perfis alares a angulo de ataque gerando uma forca de sustentacao.Esta forca de sustentacao contribui para a forca propulsiva axial e para o binario resistenteao veio.

Classificam-se com helices “direitos” aqueles que, quando observados de re, rodam nosentido horario. Nos navios com dois helices, sao normalmente utilizados:

35

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36 CAPITULO 3. PROPULSAO

- um helice direito a estibordo;

- e um helice esquerdo a bombordo.

Nestes navios, a popa e relativamente plana e os veios estao expostos e suportados poraranhas (“shaft brackets”). A presenca destas aranhas provoca ainda nao-uniformidades naesteira em que, devido a forma da popa, o escoamento entra no helice com um certo angulo.

Figura 3.1: Helice com tubeira.

A aplicacao de uma tubeira aceleradora, Fig. 3.1, permite aumentar o rendimento, relati-vamente a um helice convencional, no caso de helices fortemente carregados como os aplicadosem rebocadores, arrastoes, petroleiros, etc. Outro objectivo da aplicacao das tubeiras podeser a uniformizacao do escoamento de entrada no helice. Para este fim trata-se normalmentede tubeiras assimetricas colocadas avante do helice. Frequentemente este tipo de tubeiras einstalada depois de o navio estar em servico.

Figura 3.2: Helices de passo fixo e de passo controlavel.

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3.1. SISTEMAS DE PROPULSAO 37

Para um helice de passo fixo, a velocidade do navio e a forca propulsiva sao controladaspela velocidade de rotacao do helice. Para um helice de passo controlavel, a forca propulsivapode tambem ser controlada por variacao do passo do helice. A variacao do passo obtem-sepor rotacao das pas em torno de um eixo, a direita na Fig. 3.2. Utiliza-se quando a velocidadede rotacao e constante, ou variavel numa gama restrita, quando o helice tem de funcionar emmais de uma condicao.

Apesar de constituırem uma solucao cara, pela complicacao de chumaceiras e engranagensnecessaria, encontram-se exemplos de propulsao por helices contrarotativos. Sao dois helices,em que o helice de tras tem um diametro ligeiramente menor que o helice da frente, a rodarem sentidos contrarios, permitindo ao helice de tras eliminar a perda de energia cineticade rotacao do helice da frente, Fig. 3.3. Em consequencia, apresentam rendimentos tıpicossuperiores a um helice isolado.

Figura 3.3: Helices em contra-rotacao.

Outro tipo particular de helice e o helice supercavitante, Fig. 3.4. E um helice parafuncionar com elevada velocidade de rotacao em que as seccoes das pas sao concebidas paraprovocar uma bolsa de cavitacao que envolve toda a pa. O perigo de implosao e eliminadoporque a implosao das bolhas de cavitacao ocorre longe das faces das pas. Aplicam-se emnavios de alta velocidade com rendimento, em geral, fraco.

3.1.2 Outros meios de propulsao

Jacto de agua

Nestes sistemas, a forca propulsiva e obtida pela descarga de um jacto de agua a popa donavio. Para transmitir a energia pretendida ao jacto podem ser utilizadas bombas axiais,como no caso da Fig. 3.5, ou bombas centrıfugas.

Os sistemas de jacto de agua constituem actualmente um solucao comprovada para a pro-pulsao de embarcacoes rapidas, com divulgacao crescente nas embarcacoes de recreio,“ferries”,embarcacoes de patrulha, etc. Sao boas solucoes quando os principais requisitos colocadospassam pela manobrabilidade do navio, bom rendimento propulsivo, bom comportamento emaguas restritas e pouca necessidade de manutencao. Actualmente, ja estao disponıveis nomercado solucoes deste tipo para potencias propulsivas da ordem dos 30MW.

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38 CAPITULO 3. PROPULSAO

Figura 3.4: Helices supercavitante.

Figura 3.5: Propulsao por jacto de agua.

Propulsores azimutais

Esta configuracao, ver Fig. 3.6, possibilita a geracao de forca propulsiva em qualquer direccaopor rotacao do propulsor em torno do eixo vertical. No sistema tradicional de propulsaoazimutal, o motor era colocado no interior do casco e um sistema mecanico relativamentecomplexo fazia a transmissao do movimento as pas. Actualmente, o accionamento e feitopor um motor electrico colocado no veio de propulsor. Estes sistemas permitem combinar apropulsao e o governo do navio, dispensando a presenca do leme.

Apresentam como principais vantagens um bom rendimento, justificado em grande partepela maior uniformidade do escoamento a entrada do propulsor, elevada capacidade de ma-nobra e economia de espaco. A sua aplicacao, inicialmente quase que restrita a ferries, tem-sealargado nos tempos mais recentes a praticamente quase todos os tipos de navios.

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3.1. SISTEMAS DE PROPULSAO 39

Figura 3.6: Propulsores azimutais.

Propulsores cicloidais

Esta solucao propulsiva, representada na Fig. 3.7, desenvolvida pela Voight a partir dumaideia inicial de Ernst Schneider, permite gerar impulso de magnitude variavel em qualquerdireccao. As variacoes daquele impulso sao rapidas, contınuas e precisas, combinando assimas funcoes de propulsao e governo do navio.

Figura 3.7: Propulsores cicloidais.

O propulsor, colocado no fundo do navio, e composto por um conjunto de laminas paralelascom movimento de rotacao, segundo um eixo vertical, com velocidade variavel. Para gerar oimpulso, cada uma daquelas laminas tem um movimento oscilante em torno do seu proprioeixo. O percurso das laminas vai determinar a forca impulsiva gerada, enquanto um angulode fase entre 0◦ e 360◦ vai definir a direccao do impulso. Desta forma, pode ser gerada amesma forca propulsiva em qualquer direccao. A intensidade e a direccao da forca propulsiva

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40 CAPITULO 3. PROPULSAO

sao controladas por um conjunto cinematico de transmissao mecanica.Pelas suas caracterısticas, esta solucao apresenta bom desempenho na propulsao de re-

bocadores, ferries, grandes iates, navios de apoio a plataformas petrolıferas e outros naviosespeciais.

3.2 Helices propulsores

O projecto do helice devera dar resposta as seguintes questoes:

- sera que o helice desenvolvera a desejada forca propulsiva a velocidade rpm de projecto?

- qual vai ser a eficiencia do helice?

- qual vai ser o desempenho do helice em condicoes diferentes das condicoes de projecto?

- sera a distribuicao de pressoes favoravel a prevencao da cavitacao?

- qual sera o valor das forcas e momentos gerados pelo helice sobre o veio propulsor echumaceiras de apoio e de impulso?

- qual a pressao induzida pelo funcionamento do helice no casco do navio, potencialmenteresponsavel por vibracoes e ruıdo?

Os principais metodos de calculo disponıveis para, de alguma forma, dar resposta aquelasquestoes sao:

- a teoria da quantidade de movimento;

- a teoria dos elementos de pa;

- a teoria da linha sustentadora;

- a teoria da superfıcie de sustentacao;

- o metodo de painel;

- as simulacoes RANSE.

Outro contributo importante para o projecto do helice vem das series sistematicas dehelices, para as quais sao ja conhecidos os principais parametros de funcionamento em aguaslivres.

Por ultimo, ha que citar o contributo importante dos ensaios experimentais em modelosa escala reduzida, os ensaios do helice em aguas livres e o ensaio de propulsao.

3.2.1 Geometria do helice

Na complexa geometria do helice, conjunto de pas distribuıdas uniformemente em torno docubo montado na extremidade do veio, representada esquematicamente na Fig. 3.8, distinguem-se as seguintes areas, linhas e pontos:

- o bordo de ataque (“leading edge”), a linha frontal das pas;

- o bordo de fuga (“trailing edge”), a aresta atras;

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3.2. HELICES PROPULSORES 41

Figura 3.8: Geometria do helice.

- a extremidade da pa (“tip”) e o ponto linha ou seccao de maior raio;

- o dorso (“back”) e a face da pa sao, respectivamente, a superfıcie da pa do lado do veio,aspiracao, e a superfıcie do lado de pressao;

No cubo, com uma forma axisimetrica, unem-se as pas pela sua raiz (“ blade root”).A geometria do helice propulsor e caracterizada, entre outras, pelas seguintes dimensoes,

tambem representadas naquela figura:

- diametro do helice (“propeller diameter”), D;

- diametro do cubo (“boss (or hub) diameter”), d;

- numero de pas do helice (“propeller blade number”), Z;

- passo do helice (“propeller pitch”), P ;

- area do disco, A0 = πD2/4;

- area projectada, area da projeccao das pas num plano normal ao eixo do helice, AP ;

- area expandida, soma das areas das faces das pas, AE ;

- deslocamento circunferencial (“skew”);

- abatimento axial (“rake”), iG.

3.2.2 Valores caracterısticos

Como parametros adimensionais para caracterizacao dos helices propulsores podemos apontar:

- a razao entre os diametros do cubo e do helice, d/D;

- a razao entre a area expandida e a area do disco, AE/A0, frequentemente designada por“blade area ratio” (BAR);

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42 CAPITULO 3. PROPULSAO

- e a razao entre o passo e o diametro do helice, P/D.

Sao valores tıpicos para a razao de area expandida 0.3 < AE/A0 < 1.5. Razoes superi-ores a 1 significam que o helice tem pas sobrepostas o que o torna dispendioso. O valor deAE/A0 e selecionado de tal forma que a carga das pas seja suficientemente baixa para evitaruma situacao inaceitavel de cavitacao. Quanto mais carregada for a condicao de funciona-mento prevista para o helice maior devera ser a razao AE/A0 considerada na sua seleccao. Orendimento do helice diminui com o aumento da razao AE/A0.

O numero de pas Z e um parametro muito importante para as vibracoes induzidas pelohelice. Em geral, um numero ımpar de pas Z proporciona melhores caracterısticas no que dizrespeito a vibracoes. Maior numero de pas reduz a vibracao, devido aos inferiores picos depressao, mas aumenta os custos de fabrico.

Os helices propulsores para navios sao sempre adaptados as caracterısticas especıficas donavio apos exaustivo estudo hidrodinamico. O numero de pas esta normalmente entre 4 e 7.Os helices propulsores para pequenas embarcacoes, regra geral com o numero de pas entre 2e 4, sao produzidos em massa.

3.3 Teoria da quantidade de movimento

A teoria mais simples para representar o funcionamento de um helice propulsor e a teoria daquantidade de movimento, tambem designda por vezes como do disco actuante. Esta teoriapermite relacionar a forca propulsiva do helice com as velocidades induzidas. Tem comoprincipais hipoteses simplificativas:

- considerar o escoamento de fluido perfeito e incompressıvel;

- o numero de pas do helice e infinito;

- o helice propulsor exerce uma forca axial T que se distribui uniformemente sobre o discodo helice de diametro D;

- o helice nao induz velocidade velocidade de rotacao no fluido, ou seja, nao ha velocidadecircunferencia induzida.

3.3.1 Forca propulsiva

Consideremos o escoamento axisimetrico atraves do plano do helice, representado na Fig. 3.9,e denotar por VA a velocidade de aproximacao da agua ao helice e por p∞ a pressao empontos suficientemente afastados quer a vante quer a re do helice. Conforme representado,sendo a agua incompressıvel, a seccao do escoamento reduz-se pelo aumento de velocidadetransmitido pelo helice ao escoamento de agua. Na figura podemos ainda ver que no discoexiste uma descontinuidade de pressao ∆p. Esta descontinuidade, como resultado do referido“disco actuante”, gera uma forca propulsiva do helice dada por

T = ∆pA0 (3.1)

Quanto a distribuicao de velocidades, vamos considerar que a velocidade no disco e VA+V0e, no infinito, a velocidade e VA + V∞.

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3.3. TEORIA DA QUANTIDADE DE MOVIMENTO 43

Figura 3.9: Distribuicao espacial de velocidade e pressao para a teoria daquantidade de movimento.

Representando por A−∞ e A∞ as areas no infinito, a montante e a juzante, respectiva-mente, do tubo de corrente que passa pelo disco actuante, para se verificar a conservacao demassa no escoamento sera necessario que,

VaA−∞ = (Va + V0)A0 = (Va + V∞)A∞ (3.2)

Entao, aquelas areas, A−∞ e A∞ estao relacionadas com a area do disco e com a velocidadeinduzida por

A−∞ =Va + V0Va

A0 (3.3)

e

A∞ =Va + V0Va + V∞

A0 (3.4)

Aplicando agora o princıpio da conservacao da quantidade de movimento ao escoamentode fluido no tubo de corrente, obtemos a equacao,

T = ρ (Va + V∞)2A∞ − ρV 2a A−∞ (3.5)

Usando a equacao de conservacao da massa, Eq. (3.2), podemos dizer entao que a forcapropulsiva T e dada por,

T = ρ (Va + V0)V∞A0 (3.6)

e, que o “salto de pressao” no disco actuante vale

∆p = ρ (Va + V0)V∞ (3.7)

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44 CAPITULO 3. PROPULSAO

Por fim, vamos aplicar a equacao de Bernoulli ao tubo de corrente. A montante do discotemos,

p∞ +1

2ρV 2

a = p0 +1

2ρ (Va + V0)

2 (3.8)

e, a juzante,

p∞ +1

2ρ (Va + V∞)2 = p0 + ∆p+

1

2ρ (Va + V0)

2 (3.9)

Fazendo agora a subtraccao das equacoes, Eq. (3.9) − Eq. (3.8), temos uma nova equacaopara avaliar o valor de ∆p

∆p = ρ

(Va +

1

2V∞

)V∞ (3.10)

Naturalmente que o “salto de pressao” avaliado pela ultima equacao nao pode ser diferentedaquele que resulta da Eq. (3.7). Logo,

ρ (Va + V0)V∞ = ρ

(Va +

1

2V∞

)V∞ (3.11)

e, entao, daqui resulta que a velocidade induzida no disco e metade da velocidade induzidana esteira no infinito,

V0 =1

2V∞ (3.12)

A forca propulsiva T obtida no disco actuante pode ser calculada, em funcao da velocidadeinduzida no disco, por

T =πD2

4ρ (Va + V0) 2V0 (3.13)

3.3.2 Coeficiente de carga

Se definirmos para um helice propulsor como coeficiente de carga, CT ,

CT =T

π4D

2 12ρV

2a

(3.14)

e considerarmos a forca propulsiva resultante da teoria do disco actuante, obtem-se

CT = 4V0Va

(1 +

V0Va

)(3.15)

ou, em termos de velocidade induzida no disco,

V0Va

=1

2

(−1 +

√1 + CT

)(3.16)

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3.4. ENSAIOS COM MODELOS REDUZIDOS DE HELICES 45

3.3.3 Rendimento ideal do helice

O rendimento ideal do helice e o rendimento maximo que pode ser obtido em fluido perfeitocom um helice propulsor que nao induza velocidade de rotacao no fluido.

Num referencial em repouso no fluido, considere-se que o helice avanca com velocidadeVa, exercendo uma forca propulsiva T . A potencia efectiva do helice e dada por

PE = T Va (3.17)

A perda de energia cinetica axial por unidade de tempo e o fluxo de energia por unidadede tempo atraves de um plano perpendicular a direccao de avanco, no infinito, a juzante.Este fluxo de energia e calculado pelo produto do caudal massico que se escoa pelo tubo decorrente pela energia cinetica especıfica,

Ep = ρπD2

4(Va + V0)×

1

2V 2∞

ou seja, considerando a relacao conhecida entre a velocidade no disco e na esteira no infinito,

Ep = ρπD2

2(Va + V0)V

20 (3.18)

O rendimento ideal do helice propulsor sera entao dado por

ηi =TVa

TVa + Ep(3.19)

ou, considerando (3.13) e (3.18), e simplificando, ficamos com

ηi =1

1 + V0Va

(3.20)

3.4 Ensaios com modelos reduzidos de helices

Apesar de o helice ir funcionar numa esteira nao-uniforme do navio, sao realizados ensaiospara avaliacao do seu desempenho numa esteira uniforme, recorrendo ao ensaio em aguaslivres de um modelo a escala reduzida do helice, em condicoes apropriadas de semelhanca.Neste ensaio, o chamado “open water test”, um modelo do helice e deslocado com a velocidadeda avanco Va num fluido em repouso. O escoamento de aproximacao deve ser tao uniformequanto possıvel. Durante o deslocamento do helice este e posto a rodar por um pequeno motorelectrico a velocidade n (rps) pretendida. O ensaio realiza-se normalmente a uma velocidadede rotacao constante, ou seja, para um dado numero de Reynolds.

As caracterısticas propulsivas em aguas livres, nomeadamente a forca propulsiva T e obinario Q, sao medidas em regime estacionario de funcionamento. Depois de adimensionaliza-dos, os valores medidos da forca propulsiva e do binario para varios regimes de funcionamentoconstituem o “diagrama em aguas livres” do helice em questao.

A forca propulsiva T e o binario Q disponibilizados por um helice propulsor dependem devarias variaveis:

- a velocidade de avanco Va;

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46 CAPITULO 3. PROPULSAO

- a velocidade de rotacao n;

- o diametro D;

- a massa especıfica do fluido ρ;

- a viscosidade cinematica do fluido ν.

Aplicando a analise dimensional, expressando a dependencia dos coeficientes de forcapropulsiva e de binario dos seguintes grupos adimensionais:

- coeficiente de avanco, J =VanD

;

- e numero de Reynolds, aqui definido como Re =nD2

ν;

ou seja,

KT = KT (J,Re) e KQ = KQ (J,Re)

obtem-se os seguintes expressoes para os referidos coeficientes adimensionais:

- coeficiente de forca propulsiva KT =T

ρn2D4;

- coeficiente de binario KQ =Q

ρn2D5.

3.4.1 Diagrama em aguas livres

O diagrama em aguas livres do helice integra a representacao grafica da variacao dos coefici-entes da forca propulsiva, KT , e de binario, KQ, com o coeficiente de avanco, Va. Um exemplode diagrama em aguas livres esta representado na Fig. 3.10.

As curvas tracadas nestes diagramas servem principalmente para a optimizacao do helicee determinacao do ponto de funcionamento. Na pratica, ja nao sao utilizadas aquelas re-presentacoes graficas no projecto de helices, mas sim os polinomios representativos daquelasevolucoes para permitir o calculo computacional. As tabelas tem cerca de 50 coeficientespara os polinomios relativos a serie sistematica de helices de Wageningen. Embora o trabalhoinicial de registo destes coeficientes seja moroso e fastidioso, os processos de calculo e optimi-zacao posteriores ficam muito facilitados e expeditos pela utilizacao de programas ou folhasde calculo. A importancia da representacao grafica esta actualmente restrita a verificacaoda tendencia de variacao do desempenho do helice com a alteracao de algumas condicoesoperacionais.

3.4.2 Rendimento

Definindo o rendimento de um helice propulsor como sendo a razao entre a potencia efectivae a potencia fornecida pelo veio ao helice, o rendimento em aguas livres e calculado por

η0 =PEPD

=VaT

2πnQ(3.21)

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3.5. SERIES SISTEMATICAS 47

Figura 3.10: Diagrama de aguas livres.

a partir das medicoes observadas durante o ensaio.Ou, se quisermos expressa-lo em termos dos coeficientes adimensionais, podemos obter,

η0 =JKT

2πKQ(3.22)

3.4.3 Indice de qualidade

A qualidade de um propulsor nao fica bem caracterizada apenas pelo seu rendimento maximo.O ındice de qualidade, que permite caracterizar melhor um helice para uma dada aplicacaoespecıfica, e dado por

q =η0ηi

(3.23)

em que η0 e o rendimento em aguas livres e ηi e o rendimento ideal.

Como CT =8KT

πJ2, substituindo em (3.23):

q =KT

4πKQ

(J +

√J2 +

8

πKT

)(3.24)

3.5 Series sistematicas

Uma serie sistematica de helices e um conjunto de helices obtidos por variacao sistematica deparametros geometricos. Ao longo de decadas, por todo o mundo tem sido realizados ensaiosem series sistematicas de propulsores para navios. As principais caracterısticas de algunsexemplos de series sistematicas de helices propulsores simples de passo fixo estao incluıdas naTab. 3.1.

O principal objectivo perseguido na realizacao dos ensaios sistematicos nestes conjuntosde helices e criar uma base de dados que permita ajudar o projectista a entender os principais

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48 CAPITULO 3. PROPULSAO

Serie No Z AE/A0 P/D D(mm)

Wageningen B ≈ 120 2− 7 0, 3− 1, 05 0, 5− 1, 4 250Au 34 4− 7 0, 4− 0, 758 0, 5− 1, 2 250Gawn 37 3 0, 2− 1, 1 0, 4− 2, 0 508KCA ≈ 30 3 0, 50− 1, 25 0, 6− 2, 0 406Ma 32 3 e 5 0, 75− 1, 20 1, 0− 1, 45 250Newton-Rader 12 3 0, 5− 1, 0 1, 05− 2, 08 254KCD 24 3− 6 0, 44− 0, 80 0, 6− 1, 6 406Meridian 20 6 0, 45− 1, 05 0, 4− 1, 2 305

Tabela 3.1: Series sistematicas de propulsores.

factores que influenciam o desempenho do helice, bem como a ocorrencia de cavitacao, emvarias condicoes de funcionamento. Um segundo objectivo e a construcao de diagramas quepermitam ajudar a seleccao das caracterısticas mais apropriadas para uma dada aplicacao aescala do navio.

3.5.1 Serie sistematica de Wageningen

Uma das series sistematicas de helices propulsores mais populares e a serie B de Wageningen.Esta serie, em que os trabalhos iniciais datam de 1940, sera talvez a mais vasta. As principaiscaracterısticas destes helices sao:

- ter distribuicao radial do passo constante;

- um pequeno deslocamento circunferencial (“skew”);

- distribuicao radial do abatimento axial (“rake”) linear 15◦;

- contorno largo da pa junto a extremidade;

- seccao das pas NSMB, indicada na Fig. 3.11.

Figura 3.11: Aspecto geometrico das pas da serie B de Wageningen

Os parametros cuja variacao sistematica foi considerada na realizacao desta serie foramos seguintes:

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3.5. SERIES SISTEMATICAS 49

- o numero de pas: 2 ≤ Z ≤ 7;

- a razao de area expandida: 0.3 ≤ AE/A0 ≤ 1.05;

- a razao passo-diametro: 0.5 ≤ P/D ≤ 1.4.

A nomenclatura dos helices desta serie, considerando a tıtulo de exemplo um helice B-4.85,e a seguinte:

- Serie B;

- Numero de pas: 4;

- razao de area expandida: 0.85.

Para cada caso existe um diagrama, ou uma tabela com os ja referidos coeficientes po-linomiais, com as curvas caracterısticas dos diagrams de aguas livres, para diferentes razoespasso-diametro, P/D. Na Fig. 3.12 esta representado o caso dos helices com duas pas, razaode area expandida 0, 3 e razao passo-diametro compreendida entre 0, 5 e 1, 4.

3.5.2 Outras series sistematicas

A serie sistematica de helices propulsores Au e muito popular no Japao mas, fora dele, naoconseguiu uma divulgacao semelhante a serie de Wageningen podendo, no entanto, considerar-se como uma serie complementar daquela.

A serie Gawn apresenta como caracterıstica distintiva o maior diametro dos helices quea integram. Isto significa que muitos dos efeitos de escala presentes nas outras series foramaqui evitados ou, pelo menos, reduzidos. A serie KCA, tambem designada por vezes comoGawn-Burrill, e complementar da serie de Gawn. Sao 30 helices com 3 pas, tambem comgrande diametro, 400mm. Esta serie foi ensaiada num tanque de cavitacao, e nao num tanquede reboque, a diferentes numeros de cavitacao e, consequentemente, permite verificar numdeterminado projecto de aplicacao os aspectos relacionados com o fenomeno da cavitacao.

Os helices da serie de Lindgren, serie Ma, sao mais pequenos, 250mm, e as suas pastem passo constante. Foram testados num tanque de reboque e num tanque de cavitacao e,assim, resultou dos ensaios um extenso e integrado conjunto de dados adequado para a fasepreliminar do projecto.

A serie de Newton-Rader compreende um conjunto limitado de 12 helices com tres pasvocacionados para a propulsao de embarcacoes rapidas.

Para alem destas series sistematicas de helices simples, existem tambem alguns estudosrelativos a formas particulares de helices como, por exemplo, as series de helices contra-rotativos do MARIN e SSPA, ou a serie de Wageningen de helices com tubeira.

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50 CAPITULO 3. PROPULSAO

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3.5. SERIES SISTEMATICAS 51

3.5.3 Diagrama de 4 quadrantes

No caso dos helices de passo fixo, a forma convencional de operacao do helice, velocidade derotacao positiva e velocidade de avanco nula ou positiva, corresponde ao funcionamento noprimeiro quadrante do diagrama de funcionamento.

No diagrama completo, ver Fig. 3.13, necessario por exemplo para estudar a manobrabi-lidade do navio ou o seu desempenho em marcha a re, estao definidos quatro quadrantes, deacordo o angulo de avanco,

β = tan−1(

Va0, 7 ·π ·n ·D

)(3.25)

Figura 3.13: Notacao do diagrama com 4 quadrantes.

Como ja referido, o primeiro quadrante corresponde a:

- velocidade de rotacao do helice correspondente a marcha a vante;

- velocidade do navio a vante;

- ou seja, angulo de avanco 0 ≤ β ≤ 90◦.

O segundo quadrante corresponde a:

- velocidade de rotacao do helice correspondente a marcha a re;

- velocidade do navio a vante;

- ou seja, angulo de avanco 90◦ < β ≤ 180◦.

No terceiro quadrante, as condicoes de operacao do helice sao:

- velocidade de rotacao do helice correspondente a marcha a re;

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52 CAPITULO 3. PROPULSAO

- velocidade do navio a re;

- ou seja, angulo de avanco 180◦ < β ≤ 270◦.

E, por fim, no quarto quadrante temos naturalmente:

- velocidade de rotacao do helice correspondente a marcha a vante;

- velocidade do navio a re;

- ou seja, angulo de avanco 270◦ < β < 360◦.

Se existirem dados experimentais suficientes torna-se possıvel definir uma funcao paraestimar o desempenho do helice, no que diz respeito a forca propulsiva e ao binario, nosquatro quadrantes do diagrama em aguas livres. Um exemplo de um diagrama deste tipo,multi-quadrante, esta representado na Fig. 3.14, relativo aos helices da serie de WageningenB4-70 com relacao P/D entre 0, 5 e 1, 4.

Justifica-se a introducao de uma notacao para obter maior flexibilidade para trabalharnestes diagramas multi-quadrante. De notar que para β = 90◦ ou β = 270◦, situacoes emque a velocidade de rotacao do helice e nula, o coeficiente de avanco resultaria J = ∞. Deforma semelhante, para prevenir o mesmo tipo de situacoes, sao tambem definidos os seguintescoeficientes:

- coeficiente de forca propulsiva modificado,

C∗T =T

1

2ρV 2

RA0

(3.26)

- coeficiente de binario modificado,

C∗Q =Q

1

2ρV 2

RA0D(3.27)

em que VR e a velocidade relativa de avanco para 0, 7R, ou seja,

C∗T =T

π

8ρ[V 2a + (0, 7πnD)2

]D2

(3.28)

e

C∗Q =Q

π

8ρ[V 2a + (0, 7πnD)2

]D3

(3.29)

Na Fig. 3.14 pode-se ver o efeito que a razao P/D tem no coeficiente de binario C∗Qpara praticamente toda a gama de β. Em particular, e nos intervalos 40◦ < β < 140◦ e230◦ < β < 340◦ que a magnitude de C∗Q varia mais significativamente.

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3.6. CAVITACAO 53

Figura 3.14: Diagrama em aguas livres de 4 quadrantes para os helicesWageningen B-4.70.

3.6 Cavitacao

3.6.1 Origem da cavitacao

A velocidade elevada do escoamento de agua pelo helice provoca regioes com baixa pressao.Se a pressao cair o suficiente, formar-se-ao cavidades preenchidas com vapor. Estas cavidadesdesaparecerao quando a pressao aumentar. O crescimento e o colapso destas “bolhas” eextremamente rapido.

A cavitacao envolve fenomenos fısicos complexos uma vez que se trata de escoamentos aduas fases, com modelacao nao-linear. Nos helices dos navios, a velocidade em torno das paspode ser suficiente para reduzir a localmente a pressao e desencadear a cavitacao. Devido apressao hidrostatica, a pressao total sera superior nas imediacoes da pa que se encontre coma maxima imersao (posicao 06:00) do que naquela que se encontra na posicao 12:00. Assim,as pas dos helices em cavitacao alternadamente passarao por regioes em que tendencialmentese formarao bolhas de cavitacao e regioes onde as mesmas tenderao a colapsar.

Esta rapida sucessao de explosoes e implosoes nas proximidades das pas do helice temvarias consequencias nefastas. As principais sao:

- vibracao;

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54 CAPITULO 3. PROPULSAO

Figura 3.15: Efeito da cavitacao no valor dos parametros relativos a aguaslivres.

- ruıdo;

- erosao da superfıcie das pas (sobretudo se o colapso das bolhas ocorrer na proximidade);

- reducao da forca propulsiva.

No diagrama em aguas livres da Fig. 3.15 esta assinalada a reducao que e tipicamenteprovocada pela cavitacao nos coeficientes de forca propulsiva e binario.

3.6.2 Controle da cavitacao

Num meio ideal, agua sem impurezas ou ar dissolvido, a cavitacao ocorrera quando a pressaototal atingir localmente a pressao de vapor a essa temperatura. Na pratica, a cavitacao inicia-se para valores de pressao superiores pela presenca de partıculas microscopicas e da existenciade ar dissolvido na agua que facilitam e precipitam o inıcio do processo de vaporizacao.

O numero de cavitacao σ e um parametro adimensional que estima a possibilidade deaparecimento do fenomeno de cavitacao num escoamento,

σ =p0 − p1

2ρ V 2

0

(3.30)

em que:

- p0 e a pressao ambiente de referencia;

- p e a pressao local;

- e V0 e a velocidade de referencia correspondente.

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3.6. CAVITACAO 55

Figura 3.16: Pressao de vapor da agua em funcao da temperatura.

Para σ inferior a σv, o numero de cavitacao avaliado para a pressao de vapor pv, naoocorrera cavitacao num fluido ideal. Na pratica, e necessario considerar um coeficiente deseguranca, considerando uma pressao limite superior a pressao de vapor.

Para um helice e habitual definir o numero de cavitacao σn como:

σn =p0 − p

1

2ρn2D2

(3.31)

adoptando-se como velocidade caracterıstica nD.

3.6.3 Consideracao da cavitacao na seleccao do helice

O fenomeno da cavitacao e predominantemente dominado pelo campo de pressao no esco-amento da agua pelo plano do helice. Prevenir a cavitacao passa consequentemente pelocontrolo da mınima pressao absoluta naquele escoamento. A possibilidade de ocorrencia decavitacao e evitada pela distribuicao da forca propulsiva por uma area maior, aumentando odiametro do helice ou a razao da area expandida AE /A0. A forma mais usual de estimar,ainda que de uma forma nao completamente rigorosa, o perigo de ocorrencia da cavitacaopassa pela utilizacao do diagrama de Burrill (Fig. 3.17). O diagrama indica um limite inferiorpara a area projectada do helice de um navio mercante. Nos eixos do diagrama de Burrill es-tao o numero de cavitacao, em abcissas, e o coeficiente de Burrill nas ordenadas. O coeficiente

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56 CAPITULO 3. PROPULSAO

Figura 3.17: Diagrama de Burrill.

de Burrill e calculado por

τc =T

q0,7RAp(3.32)

em que, Ap e a area projectada do helice, e o parametro q0,7R e dado por

q0,7R =1

2ρ V 2

R

em que VR e o valor absoluto da velocidade local a 0, 7 do raio do helice, ou seja,

VR =

√V 2a + (0, 7π nD )2

com Va a velocidade de entrada do escoamento no plano do helice.Nos helices da serie de Wageningen, a area expandida esta relacionada com a area projec-

tada por

AE =AP

1, 67− 0, 229P/D(3.33)

3.6.4 Ensaios experimentais

Os ensaios de cavitacao, bem como frequentemente os ensaios em aguas livres, realizam-se eminstalacoes que compreendem um canal fechado na qual e imposta a circulacao da agua porum impulsor. Na Fig. 3.18 esta representada esquematicamente uma instalacao deste tipo.

Estes tuneis sao concebidos por forma a proporcionar um escoamento tao uniforme quantopossıvel na seccao de teste. A seccao de teste, o troco horizontal superior, dispoe de visorespara inspeccao e vizualizacao do escoamento. O impulsor para a circulacao da agua esta

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3.6. CAVITACAO 57

Figura 3.18: Instalacoes de ensaio do RINA.

colocado no troco inferior horizontal para garantir que, mesmo quando a pressao no tanquefor reduzida, a coluna hidrostatica vai impedir a cavitacao neste propulsor.

Normalmente, a pressao e reduzida por bombas de vacuo para ajuste do numero de cavi-tacao e a instalacao dispoe de equipamento para reduzir o ar dissolvido na agua. Podem serinstaladas “grelhas metalicas” para induzir a turbulencia desejada no escoamento.

Os helices em teste sao sujeitos a iluminacao estroboscopica por forma a serem “vistos”sempre com as pas na mesma posicao. Obtem-se assim uma visualizacao do padrao de cavi-tacao “estacionaria”.

O funcionamento do helice tem alguns pontos caracterısticos que se passa a identificar. Aprimeira destas situacoes acontece quando o motor electrico faz rodar o veio do helice a umavelocidade n mantendo-se a velocidade de avanco nula, ou seja Va = 0. Nestas condicoes,verifica-se J = 0 e η = 0, e diz-se que o helice funciona a ponto fixo. Se em seguida sefizer avancar o helice a uma velocidade Va, mantendo a mesma velocidade de rotacao, estedesenvolvera um impulso T e absorvera um certo momento Q. Esta fase e a fase propulsora,utilizada para a propulsao dos navios. Continuando a aumentar o coeficiente de impulso pordiminuicao da velocidade de rotacao n, o impulso vai diminuindo ate o helice chegar ao pontode impulso nulo. Inicia-se a fase de travagem, ate um ponto, no qual o helice trabalha emconcordancia com o coeficiente de avanco J , com KQ = 0, helice livre. Um helice livre opoeresistencia ao avanco. Continuando a reduzir a velocidade de rotacao do helice e mantendoVa, entra-se na fase motora, em que o helice poderia fornecer energia. Quando a velocidadedo helice for nula, o helice diz-se bloqueado.

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58 CAPITULO 3. PROPULSAO

Figura 3.19: Imagem da cavitacao num helice.

3.7 Seleccao do helice

No calculo do helice procura-se a optimizacao das principais variaveis, numero e area daspas, diametro, velocidade de rotacao e passo, por forma a que a propulsao se faca com bomrendimento em todas as condicoes de carga do navio. E possıvel obter uma boa estimativadas caracterısticas de funcionamento do helice utilizando uma das varias series sistematicasreferenciadas. As variaveis de optimizacao do helice sao descritas sucintamente nos paragrafosseguintes.

3.7.1 Variaveis de optimizacao

DiametroO rendimento do helice aumenta o diametro do mesmo, estando no entanto a dimensao

deste limitada pela geometria da popa. Deve-se referir no entanto que o aumento do diametrode helice provoca vibracoes mais fortes e a reducao do rendimento do casco. As sociedadesclassificadoras tem normas proprias para definir valores mınimos de folga entre o helice e ocasco do navio.

O diametro maximo do helice e normalmente considerado como uma fraccao do caladomaximo do navio,

Dmax = a T (3.34)

dependente do tipo de navio, conforme indicado na Tab. 3.2.

Para compensar a nao uniformidade do escoamento de aproximacao ao helice quando estese encontra atras da querena, o diametro equivalente em aguas livres e considerado como:

D0 =D

1− b(3.35)

em que b toma os valores constantes na Tab. 3.3.

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3.7. SELECCAO DO HELICE 59

Tipo de Navio a

Graneleiros/Petroleiros <0,65Porta-contentores <0,74

Tabela 3.2: Coeficiente para atribuicao do diametro maximo do helice pelaEq. (3.34).

Helice b

Simples 0.05Duplo 0.03

Tabela 3.3: Constante para o calculo do diametro equivalente em agualivres pela Eq. (3.35).

Velocidade de rotacaoEm instalacoes propulsoras com transmissao directa, a velocidade de rotacao do helice e

estabelecida pela velocidade do motor. Neste caso, o diametro e ajustado para se obter umcoeficiente de avanco apropriado para a velocidade pretendida e a potencia exigida. Quandoe utilizada uma caixa redutora, procura-se utilizar o maior diametro possıvel, sendo depoisajustada a velocidade de rotacao do helice ajustada de acordo com o coeficiente de avancopretendido. Devem evitar-se velocidades que multiplicadas pelo numero de pas do helicesejam proximas das frequencias de ressonancia do casco e da instalacao propulsora. Do pontode vista da prevencao da cavitacao, sao favoraveis as velocidades de rotacao mais baixas.

Numero de pasO factor determinante na seleccao do numero de pas e a irregularidade das forcas geradas

pelo helice. Estas forcas, aplicadas com a frequencia correspondente a velocidade de rotacao,induzem vibracoes no casco e instalacao propulsora. O objectivo passa por obter um bomcompromisso entre a vibracao gerada e o rendimento obtido ja que este diminui com o aumentodo numero de pas do helice.

Distribuicao radial da pressaoA distribuicao da pressao nas pas esta relacionada com a susceptibilidade de ocorrencia da

cavitacao. Em particular, e normalmente vantajoso reduzir a pressao no extremo radial daspas. Esta reducao e ainda vantajosa na perspectiva do esforco estrutural das pas e da pressaoirregular induzida no casco.

Geometria das pasA formula de Keller permite escolher a razao de area expandida para evitar o fenomeno da

cavitacao,

AeA0

=(1, 3 + 0, 3Z)T

(p0 − pv)D2+ k (3.36)

em que k e uma margem de seguranca, que variara entre k = 0 para navios de guerra ek = 0, 2 para navios mercantes com helices muito carregados. Quanto maior a razao de areas,menor sera o risco de cavitacao mas, em compensacao menor o rendimento do helice devidoao atrito. A solucao sera a menor area que garanta o criterio de cavitacao.

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60 CAPITULO 3. PROPULSAO

No entanto, a curvatura, o angulo de ataque e a espessura das tem tambem uma grandeimportancia no controle da cavitacao. A maior espessura das pas favorece a cavitacao nas cos-tas das pas enquanto que as pas pouco espessas tem maior propensao para gerarem cavitacaono bordo de ataque.

Quanto ao rendimento, ele e favorecido pela diminuicao da corda das pas, ou seja da suaarea, mas por razoes estruturais, esta reducao tem que ser acompanhada por um aumento deespessura que vai provocar um aumento da resistencia de forma.

A utilizacao apropriada do desvio circunferencial das pas do helice (“skew”) permite con-trolar muito eficazmente a cavitacao e a vibracao induzida tendo apenas como contrapartidauma reducao do rendimento do helice em marcha a re.

3.7.2 Tipos de problema

E possıvel obter uma boa estimativa das caracterısticas de funcionamento do helice utilizandouma das varias series sistematicas referenciadas. Uma vez determinado o numero e a areadas pas, resta a determinar a combinacao do passo e do coeficiente de avanco que permiteoptimizar o rendimento do helice. De acordo com o tipo de problema em causa, podemosconsiderar varias situacoes. Quando a potencia e a velocidade de rotacao sao conhecidas, daeliminacao do diametro resulta a seguinte equacao:

KQ

J5=

PDn2

2πρV 5a

(3.37)

Quando a potencia e o diametro do helice estao determinados, a eliminacao da velocidadede rotacao permite estabelecer:

KQ

J3=

PD2πρD2V 3

a

(3.38)

Sendo prescritas a forca propulsiva e a velocidade de rotacao, a eliminacao do diametroconduz a equacao:

KT

J4=Tn2

ρV 4a

(3.39)

Por fim, quando sao conhecidos o diametro do helice e a forca propulsiva, a eliminacao davelocidade de rotacao permite estabelecer a seguinte relacao:

KT

J2=

T

ρD2V 2a

(3.40)

3.8 Interaccao entre casco e helice

Os ensaios de helices a escala reduzida em aguas livres, conseguindo efectuar uma avaliacaopreliminar das caracterısticas propulsivas de um helice, nao permitem uma previsao do seudesempenho numa dada aplicacao especıfica, porque, na realidade, o helice nao vai operar emaguas livres mas sim atras do navio.

As caracterısticas de um helice trabalhando atras de um navio a uma dada velocidadediferem consideravelmente das caracterısticas obtidas em ensaios com modelos em aguas livres,a velocidade correspondente, devido aos seguintes factores:

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3.8. INTERACCAO ENTRE CASCO E HELICE 61

- a velocidade da agua na esteira do navio e menor que a velocidade do navio;

- a nao-uniformidade da esteira do navio afecta a distribuicao das forcas aplicadas naspas do helice;

- a aceleracao da agua pelo helice reduz a pressao sobre o casco e, consequentementeaumentando a resistencia efectiva da querena.

3.8.1 Ensaios de propulsao

Os ensaios de propulsao tem por objectivo determinar, para cada velocidade de rotacao, apotencia propulsiva e a consequente velocidade do navio. Os resultados dos ensaios permitemtambem a determinacao dos coeficientes de deducao da forca propulsiva e da velocidade daesteira necessarios para a seleccao ou projecto do helice. O modelo e equipado com umhelice pre-seleccionado de acordo com as necessidades operacionais previstas para o navio. Aoptimizacao a partir deste helice-base decorrera a partir dos resultados obtidos neste ensaiode auto-propulsao. O accionamento deste helice e normalmente realizado por um pequenomotor electrico, conforme representado esquematicamente na Fig. 3.20.

Figura 3.20: Modelo para ensaios de propulsao.

As condicoes de realizacao do ensaio de propulsao contemplam:

- semelhanca geometrica;

- semelhanca cinematica;

- semelhanca de Froude;

- igual numero de cavitacao.

Pelas razoes apontadas anteriormente, nao e possıvel acumular com aquelas condicionan-tes a igualdade do numero de Reynolds. Assim, existem efeitos de escala a considerar naextrapolacao dos resultados para a escala do navio.

O primeiro efeito de escala a considerar no ensaio de propulsao e o efeito de escala naresistencia. O coeficiente de resistencia total e superior no teste do modelo ao que se verificarano navio porque o coeficiente de resistencia de atrito diminui com o aumento do numero

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62 CAPITULO 3. PROPULSAO

de Reynolds. Este efeito resultante da variacao do numero de Reynolds e resolvido pelaaplicacao de uma forca de compensacao. A intensidade da forca de compensacao necessariaFD e determinada por,

FD =1

2ρ ·V 2

m ·Sm · ((1 + k) (cFm − cFs)− cA − cAA) (3.41)

O helice tem portanto que produzir uma forca propulsiva igual a resistencia total RT menosa forca de compensacao FD.

Outro efeito de escala a considerar no ensaio de propulsao diz respeito a esteira. Aespessura da camada limite e esteira do modelo e relativamente maior que a correspondenteespessura no navio. Ou seja, o coeficiente de esteira do modelo e maior que o do navio. Avelocidade media de aproximacao ao helice, adimensionalizada pela velocidade do modelo, emenor que a correspondente velocidade adimensionalizada do navio.

Por ultimo, devera ser considerado o efeito de escala nas caracterısticas propulsivas dohelice. De facto, o numero de Reynolds do helice no modelo e menor que no helice do navioe os coeficientes de forca propulsiva e de binario sao diferentes.

Na realizacao dos ensaios de propulsao e normalmente mantida a velocidade do “carro” dereboque constante e e variada a velocidade de rotacao do helice ate ser obtida uma condicaode equilıbrio. Sao assim obtidos dados de forca propulsiva e binario em funcao da velocidade.Adicionalmente, podem ainda ser registados dados sobre o calado e o caimento do modelodurante o ensaio.

O ponto de auto-propulsao do modelo e encontrado quando as forcas exteriores sobre omodelo sao nulas. O ensaio e realizado com o numero de Froude do navio, fazendo variar avelocidade de rotacao do helice ate que a forca de reboque se anule. Nesta situacao, a forcapropulsiva iguala a resistencia da querena, alterada pela presenca de helice. Para compensara diferenca no coeficiente de resistencia do navio e do modelo, e aplicada a forca adicional dereboque FD determinada pela Eq. (3.41). E portanto mais correcto afirmar que no ponto deauto-propulsao do modelo, a unica forca exterior aplicada ao modelo e a forca FD.

Para alem do chamado ensaio de auto-propulsao, realizam-se os ensaios em sobrecarga.Cada ensaio em sobrecarga realiza-se tambem com o helice a operar atras do modelo com estea ser rebocado a velocidade constante. Faz-se variar a velocidade de rotacao do helice e, paracada uma das velocidades ensaiadas nm regista-se a forca de reboque Fm, a forca propulsivaTm e o binario Qm. Pode-se encontrar tambem o ponto de auto-propulsao do modelo porinterpolacao nos resultados dos ensaios em sobrecarga, mais concretamente interpolando nacurva da forca de reboque em funcao da velocidade de rotacao, para o valor requerido de FD.

3.8.2 Potencia e velocidade

A potencia efectiva PE , potencia necessaria para rebocar a querena, sem os apendices associ-ados a propulsao, a velocidade Vs, e obtida por

PE = RT ·Vs (3.42)

em que:

- RT e a resistencia total em aguas livres excluindo a resistencia adicional dos apendicesassociados a propulsao;

- e Vs e a velocidade do navio.

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3.8. INTERACCAO ENTRE CASCO E HELICE 63

De forma analoga, a potencia propulsiva PT pode ser obtida por

PT = T ·Va

em que:

- T e a forca propulsiva calculada a partir dos ensaios de propulsao;

- e Va e a velocidade de avanco do helice.

A forca propulsiva T e superior a resistencia RT avaliada a partir do ensaio de resistenciarealizado sem helice. Isto significa, como referido antes, que a presenca do helice induz umaresistencia adicional porque:

- a presenca do helice aumenta a velocidade do escoamento na zona da popa do navio e,em consequencia a resistencia de atrito;

- a presenca do helice provoca uma diminuicao da pressao nos paineis da popa do navio.

O segundo destes factores e normalmente o mais significativo.O aumento da resistencia devido ao efeito da presenca do helice e usualmente representado

por uma reducao da forca propulsora expressa como fraccao dessa forca. O coeficiente dededucao da forca propulsiva t associa entao a forca propulsiva e a resistencia,

t = 1− RTT

(3.43)

em que t e normalmente considerado igual no modelo e no navio.Depois de realizados os ensaios de propulsao e calculados os coeficientes de forca propul-

siva, KTm e KQm, o coeficiente de deducao da forca propulsiva e calculado por

tm =Tm + FD −RC

Tm(3.44)

em que RC e a resistencia corrigida para a diferenca de temperatura entre os dois ensaios,resistencia e propulsao. O valor de RC sera,

RC =(1 + k) cFmC + cR(1 + k) cFm + cR

RTm (3.45)

em que cFmC e o coeficiente da resistencia de atrito avaliado a temperatura da agua no ensaiode propulsao.

Para corrigir o efeito da velocidade da esteira, define-se o coeficiente de deducao da esteira,w, que permite relacionar a velocidade de avanco Va com a velocidade do navio V ,

w = 1− VaV

(3.46)

Considerando o diagrama em aguas livres do helice, com o valor de KTm avaliado com aforca propulsiva experimental do ensaio de propulsao, pode obter-se atraves daquele diagramaum valor para o coeficiente de avanco J0m. O coeficiente de esteira do modelo sera entao dadopor

wm = 1− J0mDmnmVm

(3.47)

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64 CAPITULO 3. PROPULSAO

Ou seja, a velocidade media axial no plano do helice atras do navio a velocidade V , noensaio de resistencia sem helice, e a velocidade da esteira nominal,

Va = (1− wn)V (3.48)

e, com o helice em operacao atras do navio, o escoamento devido a presenca da querena emodificado obtendo-se a velocidade da esteira efectiva,

Ve = (1− we)V (3.49)

A velocidade total sera a soma da velocidade da esteira efectiva e da velocidade axial induzidapelo helice.

O rendimento rotativo relativo ηR e calculado por

ηR =KQ0m

KQm(3.50)

em que KQ0m e obtido a partir do diagrama em aguas livres do helice e o coeficiente de binarioKQm e calculado com base nos resultados experimentais do ensaio de propulsao.

Designa-se por rendimento do casco a razao entre a potencia efectiva e a potencia propul-siva, ou seja,

ηH =PEPT

=RT ·VsT ·Va

=1− t1− w

(3.51)

A determinacao de w, t e ηH e feita preferencialmente atraves de ensaios de modelos emensaios de auto-propulsao utilizando um helice de “stock” com caracterısticas conhecidas, taoaproximadas quanto possıvel do helice optimo. Se nao for possıvel utilizar um modelo, aquelesparametros poderao ser estimados com base em dados estatısticos. Para navios com um oudois helices, o diagrama de Harvald permite estimar os valores de w, t e ηH em funcao docoeficiente de finura total e da razao B/L, com correccoes associadas ao tipo de popa, cota doveio e diametro do helice. Outros autores propuseram algumas expressoes para a estimativadaqueles parametros. Destas, destacam-se as de Taylor, Schoenherr e Luke, para navios comum helice,

w = 0, 5Cb + 0, 025 (3.52)

e,

t = 0, 5w (3.53)

com ηH = 1, 02. Para navios com dois helices,

w = 0, 4533Cb − 0, 114 (3.54)

e,

t = 0, 7w + 0, 01 (3.55)

com ηH = 0, 985. Poderao aqui ser referidas as expressoes mais complexas apresentadas porHoltrop, com base em mais de duzentos ensaios de auto-propulsao em modelos de navios dediversos tipos.

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3.8. INTERACCAO ENTRE CASCO E HELICE 65

A potencia absorvida pelo helice pode ser expressa em termos da velocidade de rotacao n(em rps) e do binario Q por

PD = 2π ·n ·Q (3.56)

Devido as perdas mecanicas no veio e chumaceiras, a potencia recebida pelo helice PD einferior a potencia efectiva do motor (’brake power’ ) PB,

PD = ηs ·PB (3.57)

em que ηs e o rendimento da linha de veios. A eficiencia do propulsor atras do navio, avaliaas perdas desde a potencia recebida pelo helice PD e a potencia propulsiva PT ,

PT = ηB ·PD (3.58)

Esta eficiencia do propulsor atras do navio ηB e diferente da eficiencia em aguas livres η0verificada experimentalmente. O rendimento rotativo relativo ηR avalia as perdas associadasa diferenca entre o escoamento em aguas livres e o escoamento tridimensional nao-uniformeno plano do propulsor,

ηB = ηR · η0 (3.59)

Em resumo, verifica-se sempre a relacao,

PB > PD > PT > PE

em que os valores daquelas potencias sao calculadas por

PE = ηH ·PT = ηH · ηB ·PD = ηH · η0 · ηR ·PD = ηH · η0 · ηR · ηS ·PB

Se o rendimento quase-propulsivo ηD espressar o conjunto de eficiencias hidrodinamicasconsideradas,

ηD = ηH · η0 · ηR (3.60)

entao, a potencia efectiva pode ser dada por

PE = ηD · ηS ·PB

As leis de semelhanca permitem a extrapolacao das medicoes efectuadas para a escala donavio,

Vs =√λVm , (3.61)

ns = nm/√λ , (3.62)

Ts = Tm · (ρs/ρm) ·λ3 (3.63)

e,

Qs = Qm · (ρs/ρm) ·λ4 (3.64)

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66 CAPITULO 3. PROPULSAO

3.8.3 Extrapolacao dos resultados do ensaio de propulsao

O procedimento recomendado pela ITTC para o tratamento dos dados experimentais resul-tantes dos ensaios de resistencia e de propulsao para a previsao do desempenho do navio estaincluıdo no Apendice A. Para alem dos ja referidos ensaios de reboque e propulsao, sao aindanecessarios testes do helice em aguas livres. De uma forma sucinta, o referido procedimentoenvolve os seguintes passos:

- prever a resistencia total do navio a partir da resistencia avaliada no modelo, corrigindode acordo com as resistencias adicionais que devam ser consideradas;

- estimar as caracterısticas do helice propulsor com base nos coeficientes propulsivos de-terminados para o modelo;

- estimar a esteira do navio e as condicoes de funcionamento do helice;

- estimar a velocidade de rotacao do helice e potencia necessaria com base em factores decorrelacao entre o modelo e o navio.

Os detalhes de cada um destes passos, bem como o formulario de calculo, devem serconsultados no referido Apendice A.

As varias condicoes consideradas nos ensaios do modelo servirao para fazer uma previsaodo desempenho do navio numa gama de velocidades para as condicoes de lastro e carregado,conforme representado na Fig. 3.21.

Figura 3.21: Resultados dos ensaios de propulsao.

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Capıtulo 4Instalacoes Propulsoras

4.1 Introducao

A escolha de uma maquina propulsora ou da configuracao mais apropriada para a instalacaopropulsora num projecto de nova construcao ou reconversao nao e actualmente uma decisaosimples. E imperioso que esta decisao seja precedida de uma analise rigorosa das varias opcoesdisponıveis para o perfil de operacao futura definido para o navio.

Uma vez determinada a potencia absorvida pelo helice, torna-se necessario identificar assolucoes que satisfazem os requisitos de potencia, velocidade de rotacao, consumo e dimensoes.A sua avaliacao tecnico-financeira sera entao realizada por criterios baseados nos seguintesfactores:

- o investimento inicial;

- a fiabilidade;

- os custos de manutencao previstos;

- os custos de operacao previstos;

- a margem do motor, relacionada com a diferenca entre a potencia maxima e a potenciade servico do motor.

Este processo de seleccao terminara sempre numa solucao de compromisso ja que nenhumtipo de instalacao apresentara apenas vantagens comparativas.

No passado, o armador ou o projectista tinha como escolha imediata um motor diesel lentoacoplado directamente a um helice de passo fixo, ou um motor diesel de media velocidade,a quatro tempos, accionando atraves de engrenagens redutoras um helice de passo fixo oucontrolavel.

Actualmente, a propulsao dos navios que entram em servico e obtida com o acoplamentodirecto, muito esporadicamente com engrenagens redutoras, de motores a dois tempos a helicesde passo fixo ou controlavel, motores de media velocidade a quatro tempos e engrenagensredutoras ou ainda por instalacoes diesel-electricas com recurso a motores diesel, a quatrotempos, rapidos ou de media velocidade. Algumas variantes de instalacoes propulsoras estaorepresentadas nas Fig. 4.1 e 4.2.

67

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68 CAPITULO 4. INSTALACOES PROPULSORAS

Figura 4.1: Variantes de instalacoes propulsoras diesel-mecanicas lentas ede media velocidade.

Os motores diesel lentos predominam no sector do transporte de graneis, lıquidos e solidos,e contentores de longo curso. Motores de media velocidade sao preferidos em navios decarga com menor dimensao, ferries, turismo de passageiros, RoRo’s, bem como em nichos demercado muito especıficos como os quebra-gelos, navios de apoio a plataformas de exploracaopetrolıfera, etc.

No passado recente, estas tradicionais zonas de influencia de cada um dos referidos tiposde motores tem-se sobreposto. As novas geracoes de motores a quatro tempos, com cilindrosde grande diametro e media velocidade apresentam-se como solucoes competitivas para naviosa operar em viagens de longo curso. Em contrapartida, os motores lentos a dois tempos comcilindros de pequeno diametro tambem se apresentam como solucoes validas para os mercadoscosteiro e fluvial.

Um aspecto fundamental a considerar no processo de decisao na escolha da instalacaopropulsora sera necessariamente o custo. Nao so o custo inicial, o investimento a fazer naaquisicao do motor, mas tambem os custos associados a operacao do navio ou, de uma formamais geral, os custos totais do ciclo de vida do navio. Naqueles custos de operacao deveraoser tidos em conta, entre outros, os seguintes aspectos:

- o tipo de combustıvel que a instalacao vai permitir consumir;

- uma previsao dos custos de manutencao;

- os recursos humanos exigidos para a operacao/conducao da instalacao;

- a disponibilidade e quantidade/custo dos sobressalentes.

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4.2. PROPULSAO DIESEL-MECANICA 69

Figura 4.2: Instalacoes propulsoras diesel-mecanica (em cima) e diesel-electrica (em baixo).

A avaliacao dos custos de operacao ao fim da vida de exploracao do navio pode variar deforma muito significativa com o tipo de motor escolhido, e com a configuracao da instalacaopropulsora adoptada.

A dimensao da casa da maquina, a cujo aumento correspondera uma reducao do espacode carga disponıvel para a exploracao do navio, e essencialmente condicionada pela dimensaoda maquina principal. A propria altura da casa da maquina e importante em alguns tipos denavios como os ferries com conves para veıculos.

4.2 Propulsao diesel-mecanica

Conforme ja referido, a propulsao por um helice de passo fixo accionado directamente por ummotor diesel lento a dois tempos continua a ser o sistema mais frequentemente encontrado emnavios de carga de longo curso. A ligeira reducao no rendimento de propulsao reconhecida eadmitida face a simplicidade da solucao obtida e, a introducao de motores de longo, super-,e ultra-longo curso veio diminuir aquelas perdas. No entanto, a velocidade de 100/110 rpmnao e necessariamente a mais adequada para a propulsao de um grande navio. Os motoresactualmente disponıveis com maior curso desenvolvem a sua potencia nominal a velocidadestao baixas como 55 rpm ate cerca de 250 rpm. Para um dado navio, e entao possıvel prescreveruma solucao de acoplamento directo motor/helice que permita optimizar o rendimento depropulsao.

Um outro aspecto a considerar e o numero de cilindros do motor. Os motores lentos actu-ais, com cilindros de grande diametro, permitem extrair a potencia necessaria a propulsao deum navio de um motor com um reduzido numero de cilindros. Um motor com menos cilindrosinfluencia naturalmente de forma favoravel a dimensao da casa da maquina, o volume de tra-balho afecto a sua manutencao e a quantidade de sobressalentes a manter no navio. Este tipode solucao e portanto bem acolhida desde que daqui nao resultem problemas de equilıbriodo motor e vibracoes. Estes motores com cilindros de grande diametro queimam bem com-bustıveis pesados de fraca qualidade e proporcionam um consumo especıfico de combustıvel

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70 CAPITULO 4. INSTALACOES PROPULSORAS

inferior ao obtido em motores com cilindros de menor diametro.

Neste tipo de instalacoes, a energia electrica necessaria ao funcionamento dos equipamen-tos auxiliares e normalmente fornecida por geradores accionados por motores diesel rapidosou de media velocidade. A grande parte dos fabricantes de motores diesel para acciona-mento de alternadores esta ja hoje em condicoes de oferecer solucoes capazes de consumir omesmo combustıvel que a maquina principal, ou “marine diesel-oil” ou ainda uma mistura(blended) de combustıveis pesado e destilado. Actualmente, sao ja comuns instalacoes pro-pulsoras “Unifuel”, nas quais maquina principal e motores auxiliares consomem o mesmo tipode combustıvel.

4.2.1 Accionamento de auxiliares

Os custos associados a producao da energia electrica necessaria ao funcionamento dos equi-pamentos auxiliares da instalacao sao tambem um factor importante na seleccao da maquinaprincipal. O desenvolvimento das maquinas tem tido como principais objectivos nesta area:

- maximizar o aproveitamento de energia para permitir complementar a producao deenergia electrica durante as viagens;

- permitir o uso de alternadores accionados pela maquina principal atraves de engrenagensmultiplicadoras ou directamente montados na linha de veio;

- possibilitar o accionamento de equipamentos auxiliares directamente pela maquina prin-cipal.

A principal motivacao para a producao de energia electrica a partir da maquina principalresulta do seu superior rendimento termico, menor consumo especıfico de combustıvel e ca-pacidade para consumir combustıveis de inferior qualidade e custo. Outra vantagem resultanaturalmente do menor consumo de oleo lubrificante, de menos intervencoes de manutencao einferiores custos com sobressalentes resultantes da reducao do tempo de funcionamento obtidacom a paragem dos diesel-geradores durante a viagem.

No caso de uma instalacao com helice de passo fixo, a utilizacao de um acoplamento porengrenagens, que permita manter constante a velocidade de rotacao do alternador (Fig. 4.3),possibilita a utilizacao do gerador a plena carga numa gama de velocidades da maquinaprincipal que habitualmente ronda os 70 a 100% da sua velocidade nominal.

A localizacao do alternador e tambem um aspecto importante para permitir a desejavelreducao de espaco ocupado pela casa da maquina. Sao actualmente possıveis diversos arranjosque vao desde a colocacao lateral ao motor ou em qualquer uma das suas extremidades.

Em alternativa, quer no caso das instalacoes com helice de passo fixo, quer no caso daquelasque dispoem de passo controlavel, podem ser utilizados sistemas baseados na conversao dafrequencia da energia electrica produzida (Fig. 4.4).

Mais recentemente, as opcoes para a producao de energia electrica a bordo alargaram-se a utilizacao de turbinas movimentadas pelos gases de evacuacao do motor. O elevadorendimento dos sobrealimentadores mais modernos torna excedentaria uma fraccao dos gasesde evacuacao. O aproveitamento destes gases de evacuacao em pequenas turbinas poderaintegrar-se em sistemas, que contemplando ainda grupos diesel-geradores, geradores-ao-veio eturbo-geradoras a vapor, de forma isolada ou combinada, permitirao a optimizacao dos custosde producao da energia electrica para os varios estados de operacao do navio.

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4.2. PROPULSAO DIESEL-MECANICA 71

Figura 4.3: Acoplamento com relacao variavel de velocidades.

4.2.2 Engrenagens redutoras

Em muitas instalacoes propulsoras espera-se da caixa redutora:

- a determinacao da velocidade e do sentido de rotacao do helice, e a capacidade deinversao;

- que proporcione uma forma de acoplamento, permitindo estabelecer e interromper atransmissao de potencia entre o motor e o helice;

- que seja capaz de absorver o impulso recebido do helice.

O projecto de engrenagens, embraiagens ou outras formas de acoplamento usadas em ins-talacoes navais tem de satisfazer varios, e por vezes conflituantes, requisitos quanto a suaflexibilidade operacional, fiabilidade, ruıdo emitido e espaco ocupado. Os desenvolvimentosnas areas do projecto, dos materiais e dos sistemas de controlo contribuıram para solucoesinovadoras para instalacoes propulsoras versateis com um ou mais motores, envolvendo toma-das de extracao de potencia (“Power Take-Off’s - PTO”) para accionamento de alternadorese tomadas para recepcao de potencia (“Power Take-In’s - PTI ”) para aumentar a potenciade propulsao.

A forma mais comum do accionamento indirecto do helice passa pela utilizacao de umou mais motores a quatro tempos de media velocidade, ligados atraves de embraiagens eacoplamentos a uma caixa redutora, para movimentar um helice de passo fixo ou controlavel(Fig. 4.5 e 4.6).

A utilizacao de helices de passo controlavel permite eliminar a necessidade da reversibili-dade do motor. Por outro lado, a utilizacao da caixa redutora permite escolher a velocidadede funcionamento do helice mais apropriada. De uma forma geral, pode-se afirmar que as per-das mecanicas na transmissao sao compensadas por um maior rendimento propulsivo, quando

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72 CAPITULO 4. INSTALACOES PROPULSORAS

Figura 4.4: Conversao da frequencia da energia electrica.

comparado com um caso de acoplamento directo para a mesma potencia. Os custos adicio-nais da transmissao sao tambem, pelo menos parcialmente, compensados pelo menor custodo motor a quatro tempos, quando comparado com um motor lento a dois tempos.

Sao normalmente identificadas como principais vantagens das instalacoes propulsoras commais de um motor, rapido ou de media velocidade:

- a redundancia permite maior disponibilidade para a operacao do navio:

- no caso de avaria num motor, o outro ou os outros mantem a navegabilidade;

- o numero de motores em servico para a propulsao pode variar para garantir a formamais economica para uma viagem:

- quando o navio viaja em lastro, carga parcial ou a velocidade reduzida umdos motores pode ser utilizado a sua potencia nominal, com bom rendimento,enquanto outro ou outros podem ser parados;

- pelo contrario, em condicoes operacionais semelhantes, um motor unico, aco-plado directamente ao helice, funcionaria durante longos perıodos a carga par-cial com pouco rendimento;

- A possibilidade de alterar o numero de motores em servico facilita o planeamento e aexecucao das tarefas de manutencao e reparacao uma vez que estas poderao ser realiza-das em viagem.

- Esta flexibilidade de operacao e particularmente valorizada numa epoca em que sepretende uma exploracao intensiva dos navios.

- As operacoes de manutencao e reparacao podem ainda decorrer em porto sempreocupacoes particulares relativas a necessidade de mudanca de cais ou partidaantecipada.

- As instalacoes propulsoras de uma frota de navios pode ser baseada num so modelode motor, ajustando o numero de motores no navio e o numero de cilindros por motorpara as necessidades de propulsao de cada um dos navios, com reducao do custo de

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4.2. PROPULSAO DIESEL-MECANICA 73

Figura 4.5: Instalacao propulsora com quatro motores, engrenagens redu-toras e dois helices.

sobressalentes e inventarios, para alem dos benefıcios resultantes da familiarizacao dastripulacoes.

Este conceito pode ainda ser alargado aos motores auxiliares (“uniform machinery instal-lations ”), em que os motores principais e auxiliares sao do mesmo modelo.

4.2.3 Configuracao ”pai-e-filho”

A flexibilidade de operacao e potenciada pela adopcao das instalacoes do tipo ”pai-e-filho”.Nestas instalacoes, motores a quatro tempos do mesmo modelo, ou de dois modelos muitosemelhantes, mas com diferente numero de cilindros, fazem o accionamento do veio do heliceacoplados a uma caixa redutora comum. Cada um daqueles motores pode ser ainda acopladoa uma maquina electrica que pode funcionar como motor ou gerador.

Numa configuracao deste tipo, a propulsao pode ser assegurada:

- conjuntamente pelos dois motores diesel;

- apenas por qualquer um dos motores diesel.

Em qualquer dos casos, podem ser ainda utilizados os, nesta situacao, motores electricosacoplados ao veio como motores propulsores, alimentados com energia electrica produzidapelos geradores auxiliares.

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74 CAPITULO 4. INSTALACOES PROPULSORAS

Figura 4.6: Instalacao com dois motores diesel diferentes, engrenagens re-dutoras, embraiagens e geradores acoplados aos veios.

4.3 Propulsao diesel-electrica

4.3.1 Propulsao por motor electrico

A propulsao diesel-electrica, baseada em grupos electrogeneos de media velocidade, e umaforma de accionamento indirecto com crescente implantacao no mercado. Apos um perıodoem que a utilizacao deste tipo de sistemas esteve confinada a nichos de mercado de actividadescom elevada especificidade, como por exemplo os quebra-gelos, navios de investigacao etc.,as mais recentes tecnologias para a conversao AC/DC alargaram o potencial de utilizacao dapropulsao electrica ao mercado dos navios de passageiros, “shuttle tanker’s” no Mar do Norte.

Estando ja estabelecido como uma boa solucao neste mercados, comecam a surgir refe-rencias da aplicacao deste tipo de instalacoes propulsoras a navios de transporte de quımicos(costeiro e longo curso), ferries e RoRo’s. Discute-se ainda as vantagens da sua aplicacaopelo menos a algumas classes de porta-contentores. A propulsao diesel-electrica, combinadacom motores “dual-fuel”, esta tambem bem implantada no sector do transporte de LNG.

A propulsao diesel-electrica exige grandes motores electricos para accionamento dos he-lices (Fig. 4.7) e grupos electrogeneos para fornecer a potencia electrica. Pode parecer emprimeira analise algo ilogico usar geradores electricos, conversores e motores electricos para oaccionamento quando um acoplamento directo ou uma engrenagem redutora pode ser sufici-ente para cumprir aquela missao. As principais razoes que justificam a complexidade e custoacrescidos daquele tipo de instalacao sao:

- maior flexibilidade na distribuicao dos equipamentos na casa da maquina;

- maior diversidade de condicoes de fundionamento;

- funcionamento mais economico a carga partial;

- facilidade de controlo;

- menor ruıdo;

- maior seguranca de operacao e proteccao ambiental.

Estes aspectos serao abordados nos paragrafos seguintes.

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4.3. PROPULSAO DIESEL-ELECTRICA 75

Figura 4.7: Motor electrico de propulsao.

Flexibilidade na distribuicao dos equipamentosA vantagem da transmissao electrica resulta de se poder escolher a localizacao em cada

caso mais apropriada para os grupos electrogeneos. E entao possıvel colocar os motores, bemcomo os respectivos auxiliares, afastados do veio propulsor. Sempre que seja adoptado estetipo de instalacao, a referida flexibilidade permite aos arquitectos navais criar navios com acasa da maquina muito compacta, libertando espaco para passageiros e/ou carga. O factode a casa da maquina ser mais compacta permite reduzir ainda a cablagem e a tubagem, emparticular a tubagem a instalar para a evacuacao dos gases do motor (ver Fig. 4.8).

A opcao por uma instalacao diesel-electrica facilita tambem ao estaleiro de construcao arecepcao de modulos de grupos electrogeneos pre-testados e prontos para serem incorporadosna instalacao.

Deve aqui ser tambem referida a dificuldade de uma instalacao diesel-electrica atingir orendimento obtido com um motor lento, a dois tempos, acoplado directamente ao veio dohelice, quando a funcionar a sua carga ideal, tal como acontece numa viagem de longo cursode um navio petroleiro. No entanto, alguns navios deste tipo tem um perfil de operacaoque inclui tambem largos perıodos a carga parcial em lastro, navegacao em aguas restritase manobras. Numa instalacao diesel-electrica, a elevada disponibilidade para producao deenergia electrica pode ser aproveitada para movimentar as bombas de carga e impulsores deproa/popa, conforme representado esquematicamente na Fig. 4.9.

Variedade de cargaAlguns tipos de navios necessitam de quantidades significativas de energia para auxiliares

quando as necessidades de propulsao sao reduzidas. Uma grande instalacao de producao

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76 CAPITULO 4. INSTALACOES PROPULSORAS

Figura 4.8: Instalacao diesel-electrica.

de energia electrica nos navios de passageiros/cruzeiros e exigida pela carga dos servicos dehotelaria e pelos propulsores tranversais de manobra. A potencia electrica necessaria nestescasos ronda os 30 a 40 % da potencia de propulsao instalada e ainda ha que contar comsignificativa redundancia por motivos de seguranca.

Estes factores tem promovido um novo conceito de instalacao, a diesel-electrica ”powerstation”, nas quais varios grupos electrogeneo movidos por motores diesel de media velocidadesatisfazem as necessidades de energia para a propulsao, manobra e servicos de hotelaria nosgrandes navios de passageiros.

Funcionamento economico a carga parcialFuncionamento economico a carga parcial e facilmente alcancado numa instalacao diesel-

electrica ”power station”. Uma instalacao tıpica inclui quatro grupos electrogeneos, podendoir no entanto ate aos nove, e, atraves do funcionamento em paralelo dos grupos, e facil ajustara capacidade de producao as necessidades de carga electrica. Por exemplo, no caso de quatrogeradores, aumentar o numero de grupos em funcionamento de dois, a carga maxima, paratres a carga parcial resulta numa condicao de carga a 67 % que, nao sendo ideal tambem naoe problematica.

Os sistemas de reducao instantanea da potencia propulsora tornam desnecessario colocarem funcionamento geradores a carga parcial para prevenir a ocorrencia subita de avaria numgrupo electrogeneo. O sistema de controlo monitoriza a capacidade de producao de energiaelectrica, e a sobrecarga de um gerador provoca um ajuste imediato no consumo dos motoresde propulsao.

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4.3. PROPULSAO DIESEL-ELECTRICA 77

Figura 4.9: Representacao esquematica de uma instalacao diesel-electrica.

Facilidade de controloOs accionamentos electricos permitem alcancar, com larga margem, as necessidades de

controlo para um sistema de propulsao.

Baixo ruıdoUm motor electrico proporciona um accionamento com vibracoes reduzidas, caracterıstica

particularmente valorizada nalguns tipos de navios como, por exemplo, os navios para cru-zeiros, navios de investigacao marinha e navios de guerra. A “transmissao electrica” permiteprocurar a melhor localizacao para os motores por forma a minimizar os efeitos da vibracaotransmitida a estrutura do navio. A emissao de vibracoes pode ainda ser reduzida atraves dorecurso a montagem de amortecedores de vibracao.

Proteccao ambiental e seguranca de operacaoO controlo das emissoes de oxidos de azoto pelos motores diesel dos navios favorece tambem

a especificacao de instalacoes com “transmissao electrica”, uma vez que o funcionamento dosmotores a velocidade constante e carga optimizada permite obter menores emissoes.

O aumento da seguranca da navegacao e tambem obtido nestas instalacoes pela redun-dancia dos seus elementos constituintes. A redundancia pode ser obtida nao apenas pelaexistencia de dois propulsores mas ainda pode ser acrescida colocando os dois, ou mais, mo-tores de propulsao em diferentes compartimentos e ligando-os por uma engrenagem redutora.

4.3.2 Propulsores azimutais

As vantagens tecnicas e economicas na concepcao, construcao e operacao de navios compropulsao por “azipod’s”, inicialmente restritos a navios quebra-gelos e navios de passageiros,tem vindo a alargar o seu campo de aplicacao a outro tipo de navios.

Um propulsor azimutal incorpora o motor electrico num alojamento submerso de formashidrodinamicas optimizadas que, podendo rodar 360◦ no plano horizontal, permite extraor-

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78 CAPITULO 4. INSTALACOES PROPULSORAS

dinaria capacidade de propulsao e manobra (ver Fig. 4.10). O motor electrico e acopladodirectamente a um helice de passo fixo. A energia electrica e provida pelos varios gruposelectrogeneos do navio.

Figura 4.10: Propulsores azimutais.

Este tipo de propulsores, quando comparados com instalacoes diesel-electricas com linha(s)de veio(s) apresentam as seguintes vantagens:

- maior liberdade para a concepcao do casco e para o arranjo de maquinas no interior dacasa da maquina;

- o espaco no interior do casco destinado aos motores pode ser libertado para outrasfinalidades;

- melhor capacidade de manobra quando comparado com o tradicional leme e possibidadede eliminar propulsores transversais;

- excelente reversibilidade e capacidade de manobra com propulsao a re;

- menor ruıdo e vibracao, caracterısticos da propulsao electrica, agora potenciados pelaposicao mais favoravel dos helices;

- na construcao do navio, as unidades de propulsao podem ser incorporadas mais tardereduzindo assim os custos de investimento;

- menor custo de producao do navio.

4.4 Seleccao do motor

Seleccionado o tipo de instalacao pretendido para a propulsao do navio, chega-se finalmentea escolha do motor. Como as caracterısticas de funcionamento das turbinas e dos motores

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4.4. SELECCAO DO MOTOR 79

electricos sao bastante diferentes das caracterısticas dos motores diesel, a abordagem tera deser tambem diferente.

Em qualquer dos casos, devera ser tida em conta a margem de servico MS. A margemde servico tem em conta a diferenca entre a potencia requerida para nas condicoes ideais daprova de mar e a potencia requerida pelas condicoes de servico. E pratica habitual definir-sea margem de servico como uma fraccao da potencia na prova de mar, ou seja,

MS =PDserv − PDtrial

PDtrial

(4.1)

O valor da margem de servico esta normalmente entre os 10 e os 25%, dependendo das opcoesestrategicas do armador e da importancia da pontualidade do servico. Em princıpio, a margemde servico atribuıda a um navio de linha sera superior a margem considerada para um navioque vai operar no mercado do “tramping”. O valor estabelecido da margem de servico deve emconta uma estimativa da degradacao de velocidade, para as condicoes de operacao do navio,bem com as condicoes habituais de mar e vento e a degradacao do casco.

4.4.1 Turbinas e motores electricos

No caso da turbinas, de vapor ou gas, a potencia desenvolvida depende essencialmente docaudal de fluido em circulacao, sendo portanto relativamente pouco sensıvel a velocidade derotacao.

As caracterısticas dos sistemas com transmissao electrica sao semelhantes as das turbinas,independentemente de os geradores serem movidos por turbinas ou motores diesel, uma vezque a velocidade destes pode ser mantida constante.

Neste tipo de situacao, em que a maquina propulsora pode trabalhar proximo da potenciamaxima em qualquer condicao de servico, a potencia instalada (PI) pode ser proxima dapotencia de servico. Na pratica, a turbina e ajustada para operar com o maximo rendimentoa uma potencia 10% inferior a maxima potencia em contınuo (MCR, Maximum ContinuousRating). Assim, a potencia instalada sera

PI(MCR) =PDserv

0, 9ηs= PDtrial

1 +MS

0, 9ηs(4.2)

em que PDserv e PDtrialsao as potencias absorvidas pelo helice nas condicoes de servico e na

prova de mar, respectivamente, para a velocidade de servico e MS e a margem de servico.

4.4.2 Motores diesel

Ao contrario das turbinas e dos motores electricos, em que a potencia disponıvel e poucosensıvel a velocidade, os motores diesel caracterizam-se por ter uma curva do binario bastanteplana. Esta caracterıstica faz com que a potencia varie de forma aproximadamente linear coma velocidade de rotacao.

Para alem dos principais criterios considerados na avaliacao dos projectos, outros aspectosque nao devem ser descurados na escolha do motor sao:

- a possibilidade de queimar combustıvel pesado de baixa qualidade sem impacto noscomponentes do motor e consequentemente nos custos previstos para sobressalentes eoperacoes de manutencao;

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80 CAPITULO 4. INSTALACOES PROPULSORAS

- o volume de trabalho de manutencao, o numero de cilindros, valvulas, camisas, arose chumaceiras a necessitar de atencao periodica em relacao ao numero de tripulantesembarcados;

- a adequabilidade para operacao nao assistida explorando sistemas de controlo automa-tico e sistemas de monitorizacao;

- a dimensao e o peso da instalacao propulsora.

O valor maximo da potencia desenvolvida por um motor diesel e condicionada pela cargatermica. Este limite e normalmente expresso em termos da pressao media efectiva. Depen-dendo das caracterısticas do helice seleccionado e das condicoes operacionais, assim o valorlimite da pressao media efectiva sera atingido, ou nao, antes de o motor atingir a velocidadede rotacao correspondente as condicoes MCR.

Figura 4.11: Diagrama de carga de um motor diesel

Os fabricantes de motores diesel incluem diagramas de carga nos guias de seleccao demotores para auxiliar a escolha do ponto de funcionamento. Nestes diagramas, como o repre-sentado na Fig. 4.11, estao marcados:

- o ponto L1, que corresponde ao MCR do motor;

- a linha vertical L1 − L2, velocidade de rotacao maxima do motor, que limita a zona defuncionamento do motor;

No Apendice D incluiu-se documentacao da ”Burmeister & Wain” que permite ilustrar aforma de seleccao do motor para uma aplicacao concreta, considerando varias hipoteses: comou sem gerador acoplado ao veio, com helice de passo fixo ou de passo controlavel.

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4.4. SELECCAO DO MOTOR 81

Alguns fabricantes anunciam um valor de “Normal Continuous Rating” (NCR) cerca de10% inferior ao valor MCR e a uma velocidade inferior, ao qual corresponde um desempenhooptimizado do motor em termos de consumo e de necessidades de manutencao. Pode aindadefinir-se uma “Service Continuous Rating” (SCR) que, dependendo da polıtica do armador,podera ser igual ou nao do NCR indicado pelo fabricante do motor.

A diferenca entre a MCR e a SCR, ou, caso nao esteja definida, a NCR, da origem achamada margem do motor (MM). A margem do motor e avaliada por,

MM =MCR− SCR

MCR(4.3)

Valores tıpicos desta margem de motor rondam os 10 a 15%. De notar que as margens deservico e de motor surgem frequentemente combinadas numa so, a margem de servico, apesarde as suas origens serem bem distintas.

Uma vez atribuıdas as margens de servico e de motor, a potencia instalada e calculadapor

PI(MCR) = PDtrial

1 +MS

(1−MM) ηs(4.4)

Nas provas de mar, nas condicoes de imersao e caimento contratuais, a potencia absorvidapelo helice, a velocidade de rotacao correspondente ao MCR, deve ser igual a potencia SCR,deduzida das perdas na linha de veios. Como objectivo das provas, devera garantir-se que acombinacao motor e helice permite que o anvio atinja a velocidade requerida sem ultrapassaros limites impostos pelo diagrama de carga.

Sem prejuızo do exposto, o forte aumento do preco dos combustıveis nos anos mais recen-tes faz com que os custos operacionais dos navios sejam cada vez mais dominados por estefactor. Neste contexto, pode ser uma hipotese de trabalho interessante a opcao por um motorcom a mesma potencia, a potencia calculada como necessaria para a propulsao nas condi-coes contratuais, mas com um cilindro extra. Esta tecnica, o chamado ”derating” do motor,exigindo maior valor de investimento inicial, pode apresentar um perıodo de retorno atrac-tivo. Wettstein e Brown apresentam as principais motivacoes para aplicacao desta tecnica ediscutem quatro casos de aplicacao numa publicacao da Wartsilla, incluıda no Apendice E.

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82 CAPITULO 4. INSTALACOES PROPULSORAS

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Bibliografia

[1] Jose P. Saraiva Cabral. Arquitectura Naval, estabilidade, calculos, avaria e bordo livre.Centro do Livro Brasileiro, 1979.

[2] Eric C. Tupper. Introduction to Naval Arquitecture. Elsevier, 2004.

[3] Volker Bertram. Practical Ship Hydrodynamics. Butterworth-Heinemann, 2000.

[4] Jorge d’Almeida. Arquitectura Naval - o dimensionamento do navio. Prime Books, 2009.

[5] Editor Doug Woodyard. Pounders Marine Diesel Engines and Gas Turbines. Butterworth-Heinemann, 2004.

[6] H. Schneekluth and V. Bertram. Ship Design for Efficiency and Economy. Butterworth-Heinemann, 1998.

83

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Indice Remissivo

Auto-propulsao, 62

Boca, 3Bolbo de proa, 22Bordo livre, 3

Calado, 3Camada limite, 24Cavitacao, 37, 53, 60Coeficiente

de avanco, 46de binario, 46de Burrill, 55de carga do helice, 44de deducao da esteira, 63de deducao da forca propulsiva, 63de forca propulsiva, 46de resistencia, 28de resistencia total, 13

Comprimentoentre perpendiculares, 3fora a fora, 3na linha de agua, 3

Consumo especıfico de combustıvel, 69Custos

de manutencao, 68de operacao, 68, 69totais, 68

Diagramade Burrill, 55em aguas livres, 45, 46

Dual-fuel, 74

Engrenagens redutoras, 71Ensaios

de auto-propulsao, 62de cavitacao, 56de helices em aguas livres, 45

de propulsao, 61de resistencia, 26em sobrecarga, 62

Formulade Alexander, 5de atrito da ATTC, 25de atrito da ITTC, 25de Keller, 59do atrito de Froude, 24do atrito de Hugues, 30

Forcade compensacao, 62de inercia, 15de origem hidrodinamica, 16gravıtica, 16propulsiva, 42

Helice, 35rendimento ideal, 45a ponto fixo, 57bloqueado, 57com tubeira, 36contrarotativo, 37de passo controlavel, 37, 67, 70, 71de passo fixo, 37, 67, 70, 71, 78diametro do, 58distribuicao radial de pressao, 59geometria do, 40, 59ındice de qualidade do, 47interaccao com o casco, 60numero de pas do, 59projecto do, 40razao de area expandida, 41supercavitante, 37

Metodode Hughes/Prohaska, 28

84

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INDICE REMISSIVO 85

Geosim, 28, 31

Hughes-Prohaska, 29

ITTC 1957, 28

ITTC 1978, 28, 30

Margem

de servico, 79

do motor, 81

Maximum Continuous Rating, 79

Numero

de cavitacao, 54

de Froude, 17, 23

de Reynolds, 18, 27, 46

Navio

coeficientes de forma, 3

de passageiros, 68, 74, 76, 77

deslocamento do, 3

dimensoes do, 3

linhas de bordo livre do, 3

planos do, 1

quebra-gelos, 68, 77

tipo ferry, 37, 38, 40, 68, 69, 74

tipo RoRo, 68, 74

tipo shuttle tanker, 74

Normal Continuous Rating, 81

PC-cluster, 10

Pontal, 3

Potencia

absorvida, 65

de reboque, 13

efectiva, 13, 62

efectiva do motor, 65

propulsiva, 63

Power Take Off/In, 71

Profundidade restrita, 23, 32

Propulsao

azimutal, 35, 38, 77

cicloidal, 35, 39

diesel-electrica, 74

diesel-mecanica, 69

por jacto de agua, 35, 37

por motor electrico, 74

Provas

de mar, 34

de potencia, 121, 133

de velocidade, 121, 133

Rendimentoaguas livres, 46da linha de veios, 65do casco, 64do helice, 46rotativo relativo, 64

Resistencia, 13adicional, 31aerodinamica, 19de atrito, 24de onda, 19decomposicao, 18dos apendices, 32viscosa de pressao, 25

Rugosidade do casco, 28, 30, 31

Serie sistematica60, 33de helices, 47, 58de querenas, 32de Taylor, 33de Wageningen, 48

Semelhancacinematica, 15dinamica, 15geometrica, 14leis da, 14

Service Continuous Rating, 81Sobrealimentadores, 70

Tanquede cavitacao, 56de Froude, 7de reboque, 26

Unifuel, 70

Velocidadeda querena, 22de aproximacao, 42de rotacao do helice, 59economica, 22

Vibracoes, 42, 53, 58–60, 77

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86 INDICE REMISSIVO

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Apendice AProcedimento Recomendado pela

ITTC para a Previsao do

Desempenho de Navios Baseada nos

Ensaios de Propulsao em Modelos

87

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88 APENDICE A. PREVISAO BASEADA NOS ENSAIOS DE PROPULSAO

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ITTC – Recommended Procedures

7.5 – 02 03 – 01.4

Page 1 of 31

Performance, Propulsion 1978 ITTC Performance Prediction

Method Effective Date

1999 Revision

00

Edited by 22nd ITTC QS Group 1999 Approved 15th ITTC 1978 pp388 – 402 17th ITTC 1984 pp326 - 333 18th ITTC 1987 pp266 - 273

15th ITTC 1978, 17th ITTC 1984 and 18th ITTC 1987

Date Date

CONTENTS 1. PURPOSE OF PROCEDURE

2. DESCRIPTION OF PROCEDURE

2.1.1 Introduction for the Original 1978 ITTC Performance Prediction Method for Single Screw Ships 2.1.2 Introduction for the 1978 ITTC Performance Prediction Method as Modified in 1984 and 1987

2.2 Model Tests 2.3 Analysis of the Model Test Results 2.4 Full Scale Predictions

2.4.1 Total Resistance of Ship 2.4.2 Scale Effect Corrections for Propeller Characteristics. 2.4.3 Full Scale Wake and Operating Condition of Propeller 2.4.4 Model-Ship Correlation Factors

2.5 Analysis of Speed Trial Results 2.6 Input Data 2.7 Output Data 2.8 Test Example

3. PARAMETERS

3.1 Parameters to be Taken into Account 3.2 Recommendations of ITTC for Parameters 3.3 Input Data

4. VALIDATION

4.1 Uncertainty Analysis 4.2 Comparison With Full Scale Results

5. ITTC- 1978 PERFORMANCE PREDICTION METHOD (COMPUTER CODE)

COMMENTS OF PROPULSION COMMITTE OF 22nd ITTC In its original form the ITTC 1978 Performance Prediction Method offers a valuable and rea-sonably accurate prediction tool for reference purposes and conventional ships.

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ITTC – Recommended Procedures

7.5 – 02 03 – 01.4

Page 2 of 31

Performance, Propulsion 1978 ITTC Performance Prediction

Method

Effective Date 1999

Revision00

1978 ITTC Performance Prediction Method

1. PURPOSE OF PROCEDURE

The method predicts rate of revolution and delivered power of a ship from model results.

2. DESCRIPTION OF PROCEDURE 2.1.1 Introduction for the Original 1978

ITTC Performance Prediction Method for Single Screw Ships

The method predicts rate of revolution and

delivered power of a ship from model results. The procedure used can be described as fol-lows:

The viscous and the residuary resistance of the ship are calculated from the model resistance tests assuming the form factor to be independ-ent of scale and speed. The ITTC standard predictions of rate of revo-lutions and delivered power are obtained from-the full scale propeller characteristics. These characteristics have been determined by cor-recting the model values for drag scale effects according to a simple formula. Individual corrections then give the final predictions. 2.1.2 Introduction for the 1978 ITTC Per-

formance Prediction Method as Modified in 1984 and 1987

The 1978 ITTC Method developed to pre-

dict the rate of propeller revolutions and deliv-ered power of a single screw ship from the model test results has been extended during the last two terms of the ITTC for a better and

more convenient use of the program. These extensions are summarized as follows. (1) Inclusion of prediction of propeller revo-

lutions on the basis of power identity. (2) Temporary measure for wTS > wTM (3) Extension to twin screw ships (4) Addition of speed trial data (5) Extension for the case of a stock propel-

ler in the self-propulsion test (6) Adaptation to the input of the non-

dimensional resistance coefficient and self-propulsion factors.

In recent years, many member organizations have been asked by their customers for a gen-eral description of the method, viz., model test and analysis of their results, calculation of full-scale power and rate of propeller revolutions, and the model-ship correlation factors used. Considering the above, it was decided to pre-pare a user's manual of the 1978 ITTC method which includes all of the extensions and modi-fications made. 2.2 Model Tests

Model tests required for a full scale com-prise the resistance test, the self-propulsion test and the propeller open-water test.

In the resistance test the model is towed at speeds giving the same Froude numbers as for the full scale ship, and the total resistance of the model RTM is measured. The computer pro-

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ITTC – Recommended Procedures

7.5 – 02 03 – 01.4

Page 3 of 31

Performance, Propulsion 1978 ITTC Performance Prediction

Method

Effective Date 1999

Revision00

gram accepts either RTM in Newton, or in a non-dimensional form of residuary resistance coef-ficient CR assuming the form factor 1 + k. In the latter case, the friction formula used can then be either of the ITTC 1957, Hughes, Prandtl-Schlichting or Schönherr's formulae.

The form factor 1 + k is usually determined from the resistance tests at low speed range or by Prohaska’s plot of CFM against Fn4

The ship model is not in general fitted with

bilge keels. In this case the total wetted surface area of them is recorded and their frictional resistance is added in calculating the full-scale resistance of the ship.

In the self-propulsion test the model is

towed at speeds giving the same Froude num-bers as for the full-scale ship. Generally a tow-ing force FD is applied to compensate for the difference between the model and the full-scale resistance coefficient.

During the test, propeller thrust (TM), torque (OM) and rate of propeller rotation (nM) are measured.

In many cases, stock propellers are used

which are selected in view of the similarity in diameter pitch and blade area to the full-scale propeller. Then the diameter and the open-water characteristics of the stock propeller have to be given as input data in the program. In the open-water test, thrust, torque and rate of revolutions are measured, keeping the rate of revolutions constant whilst the speed of ad-vance is varied so that a loading range of the propeller is examined. In the case when a stock propeller is used in the self-propulsion test, both the stock propel-

ler and the model similar to the full-scale pro-peller should be tested in open water. 2.3 Analysis of the Model Test Results

Resistance RTM measured in the resistance tests is expressed in the non-dimensional form

2

21 SV

RC TM

TM

ρ=

This is reduced to residual resistance coef-ficient CR by use of form factor k,

viz.,

CR = CTM - CFM (1 + k)

Thrust, T, and torque Q, measured in the

self-propulsion tests are expressed in the non-dimensional forms

24nDTKTM ρ

= and 25nDQKQM ρ

=

With KTM as input data, JTM and KQTM are read

off from the model propeller characteristics, and the wake fraction

VDJ

w MTMTM −=1

and the relative rotative efficiency

QM

QTMR K

K=η

are calculated. V is model speed. The thrust deduction is obtained from

T

RFTt CD −+=

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with

( )[ ]FFSFMMMMD CCCVSF ∆+−= 2

21 ρ

where RC is the resistance corrected for differ-ences in temperature between resistance and self-propulsion tests:

( )( ) TM

RFM

RFMCC R

CCkCCk

R++++

=.1.1

where CFMC is the frictional resistance coeffi-cient at the temperature of the self-propulsion test. 2.4 Full Scale Predictions 2.4.1 Total Resistance of Ship

The total resistance coefficient of a ship without bilge keels is CTS =(1+k)CFS +CR+∆ CF +CAA Where

- k is the form factor determined from the

resistance test - CFS is the frictional coefficient of the ship

according to the ITTC-1957 ship-model correlation line

- CR is the residual resistance calculated from

the total and frictional coefficients of the model in the resistance tests:

( ) FMTMR CkCC +−= 1

-. FC∆ is the roughness allowance

331

1064.0105 −

=∆

WL

SF L

kC

where the roughness kS=150.10-6 m and - CAA, is the air resistance

SA

C TAA .001.0=

If the ship is fitted with bilge keels the total

resistance is as follows:

( )[ ] AARFFSBK

TS CCCCkSSS

C ++∆+++

= 1

2.4.2 Scale Effect Corrections for Propeller

Characteristics.

The characteristics of the full scale propel-ler are calculated from the model characteris-tics as follows

TTMTS KKK ∆−=

QQMQS KKK ∆−=

where

DZc

DPCK DT

..3.0.∆−=∆

DZcCK DQ

..25.0.∆−=∆

The difference in drag coefficient DC∆ is

DSDMD CCC −=∆ where

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( ) ( )

+=

32

61

504.0212nconco

DM

RRctC

and 5.2

log.62.189.1212−

+

+=

pDS k

cctC

In the formulae listed above c is the chord

length, t is the maximum thickness, P/D is the pitch ratio and Rnco is the local Reynolds num-ber at x=0.75. The blade roughness kp is put kp=30.10-6 m. Rnco must not be lower than 2.105 at the open-water test.

2.4.3 Full Scale Wake and Operating Con-dition of Propeller

The full scale wake is calculated from the

model wake, wTM, and the thrust deduction, t:

( ) ( ) ( )( ) FM

FFSTMTS Ck

CCktwtw

+∆++

−−++=1

104.004.0

where 0.04 is to take account of rudder effect. The load of the full scale propeller is obtained from

( )( )222 11

.2 TS

TST

wtC

DS

JK

−−=

With this 2/ JKT as input value the full

scale advance coefficient JTS and the torque coefficient KQTS are read off from the full scale propeller characteristics and the following quantities are calculated

- the rate of revolutions:

( )

DJVw

nTS

STSS

−=

1 (r/s)

- the delivered power:

335 102 −=R

QTSSDS

KnDP

ηπρ (kW)

- the thrust of the propeller:

2422 ... STST

S nDJJK

T ρ= (N)

- the torque of the propeller:

25S

R

QTSS nD

KQ ρ

η= : (Nm)

- the effective power: 33 10...2/1 −= SVCP STSE ρ (kW) - the total efficiency:

E

DSD P

P=η

- the hull efficiency:

TS

H wt

−−

=1

2.4.4 Model-Ship Correlation Factors Trial prediction of rate of revolutions and de-livered power with CP - CN corrections if CHOICE=0 the final trial predictions will be calculated from nT = CN.nS (r/s) for the rate of revolutions and PDT = CP.PDS (kW)

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for the delivered power. Trial prediction with ∆CFC - ∆wC corrections

If CHOICE=1 the final trial predictions are calculated as follows:

( )( )222 11

.2

CTS

FCTST

wwt

CCDS

JK

∆+−−

∆+=

With this KT/J² as input value, JTS and KQTS

are read off from the full scale propeller char-acteristics and

( )DJ

Vwwn

TS

SCTST .

1 ∆+−= (r/s)

335 10.....2 −=RM

QTSTDT

KnDP

ηρπ (kW)

Trial prediction with CNP correction If CHOICE = 2 the shaft rate of rotation is pre-dicted on the basis of power identity as fol-lows.

( )³1²..2..1000

³ 3TSS

DSP

T

Q

wVDPC

JK

−=

ρπ

RMT

QQ

JK

JK

η.³0

=

( ) DJwVn TSTSSS ./1−= SNPT nCn =

2.5 Analysis of Speed Trial Results The analysis of trials data is performed in a

way consistent with performance prediction but starting PD and n backwards, i.e. from

³10.....2 35 RM

DQ nD

PK η

ρπ=

JS is obtained from the full-scale open-water

characteristics KQ ≈ JS then VDnJw ST /..1−=

Further from KT ≈ JS characteristics 4².. DnKT T ρ=

( )SV

tTCT

²...21

1.

ρ

−=

Then we obtain

TSTFC CCC −=∆ TTSC www −=∆ 2.6 Input Data

Input data sheets are given in ENCL.1 2.7 Output Data - Output data I gives ITTC Standard Pre-

diction with CP = CN = 1.0, together with model and full scale propulsive coeffi-cients (ENCL. 4).

- Output data II gives the final ship predic-tion (ENCL. 5).

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- Output data III gives the analysis of the

speed trial results (ENCL. 6). 2.8 Test Example

To illustrate the program a prediction was

made for a hypothetical ship with the following particulars: length between perpendiculars Lpp = 251.5m breadth B = 41.5m draft T = 16.5m

propeller diameter D = 8.2m

Calculations were carried out with the ITTC Trial Prediction Test Program with:

CP = 1.01 CN = 1.02

The input data were taken as shown in ENCL. 1 and the printout of the input data and results are given in ENCL. 4 - 6.

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3. PARAMETERS 3.1 Parameters to be Taken into Account

Froude scaling law ship-model correlation line ,friction line kinematic viscosity mass density blockage form factor propeller loading hull roughness see also 3.3 Input Data 3.2 Recommendations of ITTC for Pa-

rameters see 4.9-03-03-01.1 Propulsion Test

1987 p.263 In using the 1978 ITTC Method it is recommended that the rudder(s) be fitted in hull resistance experiments for barge type forms where inflow velocity is relatively large. 3.3 Input Data

All data are either non-dimensional or given in SI-units.

Every data card defines several parameters

which are required by the program; each of these parameters must be input according to a specific format. "I" format means that the value is to be input

without a decimal point and packed to the right of the specified field.

"F" format requires the data to be input with a decimal point; the number can appear anywhere in the field indicated.

"A" format indicates that alphanumeric char-acters must be entered in the appropriate card columns.

The card order of the data deck must fol-

low the order in which they are described below.

Card No. 1 Identifications Card column

Form at

CC Symbol

Definition

1- 8 A - Project No. 9-16 A - Ship model No

17-24 A - Propeller model No.

25-32 F SCALE Scale ratio Card No. 2 Ship particulars Card column

For-mat

CC Symbol

Definition

9-16 F LWL Length of waterline 17-24 F TF Draft, forward 25-32 F TA Draft, aft 33-40 F B Breadth 41-48 F S Wetted surface, with-

out bilge keels 49-56 F DISW Displacement

157-64 F SBK Wetted surface of bilge keels

65-72 F AT Transverse projected area of ship above waterline

72-80 F C3 Form factor deter-mined at resistance tests

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Card No. 3 Particulars of full scale

Card column

For-mat

CC Symbol

Definition

8- 8 I NOPROP Number of propellers should be 1 since method is valid only for single screw ships

15-16 I NPB Number of propeller blades

17-24 F DP Diameter of propeller 25-32 F PD075 Pitch ratio at x=0.75 33-40 F CH075 Chord length of Propeller

blade at x=0.75 41-48 F TMO75 Maximum blade thick-

ness of propeller at x=0.75

49-56 F RNCHM Reynolds number at open-water test based on chord length and local velocity 275.0.

1

+=

JVV A

π

at x-0.75. Card No. 4 General Card column

For-mat

CC Sym-bol

Definition

2.- 4 I NOJ Number of J-values in the open-water characteristics (J ≤ NOJ ≤ 10)

7- 8 I NOSP Number of speeds in the self- propulsion tests (NOSPmax=10)

9-16 F RHOM Density of tank water 17-24 F RHOS Density of sea water 25-30 F TEMM Temperature of resistance

test 31-36 F TEMP Temperature at self-

propulsion test - 36-41 F TEMS Temperature of sea water 48-48 I CHOICE CHOICE=0 NP CC −

trial corr. CHOICE==1:

CFC wC ∆−∆ trial corr. 49-56 F CP Trial correction for shaft

power. 57-64 F CN Trial correction for rpm 65-72 F DELT

CFC Trial correction for FC∆

72-80 F DELTWC Trial correction for w∆

Mean values of the trial correction figures, Cp and CN can be obtained from the trial test material of the individual institutions by run-ning the ITTC Trial Prediction Test Program. If an institution wishes to give predictions with a certain margin the input CP-CN-values must be somewhat higher than these mean values. Cards Nos. 5-14 Result of resistance and self-propulsion tests and model propeller charac-teristics. Card column

Format CC Symbol

Definition

1- 8 F VS Ship speed in knots 9-16 F RTM Resistance of ship

model 17-24 F THM Thrust of propeller 25-32 F QM Torque of propel-

ler:QM:100 33-40 F NM Rate of revolution 41-48 F FD Skin friction correc-

tion force 49-56 F ADVC Advance coefficient,.

open water 57-64 F KT Thrust coefficient,

open water 65-72 F KQ Torque coefficient,

open water

The J-margin in the open-water character-istics must be large enough to cover the model and full scale J-values with some mar-gin.

Input data sheets are given in ENCL. 1.

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4. VALIDATION 4.1 Uncertainty Analysis not yet available 4.2 Comparison With Full Scale Results

The data that led to t ITTC-78 method can be found in the following ITTC proceedings: 1) Proposed Performance Prediction Factors

for Single Screw Ocean Going Ships

(13th 1972 pp.155-180) Empirical Power Prediction Factor ( 1+X )

2) Propeller Dynamics Comparative Tests

(13th 1972 pp.445-446 ) 3) Comparative Calculations with the ITTC

Trial Prediction Test Programme(14th 1975 Vol.3 pp.548-553)

4) Factors Affecting Model Ship Correlation

(17th 1984 Vol. 1, pp274-291)

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5. ITTC- 1978 PERFORMANCE PREDICTION METHOD (COMPUTER CODE) C C **************************************************************************************************** C * * C * 1978 ITTC PERFORMANCE PREDICTION METHOD FOR SINGLE SCREW * C * SHIPS * C * (REVISED 1983 TO INCLUDE TRIAL ANALYSIS AND TWIN SCREW SHIPS* * C * * C **************************************************************************************************** C C DECLARATIONS C COMMON /A/ FILE(2),MODELS(2), MODELP(2), LPP,LWL,TF,TA,B,S, * SCALE,RNCHM,DISW,NOPROP,NPB,DP,PD075,CH075. * TM075,C3,SBK,AT,CP,CN,DELCF,DELWC,KSI,KPI, * RHOM,RHOS,TEMM,TEMP,TEMS,VS(10),RTM(10),THM(10), * QM(10),NM(10),ADVC(10),KT(10),KQ(10),THD(10),

* FD(10),IC,NOJ,NOSP,PI C COMMON /B/ ETARM(10),ETAO(10),ETAH(10),ETAD(10),AWTM(10),

* AWTS(10),ACFM(10),ACTM(10),AVS(10),AVM(10), * ATS(10),AQS(10),APDS(10),APE(10),APDT(10), * ANS(10),ANT(10),BPDT(10),BNT(10),KTSJ2(10),

* KQS(10),KTS(10),ACTS(10) DIMENSION FILE1(2),MODLS1(2),MODLP1(2) C REAL LPP, LWL, KS1, KS, KP1, KP, NM1, NM, KT, KQ, KTM, KQ0, JTM,

* KTSJ2, JTS, NS, KQTS, KTS, KQS, KQM DATA TRIAL /‘TRIA‘/ 500 FORMAT(6A4,F8.0) 501 FORMAT(10F8.0) 502 FORMAT(2I4,9F8.0) 503 FORMAT(2I4,2F8.0,3F6.0,I6,4F8.0) 504 FORMAT(9F8.0) 600 FORMAT(/5X,’NUMBER OF ADV,KT AND KQ POINTS =’,15/ * 5X,’NUMBER OF SPEEDS =’,15/ * 5X,’NUMBER OF SPEEDS OR ADVC POINTS >10’/)

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C C CONSTANTS C G=9.81 PI=3.14159 KP1=30.0 KS1=150.0 KS=1.5E-4 KP=0.3E-4 C C READ INPUT DATA C 1000 CONTINUE READ(5,500,END=999) FILE,MODELS,MODELP,SCALE READ(5,501) LPP,LWL,TF,TA,B,S,DISW,SBK,AT,C3 READ(5,502) NOPROP,NPB,DP,PD075,CH075,TM075,RNCHM READ(5,503) NOJ,NOSP,RHOM,RHOS,TEMM,TEMP,TEMS * IC,CP,CN,DELCF,DELWC NMAX=MAX0(NOJ,NOSP) IF(FILE(1).EQ.TRIAL) GOTO 100 READ(5,504)(VS(I),RTM(I),THM(I),QM(I),NM(I),FD(I), * ADVC(I),KT(I),KQ(I);I=1,NMAX) C C WRITE INPUT DATA C CALL OUTPUT(1) C C CHECK C IF(NOJ.LE.10.AND.NOSP.LE.10) GOTO 2 WRITE(6,600) NOJ.NOSP GOTO 1000 2 CONTINUE

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C C RECALCULATION OF INPUT DATA C DO 3 I=1,NOJ KT(I)=KT(I)*0.1

KQ(I)=KQ(I)*0.01 ....3 CONTINUE DELCF=DELCF*0.001 RNCHM=RNCHM*100000. VISCP=((0.585E-3*(TEMP-12.0)-0.03361)*(TEMP-12.0)+

* 1.2350)*1.0E-6 VISCM=((0.585E-3*(TEMM-12.0)-0.0361)*(TEMM-12.0)+ * 1.2350)*1.0E-6 VISCS=((0.659E-3*(TEMS-1.0)-0.05076)*(TEMS-1.0)+ * 1.7688)*1.0E-6

C C CORRECTION OF PROPELLER CHARACTERISTICS C CDM=2.0*(1.0+2.0*TM075/CH075)*(0.044/RNCHM**0.16667- * 5.0/RNCHM**0.66667) CDS=2.0*(1.0+2.0*TM075/CH075)/(1.89+1.62*ALOG10(CH075 * /KP))**2.5 DCD=CDM-CDS DKT=-0.3*DCD*PD075*CH075*NPB/DP DKQ=0.25*DCD*CH075*NPB/DP DO 4 I=1,NOJ KTS(I)=KT(I)-DKT KQS(I)=KQ(I)-DKQ KTSJ2(I)=KTS(I)/ADVC(I)**2 4 CONTINUE DO 5 I=1,NOSP VS1=VS(I)*0.15444 VM1=VS1/SQRT(SCALE) NM1=NM(I) C C

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C CALCULATE ROUGHNESS ALLOWANCE AND SHIP TOTAL RESISTANCE C RNLP=LWL*VM1/(VISCP*SCALE) RNLM=LWL*VM1/(VISCM*SCALE) RNLS=LWL*VS1/VISCS CFMC=0.075/(ALOG10(RNLP)-2)**2 CFM=0.075/(ALOG10(RNLM)-2)**2 CFS=0.075/(ALOG10(RNLS)-2)**2 CTM=RTM(I)*SCALE**3/(0.5*RHOM*VS1**2*S) CR=CTM-(1.0+C3)*CFM RTMC=RTM(I)*(1.0+C3)*CFMC+CR)/((1.0+C3)*CFM+CR) THD(I)=(THM(I)+FD(I)-RTMC)/THM(I) DELCF=(105.0*(KS/LWL)**0.33333-0.64)*0.001 CAA=0.001*AT/S CTS=((1.0+C3)*CFS*DELCF)*(S+SBK)/S+CR+CAA C C MODEL PROPULSIVE COEFFICIENTS C FNOP=NPROP KTM=(THM(I)/FNOP)/(RHOM*(DP/SCALE)**4*NM1*NM1) KQM=(QM(I)*0.01/FNOP)/(RHOM*(DP/SCALE)**5*NM1*NM1) JTM=APOL(0,KT,ADVC,NOJ,KTM,IX) KQ0=APOL(0,ADVC,KQ,NOJ,JTM,IX) WTM=1.0-JTM*DP*NM1/(VM1*SCALE) C C FULL SCALE WAKE C IF(JRUDER) 6,5,6 5 WTS=(THD(I)+0.04)+(WTM-THD(I)-0.04)*((1.0+C3)*CFS+DELCF)/

* ((1.0+C3)*CFM) GOTO 7

6 WTS=(THD(I) )+(WTM-THD(I) )*((1.0+C3)*CFS+DELCF)/ * ((1.0+C3)*CFM)

GOTO 7 7 IF(WTS.GT.WTM) WTS=WTM ETARM(I)=KQ0/KQM C C SAVE AREAS C ACTM(I)=CTM ACFM(I)=CFM AWTM(I)=WTM AWTS(I)=WTS ACTS(I)=CTS AVS(I)=VS1 AVM(I)=VM1 8 CONTINUE C C ITTC STANDARD PREDICTION

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C CALL IP C C RETURN FOR NEW INPUT C DO 20 I=1,2 FILE1(I)=FILE(I) MODLS1(I)=MODELS(I)

20 MODELP1(I)=MODELP(I) SCALE1=SCALE

GOTO 1000 C

100 CONTINUE DO 110 I=1,2 FILE(I)=FILE1(I) MODELS(I)=MODLS1(I)

110 MODELP(I)=MODLP1(I) SCALE=SCALE1

C CALL ANLSYS C C RETURN FOR NEW INPUT C C GOTO 1000 999 STOP END C

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C C ******************************************************************************************************** C C OUTPUT IS USED FOR PRINTING INPUT DATA AND RESULTS C C IOUT= 1 INPUT DATA IS PRINTED C 2 RESULT PAGE 1 C 3 RESULT PAGE 2 C C ******************************************************************************************************** C SUBROUTINE OUTPUT(IOUT) COMMON /A/ FILE(2),MODELS(2),MODELP(2),LPP,LWL,TF,TA,B,S * SCALE,RNCHM,DISW,NOPROP,NPB,DP,PD075,CH075, * TM075,C3,SBK,AT,CP,CN,DELCFC,DELWC,KSI,KPI, * RHOM,RHOS,TEMM,TEMP,TEMS,VS(10),RTM(10);THM(10), * QM(10),NM(10),ADVC(10),KT(10),KQ(10),THD(10), * FD(10),IC,NOJ,NOSP,PI C COMMON /B/ ETARM(10),ETA0(10),ETAH(10),ETAD(10),AWTM(10), * AWTS(10),ACFM(10),ACTM(10),AVS(10),AVM(10), * ATS(10),AQS(10),APDS(10),APE(10),APDT(10), * ANS(10),ANT(10),BPDT(10),BNT(10),KTSJ2(10), * KQS(10),KTS(10),ACTS(10) C REAL LPP,LWL,KS1,KS,KP1,KP,NM1,NM,KT,KQ,KTM,KQ0,JTM, KTSJ2,JTS,NS,KQTS,KTS,KQS DIMENSION TEXT (16) DATA TEXT /’INPU’,’T DA’,’TA ‘,’ ‘, * ‘OUTP’,’UT D’,’ATA ‘,’1 ‘, * ‘OUTP’,’UT D’,’ATA..’,’2 ‘; * `TRIA`,`L AN`,ÀLYS`,ÌS `/ 600 FORMAT(‘1’,19X,’1978 ITTC PERFORMANCE PREDICTION’,10X, * ‘ENCL:’/ C?? * 20X,’METHOD ‘,8X,

* ‘REPORT:’/20X,4A4/)

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601 FORMAT(5X,’IDENTIFICATION :’,18X,’SHIP:’// * 5X,‘PROJECT :’,2A4, * 10X,’LENGTH PP :’,F8.2,’ (M)’/ * 5X,’SHIP MODEL’ :’,2A4, * 10X,’LENGTH WL :’,F8.2,’ (M)’/ * 5X,’PROPELLER MODEL :’,2A4, * 10X,’DRAFT FWD :’,F8.2,’ (M)’/ * 5X,’SCALE FACTOR :’,F8.2, * 10X,’DRAFT AFT :’,F8.2,’ (M)’/ * 43X,’BREADTH :’,F8.2,’ (M)’/ * 5X,’PROPELLER:’, * 28X,’WETTED SURFACE :’,F8.0,’ (M**2)’/ * 43X,’DISPLACEMENT :’,F8.0,’ (M**3)’) 602 FORMAT(5X,’NUMBER OF PROPELLERS:’,I8/ * 5X,’NUMBER OF BLADES :’,I8, * 6X,’FRICTION COEFFICIENT CF’/ * 5X,’DIAMETER :’,F8.3,’ (M)’, * 2X,’CALCULATED ACCORDING TO ITTC-57’/ * 5X,’PITCH RATIO 0.75R :’,F8.4, * 6X,’FORM FACTOR :’,F6.3,’ (BASED ON ITTC-57)’/) 603 FORMAT(5X,’HULL ROUGHN.*10**6 :’,F6.1,’ (M)’, * 2x,’BILGE KEEL AREA :’,F6.1,’ (M**2)’, * 5X,’PROPELLER BLADE ROUGHN.*10**6:’,F6.1,’ (M)’, * 2X,’PROJ.AREA ABOVE WL. :’,F6.1,’ (M**2)’/) 604 FORMAT(5X,’CHORD LENGTH OF PROP.BLADE AT X=0.75:’, * F7.4,’ (M)’/ * 5X,’THICKNESS OF PROP.BLADE AT X=0.75:’, * F7.4’ (M)’/) 605 FORMAT(5X,’DENSITY OF WATER (TANK ) :’F7.1, * ‘ (KG/M**3)’/ * ’DENSITY OF WATER (SEA ) :’F7.1, * ‘ (KG/M**3)’/ * 5X,’TEMP. OF WATER (RESISTANCE TEST) :’F7.2, * ‘ (CENTIGRADES)’/ * 5X,’TEMP. OF WATER (SELF PROP. TEST) :’F7.2, * ‘ (CENTIGRADES)’/ * 5X,’TEMP. OF WATER (SEA ) :’F7.2, * ‘ (CENTIGRADES)’// * 5X,’MODEL TEST RESULTS:’, * 30X,’OPEN WATER CHARACT.;’/ * 54X,’RNC :’’F5.2,’*10**5’/)

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606 FORMAT(5X,’SHIP RESIS- FRICT. THRUST TORQUE RATE OF ‘, * 2X,’ADVANCE THRUST TORQUE’/ * 20X,’REVS. RATIO COEFF. COEFF.’/ * 5X,’KNOTS N N N NM RPS ’, * 7X,’J 10*KT 100*KQ’/) 607 FORMAT(1X) 608 FORMAT(‘+’,3X,F5.1,1X,F7.1,1X,F7.2,2X,2F7.1,F9.2) 609 FORMAT(‘+’,49X,F10.3,F7.3,F8.3) 610 FORMAT(5X,’SHIP MODEL:’// * 8X,’SPEED RES. COEFF. FRICT. COEFF. THRUST DED.’, * 2X,’MEAN REL.ROT.’/ * 6X,’VS VM TOTAL’,32X, ‘WAKE EFFIC.’/ * 5X,’KNOTS M/S CTM*1000 CFM*1000’,8X,’TM’, * 7X,’WTM ETARM’/) 611 FORMAT(4X,F5.1,F7.3,F8.3,6X,F7.3,7X,F7.3,3X,F7.3,F8.3) 612 FORMAT(/5x,’ITTC STANDARD PREDICTION CP=CN=1.0 :’// * 5X,’SPEED EFF. POWER DELIV. POWER RSATE OF REVS’, * 2X,’ THRUST TORQUE’/ * 6X,’VS’,7X,’PE’,10X,’PD’,12X,’N’,10X,’T’,8X,’Q’/ * 5X,’KNOTS’,5X,’KW’,10X,’KW’,11X,’RPS’,9X,’KN’, * 6X,’KNM’/) 613 FORMAT(4X,F5.1,F10.0,3X,F9.0,4X,F9.3,3X,F9.0,F8.0) 614 (FORMAT(/5X,’SPEED TOT. EFF. PROP.EFF. HULL EFF. SHIP WAKE’, * 3X,’OPEN WATER CHAR. FULL SCALE:’/ * 5X,’KNOTS ETAD ETA0 ETAH’,/X,’WTS’, * 9X,’J 10*KT 100*KQ’/) 615 FORMAT(‘+’,3X,F5.1,F8.3,3(3X,F7.3)) 616 FORMAT(‘+’,50X,3F7.3) 617 FORMAT(/5X,’SHIP DELIVERED POWER RATE OF REVS.’/ * 5X, ‘SPEED --------------------------- ---------------------‘/ * 5X,’KNOTS KW HP RPS RPM’/) 618 FORMAT(4X,F5.1,2X,2F8.0,3X,F7.3,F8.2) 619 FORMAT(/5X,’SHIP TRIALS PREDICTION CP=’,F7.3,’ CN=,F7.3) 620 FORMAT(/5X,’SHIP TRIALS PREDICTION DELCFC*1000=’, * F6.3,’ DELCW=’,F6.3) ITEX=ICUT*4-4 WRITE(6,600) (TEXT(ITEX+1),I=1,4) WRITE(6,601) FILE,LPP,MODELS,LWL,MODELP,TF,SCALE,TA,B,S,DISW WRITE(6,602) NOPROP,NPB,DP,PD075,C3 C GOTO(10,20,30,40) , IOUT

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Method

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Revision00

C C INPUT DATA IS LISTED C 10 CONTINUE WRITE(6,603) KS1,SBK,KP1,AT WRITE(6,604) CH075,TM075 WRITE(6,605) RHOM,RHOS,TEMM,TEMP,TEMS,RNCHM WRITE(6,606) NMAX=MAX0(NOJ,NOSP) DO 1 I=1,NMAX WRITE(6,607) IF(I. LE. NOSP) WRITE(6,608) VS(I);RTM(I);FD(I),THM(I), QM(I),NM(I) IF(I. LE.NOJ) WRITE(6,609) ADVC(I),KT(I),KQ(I) 1 CONTINUE RETURN C C RESULTS PAGE 1 C 20 CONTINUE WRITE(6,610) DO 21 I=1,NOSP CFM=ACFM(I)*1000.0 CTM=ACTM(I)*1000.0 WRITE(6,611) VS(I),AVM(I),CTM,CFM,THD(I),AWTM(I),ETARM(I) 21 CONTINUE WRITE(6,612) DO 22 i=1,NOSP WRITE(6,613) VS(I),APE(I),APDS(I),ANS(I),ATS(I),AQS(I) 22 CONTINUE WRITE(6,614) DO 23 i=1,NMAX WRITE(6,607) IF(I.LE.NOSP) WRITE(6,615) VS(I),ETAD(I),ETA0(I),ETAH(I); AWTS(I) XKTS=KTS(I)*10.0 XKQS=KQS(I)*100.0 IF(I.LE.NOSP) WRITE(6,616) ADVC(I),XKTS,XKQS 23 CONTINUE RETURN

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Method

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C C RESULTS PAGE 3 C 30 CONTINUE DCFC=DELCFC*1000.0 IF(IC.EQ.1) WRITE(6,620) DCFC,DELWC IF(IC.NE.1) WRITE (6,619) CP,CN WRITE(6,617) DO 31 I=1,NOSP WRITE(6,618) VS(I),APDT(I),BPDT(I),ANT(I),BNT(I) 31 CONTINUE ....40 RETURN END C C ******************************************************************************************************** C C IRAT= 0 INTERPOLATION WITH A 2:ND DEGREE POLYNOMIAL C = 1 INTERPOLATION WITH A RATIONAL FUNCTION OF 2:ND DEGREE C X = ARGUMENT ARRAY C Y = VALUE ARRAY C N = NUMBER OF ARGUMENTS C EX = ARGUMENT C IFEL = ERROR RETURN CODE C C ******************************************************************************************************** C REAL FUNCTION APOL(IRAT,X,Y,N,EX,IFEL) DIMENSION X(1),Y(1) C C CHECK NUMBER OF POINTS > 2 C IFEL=0 IF(X(1).GT.X(N)) GOTO 2 IF(X(1).GT.EX.OR.X(N).LT.EX) GOTO 7 DO 1 I=1,N L=1 IF(EX-X(I)) 4,4,1 1 CONTINUE GOTO 4 2 CONTINUE IF(X(1).LT.EX.OR.X(N).GT.EX) GOTO 7 DO 3 I=1,N L=I IF(EX-X(I)) 3,4,4

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3 CONTINUE 4 CONTINUE M=2 IF(L.EQ.1) M=1 IF(L.EQ.3) M=3 LM=L-M X1=X(LM+1) X2=X(LM+2) X3=X(LM+3) Y1=Y(LM+1) Y2=Y(LM+2) Y3=Y(LM+3) C C INTERPOL. 2:ND DEGREE POLYNOMIAL C X21=X2-X1 X31=X3-X1 X32=X3-X2 IF(IRAT.EQ.1) GOTO 6 C1=Y1 C2=(Y2-C1)/X21 C3=(Y3-C1-C2*X31)/(X31*X32) APOL=C1+(EX-X1)*(C2+C3*(EX-X2)) RETURN 6 CONTINUE C C INTERPOL. RAT. FUNCTION C Y21=Y2*X2*X2-Y1*X1*X1 Y32=Y3*X3*X3-Y2*X2*X2 A0=(Y32-X32*Y21/X21)/(X32*X31) B0=(Y21/X21-A0*(X1+X2) C0=((Y1-A0)*X1-B0)*X1 APOL=(C0/EX+B0)/EX+A0 RETURN 7 CONTINUE WRITE(6,8) 8 FORMAT(/5X,’INCREASE THE J-RANGE’) STOP END

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Method

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C C ******************************************************************** C C ITTC PREDICTIONS C C ******************************************************************** C SUBROUTINE IP COMMON /A/ FILE(2),MODELS(2),MODELP(2),LPP,LWL,TF,TA,B,S, * SCALE,RNCHM,DISW,NOPROP,NPB,DP,PD075,CH075, * TM075,C3,SBK,AT,CP,CN,DELCFC,DELWC,KSI,KPI, * RHOM,RHOS,TEMM,TEMP,TEMS,VS(10),RTM(10),THM(10), * QM(10),NM(10),ADVC(10),KT(10),KQ(10),THD(10), * FD(10),IC,NOJ,NOSP,PI C COMMON /B/ ETARM(10),ETA0(10),ETAR(10),ETAD(10),AWTM(10), * AWTS(10),ACFM(10),ACTM(10),AVS(10),AVM(10), * ATS(10),AQS(10),APDS(10),APE(10),APDT(10), * ANS(10),ANT(10),BPDT(10),BNT(10),KTSJ2(10), * KQS(10),KTS(10),ACTS(10) C REAL LPP,LWL,KS1,KS,KPI,KP,NM1,NM,KT,KQ,KTM,KQD,JTM, * KTSJ2,JTS,NS,KQTS,KTJT2,KQOS,KQS,KTS DO 3 I=1,NOSP VS1=AVS(I) CTS=ACTS(I) WTS=AWTS(I) C C CALCULATE THE FULL SCALE LOAD ADVANCE COEFF: AND C TORQUE COEFF. C FNOP=NOPROP KTJT2=S*CTS*0.5/((DP*(1.0-WTS))**2*(1.0-THD(I))) /FNOP JTS=APOL(1,KTSJ2,ADVC,NOJ,KT,KTJT2,IX) KQOS=APOL(0,ADVC,KQS,NOJ,JTS,IX) C C THE RATE OF REV. AND THE DELIVERED POWER C NS=(1.0-WTS)*VS1/(JTS*DP) APDS(I)=2.0*PI*RHOS*DP**5*NS**3*KQOS/ETARM(I)*0.001 ANS(I)=NS

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Method

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Revision00

C C THE THRUST AND TORQUE OF THE PROPELLER C ATS(I)=KTJT2*JTS**2*RHOS*DP**4*NS*NS*0.001 AQS(I)=KQOS*RHOS*DP**5*NS*NS/ETARM(I)*0.001 C C THE EFFECTIVE POWER, TOTAL AND HULL EFFICIENCY C APE(I)=CTS*0.5*RHOS*VS1**3*S*0.001 ETAD(I)=APE(I)/APDS(I) ETAH(I)=(1.0-THD(I))/(1.0-WTS) IF(IC.EQ.1) GOTO 1 C IC1=IC-1 IF(IC1)10,11,12 C C TRIAL PREDICTION WITH CP-CN CORRECTIONS (ITTC1978 ORIGINAL) C 10 ANT(I)=CN*NS

BNT(I)=ANT(I)*60.0 APDT(I)=CP*APDS(I) BPDT(I)=1.36*APDT(I) GOTO 100

C C TRIAL PREDICTION WITH CP-CN CORRECTIONS C CN BASED ON POWER IDENTITY C

12 APDT(I)=CP*APDS(I) BPDT(I)=1.36*APDT(I)

KQJ3T=1000.0*APDT(I)/(2.0*PI*RHOS*DP**2) /FNOP KQJ3T=KQJ3T/(VS1**3*(1.0-WTS)**3) KQ0J3=KQJ3T*ETARM(I) JTS=APOL(1,KQSJ3,ADVC,NOJ,KQ0J3,IX) NS=(1.0-WTS)*VS1/(JTS*DP) ANT(I)=CN*NS BNT(I)=ANT(I)*60.0 GOTO 100

11 CONTINUE

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C C TRIAL PREDICTION WITH DELCF-DELWC CORRECTIONS C KTJT2=S*(CTS+DELCFC)/(2.0*(1.0-THD(I))*(DP* * (1.0-(WTS-DELWC)))**2) JTS=APOL(1,KTSJ2,ADVC,NOJ,KTJT2,IX) KQOS=APOL(0,ADVC,KQS,NOJ,JTS,IX) ANT(I)=(1.0-WTS+DELWC)*VS1/(JTS*DP) BNT(I)=ANT(I)*60.0 APDT(I)=2.0*PI*RHOS*DP**5*ANT(I)**3*KQOS/ETARM(I)*0.001 BPDT(I)=1.36*APDT(I) 2 CONTINUE ETAD(I)=KTJT2*JTS**3/(2.0*PI*KQOS) 3 CONTINUE C C WRITE OUTPUT C CALL OUTPUT(2) CALL OUTPUT(3) RETURN

SUBROUTINE ANLSYS C C*************************************************************************************************************** C * * C * ANALYSIS ACCORD1NG TO 1978 ITTC PREDICTION METHOD * C * * C*************************************************************************************************************** C C DIMENSION VST(10),XNT(10),XPD(10), * THDT(10),WTMT(10),WTST(10),ETART(10),CRWT(10), * YNT(10),YPD(10),CPT(10),CNT(10),CNPT(10),ZNT(10) * DCFT(10),WTSS(10),DWT(10),DCFM(10),DWM(I0), * KQJ3(10) C

COMMON /A/ FILE(2),MODELS(2),MODELP(2),LPP,LWL,TF,TA,B,S, * SCALE,RNCHM,DISW,NOPROP,NPB,DP,PD075,CH075, * TM075,C3,SBK,AT,CP,CN,DELCFC,DELWC,KS1,KP1, * RHOM, RHOS,TEMM,TEMP,TEMS,VS(10),RTM(10),THM(10), * QM(10),NM(10),ADVC(10),KT(10),KQ(10),THD(10), * RA(10),IC,NOJ,NOSP,PI

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C

COMMON /B/ ETARM(10), ETA0(10),ETAH(10),ETAD(10),AWTM(10), * AWTS(10),ACFM(10),ACTM(10),AVS(10),AVM(10), * ATS(10),AQS(10),APDS(10),APE(10),APDT(10), * ANS(10),ANT(10),BPDT(10),BNT(10),KTSJ2(10), * KQS(10),KTS(10),ACTS(10) C

REAL LPP,LWL,KS1,KS,KP1,KP,NM1,NM,KT,KQ,KTM,KQ0,JTM, * KTSJ2,JTS,NS,KQTS,KTJT2,KQOS,KTS,KQS,KQM, * KQJ3,KQJ3T C C

DO 5 I = 1,NOJ 5 KQJ3(I) = KQS(I) /ADVC(I)**3 C NOST=10

READ(5,510) (VST(I), I=1,NOST) READ(5,510) (XNT(I), I=1,NOST)

READ(5,510) (XPD(I), .I=1,NOST)

510 FORMAT (10F8.0) C C COUNT NO. OF TRIAL RUNS NOST = 0 DO 8 I = 1, 10 IF (VST(I).GT.0. ) NOST=NOST+1 8 CONTINUE IF(XNT(1).GT.20.) GOTO 20 DO 10 I=1, NOST XNT(I) = XNT(I)*60.0 10 XPD(I) = XPD(I)*1.36 20 CONTINUE DO 50 I=1, NOST VST1=VST(I)*1852.0/3600.0 CTST = APOL(0,AVS, ACTS, NOSP,VST1, IX) THDT(I)= APOL(0,AVS, THD, NOSP,VST1, IX) WTMT(I)= APOL(0,AVS, AWTM, NOSP,VST1, IX) WTST(I)= APOL(0,AVS, AWTS, NOSP,VST1, IX) ETART(I)= APOL(0,AVS, ETARM,NOSP,VST1, IX) CF =APOL(0,AVS, ACFM, NOSP,VST1, IX) CT =APOL(0,AVS, ACTM, NOSP,VST1, X)

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CRWT(I)= CT - (1.0+C3)*CF FNOP =NOPROP KTJT2 =S*(CTST/FNOP )*0.5 / ((DP*(1.0-WTST(I)))**2*(1.0-THDT(I))) JTS =APOL(1, KTSJ2, ADVC, NOJ, KTJT2, IX) KQOS=APOL (0, ADVC, KQS, NOJ, JTS, IX) NS=(1.0-WTST(I))*VST1/(JTS*DP) PDS = 2.0*PI*RHOS*DP**5*NS**3*KQ0S/ETART(I)*0.001*FNOP YNT(I)= NS*60.0 YPD(I) = PDS*1.36 CPT(I)= XPD(I)/YPD(I) CNT(l)=XNT(I)/YNT(I) PDT1 = XPD(I) /1.36 XNT1 = XNT(I) / 60.0 FKQ = PDT1*START(I)*1000.0 / (2.0*PI*RHOS*DP**5*XNT1**3) / FNOP FJT = APOL(0,KQS,ADVC,NOJ,FKQ,IX) FKT = APOL(0,ADVC, KTS,NOJ,FJT,IX) KQJ3T=FKQ * (DP*XNT1)**3 / ((1-WTST(I))*VST1)**3 FJQ= APOL( 1,KQJ3,ADVC,NOJ,KQJ3T,IX) ZNT(I)=(1.0 -WTST(I)) * VST1 / (FJQ*DP) * 60.0 CNPT(I)=XNT(I) / ZNT(I) THS= FKT * RHOS * DP**4*XNT1**2 CTS=THS*(1.0 - THDT(I)) / (0.5*RHOS*VST1**2*S) * FNOP DCFT(I)=(CTS - CTST)*1000.0 WTSS(I)= 1.0 - FJT*DP*XNT1/VST1 DWT(I) = WTST(I) - WTSS(I) DWM(I) = WTMT(I) - WTSS(I) C C CALCULATION OF FRICTIONAL RESISTANCE ~COEFF. OF SHIP C T = TEMS FNU = ((0.659E-3*(T-l.0)-0.05076)*(T-1)+1.7688)*1.0E-6 RNLS= ALOG10(LWL*VST1/FNU) CFS = 0.075 / (RNLS-2.0)**2 C DCFM(I) = CTS - (l.0+C3)*CFS - ( CRWT(I)+0.001*AT / S )*S / (S+SBK) DCFM(I) = DCFM(I) * 1000.0 CRWT(I) = CRWT(I) * 1000.0

50 CONTINUE C CALL OUTPUT(4) WRITE(6,600)

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600 FORMAT(' ',19X,'TRIAL ANALYSIS ACCORDING TO ITTC 1978 METHOD',///) WRITE(6,610) ( VST(I), I=1, NOST) 610 FORMAT(5X.. ' SHIP SPEED - TRTAL',7(F10.2, 2X) /) WRITE(6,620) ( XNT(I), I=1, NOST) 620 FORMAT(5X, ‘ PROP, RPM –TRTAL ',7(F10.2, 2X) /) WRITE(6,630) ( XPD(I), I=1, NOST) 630 FORMAT(4X, 'DELIV.POWER-TRIAL ',7(F11.0,1X) //) WRITE(6,640) ( YNT(I), I=1, NOST) 640 FORMAT(/5X, ‘ PROP. RPM -CN=1 ',7(F10.2,2X) /) WRITE~(6,650) ( ~YPD(I), I=1,NOST) 650 FORMAT(4X, ' DELIV. POWER -CP =1',7(F11.0,1X) /) WRITE(6,660) ( ZNT(I), I=1, NOST) 660 FORMAT(5X, ‘ PROP. RPM -CNP=1 ',7(F10.2,2X), //) WRITE(6,670) ( CPT(I), I=1, NOST) 670 FORMAT(/5X, ‘ CP ‘,7(F10.3,2X) /) WRITE(6,680) (CNT(I), I=1, NOST) 680 FORMAT(5X, ‘CN ‘,7(F10.3,2X) /) WRITE(6,690) (CNPT(I), I=1,NOST) 690 FORMAT(5X, ‘CNP ',7(F10.3,2X) //)

WRITE(6,700) (DCFT(I), I=1,NOST) 700 FORMAT(/5X, ‘DCFC*1000 -CP=CN=1’,7(F10.3,2x) /)

WRITE(6,710) ( DWT(I), I=1, NOST) 710 FORMAT(5X, ' DWC CP=CN=1’,7(F10.3,2X) //) WRITE(6,715) ( DCFM(I), I=1, NOST) 715 FORMAT(/5X, 'DCF *1000 ITTC-57’,7(F10.3,2x) /) WRITE(6,717) ( DWM(I), I=1,NOST) 717 FORMAT(5X, ‘DW = WM-WTRIAL ',7(F10.3,2X) //) WRITE(6,720) ( CRWT(I) ,I=1, NOST) 720 FORMAT(/5X, ‘ CR*1000 ‘,7(F10.3,2X) /) WRITE (6,730) ( THDT(I), I=1, NOST) 730 FORMAT(5X, ‘ THDM ',7(F10.3,2X) /) WRITE(6,740) ( WTMT(I), I=1, NOST) 740 FORMAT(5X, ’ WTM ',7(F10.3,2X) /) WRITE(6,750) ( WTST(I), I=1, NOST) 750 FORMAT(5X, ‘ WTS CP=CN=1 ’,7(F10.3,2x) /) WRITE(6,760) ( WTSS(I), I=1, NOST) 760 FORMAT(5X, ’ WTS TRIAL ’,7(F10.3,2X) /) WRITE(6,770) ( ETART(I), I=1, NOST) 770 FORMAT(5X, ‘ ETARM ‘ ,7(F10.3,2X) /)

RETURN END

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120 APENDICE A. PREVISAO BASEADA NOS ENSAIOS DE PROPULSAO

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Apendice BProcedimentos Recomendados pela

ITTC para a Preparacao e

Realizacao das Provas de Velocidade

e Potencia

121

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122 APENDICE B. PROVAS DE VELOCIDADE E POTENCIA

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Full Scale Measurements Speed and Power Trials

Preparation and Conduct of Speed/Power Trials

Effective Date 2005

Revision03

Updated / Edited by Approved

Specialist Committee on Powering Perform-ance of 24th ITTC

24th ITTC 2005

Date 2005 Date 2005

Table of Contents

1. PURPOSE ..............................................2

2. DEFINITIONS.......................................2

3. RESPONSIBILITIES............................3

3.1 Shipbuilders Responsibilities............3

3.2 The Trial Team ..................................4

4. PROCEDURES......................................4

4.1 Trial Preparation...............................4 4.1.1 Shipbuilder’s Support Requirement:4 4.1.2 Space Requirements ........................4

4.2 Ship Inspection...................................5 4.2.1 Preparation for the trials ..................5 4.2.2 Ship Inspection ................................5 4.2.3 Reporting of Results and

Distribution of Information .............5

4.3 Hull- and Propulsor Survey..............5

4.4 Instrumentation Installation and Calibration .........................................5

4.4.1 Instrumentation Installation.............5 4.4.2 Instrumentation Calibration Check .6

4.5 Trial Conditions.................................6 4.5.1 Wind: ...............................................8 4.5.2 Sea State: .........................................8 4.5.3 Current:............................................8

4.6 Trial Conduct: ...................................8

5. REFERENCES ....................................10

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Preparation and Conduct of Speed/Power Trials

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Revision03

Preparation and Conduct of Speed/Power Trials

1. PURPOSE

The general purpose of this procedure is to define basic requirements for the preparation and conduct of speed trials.

The primary purpose of speed trials is to determine ship performance in terms of speed, power and propeller revolutions under pre-scribed ship conditions, and thereby verify the satisfactory attainment of the contractually stipulated ship speed.

The applicability of this procedure is lim-ited to commercial ships of the displacement type.

The procedure is

• to provide guidelines to document the trial preparation prior to the conduct of a full scale Speed/Power trial,

• to define the responsibility sharing among the parties who take part in the sea trial for the smooth preparation and execution of the speed trial

• to establish a guideline for conducting inspections for the purpose of installing instrumentation prior to the conduct of a full scale Speed/Power trial,

• to establish a baseline of the ship hull and propulsor condition prior to the conduct of a full-scale Speed/Power trial;(hull and propulsor surveys are

recommended to allow an evaluation of the trial results for scientific purposes),

• to install and calibrate trial instrumenta-tion for full scale Speed/Power trials,

• to define acceptable limits for trial con-ditions needed to validate hydrody-namic design and/or satisfy contractual requirements,

for acceptable conduct of each speed trial.

2. DEFINITIONS

• Ship Speed is that realized under the con-tractually stipulated conditions. Ideal condi-tions to which the speed would be corrected would be

• no wind (or maximum wind speed ac-cording to Beaufort 2)

• no waves (or waves with maximum wave heights and wave periods accord-ing to Beaufort 1)

• no current

• deep water

• smooth hull and propeller surfaces

• Docking Report: Report that documents the condition of the ship hull and propul-sors (available from the most recent dry - docking).

• Trial Agenda: Document outlining the scope of a particular Speed/Power trial. This document contains the procedures on

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how to conduct the trial and table(s) por-traying the runs to be conducted.

• Trial Log: For each run, the log contains the run number, type of maneuver, ap-proach speed by log, approach shaft speed, times when the maneuvers start and stop, and any comments about the run.

• Propeller Pitch: the design pitch also for controllable pitch propellers.

• Running Pitch: the operating pitch of a CPP

• Brake Power: Power delivered by the out-put coupling of the propulsion machinery before passing through any speed reducing and transmission devices and with all con-tinuously operating engine auxiliaries in use.

• Shaft Power: Net power supplied by the propulsion machinery to the propulsion shafting after passing through all speed-reducing and other transmission devices and after power for all attached auxiliaries has been taken off.

3. RESPONSIBILITIES

3.1 Shipbuilders Responsibilities

• The Shipbuilder has the responsibility for planning, conducting and evaluating the tri-als.

• Speed – Power - Trials may be conducted by institutions acknowledged as competent to perform those trials, as agreed between the Shipbuilder and the Ship owner

• The Shipbuilder has to provide all permits and certificates needed to go to sea.

• The Shipbuilder is responsible to ensure that all qualified personnel, needed for op-erating the ship and all engines, systems and equipment during the trials have been ordered.

• The Shipbuilder is responsible to ensure that all regulatory bodies, Classification Society, Ship Owner, ship agents, suppliers, subcontractors, harbor facilities, delivering departments of provisions, fuel, water, tow-ing, etc., needed for conducting the sea tri-als, have been informed and are available and on board, if required.

• It is the Shipbuilder’s responsibility that all safety measures have been checked and all fixed, portable and individual material (for crew, trial personnel and guests) is on board and operative.

• It is the Shipbuilder’s responsibility that dock trials of all systems have been exe-cuted as well as all alarms, warning and safety systems.

• It is the Shipbuilder’s responsibility that an inclining test has been performed and/or at least a preliminary stability booklet has been approved, covering the sea trial condi-tion, in accordance with the 1974 SOLAS Convention.

• The Shipbuilder is responsible for the over-all trial coordination between the ship's crew, trial personnel, and the owner repre-sentative. A pre-trial meeting between the trial team, owner and the ship’s crew will be held to discuss the various trial events and to resolve any outstanding issues.

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• The Shipbuilder has, if necessary, to ar-range for divers to inspect the ship’s hull and propellers.

• The Trial Leader is the duly authorized (shipbuilder’s representative) person re-sponsible for the execution of all phases of the Speed/Power trials including the pre-trial preparation.

3.2 The Trial Team

The trial team is responsible for correct measurements and analysis of the measured data according to the state of the art.

The trial team is responsible for the follow-ing:

a. Conduct ship inspection, if possible or necessary.

b. Provide, install and operate all required trial instrumentation and temporary ca-bling.

c. If previously arranged, provide the ship master and owner’s representative with a preliminary data package before de-barking. The contents of the data pack-age will be determined in consultation with the owner’s representative at the initial pre-trial briefing.

d. Provide a final report after completion of the trials in accordance with any agreement between the shipbuilder and the ship owner.

4. PROCEDURES

4.1 Trial Preparation

4.1.1 Shipbuilder’s Support Requirement:

Prior to the trials the required instrumenta-tion has to be installed. The assistance of the ship’s or shipbuilder’s crew will be required when making electrical connections to the ship's systems and circuits such as heading, wind speed, wind direction, and rudder angle synchronous repeaters. The following support is requested from the Shipbuilder to properly prepare for the trials:

a. Provide access to the ship for trial in-strumentation.

b. Assistance is required for the following electrical connections: • Gyrocompass • Wind meter • Rudder angle indicator • Log Speed • Propeller Pitch

c. Vary the output level of each of the above measurement sources to ensure the proper operation and alignment of the test instrumentation

4.1.2 Space Requirements

Spaces and an electric supply adequate for the trial equipment will be required for the trial instrumentation and computers.

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4.2 Ship Inspection

There are three stages of a ship inspection: in-house preparation, the actual inspection, and the reporting of results and distribution of in-formation to the various parties involved in the trial.

4.2.1 Preparation for the trials

• Review shafting dimensions, propulsion plant specifications, etc.

• Review trials agenda, if available.

4.2.2 Ship Inspection

• Inspect hull- and propeller surface con-dition, if possible.

• Inspect ship’s instrumentation for ac-cessibility.

• Determine routes for cable runs/data transfer conduits between trial room and bridge or control area.

• Contact the Engineer on duty to discuss trial instrumentation requirements. In-spect machinery spaces as applicable.

4.2.3 Reporting of Results and Distribution of Information

Document all pertinent information related to the ship inspection

a) Last date of cleaning.

b) Means of cleaning.

c) Propeller roughness measurement, if available, which should include aver-age, standard deviation, distribution

along the blades, and existing physical damage.

d) For a clean hull; documentation indi-cating manufacturer and kind of paint used, paint layer thickness and, if avail-able, roughness measurements (average, standard deviation, and distribution along the hull) should be provided. The majority of this information may be contained in the docking report.

e) For a dirty hull, documentation indi-cating visual observations of any foul-ing and date of last dry-docking should be provided.

4.3 Hull- and Propulsor Survey

A roughness survey is recommended to document the conditions of the ship hull, ap-pendages, and propulsor(s) prior to the start of the full-scale speed/ power trial. Cleaning may be required if fouling is found to be such that it would bias the trial data.

Ideally, roughness surveys should be con-ducted prior to the trials. The average hull roughness should not exceed 250 µm (µ = 1x10-6 m) (6.35 mils) and the average propul-sor roughness level should not be greater than 150 µm (3.81 mils).

4.4 Instrumentation Installation and Cali-bration

4.4.1 Instrumentation Installation

The installation of instrumentation should be scheduled at a time of minimal conflict with ship operations.

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The bias limits of the instrumentation used for the measurements should be known and as-sessed.

The instrumentation used for the on-board-measurements must be calibrated before appli-cation on board. If this is not possible, for some reason, the consequences of this should be highlighted in the final trial report. Electrical calibration is recommended for the torque measurement device and, in case of use during the sea trials, for the thrust measurement device. Further a calibration should be done for the pick ups and the respective amplifiers used for the measurement of the rate of revolutions. A “calibration” of a (differential) GPS-System is not possible without excessive measures, but at least the function of the device should be checked before use on board.

If portable radar tracking or (differential) GPS is utilized, a Receiver/Transmitter (R/T) unit or GPS antenna is to be installed. In case the soft ware program used for the evaluation of the data received does not allow for varying positions on the uppermost deck of the ship the antenna should be placed in a location along the ship’s centerline as close to the ship’s CG as possible. This location will ideally be lo-cated on a mast or site that is clear of obstruc-tions, such as the ship’s superstructure.

4.4.2 Instrumentation Calibration Check

All shipboard signals to be recorded during the trials must be adjusted to zero or should have their zero value checked (e.g. for a (D) GPS-device) after the instrumentation installa-tion is completed and prior to the trials. The zero values of the torsiometers, the thrust measurement devices and the devices for the

measurement of the rates of revolutions must be checked before the trial runs start and after they have been finished.

As part of the pre-trial calibration, the tor-sion meters zero torque readings must be de-termined since there is a residual torque in the shaft, which is resting on the line shaft bearings. This might be done in different ways; one pos-sible way is to use the jacking motors. The shaft is jacked both ahead and astern and the average of the readings noted. The zeroes are set at the midpoint of the torque required to jack each shaft ahead and the torque required to jack each shaft astern. An allowance is nor-mally made for frictional losses in the stern tube bearings.

As part of the pre-trial calibration for a ship equipped with controllable pitch propellers, maximum ahead pitch, the design pitch and the maximum astern pitch should be determined and then the ship indicators should be adjusted to reflect the measurement.

4.5 Trial Conditions

Speed/Power trials require accurate position data. The use of (D) GPS provides great lati-tude in choosing a trial site. Regardless of the instrumentation utilized for obtaining posi-tional data, the operational area should be free from substantial small boat traffic.

The tracking range should be agreed be-tween the Trial Director and the ship’s master.

Draft, trim and displacement of the ship on trials should be obtained by averaging the ship draft mark readings. The ship should be brought into a condition that is as close as pos-sible to the contract condition and/or the condi-

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tion on which model tests have been carried out. This will allow for the correction of the dis-placement and trim with respect to the trials that were conducted and will be applicable to the suggestions outlined in the ITTC Procedure for the Analysis of Speed/Power Trial Data.

Draft, trim and displacement should be ob-tained at the beginning and at the end of the trial. This may be accomplished using a load-ing computer or by taking a second draft read-ing. The accuracy of the draft readings and the method used to establish draft and displace-ment underway will be compared in port by di-rect draft readings both port and starboard in conjunction with a liquid load calculation.

Displacement should be derived from the hydrostatic curves by utilizing the draft data and the density of the water.

Environmental factors may significantly in-fluence the data obtained during sea trials; con-sequently, these factors should be monitored and documented to the greatest extent possible:

• High wind and sea states can force the use of excessive rudder to maintain heading, and thus cause excessive fluc-tuations in shaft torque, shaft speed and ship speed.

• Sea states of 3 or less and a true wind speed below Beaufort 6 (20 Kn) are the desired conditions for sea trials. When working under the time constraints of a contract, corrections to the trials data can be made in accordance with the rec-ommendations provided in the ITTC Procedure for the Analysis of Speed/Power Trial Data for sea states less than or equal to 5. For sea states

greater than 5, corrections to the trials data can be applied but are not consid-ered reliable from a scientific stand-point.

• The local seawater temperature and spe-cific gravity at the trial site are recorded to enable the calculation of ship's dis-placement.

• An acceptable minimum water depth for the trials where the data do not need to be corrected for shallow water can be calculated using: h > 6.0(Am)0.5 and h > 0.5 V2 (1) with Am= midship section area, [m2] V= ship speed, [m/s] The larger of the 2 values obtained from the two equations should be used.

• Current speed and direction should be determined in the test area by prognos-tic analysis. When current speed and di-rection is unknown, the ship’s global drift (also including wind effect) in some cases might be determined by a 360° turning test conducted at low ahead speed to magnify any environ-mental effect.

• The runs should be conducted into and against the waves; i.e., head and follow-ing seas, respectively. To ensure that tests are performed in comparable con-ditions, the data between reciprocal runs should be reviewed for consistency and/or anomalies. Individual speed runs conducted in the same conditions should be averaged with their reciprocal runs to take into account global drift.

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In accordance with ISO 15016 the follow-ing, general recommendations can be given:

4.5.1 Wind:

Wind speed and direction shall be measured as relative wind; continuous recording of rela-tive wind during each run is recommended. Care has to be taken whether the data derived from the wind indicator are reliable; checks, such as parallel measurements with a portable instrument, comparison of the data received from the wind indicator with wind speeds and directions received from local weather stations sufficiently close to the actual position of the ship or, if possible, calibration of the wind in-dicator (taking into consideration the effects of boundary layers of the superstructure on the measured values) in a wind tunnel are recom-mended.

It is suggested that wind force during the trial runs under no conditions should be higher than

• Beaufort 6 for ships with lengths equal or exceeding 100m and

• Beaufort 5 for ships shorter than 100m.

4.5.2 Sea State:

If possible, instruments such as buoys or in-struments onboard ships (e.g. seaway analysis radar) should be used to determine the wave height, wave period and direction of seas and swell. Considering usual practice the wave heights may be determined from observations by multiple, experienced observers, including the nautical staff on board.

During the trial runs the total wave height (double amplitude), which allows for the wave heights of seas and swell (see ISO 15016), should not exceed

• 3m for ships of 100m length and more and

• 1,5m for ships with lengths smaller than 100m

4.5.3 Current:

Current speed and direction shall be ob-tained either as part of the evaluation of run and counter-run of each double run, by direct measurement with a current gauge buoy or by use of nautical charts of the respective trial area. It is recommended to compare measured data with those included on the nautical charts.

4.6 Trial Conduct:

All speed trials shall be carried out using double runs, i.e. each run is followed by a re-turn run in the opposite direction, performed with the same engine settings.

The number of such double runs should not be less than three. This three runs should be at different engine settings.

The time necessary for a speed run depends on the ship’s speed, size and power. Steady state conditions should be achieved before the speed runs start. It is recommended that the time of one run should be as long as possible but should at least be 10 min.

The ideal path of a ship in a typical speed/power maneuver is shown in Figure 1:

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Steady ApproachMin 10 min

Steady Approach

Min. 10 min

Figure 1

Prior to the trial, the data specified below shall be recorded, based on measurements where relevant:

• Date • Trial area • Weather conditions • Air temperature • Mean water depth in the trial area • Water temperature and density • Draughts • Corresponding displacement • Propeller pitch in the case of a CPP

It is recommended to retain a record of the following factors, which should prove useful for verifying the condition of the ship at the time of the speed trial:

• Time elapsed since last hull and propel-ler cleaning

• Surface condition of hull and propeller.

The following data should be monitored and recorded on each run:

Clock time at commencement • Time elapsed over the measured dis-

tance • Ship heading • Ship’s speed over ground • Propeller rate of revolutions • Propeller shaft torque and/or brake

power • Water depth • Relative wind velocity and direction • Air temperature • Observed wave height (or: wave height

corresponding to observed and/or agreed wind conditions)

• Rudder angle • Ship position and track

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Data such as ship’s speed, rate of revolu-tions of the propeller, torque, rudder angle and drift angle to be used for the analyses shall be the average values derived on the measured distance.

5. REFERENCES

(1) ISO 15016, Ships and marine technology – Guidelines for the assessment of speed and power performance by analysis of speed trial data

(2) ITTC Procedure for the Analysis of Speed/Power Trial Data

(3) ISO 19019

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Apendice CCondicoes de Realizacao das Provas

de Velocidade e Potencia

Recomendadas pela ITTC

133

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134 APENDICE C. CONDICOES DAS PROVAS DE VELOCIDADE E POTENCIA

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Updated by Approved

Specialist Committee of 23rd ITTC on Speed and Powering

23rd ITTC 2002

Date Date 2002

CONTENTS 1. PURPOSE

2. SCOPE

3. RESPONSIBILITIES

4. DEFINITIONS

5. PROCEDURE

6. REFERENCES

7. RECORDS

8. ATTACHMENTS

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Trial Conditions

1. PURPOSE

The purpose of this procedure is to estab-lish guidelines for the definition of acceptable limits for trial conditions needed to validate hydrodynamic design and/or satisfy contractual requirements.

2. SCOPE

This procedure applies to the documenta-tion of trial conditions (environmental and ship) in which the full-scale Speed/Power trial are performed.

3. RESPONSIBILITIES

• The Trial Director is the duly authorized shipbuilder’s representative responsible for the execution of all phases of the Speed/Power trials. When unforeseen prob-lems, such as weather or technical difficul-ties require that the trial schedule or trial logistics be modified, the Trial Director shall make the final decision, subject to the concurrence of the ship’s master and the owner’s representative.

• The shipbuilder is responsible for the over-all trial coordination between the ship's crew, trial personnel, and the owner repre-sentative. A pre-trial meeting between the trial team, owner and the ship’s crew will be held to discuss the various trial events and to resolve any outstanding issues.

• The trial team is responsible for the follow-ing: a. Operate and maintain all required trial

instrumentation and temporary cabling.

b. Collect and record seawater tempera-ture and specific gravity during trial, daily.

4. DEFINITIONS

None

5. PROCEDURE

1. Speed/Power trials require accurate posi-tion data and therefore will ideally be con-ducted at an instrumented tracking range located in a sheltered body of water. Lack-ing availability of an instrumented tracking range, the use of DGPS provides great lati-tude in choosing a trial site. Regardless of the instrumentation utilized for obtaining positional data, the operational area should be free from substantial small boat traffic.

2. If an instrumented tracking range is util-ized, the ship’s master will receive a formal briefing on tracking range procedures by the Trial Director prior to the conduct of the trials. During the briefing, specific trial runs will be reviewed. The trial team will provide an on-shore observer to monitor data collection by the tracking range facil-ity. If DGPS is utilized, the Trial Director will brief the ship’s master on specific trial runs and procedures.

3. Ship characteristics and environmental fac-tors are carefully monitored and docu-mented throughout the trials (see Table 1). Accurate quantification of these conditions is necessary because a ship's speed and powering characteristics are extremely sen-sitive to conditions such as ship and propel-ler condition, ship displacement, shallow water effects, sea state and wind velocity.

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4. Speed/Power Trials are normally scheduled within 30 days of undocking to minimize the adverse effects of hull and propulsor fouling and provide a more "standard" con-dition for testing. In situations where the ship has become fouled after undocking, a hull cleaning, propeller polishing and hull and propeller roughness survey should be performed within 30 days of the Speed/Power trial date. Guidance may be found in Hull and Propulsor Survey Proce-dure 7.5-04-01-01.3. At a minimum, the ship’s latest docking report and diver in-spection should be provided to fulfill this requirement. Guidance may be found in Speed/Power Trial Ship Inspection Proce-dure 7.5-04-01-01.2.

5. Draft, trim and displacement of the trials must be obtained by averaging the ship draft mark readings. The ship should be brought into a condition that is as close as possible to the contract condition and/or the condition by which model tests have been carried out. This will allow for the correc-tion of the displacement and trim with re-spect to the trials that were conducted and will be applicable to the suggestions out-lined in the 23rd ITTC Speed and Powering Trials Specialist Committee final report. a. Draft, trim and displacement must be

obtained at the beginning and at the end of the trial. This may be accomplished using a loading computer or by taking a second draft reading. The accuracy of the ship's draft marks and the method used to calculate draft and displacement underway will be compared in port by direct draft readings both port and star-board in conjunction with a liquid load calculation. The trial team will verify and document the results prior to the Speed/Power trials.

b. Displacement must be derived from the hydrostatic curves by utilizing the draft data and the density of the water. When dealing with Froude numbers higher than 0.5 (e.g. a Fast Ferry with 100 m length and speed over 30 kn) intermedi-ate ship loading conditions must be documented. This is better accom-plished through tank soundings.

6. Environmental factors can significantly in-fluence the data obtained during sea trials. Consequently, these factors must be moni-tored and documented to the greatest extent possible. a. High wind and sea states can force the

use of excessive rudder to maintain heading, and thus cause excessive fluc-tuations in shaft torque, shaft speed and ship speed.

b. Sea states of 3 or less and a true wind speed below Beaufort 6 (20 kn) are the desired conditions for sea trials. When working under the time constraints of a contract, corrections to the trials data can be made in accordance with the rec-ommendations provided in the 23rd ITTC Speed and Powering Trials Spe-cialist Committee final report for sea states less than or equal to 5. For sea states greater than 5, corrections to the trials data can be applied but are not considered reliable from a scientific standpoint.

c. The local seawater temperature and spe-cific gravity at the trial site are recorded to enable the calculation of ship's dis-placement.

d. Air temperature and atmospheric pres-sure should be measured at the trial lo-cation using a calibrated thermometer and barometer.

e. An acceptable minimum water depth for the trials where the data do not need to be cor-

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rected for shallow water can be calculated using:

h > 6.0(Am)0.5 and h > 0.5 V2 (1)

Use the larger of the 2 values obtained from the two equations.

Other accepted formulae are:

1. SNAME 1973/21st ITTC Powering

Performance Committee d ≥ 10TV/(L)0.5 (2) d = water depth, ft T =´trial draft, ft V = speed, kn L = length between perpendicu-lars, ft

2. SNAME 1989 from Det Norske

Veritas Nautical Safety- Additional Classes NAUT-A, NAUT-B AND NAUT-C, July 1986 h > 5.0(Am)0.5 and h > 0.4 V2 (3) Use the larger of the 2 values ob-tained from the two equations. h = water depth, m Am = midship section area, m2

V = ship speed, m/s or h > 5 (T) (4) T = Mean draft, m

3. 22nd ITTC Trials & Monitoring Specialist Committee/12th ITTC based on ship section and Froude Number. h > 3.0(BT)0.5 and h > 2.75 V2/g (5) Use the larger of the 2 values ob-tained from the two equations. h = depth in appropriate length units B = beam in appropriate length units T = draft in appropriate length units V = speed in system of units con-sistent with the above dimension g = acceleration due to gravity in units consistent with the above di-mension

4. ISO/FDIS 15016:(E) based on Lack-

enby’s Formula

∆VV

= 0.1242A m

h2 − 0.05

+1 − tanh(

ghV2 )

0.5

for h ≤ (Am/0.05)0.5 (6) ∆VV

≤ 0.02

h = water depth, m Am = midship section area under water, m2 V = ship speed, m/s ∆V = speed loss due to shallow wa-ter effect, m/s g = acceleration due to gravity, m/s2

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f. Current speed and direction should be determined in the test area by prognos-tic analysis. When current speed is sus-pected to be varying and direction is unknown, the ship’s global drift (also including wind effect) should be deter-mined by a 360° turning test conducted at low ahead speed to magnify any en-vironmental effect. Test runs should be conducted against and with global drift. It should be noted that this method of determining the direction of the trial runs is extremely important in the case of small ships whose performance is strongly effected by environmental con-ditions. For large ships, such as ULCCs, performance is not impacted as greatly by environmental conditions. If time is a critical factor, then the runs can be conducted into and against the waves; i.e., head and following seas, re-spectively. To ensure that tests are per-formed in comparable conditions, the data between reciprocal runs should be reviewed for consistency and/or anoma-lies. Individual speed runs conducted in the same conditions should be averaged with their reciprocal runs to take into account global drift.

6. REFERENCES

1. SNAME 1973/21st ITTC Powering Per-formance Committee Final Report

2. 22nd ITTC Trials & Monitoring Specialist Committee Final Report

3. Ships and marine technology – Guidelines for the assessment of speed and power per-formance analysis of speed trial data, Final Draft International Standard ISO/FDIS 15016: (E), ISO/TC 8/SC 9/WG 2 of 2001

4. 23rd ITTC Speed and Powering Trials Spe-cialist Committee Final Report

5. Speed/Power Trial Ship Inspection Proce-dure 7.5-04-01-01.2

6. Hull and Propulsor Survey Procedure 7.5-04-01-01.3

7. RECORDS

1. Ship conditions – displacement, draft, pro-pulsor and hull roughness

2. Environmental conditions – water depth, water temperature, wind direction and speed, sea state, specific gravity, air tem-perature, atmospheric pressure, current speed and direction

8. ATTACHMENTS

1. Table 1. Documented Ship and Trial Con-ditions Reported

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Table 1. Documented Ship and Trial Conditions Reported

DescriptionShip HullDraftTrimDisplacement and Load

Hull ConditionRoughness of shell and bottom paintHeight of welding beadsWaviness of hullSize, number and position of zinc anodesSize, number and position of openings of sea water inlets and outletsPaint system

Hull Appendages and RudderGeometry, deviations, roughnessTypeRate of movement

Propeller(s)Geometry, deviations, roughnessPitchDirection of rotationNumber of blades

Propeller Shaft(s)GeometryMaterial

Trial SiteWater depthWater temperatureAir temperatureSea StateSpecific gravity of water

Environmental ConditionsWindWavesCurrentAtmospheric pressure

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Seleccao de Motores Propulsores

141

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142 APENDICE D. SELECCAO DE MOTORES PROPULSORES

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Contents:

Basic Principles of Ship Propulsion

Page

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Scope of this Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Chapter 1Ship Definitions and Hull Resistance . . . . . . . . . . . . . . . . . . 4

• Ship types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

• A ship’s load lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

• Indication of a ship’s size . . . . . . . . . . . . . . . . . . . . . . . . 5

• Description of hull forms . . . . . . . . . . . . . . . . . . . . . . . . 5

• Ship’s resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Chapter 2Propeller Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

• Propeller types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

• Flow conditions around the propeller . . . . . . . . . . . . . . . . . . 11

• Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . · · · · 11

• Propeller dimensions . . . . . . . . . . . . . . . . . . . . . . · · · · 13

• Operating conditions of a propeller . . . . . . . . . . . . . . . . . . . 15

Chapter 3Engine Layout and Load Diagrams . . . . . . . . . . . . . . . . . . 20

• Power functions and logarithmic scales . . . . . . . . . . . . . . . . . 20

• Propulsion and engine running points . . . . . . . . . . . . . . . . . . 20

• Engine layout diagram . . . . . . . . . . . . . . . . . . . . . . . . . 22

• Load diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

• Use of layout and load diagrams – examples . . . . . . . . . . . . . . 25

• Influence on engine running of different typesof ship resistance – plant with FP�propeller . . . . . . . . . . . . . . . 27

• Influence of ship resistanceon combinator curves – plant with CP�propeller . . . . . . . . . . . . 29

Closing Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

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Introduction

For the purpose of this paper, the term“ship” is used to denote a vehicle em�ployed to transport goods and personsfrom one point to another over water.Ship propulsion normally occurs withthe help of a propeller, which is theterm most widely used in English, al�though the word “screw” is sometimesseen, inter alia in combinations such asa “twin�screw” propulsion plant.

Today, the primary source of propellerpower is the diesel engine, and the powerrequirement and rate of revolution verymuch depend on the ship’s hull formand the propeller design. Therefore, inorder to arrive at a solution that is asoptimal as possible, some generalknowledge is essential as to the princi�pal ship and diesel engine parametersthat influence the propulsion system.

This paper will, in particular, attempt toexplain some of the most elementaryterms used regarding ship types,ship’s dimensions and hull forms andclarify some of the parameters pertain�ing to hull resistance, propeller condi�tions and the diesel engine’s loaddiagram.

On the other hand, it is considered be�yond the scope of this publication togive an explanation of how propulsioncalculations as such are carried out, asthe calculation procedure is extremelycomplex. The reader is referred to thespecialised literature on this subject, forexample as stated in “References”.

Scope of this Paper

This paper is divided into three chapterswhich, in principle, may be considered asthree separate papers but which also,with advantage, may be read in closeconnection to each other. Therefore,some important information mentioned inone chapter may well appear in anotherchapter, too.

Chapter 1, describes the most elemen�tary terms used to define ship sizesand hull forms such as, for example,the ship’s displacement, deadweight,design draught, length between per�pendiculars, block coefficient, etc.Other ship terms described include theeffective towing resistance, consistingof frictional, residual and air resistance,and the influence of these resistancesin service.

Chapter 2, deals with ship propulsionand the flow conditions around the pro�peller(s). In this connection, the wakefraction coefficient and thrust deduc�tion coefficient, etc. are mentioned.

The total power needed for the propel�ler is found based on the above effec�tive towing resistance and variouspropeller and hull dependent efficien�cies which are also described. A sum�mary of the propulsion theory is shownin Fig. 6.

The operating conditions of a propelleraccording to the propeller law valid fora propeller with fixed pitch are describedfor free sailing in calm weather, and

followed up by the relative heavy/lightrunning conditions which apply whenthe ship is sailing and subject to differenttypes of extra resistance, like fouling,heavy sea against, etc.

Chapter 3, elucidates the importanceof choosing the correct specified MCRand optimising point of the main engine,and thereby the engine’s load diagramin consideration to the propeller’s designpoint. The construction of the relevantload diagram lines is described in detailby means of several examples. Fig. 24shows, for a ship with fixed pitch pro�peller, by means of a load diagram, theimportant influence of different types ofship resistance on the engine’s contin�uous service rating.

3

Basic Principles of Ship Propulsion

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Ship Definitions and HullResistance

Ship types

Depending on the nature of their cargo,and sometimes also the way the cargois loaded/unloaded, ships can be dividedinto different categories, classes, andtypes, some of which are mentioned inTable 1.

The three largest categories of shipsare container ships, bulk carriers (forbulk goods such as grain, coal, ores,etc.) and tankers, which again can bedivided into more precisely definedclasses and types. Thus, tankers canbe divided into oil tankers, gas tankersand chemical tankers, but there arealso combinations, e.g. oil/chemicaltankers.

Table 1 provides only a rough outline.In reality there are many other combi�nations, such as “Multi�purpose bulkcontainer carriers”, to mention just oneexample.

A ship’s load lines

Painted halfway along the ship’s sideis the “Plimsoll Mark”, see Fig. 1. Thelines and letters of the Plimsoll Mark,which conform to the freeboard ruleslaid down by the IMO (InternationalMaritime Organisation) and local au�thorities, indicate the depth to whichthe vessel may be safely loaded (thedepth varies according to the seasonand the salinity of the water).

There are, e.g. load lines for sailing infreshwater and seawater, respectively,with further divisions for tropical condi�tions and summer and winter sailing.According to the international freeboardrules, the summer freeboard draughtfor seawater is equal to the “Scantlingdraught”, which is the term applied tothe ship’s draught when dimensioningthe hull.

The winter freeboard draught is lessthan that valid for summer because of

the risk of bad weather whereas, on theother hand, the freeboard draught for

tropical seas is somewhat higher thanthe summer freeboard draught.

4

Category Class Type

TankerOil tanker

Gas tankerChemical tanker

OBO

Crude (oil) CarrierVery Large Crude CarrierUltra Large Crude CarrierProduct Tanker

Liquefied Natural Gas carrierLiquefied Petroleum Gas carrier

Oil/Bulk/Ore carrier

CCVLCCULCC

LNGLPG

OBO

Bulk carrier Bulk carrier

Container ship Container shipContainer carrierRoll On�Roll Off Ro�Ro

General cargo shipGeneral cargoCoaster

Reefer Reefer Refrigerated cargo vessel

Passenger shipFerryCruise vessel

Table 1: Examples of ship types

T TropicalS SummerW WinterWNA Winter - the North Atlantic

D L

D: Freeboard draught

SeawaterFreshwater

Danish load mark

TF

F

D

Freeboard deck

Fig. 1: Load lines – freeboard draught

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Indication of a ship’s size

Displacement and deadweightWhen a ship in loaded condition floats atan arbitrary water line, its displacement isequal to the relevant mass of water dis�placed by the ship. Displacement is thusequal to the total weight, all told, of therelevant loaded ship, normally in seawa�ter with a mass density of 1.025 t/m3.

Displacement comprises the ship’slight weight and its deadweight, wherethe deadweight is equal to the ship’sloaded capacity, including bunkers andother supplies necessary for the ship’spropulsion. The deadweight at any timethus represents the difference betweenthe actual displacement and the ship’slight weight, all given in tons:

deadweight = displacement – light weight.

Incidentally, the word “ton” does notalways express the same amount ofweight. Besides the metric ton (1,000kg), there is the English ton (1,016 kg),which is also called the “long ton”. A“short ton” is approx. 907 kg.

The light weight of a ship is not normallyused to indicate the size of a ship,whereas the deadweight tonnage(dwt), based on the ship’s loading ca�pacity, including fuel and lube oils etc.for operation of the ship, measured intons at scantling draught, often is.

Sometimes, the deadweight tonnagemay also refer to the design draught ofthe ship but, if so, this will be mentioned.Table 2 indicates the rule�of�thumb rela�tionship between the ship’s displacement,deadweight tonnage (summer freeboard/scantling draught) and light weight.

A ship’s displacement can also be ex�pressed as the volume of displacedwater ∇, i.e. in m3.

Gross register tonsWithout going into detail, it should bementioned that there are also suchmeasurements as Gross Register Tons(GRT), and Net Register Tons (NRT)where 1 register ton = 100 English cubicfeet, or 2.83 m3.

These measurements express the sizeof the internal volume of the ship in ac�cordance with the given rules for suchmeasurements, and are extensivelyused for calculating harbour and canaldues/charges.

Description of hull forms

It is evident that the part of the shipwhich is of significance for its propulsion

is the part of the ship’s hull which isunder the water line. The dimensionsbelow describing the hull form referto the design draught, which is lessthan, or equal to, the scantlingdraught. The choice of the designdraught depends on the degree ofload, i.e. whether, in service, the shipwill be lightly or heavily loaded. Gen�erally, the most frequently occurringdraught between the fully�loaded andthe ballast draught is used.

Ship’s lengths LOA, LWL, and LPP

The overall length of the ship LOA isnormally of no consequence whencalculating the hull’s water resistance.The factors used are the length of thewaterline LWL and the so�called lengthbetween perpendiculars LPP. The di�mensions referred to are shown inFig. 2.

5

Ship type dwt/lightweight ratio

Displ./dwtratio

Tanker andBulk carrier 6 1.17

Container ship 2.5�3.0 1.33�1.4

Table 2: Examples of relationship between dis�placement, deadweight tonnage and light weight

L

L

L

PP

WL

OA

AM

DA

BWL

DF

D

Length between perpendiculars: LLength on waterline: LLength o : LBreadth on waterline: BDraught: D = 1/2 (D +D )Midship section area: A

PP

WL

OA

WL

m

F A

verall

Fig. 2: Hull dimensions

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The length between perpendiculars isthe length between the foremost per�pendicular, i.e. usually a vertical linethrough the stem’s intersection withthe waterline, and the aftmost perpen�dicular which, normally, coincides withthe rudder axis. Generally, this length isslightly less than the waterline length,and is often expressed as:

LPP = 0.97 × LWL

Draught DThe ship’s draught D (often T is used inliterature) is defined as the vertical dis�tance from the waterline to that point ofthe hull which is deepest in the water,see Figs. 2 and 3. The foremost draughtDF and aftmost draught DA are normallythe same when the ship is in the loadedcondition.

Breadth on waterline BWLAnother important factor is the hull’slargest breadth on the waterline BWL,see Figs. 2 and 3.

Block coefficient CB

Various form coefficients are used toexpress the shape of the hull. The mostimportant of these coefficients is theblock coefficient CB, which is definedas the ratio between the displacementvolume ∇ and the volume of a box withdimensions LWL × BWL × D, see Fig. 3, i.e.:

CL B DB

WL WL

=∇

× ×

In the case cited above, the block co�efficient refers to the length on water�line LWL. However, shipbuilders often useblock coefficient CB, PP based on thelength between perpendiculars, LPP, inwhich case the block coefficient will, as arule, be slightly larger because, as previ�ously mentioned, LPP is normally slightlyless than LWL.

CL B DB PP

PP WL

, =∇

× ×

A small block coefficient means less re�sistance and, consequently, the possibil�ity of attaining higher speeds.

Table 3 shows some examples of blockcoefficient sizes, and the pertaining

service speeds, on different types ofships. It shows that large block coeffi�cients correspond to low speeds andvice versa.

Ship typeBlock

coefficientCB

Approxi�mate shipspeed Vin knots

Lighter 0.90 5 – 10

Bulk carrier 0.80 – 0.85 12 – 17

Tanker 0.80 – 0.85 12 –16

General cargo 0.55 – 0.75 13 – 22

Container ship 0.50 – 0.70 14 – 26

Ferry boat 0.50 – 0.70 15 – 26

Table 3: Examples of block coefficients

Water plane area coefficient CWL

The water plane area coefficient CWL

expresses the ratio between the ves�sel’s waterline area AWL and the productof the length LWL and the breadth BWL ofthe ship on the waterline, see Fig. 3, i.e.:

CA

L BWL

WL

WL WL

Generally, the waterplane area coeffi�cient is some 0.10 higher than the blockcoefficient, i.e.:

CWL ≅ CB + 0.10.

This difference will be slightly larger onfast vessels with small block coefficientswhere the stern is also partly immersedin the water and thus becomes part ofthe ”waterplane” area.

Midship section coefficient CM

A further description of the hull form isprovided by the midship section coeffi�cient CM, which expresses the ratio be�tween the immersed midship sectionarea AM (midway between the foremostand the aftmost perpendiculars) and theproduct of the ship’s breadth BWL anddraught D, see Fig. 3, i.e.:

CA

B DM

M

WL

6

LWL

AWL

BWL

DAMWaterline plane

LPP

,

Midship section coefficient

Volume of displacement

Waterline area

Block coefficient L based

Waterplane area coefficient

WL

Longitudinal prismatic coefficient

:

:

: =

: =

: =

: =

A

C

C

C

C

B

WL

M

P

L BWL x x DWL

B x DWL

A x LM WL

L BWL WLxAWL

AM

WL

Fig. 3: Hull coefficients of a ship

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For bulkers and tankers, this coefficientis in the order of 0.98�0.99, and forcontainer ships in the order of 0.97�0.98.

Longitudinal prismatic coefficient CP

The longitudinal prismatic coefficientCP expresses the ratio between dis�placement volume ∇ and the productof the midship frame section area AM

and the length of the waterline LWL,see also Fig. 3, i.e.:

CA L C B D L

C

Cp

M WL M WL WL

B

M

=∇×

=∇

× × ×=

As can be seen, CP is not an independ�ent form coefficient, but is entirely de�pendent on the block coefficient CB

and the midship section coefficient CM.

Longitudinal Centre of Buoyancy LCBThe Longitudinal Centre of Buoyancy(LCB) expresses the position of thecentre of buoyancy and is defined asthe distance between the centre ofbuoyancy and the mid�point betweenthe ship’s foremost and aftmost perpen�diculars. The distance is normally statedas a percentage of the length betweenthe perpendiculars, and is positive ifthe centre of buoyancy is located tothe fore of the mid�point between theperpendiculars, and negative if locatedto the aft of the mid�point. For a shipdesigned for high speeds, e.g. containerships, the LCB will, normally, be nega�tive, whereas for slow�speed ships,such as tankers and bulk carriers, it willnormally be positive. The LCB is gener�ally between �3% and +3%.

Fineness ratio CLD

The length/displacement ratio or fine�ness ratio, CLD, is defined as the ratiobetween the ship’s waterline length LWL,and the length of a cube with a volumeequal to the displacement volume, i.e.:

CL

LD

WL=∇3

Ship’s resistance

To move a ship, it is first necessary toovercome resistance, i.e. the force work�ing against its propulsion. The calculationof this resistance R plays a significant role

in the selection of the correct propeller andin the subsequent choice of main engine.

GeneralA ship’s resistance is particularly influ�enced by its speed, displacement, andhull form. The total resistance RT, con�sists of many source�resistances Rwhich can be divided into three maingroups, viz.:

1) Frictional resistance2) Residual resistance3) Air resistance

The influence of frictional and residualresistances depends on how much ofthe hull is below the waterline, while theinfluence of air resistance depends onhow much of the ship is above the wa�terline. In view of this, air resistance willhave a certain effect on container shipswhich carry a large number of contain�ers on the deck.

Water with a speed of V and a densityof � has a dynamic pressure of:

½ × � × V 2 (Bernoulli’s law)

Thus, if water is being completelystopped by a body, the water will reacton the surface of the body with the dy�namic pressure, resulting in a dynamicforce on the body.

This relationship is used as a basiswhen calculating or measuring thesource�resistances R of a ship’s hull,by means of dimensionless resistancecoefficients C. Thus, C is related to thereference force K, defined as the forcewhich the dynamic pressure of waterwith the ship’s speed V exerts on asurface which is equal to the hull’s wet�ted area AS. The rudder’s surface isalso included in the wetted area. Thegeneral data for resistance calculationsis thus:

Reference force: K = ½ × � × V 2 × AS

and source resistances: R = C × K

On the basis of many experimentaltank tests, and with the help of pertain�ing dimensionless hull parameters,some of which have already been dis�cussed, methods have been estab�lished for calculating all the necessary

resistance coefficients C and, thus, thepertaining source�resistances R. Inpractice, the calculation of a particularship’s resistance can be verified bytesting a model of the relevant ship ina towing tank.

Frictional resistance RF

The frictional resistance RF of the hulldepends on the size of the hull’s wet�ted area AS, and on the specific fric�tional resistance coefficient CF. Thefriction increases with fouling of thehull, i.e. by the growth of, i.a. algae,sea grass and barnacles.

An attempt to avoid fouling is made bythe use of anti�fouling hull paints toprevent the hull from becoming“long�haired”, i.e. these paints reducethe possibility of the hull becomingfouled by living organisms. The paintscontaining TBT (tributyl tin) as theirprincipal biocide, which is very toxic,have dominated the market for decades,but the IMO ban of TBT for new appli�cations from 1 January, 2003, and afull ban from 1 January, 2008, may in�volve the use of new (and maybe notas effective) alternatives, probably cop�per�based anti�fouling paints.

When the ship is propelled through thewater, the frictional resistance increasesat a rate that is virtually equal to thesquare of the vessel’s speed.

Frictional resistance represents a con�siderable part of the ship’s resistance,often some 70�90% of the ship’s totalresistance for low�speed ships (bulkcarriers and tankers), and sometimesless than 40% for high�speed ships(cruise liners and passenger ships) [1]. Thefrictional resistance is found as follows:

RF = CF × K

Residual resistance RR

Residual resistance RR comprises waveresistance and eddy resistance. Waveresistance refers to the energy losscaused by waves created by the vesselduring its propulsion through the water,while eddy resistance refers to the losscaused by flow separation which cre�ates eddies, particularly at the aft endof the ship.

7

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Wave resistance at low speeds is pro�portional to the square of the speed,but increases much faster at higherspeeds. In principle, this means that aspeed barrier is imposed, so that a fur�ther increase of the ship’s propulsionpower will not result in a higher speedas all the power will be converted intowave energy. The residual resistancenormally represents 8�25% of the totalresistance for low�speed ships, and upto 40�60% for high�speed ships [1].

Incidentally, shallow waters can alsohave great influence on the residualresistance, as the displaced water un�der the ship will have greater difficultyin moving aftwards.

The procedure for calculating the spe�cific residual resistance coefficient CR isdescribed in specialised literature [2]and the residual resistance is found asfollows:

RR = CR × K

Air resistance RA

In calm weather, air resistance is, in prin�ciple, proportional to the square of theship’s speed, and proportional to thecross�sectional area of the ship above thewaterline. Air resistance normally repre�sents about 2% of the total resistance.

For container ships in head wind, theair resistance can be as much as 10%.The air resistance can, similar to theforegoing resistances, be expressed asRA = CA × K, but is sometimes basedon 90% of the dynamic pressure of airwith a speed of V, i.e.:

RA = 0.90 × ½ × �air × V 2 × Aair

where �air is the density of the air, andAair is the cross�sectional area of thevessel above the water [1].

Towing resistance RT

and effective (towing) power PE

The ship’s total towing resistance RT isthus found as:

RT = RF + RR + RA

The corresponding effective (towing)power, PE, necessary to move the ship

through the water, i.e. to tow the shipat the speed V, is then:

PE = V × RT

The power delivered to the propeller,PD, in order to move the ship at speedV is, however, somewhat larger. This isdue, in particular, to the flow conditionsaround the propeller and the propellerefficiency itself, the influences of whichare discussed in the next chapterwhich deals with Propeller Propulsion.

Total ship resistance in generalWhen dividing the residual resistanceinto wave and eddy resistance, as earlierdescribed, the distribution of the total shiptowing resistance RT could also, as aguideline, be stated as shown in Fig. 4.

The right column is valid for low�speedships like bulk carriers and tankers, andthe left column is valid for very high�speedships like cruise liners and ferries. Con�tainer ships may be placed in betweenthe two columns.

The main reason for the differencebetween the two columns is, as earliermentioned, the wave resistance. Thus,in general all the resistances are pro�portional to the square of the speed,but for higher speeds the wave resis�tance increases much faster, involvinga higher part of the total resistance.

This tendency is also shown in Fig. 5for a 600 teu container ship, originallydesigned for the ship speed of 15 knots.Without any change to the hull design,

8

RF

V

RA

V

RW

RE

Ship speed V

% of RTType of resistance

RA

RW

RE

RF = Friction= Wave= Eddy= Air

Highspeed

ship

Lowspeedship

45 � 9040 � 5

5 � 310 � 2

Fig. 4: Total ship towing resistance RT = RF + RW + RE + RA

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the ship speed for a sister ship was re�quested to be increased to about 17.6knots. However, this would lead to arelatively high wave resistance, requir�ing a doubling of the necessary propul�sion power.

A further increase of the propulsionpower may only result in a minor shipspeed increase, as most of the extrapower will be converted into wave en�ergy, i.e. a ship speed barrier valid forthe given hull design is imposed bywhat we could call a “wave wall”, seeFig. 5. A modification of the hull lines,suiting the higher ship speed, is neces�sary.

Increase of ship resistance in service,Ref. [3], page 244During the operation of the ship, thepaint film on the hull will break down.Erosion will start, and marine plantsand barnacles, etc. will grow on thesurface of the hull. Bad weather, per�haps in connection with an inappropri�ate distribution of the cargo, can be areason for buckled bottom plates. Thehull has been fouled and will no longerhave a “technically smooth” surface,

which means that the frictional resist�ance will be greater. It must also beconsidered that the propeller surfacecan become rough and fouled. The to�tal resistance, caused by fouling, mayincrease by 25�50% throughout thelifetime of a ship.

Experience [4] shows that hull foulingwith barnacles and tube worms maycause an increase in drag (ship resis�tance) of up to 40%, with a drasticalreduction of the ship speed as the con�sequence.

Furthermore, in general [4] for every 25µm (25/1000 mm) increase of the aver�age hull roughness, the result will be apower increase of 2�3%, or a shipspeed reduction of about 1%.

Resistance will also increase becauseof sea, wind and current, as shown inTable 4 for different main routes ofships. The resistance when navigatingin head�on sea could, in general, in�crease by as much as 50�100% of thetotal ship resistance in calm weather.

Estimates of average increase inresistance for ships navigating themain routes:

North Atlantic route,navigation westward 25�35%

North Atlantic route,navigation eastward 20�25%

Europe�Australia 20�25%

Europe�East Asia 20�25%

The Pacific routes 20�30%

Table 4: Main routes of ships

On the North Atlantic routes, the firstpercentage corresponds to summernavigation and the second percentageto winter navigation.

However, analysis of trading conditionsfor a typical 140,000 dwt bulk carriershows that on some routes, especiallyJapan�Canada when loaded, the in�creased resistance (sea margin) canreach extreme values up to 220%, withan average of about 100%.

Unfortunately, no data have been pub�lished on increased resistance as a function of type and size of vessel. Thelarger the ship, the less the relative in�crease of resistance due to the sea.On the other hand, the frictional resis�tance of the large, full�bodied ships willvery easily be changed in the course oftime because of fouling.

In practice, the increase of resistancecaused by heavy weather depends onthe current, the wind, as well as thewave size, where the latter factor mayhave great influence. Thus, if the wavesize is relatively high, the ship speedwill be somewhat reduced even whensailing in fair seas.

In principle, the increased resistancecaused by heavy weather could berelated to:

a) wind and current against, andb) heavy waves,

but in practice it will be difficult to dis�tinguish between these factors.

9

Power and speed relationship for a 600 TEU container ship

20 knots

6,000

Normal service point

Ship speed

Propulsion power

10 15

4,000

2,000

0

8,000"Wave wall"

New service point

kW

Fig. 5: The “wave wall” ship speed barrier

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Chapter 2

Propeller Propulsion

The traditional agent employed tomove a ship is a propeller, sometimestwo and, in very rare cases, more thantwo. The necessary propeller thrust Trequired to move the ship at speed Vis normally greater than the pertainingtowing resistance RT, and the flow�relatedreasons are, amongst other reasons,explained in this chapter. See also Fig. 6,where all relevant velocity, force, powerand efficiency parameters are shown.

Propeller types

Propellers may be divided into the follow�ing two main groups, see also Fig. 7:

• Fixed pitch propeller (FP�propeller)

• Controllable pitch propeller(CP�propeller)

Propellers of the FP�type are cast inone block and normally made of a copperalloy. The position of the blades, andthereby the propeller pitch, is once andfor all fixed, with a given pitch that can�not be changed in operation. Thismeans that when operating in, for ex�ample, heavy weather conditions, thepropeller performance curves, i.e. thecombination of power and speed(r/min) points, will change according tothe physical laws, and the actual pro�peller curve cannot be changed by thecrew. Most ships which do not need aparticularly good manoeuvrability areequipped with an FP�propeller.

Propellers of the CP�type have a rela�tively larger hub compared with theFP�propellers because the hub has tohave space for a hydraulically activatedmechanism for control of the pitch (an�gle) of the blades. The CP�propeller isrelatively expensive, maybe up to 3�4times as expensive as a correspondingFP�propeller. Furthermore, because ofthe relatively larger hub, the propellerefficiency is slightly lower.

CP�propellers are mostly used forRo�Ro ships, shuttle tankers and simi�lar ships that require a high degree of

10

Efficiencies1 t1 w

Relative rotative efficiency :Propeller efficiency � open water :Propeller efficiency � behind hull : =Propulsive efficiency : =Shaft efficiency :Total efficiency :

__

x

x

VelocitiesShip’s speed : VArriving water velocity to propeller : V

Effective wake velocity : V = V _ V

A

W A

ForcesTowing resistance : R

Thrust force : TThrust deduction fraction : F = T _ R

T _ RT

T

T

T

PowerEffective (Towing) power : P = R V

by the propeller to water : P = P /

Power delivered to propeller : P = P /

Brake power of main engine : P = P /

E T

T E

D T

B D

x

Thrust deduction coefficient : t =

Hull efficiency : =

Thrust power delivered

H

H

B

D

S

T B

S

B

0 R

T

���� ���� x ���� x ���� x x x x x= = = =P P P PB T D B

P P P PE E T D

H

S H 0 R SH

VA

V

VW

PD PEPT PB

V

TRT

F

Wake fraction coefficient : w =

R

0

B

(Speed of advance of propeller)

V _ V

VA

Fig. 6: The propulsion of a ship – theory

Controllable pitch propeller (CP�Propeller)Fixed pitch propeller (FP�Propeller)

Monobloc with fixedpropeller blades(copper alloy)

Hub with a mechanismfor control of the pitchof the blades(hydraulically activated)

Fig. 7: Propeller types

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manoeuvrability. For ordinary ships likecontainer ships, bulk carriers and crudeoil tankers sailing for a long time in nor�mal sea service at a given ship speed,it will, in general, be a waste of moneyto install an expensive CP�propeller in�stead of an FP�propeller. Furthermore, aCP�propeller is more complicated, invol�ving a higher risk of problems in service.

Flow conditions around the propeller

Wake fraction coefficient wWhen the ship is moving, the friction ofthe hull will create a so�called frictionbelt or boundary layer of water aroundthe hull. In this friction belt the velocityof the water on the surface of the hull isequal to that of the ship, but is reducedwith its distance from the surface of thehull. At a certain distance from the hulland, per definition, equal to the outer“surface” of the friction belt, the watervelocity is equal to zero.

The thickness of the friction belt increaseswith its distance from the fore end ofthe hull. The friction belt is thereforethickest at the aft end of the hull andthis thickness is nearly proportional tothe length of the ship, Ref. [5]. Thismeans that there will be a certain wakevelocity caused by the friction along thesides of the hull. Additionally, the ship’sdisplacement of water will also causewake waves both fore and aft. All thisinvolves that the propeller behind thehull will be working in a wake field.

Therefore, and mainly originating fromthe friction wake, the water at the pro�peller will have an effective wake veloc�ity Vw which has the same direction asthe ship’s speed V, see Fig. 6. Thismeans that the velocity of arriving waterVA at the propeller, (equal to the speedof advance of the propeller) given asthe average velocity over the propeller’sdisk area is Vw lower than the ship’sspeed V.

The effective wake velocity at the pro�peller is therefore equal to Vw = V – VA

and may be expressed in dimensionlessform by means of the wake fractioncoefficient w. The normally used wakefraction coefficient w given by Taylor isdefined as:

wV

V

V V

V

you getV

Vw

W A

A

= =−

= −( )1

The value of the wake fraction coefficientdepends largely on the shape of thehull, but also on the propeller’s locationand size, and has great influence onthe propeller’s efficiency.

The propeller diameter or, even better,the ratio between the propeller diameterd and the ship’s length LWL has someinfluence on the wake fraction coeffi�cient, as d/LWL gives a rough indicationof the degree to which the propellerworks in the hull’s wake field. Thus, thelarger the ratio d/LWL, the lower w willbe. The wake fraction coefficient w in�creases when the hull is fouled.

For ships with one propeller, the wakefraction coefficient w is normally in theregion of 0.20 to 0.45, correspondingto a flow velocity to the propeller VA of0.80 to 0.55 of the ship’s speed V. Thelarger the block coefficient, the larger isthe wake fraction coefficient. On shipswith two propellers and a conventionalaftbody form of the hull, the propellerswill normally be positioned outside thefriction belt, for which reason the wakefraction coefficient w will, in this case,be a great deal lower. However, for atwin�skeg ship with two propellers, thecoefficient w will be almost unchanged(or maybe slightly lower) comparedwith the single�propeller case.

Incidentally, a large wake fraction co�efficient increases the risk of propellercavitation, as the distribution of thewater velocity around the propeller isgenerally very inhomogeneous undersuch conditions.

A more homogeneous wake field forthe propeller, also involving a higherspeed of advance VA of the propeller,may sometimes be needed and can beobtained in several ways, e.g. by hav�ing the propellers arranged in nozzles,below shields, etc. Obviously, the bestmethod is to ensure, already at the de�sign stage, that the aft end of the hull isshaped in such a way that the opti�mum wake field is obtained.

Thrust deduction coefficient tThe rotation of the propeller causes thewater in front of it to be “sucked” backtowards the propeller. This results in anextra resistance on the hull normallycalled “augment of resistance” or, if re�lated to the total required thrust force Ton the propeller, “thrust deduction frac�tion” F, see Fig. 6. This means that thethrust force T on the propeller has toovercome both the ship’s resistance RT

and this “loss of thrust” F.

The thrust deduction fraction F may beexpressed in dimensionless form bymeans of the thrust deduction coeffi�cient t, which is defined as:

tFT

T R

T

you getR

Tt

T

T

= =−

= −( )1

The thrust deduction coefficient t canbe calculated by using calculationmodels set up on the basis of researchcarried out on different models.

In general, the size of the thrust deduc�tion coefficient t increases when thewake fraction coefficient w increases.The shape of the hull may have a sig�nificant influence, e.g. a bulbous stemcan, under certain circumstances (lowship speeds), reduce t.

The size of the thrust deduction coeffi�cient t for a ship with one propeller is,normally, in the range of 0.12 to 0.30,as a ship with a large block coefficienthas a large thrust deduction coefficient.For ships with two propellers and aconventional aftbody form of the hull,the thrust deduction coefficient t will bemuch less as the propellers’ “sucking”occurs further away from the hull.However, for a twin�skeg ship with twopropellers, the coefficient t will be almostunchanged (or maybe slightly lower)compared with the single�propeller case.

Efficiencies

Hull efficiency �H

The hull efficiency �H is defined as theratio between the effective (towing)power PE = RT × V, and the thrust power

11

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which the propeller delivers to the waterPT = T × VA, i.e.:

�H = =×

×= =

P

P

R V

T V

R T

V Vt

w

E

T

T

A

T

A

//

1

1

For a ship with one propeller, the hullefficiency ηH is usually in the range of1.1 to 1.4, with the high value for shipswith high block coefficients. For shipswith two propellers and a conventionalaftbody form of the hull, the hull effi�ciency ηH is approx. 0.95 to 1.05, againwith the high value for a high block co�efficient. However, for a twin�skeg shipwith two propellers, the hull coefficientηH will be almost unchanged comparedwith the single�propeller case.

Open water propeller efficiency ηO

Propeller efficiency ηO is related toworking in open water, i.e. the propel�ler works in a homogeneous wake fieldwith no hull in front of it.

The propeller efficiency depends, es�pecially, on the speed of advance VA,thrust force T, rate of revolution n, di�ameter d and, moreover, i.a. on the de�sign of the propeller, i.e. the number ofblades, disk area ratio, and pitch/diam�eter ratio – which will be discussedlater in this chapter. The propeller effi�ciency ηO can vary between approx.0.35 and 0.75, with the high value be�ing valid for propellers with a highspeed of advance VA, Ref. [3].

Fig. 8 shows the obtainable propellerefficiency ηO shown as a function of thespeed of advance VA, which is given indimensionless form as:

JV

n dA=

×

where J is the advance number of thepropeller.

Relative rotative efficiency ηR

The actual velocity of the water flowingto the propeller behind the hull is nei�ther constant nor at right angles to thepropeller’s disk area, but has a kind ofrotational flow. Therefore, comparedwith when the propeller is working inopen water, the propeller’s efficiency is

affected by the ηR factor – called thepropeller’s relative rotative efficiency.

On ships with a single propeller therotative efficiency ηR is, normally, around1.0 to 1.07, in other words, the rotationof the water has a beneficial effect. Therotative efficiency ηR on a ship with aconventional hull shape and with twopropellers will normally be less, approx.0.98, whereas for a twin�skeg ship withtwo propellers, the rotative efficiency ηR

will be almost unchanged.

In combination with w and t, ηR is prob�ably often being used to adjust the re�sults of model tank tests to the theory.

Propeller efficiency ηB working behindthe shipThe ratio between the thrust power PT,which the propeller delivers to the wa�

ter, and the power PD, which is deliv�ered to the propeller, i.e. the propellerefficiency ηB for a propeller workingbehind the ship, is defined as:

� � �B

T

Do R

P

P= = ×

Propulsive efficiency ηD

The propulsive efficiency ηD, whichmust not be confused with the openwater propeller efficiency ηO, is equal tothe ratio between the effective (towing)power PE and the necessary powerdelivered to the propeller PD, i.e.:

�D

E

D

E

T

T

D

P

P

P

P

P

P= = ×

= ηH × ηB = ηH × ηO × ηR

12

0.3

0.2

0.4

00.6

0.1

0.6

0.5

Vn x d

AAdvance number J =

0.4 0.50.2 0.30 0.1

o

0.7

Propellerefficiency

ReefersContainer ships

Small tankers20,000 DWT

Large tankers>150,000 DWT

n ( revs./s )1.66

2.00

0.7

Fig. 8: Obtainable propeller efficiency – open water, Ref. [3], page 213

Page 163: Hidrodinamica e Propulsao.pdf

As can be seen, the propulsive efficiencyηD is equal to the product of the hullefficiency ηH, the open water propellerefficiency ηO, and the relative rotativeefficiency ηR, although the latter hasless significance.

In this connection, one can be led tobelieve that a hull form giving a highwake fraction coefficient w, and hencea high hull efficiency ηH, will also providethe best propulsive efficiency ηD.

However, as the open water propellerefficiency ηO is also greatly dependenton the speed of advance VA, cf. Fig. 8,that is decreasing with increased w,the propulsive efficiency ηD will not,generally, improve with increasing w,quite often the opposite effect is obtained.

Generally, the best propulsive efficiencyis achieved when the propeller works ina homogeneous wake field.

Shaft efficiency ηS

The shaft efficiency ηS depends, i.a. onthe alignment and lubrication of theshaft bearings, and on the reductiongear, if installed.

Shaft efficiency is equal to the ratio be�tween the power PD delivered to thepropeller and the brake power PB deliv�ered by the main engine, i.e.

� �S

D

B

P

P

The shaft efficiency is normally around0.985, but can vary between 0.96 and0.995.

Total efficiency ηT

The total efficiency ηT, which is equal tothe ratio between the effective (towing)power PE, and the necessary brakepower PB delivered by the main engine,can be expressed thus:

�T

P

P

P

P

P

PE

B

E

D

D

B

= = ×

= ηD

× ηS

= ηH

× ηO

× ηR

× ηS

Propeller dimensions

Propeller diameter dWith a view to obtaining the highestpossible propulsive efficiency ηD, thelargest possible propeller diameter dwill, normally, be preferred. There are,however, special conditions to be con�sidered. For one thing, the aftbody formof the hull can vary greatly depending ontype of ship and ship design, for another,the necessary clearance between thetip of the propeller and the hull will de�pend on the type of propeller.

For bulkers and tankers, which are oftensailing in ballast condition, there arefrequent demands that the propellershall be fully immersed also in this con�dition, giving some limitation to the pro�peller size. This propeller size limitationis not particularly valid for containerships as they rarely sail in ballast condi�tion. All the above factors mean that anexact propeller diameter/design draughtratio d/D cannot be given here but, asa rule�of�thumb, the below mentionedapproximations of the diameter/designdraught ratio d/D can be presented,and a large diameter d will, normally,result in a low rate of revolution n.

Bulk carrier and tanker:

d/D < approximately 0.65

Container ship:

d/D < approximately 0.74

For strength and production reasons,the propeller diameter will generally notexceed 10.0 metres and a power out�put of about 90,000 kW. The largest�diameter propeller manufactured so faris of 11.0 metres and has four propellerblades.

Number of propeller bladesPropellers can be manufactured with 2,3, 4, 5 or 6 blades. The fewer the num�ber of blades, the higher the propellerefficiency will be. However, for reasonsof strength, propellers which are to besubjected to heavy loads cannot bemanufactured with only two or threeblades.

Two�bladed propellers are used onsmall ships, and 4, 5 and 6�bladedpropellers are used on large ships.Ships using the MAN B&W two�strokeengines are normally large�type vesselswhich use 4�bladed propellers. Shipswith a relatively large power requirementand heavily loaded propellers, e.g. con�tainer ships, may need 5 or 6�bladedpropellers. For vibrational reasons, pro�pellers with certain numbers of bladesmay be avoided in individual cases inorder not to give rise to the excitationof natural frequencies in the ship’s hullor superstructure, Ref. [5].

Disk area coefficientThe disk area coefficient – referred to inolder literature as expanded blade arearatio – defines the developed surfacearea of the propeller in relation to itsdisk area. A factor of 0.55 is consideredas being good. The disk area coefficientof traditional 4�bladed propellers is oflittle significance, as a higher value willonly lead to extra resistance on thepropeller itself and, thus, have little ef�fect on the final result.

For ships with particularly heavy�loadedpropellers, often 5 and 6�bladed pro�pellers, the coefficient may have ahigher value. On warships it can be ashigh as 1.2.

Pitch diameter ratio p/dThe pitch diameter ratio p/d, expressesthe ratio between the propeller’s pitchp and its diameter d, see Fig. 10. Thepitch p is the distance the propeller“screws” itself forward through the wa�ter per revolution, providing that thereis no slip – see also the next sectionand Fig. 10. As the pitch can varyalong the blade’s radius, the ratio isnormally related to the pitch at 0.7 × r,where r = d/2 is the propeller’s radius.

To achieve the best propulsive efficiencyfor a given propeller diameter, an optimumpitch/diameter ratio is to be found,which again corresponds to a particu�lar design rate of revolution. If, forinstance, a lower design rate of revolutionis desired, the pitch/diameter ratio hasto be increased, and vice versa, at thecost of efficiency. On the other hand, ifa lower design rate of revolution is de�sired, and the ship’s draught permits,the choice of a larger propeller diame�

13

Page 164: Hidrodinamica e Propulsao.pdf

ter may permit such a lower design rateof revolution and even, at the same time,increase the propulsive efficiency.

Propeller coefficients J, KT and KQ

Propeller theory is based on models,but to facilitate the general use of thistheory, certain dimensionless propellercoefficients have been introduced in re�lation to the diameter d, the rate of rev�olution n, and the water’s mass density�. The three most important of thesecoefficients are mentioned below.

The advance number of the propeller Jis, as earlier mentioned, a dimensionlessexpression of the propeller’s speed ofadvance VA.

JV

n dA=

×

The thrust force T, is expresseddimensionless, with the help of thethrust coefficient KT, as

KT

n dT =× ×�

2 4

and the propeller torque

QP

nD=×2�

is expressed dimensionless with thehelp of the torque coefficient KQ, as

KQ

n dQ =× ×�

2 5

The propeller efficiency �O can be cal�culated with the help of the above�men�tioned coefficients, because, as previouslymentioned, the propeller efficiency �O isdefined as:

�� �

�= =

×× ×

= ×P

P

T V

Q n

K

KJT

D

A T

Q2 2

With the help of special and very com�plicated propeller diagrams, whichcontain, i.a. J, KT and KQ curves, it ispossible to find/calculate the propeller’sdimensions, efficiency, thrust, power, etc.

Manufacturing accuracy of the propellerBefore the manufacturing of the propeller,the desired accuracy class standard ofthe propeller must be chosen by thecustomer. Such a standard is, for ex�ample, ISO 484/1 – 1981 (CE), whichhas four different “Accuracy classes”,see Table 5.

Each of the classes, among other de�tails, specifies the maximum allowabletolerance on the mean design pitch ofthe manufactured propeller, andthereby the tolerance on the correspond�ing propeller speed (rate of revolution).

The price of the propeller, of course,depends on the selected accuracyclass, with the lowest price for class III.However, it is not recommended touse class III, as this class has a toohigh tolerance. This again means thatthe mean pitch tolerance should nor�mally be less than +/– 1.0 %.

The manufacturing accuracy tolerancecorresponds to a propeller speed toler�ance of max. +/– 1.0 %. When also in�corporating the influence of the toleranceon the wake field of the hull, the totalpropeller tolerance on the rate of revo�lution can be up to +/– 2.0 %. This tol�erance has also to be borne in mindwhen considering the operating condi�tions of the propeller in heavy weather.

Influence of propeller diameter andpitch/diameter ratio on propulsiveefficiency D.As already mentioned, the highest pos�sible propulsive efficiency required toprovide a given ship speed is obtainedwith the largest possible propeller dia�meter d, in combination with the corre�sponding, optimum pitch/diameter ra�tio p/d.

14

ISO 484/1 – 1981 (CE)

ClassManufacturing

accuracy

Mean pitchfor propel�

ler

SIIIIII

Very high accuracyHigh accuracyMedium accuracyWide tolerances

+/– 0.5 %+/– 0.75 %+/– 1.00 %+/– 3.00 %

Table 5: Manufacturing accuracy classesof a propeller

110 120100 r/min130

Shaft power

80 90

8,800

70

8,700

8,900

9,100

8,600

8,500

9,400

0.95

9,200

9,300

9,000

d = Propeller diameterp/d = Pitch/diameter ratio

Power and speed curvefor various propellerdiameters d withoptimum p/d Propeller speed

Power and speed curvefor the given propellerdiameter d = 7.2 m withdifferent p/d

80,000 dwt crude oil tankerDesign draught = 12.2 mShip speed = 14.5 kn9,500

0.90

0.850.80

0.71

1.00

0.60

0.75

d

0.65

0.55

6.8 m

p/d0.67

7.2 m

6.6 m

7.4 m

7.0 m

0.70

p/d

0.68

0.69

0.50

p/d

p/dd

kW

Fig. 9: Propeller design – influence of diameter and pitch

Page 165: Hidrodinamica e Propulsao.pdf

As an example for an 80,000 dwt crudeoil tanker, with a service ship speed of14.5 knots and a maximum possiblepropeller diameter of 7.2 m, this influenceis shown in Fig. 9.

According to the blue curve, the maxi�mum possible propeller diameter of 7.2m may have the optimum pitch/diame�ter ratio of 0.70, and the lowest possi�ble shaft power of 8,820 kW at 100r/min. If the pitch for this diameter ischanged, the propulsive efficiency willbe reduced, i.e. the necessary shaftpower will increase, see the red curve.

The blue curve shows that if a biggerpropeller diameter of 7.4 m is possible,the necessary shaft power will be re�duced to 8,690 kW at 94 r/min, i.e. thebigger the propeller, the lower the opti�mum propeller speed.

The red curve also shows that propul�sion�wise it will always be an advan�tage to choose the largest possiblepropeller diameter, even though theoptimum pitch/diameter ratio wouldinvolve a too low propeller speed (in rela�tion to the required main engine speed).Thus, when using a somewhat lowerpitch/diameter ratio, compared with theoptimum ratio, the propeller/ enginespeed may be increased and will onlycause a minor extra power increase.

Operating conditions of a propeller

Slip ratio SIf the propeller had no slip, i.e. if thewater which the propeller “screws”itself through did not yield (i.e. if thewater did not accelerate aft), the pro�peller would move forward at a speedof V = p × n, where n is the propeller’srate of revolution, see Fig. 10.

The similar situation is shown in Fig. 11for a cork screw, and because the corkis a solid material, the slip is zero and,therefore, the cork screw always movesforward at a speed of V = p × n. How�ever, as the water is a fluid and doesyield (i.e. accelerate aft), the propeller’sapparent speed forward decreaseswith its slip and becomes equal to theship’s speed V, and its apparent slipcan thus be expressed as p × n – V.

The apparent slip ratio SA, which isdimensionless, is defined as:

Sp n V

p nV

p nA =× −

×= −

×1

The apparent slip ratio SA, which is cal�culated by the crew, provides usefulknowledge as it gives an impression ofthe loads applied to the propeller underdifferent operating conditions. The ap�parent slip ratio increases when the

15

Velocity of corkscrew: V = p x n Pitch p

Wine bottleCorkscrew Cork

V

n

Fig. 11: Movement of a corkscrew, without slip

S x p x nV or VA

Pitch p

n

0.7 x r

r

d

p x n

Slip

The apparent slip ratio : S = = 1A_

The real slip ratio : S = = 1R_p x n _ V V

p x n p x nA A

p x n _ V Vp x n p x n

Fig. 10: Movement of a ship´s propeller, with pitch p and slip ratio S

Page 166: Hidrodinamica e Propulsao.pdf

vessel sails against the wind or waves,in shallow waters, when the hull isfouled, and when the ship accelerates.Under increased resistance, this in�volves that the propeller speed (rate ofrevolution) has to be increased in orderto maintain the required ship speed.

The real slip ratio will be greater thanthe apparent slip ratio because the realspeed of advance VA of the propeller is,as previously mentioned, less than theship’s speed V.

The real slip ratio SR, which gives a truerpicture of the propeller’s function, is:

SV

p nV w

p nR

A= −×

= −× −

×1 1

1( )

At quay trials where the ship’s speed isV = 0, both slip ratios are 1.0. Incidentally,slip ratios are often given in percentages.

Propeller law in generalAs discussed in Chapter 1, the resis�tance R for lower ship speeds is pro�portional to the square of the ship’sspeed V, i.e.:

R = c × V2

where c is a constant. The necessarypower requirement P is thus propor�tional to the speed V to the power ofthree, thus:

P = R × V = c × V3

For a ship equipped with a fixed pitchpropeller, i.e. a propeller with unchange�able pitch, the ship speed V will be pro�portional to the rate of revolution n, thus:

P = c × n3

which precisely expresses the propellerlaw, which states that “the necessarypower delivered to the propeller is pro�portional to the rate of revolution to thepower of three”.

Actual measurements show that thepower and engine speed relationshipfor a given weather condition is fairlyreasonable, whereas the power andship speed relationship is often seenwith a higher power than three. A rea�

sonable relationship to be used for esti�mations in the normal ship speed rangecould be as follows:

• For large high�speed ships like con�tainer vessels: P = c × V 4.5

• For medium�sized, medium�speedships like feeder container ships,reefers, RoRo ships, etc.: P = c × V 4.0

• For low�speed ships like tankers andbulk carriers, and small feeder con�tainer ships, etc.: P = c × V 3.5

Propeller law for heavy running propellerThe propeller law, of course, can onlybe applied to identical ship runningconditions. When, for example, theship’s hull after some time in servicehas become fouled and thus becomemore rough, the wake field will be differentfrom that of the smooth ship (clean hull)valid at trial trip conditions.

A ship with a fouled hull will, conse�quently, be subject to extra resistancewhich will give rise to a “heavy propellercondition”, i.e. at the same propellerpower, the rate of revolution will be lower.

The propeller law now applies to an�other and “heavier” propeller curvethan that applying to the clean hull,propeller curve, Ref. [3], page 243.

The same relative considerations applywhen the ship is sailing in a heavy seaagainst the current, a strong wind, andheavy waves, where also the heavywaves in tail wind may give rise to aheavier propeller running than whenrunning in calm weather. On the otherhand, if the ship is sailing in ballastcondition, i.e. with a lower displace�ment, the propeller law now applies toa “lighter” propeller curve, i.e. at thesame propeller power, the propellerrate of revolution will be higher.

As mentioned previously, for ships witha fixed pitch propeller, the propeller lawis extensively used at part load running.It is therefore also used in MAN B&WDiesel’s engine layout and load diagramsto specify the engine’s operationalcurves for light running conditions (i.e.clean hull and calm weather) and heavyrunning conditions (i.e. for fouled hull

and heavy weather). These diagrams us�ing logarithmic scales and straight linesare described in detail in Chapter 3.

Propeller performance in general atincreased ship resistanceThe difference between the above�men�tioned light and heavy running propellercurves may be explained by an exam�ple, see Fig. 12, for a ship using, as ref�erence, 15 knots and 100% propulsionpower when running with a clean hull incalm weather conditions. With 15% morepower, the corresponding ship speedmay increase from 15.0 to 15.6 knots.

As described in Chapter 3, and com�pared with the calm weather conditions,it is normal to incorporate an extrapower margin, the so�called sea mar�gin, which is often chosen to be 15%.This power margin corresponds to ex�tra resistance on the ship caused bythe weather conditions. However, forvery rough weather conditions the influ�ence may be much greater, as de�scribed in Chapter 1.

In Fig. 12a, the propulsion power isshown as a function of the ship speed.When the resistance increases to alevel which requires 15% extra powerto maintain a ship speed of 15 knots,the operating point A will move towardspoint B.

In Fig. 12b the propulsion power isnow shown as a function of the propellerspeed. As a first guess it will often be as�sumed that point A will move towards B’because an unchanged propeller speedimplies that, with unchanged pitch, thepropeller will move through the waterat an unchanged speed.

If the propeller was a corkscrew movingthrough cork, this assumption wouldbe correct. However, water is not solidas cork but will yield, and the propellerwill have a slip that will increase with in�creased thrust caused by increasedhull resistance. Therefore, point A willmove towards B which, in fact, is veryclose to the propeller curve through A.Point B will now be positioned on apropeller curve which is slightly heavyrunning compared with the clean hulland calm weather propeller curve.

16

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Sometimes, for instance when the hullis fouled and the ship is sailing in heavyseas in a head wind, the increase inresistance may be much greater, cor�responding to an extra power demandof the magnitude of 100% or even higher.An example is shown in Fig. 12c.

In this example, where 100% powerwill give a ship speed of 15.0 knots,point A, a ship speed of, for instance,12.3 knots at clean hull and in calmweather conditions, point C, will requireabout 50% propulsion power but, atthe above�mentioned heavy runningconditions, it might only be possible toobtain the 12.3 knots by 100% propulsionpower, i.e. for 100% power going frompoint A to D. Running point D may nowbe placed relatively far to the left of pointA, i.e. very heavy running. Such a situ�ation must be considered when laying�out the main engine in relation to thelayout of the propeller, as described inChapter 3.

A scewed propeller (with bent bladetips) is more sensitive to heavy runningthan a normal propeller, because thepropeller is able to absorb a highertorque in heavy running conditions. For

a ducted propeller, the opposite effectis obtained.

Heavy waves and sea and wind againstWhen sailing in heavy sea against, withheavy wave resistance, the propeller

can be up to 7�8% heavier runningthan in calm weather, i.e. at the samepropeller power, the rate of revolutionmay be 7�8% lower. An example validfor a smaller container ship is shown inFig. 13. The service data is measured

17

(Logarithmic scales)

Power

Propeller speed

15.0 knots100% power

Propeller curvefor clean hull andcalm weather

Propellercurve forfouled hulland heavyseas

LR

Slip

HR HR = Heavy runningLR = Light running

D´ A

C

12.3 knots100% power

12.3 knots50% power

10.0 knots50% power

D

Fig. 12c: Propeller speed performance atlarge extra ship resistance

(Logarithmic scales)

Power

Propeller speed

15.6 knots115% power

15.0 knots100% power

15%Seamargin

Slip

Propeller curve for cleanhull and calm weather

15.0 knots115% power

A

B

Fig. 12b: Propeller speed performance at15% sea margin

BHP21,000

18,000

15,000

12,000

9,000

6,00076 80 9284 9688 100

Ship speedknots

Shaft power

Clean hull and draught DD = 6.50 mD = 5.25 mD = 7.75 m

Source: Lloyd's Register

MEAN

F

A

Average weather 3%

Extremely good weather 0%

Extremely bad weather 6%

Propeller speed

Apparent slip

10%6%

Heavyrunning

2%�2%

1316

19

22

CB

A

C

B

A

r/min

Fig. 13: Service data over a period of a year returned from a single screw container ship

(Logarithmic scales)

15.6 knots115% power

15.0 knots100% power

15%Seamargin

Power

Ship speed

Propeller curve for cleanhull and calm weather

15.0 knots115% power

B

A

Fig. 12a: Ship speed performance at 15%sea margin

Page 168: Hidrodinamica e Propulsao.pdf

over a period of one year and onlyincludes the influence of weather con�ditions! The measuring points havebeen reduced to three average weatherconditions and show, for extremely badweather conditions, an average heavyrunning of 6%, and therefore, in prac�tice, the heavy running has proved tobe even greater.

In order to avoid slamming of the ship,and thereby damage to the stem andracing of the propeller, the ship speedwill normally be reduced by the navigat�ing officer on watch.

Another measured example is shownin Fig. 14, and is valid for a reefer shipduring its sea trial. Even though thewind velocity is relatively low, only 2.5m/s, and the wave height is 4 m, the

measurements indicate approx. 1.5%heavy running when sailing in headwind out, compared with when sailingin tail wind on return.

Ship accelerationWhen the ship accelerates, the propel�ler will be subjected to an even largerload than during free sailing. The powerrequired for the propeller, therefore, willbe relatively higher than for free sailing,and the engine’s operating point will beheavy running, as it takes some timebefore the propeller speed has reachedits new and higher level. An examplewith two different accelerations, for anengine without electronic governor andscavenge air pressure limiter, is shownin Fig. 15. The load diagram and scav�enge air pressure limiter are is describedin Chapter 3.

Shallow watersWhen sailing in shallow waters, the re�sidual resistance of the ship may be in�creased and, in the same way as whenthe ship accelerates, the propeller willbe subjected to a larger load than dur�ing free sailing, and the propeller will beheavy running.

Influence of displacementWhen the ship is sailing in the loadedcondition, the ship’s displacement vol�ume may, for example, be 10% higheror lower than for the displacement validfor the average loaded condition. This,of course, has an influence on the ship’sresistance, and the required propellerpower, but only a minor influence onthe propeller curve.

On the other hand, when the ship issailing in the ballast condition, the dis�placement volume, compared to theloaded condition, can be much lower,and the corresponding propeller curvemay apply to, for example, a 2% “lighter”propeller curve, i.e. for the same powerto the propeller, the rate of revolutionwill be 2% higher.

Parameters causing heavy runningpropellerTogether with the previously describedoperating parameters which cause aheavy running propeller, the parame�ters summarised below may give an in�dication of the risk/sensitivity of gettinga heavy running propeller when sailingin heavy weather and rough seas:

1 Relatively small ships (<70,000 dwt)such as reefers and small containerships are sensitive whereas large ships,such as large tankers and containerships, are less sensitive because thewaves are relatively small comparedto the ship size.

2 Small ships (Lpp < 135 m≈ 20,000 dwt)have low directional stability and,therefore, require frequent ruddercorrections, which increase the shipresistance (a self�controlled rudderwill reduce such resistance).

3 High�speed shipsare more sensitive than low�speedships because the waves will act onthe fast�going ship with a relatively

18

Propell

er cu

rve

SMCR: 13,000 kW x 105 r/minWind velocity : 2.5 m/sWave height : 4 m

Propeller/engine speed

100

90

105

85

100

95

80

10199 103 105 % SMCR10297 9896 104

Heavyrunning

Engine

"pro

peller

curve

"

Propell

er cu

rve

Propeller designlight running

* 20.521.5

*

20.5*

*20.8

*21.2

*22.0

21.1 *

7

51

3

4

Shaft power% SMCR

22.3 *

21.8*

SMCR

* 21.1

Head wind

Tail wind

(Logarithmic scales)

Fig. 14: Measured relationship between power, propeller and ship speed during seatrial ofa reefer ship

Page 169: Hidrodinamica e Propulsao.pdf

larger force than on the slow�goingship.

4 Ships with a “flat” stemmay be slowed down faster by wavesthan a ship with a “sharp” stem.Thus an axe�shaped upper bow maybetter cut the waves and therebyreduce the heavy running tendency.

5 Fouling of the hull and propellerwill increase both hull resistance andpropeller torque. Polishing the pro�peller (especially the tips) as often aspossible (also when in water) has apositive effect. The use of effectiveanti�fouling paints will prevent foulingcaused by living organisms.

6 Ship accelerationwill increase the propeller torque,and thus give a temporarily heavyrunning propeller.

7 Sailing in shallow watersincreases the hull resistance and re�duces the ship’s directional stability.

8 Ships with scewed propellerare able to absorb a higher torqueunder heavy running conditions.

Manoeuvring speedBelow a certain ship speed, called themanoeuvring speed, the manoeuvra�bility of the rudder is insufficient be�cause of a too low velocity of the waterarriving at the rudder. It is rather difficultto give an exact figure for an adequatemanoeuvring speed of the ship as thevelocity of the water arriving at the rud�der depends on the propeller’s slipstream.

Often a manoeuvring speed of themagnitude of 3.5�4.5 knots is men�tioned. According to the propeller law,a correspondingly low propulsion

power will be needed but, of course,this will be higher for running in heavyweather with increased resistance onthe ship.

Direction of propeller rotation (side thrust)When a ship is sailing, the propellerblades bite more in their lowermost po�sition than in their uppermost position.The resulting side�thrust effect is largerthe more shallow the water is as, forexample, during harbour manoeuvres.

Therefore, a clockwise (looking from aftto fore) rotating propeller will tend topush the ship’s stern in the starboarddirection, i.e. pushing the ship’s stemto port, during normal ahead running.This has to be counteracted by therudder.

When reversing the propeller to asternrunning as, for example, when berthingalongside the quay, the side�thrust ef�fect is also reversed and becomes fur�ther pronounced as the ship’s speeddecreases. Awareness of this behav�iour is very important in critical situa�tions and during harbour manoeuvres.

According to Ref. [5], page 15�3, thereal reason for the appearance of theside thrust during reversing of the pro�peller is that the upper part of the pro�peller’s slip stream, which is rotative,strikes the aftbody of the ship.

Thus, also the pilot has to know pre�cisely how the ship reacts in a givensituation. It is therefore an unwrittenlaw that on a ship fitted with a fixedpitch propeller, the propeller is alwaysdesigned for clockwise rotation whensailing ahead. A direct coupled mainengine, of course, will have the samerotation.

In order to obtain the same side�thrusteffect, when reversing to astern, onships fitted with a controllable pitchpropeller, CP�propellers are designedfor anti�clockwise rotation when sailingahead.

19

80 100 10585

50

7565 90 9560

60

70

80

90

mep110%

Engine speed, % A

40

A=M100

Engine shaft power, % A

100%

90%

80%

70%

60%

O

A 100% reference pointM Specified engine MCRO Optimising point

110

(Logarithmic scales)

70

Fig. 15: Load diagram – acceleration

Page 170: Hidrodinamica e Propulsao.pdf

Engine Layout andLoad Diagrams

Power functions and logarithmicscales

As is well�known, the effective brakepower PB of a diesel engine is propor�tional to the mean effective pressure(mep) pe and engine speed (rate of rev�olution) n. When using c as a constant,PB may then be expressed as follows:

PB = c × pe × n

or, in other words, for constant mepthe power is proportional to the speed:

PB = c × n1 (for constant mep)

As already mentioned – when runningwith a fixed pitch propeller – the powermay, according to the propeller law, beexpressed as:

PB = c × n3 (propeller law)

Thus, for the above examples, the brakepower PB may be expressed as a func�tion of the speed n to the power of i, i.e.

PB = c × ni

Fig. 16 shows the relationship betweenthe linear functions, y = ax + b, see (A),using linear scales and the power func�tions PB = c × ni, see (B), using logarith�mic scales.

The power functions will be linear whenusing logarithmic scales, as:

log (PB) = i × log (n) + log (c)

which is equivalent to: y = ax + b

Thus, propeller curves will be parallel tolines having the inclination i = 3, andlines with constant mep will be parallelto lines with the inclination i = 1.

Therefore, in the layout and load diagramsfor diesel engines, as described in thefollowing, logarithmic scales are used,making simple diagrams with straightlines.

Propulsion and engine runningpoints

Propeller design point PDNormally, estimations of the necessarypropeller power and speed are basedon theoretical calculations for loadedship, and often experimental tank tests,both assuming optimum operatingconditions, i.e. a clean hull and goodweather. The combination of speedand power obtained may be called theship’s propeller design point PD placedon the light running propeller curve 6,

see Fig. 17. On the other hand, someshipyards and/or propeller manufactur�ers sometimes use a propeller designpoint PD´ that incorporates all or part ofthe so�called sea margin described be�low.

Fouled hullWhen the ship has been sailing forsome time, the hull and propeller be�come fouled and the hull’s resistancewill increase. Consequently, the shipspeed will be reduced unless the enginedelivers more power to the propeller, i.e.the propeller will be further loaded andwill become heavy running HR.

Furthermore, newer high�efficiency shiptypes have a relatively high ship speed,and a very smooth hull and propellersurface (at sea trial) when the ship isdelivered. This means that the inevitablebuild�up of the surface roughness onthe hull and propeller during sea serviceafter seatrial may result in a relativelyheavier running propeller, comparedwith older ships born with a more roughhull surface.

Heavy weather and sea margin usedfor layout of engineIf, at the same time, the weather isbad, with head winds, the ship’s resis�tance may increase much more, andlead to even heavier running.

When determining the necessary en�gine power, it is normal practice to addan extra power margin, the so�calledsea margin, which is traditionally about15% of the propeller design PD power.However, for large container ships,20�30% may sometimes be used.

When determining the necessary en�gine speed, for layout of the engine, itis recommended – compared with theclean hull and calm weather propellercurve 6 – to choose the heavier propel�ler curve 2, see Fig. 17, correspondingto curve 6 having a 3�7% higher rate ofrevolution than curve 2, and in generalwith 5% as a good choice.

Note that the chosen sea power mar�gin does not equalise the chosenheavy engine propeller curve.

20

A. Straight lines in linear scales

a

2

X1 20

1

0

b

y = ax + b

B. Power function curvesin logarithmic scales

P

P

B

B

= engine brake powerc = constantn = engine speed

log( ) = i x log(n) + log(c)

y = ax + bP = c x ni

i = 1

i = 2

i = 3

y = log (P )B

i = 0

x = log (n)

y = log (P ) = log (c x n )Bi

y

B

Fig. 16: Relationship between linear functionsusing linear scales and power functionsusing logarithmic scales

Page 171: Hidrodinamica e Propulsao.pdf

Continuous service propulsion point SPThe resulting speed and power combi�nation – when including heavy propellerrunning and sea margin – is called the“continuous service rating for propulsion”SP for fouled hull and heavy weather.The heavy propeller curve, curve 2, forfouled hull and heavy weather will nor�mally be used as the basis for the en�gine operating curve in service, and thepropeller curve for clean hull and calmweather, curve 6, is said to represent a“light running” LR propeller.

Continuous service rating SThe continuous service rating is thepower at which the engine, includingthe sea margin, is assumed to operate,and point S is identical to the servicepropulsion point SP unless a main en�gine driven shaft generator is installed.

Light running factor fLR

The heavy propeller curve for a fouledhull and heavy weather, and if no shaftgenerator is installed may, as mentionedabove, be used as the design basis for

the engine operating curve in service,curve 2, whereas the light propellercurve for clean hull and calm weather,curve 6, may be valid for running con�ditions with new ships, and equal tothe layout/design curve of the propel�ler. Therefore, the light propeller curvefor clean hull and calm weather is saidto represent a “light running” LR pro�peller and will be related to the heavypropeller curve for fouled hull andheavy weather condition by means of alight running factor fLR, which, for thesame power to the propeller, is definedas the percentage increase of the rateof revolution n, compared to the rate ofrevolution for heavy running, i.e.

fn n

nLR

light heavy

heavy

=−

×100%

Engine marginBesides the sea margin, a so�called“engine margin” of some 10�15% isfrequently added as an operationalmargin for the engine. The correspond�ing point is called the “specified MCRfor propulsion” MP, see Fig. 17, andrefers to the fact that the power forpoint SP is 10�15% lower than forpoint MP, i.e. equal to 90�85% of MP.

Specified MCR MThe engine’s specified MCR point M isthe maximum rating required by theyard or owner for continuous operationof the engine. Point M is identical to thespecified propulsion MCR point MP un�less a main engine driven shaft genera�tor is installed. In such a case, the extrapower demand of the shaft generatormust also be considered.

Note:Light/heavy running, fouling and seamargin are overlapping terms.Light/heavy running of the propeller re�fers to hull and propeller deterioration,and bad weather, and sea margin, i.e.extra power to the propeller, refers tothe influence of the wind and the sea.

Based on feedback from service, itseems reasonable to design the pro�peller for 3�7% light running. The de�gree of light running must be decidedupon, based on experience from theactual trade and hull design, but 5%is often a good choice.

21

Fig. 17: Ship propulsion running points and engine layout

LR(5%)

Engine speed

Power

MP

Sea margin(15% of PD)

2 6

SP

HR

PD´

PD

Engine margin(10% of MP)

2 Heavy propeller curve fouled hull and heavy weather6 Light propeller curve clean hull and calm weather

MP: Specified propulsion pointSP: Service propulsion pointPD: Propeller design point

Alternative propeller design pointLR: Light running factorHR: Heavy running

_

_

Pd´:

Page 172: Hidrodinamica e Propulsao.pdf

Engine layout diagram

An engine’s layout diagram is limited bytwo constant mean effective pressure(mep) lines L1�L3 and L2�L4, and by twoconstant engine speed lines L1�L2 andL3�L4, see Fig. 17. The L1 point refers tothe engine’s nominal maximum contin�uous rating. Within the layout areathere is full freedom to select the en�gines specified MCR point M and rele�vant optimising point O, see below,

which is optimum for the ship and theoperating profile. Please note that thelowest specific fuel oil consumption fora given optimising point O will be ob�tained at 70% and 80% of point O’spower, for electronically (ME) and me�chanically (MC) controlled engines,respectively.

Based on the propulsion and enginerunning points, as previously found, thelayout diagram of a relevant main en�

gine may be drawn�in. The specifiedMCR point M must be inside the limita�tion lines of the layout diagram; if it isnot, the propeller speed will have to bechanged or another main engine typemust be chosen. Yet, in special cases,point M may be located to the right ofline L1�L2, see “Optimising/MatchingPoint” below.

Optimising point OThe “Optimising (MC)/Matching (ME)point” O – or, better, the layout point ofthe engine – is the rating at which theengine (timing and) compression ratioare adjusted, with consideration to thescavenge air pressure of the turbocharger.

As mentioned below, under “Load dia�gram”, the optimising point O (later onin this paper also used in generalwhere matching point for ME engineswas the correct one) is placed on line 1(layout curve of engine) of the load dia�gram, and the optimised power can befrom 85 to 100% of point M‘s power.Overload running will still be possible(110% of M‘s power), as long as consid�eration to the scavenge air pressure hasbeen taken.

The optimising point O is to be placedinside the layout diagram. In fact, thespecified MCR point M can be placedoutside the layout diagram, but only byexceeding line L1�L2, and, of course,only provided that the optimising pointO is located inside the layout diagram.

It should be noted that MC/MC�C en�gines without VIT (variable injection tim�ing) fuel pumps cannot be optimised atpart�load. Therefore, these engines arealways optimised in point A, i.e. havingpoint M‘s power.

Load diagram

DefinitionsThe load diagram (Fig. 18) defines thepower and speed limits for continuousas well as overload operation of an in�stalled engine which has an optimisingpoint O and a specified MCR point Mthat conforms to the ship’s specification.

Point A is a 100% speed and powerreference point of the load diagram,and is defined as the point on the pro�

22

Line 1: Propeller curve through optimising point (O) layout curve for engine

Line 2: Heavy propeller curve fouled hull and heavy seasLine 3: Speed limitLine 4: Torque/speed limitLine 5: Mean effective pressure limit

Line 6: Light propeller curve clean hull and calm weather layout curve for propellerLine 7: Power limit for continuous runningLine 8: Overload limitLine 9: Sea trial speed limitLine 10: Constant mean effective pressure (mep) lines

__

_ _

80 100 10585

50

70 7565 90 9560

60

70

80

90

mep110%

Engine speed, % A

40

2

4

A=M

9

7

8

5100

Engine shaft power, % A

6100%

90%

80%

70%

60%

1

10

3

O

A 100% reference pointM Specified engine MCRO Optimising point

110

Fig. 18: Engine load diagram

Page 173: Hidrodinamica e Propulsao.pdf

peller curve (line 1) – the layout curve ofthe engine – through the optimising pointO, having the specified MCR power.

Normally, point M is equal to point A,but in special cases, for example if ashaft generator is installed, point Mmay be placed to the right of point Aon line 7. The service points of the in�stalled engine incorporate the enginepower required for ship propulsion andfor the shaft generator, if installed.

During shoptest running, the engine willalways operate along curve 1, withpoint A as 100% MCR. If CP�propellerand constant speed operation is re�quired, the delivery test may be fin�ished with a constant speed test.

Limits to continuous operationThe continuous service range is limitedby the four lines 4, 5, 7 and 3 (9), seeFig. 18:

Line 3 and line 9Line 3 represents the maximum accept�able speed for continuous operation, i.e.

105% of A, however, maximum 105%of L1. During sea trial conditions themaximum speed may be extended to107% of A, see line 9.

The above limits may, in general, beextended to 105% and, during sea trialconditions, to 107% of the nominal L1

speed of the engine, provided the tor�sional vibration conditions permit.

The overspeed set�point is 109% ofthe speed in A, however, it may bemoved to 109% of the nominal speedin L1, provided that torsional vibrationconditions permit.

Running at low load above 100% ofthe nominal L1 speed of the engine is,however, to be avoided for extendedperiods.

Line 4:Represents the limit at which an ampleair supply is available for combustion andimposes a limitation on the maximumcombination of torque and speed.

Line 5:Represents the maximum mean effec�tive pressure level (mep) which can beaccepted for continuous operation.

Line 7:Represents the maximum power forcontinuous operation.

Line 10:Represents the mean effective pressure(mep) lines. Line 5 is equal to the 100%mep�line. The mep�lines are also anexpression of the corresponding fuelindex of the engine.

Limits for overload operationThe overload service range is limited asfollows, see Fig. 18:

Line 8:Represents the overload operation limi�tations.

The area between lines 4, 5, 7 and thedashed line 8 in Fig. 18 is available foroverload running for limited periodsonly (1 hour per 12 hours).

23

Point A of load diagram

Line 1: Propeller curve through optimising point (O)

Line 7: Constant power line through specified MCR (M)

Point A: Intersection between lines 1 and 7

Engine speed

Power

M: Specified MCR of engineS: Continuous service rating of engineO: Optimising point of engineA: Reference point of load diagram

A=M=MP

Propulsion andengine service curvefor heavy running

7

S=SPO

2

16

Fig. 19a: Example 1 with FPP – engine layout without SG (normal case)

M: Specified MCR of engineS: Continuous service rating of engineO: Optimising point of engineA: Reference point of load diagram

Engine speed

A=M

Propulsion and engine servicecurve for heavy running

3.3% A5

62

4

Power 1

S

7

O5

6

3

4 1

7

2

5% A

5% L1

Fig. 19b: Example 1 with FPP – load diagram without SG (normal case)

Page 174: Hidrodinamica e Propulsao.pdf

Electronic governor with load limitationIn order to safeguard the diesel engineagainst thermal and mechanical overload,the approved electronic governors includethe following two limiter functions:

• Torque limiterThe purpose of the torque limiter isto ensure that the limitation lines ofthe load diagram are always observed.The torque limiter algorithm comparesthe calculated fuel pump index (fuelamount) and the actually measuredengine speed with a reference limitercurve giving the maximum allowablefuel pump index at a given enginespeed. If the calculated fuel pumpindex is above this curve, the result�ing fuel pump index will be reducedcorrespondingly.

The reference limiter curve is to beadjusted so that it corresponds to thelimitation lines of the load diagram.

• Scavenge air pressure limiterThe purpose of the scavenge air

pressure limiter is to ensure that theengine is not being overfuelled duringacceleration, as for example duringmanoeuvring.

The scavenge air pressure limiteralgorithm compares the calculatedfuel pump index and measuredscavenge air pressure with a refer�ence limiter curve giving the maxi�mum allowable fuel pump index at agiven scavenge air pressure. If thecalculated fuel pump index is abovethis curve, the resulting fuel pumpindex will be reduced correspondingly.

The reference limiter curve is to beadjusted to ensure that sufficient airwill always be available for a goodcombustion process.

RecommendationContinuous operation without a timelimitation is allowed only within the arealimited by lines 4, 5, 7 and 3 of theload diagram. For fixed pitch propelleroperation in calm weather with loaded

ship and clean hull, the propeller/enginemay run along or close to the propellerdesign curve 6.

After some time in operation, the ship’shull and propeller will become fouled,resulting in heavier running of the pro�peller, i.e. the propeller curve will moveto the left from line 6 towards line 2, andextra power will be required for propulsionin order to maintain the ship speed.

At calm weather conditions the extentof heavy running of the propeller willindicate the need for cleaning the hulland, possibly, polishing the propeller.

The area between lines 4 and 1 is avail�able for operation in shallow water,heavy weather and during acceleration,i.e. for non�steady operation withoutany actual time limitation.

24

Point A of load diagram

Line 1: Propeller curve through optimising point (O)

Line 7: Constant power line through specified MCR (M)

Point A: Intersection between lines 1 and 7

Engine speed

M=MP

Propulsion andengine service curvefor heavy running

7

S=SP

621

O

Power

A

M: Specified MCR of engineS: Continuous service rating of engineO: Optimising point of engineA: Reference point of load diagram

Fig. 20a: Example 2 with FPP – engine layout without SG (special case)

M

Propulsion and engine servicecurve for heavy running

3.3% A5

62

4

1

S

7

5

6

3

4 1

7

2

5% A

5% L1

A

O

Engine speed

Power

M: Specified MCR of engineS: Continuous service rating of engineO: Optimising point of engineA: Reference point of load diagram

Fig. 20b: Example 2 with FPP – load diagram without SG (special case)

Page 175: Hidrodinamica e Propulsao.pdf

The recommended use of a relativelyhigh light running factor for design ofthe propeller will involve that a relativelyhigher propeller speed will be used forlayout design of the propeller. This, inturn, may involve a minor reduction ofthe propeller efficiency, and may possi�bly cause the propeller manufacturer toabstain from using a large light runningmargin. However, this reduction of thepropeller efficiency caused by the largelight running factor is actually relativelyinsignificant compared with the improvedengine performance obtained whensailing in heavy weather and/or withfouled hull and propeller.

Use of layout and loaddiagrams � examples

In the following, four different examplesbased on fixed pitch propeller (FPP)and one example based on controllablepitch propeller (CPP) are given in orderto illustrate the flexibility of the layoutand load diagrams.

In this respect the choice of the optimi�sing point O has a significant influence.

Examples with fixed pitch propeller

Example 1:Normal running conditions, withoutshaft generator

Normally, the optimising point O, andthereby the engine layout curve 1, willbe selected on the engine servicecurve 2 (for heavy running), as shownin Fig. 19a.

Point A is then found at the intersectionbetween propeller curve 1 (2) and theconstant power curve through M, line7. In this case, point A will be equal topoint M.

Once point A has been found in thelayout diagram, the load diagram canbe drawn, as shown in Fig. 19b, andhence the actual load limitation linesof the diesel engine may be found.

Example 2:Special running conditions, withoutshaft generator

When the ship accelerates, the propel�ler will be subjected to an even largerload than during free sailing. The sameapplies when the ship is subjected toan extra resistance as, for example,when sailing against heavy wind andsea with large wave resistance.

In both cases, the engine’s operatingpoint will be to the left of the normaloperating curve, as the propeller willrun heavily.

In order to avoid exceeding theleft�hand limitation line 4 of the loaddiagram, it may, in certain cases, benecessary to limit the accelerationand/or the propulsion power.

If the expected trade pattern of theship is to be in an area with frequentlyappearing heavy wind and sea and

25

Shaf

t gen

erat

or

Propulsion curvefor heavy running

O7

1 2

Engine service curvefor heavy running

MP

SG

6

SSG

SP

Engine speed

Power A=M

M: Specified MCR of engineS: Continuous service rating of engineO: Optimising point of engineA: Reference point of load diagram

Point A of load diagram

Line 1: Propeller curve through optimising point (O)

Line 7: Constant power line through specified MCR (M)

Point A: Intersection between lines 1 and 7

Fig. 21a: Example 3 with FPP – engine layout with SG (normal case)

Shaf

t gen

erat

or

Propulsion curvefor heavy running

3.3% A

S

5

62

4

1

7

O5

6

3

4 1

7

2

5% A

5% L1

A=M

Engine service curvefor heavy running

MP

SP

Engine speed

Power

M: Specified MCR of engineS: Continuous service rating of engineO: Optimising point of engineA: Reference point of load diagram

Fig. 21b: Example 3 with FPP – load diagram with SG (normal case)

Page 176: Hidrodinamica e Propulsao.pdf

large wave resistance, it can, therefore,be an advantage to design/move theload diagram more towards the left.

The latter can be done by moving theengine’s optimising point O – and thusthe propeller curve 1 through the opti�mising point – towards the left. How�ever, this will be at the expense of aslightly increased specific fuel oil con�sumption.

An example is shown in Figs. 20a and20b. As will be seen in Fig. 20b, andcompared with the normal case shownin Example 1 (Fig. 19b), the left�handlimitation line 4 is moved to the left, giv�ing a wider margin between lines 2 and4, i.e. a larger light running factor hasbeen used in this example.

Example 3:Normal case, with shaft generator

In this example a shaft generator (SG)is installed, and therefore the servicepower of the engine also has to incor�porate the extra shaft power required

for the shaft generator’s electricalpower production.

In Fig. 21a, the engine service curveshown for heavy running incorporatesthis extra power.

The optimising point O, and thereby theengine layout curve 1, will normally bechosen on the propeller curve (~ en�gine service curve) through point M.

Point A is then found in the same wayas in example 1, and the load diagramcan be drawn as shown in Fig. 21b.

Example 4:Special case, with shaft generator

Also in this special case, a shaft gener�ator is installed but, unlike in Example3, now the specified MCR for propul�sion MP is placed at the top of the lay�out diagram, see Fig. 22a. This involvesthat the intended specified MCR of theengine (Point M’) will be placed outsidethe top of the layout diagram.

One solution could be to choose adiesel engine with an extra cylinder,but another and cheaper solution is toreduce the electrical power productionof the shaft generator when running inthe upper propulsion power range.

If choosing the latter solution, the re�quired specified MCR power of the en�gine can be reduced from point M’ topoint M as shown in Fig. 22a. Therefore,when running in the upper propulsionpower range, a diesel generator has totake over all or part of the electricalpower production.

However, such a situation will seldomoccur, as ships rather infrequently op�erate in the upper propulsion powerrange. In the example, the optimisingpoint O has been chosen equal topoint S, and line 1 may be found.

Point A, having the highest possiblepower, is then found at the intersectionof line L1�L3 with line 1, see Fig. 22a,and the corresponding load diagram is

26

Shaf

t gen

erat

or

Propulsion curve for heavy running

SG

O=S

61

7

2

M

Engine service curvefor heavy running

MP

SP

AM´

Engine speed

Power

M: Specified MCR of engineS: Continuous service rating of engineO: Optimising point of engineA: Reference point of load diagram

Point A and M of load diagramLine 1: Propeller curve through optimising point (O)

M: Located on constant power line 7 through point Aand at MP’s speed

Point A: Intersection between line 1 and line L � LPoint

1 3

Fig. 22a: Example 4 with FPP – engine layout with SG (special case)

M: Specified MCR of engineS: Continuous service rating of engineO: Optimising point of engineA: Reference point of load diagram

Shaf

t gen

erat

or

Propulsion curvefor heavy running

3.3% A

SG

5

62

4

1

7

O=S

6

3

1

7

2

5% A

5% L1

M

Engine service curvefor heavy running

MP

SP

AM´

5

4

Engine speed

Power

Fig. 22b: Example 4 with FPP – load diagram with SG (special case)

Page 177: Hidrodinamica e Propulsao.pdf

drawn in Fig. 22b. Point M is found online 7 at MP’s speed.

Example with controllable pitch propeller

Example 5:With or without shaft generator

Layout diagram – without shaft generatorIf a controllable pitch propeller (CPP)is applied, the combinator curve (ofthe propeller with optimum propellerefficiency) will normally be selected forloaded ship including sea margin.

For a given propeller speed, the com�binator curve may have a given propellerpitch, and this means that, like for a fixedpitch propeller, the propeller may beheavy running in heavy weather.

Therefore, it is recommended to use alight running combinator curve (the dottedcurve), as shown in Fig. 23, to obtain anincreased operating margin for the dieselengine in heavy weather to the load limitsindicated by curves 4 and 5.

Layout diagram – with shaft generatorThe hatched area in Fig. 23 shows therecommended speed range between100% and 96.7% of the specified MCRspeed for an engine with shaft generatorrunning at constant speed.

The service point S can be located atany point within the hatched area.

The procedure shown in Examples 3and 4 for engines with FPP can also be

applied for engines with CPP runningon a combinator curve.

The optimising point O for engines withVIT can be chosen on the propeller curve1 through point A = M with an optimisedpower from 85 to 100% of the specifiedMCR as mentioned before in the sectiondealing with optimising point O.

Load diagramTherefore, when the engine’s specifiedMCR point M has been chosen includingengine margin, sea margin and thepower for a shaft generator, if installed,point M can be used as point A of theload diagram, which can then be drawn.

The position of the combinator curveensures the maximum load rangewithin the permitted speed range forengine operation, and it still leaves areasonable margin to the load limitsindicated by curves 4 and 5.

Influence on engine running ofdifferent types of ship resistance– plant with FP�propeller

In order to give a brief summary regard�ing the influence on the fixed pitchpropeller running and main engine opera�tion of different types of ship resistance,an arbitrary example has been chosen,see the load diagram in Fig. 24.

The influence of the different types ofresistance is illustrated by means ofcorresponding service points for propul�sion having the same propulsion power,using as basis the propeller designpoint PD, plus 15% extra power.

Propeller design point PDThe propeller will, as previously described,normally be designed according to aspecified ship speed V valid for loadedship with clean hull and calm weatherconditions. The corresponding enginespeed and power combination isshown as point PD on propeller curve6 in the load diagram, Fig. 24.

Increased ship speed, point S0If the engine power is increased by, forexample, 15%, and the loaded ship isstill operating with a clean hull and incalm weather, point S0, the ship speed

27

Minspeed

A=M

S

3.3%A

5

4

1

75%A

5%L

Recommended rangefor shaft generatoroperation withconstant speed

3

15

1

O

7

Combinator curvefor loaded shipand incl. sea margin

Maxspeed

M: Specified MCR of engineS: Continuous service rating of engineO: Optimising point of engineA: Reference point of load diagram

Engine speed

Power

4

Fig. 23: Example 5 with CPP – with or without shaft generator

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V and engine speed n will increase inaccordance with the propeller law (moreor less valid for the normal speed range):

V V V

n n nS

S

03 5

03 0

115 1041

115 1048

= × = ×= × = ×

. .

. .

.

.

Point S0 will be placed on the samepropeller curve as point PD.

Sea running with clean hull and 15%sea margin, point S2Conversely, if still operating with loadedship and clean hull, but now with extra

resistance from heavy seas, an extrapower of, for example, 15% is neededin order to maintain the ship speed V(15% sea margin).

As the ship speed VS2 = V, and if thepropeller had no slip, it would be expectedthat the engine (propeller) speed wouldalso be constant. However, as the waterdoes yield, i.e. the propeller has a slip,the engine speed will increase and therunning point S2 will be placed on apropeller curve 6.2 very close to S0, onpropeller curve 6. Propeller curve 6.2will possibly represent an approximate0.5% heavier running propeller thancurve 6.

Depending on the ship type and size,the heavy running factor of 0.5% maybe slightly higher or lower.

For a resistance corresponding toabout 30% extra power (30% sea mar�gin), the corresponding relative heavyrunning factor will be about 1%.

Sea running with fouled hull, andheavy weather, point SPWhen, after some time in service, theship’s hull has been fouled, and thusbecomes more rough, the wake fieldwill be different from that of a smoothship (clean hull).

A ship with a fouled hull will, conse�quently, be subject to an extra resis�tance which, due to the changedwake field, will give rise to a heavierrunning propeller than experiencedduring bad weather conditions alone.When also incorporating some aver�age influence of heavy weather, thepropeller curve for loaded ship willmove to the left, see propeller curve2 in the load diagram in Fig. 24. Thispropeller curve, denoted fouled hulland heavy weather for a loaded ship,is about 5% heavy running comparedto the clean hull and calm weatherpropeller curve 6.

In order to maintain an ample airsupply for the diesel engine’s com�bustion, which imposes a limitationon the maximum combination oftorque and speed, see curve 4 of theload diagram, it is normal practice tomatch the diesel engine and turbo�

28

8

5

932

1

7

4

90

85

95

75

7085

105

100

110

6.3

80

90 95 100 105

S3

80 110

SP

100% ref. point (A)Specified MCR (M)

6

6.2 6.1

S2S1S0

PD

Engine speed, % of A

A=M

Engine shaft power % of A

PD: Propeller design point, clean hull and calm weather

Continuous service rating for propulsion witha power equal to 90% specified MCR, based on:

S0: Clean hull and calm weather, loaded ship

S1: Clean hull and calm weather, ballast (trial)

S2: Clean hull and 15% sea margin, loaded ship

SP: Fouled hull and heavy weather, loaded ship

S3: Very heavy sea and wave resistance

Line 1: Propeller curve through point A=M, layout curve for engine

Line 2: Heavy propeller curve, fouled hull and heavy weather, loaded ship

Line 6: Light propeller curve, clean hull and calm weather,loaded ship, layout curve for propeller

Line 6.1: Propeller curve, clean hull and calm weather, ballast (trial)

Line 6.2: Propeller curve, clean hull and 15% sea margin, loaded ship

Line 6.3: Propeller curve, very heavy sea and wave resistance

Fig. 24: Influence of different types of ship resistance on the continuous service rating

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charger etc. according to a propellercurve 1 of the load diagram, equal tothe heavy propeller curve 2.

Instead of point S2, therefore, point SPwill normally be used for the engine lay�out by referring this service propulsionrating to, for example, 90% of the engine’sspecified MCR, which corresponds tochoosing a 10% engine margin.

In other words, in the example the pro�peller’s design curve is about 5% lightrunning compared with the propellercurve used for layout of the main engine.

Running in very heavy seas withheavy waves, point S3When sailing in very heavy sea against,with heavy waves, the propeller can be7�8% heavier running (and even more)than in calm weather, i.e. at the samepropeller power, the rate of revolutionmay be 7�8% lower.

For a propeller power equal to 90% ofspecified MCR, point S3 in the loaddiagram in Fig. 24 shows an exampleof such a running condition.

In some cases in practice with strongwind against, the heavy running hasproved to be even greater and even tobe found to the left of the limitation line4 of the load diagram.

In such situations, to avoid slamming ofthe ship and thus damage to the stemand racing of the propeller, the shipspeed will normally be reduced by thenavigating officers on watch.

Ship acceleration and operation inshallow watersWhen the ship accelerates and thepropeller is being subjected to a largerload than during free sailing, the effecton the propeller may be similar to thatillustrated by means of point S3 in theload diagram, Fig. 24. In some cases inpractice, the influence of accelerationon the heavy running has proved to beeven greater. The same conditions arevalid for running in shallow waters.

Sea running at trial conditions, point S1Normally, the clean hull propeller curve6 will be referred to as the trial trip pro�peller curve. However, as the ship is

seldom loaded during sea trials andmore often is sailing in ballast, the ac�tual propeller curve 6.1 will be morelight running than curve 6.

For a power to the propeller equal to90% specified MCR, point S1 on theload diagram, in Fig. 24, indicates anexample of such a running condition. Inorder to be able to demonstrate opera�tion at 100% power, if required, duringsea trial conditions, it may in somecases be necessary to exceed the pro�peller speed restriction, line 3, whichduring trial conditions may be allowedto be extended to 107%, i.e. to line 9of the load diagram.

Influence of ship resistance oncombinator curves – plant withCP�propeller

This case is rather similar with the FP�propeller case described above, andtherefore only briefly described here.

The CP�propeller will normally operateon a given combinator curve, i.e. for agiven propeller speed the propellerpitch is given (not valid for constantpropeller speed). This means thatheavy running operation on a givenpropeller speed will result in a higherpower operation, as shown in the ex�ample in Fig. 25.

29

S=PD Propeller design point incl. sea margins, and continuous service rating of engine

Line 1 Propeller curve for layout of engine

Line 1 Combinator curve for propeller design, clean hull and 15% sea margin, loaded ship

Line 6.1 Light combinator curve, fouled hull and calm weather, loaded ship

Line 2 Heavy combinator curve, fouled hull and heavy weather, loaded ship

Line 2.1 Very heavy combinator curve, very heavy sea and wave resistance

Fig. 25: Influence of ship resistance on combinator curves for CP�propeller

Engine speed, % of A

Engine shaft power % of A

50

55

60

65

70

75

80

85

90

95100105110

65 70 75 80 85 90 95 100 105 110

8 4 1 6 3

75

6.12.1

2

A=M

S=PD

100% ref. point (A)Specified MCR (M)

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Closing Remarks

In practice, the ship’s resistance willfrequently be checked against the resultsobtained by testing a model of the shipin a towing tank. The experimental tanktest measurements are also used foroptimising the propeller and hull design.

When the ship’s necessary power re�quirement, including margins, and thepropeller’s speed (rate of revolution)have been determined, the correctmain engine can then be selected, e.g.with the help of MAN B&W Diesel’scomputer�based engine selectionprogramme.

In this connection the interaction betweenship and main engine is extremely im�portant, and the placing of the engine’sload diagram, i.e. the choice of enginelayout in relation to the engine’s (ship’s)operational curve, must be made care�fully in order to achieve the optimumpropulsion plant. In order to avoid over�loading of the main engine for excessiverunning conditions, the installation of anelectronic governor with load control maybe useful.

If a main engine driven shaft generator –producing electricity for the ship – is in�stalled, the interaction between ship andmain engine will be even more complex.However, thanks to the flexibility of thelayout and load diagrams for the MANB&W engines, a suitable solution willnearly always be readily at hand.

References

[1] Technical discussion withKeld Kofoed Nielsen,Burmeister & Wain Shipyard,Copenhagen

[2] Ship ResistanceH.E. Guldhammer andSv. Aa. Harvald, 1974

[3] Resistance and Propulsion of Ships,Sv. Aa. Harvald, 1983

[4] Paint supplier “InternationalCoatings Ltd.”, 2003

[5] Fartygspropellrar och Fartygs Framdrift,Jan Tornblad, KaMeWa Publication,1985

Furthermore, we recommend:

[6] Prediction of Power of ShipsSv. Aa. Harvald, 1977 and 1986

[7] Propulsion of Single�Screw ShipsSv. Aa. Harvald & J.M. Hee, 1981

1

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1

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174 APENDICE D. SELECCAO DE MOTORES PROPULSORES

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Apendice EDerating para Reduzir Consumo de

Combustıvel

175

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176 APENDICE E. DERATING

Page 185: Hidrodinamica e Propulsao.pdf

— 1 — © Wärtsilä Corporation, June 2008

Rudolf Wettstein1 & David Brown2

Wärtsilä Switzerland Ltd, Winterthur

SummaryThis paper sets out ways to achieve worthwhile reductions in the fuel consumption of Wärtsilä low-speed engines when designing newbuildings. The key approach is to use the flexibility offered by the full power/speed layout field to select a better layout point at a derated power with a lower BSFC and also possibly a higher propeller efficiency.

Derating: a solution for high fuel savings and lower emissions

IntroductionFuel efficiency and environmental friendliness are high on the list of requirements for ship propulsion engines from today’s shipping- and shipbuilding industries. Thus Wärtsilä is committed to creating better technology in these areas that will benefit both the customers and the environment.

Yet it is often forgotten by many ship designers and those specifying low-speed main engines that advantage can be taken of the power/speed layout field of Wärtsilä low-speed engines to select an engine rating point with a still lower fuel consumption.

The concept of the power/speed layout field for low-speed marine diesel engines originated in the 1970s. The layout options were step-by-step widened until, in 1984, our low-speed engines began to be offered with a broad power/speed layout field. An engine’s contracted maximum continuous rating (CMCR) can be selected at any point in the power/speed field defined by the four corner points: R1, R2, R3 and R4 (Fig. 1). The rating point R1 is the maximum continuous rating (MCR) of the engine.

Most recently, the layout fields for certain engines, the RT-flex82C, RTA82C, RT-flex82T and RTA82T, are extended to increased speeds for the R1+ and R2+ points (Fig. 2). The extended fields offer widened flexibility to select the most efficient propeller speed for lowest daily fuel consumption, and the most economic propulsion equipment,

Fig. 1: Typical layout field for RTA and RT-flex engines. The contracted maximum continuous rating (CMCR) can be selected at any point, such as Rx, within the layout field. The ∆BSFC is the reduction in full-load BSFC for any rating point Rx relative to that at the R1 rating.[08#044]

Engine power, %R1

Engine speed, %R1

100

90

100

80

70

60908070

R1

R2

R3

R4

Consta

nt to

rque

line

0-1-2-3-4

-5

-6

-7

∆BSFCg/kWh

Rx

Higher propulsiveefficiency

Lowerspecificfuelconsumption

namely the propeller, shafting, etc.One basic principle of the engine layout field is

that the same maximum cylinder pressure (Pmax) is employed at all CMCR points within the layout field. Thus the reduced brake mean effective pressure (BMEP) obtained at the reduced power outputs in the field results in an increased ratio of Pmax/BMEP and thus lower brake specific fuel consumption (BSFC).

The other principle behind the layout field is

1 Rudolf Wettstein is Director, Marketing & Application Development, Ship Power, Wärtsilä Switzerland Ltd.

2 David Brown is Manager, Marketing Support, Wärtsilä Switzerland Ltd.

Page 186: Hidrodinamica e Propulsao.pdf

— 2 — © Wärtsilä Corporation, June 2008

that the lower CMCR speeds allow flexibility in selection of the optimum propeller with consequent benefits in propulsion efficiency and thus lower fuel consumption in terms of tonnes per day.

One feature to be borne in mind when selecting the rating point for the derated engine is the rating

Engine power, %R1

Engine speed, %R1

R1+

R2+

R3

R4

100

100

90

80

9080

R1

R2

Engine power, %R1

Engine speed, %R1

100

90

100

80

70

60908070

R1

R2

R3

R4

Rx2

Rx1

Rating lineslope = α

line (Fig. 3). This is the line through a CMCR rating point such that any point on the line represents a new power/speed combination that will give the same ship speed in knots. The points on the rating line all require the same propeller type but with different adaptations to suit the power/speed combination. In general, lower speeds of rotation require larger propeller diameters and thereby increase the total propulsive efficiency. Usually the selected propeller speed depends on the maximum permissible propeller diameter. The maximum diameter is often determined by operational requirements, such as design draught and ballast draught limitations, as well as class recommendations concerning propeller–hull clearance (pressure impulse induced by the propeller on the hull).

The slope of the rating line (α) depends broadly upon the ship type. It can range from 0.15 for tankers, bulk carriers and general cargo ships up to about 10,000 tdw to 0.22 for container ships larger than 3000 TEU and 0.25 for tankers and bulk carriers larger than 30,000 tdw.

Changing engine selection strategiesWhen the broad layout field was introduced in RTA engines in 1984 it was widely welcomed by shipowners and shipbuilders. Afterwards RTA engines were frequently selected at ratings in the lower part of the layout field to gain the benefits of

Fig. 2: For the RT-flex82C, RTA82C, RT-flex82T and RTA82T engines the layout fields are extended to the ratings R1+ and R2+ at the same powers as R1 and R2 respectively but with increased shaft speed.[08#049]

Fig. 3: For a given ship, a rating line (slope α) can be applied to the layout field so that all rating points on that line would give the same ship speed with a suitably optimized propeller. Rating points at lower speeds on the rating line require a larger propeller diameter and give a greater propulsive efficiency.

Fig. 4: Since the 1980s engine ratings have been selected over a steadily smaller area of the layout field.[08#051]

Engine power, %R1

Engine speed, %R1

100

90

100

80

70

60908070

R1

R2

R3

R4

Area of recentCMCR selection

Area of CMCRselection inthe 1980s

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— 3 — © Wärtsilä Corporation, June 2008

100

200

300

400

500

2004 2005 2006 2007 2008

Bunker price, US$/tonne380cSt HFO

Fig. 5: Bunker prices have considerably increased in recent times. The chart shows the average price of 380 cSt heavy fuel oil (HFO) from various ports around the world from 2004 to 2008. The green bars indicate the mean price for each year.[08#045]

lower fuel consumption.However, under the pressure of first costs and

softening bunker prices the strategy was changed and the selected power/speed combination has, during the past 15 years or so, been selected to be closer to the R1 rating (Fig. 4).

Yet, more recently, bunker prices have steadily climbed, rising by some 85 per cent in the course of 2007 from US$ 270 to US$ 500 per tonne (Fig. 5). The result is that bunkers are now the dominant part of ship operating costs.

Such drastic increases in bunker prices give a strong impetus to reduce fuel costs. They can also justify additional investment cost such as selecting an engine with an extra cylinder. The consequent fuel saving may make for an acceptable payback time on the additional investment cost. It would justify any efforts to increase the overall efficiency of the complete propulsion system.

Further impetus to implementing such changes in engine selection strategy will come from a future need to cut CO2 emissions. If a carbon trading

scheme is imposed on shipping it would give further economic advantage to reducing fuel consumption and further help to pay for any necessary extra investment costs.

In addition it is important to bear in mind that the fuel savings measures discussed here will also result in lower NOX emissions in absolute terms.

Derating engines for greater fuel savingsIn the following pages are some case studies for ship installations for which an engine is selected with an extra cylinder without increasing the engine’s power. These cases demonstrate that such engine derating can be an advantageous solution with remarkable saving potential. Depending on bunker costs, such a strategy can have a very attractive pay-back time.

The four case studies are for a Suezmax tanker, a Capesize bulk carrier, a Panamax container ship and a Post-Panamax container ship. They include estimations of the respective pay-back times for the additional engine costs.

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— 4 — © Wärtsilä Corporation, June 2008

In this case, a typical Suezmax tanker might be specified with a six-cylinder Wärtsilä RT-flex68-D main engine. However, if a seven-cylinder engine is employed instead, the daily fuel consumption can be reduced by some 3.4 per cent.

In the engine/propeller layout for this ship as shown in figure 6, the CMCR points for the two alternative engines are on the same rating line (α = 0.3) through a common design point for the same ship service speed (knots).

The calculation of annual fuel costs given in table 2 is based on 6000 hours running with heavy fuel oil

costing US$ 500 per tonne.The resulting payback time for the extra cost

associated with the additional engine cylinder is estimated to be between 3.5 and six years depending on the bunker price of US$ 600–400 per tonne respectively (Fig. 7). The calculations of the payback are based on an interest rate of eight per cent.

A similar case may be made for a Capesize bulk carrier as it would be similar in size and speed to a Suezmax tanker and would thus require a similar engine.

Table 1: Typical ship parameters for a Suezmax tanker

Length overall: about 274 mBeam: 46–50 mDesign draught: 16 mScantling draught: 17 mSea margin: 15 %Engine service load: 90 %

Table 2: Main engine options

Alternative engines: 6RT-flex68-D 7RT-flex68-DCylinder bore, mm: 680 680Piston stroke, mm: 2720 2720Stroke/bore ratio: 4:1 4:1MCR, kW / rpm: 18,780/95 21,910/95CMCR, kW / rpm: 18,780/95 18,460/89.7BMEP at CMCR, bar: 20.0 17.9CSR at 90% CMCR, kW/rpm: 16,902/91.7 16,614/86.6BSFC at CMCR, g/kWh:– 100% load: 169.0 164.8– 90% load: 165.6 162.6Daily fuel consumption, tonnes/day:– ISO fuel, LCV 42.7 MJ/kg: 67.2 64.8– LCV 40.5 MJ/kg: 70.8 68.4– As percentage, %: 100 96.6 –3.4%Annual fuel costs, US$: 8,853,000 8,544,000Fuel saving, US$: 0 – 309,000

Engine length, mm: 8690 9870Engine mass, tonnes: 472 533

Case 1: Suezmax tanker & Capesize bulk carrier

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— 5 — © Wärtsilä Corporation, June 2008

Engine speed, rpm8075 85 90 95 100

22,000

20,000

18,000

16,000

Engine power, kW

6RT-flex68-D

7RT-flex68-D

α = 0.3Constant ship speed

CSR16,614 kW86.6 rpm

CSR16,902 kW91.7 rpm

CMCR18,460 kW89.7 rpm

Design pointCMCR = R118,780 kW, 95 rpm

Case 1: Suezmax tanker & Capesize bulk carrier

Fig. 6: Engine/propeller layouts for a typical Suezmax tanker with a

derated seven-cylinder RT-flex68-D engine compared with a six-cylinder

engine at the full MCR power and speed.

[08#052]

Fig. 7: Variation of payback times from fuel savings according to

bunker costs for the derated engine with an extra cylinder for a typical

Suezmax tanker.[08#144]

3.0

2.0

1.0

0

Millions US$

2 4 6 8 10 12 14Years

Bunker price, HFO:$600/tonne

$500/tonne

$400/tonne

Investment approx. ($)

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— 6 — © Wärtsilä Corporation, June 2008

In this case, a typical Panamax container ship with a container capacity of up to 5000 TEU might be specified with an eight-cylinder Wärtsilä RT-flex82C main engine. However, if a nine-cylinder engine is employed instead, the daily fuel consumption can be reduced by some two per cent.

In the engine/propeller layout for this ship as shown in figure 8, the CMCR points for the two alternative engines are on the same rating line (α = 0.2) through a common design point for the same ship service speed (knots).

Case 2: Panamax container ship

The calculation of annual fuel costs given in table 4 is based on 6000 hours running with heavy fuel oil costing US$ 500 per tonne.

The resulting payback time for the extra cost associated with the additional engine cylinder is estimated to be between four and seven years depending on the bunker price of US$ 600–400 per tonne respectively (Fig. 9). The calculations of the payback are based on an interest rate of eight per cent.

Table 3: Typical ship parameters for a Panamax container ship

Length overall: about 295 mBeam: 32.2 mDesign draught: 12 mScantling draught: 13.5 mSea margin: 15 %Engine service load: 90 %

Table 4: Main engine options

Alternative engines: 8RT-flex82C 9RT-flex82CCylinder bore, mm: 820 820Piston stroke, mm: 2646 2646Stroke/bore ratio: 3.2:1 3.2:1MCR, kW / rpm: 36,160/102 40,680/102CMCR, kW / rpm: 36,160/102 35,480/97.5BMEP at CMCR, bar: 19.0 17.5CSR at 90% CMCR, kW / rpm: 32,544/98.5 32,250/94.3BSFC at CMCR, g/kWh:– 100% load: 169.0 166.6– 90% load: 166.5 164.6Daily fuel consumption, tonnes/day:– ISO fuel, LCV 42.7 MJ/kg: 130.0 127.4– LCV 40.5 MJ/kg: 137.1 134.3– As percentage, %: 100 98 – 2.0%Annual fuel costs, US$: 17,138,000 16,790,000Fuel saving, US$: 0 – 348,000

Engine length, mm: 14,055 16,500Engine mass, tonnes: 1020 1140

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— 7 — © Wärtsilä Corporation, June 2008

Case 2: Panamax container ship

Fig. 8: Engine/propeller layouts for a typical Panamax container ship with a derated nine-cylinder RT-flex82C

engine compared with an eight-cylinder engine at the full MCR

power and speed.[08#062]

Fig. 9: Variation of payback times from fuel savings according to

bunker costs for the derated engine with an extra cylinder for a typical

Panamax container ship.[08#145]

Engine power, kW

8RT-flex82C

9RT-flex82C

α = 0.2Constant ship speed

42,000

40,000

38,000

36,000

34,000

32,000

85 90 95 100 105

Engine speed, rpm

CMCR35,850 kW97.5 rpm

Design pointCMCR = R1+36,160 kW, 102 rpm

CSR32,544 kW98.5 rpm

CSR32,250 kW94.3 rpm

3.0

2.0

1.0

0

Millions US$

2 4 6 8 10 12 14Years

Bunker price, HFO:$600/tonne

$500/tonne

$400/tonne

Investment approx. ($)

4.0

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— 8 — © Wärtsilä Corporation, June 2008

In this case, a typical Post-Panamax container ship with a container capacity of around 7000 TEU might be specified with an eleven-cylinder Wärtsilä RT-flex96C main engine. However, if a 12-cylinder engine is employed instead, the daily fuel consumption can be reduced by some 2.4 per cent.

In the engine/propeller layout for this ship as shown in figure 10, the CMCR points for the two alternative engines are on the same rating line (α = 0.2) through a common design point for the same ship service speed (knots).

Case 3: Post-Panamax container ship

The calculation of annual fuel costs given in table 6 is based on 6000 hours running with heavy fuel oil costing US$ 500 per tonne.

The resulting payback time for the extra cost associated with the additional engine cylinder is estimated to be between two-and-a-half and four years depending on the bunker price of US$ 600–400 per tonne respectively (Fig. 11). The calculations of the payback are based on an interest rate of eight per cent.

Table 5: Typical ship parameters for a Post-Panamax container ship

Length overall: about 325 mBeam: 42.8 mDesign draught: 13 mScantling draught: 14.5 mSea margin: 15 %Engine service load: 90 %

Table 6: Main engine options

Alternative engines: 11RT-flex96C 12RT-flex96CCylinder bore, mm: 960 960Piston stroke, mm: 2500 2500Stroke/bore ratio: 2.6:1 2.6:1MCR, kW / rpm: 66,330/102 72,360/102CMCR, kW / rpm: 66,330/102 65,919/98.9BMEP at CMCR, bar: 19.6 18.4CSR at 90% CMCR, kW / rpm: 59,697/98.5 59,327/95.5BSFC at CMCR, g/kWh:– 100% load: 171.0 168.0– 90% load: 166.8 163.8Daily fuel consumption, tonnes/day:– ISO fuel, LCV 42.7 MJ/kg: 239 233.2– LCV 40.5 MJ/kg: 252 245.9– As percentage, %: 100 97.6 – 2.4%Annual fuel costs, US$: 31,500,000 30,738,000Fuel saving, US$: 0 – 762,000

Engine length, mm: 21,550 23,230Engine mass, tonnes: 1910 2050

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— 9 — © Wärtsilä Corporation, June 2008

Case 3: Post-Panamax container ship

Fig. 10: Engine/propeller layouts for a typical Post-Panamax container

ship with a derated 12-cylinder RT-flex96C engine compared with an

11-cylinder engine at the full MCR power and speed.

[08#127]

Fig. 11: Variation of payback times from fuel savings according to

bunker costs for the derated engine with an extra cylinder for the typical

Post-Panamax container ship.[08#146]

Engine speed, rpm90 95 100 105

72,000

70,000

66,000

62,000

Engine power, kW

11RT-flex96C

12RT-flex96C

α = 0.2Constant ship speed

CSR59,697 kW98.5 rpm

CMCR65,919 kW98.9 rpm

Design pointCMCR = R166,330 kW, 102 rpm

68,000

64,000

60,000

58,000

CSR59,327 kW95.5 rpm

8.0

4.0

2.0

0

Millions US$

2 4 6 8 10 12 14Years

Bunker price, HFO:$600/tonne

$500/tonne

$400/tonne

Investment approx. ($)

6.0

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Case 4: Derating without adding an engine cylinderIt is also feasible to apply a derated engine to obtain fuel savings in such a way that an additional engine cylinder is not required.

An example of this can be seen with the Wärtsilä RT-flex50 engine. In October 2007, the D version of this engine was announced, in which the engine power was increased by 5.1 per cent and the BSFC at full-load was reduced by 2 g/kWh compared with the B version.

Thus if a ‘-D’ engine is derated to the same cylinder power output as the original version of the RT-flex50, then the BSFC at full load is reduced by 4.5 g/kWh, or 2.7 per cent (see Table 7). For a typical bulk carrier with a six-cylinder RT-flex50 engine this can translate into annual savings of US$ 124,000 when operating for 6000 running hours a year with heavy fuel oil costing US$ 500 per tonne. Even greater savings are possible if the engine is derated to a lower running speed (rpm) at the derated power to gain the benefits of a better propulsion efficiency.

There are already a number of standard ship designs delivered and on order with RT-flex50-B or even the original RT-flex50 engine. So it would be perfectly feasible to install a derated RT-flex50-D in further newbuildings to the same ship designs and obtain the benefit of the substantial savings in operating costs. The overall dimensions of the D version are identical to those of the B and original versions of the RT-flex50. There would, however, be

a modest increase in cost of the D version for the higher-efficiency turbochargers used, but the extra cost would soon be repaid by the fuel cost savings.

Derating with flexibility to full ratingAlthough derating offers attractive economics, it can be frustrating to buy more ‘engine’ than seems necessary. Yet there is an interesting option to retain an ability to utilise the full available installed engine power, even up to the full R1 rating for future use to obtain higher ship service speeds.

The concept would be to set up the engine for the derated output at the chosen reduced service speed. Then for a later date, the engine could be re-adapted to the higher output. However, this needs corresponding provisions in the selection and design of the propeller, shafting and ancillary equipment to meet the requirements of the envisaged higher power. Furthermore the engine would need to be tested and approved by the Classification Society for both ratings with all the necessary emissions certification.

RT-flex technology as an important contribution to fuel savingWärtsilä RT-flex technology plays an important role in fuel saving. Wärtsilä RT-flex low-speed engines incorporate the latest electronically-controlled common-rail technology for fuel injection and valve actuation. The result is great flexibility in engine setting, bringing benefits in lower fuel consumption, lower minimum running speeds, smokeless operation

Table 7: Options for the Wärtsilä RT-flex50 engine type

Alternative engines: 6RT-flex50 6RT-flex50-DCylinder bore, mm: 500 500Piston stroke, mm: 2050 2050S/B ratio: 4.1:1 4.1:1MCR, kW / rpm: 9720/124 10,470/124CMCR, kW / rpm: 9720/124 9720/124BMEP at CMCR, bar: 19.5 19.5CSR at 90% CMCR, kW / rpm: 8748/119.7 8748/119.7BSFC at CMCR, g/kWh:– 100% load: 171 165.7– 90% load: 167.6 163.0Daily fuel consumption, tonnes/day:– ISO fuel, LCV 42.7 MJ/kg: 35.2 34.2– LCV 40.5 MJ/kg: 37.1 36.2– As percentage, %: 100 97.3 – 2.7%Annual fuel costs, US$: 4,637,000 4,513,000Fuel saving, US$: 0 – 124,000

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at all running speeds, and better control of other exhaust emissions.

Not only do RT-flex engines have a lower part-load fuel consumption than RTA engines but they can be adapted through Delta Tuning so that their part-load fuel consumtion is even lower. [1]

Owing to the interaction between fuel economy and NOX emissions, there is always the possibility that fuel saving measures will have an impact on NOX emissions. As with all new marine engines nowadays, Wärtsilä RTA and RT-flex engines are all fully compliant with the NOX emission regulation of Annexe VI of the MARPOL 1973/78 convention. Moreover, the engines in the Wärtsilä portfolio will be adapted to meet the coming IMO NOX reduction level Tier II.

ConclusionThe paper shows that there are techniques to achieve worthwhile reductions in the fuel consumption of Wärtsilä low-speed engines when designing newbuildings. The key approach is to use the flexibility offered by the full power/speed layout field to select a better layout point with a lower BSFC and

also possibly a higher propeller efficiency.It must also not be forgotten that any fuel savings

achieved at the ship design stage will have benefits in also reducing exhaust emissions.

If you have a project for which you wish to explore the fuel-saving possibilities through derating as set out in this paper, then please contact your nearest Wärtsilä office. Our experts will be delighted to calculate various alternatives for your evaluation.

References1. German Weisser, ‘Fuel saving with RT-flex’,

Wärtsilä Switzerland Ltd, July 2004.

Published June 2008 by:Wärtsilä Switzerland LtdPO Box 414CH-8401 WinterthurTel: +41 52 262 49 22Fax: +41 52 262 07 18www.wartsila.com