wp 2 report 3 regression analysis for container ships
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Wp 2 Report 3 Regression Analysis for Container ShipsTRANSCRIPT
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
Yellow dots indicate DTU and SDU
default model values
14
22
30
38
46
54
0 2000 4000 6000 8000 10000 12000 14000 16000
Container capacity (TEU)
Bre
ad
th (
m)
All container ships
Yellow dots indicate DTU and SDU
default model values
5
9
13
17
21
25
29
33
0 2000 4000 6000 8000 10000 12000 14000 16000
Container capacity (TEU)
De
pth
(m
)
All container ships
Yellow dots indicate DTU and SDU
default model values
4
7
10
13
16
0 2000 4000 6000 8000 10000 12000
Container capacity (TEU)
Dra
ug
ht
(m)
All container ships
Yellow dots indicate DTU and SDU
default model values
0
10000
20000
30000
40000
50000
0 2000 4000 6000 8000 10000 12000
Container capacity (TEU)
Lig
htw
eig
ht
(t)
All container ships
Yellow dots indicate DTU and SDU
default model values
0
20000
40000
60000
80000
100000
120000
140000
0 2000 4000 6000 8000 10000 12000
Container capacity (TEU)
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
Yellow dots indicate DTU and SDU
default model values
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 2000 4000 6000 8000 10000 12000 14000 16000
Container capacity (TEU)
Lig
htw
eig
ht/
Lp
p/B
/D (
t/m
3)
All container ships
Yellow dots indicate DTU and SDU
default model values
8
10
12
14
16
18
0 2000 4000 6000 8000 10000 12000 14000 16000
Container capacity (TEU)
Dw
/TE
U t
/m3)
All container ships
Yellow dots indicate DTU and SDU
default model values
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0 2000 4000 6000 8000 10000 12000
Container capacity (TEU)
Blo
ck
co
eff
icie
nt
All container ships
Yellow dots indicate DTU and SDU
default model values
4.0
4.5
5.0
5.5
6.0
6.5
7.0
0 2000 4000 6000 8000 10000 12000
Container capacity (TEU)
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
Container capacity (TEU)
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
Container capacity (TEU)
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
Container capacity (TEU)
De
pth
(m
)
IHS Fairplay data
DTU-SDU model
Potens (IHS Fairplay data)
y = 0.827x0.336
R2 = 0.88
4
6
8
10
12
14
0 500 1000 1500 2000 2500 3000
Container capacity (TEU)
Dra
ug
ht
(m)
IHS Fairplay data
DTU-SDU model
Potens (IHS Fairplay data)
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
Container capacity (TEU)
Blo
ck
co
eff
icie
nt
IHS Fairplay data
DTU-SDU model
Potens (IHS Fairplay data)
4.0
4.5
5.0
5.5
6.0
6.5
0 500 1000 1500 2000 2500 3000
Container capacity (TEU)
Lp
p/D
ep
l.v
ol1
/3
IHS Fairplay data
DTU-SDU model
Potens (IHS Fairplay data)
8
10
12
14
16
18
20
0 500 1000 1500 2000 2500 3000
Container capacity (TEU)
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
Container capacity (TEU)
Lig
htw
eig
ht/
Lp
p/B
/D (
t/m
3)
IHS Fairplay data
DTU-SDU model
Potens (IHS Fairplay data)
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
Container capacity (TEU)
Le
ng
th p
p (
m)
IHS Fairplay data
DTU-SDU model
Potens (IHS Fairplay data)
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
Container capacity (TEU)
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
Container capacity (TEU)
De
pth
(m
)
IHS Fairplay data
DTU-SDU model
Lineær (IHS Fairplay data)
x < 3300
y = 2.19x0.211
R2 = 0.59
10
11
12
13
14
1800 2300 2800 3300 3800 4300 4800 5300
Container capacity (TEU)
Dra
ug
ht
(m)
IHS Fairplay data
DTU-SDU model
Potens (IHS Fairplay data)
0.50
0.55
0.60
0.65
0.70
0.75
0.80
1800 2300 2800 3300 3800 4300 4800 5300
Container capacity (TEU)
Blo
ck
co
eff
icie
nt
IHS Fairplay data
DTU-SDU model
Potens (IHS Fairplay data)
4.5
5.0
5.5
6.0
6.5
7.0
1800 2300 2800 3300 3800 4300 4800 5300
Container capacity (TEU)
Lp
p/D
ep
l.v
ol1
/3
IHS Fairplay data
DTU-SDU model
Potens (IHS Fairplay data)
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
Container capacity (TEU)
Lig
htw
eig
ht/
Lp
p/B
/D (
t/m
3)
IHS Fairplay data
DTU-SDU model
Lineær (IHS Fairplay data)
y = - 0.00038x + 14.6
R2 = 0.06
10
12
14
16
1800 2300 2800 3300 3800 4300 4800 5300
Container capacity (TEU)
Dw
/TE
U (
t/T
EU
)
IHS Fairplay data
DTU-SDU model
Lineær (IHS Fairplay data)
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
Container capacity (TEU)
Le
ng
th p
p (
m)
IHS Fairplay data
DTU-SDU model
Statistical outliers
Additional data (<8000 TEU)
Power (IHS Fairplay data)
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
Container capacity (TEU)
Bre
ad
th (
m)
IHS Fairplay data
DTU-SDU model
Statistical outliers
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
Container capacity (TEU)
De
pth
(m
)
IHS Fairplay data
DTU-SDU model
Statistical outliers
y = 0.0002x + 12.73
R2 = 0.30
11
12
13
14
15
16
17
4000 6000 8000 10000 12000 14000 16000
Container capacity (TEU)
Dra
ug
ht
(m)
IHS Fairplay data
DTU-SDU model
Statistical outliers
Linear (IHS Fairplay data)
0.50
0.55
0.60
0.65
0.70
0.75
0.80
4000 6000 8000 10000 12000 14000 16000
Container capacity (TEU)
Blo
ck
co
eff
icie
nt
IHS Fairplay data
Statistical outliers
DTU-SDU model
Power (IHS Fairplay data)
5.6
5.8
6.0
6.2
6.4
6.6
4000 6000 8000 10000 12000 14000 16000
Container capacity (TEU)
Lp
p/D
ep
l.v
ol1
/3
IHS Fairplay data
DTU-SDU model
Statistical outliers
Power (IHS Fairplay data)
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
Container capacity (TEU)
Lig
htw
eig
ht/
Lp
p/B
/D (
t/m
3)
IHS Fairplay data
DTU-SDU model
Linear (IHS Fairplay data)
y = 50.43x-0.16
R2 = 0.29
10
11
12
13
14
15
4000 6000 8000 10000 12000 14000 16000
Container capacity (TEU)
Dw
/TE
U (
t/T
EU
)
IHS Fairplay data
DTU- SDU model
Statistical outliers
Power (IHS Fairplay data)
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
Container capacity (TEU)
Dra
ug
ht
(m)
Max. draught (IHS Fairplay)
Scantling draught (Significant Ships)
4
7
10
13
16
0 3000 6000 9000 12000 15000
Container capacity (TEU)
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
Container capacity (TEU)
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
Container capacity (TEU)
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
Container capacity (TEU)
De
sig
n d
ea
dw
eig
ht
(m)
Panamax ships (Significant Ships)
Post Panamax ships (Significant Ships)
DTU-SDU model
0
40000
80000
120000
160000
0 3000 6000 9000 12000 15000
Container capacity (TEU)
Ma
xim
um
de
ad
we
igh
t (t
)
Panamax ships (Significant Ships)
Post Panamax ships (Significant Ships)
DTU-SDU model