Vol. 43 • No. 3 August 1996
SCHIfFüfECHKIK
Inviscid and Viscous Flow Calculations around YachtingSails
by Kai U . Graf
Seawaves - Basis for Dimensioning of Ship Structures by Hans-Joachim Hansen
Knowledge-Based O p t i m u m Conceptual Ship Design by Kyu-Yeul Lee, Kyung-Ho Lee
Ship Geometry Modelling by Uwe Rabien
Resistance and Wake Prediction by Computing Turbulent Ship Flows by Pierre Sames T E C H N I S C H E U N I V E R S T T E I T Sdieepshydroanechanica A r c h i e f M e k e l w e g 2 , 2 6 2 8 CD D e l f t T e l : 0 1 5 - 2 7 8 6 8 7 3 / F a a : : 2 7 8 1 8 3 6 P u b l i s h e d b y S c h i f f a h r t s - V e r l a g „ H A N S A " , H a m b u r g
D a s F a c h b u c h
oer
^ erf ten
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H e r a u s g e b e r P r o f . D r . - I n g . H . K e i l 3 3 8 S e i t e n , F o r m a t 1 4 , 5 X 2 1 , 5 c m , z a h i r e i c h e S k i z z e n u n d T a b e l l e n , E f a l i n , D M 9 8 , 4 0 z z g l . V e r s a n d k o s t e n , i n k l . M w S t . I S B N 3 - 8 7 7 0 0 - 0 8 9 - 4 T E I L I SCHIFFBAU - SCHIFFSMASCHINENBAU Betriebsfestlgkelt schiffbaullcher KonstruktlonenProf. Dr.-Ing. H. Petershagen, Dr.-Ing. W. Fricke und Dr.-Ing. H. Paetzold
Fatigue Strength of Ship Structures
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Moderne Schlffslinien
Dr.-Ing. G. Jensen
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Dr.-Ing. G. Jensen
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Prof. Dr.-Ing. C. F. L. Kruppa
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Dr.-Ing. W. PInnekamp
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Dr.-Ing. W. PInnekamp
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Vol. 43 • No. 3 • August 1996
Kai U. Graf
Inviscid and Viscous Flow Calculations around Yachting Sails Ship Technology Research (1996) 95-101
Inviscid and viscous methods are employed to calculate the flow around sails of small racing dinghies and yachts. The inviscid lifting-surface method allows calculation of lift and induced drag for arbitrary sail geometry and different configurations of mainsail and jib. The method is applied to calculate the influence of various sail trim parameters, e.g. camber ratio, sail twist, mast slope and the mutual dependence of forces of two sails working in close proximity. In conjunction with a simple velocity prediction procedure, the dependence of windward boat speed on these parameters is calculated. First viscous flow calculations around rectangular sails have been carried out using a commercial Navier-Stokes solver.
Keywords: sail flow, lifting surface, lift coefficient, sail trim, Navier-Stokes solver, yacht
Hans-Joachim Hansen
Seawaves - Basis for Dimensioning of Ship Structures Ship Technology Research 43 (1996), 102-105
Historical and recent trends in classification rules on ship loads are discussed. An example are hatch cover loads which, according to the Load Line convention (of 1966), are 17.5 kN/m^, whereas the current GL rules require, for the same ship, 68 kN/m^ in the forebody. In a number of fields, the International Association of Classification Societies (lACS) proposed or discusses unified load assumptions. Examples are a seaway statistic for merchant ships and bending moments as well as bulkhead and double bottom strength in case that one compartment of a bulker is flooded. Earlier and recent efforts of Germanischer Lloyd comprise hull strength monitoring systems, a "black box" to register crucial ship data to be retrieved in case of an accident, and full-scale pressure measurements on the side shell.
Keywords: load, strength, wave, seaway, hull pressure, corrosion, classiflcation
Kyu-Yeul Lee, Kyung-Ho Lee
Knowledge-Based Optimum Conceptual Ship Design Ship Technology Research 43 (1996), 106-114
A new hybrid optimization method - combining sequential linear optimization with a genetic algorithm - is shown to be more efficient than purely numerical optimization ™ < ^ ^ I { | f U H i ^ S h ^ D f T S i r ^
laboratorium voor Schespshydromechanfca
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nonlinear optimization problems. A knowledge-based prototype system for the compartment arrange-ment design is also presented. The approach can assist interactive design by applying rules for design evaluation and improvement. The system is applied to the positioning of the longitudinal bulkheads of a double-hull tanker to comply with the IMO regulations during conceptual design.
Keywords: expert system, genetic algorithm, optimization, ship design, general arrangement, tanker
Uwe Rabien
Ship Geometry Modelling
Ship Technology Research 44 (1996), 115-123
A review is given on the development of ship hull form modelling in computers during the last 30 years. A geometry basis for computer definition of ship structures in early design and some derived numerical geometry models are discussed briefly, e.g. geometry models for FEM, CFD, and dimensioning of hull cross sections. The ISO10303/STEP approach for standardization of exchange of product data is discussed with respect to ship geometry modelling.
Keywords: hull shape, free form surface, product data, data exchange, ISO10303/STEP, EXPRESS
Pierre Sames
Resistance and Wake Prediction by Computing Turbulent Ship Flows Ship Technology Research 43 (1996), 124-135
A finite-volume method to solve the Reynolds-averaged Navier-Stokes equations uses either a Low-Re or a standard k-e turbulence model with wall functions. A nonlinear extension to the eddy viscosity hypothesis is employed. Flows about two ship models at R„ = 5 -10^ and a full-scale ship at R„ = 1.2-10^ are computed neglecting free surface deformations. The predicted velocity distributions in the propeller plane agree well with experiments. Resistance is slightly overpredicted.
Keywords: viscous ship flow, turbulence model, finite-volume method, RANSE, resistance, wake Book Review: Advances in Marine Hydrodynamics by Makoto Ohkusu (p. 136)
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Inviscid and Viscous Flow Calculations around Yachting Sails
K a i U . G r a f , FH Kiel^
1. I n t r o d u c t i o n
For conventional trade vessels, service or trial speed is a given design parameter. In contrast to this, speed achieved by sailboats is rather an optimization goal influenced by many para-meters, some of them under control of the sailors, e.g. sail t r i m or course relative to the wind, others completely arbitrary, e.g. weather conditions. Therefore, the hydrodynamic investigations must consider many combinations of boat speed, wind velocity, angle of attack of wind etc. Numerical flow calculations can do this in optimizing hydrodynamic properties more efficiently than experiments. Thus, in the design stage of racing yachts for important races (e.g. America's Cup), numerical flow investigations for design optimizations are already common practice. With widely available computer power and flow calculation methods, these methods may be applied now for any kind of yacht.
2. L i f t i n g - s u r f a c e m e t h o d f o r the c a l c u l a t i o n o f sail forces
Lifting-surface methods distribute bound and trailing vortices on the sail surface. While bound vortices produce lift, trailing vortices account for the three-dimensional flow around the wing. The method applied here discretizes the sail into quadrilateral panels. Panels may be distributed on more than one sail or wing. The sails may overlap. Unstructured grids allow easy discretization also of triangular sails, e.g. in Fig. 1 for a modern racing rig.
Fig. 1: Discretization of mainsail and j i b Fig. 2: Arrangement of vortex rings and horseshoe vortices
Vortices of constant vorticity are arranged at the edges of each panel. A t the leech o f t h e sail a horseshoe vortex is arranged instead of a vortex ring to satisfy Kutta's condition. Fig. 2. In the center of each panel a collocation point is arranged. A l l vortices are arranged at the exact geometric position of the panel discretizing the sail. Thus sails of arbitrary shape, sail twist, camber ratio and position, and interaction of mainsail and j i b are modelled accurately.
For details of the following derivation see e.g. Jiirgens (1994). Ring and horseshoe vortices induce a velocity according to Biot-Savart's law:
r ( f x ds . .
'Legienstr. 35, 24103 Kiel, Germany, Kai.Grar@ni-kiel.de
r is the vorticity, r a vector form the position where the induced velocity is calculated to ds. The integration is carried out over all vortex lines s. A single straight vortex filament of constant vorticity F running form point PA to Pg induces a velocity Vs in point P^, Fig. 3:
Vs = \Vs\^, (2)
with \vs\ = 4 ^ ( c o s a + cos7), HK = {PB and a = | r 4 | \ / l — cos^ a.
Fig. 3: Straight vortex line
The vorticities F are calculated using the boundary condition on the sail surface: the sum of induced velocity v of all vortex rings and horseshoe vortices and the wind velocity ü has no component normal to the sail surface:
(u + u) • n = 0 (3)
n is the unit normal on the sail surface. Applying this boundary condition to the collocation
points in all panels yields the linear system of equations:
niijFj =-Hi • iii (4)
i
Tj is the vorticity of the vortex ring or tlie vortex horseshoe in panel j , (7,- the wind velocity, Hi
the unit normal in collocation point ?', and
777,;, - Vij • Ui (5) 1 J
Vij is the velocity induced by the horseshoe or ring vortex j at collocation point i. Vij is calculated
as sum of the velocities induced by the four (three) straight vortex filaments which form a vortex ring (horseshoe vortex).
After calculation of all discrete vorticities using (4), the force on a particular straight vortex line is
F = pr{u + i J ) x { f B - f A ) (6) p is the fluid density and v the velocity induced in the center of the straight vortex filament by
all other horseshoe and ring vortices discretizing the sail. The moment M is
M = f x F (7)
Forces and moments on the complete sail are calculated by summing the discrete forces and moments arising from (6) and (7) for all ring and horseshoe vortices.
The viscous drag Dy of the sail is approximated by the I T T C formula for the friction resistance of flat plates and a resistance coefficient Cpj^^g^ accounting for the viscous resistance of the mast to increase the accuracy of the calculated forces in a real flow;
Dv = \pu\u\ (^iQg()^'^^^ 2Y ^ ^'^mastCmast) (8) A is the sail area, /?„ the average Reynolds number of the sail, h the mast height, and f^niast
the average mast diameter.
Results for l i f t calculations of rectangular flat plates and thin wings with circular sections were compared with numerical calculations and estimation formulas. For one sail, 30 to 40 rows and 20 columns of vortex rings were in general needed for grid-independent results. Fig. 4 shows results for flat plates. The l i f t gradient dci/da is plotted against the wing aspect ratio A for various discretizations (vertical • horizontal). The lift gradients are slightly larger than those of Söding
(1982) and Schlichting and Truckenbrodt (1967). However, the differences between all methods
are of same quantity and acceptably small. Fig. 5 shows the ra.tio of the lift of a wing with circular sections to a flat plate's l i f t against the camber ratio t/c. The angle of attack is /? = 5.73°, the aspect ratio is A = 4. For discretizations beginning with 20 columns of vortex rings, the results agree fairly well with the one known for section flow: CL[t/c)/ci[t/c = 0) = 1 -H 2t/{(5c).
A n g l e o f i n c i d e n c e p [°l :— c
Fig. 6: L i f t and drag coefficients CL and for a triangular sail
Results of flow calculations around real sails were compared to wind tunnel tests, Schenzle
and Siegel (1983), Fig. 6. The investigated sail is a j i b in front of a mast. Camber ratio is t/c = 0.09 averaged and sail twist is r = 18°. Calculated and measured lift coefficients agree
well for incidence angles P < 20°. For higher angles of incidence, the flow separates. Calculated drag coefficients were less accurate. Calculated drag agrees best with measurements, if the drag coefficient of the mast is set to cw = 1-4, which is about 16% larger than values given in the fiterature. However, here the experimental data show minimal drag coefficients at lift coefficients close to Cl, = 0.5, which is not consistent with theory. However, the accuracy of the method will suffice for the intended calculations of trim and tactics optimization.
Sail twist is controlled by the sailor using main sheet, traveller and Cunningham haul. I t decreases the height of the center of sail forces. For given heel stability, lower height of the center of sail forces allows higher lift of the sail, usually established with larger angle of incidence. However, sail twist leads to disadvantageous lift distribution along the sail span increasing induced drag. Fig. 7 shows lift and drag coefficients against angle of incidence for various sail twists, calculated for an OK-dinghy. Optimum twist can be determined best if lift and drag calculations are combined with a velocity prediction procedure (VPP), Graf (1995), that calculates boat velocity in windward direction, the "Velocity Made Good" ( V M G ) , Fig. 8. The V P P is based on a Newton-Rawson method to calculate equilibrium of sail, centerboard, rudder and hull forces, where the latter ones are estimated using approximation formulas derived from towing tank tests. In this example, the heeling moment is restricted to 565Nm and wind velocity is 5m/s. The optimum twist is then 3 ° / m corresponding to a boom angle with respect to boats centerline of a = 6°.
10 15 A n g l e o f I n c i d e n c e p [°]
Co V M G [mis]
Fig. 7: L i f t and drag coefficients of untwis-ted and twisuntwis-ted sail of an OK-dinghy
2 3 T w i s t [°/m]
Fig. 8: Velocity made good for OK-dinghy as function of sail twist
Fig. 9: Mast positions and rudder angles
Mast position is another important sail trim parameter. Yachtsmen usually find optimum mast position by trial and error. The optimal mast position depends rather on the interaction of centerboard and rudder than of sail t r i m . A mast position too far astern results in large leeward rudder angles to baiance yawing moment of the sails. Large rudder angles produce large lift coefficients as intended, but produce quadratica.lly large drag coefficients to be avoided. A mast position close to the stem results in windward rudder angles, which is even worse, since the rudder produces lift towards an unwanted direction. Fig. 9. In this example centerboard and
rudder forces are calculated as two flat wings using the described lifting-surface method. For the OK-dinghy and mentioned weather conditions, V M G has been predicted for various mast positions. I f the mast position changes, the rudder angle must also change to balance yawing moments. The optimal mast position is approximately I m (in front of centerboards trailing edge). Fig. 10, and the corresponding rudder angle is 6 = 2.5°.
Other investigated examples show the capability of the described method to find an optimal set o f t h e most important sail trim parameters of racing dinghies, e.g. mast slope, camber ratio and others. Optimized sail trim results in better boat speed. However, tactics during races are of same importance. Numerical hydrodynamics can help in this field, since they allow to study mutual dependence of sail forces for two boats sailing close together. A typical example is the leeward tactical position for two boats at close-hauled course. Fig. 11. Calculations were carried out for two OK-dinghies sailing close-hauled in wind velocity of 5m/s. Fig. 12 shows lift and drag coefficients normalized with the respective values of the single sail not interacting with other sails. L i f t and drag coefficient ratios are plotted against the dimensionless longitudinal distance rc/L of the luffs of the sails. The leeward distance of the two boats is set to the footer length of the sail L. A leeward tactical position means a disadvantage for boat A. Lift coefficient decreases while drag coefficients increases. Boat B takes ad vantage from this position even compared to the single boat, as soon as x/L > 1. .'\ racing yachtsman might seek this position not only in match races where only two boats compete, but also in regular races with many competitors.
VMG [m/s]
Mast P o s i t i o n [m]
Fig. 10: Velocity Made Good and resulting rudder angle against mast position
Win
Fig. 11: Leeward position of boat B
C l / C i . s i n g l e * - L i f t c o e l f i c r e n l B o a l B * • O r a g c o e f f i c i e n t B o a t B Lift c o e f f i c i e n t B o a t A » • D r a g c o e f f i c i e n t B o a t A X/L
Fig. 12: L i f t and drag coefficient ratios for two dinghies sailing in leeward tactical position
3. Viscous turbulent flow calculations
Calculation of turbulent flow usually is based on solving the time-averaged Navier-Stokes equations. Progress in the development of turbulence models, solution algorithms, and computer hardware has led to a penetration of numerical methods in areas where formerly experimental methods dominated. For some problems - e.g. free-surface ship flows - the development of numerical methods still is in a stage of research. In other areas already satisfactory results can be achieved using Navier-Stokes solver. Na.vier-Stokes calculations a,re ressource-intensive. ModelHng a sail flow for a Na.vier-Stokes solver is much more time consuming than modelling the same problem for a lifting-surface method. Thus turbulent flow investigations have to be restricted with respect to the number of shape variations. However, inviscid flow calculations fail as soon as flow separation occurs. While separation can be avoided in strong wind condition, the effects of flow separation cannot be neglected in lightwind condition, where the sails angle of attack is large. To calculate flow separation phenomena on sails, a commercial Navier Stokes solver - the program CFX of CFDS - was used. The flow around a wing of rectangular shape of aspect ratio A = 2 was calculated. The circular section of the wing has a camber depth of 5% of its length, Fig. 13. The Reynolds number is iï„ = 0.35 • 10*^ corresponding to a dinghy sail at wind velocity of approximately 3m/s. Calculations are carried out for angles of incidence
= 0°, 11°, 15°, 20°, 25°, and 30°.
Fig. 13: Sail shape and section
The flow domain of length of approximately 4 times chord length, width of 2 times chord length, and a height of 3 times wing height was discretized by 48 • 32 • 48 = 73728 grid cells. Calculations were carried out using the k-£ turbulence model with standard set of constants and wafl functions. A dimensionless wall distance y+ = ysjrjpjv (wall distance y, wall shear stress r , viscosity v) between 90 and 330 was realized. The standard SIMPLE method was used as the global solution algorithm. Underrelaxation factors of = 0.8 and = 0.2 for momentum equation and pressure correction equation were used. The inner iteration used the SIP-method. Inner iterations were terminated as soon as the residuals for momentum, turbulent kinetic energy and its dissipation rate were less than 10% of the values at the beginning of the inner iteration. For the pressure correction, equation residuals were reduced to less than 1% for each inner iteration. With this set of parameters, approximately 180 global iteration cycles were neccessary for non-separating flow to decrease the 1-norm of the momentum equation by four orders of magnitude. I f flow separation occurred, approximately 300 global iteration cycles were neccessary.
Vector fields for velocity in a plane orthogonal to the sail surface show flow separation begin-ning for angles of incidence larger (S > 15°. No experimental results are available for velocity and pressure fields, but lift and drag can be compared for the two methods described here. Fig. 14. For the lifting-surface method lift coeflicient is linear and drag coefficient qua,dratic with respect to b. L i f t coefficients of the Navier-Stokes solver indicate flow separation for ?> > 15°. Low Reynolds numbers and low aspect ratios produce a smooth decrease of the lift coefficient gradi-ent as expected. Agreemgradi-ent of lift coefficigradi-ents of the two methods is acceptable. Finer grids and
calculations at higher Reynolds numbers for the Navier-Stokes solver may improve agreement further. Agreement of drag coefficients is only acceptable for small angles of incidence, where shear forces dominate. Inclusion of the resistance of lower and upper edge into the vortex-lattice method using simple estimation formulas should improve the prediction of lift and drag coeffi-cients. Finer grids are neccessary to calculate accurate drag coeflicients for the Navier-Stokes solver.
0 5 10 16 20 25 30 A n g l e of i n c i d e n c e 5 1°]
Fig. 14: Calculated lift and drag coefficient for rectangular wing with circular section
4. Conclusion
The lifting-surface method can estimate the influence of various sail t r i m parameters on lift and drag coefficients. Together with a velocity prediction method, sail trim can be optimized taking into account the effect of centerboard (or keel) and rudder balance. A commercial Navier-Stokes solver is used to calculate flow separation phenomena at a thin rectangular wing with circular sections. While results give lift and drag coeflicients as expected, for a final assessment of the method further calculations with higher grid discretization need to be compared with detailed experimental data. Turbulent viscous flow simulations using Navier-Stokes solver need much more human and computational ressources. The lifting-surface method allows hundred or more calculations of l i f t and drag coefficient diagrams for form variants of sails within a week on an average engineering workstation. Navier-Stokes pre- and postprocessing takes several days of human work just for the single rectangular wing flow model and the computation requires high workstation performance. The large number of form variants to be considered for sail t r i m optimizations suggests to use lifting surface like methods for sail trim optimization. Viscous turbulent flow calculations will be used for selected flow problems where flow separation effects dominate. With flner grids and better turbulence models, these methods may deliver results close to reality, which inviscid methods can never achieve for principle reasons.
References
GRAF, K. (1995), Berechnung der Krcifte und Geschwindigkeit eines Segelfahrzeuges am Wind, 16. Symp. Yachtentwurf und Yachtbau, Deutscher Boots- und SchifTbauer-Verband, Hamburg
JÜRGENS, D. (1994), Theoretische und experimentelle Untersuchung instationarer
Tragflügelumströ-mungen und Entwicklung eines Berechnungsverfahrens fiir Vertikalaclisenrotoren, Ph.D. Thesis, Univ.
Rostock
SCHENZLE, P.; SIEGEL, R. (1983), SegdkrHfte aus dem Wmdkanal, IfS-Schrift 2378, Univ. Hamburg SCHLICHTING, H.; TRUCKENBRODT, E. (1967), Aerodynamik des Flugzenges, Band 1, Springer SÖDING, H. (1982), Prediction of ship steering capahilities, Schiffstechnik 29
Seawaves - Basis for Dimensioning of Ship Structures
Hans-Joachim Hansen, Germanischer Lloyd^
The 5. Shipbuilding Colloquium of shipyard industry and Germanischer Lloyd (GL) on 29.2.1968 pubHshed a Hst of damage case studies for bulk carriers. This marked the start of my studies of seawaves and their effect on ships. Seawaves induce heave, pitch and roll motions, and in turn dynamic loads. The Colloquium reported numerous damages in the forecastle region of bulkers. In most cases, pillars under the forecastle deck had buckled, and large deck areas had lowered. Subsequent computations showed that loads of about 40-60 k N / m ^ must have acted. Pressures were computed based on the relative motions for a ship sailing from Narvik to Rotterdam. The difference of relative motion and freeboard was assumed as static water column with amplified pressure effect due to the acceleration of the ship hull. Computers back then did not allow to determine design values for the pressure by integrating the two-dimensional normal distribution of relative motions and accelerations over all seaways of the Walden statistics (North Atlantic 40.-55. latitude). Nevertheless, an example calculation for a significant seaway (Hy/Ty) of the statistics showed clearly that the assumed loads of 17.5 kN/m^ back then (1967) were too low. The effect of the accelerations nearly doubled the pressure. Today's rules of Germanischer Llyod require for a ship of this size a design pressure of p(96)=68 k N / m ^ . With the many bulker accidents in mind, ABS intended recently to unify the load assumptions for the hatch covers as some accidents were obviously caused by water pouring through hatch covers damaged by sea impact. The intended design value lies in the vicinity of the present GL value, i.e. considerably higher than the value of 17.5 k N / m ^ of the Load Line Convention of 1966. The unified rules shall cover the region ahead of 0.75L f r o m A P which concerns the two foremost hatches respect-ively their hatch covers. The design pressures increase from this position forward reaching their maximum at L .
Design values for the pressures on deck were difficult to compute because the pressure is not proportional to the wave height. But by the end of the 60's we were able to compute design values for internal forces (bending moment and shear force) for the ship, which was modelled as beam with varying cross section, based on strip methods and the above mentioned seaway data. Considering both vertical and horizontal moments and forces in addition to torsional moments allowed to determine the combined stresses in the beam model due to the seaway. The results of these extensive computations were of course compared to the classification society's requirements for global strength in longitudinal direction. Different classification societies assumed at this point in time different vertical wave bending moments and had also different permissible stresses. This resulted in different permissible still water bending moments. In 1978, the internationally recognized classification societies started to develop unified rules for the dynamic longitudinal strength. A model ship was taken and design values based on strip method computations compared. Seaway statistics were of course one decisive parameter amoung many, like modeling mass distribution, strip method employed, or the integration method for the long-term statistics. Results differed considerably. Fig. 1. The largest differences were due to the different seaway statistics. Therefore a common seaway statistics was recommended for computations of long-term statistics. The formulas in the rules were treated pragmatically. As apparently structures were reasonable so far, the relation of wave bending moment and permissible stress were compared. E.g. ABS required a higher wave bending moment than the GL, but permitted also higher stresses which resulted in virtually the same section modulus. The classification societies agreed finally on two different formulas for hogging and sagging moments which were included in the rules as Unified Requirement. The previous (CB + 0.7) dependence prevailed only for the sagging moment. The hogging moment was taken as proportional to only Cjg. The relations to L and B remained, the sagging/hogging ratio is maximum 1.25 for a CB of 0.6, Fig. 2. Experiments, however, indicate higher ratios.
fBending moment midship (tm -10^)
100--2
Log of probability level i r
-10
Fig. 1: Long-term bending moment amidships (v=21 knots); upper limit curve Bureau Veritas, lower limit curve Germanischer Lloyd and American Bureau of Shipping; other
classification societies lie in between
2.0 ^ 1.8 1.6 1.4 1.2 1.0 Sagging-Hogging Ratio
Fig. 2: Sagging-Hogging ratio over block coefficient;
LR computations, regression of L R computations, lACS rules
Hydrodynamic calculations also show that values of 2 are possible, Hachmann (1991). Long-term measurements show also a tendency to higher values, Hansen (1993). Now every classi-fication society has the right to go beyond minimum requirements. This is done to a limited extent. The sagging moment is slightly increased, but no bonus is given for a lower hogging moment. Using proven and new hydrodynamic approaches, the reform of the load assumptions will be continued. A t present we are still in a discussion stage, back to seaway and its statistics, whether the statistics should be adjusted to the above mentioned formulas or vice versa. The
latter should be valid and thus the discussion over a reliable seaway statistics will continue. I have tried to extrapolate the findings of Germanischer Lloyd measurements to 20 years and derived what I think is a reasonable coincidence with the formulae in the new rules.
The eff"ect of seawaves is our concern again and again, not just before or during the construc-tion of the ship, but also during the operaconstruc-tion and - worst case - after the loss of a ship. In 1983, the ministry of transport ordered us to develop a 'black box' for ships after several accidents with total losses had occurred where it was difficult, if not impossible, to determine clearly the circumstances leading to the loss. The seaway was registered in the 'black box' through several sensors which recorded the motions. Four acceleration sensors captured vertical and horizontal values allowing to draw conclusions on the seaway if necessary. Despite the successes that we and other institutions had with 'black box' systems, they have not been employed at all in Germany. In England they are used only as 'hull strength monitoring systems' in a form as developed in the 'Schiffder Zukunft' project by A E G and GL. Despite the recent severe accidents, IMO could not decide to make 'black boxes' mandatory at least for ferries. Such systems cannot avoid accidents, but contribute to clarifying the reasons for an accident. 'Hull strength monitoring systems' for bulkers of more than 20000 tdw are also only recommended by IMO. The German ministry of transport recommends such systems for operating ships and requires them for newbuildings.
If we think of the many losses of bulkers, seaway comes into the discussion again. Often we read in the accident reports 'loss in heavy seas' or 'sea impact destroys hull'. The implicit scenario is that water pours through the damaged hull, flooding one hold which in turn may lead to failure of the bulkheads due to overloads. Since these ships are designed with a one-compartment status, this leads to a loss of the ship. Now the question arises why a well designed and constructed huU cannot withstand the water pressure in the sea. The answer has many aspects. Corrosion and damage due to improper cargo handling are the main reasons. Especially coal with a high sulphure content is very aggressive. "Coal eats the vessel and ore breaks the vessel", as an Israeli delegate so aptly put i t . Now, ore does not have to lead to breaking, even if the increase in transverse forces when flooded is considerable. But i f at the same time corrosion has weakened the structure, the strength reserves are not too large anymore. In addition, the cargo stuck between frames is not always carefully removed, instead grab impact is quite frequent. So the in many regards rough operation of single-skin bulkers may lead to damages even i f design and construction are good. Maintenance is of special importance for these ships.
The design sealoads on the hull are subject to worldwide discussion. lACS tries currently to unify design loads and rules. Load components due to heave, pitch, and roll shall be given preferably explicitly and reasonably combined. Again we will have to resort to proven and newer hydrodynamic approaches.
Germanischer Lloyd started a research project to determine at least in one case the external load in ship operation due to seaway. A bulker of 210m length was equipped with 11 pressure sensors at the midship section which are located below the design waterline. In ballast, some of the pressure sensors will be above the calm-water waterline. We hope to gain insight about the pressures around the waterline and correlate motions with pressure components. Parallel to the pressure measurements, strain gauges are distributed on deck and on the flanges of frames to determine a correlation between water pressures and bending stresses in the frames. As usual, the seaway will be determined only by subjective observations of the ship's crew in addition to operational data such as speed and course. We hope for 'good' results (automatically registered) about which we will report in due time.
In summary, lACS has started an intensive program in 1995 to increase safety standards for bulkers. This program has just been finished in its first step. Several unified requirements were agreed upon to increase the strength standard. The three main points regard the longitudinal strength in flooded condition, the watertight bulkheads and the double bottom, and the loads on the hatch covers. Considering the longitudinal strength in flooded condition leads to thicker shell
plate and increased sectional modulus. GL has proposed a general increase to avoid additional computations for the longitudinal strength. As each hold has to be considered as individually flooded, the number of additional cases is considerable. Especially in the beginning of a project, a general consideration would be helpful. Fig. 3 shows the proposed increase of shell thickness which has been validated by a number of computations. For the operating fleet, equivalent meas-ures have to be taken, e.g. restrictions of load cases.
References
HACHMANN, D. (1991), Calculation of pressures on a ship's hull in waves, Ship Technology Research 38/3
HANSEN, H.J. (1993), Ergebnisse von Langzeitmessungen auf Schiffen im Seegang, Proc. Schiffbau-technische Gesellschaft 87
Knowledge-Based Optimum Conceptual Ship Design^
K y u - Y e u l Lee, Seoul National University^
K y u n g - H o Lee, Korea Research Institute of Ships and Ocean Engineering^
1. I n t r o d u c t i o n
Conceptual ship design is often described as an iterative process in which compromises must be made between various conflicting requirements. The design process can be envisioned as a spiral. Numerical optimization can provide an analytically defined optimal solution. In recent years, artificial intelligence research has provided tools that can emulate some characteristics of human decision making. Knowledge-based systems which simulate human intelligence in spe-cific domains and a genetic algorithm, which can be interpreted as a form of machine learning, are used for assisting engineering design. This research investigates the feasibility of applying knowledge-based systems, a genetic algorithm, and numerical optimization to conceptual ship design.
2.. O p t i m i z a t i o n M e t h o d
The numerical optimization algorithm which is most appropriate to use depends on the nature o f t h e problem. Different algorithms need to be explored to find that which is best suited for the problem at hand. Hybrid systems can create design procedures with the desirable qualities o f t h e constituent systems, while minimizing their disadvantages.
Many numerical optimizations use gradient approximation to search for optimal solutions in the design space. There are many algorithms to optimize nonlinear, multi-dimensional, con-tinuous functions. The majority uses a form of gradient descent. The advantage of numerical optimization is that it is extremely good at design space exploitation because the method focuses on the immediate area around the current design point, using local gradients to move to a better design. However, there is no guarantee that the global design optimum is reached. The methods are also sensitive to the starting point. The computational effort depends on where the initial design point is relative to the optimal point.
Genetic algorithms are based on the premise that design can be viewed as an evolutionary process (Goldberg 19S9). A population in the design space evolves through a selection process. The selection criterion is based on the survival of the fittest, subject to the existing environment. Genetic operations such as mutation and cro.ssover are used to produce new generations. The intrinsic nature of elimination of bad design attributes and selection of good design attributes from generation to generation implicates tho capability of learning during the process. Genetic algorithms offer the following advantages: It explores the parameter space so that the complete topology of the design space can be determined. The major drawback is that the approach is computationally intensive compared to other numerical optimization methods. Genetic al-gorithms are desirable if the design problem has multiple locai optima, and if the topology is unfamiliar to the designer.
Lee and Lee (1995) introduced a hybrid optimization method - a combination of a sequential
linearized approximation method and a genetic algorithm - to overcome the drawbacks of the usual optimization methods. The genetic algorithm quickly produces a potentially good design point which then becomes the initial condition for the sequential optimization. This can greatly reduce the computational requirements as compared to purely numerical optimization alone. Genetic algorithms are not based on gradients and will not get trapped at a local optimum or at constraint boundaries. They also define the general topology of tho design space. This is useful
' T h i s research was supported by (lie Korean ttesearch Foiinclalion, Grant No. 9.5-3010 ^Dept. of N A & O E , Shin-Rhim Dong, kwan-ak kn, .Seoul, Korea
to compare design features between different local optima.
Four simple problems were tested using the following three optimization approaches: Sequen-tial Linear Programming (SLP) Method Söding (lOOS/J,), Genetic Algorithm ( G A ) , and the hybrid method combining the two approaches. The results are compared with the exact global optima. Comparisons are made in terms of finding exact solutions for different starting points, as shown in Table 1 where, e.g., 4/5 means 4 successes for 5 different starting points. The hybrid approach succeeded always, whereas GA and SLP Method found tho optimum solutions only for some test cases.
Problem 1: Minimize f { X ) ^ A , + 2X2, subject to g{l) = [Xi^ + (.Y2 - 5)2)/25 - 1 > 0, ^(2) = ((A2 - 5)2 - A2')/25 - 1 > 0, .<7(3) = A , - 1 > 0, g{A) = X2 - 1 > 0. The global optimum is X* = (9.9,1.0), / ( A * ) = 11.9.
Problem 2: Minimize / ( A ) = ( A i - 2)^ + (A2 - 1)^, subject to .7(1) = -Q.2bX{^ + X2^ + 1 > 0, = A l - 2 A 2 + 1 = 0. The global optimum is A * = (0.8229,0.9114), / ( A * ) = 1.3935.
Problem 3: Minimize / ( A ) = ( A j - 1)^ + ( A j -
A2)''^
+(A'2
- A^a)'', subject to - 1 0 < A,- <10 [i = 1,2,3), / i ( l ) = A i ( l + A22) + A'3'' - 4 - •^^/2 = 0. The global optimum is A * = (1.10486,1.19667,1.53526), / ( A * ) = 0.0325682.
Problem 4: Minimize / ( A ) = 4Ai2+2.Y2^+2.V3'^33.Y,+ 16.\'224.Y3, subject t o / i ( l ) = 3 A i
-2 A -2 -2 - 7 = 0,/i(2) = 4 Ai -A V - 1 1 = 0. The global optimum is A * = (5.3267,-2.1190,3.2105), / ( X * ) = -143.6461422
Table I : Reliability of Sequential Linear Programming Method, Genetic Algorithm, and f f y b r i d Approach (No. of Successes / No. of Different Starting Points)
SLP GA Hybrid Problem 1 1/5 3/3 3/3 Problem 2 5/5 3/3 3/3 Problem 3 1/5 3/3 3/3 Problem 4 4/5 1/3 3/3 3. K n o w l e d g e - B a s e d O p t i m i z a t i o n M e t h o d
Artificial intelligence ( A l ) is the science of creating intelligent behavior on computers. One approach for this are expert or knowledge-based systems. They perform a task normally done by experts or specialists in a field, capturing often also heuristic knowledge. A I concepts can also be used in optimal systems design. So far, methods of optimization and associated programs have been used mostly by experts in the respective field. The limited use of the methodology by general designers has resulted in failure more often than in success. We examined why the experts ha.ve been able to apply techniques to almost any design problem but the general designers have not. The main reason is that experts can observe the behavior of the algorithm, diagnose failures and erratic behavior, and fix them by adjusting certain parameters.
Söding (1977,1978) introduced the concept of "machine intelligence" for optimization; Söding and Wrede (1983) developed an intelligent numerical optimization shell CHWARISMI which
automates the design synthesis process and provides a platform for the use of numerical optimiz-ation. The optimization shell eliminates many features which complicate most design programs: There are no approximate formulae necessary for variables which are to be corrected later; no i t -eration cycles have to be programmed; no subroutine calls for solving the equations are necessary; equations need not be described in a separate subroutine; variables need not be renamed to x ( l ) , x(2),...; the order of equations need not bo determined such that there are known values only on the right-hand side; no equations have to bo inverted analytically or numerica,lly by the user to determine one unknown value from known values only or to eliminate certain variables. Thus, the program reflects very clearly the logical structui'o of tho design problem. The generality of
this software concept allowed a wide variety of design problems to be handled. Besides prelim-inary ship design applications, e.g. Lee (1983), Rupp and Lee (1984), Gudenschwager (1984), the shell was used also for ship structure design, the optimization of the design and handling of sailing rigs, and the solution of nonlinear systems of equations in various hydrodynamic and structural investigations.
Lee and Lee (1995) developed a knowledge-based hybrid optimization program consisting of
a genetic algorithm, a sequential optimization algorithm, an optimization shell, an optimization language generator, and a design model (Fig. 1 ) . The system can combine three different op-timization approaches to the design process. The idea behind the hybrid approach is to take advantages of each method's strong points so that the combination can provide a better design solution than that provided by any single method. Numerical optimization, knowledge-based approach and genetic algorithm have been employed in both stand alone and in a hybrid mode.
G e n s t i c Algorithm Reproducrtion C r o B s o v o r Mutation G l o b a l O p t i m u m C o n v a r e l o n Optimization L a n g u a g o G s n e r a t o r KB UNIX S h e l l Script X X X . O F T Fortran C o d e R U N 1 ^ Mathematical optimization Optimization L a n g u a g e P r e C o m p i l e r Optimization Algorithm Design Model
Hybrid Optimization IVIodel
Fig. 1: Configuration of the hybrid model and dataflow
4, Knowledge-Based System for Compartment Arrangement Design
In the early stage of design, it is difficult to arrange compartments and to position longitudinal bulkheads in double-hull tankers automaticaily because of many restrictions such as total tank capacity, ballast tank capacity, limitation of each tank size, etc. Human designers follow this way: (1) assume a start design, (2) evaluate i t , (.3) change it so as to satisfy restrictions and to come nearer to an optimum, (4) repeat 2 and 3 until satisfactory design is obtained. In this approach, designer's know-how of redesign is essential. Application of Af can help in a stepwise and heuristic approach like this.
Knowledge-based systems offer the capability to guide a ship design by emulating a ship design expert. A n expert is defined as an individual who has acquired knowledge in a particular field and can apply that knowledge effectively and efficiently in .solving problems in that particular field. Often this knowledge is subconscious and difficult to express completely and clearly even by the expert himself. An expert can make good estimates based on incomplete information by using heuristics to fill the gaps. Developing a good set of heuristics is important in building a knowledge-based system. Such systems, in general, consist of a user interface, a knowledge
base for storing domain-specific rules, a rule control structure for determining the order in which the rules are examined, and a rule interpreter (inference engine), which infers new facts when all rules are met. Each rule consists of a goal, one or more actions, and conditions. The goal specifies an output of the design code and the direction it is to be moved. The actions describe inputs to the simulation code, their direction of change and the order of change to get the effect specified by the goal. The conditions specify the portion of the design space in which this rule is applicable.
4.1 Knowledge Base
The knowledge base affects the overall architecture of a knowledge system. To organize a practical knowledge base, first steps are the knowledge acquisition and the representation of acquired knowledge. The completeness of related knowledge in a knowledge base plays an important role in a practical system.
Generally, there are two approaches to collecting the knowledge necessary for an expert system:
(1) Survey related literature and reference material.
(2) Collect from ship design practice and experts' experience.
Both approaches were utilized in developing this system, mainly to gather qualitative knowledge. The knowledge representation must encode the knowledge (rules) and set up the interaction with the inference engine. The rules for our design problem mainly consist of experience, part of which in the form "condition-action". A production-type system is best suited for knowledge representation in this type of problem. The problem-solving process rea,sons and calculates in such a way that the reasoning will lead to a calculation while in turn the results of calculation will add new information to lead the reasoning to a deeper stage. The production rules are of the form:
GOAL: Increase cargo hold capacity ACTIONS: Increase cargo hold section area
Generate knuckled position o f t h e inner longitudinal bulkhead Introduce double knuckle point of the hold section
C O N D I T I O N : Minimum clearance between hull and both side and bottom tank
Generally the number of rules may be huge when the efi^ects of various related factors are fully considered in complex design problems. To raise the efiiciency of the problem solving, rules are categorized as follows:
- Constraint knowledge: Constraints applied by standards and regulations which must be satisfied in the final design proposal.
- Procedural knowledge: Knowledge of the design process. The fundamental activity o f t h e conceptual design process is the identification and application of constraints. These cannot be applied in isolation as their nature will be infiuenced by the current state o f t h e design. - Analysis algorithms: Knowledge of how to evaluate and analyse preliminary and final
proposals. The algorithms are used to analyse, evaluate and compare the performance of the proposals with respect to the specified requirements.
- Proposal knowledge: Knowledge of the design. Graphical and textual descriptions are used to represent the design.
The ability of a knowledge-based system shell to acce,ss external analysis routines is essential for developing engineering design applications. Communication with these external procedures is via input and output datafiles which are specified in the knowledge base.
4.2. Knowledge-Base Modeling
In our knowledge base, the major part of knowledge is represented by IF-THEN rules. To simplify and access the design problem easily, the knowledge is classified as follows:
1. Determination of initial values: Temporary design
The design guidance related to compartment subdivision and bulkhead positioning depend on production capabilities of shipyards such as dock capacity and production facilities. The knowledge base for initial value determination is implemented according to rules of the type:
"Longitudinal positions of knuckle points are determined from the positions of block sub-division";
"The position of a 1st block division is set relative to the collision bulkhead";
"The positions of 2nd, 3rd block divisions follow from the previous division position and the block length."
2. Determination of section types
In this knowledge, a section type is described with regard to the longitudinal position and hull clearance, e.g. in the form:
"For V L C C type, if the hull clearance at lower KP (Knuckle Point) between pump room forward bulkhead and 2nd block division is not enough, let the section type be box type"; "Tankers below the SUEZMAX must have a double KP because of excessive clearance." By using these section type determination rules, a section definition module can be executed easily on the basis of the genera,ted section data.
3. Design evaluation
Design evaluation rules mainly consist of design constraints. That is, longitudinal knuckle positions determined by initial value rules are transferred and evaluated according to the following criteria:
1) M A R P O L 73/78 regulation 13F, e.g.:
Minimum clearance of wing tanks or spaces ur. w > min(0.5-|- L'H/'T/20000, 2.0) In practice, the value of w is determined according to the following design guidance: SUEZMAX: w at lower K P (knuckle point) > 2.1m
P A N A M A X : lo at lower KP (knuckle point) > 2.05m
Minimum clearance of double bottom tanks or spaces /;.: Ii > m i n ( ö / 1 5 , 2.0) 2) Capacity of ballast and cargo tank > required values
4. Design changes
Design variables are defined by object slots in the knowledge base. To implement the inference mechanism for design changes, the values of slots must be changed in the inference process. In addition, if the value of any slot is changed, the values of related slots must be changed automatically. The methodology for implementing this concept of design change is the non-monotonic reasoning technique, and the revision of slot values is implemented by an IF-Change method. Design changing rules are e.g.:
Rule 1: IF < cargo.volume volume_req > volume_diff criterial Hypo DoubleJ<P_Case
Action Execute "gen_double.kp" Reset cargo_volume
Rule 2: IF Yes Double.KP.Case Execute "calculate.vol" > volume.diff criteria2 Hypo SmalLChange.Case Action Execute "change_theta"
Reset cargo_volume
The rules are represented in a general-purpose expert system development shell. Rule 1 performs a design change by introducing a double knuckle point after evaluating the current design state. In this rule, if the actual total volume is less than the required volume and the difference is greater than criterial, then the "gen_double.kp" module is exectued. I t generates a section double knuckle point, and the value of cargo_volume slot is reset. Then IF-Change methods which are defined at cargo_volume slot are operated, and related slots are initialized by sending an appropriate message.
Rule 2 shows that, in case of a double knuckle point, the volume is calculated by using the ship basic calculation program, and if the volume difference is greater than criteria2, the angle of theta is changed (Fig. 2). Criterial and criteria^ are obtained from designer's expertise. They are defined as methods, and utilized in the process of reasoning.
1
\^3^
\ \ \ \ \ \ \ \ \ \ \ \ Double K P \ V / theta 0 ^^^S, ~ ^ ^ s \ / Initial Section \ t h e t a ^ ^ A r Changed SectionFig. 2: Design changes with double knuckle point
The inference engine interrogates the knowledge base, invokes the associated rules and cre-ates relevant facts. I t performs four main tasks: matching, selecting, firing and actioning. I t is responsible for invoking the rules held in the knowledge base and updating the working memory with the newly generated facts. I t decides on the best path to be taken through the knowledge-base in its attempt to arrive at a solution. Here the commercial inference engine NEXPERT SHELL was used.
5. A p p l i c a t i o n
A set of routines have been developed which provide geometric data for defined tank rangements. Advisory elements provide the designer with an indication of promising tank ar-rangements and their eff"ect on hold capacity and ballast water tank volume. Fig. 3 shows the information flow between knowledge base and external ship basic calculation modules. Fig. 4 shows a section at the longitudinal knuckled position, in this case .52nd frame, generated in initial value determination rules. Generated section data, e.g. upper knuckle point clearance, lower knuckle point clearance etc., are transferred from the section definition program to the object slots in the knowledge base. When preliminary knuckle positions are determined by the initial value rules, the design restrictions are evalua.tcd. According to the evaluation, appropriate
design changes are carried out. Rules for design changes are subdivided as follows: - Changes of longitudinal compartment division
- Changes of section type (double knuckle point) - Changes of hopper angle (theta)
Knowledge-Base
Initial Determination Rule Section Determination Rule
o 1st Block :13M from Collision BHD KP Position Evaluation Rule 1
1
KP Position0 Box Type Case o Double KP Case
Section data a
0 Restriction about W o Restriction about H 0 Restriction about
Ballast Tank Capacity 0 Restriction about
Cargo Tank Capacity
Geometrk; Data
o Modify the section : Double Knuckle Point 0 Double KP : theta change o Longitudinal Knuckle Point
change o r r D > 3 ^ 1 ( Q < D JS. O Q .
Ship Basic Calculation Program
Fig. 3: Information flow and message sending between knowledge base and external program
Fig. 5 shows the represented knowledge for changes of section type in the expert system shell. The purpose of this system is to perform the arrangement of the longitudinal bulkhead of a double-hull tanker. Fig, 6 is the result of the arrangement of the longitudinal bulkhead. The black points denote the longitudinal knuckle positions. In a real design, these evaluations and changes are repeated.
The concept of callable interfaces is adopted to connect the knowledge base with the ship basic calculation program effectively All knowledge bases are controlled by the A P I (Application Programming Interface) program, and the ship basic calculation program is executed from the knowledge base. Fig. 7 shows the results of a changed section according to the calculated volume by using the integra.ted system.
Fig. 4: The interface of knowledge base and external ship basic calculation program
O h ) a c t H a t w o f K
Fig. 5: Representation of design knowledge
V A \ / \ / s / S / \ / X '' ^ \ / \ / X y \ \ / \ / X \ / X u6.:tv( / \ \ / \ / X • Knuckle point of the Inner Longitudinal Bulkhead
Fig. 6: Compartment division and the arrangement of longitudinal bulkheads
NO CWfAftTKDfT BCl hP.l C.lAti s c i w:-.i c . T . i s i SO! KC.! C . T . l r i S « NO.1 C.T.fSl 5t-5 W.3 C . T . l r i SM KO.3 C.T.ISI =07 MP.4 C . T . i r i 508 W?.* C . I . I S I » ï Ml.S C.T,(Pl SIO Kti.9 C ; I , I S I ÜU « / . 6 c . i . i r i SIZ M).6 c . r . i s i sia W',? c . i . i r i 5M K'.7 C , 1 , J S I V O - I W E CEKISE OF GRAVITY fWH M 5 I . Ï 3H72.0 35S3.0 ; S6a.7 ; 5C7i3 Ï S H . 0 3565.7 J M H . 0 3566.7 35TO,6 3315.3 es.ts 65.63 • « B . S J 33.60 16.13 16.IS - Ï . 7 2 7 S.723 -7.315 7.4M -7.509 7. «es -7.509 7.483 -7.414 HO c » r « m t o t T 501 Kl.1 C . T , ( r ) so; HO.] c . i . c s : 503 HO.! c . r . i p : 504 HO.! C . T . ( 5 ! 603 NO.3 C . T . t r J 50» HO.J C . T . f S ; 507 MO.4 c . t . c p : 500 «0.4 c . T . c s ; 90t HD.3 C . I . ( f ) 510 HO.3 C . T . I S : 911 Ho.t c . t . i p : 91! m.ê c.T.<s: 513 HO.7 C . T . I P J - • HO.7 C . T . I S ) 2S14.0 Ï 3 H . 3 34SS.: 3553.0 35Ï5.7 3S34.5 3557.3 3333.0 3B54.0 35S5.7 33!».a 33il.3 B S . M 10. fiS.66 •• 49.33 4S.33 10, 32.SO 10 3!.to 10 IS.15 10 15.15 10 -33.17 7 . ï g 3 -7,W>9 7 . « 3 -7.509 2490.0 2479.9 4264,3 4317,9 7.390 46Z?
Fig. 7: Calculated volume and design changes
References
GOLDBERG, D.E. (1989), Genetic Algorithm in Search, Optimization and Machine Learning, Addison Wesley
GUDENSCHWAGER, H. (1984), PREOPT nemUzeranleitung, IfS-Schrift 2351, Univ. Hamburg LEE, K.-H.; LEE, D.; HAN, S.-H. (1996), Object-oriented approach to a knowledge-based structural
design system, Expert Systems With Applications 10/2, pp. 223-231
LEE, K.-H. ; LEE, K.-Y.(1995), Knowledge based hybrid optimization method, Symp. Soc. Nav. Arch, in Korea (in Korean)
LEE, K.-H. ; LEE, K.-Y.(1996), Knowledge based compartment layout design for double hull tanker, Symp. Soc. Nav. Arch, in Korea (in Korean)
LEE, K.-Y. (1983), Economic ship design for variable operating conditions, PRADS
RUPP, K.-H.; LEE, K.-Y. (1984), Economic consequences of different dimensions, Stability Require-ments and Propulsion Concepts in Cargo Ships, West European Conf. on Maritime Technology SODING, H. (1977), Maschinelle Intelligenz beim. Schijjsentwurf ESS-Report 24, TU Hannover SODING, H. (1978), Design software, Optimization in Ship Design, WEGEMT 1978
SÖDING, H.(1993/4), Description of the Subroutines OPT and DANTZIG, STR 40/1,2,3,4, STR 41/4 SÖDING, H.; WREDE, J. (1983), CHWARISMI I unci II: Compiler fiir technische Entwurfsprobleme, ESS-Report 15, TU Hannover (revised version)
Ship Geometry Modelling
Uwe Rabien, Germanischer Lloyd^ 1. Introduction
When discussing ship geometry, we think first of hull fairing, of the difficulty to find the optimum shape, the problem to represent unusually shaped surfaces using some mesh lines. The hull shape is something of its own - more or less independent from the ship's internal geometry. In contrary, the internal ship structure geometry is subjected to diiferent conditions and constraints. But i t does not require too much mathematics. Defining steel structure geometry is rather a matter of topology. Parts delimit each other and are enclosed by the ship hull forming an outer bound. During the past 30 years, methods of geometry definition changed. Manual techniques were replaced by algorithms and mathematical models. More recently, we focus on data exchange rather than mathematical definitions.
To define the shape of the huh was always a delicate task requiring experience and work-manship. Elastic splines were used to adopt fair hull forms. The three-dimensional web of lines could only be represented by projections. Where more than two lines met they should share the same tangent plane of the hull shape, but did not necessarily so. First computer lofting and fairing was implemented in algorithms cribbed from drawing loft techniques, allowing to check geometric properties of wireframe and surface models automatically (Söding 1967b). Differing objectives led to various mathematical models for shape definition using different types of lines or surface objects. Söding's early work yielded practical solutions for hull shape definition which spread in German shipbuilding.
2. H u l l Shape Models
A simple numerical ship hull model still in use consisted of a set of planar section curves represented by point coordinates and often some additional information on knuckles or local curve segment type (line, circle, parabola) etc. In some programs, spline algorithms were used to produce a best fit curve from given section point data. However, internally the curve was used to interpolate some intermediate points to approximate the spline by easier parabolic curve segments, e.g. in the hydrostatics program Archimedes (Söding 1966), Fig. 1.
Fig. 1: Simple numerical hull model as used for hydrostatic calculations
The exchange of such section curve data, i.e. the reproduction of the kind of mathematical model of section curves did not pose problems for originator and receiver. Longitudinal hull
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shape interpolation was rough and local. The model was not surface oriented. Nevertheless such techniques are still applied in hydrostatics, hydrodynamics, and elsewhere since in many cases the ciccuracy of integral results is not so much affected by local geometric quality. Fast algorithms due to simple models are still important in iterative processing, e.g. when calculating equilibrium conditions.
In Germany one of the first surface-oriented hull-shape models for 'lofting' was spread with the lines fairing program Euklid (Söding 1967b). The curve mesh information was given at mesh nodes or vertices. Curve tangents could be specified or were generated by the spline algorithm. An approximation technique to obtain certain mixed derivatives ('twists') was used to uniquely describe the surface defined by the curve mesh. Fig. 2. The twists were derived f r o m transverse section slopes by submitting slope values to spline interpolation following the longitudinal mesh curves. The procedure was appropriate to define a fair surface for which g l continuity could be obtained. Under certain conditions also g2 continuity was provided. The data input scheme did not request all mesh point coordinates or tangents; much of the information required for establishing a complete curve mesh was derived from intersecting curves already given. This again was adopted from earlier manual lofting techniques. Rules of meshing were e.g.: patches have 3 or 4 vertices, and adjacent edges of patches should be identical.
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. J>- ^^yiiL^Fig. 2: Curve mesh for program Euklid, given coordinates marked by 'o'
It is only a short step from the lofting model towards spline surfaces with a complete set of parameters. A similar concept was followed by the developers of the NAPA system. More freedom was given with respect to meshing rules, e.g. more than 4 vertices per patch became valid. However, that holds only for the external definition; internally the mesh will be transformed to patches of the type described above - 4 vertices at most. A n example is given in Fig. 3. There the aft flat side is a multi-vertex patch. The fore flat side is already subdivided in a way that fits better to the rest of the surface model. Only few additional patches will be necessary to make it a valid internal surface mesh representation.
The less restrictive input strategy is just a matter of the user interface. The underlaying mathematical concept is in principle the same as described before. With respect to capabilities of today's C A D software and data communication aspects, the following requirements can be formulated:
- The hull shape description should consist of patches with three or four vertices (triangles or quads) defined by point coordinates and derivatives at the vertex points which may either be given or determined by the program.
- When data exchange is intended between different software systems, data models not providing all the information to define a surface mesh should be completed in an adequate way by the originator rather than by the receiver. For transverse section curve represent-ation of the hull this would imply curve points arranged such that fair longitudinal Hues can be generated to provide proper meshing. In most cases data transfer interfaces now work in such a way using cubic spline surface patches or NURBS since many C A D systems accept these type of data for free form design. Fig. 4 shows a Bezier patch defined by 16 control points.
Fig. 4: Control points of a Bezier patch (Foley/van Dam)
There were also suggestions to use biquintic spline surfaces and to determine left-over para-meters by a smoothing condition. That was done using the mechanical analogon of strain energy induced in plates by small displacements (Walter 1974). However, the somewhat complicated mesh topology of real hull forms could not be handled sufficiently. Furthermore, derivatives higher than curvature are not of much interest in practical surface definition and fairing.
3. Shape transformation
Often, when a completely defined wireframe or surface representation already exists, some design condition changes and the shape has to be modified accordingly. Center of gravity or block coefficient can be changed e.g. by moving locations of stations, i.e. moving corresponding mesh curves. That will not always result in an acceptable new hull shape. For more general shape transformations Söding (1967a) proposed a method of distorting the surface definition using cértain expressions of simple standard functions.
xn = fi{x)\ yn = fi{x) • f^{y) • fe,{z)\ zn = fr{x) • fsiy) • fgiz)
