Design tool for high speed slender catamarans

HIGH SPEED MARINE CRAFT 1990 KRISTIANSAND, NORWAY.

DESIGN TOOL FOR HIGH SPEED SLENDER CATAMARANS

BY

PER WERENSKIOLD

MARINTEK A / S , OCEAN LABORATORIES P.O.BOX 4125 YALENTINLYST

7002 TRONDHEIM NORWAY

Per Werenskiold, P r i n c i p a l Research E n g i n e e r , MARINTEK. (Norwegian Marine Technology I n s t i t u t e )

INTRODUCTION.

Performance p r e d i c t i o n tools f o r use in p r e l i m i n a r y design e x i s t f o r

planing and round b i l g e monohulls, s u r f a c e e f f e c t ships and h y d r o f o i l s , but no published p r e d i c t i o n tool e x i s t s f o r catamarans. This i s remarkable in that catamarans have become by f a r the leading type of commercial high speed c r a f t . As of mid 1989 there were 263 catamarans compared to 215 h y d r o f o i l s (the previous leading type of high speed c r a f t ) . Approximately 25 companies in 12 c o u n t r i e s are now involved in catamaran c o n s t r u c t i o n , with Norway being the leading producer.

MARINTEK, Ocean L a b o r a t o r i e s in Trondheim, Norway, has s i n c e 1987 t e s t e d a l a r g e number of catamaran designs both in calm water and i n head/following s e a s . Model to f u l l s c a l e c o r r e l a t i o n f o r high speed catamarans has been developed based on extensive f u l l s c a l e experiments. T h i s unique amount of emphirical data makes i t p o s s i b l e to present a simple tool f o r p r e l i m i n a r y d e s i g n , speed-powering p r e d i c t i o n s as well as seakeeping assessment of high speed slender catamarans.

SLENDER CATAMARAN CHARACTERISTICS.

The s l e n d e r catamaran i s c h a r a c t e r i z e d by having extremely s l e n d e r , sym-m e t r i c h u l l s without u t i l i z i n g sym-much planing e f f e c t s . The c r a f t thus opera-tes e s e n t i a l l y as a displacement v e s s e l and i s the most e f f e c t i v e concept f o r passenger t r a n s p o r t a t speeds up to Froude Number of about

F n = l . l , ( F n = V / / g - L , V ( m / s ) ) .

T h i s concept has been well received by commercial operators as market share of the t o t a l number of high speed f e r r i e s has grown from 13% in 1 9 7 1 - 7 5 to an expected 4 0 % in 1 9 9 1 - 9 5 ( F i g . 1 of r e f . 1 ) .

A l a r g e number of s l e n d e r catamarans has been tested at MARINTEK, Ocean L a b o r a t o r i e s . A l l models in s c a l e 1 : 1 0 or 1 : 1 2 . 5 . The models cover the length displacement r a t i o L / A I / 3 = 5 . 7 5 to 7 . 5 . Typical main c h a r a c -t e r i s -t i c s f o r good designs a r e :

(a) S t r a i g h t V-formed t r a n s v e r s e sections in forebody with t o t a l angle of entrance 1 2 to 1 6 degrees.

(b) Minimum h u l l beam c l o s e l y r e l a t e d to machinery i n s t a l l a t i o n . (c) Round b i l g e s along the e n t i r e h u l l .

(d) Transom width equal to the midship and transom depth reduced compared to the midship s e c t i o n .

(e) Longitudinal center of g r a v i t y ( e g . ) approx. 5% of Lpp a f t of m i d s h i p .

( f ) Wet-tunnel width minimum 1/3 of the c r a f t beam.

The p o s i t i o n of the center of g r a v i t y i s the primary design parameter, together with the length/displacement r a t i o and wet-tunnel h e i g h t .

- The eg. should not be placed too f a r a f t . Large a f t body volume and deep s t e r n p l a t e g i v e s r e l a t i v e l y large i n c r e a s e in wave r e s i s t a n c e . T h i s e f f e c t i s considerable f o r eg. p o s i t i o n s more than 7 . 5 % of Lpp a f t of midship.

- The eg. should not be placed forward of 2 . 5 % a f t of midship in order to ensure that too large negative t r i m angles are avoided in f o l l o w i n g s e a .

The combination of s l e n d e r forebody. a forward p o s i t i o n of eg. and opera-t i o n in even moderaopera-te following seas wiopera-th speed of wave propagaopera-tion c l o s e to ship speed has r e s u l t e d in hazardous e f f e c t s such as green water and bow d i v i n g . These e f f e c t s are e f f e c t i v e l y studied in model tank t e s t s and

MARINTEK h i g h l y recommends that a l l high-speed vessel concepts are tested to a s s e s s the r i s k of bow down d i v i n g tendencies in following s e a s .

The optimal p o s i t i o n of eg. i s a f u n c t i o n of a f t body design, type of propulsion system, use of trim f l a p s , s e r v i c e speed and above water bow d e s i g n . The above water bow design i n f l u e n c e s both the seakeeping perform-ance in head seas and the s a f e t y q u a l i t i e s in following s e a s .

In general a running trim of 0.5 to 1.0 degree w i l l be optimal at design speed and the s l e n d e r catamaran should be designed to run at t h i s trim without the use of trim f l a p s .

Ride q u a l i t y in waves i s mainly determined by the magnitude and frequency of the v e r t i c a l a c c e l e r a t i o n s . The v e r t i c a l a c c e l e r a t i o n of catamarans i s c l o s e l y r e l a t e d to ship speed, length-displacement r a t i o and height of w e t - t u n n e l . Rules f o r Light C r a f t allows a 1 "g" maximum eg. a c c e l e r a t i o n

l i m i t f o r s t r u c t u r a l design purposes. S t a t i s t i c a l l y t h i s corresponds to a 0.33 "g" RMS-value. As a "rule of thumb" the slender catamaran wet-tunnel height measured 10% of Lpp a f t of the forward perpendicular should be at l e a s t 0.85 * Hs (Hs = design s i g n i f i c a n t waveheight) to meet the DnV requirement f o r a speed corresponding to a Froude Number = approx. 0 . 6 0 .

4

-SLENDER CATAMARAN DESIGN AND SPEED CALCULATION

The above mentioned f a c t o r s must be taken into account vhen designing s l e n d e r catamarans. A d e t a i l e d design process w i l l give b a s i c ship parame-t e r s however, r e l e v a n parame-t b a s i c dimensions can be deparame-termined by r e g r e s s i o n a n a l y s i s of data from e x i s t i n g c r a f t . MARINTEK High-Speed Data-Base gives these b a s i c dimensions normalized to c r a f t length between p e n d i c u l a r s ( L p p ) . The r a t i o L Q A / L P P i s t y p i c a l l y 1.1.

FIGURE 2 g i v e s the r a t i o between Lpp and BQA. AS can be seen the r a t i o i n c r e a s e s by i n c r e a s i n g l e n g t h .

FIGURE 3 g i v e s the r a t i o between Lpp and design displacement. Lpp/A^/^ i s the most s e n s i t i v e f a c t o r r e l a t e d to r e s i s t a n c e and speed.

R e s i s t a n c e curves are thus given f o r r a t i o s in the range 5.75 to 7 . 5 .

FIGURE 4 g i v e s the r a t i o between Lpp and lightweight displacement. L i g h t -weight excludes f u e l , o i l , water, crew e t c .

FIGURE 5 g i v e s t y p i c a l s l e n d e r catamaran wetted s u r f a c e , excluding stern p l a t e a r e a . The t o t a l ship r e s i s t a n c e i s proportional to the wetted s u r f a c e and a "mean l i n e " i s given as r e p r e s e n t a t i v e f o r modern s l e n d e r catamaran d e s i g n s . This r a t i o i s proposed to be used in the presented speed c a l c u l a t i o n method when no d e t a i l e d design i s a v a i l a b l e . •

FIGURE 6 g i v e s Data-Base information on the r a t i o between passenger capa-c i t y and t o t a l main decapa-ck a r e a .

The design process i s an i t e r a c t i v e one, composed of two key a c t i v i t i e s :

* S y n t h e s i s - the development of f e a s i b l e design a l t e r n a t i v e s based upon t r a d i t i o n a l parametric s t u d i e s .

* A n a l y s i s - the assessment and comparison of the performance and t r a n s p o r t economy of these f e a s i b l e design

The method by wich the s y n t h e s i s and a n a l y s i s a c t i v i t i e s take place i s decided by the d e s i g n e r . The following quick c a l c u l a t i o n method r e q u i r e s a s e t of b a s i c parameters, which can e i t h e r be e s t a b l i s h e d by the above given f i g u r e s or by a d e t a i l e d design p r o c e s s .

The e f f e c t i v e horsepower ( P ^ ) f o r the ship i s c a l c u l a t e d from:

( 1 ) PE = 0 . 0 0 6 8 6 V R T

where:

Rj = t o t a l r e s i s t a n c e f o r ship in kp.

V = ship speed in knots.

. ' ( 2 ) RT = 1 3 . 8 4 • CTV2S+RAA

where:

C j = t o t a l r e s i s t a n c e c o e f f i c i e n t f o r the s h i p .

S = wetted s u r f a c e area in m^ ( R e f . f i g . 5 or design d a t a ) . RAA = a i r r e s i s t a n c e in kp.

( 3 ) C j = Cp + ACp + CR

where:

Cp = f r i c t i o n a l r e s i s t a n c e c o e f f i c i e n t

ACp = roughness allowance equal to 0 . 0 0 0 5 , corresponding to a h u l l roughness of approx. 1 5 0 my in the maximum speed range. ITTC 1 9 5 9 ship-model c o r r e l a t i o n l i n e g i v e s :

( 4 ) Cp = 0 . 0 7 5

(log R n - 2 ) 2

where:

Rn = Reynolds Number = 0 . 4 3 3 ' V « L W L * 1 0 ^ *

FIGURE 7 CR i s e s t a b l i s h e d by comprehensive s t u d i e s of model t e s t data and , ship-model c o r r e l a t i o n . The r e s u l t s from these i n v e s t i g a t i o n s are

made a v a i l a b l e i n one f i g u r e permitting easy r e a d o f f .

6

-Some major assumptions should be recognized:

* Ship-model c o r r e l a t i o n as a function of length displacement r a t i o i s i n c l u d e d .

* Ship-model c o r r e l a t i o n r e l a t e d to i n t e r a c t i o n between propulsion system and h u l l i n t e r a c t i o n i s included in the given t o t a l propulsi c o e f f i c i e n t s .

* Conventional a f t body, without p r o p e l l e r tunnel i s assumed. * Optimal running trim r e l a t e d to r e s i s t a n c e i s assumed. * A i r r e s i s t a n c e c o r r e l a t i o n i s included.

A i r r e s i s t a n c e i s c a l c u l a t e d by the fomulae:

( 6 ) R^A = 0 . 0 1 2 V 2 A V where:

Ay = p r o j e c t e d f r o n t a l area of s u p e r s t r u c t u r e .

An a i r drag c o e f f i c i e n t of 0.70 i s assumed r e p r e s e n t a t i v e based on wind tunnel t e s t s .

The SHAFT HORSEPOWER ( P j ) i s f i n a l l y c a l c u l a t e d by:

(7) Ps = PE/n tot

The ship-model c o r r e l a t i o n s t u d i e s a t s e r v i c e speed included both p r o p e l l e r and w a t e r j e t propulsion systems. Applying the data the following

pro-p u l s i v e c o e f f i c i e n t s are to be used. Losses along the s h a f t i n g i s i n c l u d e d .

* Waterjet propulsion * P r o p e l l e r with i n c l i n e d s h a f t * P r o p e l l e r w i t h a f t body tunnel * Z - D r i v e ntot = 0.62 - 0.54 ntot = 0.64 - 0.65 ntot = 0.70 - 0.74 ntot = 0.68 - 0.70

SLENDER CATAMARAN SEAKEEPING PERFORMANCE.

A given high-speed c r a f t must withstand two f o r c i n g functions in order to accomplish t h e i r m i s s i o n , the maninduced demands on the c r a f t and the p r e -v a i l i n g en-vironmental f a c t o r s . Experience shows that c e r t a i n a c t i o n s by the operator of high-speed c r a f t can lead to major or even hazardous e f f e c t s . T h i s implies that more seakeeping data i s needed on these c r a f t so opera-t i o n a l l i m i opera-t s can be e s opera-t a b l i s h e d f o r comforopera-t and s a f e opera-t y reasons.

I t i s the o b j e c t i v e of the designer to minimize the adverse impact and degradation of c r a f t performance caused by sea environment and to ensure comfortable r i d e in normal operation and c r a f t s u r v i v a l under extreme sea and operational c o n d i t i o n s . Highspeed c r a f t seakeeping perfonnance a s s e s s ment must include s p e c i f i c model or f u l l s c a l e t e s t i n g , however, in p r e

-l i m i n a r y design p r i o r to such t e s t i n g , numerica-l and emphirica-l methods f o r p r e l i m i n a r y e v a l u a t i o n of motions and a c c e l e r a t i o n s have been developed at MARINTEK.

A numerical method based on t h e o r e t i c a l c a l c u l a t i o n for p r e d i c t i n g steady hydrodynamic f o r c e s and wave induced motions f o r high-speed catamarans i s presented in r e f .2 . The main d i f f e r e n c e between t h i s method and the conven-t i o n a l s conven-t r i p conven-theory approach i s conven-thaconven-t 1t incorporates in a r a t i o n a l way the important wave systems generated at high speed by the c r a f t I t s e l f .

By using t h i s improved method MARINTEK i s able to p r e d i c t RMS-values and extreme values of motions, a c c e l e r a t i o n s , slamming loads, global dynamic loads and added r e s i s t a n c e due to waves f o r slender catamarans in any sea s t a t e .

In the present paper a simple emphirical method based on extensive model t e s t r e s u l t s i s presented. Slender catamaran seakeeping performance i s mainly dependant on s i z e of c r a f t , length displacement r a t i o and speed. Relevant Data-Base information on p i t c h and center of g r a v i t y a c c e l e r a t i o n s

(RMS-values) are presented f o r speed range up to Froude Number 1.0. Pierson-MoskowUz s p e c t r a waves are assumed.

8

-FIGURE 7 g i v e s the r a t i o between L p p / S i g n i f i c a n t Wave Height and the p i t c h motion (RMS-values) at maximum Froude Number 1.0 - 0 . 8 . Data i s given f o r two length displacement r a t i o s and i t i s seen that p i t c h i s s i g n i f i c a n t l y i n c r e a s e d by i n c r e a s i n g the length displacement r a t i o .

FIGURE 8 g i v e s the v e r t i c a l center of g r a v i t y a c c e l e r a t i o n s (RMS-values) f o r the same speed and displacement ranges. I t i s seen that unlike p i t c h ( f i g . 7 ) a c c e l e r a t i o n s are decreased by i n c r e a s i n g the length to displacement r a t i o .

CONCLUSION.

An e a s i l y used tool f o r p r e l i m i n a r y slender catamaran hull design; s e l e c -t i o n of b a s i c h u l l parame-ters speed c a l c u l a -t i o n and seakeeping assessmen-t i s presented. The method can be used throughout the design process. The Data-Base F i g u r e s can be used to e s t a b l i s h a s t a r t i n g c o n f i g u r a t i o n as well as a s s e s s i n g the s p e c i f i c ship design as i t e v o l v e s .

The design process can e a s i l y be transformed to a computer program or be used in a standard PC-Data-Sheet system.

REFERENCES:

lo NTNF High Speed C r a f t P r o j e c t :

2. NTNF High Speed C r a f t P r o j e c t :

Report MV-11.22690, May 1989 "Summary of High-Speed C r a f t S t a t i s t i c s . "

Report MV-11.24898, March 1990

"Seakeeping of High-Speed Catamarans".

NO. AND TYPE OF VESSELS

1970 1975 1980 1985 1990 1995

•* > 50 PASSENGERS & > 25 KNOTS SPEED

(PARAMILITARY CRAFT EXCLUDED)

4 " 3.8 3.6 SA 3.2 2.8 2.6 ZA 2.2

FIGURE 2

LENGTH - BEAM RATIO

Lpp / Boa

Lpp [ m ]

7.4 Y 6.6 6.2 5.8 5.4 .5 4.6

FIGURE 3

LENGTH - DISPLACEMENT RATIO

Lpp/Displ**0.333

Lpp [m]

FIGURE 4

LENGTH - LIGHTWEIGHT RATIO

Lpp/Lightweight**0.333 t

1

1

1

1

Lpp [ m ]

WET AREA - LENGTH RATIO

=^ Sw / L p p - 2 ^ J ^ C f ^ J ) ^ / ^

- Lpp / Displ**0.333

r

FIGURE 6

PASSENGER CAPACITY

LOA*BOA [in**2]

PASSENGER NUMBER

I

FIGURE 7

RESIDUARY COEFFICIENT

0.85

'

' ' ' ^ '

1

0.8 0.9

1

1.1 1.2 1.3 1.4: 1.5 1.6

Froude number, Fn

MiBINTSC DAXiBlSB

RMS-VALUES PICTH (Deg.)

LPP / SIGNIFICANT TTATfEHEIGHT

FIGURE 9

SEAKEEPING - VERT.ACC CG.

LPP / SIGNIFICANT VAWEHEIGHT