Seakeeping of high speed vessels

S E A K E E P I N G O F H I G H S P E E D V E S S E L S 0 . F a l t i n s e n D e p a r t m e n t of M a r i n e Hydrodynamics Norwegian I n s t i t u t e of Technology N-7034 T r o n d h e i m - N T H , Norway j^ r ^ \. _ i iC_d0.'cn5sutc ^^^^ 1 To be presented a t U E T P course on "New Techniques for Assessing and

Q u a n t i f y i n g Vessel S t a b i l i t y and Seakeeping Quahties", Trondheim, M a r c h 1993.

E S T T R O D U C T I O N - r x v ^ ^ . ^ ^

Catamarans and SES are well k n o w n to the high-speed conmiunity, w h i l e foilcatamarans are new concepts. The foils of the two Norwegian concepts are designed so t h a t the catamaran h u l l s are out of the water at h i g h speed i n both calm w a t e r a n d small sea states. A consequence of this is t h a t a f o i l c a t a m a r a n has a m u c h lower resistance t h a n a s i m i l a r sized catamaran at the same speed. W h e n the h u l l s of the f o i l c a t a m a r a n are out of the water, the vessel can easily r o l l over to one side. The reason is a small restoring r o l l moment. To counteract t h i s undesired behaviour a ride control system is used. The control system is also used to keep a n e a r l y constant vertical position of the center of g r a v i t y and to control the t r i m angle of the vessel.

I n the f o l l o w i n g text we w i l l discuss the seakeeping behaviour, of catamarans, foilcatamarans and SES. Some of the discussion w i l l be based on numerical results.

S E A K E E P I N G C H A R A C T E R I S T I C S

A catamaran, foilcatamaran and a SES have quite d i f f e r e n t seakeeping behaviour. T h i s can p a r t l y by exemplified by Fig. 1, w h i c h shows operational l i m i t s based on n u m e r i c a l calculations of vertical accelerations a t the centre of g r a v i t y (CG) of a 40 m long catamaran w i t h o u t f o i l , a 40 m long SES w i t h o u t ride control a n d a 36 m l o n g f o i l c a t a m a r a n w i t h o u t ride control. A ride control v ^ l l have a significant positive influence on the seakeeping behaviour of a foil catamaran. The same is t r u e f o r a SES i n low sea states. A RMS-value of 0.2 g is used as a c r i t e r i o n i n t h i s example. The vertical accelerations w i l l of course depend on the details of the h u l l and f o i l design. The i n t e n t i o n w i t h F i g . 1 is to i l l u s t r a t e features of the acceleration level a t CG of the three d i f f e r e n t vessel types i n head seas. The results i n F i g . 1 are f o r longcrested waves described by the two-parameter J O N S W A P spectrum recommended by I T T C . T-j^ is the mean wave period defined by the first m o m e n t of the wave spectrum and H^yg is the s i g n i f i c a n t wave height. The vessel speed i n calm water is 50 knots f o r the SES, 40 knots f o r the c a t a m a r a n and 50 knots f o r the f o i l c a t a m a r a n . The SES w i l l have the highest i n v o l u n t a r y speed loss i n a seaway. I n v o l u n t a r y speed loss due to waves and w i n d is accovmted f o r i n the calculations f o r the SES and the catamaran ( F a l t i n s e n et a l . (1991)).

Fig. 1 i l l u s t r a t e s t h a t the SES has the lowest and the f o i l c a t a m a r a n has the second lowest vertical acceleration level when > ~6 s. The results for the f o i l c a t a m a r a n suggest t h a t foil appendages on the catamaran may improve the seakeeping qualities of a catamaran. However care must be shown i n doing that. A n example w i l l i l l u s t r a t e t h a t foil appendages may not improve the seakeeping quahties. Three h u l l s were numerically investigated. H u l l 1 was a basis h u l l w i t h o u t foils. H u l l 2 and 3 were modifications of H u l l 1. The displacement was reduced respectively by 10% and 20% relative to H u l l 1. T h i s was done by reducing the displacement volume i n the a f t end of the ship. The h u l l s had t r a n s o m stems and the reduction i n the displaced volume resulted i n a decrease i n the local beam at the transom s t e m . The reduction i n displacements of H u l l 2 and 3 were compensated by h f t fi-om foils at the a f t end of the h u l l s . The net result of t h i s was t h a t the vertical accelerations of the three h u l l s d i d not d i f f e r very much. One reason is probably t h a t the increase i n d a m p i n g by the foils was compensated by a decrease i n the damping due to the h u l l s . The l a t t e r is due to both wave r a d i a t i o n damping and dynamic l i f t i n g effects. The magnitude of the l i f t force and moment on the h u l l depends on the local beam at the t r a n s o m s t e m . However adding passive foils to a h u l l w i t h o u t changing the h u l l is h k e l y to lower the vertical accelerations. I t has probably most eff'ect i f the foils are placed i n the bow p a r t were the relative v e r t i c a l motions are largest. However, out of water effects of the foils or cavitation w i l l degrade the damping eff'ect of the foils. Fig. 1 shows t h a t the operational l i m i t s f o r small wave periods are clearly lowest for the SES. The reason is the cobblestone effect, w h i c h is due to resonances occurring i n the a i r cushion. No ride control was accounted for i n the calculations. Use of ride control w i l l increase the operational Hmits for the SES at lower wave periods. F u l l scale measurements have shown t h a t there are two resonance frequencies t h a t are i m p o r t a n t . One is around 2 H z for a 35 m long vessel. T h i s can be analysed by K a p l a n et al.'s (1981) procedure. Details m a y also be f o u n d m F a l t i n s e n (1990). According to t h e i r theoretical model the dynamic p a r t of the excess pressure i n the cushion is oscillating w i t h the same a m p l i t u d e a l l over the cushion. I t is caused by compressibility effects of the air and excited because the waves change the air cushion volume. I n the past most a t t e n t i o n has been focused on this resonance phenomena and ride control systems have been designed to increase the d a m p i n g of those resonance oscillations. However acoustic resonance can be j u s t as i m p o r t a n t . T h i s was studied by S0rensen et a l . (1992) for a SES w i t h a r i g i d panel as a seal i n the a f t p a r t of the cushion. They showed t h a t a standing one-dimensional l o n g i t u d i n a l l y v a r y i n g acoustic pressure system w i t h nodes midships was excited. The n a t u r a l frequency is 6 H z f o r a 28 m long cushion. The acoustic pressure d i s t r i b u t i o n causes a p i t c h moment and p i t c h acceleration of the vessel. I f the vessel has a bag as an a f t seal a n d there is an air connection between the bag and the air cushion, f u l l scale measurements show t h a t the acoustic resonance frequency is lower relative to a vessel w i t h a r i g i d panel as an a f t seal. T h i s has been theoretically studied by Steen (1993). B o t h the u n i f o r m pressure resonance a n d the acoustic resonance cannot be investigated i n model scale. The reason is t h a t the n a t u r a l periods scale h k e L ^ / L where L ^ ^ s model l e n g t h and L is f u l l scale l e n g t h , and t h a t wave periods scale Hke ( L j ^ / L ) i n model sale. W h e n f u l l scale measurements of cobblestone effects are performed, i t is necessary w i t h accurate measurements of the wave environment. I t is not

sufficient w i t h visual observations. The shape of the wave spectrum, the peak period, the significant wave height, the mean wave direction and the directional spreading of the waves w i l l influence the results. Since the wave periods of interest are quite low (typicafly wave peak periods between 1 a n d 2 s) conventional wave buoys cannot be used.

W h e n characterizing the seakeeping behaviour of a vessel, i t is of course not sufficient w i t h figures l i k e F i g . 1. D i f f e r e n t wave headings have to be studied. Other i m p o r t a n t quantities are vertical accelerations along the l e n g t h of the ship, rolling, relative vertical motions and velocities between the ship and the waves, and the influence of other wave directions. The c r i t e r i a for operational l i m i t s are also i m p o r t a n t .

Operational l i m i t s are set by

- safety, comfort and w o r k a b i l i t y criteria - s t r u c t u r a l loading and response

- machinery and propulsion loading and response

Seakeeping c r i t e r i a f o r ships at moderate speed have been discussed by the Seakeeping Committee of the I T T C , see f o r instance the report of the 1 8 t h and

19th I T T C . Those c r i t e r i a are n o r m a l l y related to s l a m m i n g , deck wetness, r o l l rms-values and rms-values for vertical accelerations. They can be used to determine v o l u n t a r y speed loss and operabiUty of vessels i n d i f f e r e n t sea areas. Faltinsen & Svensen (1990) have pointed out the relative large v a r i a t i o n i n published c r i t e r i a . T h i s may lead to quite diff"erent predictions of v o l u n t a r y speed reduction. For high-speed vessels other criteria are also needed. One example is operational l i m i t s due to the propulsion and engine system i n a seaway. Meek-Hansen (1990, 1991) presented service experience w i t h a 37 m long SES equipped w i t h diesel engines and water j e t propulsion. A n example w i t h s i g n i f i c a n t wave height around 2 m , head sea, 35 knots speed showed s i g n i f i c a n t engine load fluctuations a t i n t e r v a l s of 3 to 5 seconds. These fluctuations result i n increased t h e r m a l loads i n a c e r t a i n t i m e period, caused by a very h i g h f u e l / a i r r a t i o . These h i g h t h e r m a l loads combined w i t h high-rated engines a n d reduced engine condition between m a j o r overhauls may lead to engine breakdowns.

Possible reasons to the engine loads fluctuations are believed to be A. Exposure of the water j e t i n l e t to the free air.

B. Flow separation i n f r o n t of and inside the i n l e t .

C. V e n t i l a t i o n and penetration of a i r from the free surface or f r o m e n t r a i n e d a i r i n the boundary layer.

The phenomenon mentioned above are o f t e n coupled i n a complicated way. As an example separation m a y be one of the requirements for onset of v e n t i l a t i o n . C a v i t a t i o n occurs i n connection w i t h separation. U n d e r given conditions a cavity w i l l be penetrated and filled w i t h air. Separation a n d cavitation are first of a l l depending on the pressure d i s t r i b u t i o n i n and near the water j e t i n l e t . For a given shape t h i s d i s t r i b u t i o n depends m a i n l y on speed and t h r u s t (resistance) of the

ship.

I t e m A , i.e. exposure to free air, is a result of the relative v e r t i c a l motions of the c r a f t . A n operational l i m i t w i l l be related to the probabihty of the relative vertical motions amphtude between the vessel and the waves at the w a t e r j e t is beyond a certain l i m i t . Faltinsen et a l . (1991) used a rather strict c r i t e r i o n , i.e. t h a t the mean submergence d of the i n l e t relative to the local steady free surface should be at least 4 a^, where is the standard deviation of the relative v e r t i c a l motion at the w a t e r j e t inlet. For a catamaran this d i d not represent a m a j o r problem. However for a 40 m SES equipped w i t h flush i n l e t i t represented a problem for a l l sea states w i t h significant wave heights of 1 m and higher. The problem can be solved by using a scoop i n l e t . The consequence is increased power or drag. For instance i f the i m m e r s i o n of the i n l e t is increased by 1.25 m compared to a flush i n l e t , i t means the order of 10% increased power or drag. Other possibiUties are to drop the pressure i n the air cushion or to change the t n m . The penalty is t h e n also increased drag.

M i s h i m a (1992) presented experimental results of a i r d r a w i n g of waterjets i n waves. U n d e r w a t e r video camera was used to study the flow. M i s h i m a suggests t h a t the allowable ft-equency of a i r d r a w i n g should be less t h a n one m i n u t e i n f u l l scale. T h i s is a less strict c r i t e r i o n t h a n Faltinsen et al. (1991) used. M i s h i m a points out t h a t the allowable frequency for gas turbines should be chosen very low because gas turbines are very sensitive to overspeed due to a i r d r a w i n g . M o r e studies are needed to f o r m u l a t e a l i m i t i n g criterion due to w a t e r j e t a i r ingestion. This implies both better understanding of the physics and t h a t the performance of ships at sea should be monitored.

A n i m p o r t a n t l i m i t i n g c r i t e r i o n f o r v o l u n t a r y speed reduction f o r high-speed vessel is associated w i t h s l a m m i n g loads on the wet deck and the h u l l s . One cannot simply use the s l a m m i n g c r i t e r i o n for ship h u l l s operating at moderate speed. The seakeeping committee of the 19th I T T C is also questiomng t h i s criterion for conventional ships. This criterion does not d i s t i n g u i s h s u f f i a e n t l y between d i f f e r e n t h u h forms. M a n y high-speed vessels have very slender forebodies. A p p l y i n g the conventional c r i t e r i o n of s l a m m i n g i n terms of threshold velocity V^,. for slender h u l l s could mean t h a t s l a m m i n g was predicted to be a problem, w h i l e i t was not i n r e a l i t y . For wetdeck s l a m m i n g i t m a y be more appropriate to directly use the c r i t e r i o n associated w i t h s l a m m i n g loads on ships operating at moderate speed.

A special "deck wetness" problem t h a t occurs for h i g h speed vessels are "deck diving". T h i s can occur for a catamaran and a f o f l catamaran i n f o f l o w i n g sea. ( J u l l u m s t r 0 (1990)). A dangerous s i t u a t i o n i n regular waves is w h e n the ship speed is close to the wave speed. One of the reasons w h y "deck diving" can occur is t h a t high-speed vessel may have a slender forebody, i.e. not enough buoyancy i n the f o r e p a r t to avoid "deck diving".

The seasickness criteria according to ISO 2631/3 seems to be common to use for assessment of passenger comfort. I t gives l i m i t s of R M S values of the accelerations as a ftinction of frequency (see F i g . 2). F i g . 2 needs some

explanations. I t is referred to the a^-component of the acceleration. T h i s refers to a coordinate-system h a v i n g its origin i n the heart of a man. The a^-component is along a direction i n the foot-(or buttocks) to-head axis. For a broad band spectrum the frequency i n F i g . 2 means the average frequency of a 1/3 octave band. A 1/3 octave band is defined as follows. Consider f j and f2 to be the lower a n d upper frequency of the 1/3 octave band, then f2=2^%^. The centre frequency of the 1/3 octave band is (fif2)^^. T h i s means {^=^2^^ and {^=^^2^^. For a broad band spectrum the spectrum should be divided i n t o 1/3 octave bands. The RMS-value should be evaluated separately for each 1/3 octave band. The RMS-value should be compared w i t h the l i m i t s given i n F i g . 2 for d i f f e r e n t exposure t i m e . Since the motion sickness region i n F i g . 2 is f r o m 0.1 to 0.63 Hz, i t implies t h a t the cobblestone effect of a SES does not cause m o t i o n sickness. I n the frequency range 1 to 80 H z there are other criteria according to ISO 2631/1. These are related to w o r k a b i l i t y (fatigue). A n example is shown i n F i g . 3. The f i g u r e expresses the l i m i t s of the R M S value of the a^-component of the acceleration as a f u n c t i o n of frequency. F i g . 3 should be interpreted i n the same way as F i g . 2. B y m u l t i p l y i n g the acceleration values i n F i g . 3 by 2, one get boundaries related to h e a l t h and safety and by d i v i d i n g the acceleration values i n F i g . 3 by 3.15 one get boundaries for reduced comfort.

I N V O L U N T A R Y S P E E D L O S S I N W A V E S

F a l t i n s e n et a l . (1991) have presented a theoretical method to predict added resistance i n waves of high-speed mono- and m u l t i h u l l s . I t is p a r t l y based on a direct pressure i n t e g r a t i o n method using expressions f r o m a l i n e a r unsteady f l o w analysis i n regular waves. The problem is solved to second order i n wave amplitude. The regular wave expressions can be combined w i t h a sea spectrum i n the n o r m a l way to obtain mean wave forces or added resistance i n a sea state (see for instance F a l t i n s e n (1990)). Transom stern effects are i n c l u d e d i n the ex-pressions a n d are of importance. The i n t e r a c t i o n w i t h the local steady flow is accounted f o r i n an approximate way. I t was demonstrated by F a l t i n s e n et a l . (1991) t h a t the l a t t e r effect is i m p o r t a n t for h u l l s w i t h non-vertical sides at the w a t e r l i n e i n the bow region. Comparisons w i t h model tests show i n general satisfactory results. The i n t e r a c t i o n w i t h the local steady flow was evaluated by a quasi-steady approach where the steady l o n g i t u d i n a l force on the vessel was calculated i n d i f f e r e n t oscillatory positions of the ship. The expressions were t h e n time-averaged. The d i f f i c u l t i e s i n consistently h a n d l i n g the i n t e r a c t i o n between the local steady flow and the unsteady flow, i m p l y t h a t one should investigate the possibility o f u s i n g a time-domain solution. A n obvious drawback w i l l be the required C P U - t i m e relative to a frequency domain solution.

The air leakage f r o m the cushion i n waves has an i m p o r t a n t effect on the added resistance of a SES i n waves. The a i r leakage causes the SES to sink a n d the s t i l l w a t e r resistance components to change. For instance the altered excess pressure i n the cushion changes the wave resistance due to the a i r cushion. F u r t h e r the increased wetted surface area of the h u l l s changes the f r i c t i o n a l a n d w a v e m a k i n g resistance due to the hulls. I n a d d i t i o n there is a c o n t r i b u t i o n to the added resistance i n a s i m i l a r way as described previously f o r mono- and m i i l t i h u l l s . T h i s is due to second order non-linear i n t e r a c t i o n between the dynamic

vessel oscillations and the incident waves. The air resistance on a SES due to w i n d and the vessel's own speed is also i m p o r t a n t . This is not so much the case for a catamaran. Reasons for t h i s are the presence of the s k i r t on a SES and a lower h u l l resistance on a SES relative t o a catamaran. A method to predict the added resistance i n waves of a SES is presented by Faltinsen et a l . (1991). T h i s is based on finding the mean air leakage i n waves. The expected value for the drop i n pressure i n the cushion is found by using the characteristics for the cushion fans i n combination w i t h an expression for the expected value of the dynamic change i n the leakage area. The f a n characteristic gives a relation between the excess pressure and the volume flux for constant R P M of the fans. W h e n the pressure drop i n the cushion has been found, an estimate of the sinkage is f o u n d by balancing the w e i g h t of the SES w i t h the vertical forces due to the excess pressure i n the cushion and the buoyancy forces on the h u l l s . Due to the increased sinkage of the SES, there occurs a change i n the s t i l l water resistance on the h u l l s . Due to the change i n the excess pressure i n the cushion there occurs also a change i n the s t i l l water wave resistance due to the cushion pressure. The results w i l l for instance depend on the condition of the skirts and how the R P M of the fans are regulated.

Fig. 4 i l l u s t r a t e s computed i n v o l u n t a r y speed loss of a 40 m SES and a 40 m catamaran as a f u n c t i o n of significant wave height i n head sea waves ( F a l t i n s e n et al. (1991)). The calculations were done for mean wave periods T^ between 3.3 s and 11.7 s. We note t h a t the speed is dependent on T^ for a given value of H^yg. For the catamaran t h i s is due to the added resistance i n waves acting on the h i i l l s . I t can be explained by the dominant peak i n the added resistance curve for regular waves. For the SES i t is also associated w i t h the increased air leakage f r o m the cushion, w h i c h depends strongly on the relative v e r t i c a l motions at the s k i r t . I t was assumed i n the calculations t h a t the s k i r t i n the fi-ont p a r t of the SES j u s t touched the water surface i n calm water and t h a t the R P M of the fans was constant for a l l sea states. The figure illustrates a very d i f f e r e n t behaviour i n the speed loss of a SES and a catamaran. The reason to the more r a p i d drop i n speed of a SES w i t h increasing significant wave height is due to the a i r leakage i n waves. The example i n F i g . 4 demonstrates t h a t one should not use a sea-state system where there is only one mean wave period associated w i t h one s i g n i f i c a n t wave height. I t should be realized t h a t the total shaft powers f o r the catamaran and the SES are respectively 8300 K W and 5500 K W . E v e n by a l l o w i n g f o r a 20¬ 25% increase i n power due to the fans of the SES i t is seen t h a t the SES uses less power and keeps a higher speed t h a n the catamaran for nearly a l l sea states of practical interest.

S L A M M I N G

S l a m m i n g loads are i m p o r t a n t i n the s t r u c t u r a l design of h i g h speed vessels. S l a m m i n g causes also the ship master to reduce the ship speed. The n o r m a l way to predict the v o l u n t a r y speed loss due to s l a m m i n g is to first calculate the standard deviations of relative v e r t i c a l velocity and motion i n a vessel-fixed coordinate system at places where s l a m m i n g is h k e l y to occur. The s l a m m i n g p r o b a b i l i t y is f o u n d by d e f i n i n g a threshold velocity f o r s l a m m i n g to occur. A n often used criterion is t h a t a typical ship master reduces the speed i f slams occur

more t h a n 3 of 100 times t h a t waves pass the ship. The conventional way of d e f i n i n g a threshold velocity does not reflect the effect of the s t m c t u r a l f o r m . I n order to come up w i t h better criteria i t is necessary to study theoretical models or p e r f o r m i n g experiments for water impact against wet decks and h u l l shapes typical f o r h i g h speed vessel. This is also necessary i n order to develop r a t i o n a l c r i t e r i a for operational l i m i t s due to slanmiing. The criteria should be related to s l a m m i n g loads used i n the s t r u c t u r a l design.

I m p o r t a n t parameters characterizing s l a m m i n g are the position and value of the m a x i m u m pressure, the time d u r a t i o n and the spacial extent of the s l a n m i i n g pressure. The pressure is heavily dependent on the local geometry relative to the water surface. W h e n the deadrise angle a is small, one should not p u t too m u c h emphasize on the peak pressures. I t is the pressure integrated over a given area t h a t is of interest i n s t r u c t u r a l design. W h e n a is s m a l l , the mean pressure over a plate area w i l l obviously be smaller t h a n the peak pressure. Experiments on s l a m m i n g loads should more oft,en realize w h a t the results should be used for. T h i s means one may avoid using pressure gauges to t r y to find s l a m m i n g loads. The use of panels mounted on force transducers w i l l give a more appropriate i n p u t for design load calculations. H i g h sampling frequency i n order to determine the correct rise t i m e d u r a t i o n and m a x i m u m value of the impact load is i m p o r t a n t . There is need f o r systematic studies t h a t show how the s l a m m i n g pressure effects the global accelerations of the vessel. D e t norske V e r i t a s ' ( D n V ) rules for s l a m m i n g pressure on high-speed vessel relates the pressure to the acceleration of the vessel. I m p l i c i t l y one assumes t h a t the acceleration is a f u n c t i o n of the water impact. The occurrence and the magnitude of the s l a m m i n g pressure are strongly dependent on the relative v e r t i c a l motions and velocities between the vessel and the waves. F i g . 5 gives an example on how sensitive the relative vertical motions and velocities are to the mean wave period T2 and the s i g n i f i c a n t wave height H^^yg. A two-parameter J O N S W A P spectrum recommended by I T T C was used i n the calculations.

G L O B A L W A V E L O A D S

I n the discussion of global loads we w i l l concentrate on catamarans. Global wave loads are expected to be significant for catamarans of lengths larger t h a n approximately 50 m . I m p o r t a n t global loads are v e r t i c a l bending moments, v e r t i c a l shear forces and p i t c h connecting moments on the h a l f p a r t of the catamaran obtained by intersecting along the centre plane. The catamaran can n o r m a l l y be considered rigid i n the determination of the global loads. However, for "steady-state" response i t should be ensured t h a t the n a t u r a l frequencies of global elastic modes are sufficiently smaller t h a n encounter fi-equencies of practical interest. M o r r i s (1991) reported n a t u r a l frequencies f o r a 9 1 m long wave piercing catamaran, t h a t has 1.6 H z n a t u r a l frequency i n torsion and 1.5 H z n a t u r a l frequency i n transverse arching. S u f f i c i e n t i n f o r m a t i o n on mass d i s t r i b u t i o n is sometimes l a c k i n g when model test results are presented. I t is recommended t h a t the f o l l o w i n g data are given when global loads i n the centre plane of a m u l t i h u l l is examined.

Centre of g r a v i t y position

Distance f r o m centerline to centre of g r a v i t y of one h a l f part*

Pitch, r o l l and yaw radius of g y r a t i o n w i t h respect to axis t h r o u g h centre of g r a v i t y

Coupled i n e r t i a moments i n roll-pitch, roll-yaw and pitch-yaw of one h a l f part*

*) H a l f p a r t obtained by intersecting along the centre plane of the m u l t i h u l l F a l t i n s e n et al. (1992) presented n i m i e r i c a l and experimental results of global wave loads on a catamaran at Froude number 0.49. The n u m e r i c a l method is a f u r t h e r development of the high-speed theory presented by F a l t i n s e n & Zhao (1991 a&b). "Steady-state" response is assimied. The agreement between theory and experiments is generally satisfactory except for vertical shear forces. The experiments were done w i t h a free r u n n i n g model i n a basin of l e n g t h 80 m and breadth 50 m . Regular incident waves of d i f f e r e n t wave headings were used. Examples of experimental error sources are: a) Non-constant wave a m p l i t u d e along the t r a c k of the model; b) D i f f i c u l t i e s i n accurate heading control; c) I n s u f f i c i e n t number of response oscillations and t r a n s i e n t effects i n beam, q u a r t e r i n g and following seas; d) N o n l i n e a r effects. S m a l l deviations i n heading may have a noticeable influence on the global loads. The effect of the autopilot system and the rudder-propulsion system on the global loads were not investigated systematically. There is need for good numerical modelHng of these effects to scale the results properly to fullscale conditions w i t h o u t autopilot systems. The numerical model for h i g h speed shows t h a t vertical shear forces and vertical bending moments are generafly largest i n beam sea, while the largest values f o r pitch connecting moments occur at wave heading 60° for most wave periods. V e r t i c a l shear force and pitch connecting moment are zero i n head and f o l l o w i n g

sea according to the numerical model.

Fig. 6 gives an example of how sensitive the global loads are to wave heading. Roll m o t i o n is i m p o r t a n t for vertical shear force and p i t c h connecting moment, while heave and p i t c h acceleration influence the vertical bending moment. I t is sometimes advocated t h a t results for beam sea can be based on zero-speed results. This is not adviceable due to the f o r w a r d speed effects on the h y d r o d y n a m i c pressure d i s t r i b u t i o n .

F a l t i n s e n et al (1992) presented l o n g t e r m predictions of global wave loads on a catamaran. The effect of i n v o l u n t a r y speed reduction was neglected. The vessel had a Froude number 0.7. I f the catamaran d i d not satisfy the s l a m m i n g c r i t e r i u m often reducing the ship speed to Froude number 0.45, i t was decided to exclude the sea state f r o m the long t e r m prediction of the response. T h i s means t h a t operational l i m i t s are imposed. I n practice operational Hmits have to be decided i n a d i f f e r e n t way. This wiU influence the final results. The long t e r m predictions were based on a standard procedure (Faltinsen (1990). T h i s means t h a t for each sea state the proper Rayleigh d i s t r i b u t i o n was multipHed w i t h the p r o b a b i h t y of occurrence of the sea state. These products were t h e n added together. I t was decided to select design values corresponding to a p r o b a b i l i t y of 10" . Results were presented f o r d i f f e r e n t ship lengths between 50 m and 120 m . The predicted

design values for global loads were clearly lower t h a n recommended values by D n V . However, the design values w i l l depend on the philosophy behind the rules. I t w i l l results i n lower values i f operational l i m i t s are imposed. The design philosophy is therefore i m p o r t a n t when considering weight optimization of h i g h speed crafts.

C O N C L U S I O N S

The seakeeping characteristics and the d i f f e r e n t behaviour of a SES, catamaran and a foil-catamaran i n waves are discussed. I t is pointed out t h a t cobblestone effects on a SES are also due to acoustic resonance i n the a i r cushion and t h a t cobblestone effects are troublesome for a SES i n s m a l l sea states. A SES has a good seakeeping behaviour i n moderate sea conditions. A ride control system w i l l have a significant positive influence on the seakeeping behaviour of a foilcatamaran.

The necessity for establishing r a t i o n a l procedures for o b t a i n i n g operational l i m i t s f o r high-speed vessels are discussed. A n example is operational l i m i t s due to the propulsion and engine system i n a seaway. For instance exposure of the w a t e r j e t i n l e t of a SES to free a i r can represent a problem. A special "deck wetness"problem t h a t can occur f o r high-speed catamarans i n f o l l o w i n g and q u a r t e r i n g waves are "deck-diving".

Speed loss of catamarans and SES i n a seaway are discussed. E v e n is a SES looses easily the speed i n a seaway and the catamaran does not, i t is possible f o r the SES to use less power and to keep a higher speed t h a n a s i m i l a r sized catamaran i n nearly a l l sea states of practical interest.

Design rules for s l a m m i n g and global wave loads on h i g h speed vessels are discussed. The design philosophy is i m p o r t a n t w h e n considering w e i g h t optimization of h i g h speed crafts.

R E F E R E N C E S

Faltinsen, O., 1990, Sea loads on ships and offshore structures, Cambridge U n i v e r s i t y Press.

Faltinsen., Svensen, T., 1991, Incorporation of seakeeping theories i n C A D , Proceedings I n t . Symp. on CDF and CAD i n Ship Design, Wageningen, Netherlands, E d i t o r G. van Oortmerssen, Elsevier Science PubUshers B.V., pp.

147-164.

Faltinsen, O., Zhao, R., 1991a, Numerical predictions of ship motions at h i g h f o r w a r d speed. P h i l . Trans. Royal Society, Series A . , V o l . 334, pp. 241-252. Faltinsen, O., Zhao, R., 1991b, Flow prediction around high-speed ships i n waves, "Mathematical approaches i n hydrodynamics", E d i t o r T. M i l o h , S I A M , pp. 265-288. Faltinsen, C M . , Helmers, J.B., Minsaas, K . J . , Zhao, R., 1991, Speed loss and operabihty of catamarans and SES i n a seaway, Proceedings F A S T ' 9 1 , T r o n d h e i m , Norway, T a p i r publishers, Vol. 2, pp. 709-725.

F a l t i n s e n , C M . , Holden, K . C , Minsaas, K . J . , 1991, Speed loss and operational h m i t s of high-speed marine vehicles, Proceedings I M A S ' 9 1 - H i g h Speed M a r i n e Transportation, Sydney, A u s t r a l i a , pp. 2-1 to 2-9.

Faltinsen, C M . , Hoff, J.R., Kvalsvold, J., Zhao, R., 1992, Global wave loads on high-speed catamarans. Proceedings PRADS'92, Newcastle, E n g l a n d , V o l . 1, pp. 1.360-1.375.

H o f f , J.R., 1990, Three-dimensional Green f i m c t i o n of a vessel w i t h f o r w a r d speed i n waves, D r . i n g . Thesis 1990-25, Division of M a r i n e Hydrodynamics, N o r w e g i a n I n s t i t u t e of Technology, Trondheim, M T A report 1990:71.

J u l l u m s t r 0 , E., 1990, Stabihty of high-speed vessels", Proceedings STAB'90, N a p o l i , I t a l y .

K a p l a n , R., Bentson, J., Davies, S., 1981, Dynamics and hydrodynamics of surface effect ships, S N A M E , V o l . 89, pp. 211-248.

Meek-Hansen, B . , 1990, Damage investigation on diesel engines i n h i g h speed vehicles. Proceedings F i f t h I n t . Congress on M a r i n e Technology Athens'90, Hellenic I n s t i t u t e of M a r i n e Technology, A t h e n , Greece.

Meek-Hansen, B., 1991, Engine r u n n i n g conditions d u r i n g h i g h speed marine c r a f t operation, Pore. FAST'91, T r o n d h e i m , T a p i r Pubhshers, N o r w a y , V o l . 2, pp. 861¬ 876.

M i s h i m a , S. 1992, A n experimental study on air d r a w i n g of w a t e r j e t i n l e t for suface effect ship. Proceedings H P M V ' 9 2 , ArUngton, V A , U S A , pp. SES95-SES105.

O h k u s u , M . , Faltinsen, O., 1990, Prediction of radiation forces on a catamaran at high Froude number, Proceedings 18th Symposium on N a v a l Hydrodynamics, U n i v . of M i c h . , A n n Arbor, N a t i o n a l Academy Press, Washington D.C. pp. 5-19. S0rensen, A., Steen, S., Faltinsen, O., 1992, Cobblestone effect on SES, Proceedings H P M V 9 2 , A r l i n g t o n , V A , USA, pp. SEsl7-SES30.

Steen, S., 1993, Vertical plane dynamics of SES w i t h flexible bag, Dr.ing.Thesis, D e p a r t m e n t of M a r i n e Hydrodynamics, Norwegian I n s t i t u t e of Technology.

3 . 0 5 . 0 1.0 2 . 0 H 3 . 0 4 . 0 ^ 5 . 0 4 0 m l o n g c a t a m a r a n ( 4 0 k n o t s ) \ 3 6 m l o n g f o i l c a t a m a r a n ( 5 0 k n o t s ) \ 4 0 m l o n g S E S ( 5 0 k n o t s ) O P E R A T I O N A L L I M I T 0 . 2 g R M S V E R T . A C C . C G . H, / ^ ( m )

F i g 1 Operational l i m i t s for a 40 m long catamaran, 36 m l o n g foilcatamaran, 40 m long SES i n head sea longcrested waves. Uy^ = significant wave height, T i = mean wave period. Speed i n calm w a t e r is shown on the figure. I n v o l u n t a r y speed loss used for the SES and the catamaran. No ride controls are accounted for.

(m/s' 10 8.0 6.3 5.0 4.0 3.15 2.5 2.0 1.6 1.25 1.0 0.8 0.63 0.5 0.4 0.315 0.25 0.2 0.16 0.125 0.1 1 j 1 i ^ M o t i o n sickness r e g i o n ^ 30 min.

/

F i g . 2 Severe discomfort boundaries according to ISO 2631/3 f o r the a -component of the acceleration, as a f u n c t i o n of frequency and exposure time, a^ = RMS-value of one-third octave band, f = centre frequency of one-third octave band.

a 2 ( m/ s 2) 1.0 2.0 4.0 8,0 j j <' /A i j / / * 1 •

—

——

—

—

Fatigue-decreased profiency boundaries for the a^-component of the acceleration as a f u n c t i o n of frequency and exposure time (ISO 2631/1). a^ = RMS-value of third octave band, f^, = centre frequency of one-t h i r d ocone-tave band.

V e s s e l s p e e d ( k n o t s )

t H e a d s e a

N u m e r i c a l calculations of vessel speed range of a 40 m SES and a 40 m c a t a m a r a n as f u n c t i o n of significant wave height i n head sea. Only i n v o l u n t a r y speed loss effects (Faltinsen et a l . (1991)).

R M S - R E L A T I V E V E L O C I T Y 5 H

l.S 2.0 25 3.0 3.5 4.0

4gTL

R M S - R E L A T I V E M O T I O N

Fig. 5 Examples on R M S values of relative vertical motions (GJ^) and velocities (Gy^f^) at FP for a catamaran i n head sea longcrested waves. L = ship length, g = acceleration of gravity. F n = Froude number.

0.0010 0.0008 0.0006 0.0004 0.0002 0.0000 Q \ v • <'' y' ' ""^ •X. J - ^ ^ ^ i ^ ^ " ^ w' ' • TJ.-.---.. _^ _ "-9-.. . . ^ „ ^ ^ ^ • ' . • - . « . . ^ o -O-Heading Heading Heading Heading Heading Heading Heading Heading Heading Heading Heading Heading Heading 0.0 deg 15.0 deg 30.0 deg 45.0 deg 60.0 deg 75.0 deg 90.0 deg 105.0 deg 120.0 deg 135.0 deg 150.0 deg 165.0 deg 180.0 deg

Fig. 6 Examples on R M S values of pitch connecting moments (G^) i n the centre plane of a catamaran i n longcrested i r r e g u l a r sea as a f u n c t i o n of wave heading and mean wave period T , . Fn=0.7. ( F a l t i n s e n et al (1992)).