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HULL DESIGN BY CAD/CFD SIMULATION 181
HULL DESIGN by CAD/CFD SIMULATION
Hideaki Miyata and Koji Gotoda
(Department of Environmental and Ocean Engineering, University of Tokyo)
ABSTRACT
A CAD system and two CFD simulation techniques are combined to compose a design method for ship hull forms.
The first CFD technique is for the ship performance in steady straight course, which provides resistance properties, and the
second technique is for the motion performance in waves, which provides added resistance and motion properties. By
repeating the cycle of CAD/CFD procedure the hull form is successively improved to meet the design requirement. Since
added resistance is also estimated the design is made from the viewpoint of life-range fuel-consumption. This system is also
applied to the design of the IACC class sailing boat with the statistical wave data of the race area.
INTRODUCTION
The CFD simulation technique based on Navier-Stokes equation was first applied to the hull-form design in 1983
when the TUMMAC-IV code was completed at the University of Tokyo and distributed to the major shipbuilding
companies. Since then a number of codes have been developed and introduced to the design office. In the past 10 years
such CFD techniques have been extended to the planary motion and motion in waves. The use has been made of the time-
marching solution procedure such as that of the MAC method and the technique of combining the CFD solution with the
solution of the equations of motion. The technical difficulties consist mostly in the treatment of the moving boundaries,
that is the free-surface and the body-boundary of a ship in motion. The density function method is often employed for the
strongly interacting free-surface motion and the moving boundary technique is well used. However the use of the fixed grid
system is used to be more versatile when the motion is expressed by coordinates transformation and virtual accelerations.
When the wave spectrum of the sea on which the ship will be expected to sail in her life-range is given for the
estimation of the total resistance and the resultant fuel consumption, the design of hull-form is made from the total life-
cycle viewpoint. This means that the hull-form design can be made with the prediction of the overall performance of the
ship in her life. For the special case of the design of the hull-form of the International America's Cup Class (IACC) sailing
boat this design procedure is very suitably applied. Since the race area is announced about 3 years before, the statistical
wave data can be collected and then the CAD/CFD design procedure above mentioned is successfully applied, although the
statistical wind data plays more important role in the design procedure.
In this paper one of the most advanced design procedure for hull-form is described especially for the IACC class
sailing boat and another case of the high-speed ferry.
HULL DESIGN SYSTEM
Design system for America's Cup 2000
For the research and development work for the 30th America's Cup yacht race the technical team of the Nippon
Challenge made the R&D plan in 1995.
The most scientific R&D work was first pursued for the race of 1987 by the syndicate at San Diego, which is reported
by Oliver et al. This procedure seems us still very useful as far as the boat hardware design is concerned. However the
computer technology has made rapid progress in the past 15 years. The performance of the computer has been raised by
10000 times in 15 years. The performance of the first supercomputer of the University of the Tokyo, which was introduced
in 1983 and I used for ship wave computation with TUMMAC-IV method for the second workshop on wave resistance
computation, is almost same with that of a PC in 2000. In the meanwhile the CFD technique also made rapid progress.
For the development and design job of Nippon Challenge America's Cup 2000, the procedure described in Fig. 1 was
adopted, see article by Miyata et al., 2000 and a book by Miyata, 2000. The design is mostly done by the reciprocal use of
CAD and CFD simulation. More than 200 hulls are designed and their performance is
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HULL DESIGN BY CAD/CFD SIMULATION 182
predicted by the simulation. When certain progress is attained, three to four 1/7th models are manufactured and served for
tank test at the University of Tokyo. Selected designs are put into the next stage of 1/5th model experiment with keel and
rudder. This is repeated several times. The hull form in 3D data made by the CAD software is used by the grid-generator as
pre-processing for CFD simulation. This data is also used for the numerical shaping process at a model manufacturer. In the
latter stage when some new hull forms are obtained the race simulation is performed with the wind data of 1700 days at
Hauraki Gulf of New Zealand. The data are given by the measurement on a boat for three years from 1995 to 1997. The win
probability and regret are obtained for the final decision of the two hulls used in the race.
Fig. 1 Design procedure of Nippon Challenge 2000.
The most important technology is the performance prediction simulation (PPS). PPS is composed of CFD simulation
technique and the solution method of equations of motion.
Fig. 2 Prototype models at the University of Tokyo.
Advanced design system with wave statistics
The above procedure is mostly based on the performance of the boat in a steady straight course. However the averaged
added resistance of the America's Cup (AC) boat is approximately 20% of the resistance on calm water. Therefore the hull
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form optimization

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HULL DESIGN BY CAD/CFD SIMULATION 183
would better be made considering the added resistance. The CFD simulation technique must be developed for the condition
in waves and a series of simulation in regular waves provide the response function and the added resistance on the
respective hull are given. Together with the wave spectrum of the race area the prediction of total resistance of candidate
hulls is made and the optimum hull of statistically minimum resistance is selected. Thus the advanced hull design method
by simulation is composed as shown in the flow chart of Fig. 3.
This method is commonly used for merchant ships of any kind. The hull of minimum resistance in the whole life can
be designed in the same procedure when the wave spectrum of the sea she will sail in her whole life is given. It is said that
the life-cycle engineering of a ship is completed by the CAD/CFD simulation method from the hydrodynamical viewpoint
In order to complete such computer simulation technique the CFD simulation of a ship in waves is most important. In
the 1990s the finite-volume method in the framework of boundary-fitted coordinate system is extended to the problem of
maneuvering motion (Ohmori 1998 and Izumi et al. 1998) and then to arbitrary 3D motion (Takada et al. 1998 and Sato et
al. 1999). However these works remain to be within preliminary level. They cannot cope with large amplitude motion or
motion in oblique waves. Further efforts must be devoted to improve the simulation technique for large-amplitude motion
in waves.
Fig. 3 Flow chart for life-cycle oriented hull-form design
Fig. 4 Some drawings of PPS
CFD SIMULATION FOR STEADY PERFORMANCE
Performance pre diction simulation
The development of PPS was started in 1993 and completed in 1995. The principal technology is the finite-volume
method in the framework of the body-boundary fitted coordinate system, which is a well-established technique in the fluid
engineering field. The finite-volume code WISDAM-VI in the O-O type grid system is combined with the solution method
for the equations of motion (Akimoto 1995 and Miyata 1996). The time-marching solution of the Navier-Stokes equation
provides forces and moments in 6 degrees of freedom and they are put into the equations of motion to calculate
acceleration, motion and trajectories. The resultant motions, except for the steady advance motion and rolling motion, are
expressed by the deformation of the grid system. When the hull makes rolling motion, the body surface slips on the
surrounding grids and the grids are regenerated so that they keep to be fitted to the body-boundary, see Fig. 4.
Two versions of PPS were developed; one is PPS for the performance in steady straight motion (Hiroshima 1997). In
the close-hauled sailing simulation the resistance at a pre-determined boat speed is obtained as well as the boat attitude such
as trim, heel angles and sinkage. All these data are very important for the improvement of the boat performance. Difference
of 0.1 degree of trim angle gives meaningful difference of performance. The other is the dynamic PPS (Akimoto 1995) in
which all 6-degrees of freedom motion are computed and the boat speed is obtained as a solution of the translational motion
equation. Although the keel and sail forces are given by model equations, this can give important information for the polar
characteristics and transient maneuvering motion. However the use of the dynamic PPS in the design procedure causes
difficult problems, such as too long CPU time for the simulation.
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HULL DESIGN BY CAD/CFD SIMULATION 184
Accuracy proble m
The accuracy problem is very important in the dissemination process of CFD. So-called CFD validation is a noticeable
theme of research. However this seriously depends on the application technology. The method of design can determine the
role of CFD simulation.
The obtained resistance value for an AC boat by the WISDAM-VI is usually 10% smaller than the measured one.
Since the goal of resistance reduction is 10%, a designer is liable to be suspicious to the use of CFD simulation. However
most of the design process is composed of compromise and trade-off, and the most important decision is made based on
comparison. The accuracy in the relative relation of magnitude is of essential value for sound selection of better hull.
The reliability of the CFD simulation by PPS (WISDAM-VI) during the design procedure with 210 hull forms is,
grossly speaking, 75%, which means that the relative relation between two designed hulls is 75% correct. The wrong
suggestion of 25% used to be compensated by the empirical knowledge and the verification by tank test. By use of
computer-graphics the results of simulation provide us a variety of drawings. These are also useful information to the
designers, especially those with rich physical insight. For example the contour of wave height is good information to
modify the local hull form.
In the final stage of hull form improvement of AC boat it was so difficult to attain further reduction of resistance in the
spring of 1998. The CAD/CFD design work with our designers produced a number of worse hull forms as shown in Fig. 5.
And finally about 1% of resistance reduction was attained. After this final stage four prototype models of the scale of 1/7th
were manufactured to verify the design and simulation results, that is, 1% reduction of resistance, and to decide the hull of
the race boat. With the hybrid use of CFD and experiment 1% reduction of resistance was successfully attained.
In any ways the CFD simulation can be efficiently applied to the design of hull form. Nowadays it takes only 12 hours
to complete the process from the CAD design of hull to the receipt of simulation results, while it takes at least 60 days when
same thing is made by physical experiment.
Fig. 5 Relative magnitude of resistance of AC boats, 20 hulls are designed before 1% reduction was attained.
CFD SIMULATION FOR MOTION PERFORMANCE IN WAVES
Grid system for motion in waves
For the PPS mostly used for steady motion simulation, the O-O type grid system is used. The movement of the boat
except for the steady advancement is treated by the deformation of the grid. Therefore only gentle motion can be treated,
although the rolling motion is allowed making use of the “slip” technique on the hull surface. In order to complete the
motion simulation in waves, different techniques must be introduced for grids and motion treatment.
Then, in the framework of the boundary-fitted grid system all motions except rolling are treated as external forces in
the Navier-Stokes equations, and the rolling is treated by the rotation of the water-surface plane about the x-axis. The
employed grid system is O-H type so that wave generation is more rigorously performed than the O-O type grid system as
shown in Fig. 6. Since the resolution on the free-surface is most important for the ship flow problem, the grids are clustered
to the free-surface, which moves with the rolling motion. This means that it is a free-surface adaptive mesh system, as
illustrated in Fig. 7.
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Fig. 6 O-H grid system.

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HULL DESIGN BY CAD/CFD SIMULATION 185
Fig. 8 Results of numerical wave generation test.
Fig. 7 Free-surface adaptive grid deformation.
Density function method for free-surface motion
We have a lot of methods for the implementation of the free-surface condition. They have respective advantages and
disadvantages, and a most suitable method must be chosen for respective problem. For the present problem in which strong
nonlinear wave motion is expected the density function method is supposed to be most suitable, since one of the ultimate
goal of the present method is to simulate slamming motion in large-amplitude waves. Because one of the disadvantages of
the density function method is lower degree of accuracy, this must be tested. One of the test results is shown in Fig. 8 for
the case of regular waves generated by the numerical wave-maker. Time-historical records of wave height are compared at
five points, A to E in the longitudinal direction. It is noted that the dissipation of wave height is of the satisfactory level
when sufficient number of grids are allocated on the free-surface.
Motion simulation method
The finite-volume method is employed in the framework of the above-mentioned grid system. The solution algorithm
for the Navier-Stokes equation is of the time-marching MAC type. Since the grids are deformed, the moving velocity
vector is introduced into the Navier-Stokes equation as follows,
(1)
(2)
Here, u is the velocity vector, v is the moving velocity; Re is the Reynolds number, and K is the external forces. The
following inertia forces are included in K.
(3)
Here, the first term is the Coriolis force, the second is the circumferential force, the third is the angular acceleration
and the fourth is the translational acceleration, where w is angular velocity vector, V is the velocity vector, r is the position
vector and Vs is the velocity of the origin of the body-fixed coordinates.
All vector variables are defined in the Cartesian coordinates, and the velocity components and pressure are defined in
the staggered arrangement. The third order
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HULL DESIGN BY CAD/CFD SIMULATION 186
upstream differencing is used for convective terms and the second-order centered differencing for other differencing in
space. The SOR method is used for the solution of the pressure. The first-order Euler explicit scheme is used for the time-
integration for simplicity and efficiency.
The solution of the Navier-Stokes equation is combined with the solution procedure for the equation of motion as
shown in Fig. 9. The solution of the equation of motion gives the accelerations and the integration of pressure on hull
surface provides forces and moments for the equation of the motion. Thus the solution of the Navier-Stokes equation is
combined with the solution of the equation of motion in the time-marching procedure.
Fig. 10 Lines of tested model.
Fig. 9 Block diagram for the motion simulation in waves.
Two-degrees of freedom motion
The most useful simulation results will be expected when it is conducted with 6-degrees of freedom and reliable
models of sails and keel. However the robustness of the code is not very satisfactory in this case. Only 2-degrees of freedom
motion is performed for the first step. The conditions of computation are shown in Table 1. The most typical close-hauled
sailing condition, that is 25 degrees of heel angle and 2 degrees of leeway (yaw) angle, are assumed and fixed. Therefore
heaving and pitching motions are simulated in the heading wave condition.
Table 1 Condition of computation.
Grid points 100×30×80 (=240,000)
Computation domain L=4.1, Radius=1.8
1.5×10−2
Minimum grid space η
3.0×10−3
Minimum grid space ξ
1.0×106
Reynolds number
Froude number 0.366
Time of simulation 19.0
Time for acceleration 1.0
Time of beginnig of making wave 10.0
1.0×10−3
Maximum of dt
CFL 0.5
Length of Wave 1.0
Height of Wave 0.03843
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An incident angle 180.0
Heel angle of Boat 25.0
Leeway angle of Boat 2.0
The tested model is a typical IACC yacht, which is 24.5 meter long and about 4.1 meter wide. The lines are shown in
Fig. 10.
This boat is assumed to be sailing at 9.5 knot (Fn=0.366) in the regular incident waves of 700mm height and wave
length/ship length ratio of 0.77 and 1.54.
A typical computer-graphics drawings are shown in Fig. 11 for the case of 1.54 wave length ratio.

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HULL DESIGN BY CAD/CFD SIMULATION 187
Fig. 11 Distribution of resistance due to pressure on the hull (left) and waves interacting with the boat (right).
By use of this simulation method the added resistance on five different hulls are compared on the same conditions with
the case of Fig. 11. The total resistance coefficient at two wave-length conditions are compared with the experimental
results in Figs. 12 and 13, respectively.
The computed values are smaller or larger than the experimental values. However the relative relation between five
hulls is marginally reliable, and such results can provide useful information for the development of fast boat in wavy
conditions.
Fig. 13 Same as Fig. 13 in the case of 1.54 wave-length
Fig. 12 Comparison of resistance coefficient between ratio.
computation and experiment in the case of 0.77 wave-
length ratio.
Three-degrees of freedom motion
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On the upright condition of the boat four -degrees of freedom motion simulation is tried, that is only surging and
yawing motions are restricted. The boat is accelerated to the boat speed 9.5 knots in 1.0 nondimensional time and the
incident waves are generated at the inflow boundary at the incident angle 150 degree at 3.0 nondimensional time. The wave
height is 700mm for the full-scale boat and three wave-length conditions, that is 0.77, 1.15, 1.54 are tested.
The results are shown in Fig. 14. By use of the computer-graphics drawing the motion picture is created and one
instantaneous picture is shown on the left side

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HULL DESIGN BY CAD/CFD SIMULATION 188
of Fig. 14. The Poincare mapping of the time-marching records of simulated motion shown on the right side of Fig. 14
seems to be useful for the understanding of the motion characteristics.
Fig. 14 Motion and wave pictures and Poincare mapping of pitching and rolling for three wave-length conditions 0.77, 1.15 and
1.54 from above. The wave incident angle is 150 degree.
These simulation results imply that the present CFD method can be employed in the CAD/CFD based life-cycle design
system for hull forms.
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HULL DESIGN BY CAD/CFD SIMULATION 189
CASE OF HIGH-SPEED FERRY DESIGN TUMMAC-IV METHOD FOR FAST SHIP
Unfortunately the CFD method above described is not very appropriate for some group of hull forms designed at
different range of Froude number. Most suitable CFD method still depends on the ship type.
One case is a high-speed ferryboat, either mono hull or catamaran, of which design Froude number exceeds 0.4. Wave
generation of the boat is very remarkable and then accuracy in the wave height is much more important for these boats.
Since the boundary-fitted grid system results in coarser grid spacing in the region a little far from the hull surface where the
accuracy in wave height is necessary, the CFD code based on the rectangular grid system still have advantages. This is why
the TUMMAC-IV code completed in 1983 (Miyata 1985), is still used by designers of shipbuilding companies.
The slightly different version of TUMMAC-IV code is recently developed by the authors making use of the density
function method for the free-surface condition so that it can cope with wave motions with higher nonlinearity. Another
modification is that the hull data from 3D CAD are used in the pre-processing instead of the offset data.
Fig.15 A typical wave perspective view for a fast ferry.
Optimiz ation of principal particular
A typical application example is briefly described here. Hull form design is conducted for a fast ferry of 17000GT,
3400 ton, 35kt. The length is around 200m and the Froude number is about 0.4. From the harbor condition the maximum
draft is limited to 7m and the beam-length must be greater than 24.5m from the stability requirement.
By use of the CAD/CFD system the optimum length/beam ratio and block coefficient was pursued by successive
repetition of CFD computation. The midship section is shown in Fig. 16 and the computed wave profiles are shown in
Fig. 17. By integrating the pressure on the hull surface the pressure resistance mostly composed of wave resistance is given
and optimum length/beam ratio and block coefficient are suggested, although it is obvious that the larger length/beam ratio
and smaller block coefficient leads to smaller horsepower. Therefore the optimum principal particulars are determined from
other aspects of design.
The TUMMAC-IV code with density function method can also cope with catamaran hull in case each demi-hull has
symmetric hull form. Then the comparison between monohull and catamaran can be done from the resistance point of
view.
Fig. 16 Two example of frameline with different block
coefficient.
Fig. 17 Comparison of wave profiles on hull surface at
three different block coefficients.
Hull-form optimization
For the second stage of hull form design the optimization of the bow bulb is of significant importance. For low and
middle speed ships the bulbous bulb with sphere-shaped head configuration is no more used but bulbs with long protrusion
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and sharp entrance are designed mostly based on the understanding of the presence of free-surface shock wave. However
for high speed ships, of which draft changes only slightly, an old-fashioned cylindrical bulb or so-called SV-type bulb are
efficient to reduce wave resistance.
For the present fast ferry a SV-type bulb as

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HULL DESIGN BY CAD/CFD SIMULATION 190
shown in Fig. 18 is employed so that it may well fit to the V-shaped framelines. By the present CAD/CFD system the
optimum protrusion and volume are pursued as shown in Fig. 19. Since the CPU time for one case of computation is
several hours and the hull form modification is made by CAD process with some hours of labor, it may be noted that the
hull form optimization is performed very efficiently.
When the accuracy in the relative magnitude of resistance is checked by experiment for respective hull and the total
design procedure is like that for the IACC yacht, such design system will become to be a standard system. The design by
simulation will become more useful for many design purposes.
Fig. 18 Normal bow and a bow with SV-type bulb.
Fig. 19 Comparison of horsepower between hulls without bulb(left) and with three different bulbs.
CONCLUSION
A very practical application technique of CFD is presented. Since the fluid motion about a ship is so complicated the
accuracy problem of CFD is not yet fully solved. However the design problem is essentially complicated and the
introduction of CFD into the advanced design system leads to fruitful results.
The first author worked for the Nippon Challenge America's Cup 2000 as a technical director and chief designer and
the second author, a graduate student of the University of Tokyo, as a member of the design team. The design work for the
two boats JPN44 and JPN52 were mostly made by the first version of PPS for the steady sailing. It may be safe to say that
the CAD/CFD system was satisfactorily applied to one of the most difficult hull design problem.
REFERENCES
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H.Miyata, “America's Cup boat design of Nippon Challenge”, Seahorse Magazine (to appear).
H.Miyata, “Technology of America's Cup”, University of Tokyo Press (in Japanese), 2000.
T.Ohmori, “Finite-volume simulation of flows about a ship in maneuvering motion”, J. Mar. Sci. Technol. 3, 1998.
K.Izumi et al., “CFD simulation of maneuvering motion for blunt ships”, J. Soc. Nav. Archit. Jpn. Vol 184, 1998• •(in Japanese).
N.Takada et al., “CFD simulation of 3-dimensional motion of a vehicle with movable wings”, Proc. 22nd Symp. Nav. Hydrodynamics, 1998.
Y.Sato et al., “CFD simulation of 3-dimensional motion of a ship in waves: Application to an advancing ship in regular heading waves”, J. Mar. Sci.
Technol. 4–3, 1999.
H.Akimoto, et al., “Development and application of CFD simulation technique for ships in 3D motion”, PhD dissertation, University of Tokyo, 1995.
H.Miyata, “Time-marching simulation for moving boundary problems, Pro. 21st Symp. Nav. Hydrodynamics, 1996.
H.Hiroshima et al., “Design method for sailing boats by CFD performance simulation”, J. Soc. Nav. Archit. Jpn. Vol. 181, 1997 (in Japanese).
H.Miyata et al., “Finite-difference simulation of nonlinear waves generated by ships of arbitrary three-dimensional configuration”, J. Comp. Phys. 60
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(3), 1985.