Results of statistical analysis of IHS Fairplay data - … · Statistical Analysis and...

Statistical Analysis and Determination of Regression Formulas for

Main Dimensions of Container Ships based on IHS Fairplay Data

Technical University of Denmark Hans Otto Kristensen

Project no. 2010-56, Emissionsbeslutningsstøttesystem Work Package 2, Report no. 03 February 2013

1

Determination of Regression Formulas for Main Dimensions of Container Ships based on IHS Fairplay Data

This report shows the results of the analysis of IHS Fairplay main data for container ships. All possible outliers have been left out (obvious errors in data) as described in following document: Data Analyses – Standard Vessel Determination. Tankers, Bulk Carries and Container Vessels. Project no. 2010-56. Work Package 2, Report no. 01. University of Southern Denmark. Author: Marie Lützen Container ships have been categorized in following 3 groups:

1. Feeder ships (TEU < 2900) 2. Panamax ships (1900 < TEU < 5300) 3. Post Panamax ships (TEU > 4000)

The equations found by regression analysis are shown for each individual ship sub type. The equations are basis for the generic ship design model for determination of main dimension and propulsion characteristics for all types of container ships – in the following called ‘DTU and SDU model’. As can be seen there is some overlap between the three sub categories. The Panamax ships have a breadth limitation of 32.2 m, an operational draught limitation of 12.0 m and a max overall length of 294.10, which define the upper limits of this group. The same is valid for Post Panamax ships with respect to a lower limit, as all ships with a breadth more than 32.2 m are categorized as Post Panamax ships. In the coming years the Post Panamax group will be subdivided in two parts by the coming Panama Canal limitations which will be valid from 2014, when the new Panama Canal is expected to be opened. The new limitations on Panamax ships in the future will be as follows (Marine Technology 2011): Length overall: 366.00 m, breadth: 49.00 m, draught: 15.24 m List of Appendices Appendix A - Small container ships page 4 Appendix B – Panamax container ships page 6 Appendix C – Post Panamax container ships page 8 Appendix D – Water plane area coefficient and draught change page 10

2

Fig. 1 Length between pp as function of TEU Fig. 2 Breadth as function of TEU

Fig. 3 Depth as function of TEU Fig. 4 Maximum draught as function of TEU

Fig. 5 Lightweight as function of TEU Fig. 6 Deadweight as function of TEU

All container ships

Yellow dots indicate DTU and SDU

default model values

70

110

150

190

230

270

310

350

390

0 2000 4000 6000 8000 10000 12000 14000 16000

Container capacity (TEU)

Le

ng

th p

p (

m)

All container ships



14

22

30

38

46

54

0 2000 4000 6000 8000 10000 12000 14000 16000


Bre

ad

th (

m)

All container ships



5

9

13

17

21

25

29

33

0 2000 4000 6000 8000 10000 12000 14000 16000


De

pth

(m

)

All container ships



4

7

10

13

16

0 2000 4000 6000 8000 10000 12000


Dra

ug

ht

(m)

All container ships



0

10000

20000

30000

40000

50000

0 2000 4000 6000 8000 10000 12000


Lig

htw

eig

ht

(t)

All container ships



0

20000

40000

60000

80000

100000

120000

140000

0 2000 4000 6000 8000 10000 12000


De

ad

we

igh

t (t

)

3

Fig. 7 Lightweight coefficient as function of TEU Fig. 8 Deadweight/TEU as function of TEU

Fig. 9 Block coefficient as function of TEU Fig. 10 Length displacement ratio as function of

TEU

All container ships



0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 2000 4000 6000 8000 10000 12000 14000 16000


Lig

htw

eig

ht/

Lp

p/B

/D (

t/m

3)

All container ships



8

10

12

14

16

18

0 2000 4000 6000 8000 10000 12000 14000 16000


Dw

/TE

U t

/m3)

All container ships



0.50

0.55

0.60

0.65

0.70

0.75

0.80

0 2000 4000 6000 8000 10000 12000


Blo

ck

co

eff

icie

nt

All container ships



4.0

4.5

5.0

5.5

6.0

6.5

7.0

0 2000 4000 6000 8000 10000 12000


Lp

p/D

ep

l.v

ol1

/3

4

Appendix A - Small container ships (< 2900 TEU) Length pp = 10.14 * TEU0.378 Breadth = 2.9 * TEU0.3 Depth = 0.767 * TEU0.394 Draught = 0.827 * TEU0.336 Lightweight/Lpp/B/D = 0.659 * TEU-0.23 Deadweight/TEU = 13.65

Fig. A1 Length between pp as function of TEU Fig. A2 Breadth as function of TEU

Fig. A3 Depth as function of TEU Fig. A4 Maximum draught as function of TEU

y = 10.14x0.378

R2 = 0.95

80

110

140

170

200

230

0 500 1000 1500 2000 2500 3000


Le

ng

th p

p (

m)

IHS Fairplay data

DTU-SDU model

Power (IHS Fairplay data)

y = 2.9x0.3

R2 = 0.92

14

18

22

26

30

34

0 500 1000 1500 2000 2500 3000


Bre

ad

th (

m)

IHS Fairplay data

DTU-SDU model

Potens (IHS Fairplay data)

y = 0.767x0.394

R2 = 0.87

5

9

13

17

21

0 500 1000 1500 2000 2500 3000


De

pth

(m

)

IHS Fairplay data

DTU-SDU model


y = 0.827x0.336

R2 = 0.88

4

6

8

10

12

14

0 500 1000 1500 2000 2500 3000


Dra

ug

ht

(m)

IHS Fairplay data

DTU-SDU model


5

Fig. A5 Block coefficient as function of TEU Fig. A6 Length displacement ratio as function of

TEU

Fig. A7 Deadweight/TEU as function of TEU Fig. A8 Lightweight coefficient as function of TEU

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0 500 1000 1500 2000 2500 3000


Blo

ck

co

eff

icie

nt

IHS Fairplay data

DTU-SDU model


4.0

4.5

5.0

5.5

6.0

6.5

0 500 1000 1500 2000 2500 3000


Lp

p/D

ep

l.v

ol1

/3

IHS Fairplay data

DTU-SDU model


8

10

12

14

16

18

20

0 500 1000 1500 2000 2500 3000


Dw

/TE

U (

t/T

EU

)

IHS Fairplay data

DTU-SDU model

y = 0.659x-0.23

R2 = 0.25

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 500 1000 1500 2000 2500 3000


Lig

htw

eig

ht/

Lp

p/B

/D (

t/m

3)

IHS Fairplay data

DTU-SDU model


6

Appendix B – Panamax container ships (1900 – 5300 TEU) Length pp = 2.494 * TEU0.555 (< = 3800 TEU) Length pp = 241.92 + (TEU – 3800) * 0.037 (>3800 TEU) Breadth = 32.22 m Depth = 14.77 + 0.0013 * TEU Draught = 2.19 * TEU0.211 (<= 3300 TEU) Draught = 12.1 + (TEU – 3300) * 0.00082 (> 3300 TEU) Lightweight/Lpp/B/D = 0.105 Deadweight/TEU = 14.6 – 0.00038 * TEU The regression formulas for the length and the draught have been split into two formulas respectively, in order to obtain the best possible curve fit, for length and draught. These adjustments were also carried out to obtain the best fitted values for the block coefficient and the length displacement ratio, which are calculated indirectly on basis of all the regression formulas, for the main dimensions and the weights.

Fig. B1 Length between pp as function of TEU Fig. B2 Breadth as function of TEU

x < 3800

y = 2.494x0.555

R2 = 0.83

150

180

210

240

270

300

1800 2300 2800 3300 3800 4300 4800 5300


Le

ng

th p

p (

m)

IHS Fairplay data

DTU-SDU model


y = -2E-07x + 32.22

R2 = 2E-05

32.0

32.1

32.2

32.3

32.4

1800 2300 2800 3300 3800 4300 4800 5300


Bre

ad

th (

m)

IHS Fairplay data

DTU-SDU model

Lineær (IHS Fairplay data)

7

Fig. B3 Depth as function of TEU Fig. B4 Maximum draught as function of TEU

Fig. B5 Block coefficient as function of TEU Fig. B6 Length displacement ratio as function of

TEU

Fig. B7 Lightweight coefficient as function of TEU Fig, B8 Deadweight/TEU as function of TEU

y = 0.0013x + 14.77

R2 = 0.38

12

15

18

21

24

1800 2300 2800 3300 3800 4300 4800 5300


De

pth

(m

)

IHS Fairplay data

DTU-SDU model


x < 3300

y = 2.19x0.211

R2 = 0.59

10

11

12

13

14

1800 2300 2800 3300 3800 4300 4800 5300


Dra

ug

ht

(m)

IHS Fairplay data

DTU-SDU model


0.50

0.55

0.60

0.65

0.70

0.75

0.80

1800 2300 2800 3300 3800 4300 4800 5300


Blo

ck

co

eff

icie

nt

IHS Fairplay data

DTU-SDU model


4.5

5.0

5.5

6.0

6.5

7.0

1800 2300 2800 3300 3800 4300 4800 5300


Lp

p/D

ep

l.v

ol1

/3

IHS Fairplay data

DTU-SDU model


y = 2E-06x + 0.0999

R2 = 0.005

0.00

0.03

0.06

0.09

0.12

0.15

1800 2300 2800 3300 3800 4300 4800 5300


Lig

htw

eig

ht/

Lp

p/B

/D (

t/m

3)

IHS Fairplay data

DTU-SDU model


y = - 0.00038x + 14.6

R2 = 0.06

10

12

14

16

1800 2300 2800 3300 3800 4300 4800 5300


Dw

/TE

U (

t/T

EU

)

IHS Fairplay data

DTU-SDU model


8

Appendix C – Post Panamax container ships (> 4000 TEU)

Length pp = 131.31 + 0.03012 * TEU – 0.00000099556 * TEU2 (<= 8000 TEU) Length pp = 14.66 * TEU0.339 (> 8000 TEU)

Breadth = 32.51 + 0.0013 * TEU Depth = MIN(30.2,16.5 + 0.0011 * TEU) Draught = 12.73 + 0.0002 * TEU Lightweight/Lpp/B/D = MAX(0.09,0.104 – 0.00000115 * TEU) Dw/TEU = MAX(11.2;50.43 * TEU-0.16) The regression formula for the length has been split into two formulas, in order to obtain the best possible curve fit, for the length. This adjustment was also carried out to obtain the best fitted values for the block coefficient and the length displacement ratio, which are calculated indirectly on basis of all the regression formulas, for the main dimensions and the weights.

Fig. C1 Length between pp as function of TEU Fig. C2 Breadth as function of TEU

>8000 TEU

y = 14.66x0.339

R2 = 0.89

<= 8000 TEU

y = -0.00000099556x2 + 0.030116x + 131.31

240

270

300

330

360

390

4000 6000 8000 10000 12000 14000 16000


Le

ng

th p

p (

m)

IHS Fairplay data

DTU-SDU model

Statistical outliers

Additional data (<8000 TEU)


Poly. (Additional data (<8000 TEU))

y = 0.0013x + 32.51

R2 = 0.82

36

39

42

45

48

51

54

57

4000 6000 8000 10000 12000 14000 16000


Bre

ad

th (

m)

IHS Fairplay data

DTU-SDU model


Linear (IHS Fairplay data)

9

Fig. C3 Depth as function of TEU Fig. C4 Maximum draught as function of TEU

Fig. C5 Block coefficient as function of TEU Fig. C6 Length displacement ratio as function of

TEU

Fig. C7 Lightweight coefficient as function of

TEU Fig. C8 Deadweight/TEU as unction of TEU

20

23

26

29

32

4000 6000 8000 10000 12000 14000 16000


De

pth

(m

)

IHS Fairplay data

DTU-SDU model


y = 0.0002x + 12.73

R2 = 0.30

11

12

13

14

15

16

17

4000 6000 8000 10000 12000 14000 16000


Dra

ug

ht

(m)

IHS Fairplay data

DTU-SDU model



0.50

0.55

0.60

0.65

0.70

0.75

0.80

4000 6000 8000 10000 12000 14000 16000


Blo

ck

co

eff

icie

nt

IHS Fairplay data


DTU-SDU model


5.6

5.8

6.0

6.2

6.4

6.6

4000 6000 8000 10000 12000 14000 16000


Lp

p/D

ep

l.v

ol1

/3

IHS Fairplay data

DTU-SDU model



y = -0.00000115x + 0.104

R2 = 0.05

0.00

0.02

0.04

0.06

0.08

0.10

0.12

4000 5000 6000 7000 8000 9000 10000 11000 12000


Lig

htw

eig

ht/

Lp

p/B

/D (

t/m

3)

IHS Fairplay data

DTU-SDU model


y = 50.43x-0.16

R2 = 0.29

10

11

12

13

14

15

4000 6000 8000 10000 12000 14000 16000


Dw

/TE

U (

t/T

EU

)

IHS Fairplay data

DTU- SDU model



10

Appendix D – Water plane area coefficient and draught change The water plane area coefficient, Cw, at maximum draught, for container ships is shown in Fig. D1 for ships in the IHS Fairplay data base. Cw depends on the block coefficient, Cb, as follows: Cw = 0.55 + 0.45 Cb where Cw and Cb are calculated on basis of the length between pp.

Fig. D1 Water plane area coefficient as function of the block coefficient for container ships (IHS

Fairplay)

Fig. D2 Water plane area coefficient as function the relative displacement

In Fig. D2 is shown the water plane area coefficient as function of the relative displacement for some container ships, for which more detailed information has been available. Based on the

results in Fig. D2, the water plane area coefficient at a displacement can be approximated as follows:

( ) ( ) (

) ( ) (

)

It is important to know the how the water plane area coefficient depends on the displacement as it is used to calculate the draught change due to change of the displacement. Maximum/scantling draught and design draught All data presented in this report are presented as function of the maximum deadweight. Normally two draughts are specified for container ships, namely the design draught and the scantling draught. The design draught is the draught at which the ship is expected to operate normally, while the scantling draught is the maximum permissible draught according to the class rules. Comparison of scantling draught data (Significant Ships, 1990 – 2010) with summer load line draught data (denoted maximum draught in this report and in the IHS Fairplay data base) shows

y = 0.45x + 0.55

0.75

0.80

0.85

0.90

0.95

0.55 0.60 0.65 0.70 0.75 0.80

Block coefficient

Wa

terp

lan

e a

rea

co

eff

icie

nt

0.65

0.70

0.75

0.80

0.85

0.90

0.95

50 60 70 80 90 100

Relative displacement (%)

Wa

terp

lan

e a

rea

co

eff

icie

nt

(-)

Cb = 0,66 Cb = 0,61 Cb = 0,68 Cb = 0,65

Cb = 0,60 Cb = 0,64 Cb = 0,62 Cb = 0,65

11

that the summer load line draught is nearly identical with the scantling draught (Fig. D3). The summer load line is the maximum permitted draught at which both stability and strength requirements are fulfilled, i.e. it is maximum draught approved by the Maritime Authorities. The design draught is less than the scantling draught, which is shown in Fig. D4 based on data for 255 container ships from Significant Ships (1990 – 2010). Regression formulas for determination of the design draught as function of TEU have been developed as follows (see Fig. D5): Design draught = MIN(12; 1.188 * TEU0.279) for Panamax and feeder ships Design draught = 4.83 * TEU0.11 for Post Panamax ships

Fig. D3 Maximum draught for container ships

(IHS Fairplay) compared with scantling draught according to Significant Ships (1990 – 2010)

Fig. D4 Design draught versus scantling draught for container ships according to

Significant Ships (1990 – 2010)

Fig. D5 Design draught for container ships

according to Significant Ships (1990 – 2010) Fig. D6 Design and scantling draught according to DTU-SDU model

4

7

10

13

16

0 3000 6000 9000 12000 15000


Dra

ug

ht

(m)

Max. draught (IHS Fairplay)

Scantling draught (Significant Ships)

4

7

10

13

16

0 3000 6000 9000 12000 15000


Dra

ug

ht

(m)

Design draught (Significant Ships)

Scantling draught (Significant Ships)

y = 1.188x0.279

R2 = 0.89

y = 4.83x0.11

R2 = 0.27

4

7

10

13

16

0 3000 6000 9000 12000 15000


De

sig

n d

rau

gh

t (m

)

Panamax ships (Significant Ships)

Post Panamax ships (Significant Ships)

Potens (Panamax ships (Significant Ships))

Potens (Post Panamax ships (Significant Ships))

4

7

10

13

16

0 2000 4000 6000 8000 10000 12000


Dra

ug

ht

(m)

Maximum draught (IHS Fairplay data)

Design Draught (DTU-SDU model)

Maximum draught (DTU-SDU model)

12

For container ships, the design displacement is 85 % to 90 % of the maximum displacement which means that Cw ~ 0.45 ⋅ Cb + 0.55. The design deadweight can then be calculated according to this approximate formula:

( ) ⋅ ⋅ ⋅ ⋅ ( ) ⋅

The resulting design deadweight is shown in Fig. D7, where it is compared with design deadweight data from Significant Ships (1990 – 2010).

Fig. D7 Design deadweight Fig. D8 Maximum deadweight

0

30000

60000

90000

120000

150000

0 3000 6000 9000 12000 15000


De

sig

n d

ea

dw

eig

ht

(m)



DTU-SDU model

0

40000

80000

120000

160000

0 3000 6000 9000 12000 15000


Ma

xim

um

de

ad

we

igh

t (t

)



DTU-SDU model

Results of statistical analysis of IHS Fairplay data - … · Statistical Analysis and...

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