Ship Project A

2014

ASSIGNMENT ONE

RAN XIAO 467643 & THEIR TOMAS 224051

Resistance estima𝐭𝐢on

Methodology brief

As our ship concept is in form of catamaran, it is not proper to simply introduce the method and

diagrams of monohull ship series. For catamarans, the interaction of waves generated by twin hulls

cannot be ignored and thus affects the friction resistance as well as wave pattern resistance.

Different from the methodology used in the previous report where Delft Series (98’) and John

Winter’s empirical resistance diagram are introduced, here we apply the method and diagrams

deduced in <Resistance Experiments on a Systematic Series of High Speed Displacement

Catamaran Forms: Variation of Length-Displacement Ratio and Breadth-Draught Ratio>.

By this method, resistance coefficient is defined as follow:

𝐶𝑡𝑐𝑎𝑡𝑎𝑚𝑎𝑟𝑎𝑛= (1 + ∅ ∙ 𝑘) ∙ 𝜎 ∙ 𝐶𝑓 + 𝜏 ∙ 𝐶𝑊

Where ∅ is related to the pressure field change and τ is about wave resistance intereface

factor. For simplification, the formula is transformed into:

𝐶𝑡𝑐𝑎𝑡𝑎𝑚𝑎𝑟𝑎𝑛= (1 + 𝛽 ∙ 𝑘) ∙ 𝐶𝑓 + 𝜏 ∙ 𝐶𝑊

Based on this equation, the practical resistance expression is deduced as:

𝐶𝑡𝑐𝑎𝑡𝑎𝑚𝑎𝑟𝑎𝑛= 𝐶𝐹𝑠ℎ𝑖𝑝

+ 𝐶𝑅𝑚𝑜𝑑𝑒𝑙− 𝛽 ∙ 𝑘 ∙ (𝐶𝐹𝑀𝑜𝑑𝑒𝑙

− 𝐶𝐹𝑠ℎ𝑖𝑝)

According to our design, parameters are summarized as:

CB CP Cw L/√∆3

S/L B/T

0.495 0.62 0.7 6.34 0.3 1.8

Then we can select the corresponding diagram and mother ship from <Resistance Experiments

on a Systematic Series of High Speed Displacement Catamaran Forms: Variation of Length-

Displacement Ratio and Breadth-Draught Ratio>. Here model are classified as:

We choose 3b* since it is the most similar one. Relevant parameters of 3b* are:

Here are some apparent differences in terms of CP, which may lead to some unexpected estimation

result. As CP stands for how full the underwater part of hull is, a relatively larger value can make

the predicted resistance larger than it should be. But since it is a rough estimation, the estimation

error is acceptable.

Determination of coefficients

Source: <Resistance experiments on a systematic series of high speed displacement catamaran

forms: variation of length-displacement ratio and breadth-draught ratio>

As mentioned previously, we know 𝐶𝑡𝑐𝑎𝑡𝑎𝑚𝑎𝑟𝑎𝑛= (1 + 𝛽 ∙ 𝑘) ∙ 𝐶𝑓 + 𝜏 ∙ 𝐶𝑊 and in this figure, the

curves of 𝐶𝑡𝑐𝑎𝑡𝑎𝑚𝑎𝑟𝑎𝑛 and (𝐶𝑡𝑐𝑎𝑡𝑎𝑚𝑎𝑟𝑎𝑛

− 𝐶𝑊) have been given, together there are also curves of

𝐶𝑓 and (1.65) ∙ 𝐶𝑓. Apparently, illustrated in the figure, the curve of (𝐶𝑡𝑐𝑎𝑡𝑎𝑚𝑎𝑟𝑎𝑛− 𝐶𝑊)

matches very well with that of (1.65) ∙ 𝐶𝑓 outside the Froude Number zone of [0.2, 0.65].

Unfortunately the resistance we are studying is in this zone, so we have to estimate the value of

1 + 𝛽 ∙ 𝑘 one by one according to the graph above, and we yield following graph:

And from the graph below we can also conclude all the 𝐶𝑅𝑚𝑜𝑑𝑒𝑙= 𝐶𝑅𝑠ℎ𝑖𝑝

= 𝐶𝑅 at corresponding

speed..

Source: <Resistance experiments on a systematic series of high speed displacement catamaran

forms: variation of length-displacement ratio and breadth-draught ratio>

8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16

1+beta*k 1.77 1.88 1.94 2.02 2 2.25 2.38 2.5 2.63 2.88 3.03 2.95 2.76 2.56 2.43 2.16 1.98

1.77 1.881.9412.02 22.25

2.3752.5

2.6252.875

3.0252.9492.763

2.562.432

2.1621.975

0

0.5

1

1.5

2

2.5

3

3.5

1+b

eta

*k

speed (knots)

1+beta*k

1+beta*k

Resistance prediction

Now we have all the values needed for resistance calculation. According to the resistance

expression 𝐶𝑡𝑐𝑎𝑡𝑎𝑚𝑎𝑟𝑎𝑛= 𝐶𝐹𝑠ℎ𝑖𝑝

+ 𝐶𝑅𝑚𝑜𝑑𝑒𝑙− 𝛽 ∙ 𝑘 ∙ (𝐶𝐹𝑀𝑜𝑑𝑒𝑙

− 𝐶𝐹𝑠ℎ𝑖𝑝) as well as formulas

𝐶𝐹𝑚𝑜𝑑𝑒𝑙=

0.075

[log10(𝐹𝑛×5.56×106)−2}2 and ITTC’57 Correlation line: 𝐶𝐹 =0.075

[log10 𝑅𝑛−2]2, we have the

following graph:

The coefficient climbs greatly after the speed exceeds 12 knots due to the drastic increase of 𝐶𝑅

at the corresponding speed.

Now lastly, we assume our wet surface is 75 m2. We are able to calculate the drag according to

the previous formula and draw the curve in the figure below:

8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16

Ct 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01 0.01

0.0027 0.0023

0.0031 0.0036 0.0039 0.0038 0.0039 0.0042

0.0055

0.0070

0.0085

0.0097

0.0113 0.0115 0.0115 0.0110

0.0106

0.0000

0.0020

0.0040

0.0060

0.0080

0.0100

0.0120

0.0140

Re

sist

amce

co

eff

icie

nt

Speed (knots)

Resistacne Coefficient prediction

Rotation Speed & Propeller Design

Propeller

The ship will be using two propellers, one under each hull at the rear, as seen in figure 1. However,

unlike the ship in the picture, our ship will be using azimuth thrusters. The general idea will still be

the same, though, as the number of propellers and their operation points will be the same. The

number of propellers was chosen because each hull contains a separate engine, and with each

engine driving one propeller we will get some control advantages, and this means that the area

between the hulls can be kept clear.

1785.0682821655.0019242527.373656

3347.5404293994.6657954222.1068984749.460218

5590.806383

7991.980875

11158.21932

14579.67337

17922.69001

22436.49238

24514.3639

26380.9974826984.75826

27601.9221

0

5000

10000

15000

20000

25000

30000

8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16

resi

stan

ce (

N)

speed (knots)

Resistance prediction

Fig. 1, A catamaran (Aluma Marine Mana’O II) with one propeller under each hull [1]

In the initial concept design we calculated that the desired speed could be achieved using two

azimuth thrusters of 100 kW (the power needed was approximately 180 kW, so to ensure sufficient

power 2 x 100 kW could be used). By checking this to available solutions on the market we can

estimate the size of the propeller in this case.

Parameters & assumptions

According to the report and previous calculation, we can find out the following information:

Engine type: Type: Standard azimuth thrusters - type US 55P4

Max input power: 330 KW

Propeller diameter: 1050 mm

Vessel design speed: 15 knots

Resistance at 15 knots: 26381 N

Now as we are going to design the propeller initially, we have to make some assumption for further

calculation and we’ll go back to check if our assumptions are reasonable. So here we assume:

t = 0,125

Ap = 0,55

w = 0,45

𝜂𝐻

= 1−𝑡

1−𝑤= 1,591 and 𝜂

𝑠= 0,98 (taken from empirical statistics from vessels whose

engines are located at the rear part), 𝜂𝐺

= 0,96 for gear box efficiency

Propeller design

Based on the resources we have at hand, we choose Wageningen B4-55 as our propeller type. As

we already have the thrust deduction and wake factor, the table below can be work out for

application of the B-series diagram and data interpolation.

Speed (knot)/(m/s) D(m) N(round/s) J KT VA(m/s) ᵹ

15 7,716667 1,05 3 1,347354 1,344416 4,244167 0,742195

15 7,716667 1,05 3,5 1,469841 0,987734 4,244167 0,865894

15 7,716667 1,05 4 1,286111 0,756234 4,244167 0,989594

15 7,716667 1,05 4,5 1,14321 0,597518 4,244167 1,113293

15 7,716667 1,05 5 1,028889 0,48399 4,244167 1,236992

15 7,716667 1,05 5,5 0,828456 0,399992 4,244167 1,360691

15 7,716667 1,05 6 0,759418 0,336104 4,244167 1,48439

15 7,716667 1,05 6,5 0,701001 0,286385 4,244167 1,60809

15 7,716667 1,05 7 0,65093 0,246934 4,244167 1,731789

We can interpolate the ᵹ values that we have into the diagram Fig. 2 to find out the

corresponding values of 𝜂0, pitch ratio and BP with which we can calculate the deliver power and

effective power.

Fig. 2 B4-55 diagram

Source: <Ship Principle>

N(round/s) ᵹ P/D 𝜼𝟎 Bp

4 0,989594 1,17 0,734 0,41

4,5 1,113293 1,07 0,729 0,43

5 1,236992 0,99 0,712 0,45

According to the formula given in figure 1: 𝐵𝑃2 = 𝑃𝐷

0,5

𝐷∙𝑉𝐴1,5 , here comes the deliver power. Using the

efficiency we have assumed and 𝜂0 we get, the corresponding effective power and engine power

are able to be listed out.

N(round/s) Bp PD Ps PE

4 0,41 77,63311 82,52 90,65

4,5 0,43 85,3918 90,77 99,04

5 0,45 93,51996 99,40 105,93

Since in previous calculation we have known that the needed power for our design at 15 knots is

about 101,8 KW for each propeller, now we can make a graph to see where the needed power and

effective power meet so that we can determine the optimal pitch ratio and RPM for our propeller.

Apparently, the optimal configuration for our design is RPM = 278 with P/D = 1,05

Assumption Examination

Previously we assume w = 0,45. Now we know our pitch ratio and KT is available, we can check if it

makes sense.

As T = 26381 in total, KT = T/(2*1025*𝜌*N2*D4)=0,56 corresponds to the J0=0,65. Therefore, w = 1-

J0/J = 0,41 which is quite close to our estimated value.

4 4.5 5

engine power 82.52 90.77 99.40

effective power 90.65 99.04 105.93

needed power 101.8 101.8 101.8

0.00

20.00

40.00

60.00

80.00

100.00

120.00

po

we

r (K

W)

propeller speed (round/s)

RPM against Power

engine power effective power needed power

Source: <Ship Principle>

Propeller coefficient

𝜂0 𝜂

𝐻 𝜂

𝑆 𝜂

𝐺

0.718 1.591 0.98 0.96

2.2 Machinery

In this part, the choice of machinery will be discussed. We will try to explain why a certain piece of

machinery has been chosen, and what this means for the ship.

The power for the propulsion will be generated using hydrogen cells, and the energy generated will

be stored on on-board batteries as needed. With this system the ship will be able to achieve the

image of a green ship, which will appeal to both commuters and tourists. Thanks to the use of fuel

cells the energy can be generated only when needed, e.g. when the power in the batteries goes

under a certain amount, and if there is sufficient power available only the batteries will drive the

engines. This means that the ship’s machinery consists of four different components have to be

defined: The electric engines, the fuel cells, the hydrogen tanks, and the batteries.

The electric engine needs to be chosen so that it can produce sufficient energy for the propeller it

is driving. When accounting for the efficiency of the propeller the power of the engine should be

at least 150 kW. Here we could use e.g. the Siemens PEM-Motor 1DB2016 – WS54, which has a

power of 160 kW with a weight of < 350 kg [2].

The fuel cells are hard to find information on, but there are definitely fuel cells available at the

power we wish to use. The German company proton motor, for example, manufactures fuel cells

of up to several hundred kW for maritime use [3]. The price is hard to estimate, though, as the

technology improves constantly, and the price varies greatly depending on the product and its

specifications (custom/serial production, power-weight ratio etc.).

For the hydrogen tanks we calculated that we need a capacity of 70 kg. At 350 bar hydrogen has a

density of 70 kg/m3, which means that we need a total of 1000 l of tank space. This means that we

need a total of twenty 50 l tanks. The total weight of these is about 1000 kg.

Finally, the batteries need to store excess energy created by the fuel cells. In the case of the

Zemships 2 concept (which is a ship of a similar size to ours), the ship has 7 x 80 V lead-gel batteries,

giving 360 Ah. Since our ship uses a bit more power (the Zemships concept only has one 48 kW

fuel cell) we would probably need a bit more batteries. A linear approximation puts the amount at

roughly 42 x 80 V batteries. This can still be changed in the future, though, in case we e.g. want to

change to lithium-ion batteries, or get a more precise value on the needed amount of batteries.

Reference

1 Custom aluminum work boats, crew boats, rib boats, deck boats, response vessels marine

fabrication; http://www.alumamarine.com/workboat_files/alumcatamaran/2.jpg; 24.9.2014

2 https://www.industry.usa.siemens.com/drives/us/en/electric-drives/hybrid-

drives/Documents/elfa-components-data-sheets.pdf

3 http://www.eurosfaire.prd.fr/7pc/documents/1374147913_sebastian_dirk___proton_moto

r.pdf

4 Molland, A.F., Wellicome, J.F. and Couser, P.R. (1994) Resistance experiments on a systematic

series of high speed displacement catamaran forms: variation of length-displacement ratio

and breadth-draught ratio. Southampton, UK, University of Southampton, 84pp.

5 Sverre Steen and Knut Minsaas, Ship Resistance, Department of Marine Technology, NTNU,

2013.

6 Zhengbang Sheng, Zhongying Liu, Shanghai Transportation University, <Ship Principal>, 2003.