5th International Conference
on High Performance Marine Vehicles,
8-10 November, 2006, Australia
SWATH Ship Design Formulae Based on Artifical Neural Nets
Volker Bertram, ENSIETA, Brest/France, volker.bertram@ensieta.fr
Ehsan Mesbahi, University of Newcastle, Newcastle/UK, ehsan.mesbahi@newcastle.ac.uk
Abstract
Simple design formulae for resistance and power prediction for SWATH ships are derived
using Artificial Neural Nets. These formulae can be programmed easily in spreadsheets or
optimization routines. The formulae were derived from a database compiled at ENSIETA and
are supplemented by previous work. The experience with the presented applications shows
that artificial neural nets allow often a better approximation of data than classic regression
analysis, but this is largely due to the more adaptable functional relations.
1. Introduction
Experienced model basins have a long tradition of simple and fast power prediction of ships in initial
design based on very few parameters like main dimensions and speed. These traditional methods work
well for conventional ships. For unconventional ship types like SWATHs (small-waterplane area twin
hulls), Gore (1985), Lang and Slogett (1985), Bertram and Seif (2004), Figure 1, new simple estimates must be developed and updated as more experience is gathered.
Figure1: SWATH
Conventional regression has been extensively used in naval architecture in system identification to
provide required factors and coefficients. Based on databases of existing designs, coefficients are then
interpolated or even extrapolated to calculate coefficients for a new application. This procedure requires the engineer to specify not only which input parameters mainly influence the output parameter(s), but also to specify the type of functional relation between input and output parameters. Designers plotted data and by visual inspection sometimes chose simple relations, often based on polynomials.
This approach is cumbersome and unsuitable for many nonlinear relations. Shortcomings are especially apparent for multi-dimensional input/output data sets. Here we apply a more versatile and userfriendly approach to system identification: Artificial Neural Networks (ANNs) may be used to find
functional relationship for certain ship data, Mesbahi (2003). ANNs are increasingly used in naval
architecture and marine engineering for system identification. Hess and Faller (2000) give an overview of ANN application in naval architecture, Bertram and Mesbahi (2000,2004), Mesbahi and Bertram (2000), Hess et al. (2004) further applications to ship design. We present here work for SWATH
ships based on previous work, Bertram and MacGregor (1992), and updating a SWATH database of
Papanikolaou (1996).
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5th International Conference
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2. Artificial Neural Nets
ANNs have the capability of storing data during a learning process and then reproducing these data
during a recall process. ANNs can generally represent the mapping of multi-dimensional input/output
data sets as:
f: X Y
f is a non-linear function, X=(x1,x2,…,xn) is real input vector, Y=(y1,y2,…,ym) is real output vector,
Figure 2. ANNs are best used for interpolation, extrapolations can be problematic.
An ANN structure consists of several layers. Each layer consists of several nodes. In the example
shown in Figure 2 we have input layer, output layer, and one hidden layer. The values of the previous
layer are weighted, reach a node, summed up and are transformed by a function F, before passed on to
the next layer. Typically, this function is a sigmoid function of the form:
sig (x) = 1/(1+e-x)
In this study, we have used fully-connected feed-forward ANNs with one hidden layer. Hidden layer
and output layer use sigmoidal activation functions. The hidden layer may have different number of
processing elements (neurons), which depend on the number of patterns and complexity of the relationship to be approximated. The standard choice is one hidden layer. Conventional back-propagation
is used for network training. Momentum terms are added to the learning algorithm to achieve a higher
convergence rate, Rumelhart and McClelland (1986).
xi and yi are input and output data respectively, which are normalised between 0 and 1:
Normalised value = (Real value -Min. Value)/(Max. value - Min. value)
Therefore, as far as ANN training is concerned, the units of the input and output data sets are irrelevant; they are only used when the out put data is to be de-normalised to its real value.
The following equation shows the mathematical relationship between x and y the single-input/singleoutput (SISO) ANN used here:
y = c0+c1sig [b0+b1sig(a10+a11x1+a12x2+…) +b2sig(a20+a21x1+a22x2+…) +…]
After sufficient training, adjusted values for the coefficients a, b, and c are derived and the non-linear
relationship is determined.
+1
F
+1
F
x1
F
x2
.
.
.
.
.
xn
F
y1
F
y2
.
ym
F
F
F
F
F
W( n 1h )
F
W( h 1m )
Figure 2: General structure of an Artificial Neural Network
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5th International Conference
on High Performance Marine Vehicles,
8-10 November, 2006, Australia
3. Simple power prediction
We follow the ITTC standard notation here. The break power may be estimated in a most simple early
estimate by considering only speed and displacement as input variables. Conventional regression
analysis gave more than a decade ago, Bertram and MacGregor (1992):
PB = 0.0026 0.598 V2.691
and
PB = 0.077 (/LOA)0.928 V2.784
The speed V is to be taken in knots, the displacement  in tons, length overall LOA in m, giving the
power in kW. In analogy, we expressed PB= f(,V)
PB = -1562.3 +33333.33sig [1.082914 +2.848013sig(-2.509744+6.448005sig(*)+4.113247sig(V*))
– 4.638891sig(12.526969-7.726960sig(*)-12.093710sig(V*))]
with * = 0.000075+0.049024 and V* = 0.035928V-0.223054
The ANN structure representing this formula has 2 inputs (, V), 2 neurons in the hidden layer and
one output. PB results are shown in Figure 3 for 45 SWATHS:
Shaft power (KW)
35000
Shaft power (KW) ANN
30000
Pb (Bertram and
McGregor,1992)
25000
20000
15000
10000
5000
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53
Figure 3: Comparison between real and calculated shaft power using different equations
or even simpler PB/ =f(Fn) and PB/ =f(V):
PB/ = -0.88918 +3.1416sig [0.24729+1.0533sig(-1.7707+3.6916x1)-3.8069sig(2.3202-9.0464x1)]
with x1 = 0.929796Fn-0.127229
PB/ = -0.88918+3.1416sig[0.83637–0.5291sig(6.5743-12.114x1)-2.70668sig(9.7109-30.404x1)]
with x1 = 0.035928V-0.223054
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5th International Conference
on High Performance Marine Vehicles,
8-10 November, 2006, Australia
While such a simple approach may still give reasonable estimates for a narrow class of geometries, we
may alternatively use a classical decomposition of power and resistance, focusing essentially on an
approximation of the residual resistance as in traditional ship model testing. This is described in the
following section.
4. Power prediction per resistance decomposition
We express then the installed engine power as:
PB = (RTV)(SM+1)/(sD) = ((RF+RR+RAP+RAA)V)(SM+1)/(sD)
SM is the service margin, typically taken at 10% to 15%. We take typical values for shafting efficiency
s=97% and the propulsive efficiency D= 72%. The resistance components of the total resistance RT
are frictional resistance RF, residual resistance RR, appendage resistance RAP, and air resistance RAA.
RF is predicted following ITTC’57:
RF = ½ (CF+CA)SV2
If the wetted surface S is not yet known, we may estimate, Numata (1981):
S = 2/3 (7.4+0.31L/D)
Where L/D is the slenderness of the submerged hull, L its length, D its diameter. Typically L/D < 14
for modern SWATHs. The correlation allowance CA is estimated to 0.0005 as in Numata (1981). CF
follows ITTC’57:
CF = 0.075/(log10 Rn – 2)2
The Reynolds number is here defined as Rn = VLOA/ and =1.1910-6 m2/s.
There is not much information on the appendage resistance of SWATH ships in the open literature.
Nethercote and Schmitke (1982) estimate RAP to 10% RF, Bertram and MacGergeor (1992) to 28%
RF. These global estimates are always plagued by considerable scatter and it is recommended to estimated the appendage resistance for all appendages separately using simple resistance coefficients, but
actual appendage geometry, e.g. following Salvesen et al. (1985).
The air resistance RAA is estimated using a force coefficient:
RAA = ½ CAA  AF V2
AF is the front area above water of the SWATH, which may be estimated initially to A F =0.04 LOA2,
Devine (1987). Chapman (1972a) sets the air resistance coefficient CAA =0.5, Mulligan and Etkins
(1985) to 0.7. Blendermann (2003) gives a more detailed approach based on wind tunnel test data.
This leaves the residual resistance, encompassing wave resistance RW, viscous pressure resistance RFF
and spray resistance RSP. The wave resistance can be computed quite accurately using more or less
sophisticated computational methods, e.g. Bertram (1993). The viscous pressure resistance is typically
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5th International Conference
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8-10 November, 2006, Australia
estimated separately for strut and lower displacement hull. Hoerner (1965) gives form factors for the
strut, where ts/Ls is the thickness/length ratio of the strut:
RVP,strut = RF,strut [1+(ts/Ls)+30(ts/Ls)4]
The viscous pressure resistance of the lower hull is typically 10% to17% of its frictional resistance,
Chapman (1972a), Nethercote and Schmitke (1982). Zou and Luo (2004) estimate following Hoerner
(1965):
RVP,hull = RF,hull [1+1.5 (Dh/Lh)1.5+7(Dh/Lh)3]
Dh = 2(A0/)0.5 is the equivalent diameter of the lower hull, where A0 is its maximum section area, Lh
its length.
Spray resistance becomes significant only at higher Froude numbers. Papanikolaou (1988) gives:
RSP = 0.12   ts V
2
2
with
=
1.0
2.30  Fn,s
0.694 Fn,s-0.597 for 0.86  Fn,s < 2.3
0.0
Fn,s< 0.86
Fn,s is the Froude number based on strut length Ls. Savitsky and Breslin (1966) and Chapman (1972b)
give formulae which yields generally higher values than the one of Papanikolaou (1988), possibly due
to scaling effects, as these formulae are intended for surface-piercing struts of hydrofoil boats rather
than big struts of SWATH ships. These formulae require already a certain knowledge of the main
dimensions. Bertram and MacGregor (1992) give a global estimate for the residual resistance coefficient, where Fn is the Froude number based on the cubic root of the displacement 1/3:
CR =
0.00436 Fn
0.0108-0.0113 Fn
-0.007+0.0092 Fn
0.0127-0.0059 Fn
0.002
for 0.000 < Fn < 0.688
for 0.688  Fn < 0.865
for 0.865  Fn < 1.300
for 1.300  Fn < 1.808
for 1.808  Fn
Using our new database, we derived now a simple estimate based on ANN for the residual resistance
coefficient:
CR = -0.001005 +0.047712sig [5.08580 +7.04224sig(3.05889-7.98939x1-29.84767x2)
-7.34271sig(13.24880-21.75015x1-44.57205x2)
-6.33253sig(-6.75647+12.86496x1+10.95574x2)
-0.67298sig(-0.29977-15.27102x1+13.36564x2)]
1/3
x1 = 0.29347(L/ )-1.03073
x2 = 0.9298Fn-0.12723
The ANN structure representing this formula has 2 inputs (L/1/3, Fn), 4 neurons in the hidden layer
and one output CR results for 45 SWATHS are shown in Figure 4.
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5th International Conference
on High Performance Marine Vehicles,
8-10 November, 2006, Australia
Cr
0.05
0.045
Cr (ANN)
0.04
Cr (Bertram and
McGregor,1992))
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47
Figure 4: Comparison between real and calculated CR using different equations
5. Conclusions
The user-friendly ANN approach allows more general curve fitting than classical regression analysis
based on simple polynomial expressions. However, the general problem remains that depending on
how well the input parameters are chosen, more or less scatter appears and extrapolation of experience remains in principle risky. For the particular application chosen here, the ANN formulae appear
to be an excellent first estimate aiding preliminary SWATH design.
6. References
Bertram, V. MacGregor, J.R. (1992): “Leistungsprognose von SWATH-Schiffen in der frühen
Entwurfsphase“, Schiff & Hafen 44/10, pp.188-191
Bertram, V. (1993): “SUS-B: A computational fluid dynamics method for SWATH ships”, Proc. of
the 2nd International Conference on Fast Sea Transportation (FAST 1993), Yokohama
Bertram, V., Mesbahi, E. (2000): “Adaptive Neural Network Applications in Ship Design“, Jahrbuch
der Schiffbautechnischen Gesellschaft, Springer
Bertram, V., Mesbahi, E. (2004): “Estimating resistance and power of fast monohulls employing artificial neural nets”, Proc. of the 4th International Conference on. High-Performance Marine Vehicles
(HIPER 2004), Rome
Bertram, V., Seif, M.S. (2004): “New developments for fast and unconventional marine vehicles”,
Proc. of the 4th International Conference on. High-Performance Marine Vehicles (HIPER 2004),
Rome, pp.28-43
Blendermann, W. (2003): “Consideration of Reynolds number and shear wind effects on a SWATH in
wind tunnel tests”, Ship Technology Research/Schiffstechnik , 47, pp.3-10
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5th International Conference
on High Performance Marine Vehicles,
8-10 November, 2006, Australia
Chapman, R.B. (1972a): “Hydrodynamic drag of semi-submerged ships”, Trans. ASME, J. Basic Eng.
94, pp.879-884
Chapman, R.B. (1972b): “Spray drag of surface piercing struts”, AIAA/SNAME Advanced Vehicles
Conference, Annapolis
Devine, M.D. (1986): “ASSET - A computer aided engineering tool for the early stage design of advanced marine vehicles”, AIAA-1986-2389, Proc. of the 8th Advanced Marine Systems Conf., San Diego
Gore, J.L. (1985): “SWATH ships”, Naval Engineers Journal, 97/2, pp.83-112
Hess, D., Faller, W. (2000): “Simulation of ship maneuvers using recursive neural networks”, Proc. of
the 23rd Symposium on Naval Hydrodynamics, Val de Reuil
Hess, D., Faller, W., Ammeen, E. Fu, T. (2004): “Neural networks for naval applications, Proc. of the
3rd International Conference on Computer und IT Application Mar. Industries (COMPIT), Siguenza,
pp.430-446
Hoerner, S.F. (1965): “Fluid dynamic drag, Hoerner Fluid Dynamics”, Ed.1993, ISBN 9993623938
Lang, T.G., Slogett, J.E. (1985): “SWATH developments and performance comparisons with other
craft”, Proc. of the International Conference SWATH Ships and Advanced Multi-Hulled Vessels, RINA, pp.7-23
Mesbahi, E. (2003): “Artificial neural networks – Fundamentals, OPTIMISTIC – Optimization in
Marine Design”, Mensch&Buch Verlag, pp.191-216
Mesbahi, E., Bertram, V. (2000): “Empirical design formulae using artificial neural networks, Proc.
of the 1st International Conference on Computer und IT Application Mar. Industries (COMPIT), Potsdam, pp.292-301
Mulligan, R.D. Edkins, J.N. (1985): “Asset-Swath – A computer based model for SWATH ships”,
Proc. of the International Conference SWATH Ships and Advanced Multi-Hulled Vessels, RINA,
London
Nethercote, W.C.E., Schmitke, R.T. (1982): “A Concept Exploration Model for SWATH ships”,
Trans. RINA, Vol.124
Numata, E. (1981): “Predicting Hydrodynamic Behaviour of SWATH ships”, Marine Technology, 18
Papanikolaou, A.D. (1988): “Hydrodynamic aspects and conceptual design of a SWATHpassenger/car ferry”, J. Technica Italiana 52
Papanikolaou, A.D. (1996): “Developments and potential In open sea SWATH Concepts”, WEGEMT
Workshop on Conceptual Designs of Fast Sea Transportation, Glasgow
Rumelhart, D.E., McClelland, J.L. (1986): “Parallel distributed processing: explorations in the microstructure of cognition”, I&II, MIT Press, Cambridge
Salvesen, N., von Kerczek, C.H., Scragg, C.A., Cressy, C.P., Meinhold, M.J. (1985): “Hydro-numeric
design of SWATH-ships”, Trans. SNAME, pp.325-346
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8-10 November, 2006, Australia
Savitsky, D., Breslin, J.P. (1966): “Experimental study of spray drag of some vertical surface-piercing
struts”, Davidson Laboratory Report 1192, Hoboken
Zou, Z.J., Luo, Q.S. (2004): “A practical resistance prediction system for SWATH ships”, Proc. of the
9th International Symposium on Practical Design of Ships and Other Floating Structures (PRADS
2004),Lübeck-Travemünde
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5th International Conference
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8-10 November, 2006, Australia
Appendix: Database SWATH
Ship
Pursuit
Ali
Marine Ace
Marine Wave
Sun Marina
Diana
Bay Queen
Suave Lino
Betsy
Halycon
Alison
Chubasco
Houston Pilot Cutter
NN
F.G.Creed
Exlorer
RDC 400
Charwin
SSP Kaimalino
Kotozaki
Ohtori
Seagull 1
Cloud X
Seagull 2
Navatek 1
Patria
Simicat
SMURV
Thrileon
Aegean Queen
Built by
Swath Ocean
MacGregor Bros
Mitsui
Mitsui
Mitsui
Mitsui
Mitsui
Pool Boat Yard
Swath Ocean
RMI
Metal Boat Inc
James Betts
Swath Ocean
Swath Ocean
Swath Ocean
A&R
Type
St Augustine
USCG
Mitsui
Mitsui
Mitsui
Nichols Bros
Mitsui
Thompson
FBM Marine
Alpha Marine
NTUA
NTUA
NTUA
workboat
Prototype
Research
Research
Pax
Pax
Pax
Pax
Pax
Ferry
Research
Patrol
Ferry
Prototype
Prototype
Pleasure
Pleasure
Pleasure
Pleasure
Fishing
Workboat
Research
Pilotboat
Hull
Alu
Steel
Alu
FRP
FRP
Alu
Alu
Alu
Alu
Alu
Alu
Alu
Alu
Alu
Alu
Steel
Steel+alu
Steel+alu
Steel
Alu
Alu
Alu
Steel+alu
Alu
Steel
Steel+alu
Steel
Steel+alu
[t]
13
21
22
25
25
30
35
40
53
62
67
76
79
80
80
130
180
193
220
236
240
338
340
350
365
400
446
610
900
1060
23
Loa [m]
10.90
11.27
12.30
15.10
15.05
20.80
18.00
21.34
19.30
18.30
26.50
21.94
20.40
21.90
20.40
36.40
24.40
26.27
27.00
27.00
35.90
37.52
39.30
43.00
36.50
41.00
39.00
48.00
51.50
Lpp [m]
9.14
11.00
11.95
11.93
15.90
15.90
16.76
17.70
18.89
18.40
16.80
25.65
22.90
22.23
25.00
24.08
31.50
32.40
33.70
34.14
31.70
35.00
33.00
43.00
50.00
B [m]
5.00
5.00
6.50
6.20
6.20
6.80
6.80
9.14
9.10
9.20
11.00
9.45
11.30
9.40
9.75
14.26
13.00
12.20
13.70
12.50
12.50
17.10
18.07
15.60
16.20
13.00
12.50
18.00
20.20
25.00
T [m]
1.00
1.60
1.60
1.60
1.60
1.60
1.60
1.46
2.10
2.29
2.10
3.05
2.44
2.10
2.40
2.70
2.74
4.60
3.20
3.41
3.15
3.44
3.50
3.65
2.70
3.80
4.50
4.50
5.00
PB [kW]
242
104
298
405
442
545
700
626
634
760
672
1104
1501
1119
1590
1576
4080
714
3239
2797
2797
5962
5748
7890
1914
4026
5888
6992
11040
14720
V [kn]
22.0
7.6
18.0
18.0
20.5
19.0
21.6
20.0
17.0
21.0
14.8
20.0
23.0
20.0
24.0
18.0
26.1
10.0
25.1
20.5
20.0
25.0
27.0
27.5
15.0
30.0
22.0
22.0
30.0
30.0
Year
1988
1976
1985
1987
1990
1989
1981
1985
1987
1990
2004
1984
1973
1980
1981
1979
1995
1989
1989
1990
1992
1995
1989
5th International Conference
on High Performance Marine Vehicles,
8-10 November, 2006, Australia
SMUCC
NTUA
container
Steel
Ship
Twin Drill
Duplus
Regency
Goutcat Haroula
Able (T-Agos 20)
Effective (T-Agos 21)
Loyal (T-Agos 22)
Victorious (T-Agos 19)
Kaiyo
Planet
Harima (AOS 5202)
Hibiki (AOS 5202)
Impeccable (T-Agos 23)
Radisson Diamond
Built by
Boele
Boele
Type
Workboat
workboat
Alpha Marine
McDermott
McDermott
McDermott
McDermott
Mitsui
TNSW
Mitsui
Mitsui
Tampa
Finnyards
Ferry
Navy
Navy
Navy
Navy
Research
navy
Tow ship
Surveillance
Surveillance
Pax
Hull
steel
Steel
Steel
Steel
Steel
Steel
Steel
Steel
Steel
Steel
Steel
Steel
Steel
Steel
1060 51.50
[t]
1200
1450
1532
2180
3360
3360
3360
3360
3500
3500
3750
3750
5460
12000
24
Loa [m]
40.00
47.00
69.40
77.87
70.70
70.70
70.70
71.32
60.00
67.00
67.00
85.80
130.10
50.00
25.00
5.00
10893
26.0
1994
Lpp [m]
17.10
40.00
B [m]
5.20
17.10
24.40
22.00
28.70
28.70
28.70
28.70
28.00
25.00
29.90
29.90
29.90
32.00
T [m]
PB [kW]
1269
1251
30000
8979
1194
1194
1194
1194
3444
4160
2239
2208
3730
11253
V [kn]
9.0
8.0
32.7
21.0
9.6
9.6
9.6
10.4
14.1
15.0
11.0
11.0
12.0
12.5
Year
1968
1969
65.00
57.91
53.00
61.00
61.87
116.00
5.49
5.10
5.00
7.50
7.50
7.50
7.56
6.30
6.80
7.50
7.62
7.90
8.00
1996
1992
1993
1993
1991
1984
2005
1991
1991
1992