Iournal of
SHIP RESEARCH
Full-Scale Destroyer Motion Measurements
By J . Gerritsma' and W. E. Smith'
The results of full-scale destroyer motion tests in head seas are presented. A comparison is made between motion response obtained from full-scale tests, model experiments, and computer calculations. Agreement is satisfactory.
I n t r o d u c t i o n
A c a r e f u l c o r r e l a t i o n between f u l l - s c a l e s h i p m o t i o n re-sponses a n d those o b t a i n e d f r o m m o d e l e x p e r i m e n t s has l o n g been considered a n area of considerable i n t e r e s t b y seakeeping researchers. T h i s v i e w is also expressed i n t h e r e c o m m e n d a t i o n s of t h e I n t e r n a t i o n a l T o w i n g T a n k Conference, 1963: " A c -c u r a t e F u l l - S -c a l e D a t a u n d e r C o n d i t i o n s S u i t a b l e f o r A n a l y s i s t o be U s e d f o r C o r r e l a t i o n w i t h M o d e l T e s t s . " M o t i o n tests c o n d u c t e d w i t h g e o m e t r i c a l l y s i m i l a r models of d i f f e r e n t sizes i n regular l o n g - c r e s t e d h e a d waves h a v e n o t s h o w n a measurable scale e f f e c t [ 1 , 2 ] . ^ T h e range o f size considered i n [ 1 , 2 ] is, h o w e v e r , t o o re-s t r i c t e d t o p r o v i d e conclure-sive anre-swerre-s i n t h i re-s rere-spect. F u l l - s c a l e r e s u l t s w i t h t h e r e s u l t i n g scale r a t i o s o f 40 t o 1 or greater c o u l d r e v e a l a n y s i g n i f i c a n t scale effects i f present. S u c h a c o m p a r i s o n s h o u l d p r o v i d e s t r o n g sup-p o r t f o r t h e e x sup-p l a n a t i o n t h a t t h e m o t i o n - g e n e r a t e d sur-face waves a c c o u n t f o r t h e greatest p a r t of t h e energy dissipated, a n d t h a t o t h e r sources such as viscous d a m p -i n g a n d b o u n d a r y - l a y e r effects, w h -i c h c o u l d cause scale effects, are q u i t e s m a l l .
T h e a c c u r a c y of t h e f u l l s c a l e m e a s u r e m e n t is o b -v i o u s l y a m a j o r f a c t o r i n d e t e r m i n i n g t h e -v a l i d i t y of t h e c o r r e l a t i o n . T h i s i m m e d i a t e l y imposes m a j o r r e s t r i c -t i o n s o n -t h e -t e s -t c o n d i -t i o n s a n d m e a s u r e m e n -t s . T h e seaway e n c o u n t e r e d m u s t be one t h a t can be m e a s u r e d a n d analysed, i.e., v i r t u a l l y a u n i d i r e c t i o n a l seaway. T h i s c o n d i t i o n is also necessary f o r t h e a c c u r a t e d e t e r
-' Professor i n Naval Architecture, Shipbuilding Laboratory Delft, The Netherlands.
2 Physicist, David Taylor Model Basin, Washington, D . C , working at Shipbuilding Laboratory, Delft, The Netherlands.
' Numbers in braolcetB designate References at end of paper. Afanuscript received at S N A M E Headquarters, October 14, 1966.
m i n a t i o n o f m o t i o n responses w h i c h are themselves a f u n c t i o n of s h i p h e a d i n g r e l a t i v e t o t h e sea.
H e a v e a n d p i t c h d i s p l a c e m e n t s can be measured easily w i t h s u f f i c i e n t accuracy, b u t t h e m e a s u r e m e n t o f e v e n a u n i d i r e c t i o n a l w a v e a n d t h e phase r e l a t i o n s b e t w e e n t h e m o t i o n a n d t h e w a v e is m u c h m o r e d i f f i c u l t . T h e phase of t h e m o t i o n can be d e t e r m i n e d o n l y w i t h a w a v e r e -corder whose p o s i t i o n is k n o w n r e l a t i v e t o t h e s h i p , s u c h as t h e s h i p - b o r n e w a v e recorder. These d o n o t w o r k s a t i s f a c t o r i l y a t h i g h e r speeds since t h e w a v e a m p l i t u d e near t h e s h i p is seriously m o d i f i e d b y t h e a d v a n c i n g s h i p . A c o m b i n a t i o n o f shipborne w a v e m e t e r a n d f r e e -f l o a t i n g b u o y was used i n t h e W e a t h e r R e p o r t e r t r i a l s [ 3 ] . T h e waves w e r e measured a t a l o c a t i o n r e m o t e f r o m t h e s h i p u s i n g a b u o y a n d near t h e s h i p w i t h a s h i p -b o r n e i n s t r u m e n t . I f t h e w a v e s p e c t r u m is assumed t o be s t a t i o n a r y b o t h i n space a n d t i m e , a n analysis o f t h e b u o y i n f o r m a t i o n p r o v i d e s t h e w a v e a m p l i t u d e t r u m a n d t h e s h i p - b o r n e d a t a p r o v i d e t h e phase spec-t r u m . F u r t h e r c o m p l i c a t i o n s arise f r o m t h e d i r e c t i o n a l spread of t h e w a v e spectra, as discussed i n t h e analysis o f t h e W e a t h e r R e p o r t e r t r i a l s . I n a long-crested seaway, w h e r e t h e d i r e c t i o n a l spread is v e r y s m a l l , a s i m p l e f r e e -floating b u o y w h i c h measures o n l y t h e v e r t i c a l displace-m e n t of t h e sea surface can be e displace-m p l o y e d f o r t h e deter-m i n a t i o n of t h e w a v e s p e c t r u deter-m . S u c h a seastate is v e r y u n u s u a l a n d is s e l d o m a v a i l a b l e d u r i n g t h e t i m e o f sea-k e e p i n g t r i a l s . I n v i e w of t h e f o r e g o i n g r e s t r i c t i o n s , t h e d i f f i c u l t y o f such a f u l l - s c a l e c o r r e l a t i o n test i n w a v e s is r e a d i l y a p p a r e n t . H o w e v e r , c o n f i r m a t i o n o f t h e e q u i v alence b e t w e e n f u l l s c a l e a n d m o d e l tests a n d c a l c u l a -t i o n resul-ts is o f s u c h i m p o r -t a n c e -t o b o -t h -t h e designer a n d o w n e r t h a t t h e tests were a t t e m p t e d e v e n t h o u g h t h e p r o b a b i l i t y o f success was s m a l l . T h e f u l l - s c a l e tests w e r e c o n d u c t e d a b o a r d t h e de-M A R C H 1 9 6 7 i
Fig. 1 Body plan .stroyer H j \ I Groningen o f t h e R o y a l N e t h e r l a n d s N a v y . T h i s t y p e o f s h i p w a s selected because o f t h e v a s t a m o u n t of seakeeping d a t a a l r e a d y a v a i l a b l e f r o m p r e v i o u s tests. A s h i p of t h i s class was t e s t e d p r e v i o u s l y i n t h e U n i t e d S t a t e s / R o y a l N e t h e r l a n d s N a v y seakeeping c o m p a r i s o n t r i a l s . M o t i o n s were c o m p a r e d i n v a r i o u s sea c o n d i -t i o n s a n d -t h e resul-ts w e r e r e p o r -t e d i n r e f e r e n c e [ 4 ] (1960). I n J a n u a r y 1965 a series of m o t i o n a n d p r o p u l s i o n tests was p e r f o r m e d f o r a w i d e r a n g e o f f o r w a r d speed. T h e s e t r i a l s were also used t o compare t h e p e r f o r m a n c e of t h r e e d i f f e r e n t t y p e s o f f l o a t i n g w a v e - h e i g h t meters. T h i s p a p e r presents some o f t h e results o f t h e head-sea m o t i o n tests.
A l t h o u g h c o r r e l a t i o n b e t w e e n m o d e l tests, f u l l - s c a l e
tests, a n d c a l c u l a t e d results was n o t t h e o r i g i n a l o b j e c t of t h i s t r i a l , t h e results are t h o u g h t t o be s u f f i c i e n t l y i n -t e r e s -t i n g -t o be i n c l u d e d i n -t h i s paper. Full-Scale M o t i o n Trials T h e f u l l s c a l e m o t i o n t r i a l s w i t h t h e R o y a l N e t h e r -l a n d s N a v y d e s t r o y e r H M Groningen were c a r r i e d o u t d u r i n g t h e p e r i o d J a n u a r y 1 9 - 2 1 , 1965 i n t h e sea areas t o t h e w e s t o f M o r o c c o a n d P o r t u g a l . A lines p l a n o f t h i s Friesland-class vessel is g i v e n i n F i g . 1 a n d t h e m a i n c h a r a c t e r i s t i c s are s u m m a r i z e d i n T a b l e 1. T a b l e 2 s u m m a r i z e s t h e p e r t i n e n t t r i a l c o n d i t i o n s .
Table 1 Main Cfiaracteristics of Ship
Length overall, m 110.0Ü Length between perpendiculars, m 112.40
Breadth, m 11.74 Maximum draught, m 4. o i
Design displacement i n seawater, tons .3070
Bloclc coefficient 0.563 Midship coefficient [ !o!827
Waterplane coefficient ' '0^801 Longitudinal radius of gyration (design condition), m
^ 0.233 ipp = 26.2 Longitudnial moment of inertia of waterplane, m* 828000
T h e r a d i u s of g y r a t i o n g i v e n i n T a b l e 1 is f o r t h e s h i p i n a f u l l design l o a d c o n d i t i o n . T h e m e a n v a l u e d u r i n g t h e t r i a l s is e s t i m a t e d a t 27 m or 0.24 L^p, since f u e l h a d been con.sumed f r o m t h e m i d s h i p t a n k s d u r i n g t h e tests. I t appears t h a t e v e n l a r g e r v a l u e s f o r t h e r a d i u s o f g y r a -t i o n m a y occur w h e n -t h e s h i p is i n a l i g h -t c o n d i -t i o n . A l l t e s t i n g w a s d o n e o n a course e q u a l t o t h e m e a n of t h e observed d i r e c t i o n o f w a v e p r o p a g a t i o n as g i v e n i n T a b l e 2. T h e sea s t a t e a j j p e a r e d f r o m v i s u a l o b s e r v a -t i o n -t o be f a i r l y l o n g cres-ted a n d u n i d i r e c -t i o n a l . T h i s N o m e n c l a t u r e ab cd e g) ABCDEGI A:, Cb F F,' F,', F, Fa = F„ = F/(ffL„„)'/' = coefficients of tlie equations of mo-tion for heave and pitch area of waterplane area of cross section bloclc coefficient total force on ship sectionat
hydronie-chauical forces wave force
am-plitude oil re-strained ship Froude number acceleration due to gravity longitudinal mo-ment of inertia of waterplane area w i t h respect to the Ub axis real moment of i n -ertia of ship k = 27r/X = M = Ma = Xi, N' = S = ( = T = V = Vb, Zb = wave number length overall length between
per-pendiculars total moment on
ship
wave moment am-plitude on re-strained ship total added mass
for heave sectional added mass sectional damping coefficient spectral density statical moment of waterplane area time draft of ship speed of ship right-handed body axis system
yv,(x) = half width of
de-signed wateiliiie
z = heave displacement
2o = heave amplitude c = phase angle
be-tween the tions (forces, mo-ments) and the waves f = instantaneous wave elevation fa = wave amplitude 6 = pitch angle 6a = pitch amplitude X = wave length p = density of water V = displacement volume w = circular frequency
oie = circular frequency
of encounter
Table 2 Trial Conditions Wave lieiglit
Wave
direction Mean Wind speed Period of dis-Date, Wind waves placement.
1965 Area direction (estimation) tons Jan.19 36°28'N 7-9 m/s 290° 3 m Run 1-7 10''15'W 7-9 m/s 290° 305-315° 10-13S 2978 Jan. 20 34°00'N 7-5 m/s 310° 2.5-2 m Run 11-15 9°57'W 7-5 m/s 310° 310° 10-14S 2931 Jan. 21 36° 7 ' N 4 m/s 4m Run 19 10°10'W 340-320° 345° 11-13S 2870 f a c t was s u b s t a n t i a t e d f u r t h e r b y t h e a l m o s t c o m p l e t e absence o f r o l l d u r i n g t h e test runs. T h e range of speeds covered d u r i n g t h e t e s t i n g was Fn = 0.18 t o F^ = 0.44. H e a v e acceleration a n d p i t c h a n d r o l l d i s p l a c e m e n t were recorded as a f u n c t i o n of t i m e d u r i n g each test. A v e r t i -cal-referenced gyroscope was used f o r t h e r o l l a n d p i t c h measurements, a n d a g y r o - s t a b i l i z e d accelerometer was used f o r t h e heave measurements. T h e heave acceler-a t i o n signacceler-al w acceler-a s d o u b l e i n t e g r acceler-a t e d , acceler-a n d heacceler-ave displacceler-ace- displace-m e n t also was recorded. A f r e e - f l o a t i n g w a v e buoy^ was used t o measure t h e v e r t i c a l acceleration o f t h e sea sur-face. T h e b u o y t r a n s d u c e r was a p e n d u l u m - s t a b i l i z e d accelerometer.
T h e accelerometer a n d p e n d u l u m were suspended a t t h e center of a sphere filled w i t h a d a m p i n g l i q u i d . T h e p e n d u l u m a n d accelerometer were designed t o be o n l y s l i g h t l y b u o y a n t i n t h e l i q u i d , t h e r e b y o b t a i n i n g a v e r y s m a l l r e s t o r i n g m o m e n t a n d a l o n g n a t u r a l p e r i o d . T h e t i l t e r r o r i n t h e accelerometer is, t h e r e f o r e , e s t i m a t e d t o be s m a l l . A high-pass electronic filter was used i n t h e accelerometer channel t o e l i m i n a t e f r o m t h e i n t e g r a t o r a n y steady o f f s e t or d r i f t components. T h e f r e q u e n c y response of t h i s filter was such t h a t f o r a w a v e p e r i o d o f 20 sec t h e signal a m p l i t u d e was a t t e n u a t e d 10 percent.
A l l d a t a were recorded o n a 14-channel F M m a g n e t i c t a p e recorder. T h e d a t a analysis was accomplished b y d i g i t i z i n g a l l signals a n d r e c o r d i n g t h e m o n p u n c h e d paper tape. T h e analysis was p e r f o r m e d b y a s t a n d a r d d i g i t a l c o m p u t e r .
T h e spectra f o r p i t c h , heave, a n d w a v e h e i g h t as deter-m i n e d b y t h e c o deter-m p u t e r are .shown i n F i g . 2. A l l spectra are presented as a f u n c t i o n o f f r e q u e n c y of e n c o u n t e r co^. F o r ease of reference an a d d i t i o n a l scale p r o p o r t i o n a l t o
L/\ is i n c l u d e d .
T h e d u r a t i o n o f each r u n was 15 m i n ; i n v i e w o f t h e l o n g w a v e l e n g t h s e n c o u n t e r e d t h i s is considered t o be s o m e w h a t s h o r t f o r s t a t i s t i c a l purposes.
T h e c o m p u t e d one t h i r d highest values o f t h e w a v e heights are l a r g e r t h a n t h e m e a n observed w a v e h e i g h t s as g i v e n i n T a b l e 2. T h e w a v e h e i g h t e s t i m a t i o n b y ej'e p r o v e d t o be d i f f i c u l t because of t h e .small slope o f t h e d o m i n a n t l o n g waves.
T h e a m p l i t u d e c h a r a c t e r i s t i c s o f heave a n d p i t c h were * Manufactured by Datawell N . V . ffaarlem, Netherlands.
c a l c u l a t e d f r o m t h e recorded w a v e a n d m o t i o n spectra, t h u s :
F o r p i t c h t h e dimensionless response Ojk^a is t h e n f o u n d w i t h ^wW , , co' = CO H , a n d K = — g 9 I n F i g . 3 t h e a m p l i t u d e characteristics are p l o t t e d o n a base of w a v e - l e n g t h r a t i o L/X. M o d e l Tests
A scale r a t i o o f 40 t o 1 was selected f o r t h e m o d e l ex-p e r i m e n t s , w i t h a r e s u l t a n t m o d e l l e n g t h o f 2.81 m . T h e m o d e l was b a l l a s t e d t o t h e design l o a d w a t e r l i n e a n d was o p e r a t e d w i t h a r a d i u s o f g y r a t i o n o f 0.25 Loa or 0.259 Lpj,. T h i s r a d i u s of g y r a t i o n was selected since a p r e v i o u s c o m m e r c i a l test series h a d been r u n a t t h e s m a l l e r r a d i u s 0.233 a n d i t was considered desirable t o i n v e s t i g a t e t h e effects of t h e r a d i u s v a r i a t i o n s w h i c h o c c u r as l o a d c o n d i t i o n s change.
T h e u n p o w e r e d m o d e l was c o n n e c t e d t o a t o w i n g ap-p a r a t u s w h i c h was so arranged as t o r e s t r i c t a l l modes o f m o t i o n except p i t c h a n d heave. A l l t e s t i n g was d o n e i n r e g u l a r long-crested head waves w i t h a p e a k - t o - p e a k h e i g h t o f a p p r o x i m a t e l y Lpp/40. T h e w a v e h e i g h t s were reduced a t frequencies near resonance t o p r e v e n t t h e m o d e l f r o m s h i p p i n g w a t e r . T h e w a v e l e n g t h s were v a r i e d f r o m L / X = 0.5 t o L/\ = 2.0. T e s t i n g was done f o r a range of F r o u d e n u m b e r s f r o m F„ = 0.15 t o 0.55. Te.st c o n d i t i o n s w e r e as s h o w n i n T a b l e 3.
Table 3 Model Test Conditions
Speed F„ = 0.15, 0.25, 0.35, 0.45, 0.55 Wave-length ratio i / x = 0.500, 0.555, 0.625, 0.714, 0.833, 1.000, 1.250, 1.670, 2.000
Wave-height ratio 2f<./L = 1/40
P i t c h , heave, a n d w a v e displacements were r e c o r d e d f o r each test. T h e p i t c h a n d heave d i s p l a c e m e n t s were sensed b y m i c r o - t o r q u e r o t a r y p o t e n t i o m e t e r s m o u n t e d as p a r t of t h e t o w i n g a p p a r a t u s . T h e t o w i n g s t r t i t a n d m o t i o n transducers were a r r a n g e d so t h a t t h e r e s t r a i n t forces i n heave a n d p i t c h were n e g l i g i b l e .
T h e w a v e h e i g h t was sensed b y a resistance w i r e p r o b e l o c a t e d 4 m f o r w a r d of t h e m o d e l center o f g r a v i t y a n d d i r e c t l y ahead of t h e m o d e l . A l l d a t a were r e c o r d e d s i m u l t a n e o u s l y o n a m u l t i c h a n n e l s t r i p c h a r t recorder. M o t i o n i n f o r m a t i o n was recorded o n l y a f t e r t h e carriage a n d m o d e l h a d been r u n n i n g a t a c o n s t a n t speed f o r a s u f l ü c i e n t l e n g t h o f t i m e t o insure .steadystate c o n d i -t i o n s . T h e i n f o r m a t i o n recorded was a n a l y z e d m a n u a l l y b y a v e r a g i n g t h e v a l u e s f o r t e n consecutive cycles of m o t i o n . M A R C H 1 9 6 7 3
RUN 1 .11 F n =.18 RUN 4 Fn = .31 RUN 7 Fn = .37 F o r t h e w a v e h e i g h t m e a s u r e m e n t t h e phases r e l a t i v e t o t h e m o t i o n s w e r e a d j u s t e d t o compensate f o r t h e dis-tance b e t w e e n t h e w a v e p r o b e l o c a t i o n a n d t h e m o d e l center o f g r a v i t y . T h e mea.sured a m p l i t u d e a n d phase characteristics f o r speeds c o r r e s p o n d i n g t o t h e f u l l - s c a l e t r i a l c o n d i t i o n s w e r e o b t a i n e d b y i n t e r p o l a t i o n . T h e y are p l o t t e d i n F i g . 3. C a l c u l a t i o n s T h e m o t i o n s of t h e s h i p w e r e c o m p u t e d as a f u n c t i o n of w a v e l e n g t h f o r t h e v a r i o u s speeds considered i n t h e f u l l - s c a l e tests. T h i s c o m p u t a t i o n is a c c o m p l i s h e d b y : 1 E v a l u a t i n g t h e t w o - d i m e n s i o n a l d a m p i n g a n d a d d e d mass a t v a r i o u s l o c a t i o n s a l o n g t h e ship b y m e t h o d s f r o m [5,G,7]. , 2 A p p l y i n g a m o d i f i e d f o r m of s t r i p t h e o r y [8,9,10] t o o b t a i n t h e coefficients of t h e e q u a t i o n s of m o t i o n . 3 A d e t e r m i n a t i o n of t h e e x c i t i n g forces (so-called r i g h t - h a n d side of t h e e q u a t i o n ) . 4 T h e s o l u t i o n of t h e c o u p l e d d i f f e r e n t i a l e q u a t i o n s of m o t i o n . T h e e q u a t i o n s o f m o t i o n f o r heave a n d p i t c h are pgVz = F (IJ lyyë = M w h e r e z a n d d = heave a n d p i t c h displacements F a n d M = t h e t o t a l f o r c e a n d m o m e n t a c t i n g o n the ship
F a n d M each are decomposed i n t h r e e p a r t s w h i c h are
e v a l u a t e d b y i n t e g r a t i n g t h e cross-sectional values over t h e l e n g t h of t h e s h i p :
(2) = - ƒ {F^' + F^' + F^')xdx,
T h e cross-sectional values are f o u n d b y u s i n g t h e s t r i p t h e o r y , t a k i n g i n t o account t h e effects of f o r w a r d speed. F o r a r i g h t h a n d coordinate s y s t e m (see F i g . 4 f o r d e f i n i -t i o n of w a v e a n d ship m o -t i o n s ) -t h e f o l l o w i n g expressions f o r F' can be f o u n d : = -2pgy^{z - x,d - f*J F2' = -N'iz - x,é + V d - i*) (3) ^ 3 ' = - j ^ { v i ' i z - x , d + V e - n \ or 4 J O U R N A L OF SHIP RESEARCH
RUN 13 Fn =.36 RUN 15 Fn = .44 RUN 19 Fn = .28 w h e r e Fi = —m'(z — x„9 + 2VÓ — f * ) A n u m e r i c a l analysis showed t h a t T* is a p p r o x i m a t e l y , , e q u a l t o t h e m e a n d r a f t f o r f u l l cross sections: t h u s
+ +
^ ^ ^ ^
w h e r e Ax = cross-section areaV = f o r w a r d speed o f s h i p T h e equations of m o t i o n are u s u a l l y w r i t t e n i n t h e
f , ,. f o r m of t w o c o u p l e d second-order d i f f e r e n t i a l e q u a t i o n s
iju- = h a l f w i d t h of w a t e r l i n e - . i r f J 4. a: • ^ i
w i t h f r e q u e n c y - d e p e n d e n t coefficients, n a m e l y
•111' = sectional added mass / , „ s . . , , . , ,« x
(a + pV)z + bz + cz — de — ee — gd
N' = sectional d a m p i n g c o e f f i c i e n t _ cos(we< + e n )
(A + I J ë + Bé +
ce
- Dz - Ez - Gzr * = r ( 1 - - f Vö e*-'' dzA = M „ cos(a>e< + e./f)
\ Vw J -T / T = d r a f t of a s e c t i o n ( 1 ) ' (2) a n d (3) i t f o l l o w s t h a t f = v e r t i c a l d i s p l a c e m e n t of the w a t e r surface a n d a = ƒ N'dx, e = ƒ A^'.-r^^.-r T h e expression f o r f * m a y be w r i t t e n i n t h e f o l l o w i n g b = I N'dx, e = I V . , . -w h e r e T* is d e t e r m i n e d f r o m c = p^iA^ (7 = p ^ S „ - Vb T* = - j ig (1 - ~ ƒ ° y,e'"'dz,'j ^ ^ j "^'^"'^^^^ ^ ^ j M A R C H 1 9 6 7 5
O c
>
I
-O m >I
RUN 1 Fn = .18 V=11.68 Kn. S O I ^ JC 0.5 H E A V E H E A V E P H A S E PfTCH P H A S EO FULL SCALE TRIAL • MODEL EXP. / L. a , CALCULATION k / L .0.253 CALCULATION h^ y L . O . I J t a.s 1.0 RUN 11 Fn = .18 V=11.68Kn. ^ - x 0.5 H E A V E P H A S E PITCH P H A S E
O FULL SCALE TRIAL • MOOELEXP / L . O . 2 5 9 CALCULATION k V L . 0 , 2 5 9 CALCULATION V y L . 0 23L I -0.5 1.0 1.5 2.0 RUN 19 Fn = .28 V=17.92 Kn. . . X 0.5 ( J , - 9 0 H E A V E P H A S E
O FULL SCALE TRIAL
• M O D E L E X P / L . O 259
CALCULATION k ^ y L . 0 259 CALCULATION k ^ ^ y ' L . 0 23i
1.5 2.0
t i g . 3 {a) Comparison o f full-scale measurement model experiment and calculation
O/li - co
7
RUN 4 Fn = .31 V = 20.22 Kn. H E A V E " o O O T o ° \ \° 1 r V PITCH o 0 o _ o \ 1 I H E A V E P H A S E • t ' — • — PITCH P H A S E NX^ J -\ \ \ V \\0 FULL SCALE TRfAL
\ \
U • MODEL EXP. h / L . 0 . 2 5 S - CALCULATION k y L . o i s g CALCULATJON k J^'y'u . 0,23i
1 t • MODEL EXP. h / L . 0 . 2 5 S - CALCULATION k y L . o i s g CALCULATJON k J^'y'u . 0,23i
1 t I
0.S 1.0 1.5 2.0
RUN 13 Fn = .36 V=:22.91Kn. RUN 7 Fn = .37 V=24,11Kn. RUN 15
fn = M
V = 28.16Kn. ^ J: 0.5 H E A V E \ ° \ o \ c 1 1 PITCH O X 1 1 HEAVE P H A S E 1 1 1 PITCH P H A S E ^ \ / / 1 I / • \ NJ.O FULL SCALE TRIAL \ • MODEL EXP. k,,/L>0.2S9 \ - CALCULATION k / L .0 259 \ CALCULATION k^f^L ,0.23*. \ 1 t I 0 0.5 1.0 1.5 2.0 ^ 0.5 HEAVE . J , o^<ij . - - y ^ CO o \
° \ °
\ o\ °°
\ * O PITCH 1 1 — 1 • . H E A V E P H A S E . . . • » 1 PITCH P H A S E N ^ ^ .O FULL SCALE TRIAU • MODEL EXP. ll /L . O JS9 - CALCULATION k y L . 0 Ï S 9 CALCULATION k J* ^ L. 0 2 3 t 1 1 • MODEL EXP. ll /L . O JS9 - CALCULATION k y L . 0 Ï S 9 CALCULATION k J* ^ L. 0 2 3 t 1 1 • MODEL EXP. ll /L . O JS9 - CALCULATION k y L . 0 Ï S 9 CALCULATION k J* ^ L. 0 2 3 t 1 1 1 H E A V E /jryA° o / / o O \
— V
O \ o \ Vo 1 1 <^ PITCH o 0 V .\
1 1 H E A V E P H A S E JO * « 1 1 PITCH P H A S E ^ ^ V * \ \ \ \ XNO FULL SCALE TRIAL • MODEL EXP. k j V L . 0 359 - CALCULATION k^VL.0.359 CALCULATION k^^yL»0.3)l
1 1 1
Vx —
Fig. 3 (b) Comparison o f full-scale measurement model experiment and calculation
Vx-B ƒ N'x.Hxi C = pgl, - VE a n d : E = j N%dxt + Vm G = pgS^ CO r i V ' . T , e - * ^ * ^'""^^^ dx, J i cos kx„ ± coy f m ' e - * ^ * ^ ^ ^ f " dx,
J
i cos kx„ F. a cos fF( _ 9 f a Sin_eFj- OP — co(co + A: :V)ƒ
m'ecos fcr»,
- t r * cos kxt, sin fc.Ti T COMf^cose,,,^
- 2 p 3f
y.x,e-^^* + co(co + kV) f •m'x.e-"^* '^.«^ f-''^ dx,' Ji^
sin fc.-i;4
sin kx, I n tiiese expressions t h e s e c t i o n a l a d d e d mass in' a n d t h e sectional d a m p i n g c o e f f i c i e n t N' a c c o r d i n g t o T a s a i ' s m e t h o d w e r e used [ 6 ] . I n t h i s m e t h o d t h e cross sections of t h e s h i p are a p p r o x i m a t e d o n l y b y a t w o - c o e f f i c i e n t r i V ' e " * ^ * dx t r a n s f o r m a t i o n of t h e u n i t circle. T h e c a l c u l a t i o n s w e r e Jj^ cos kx, " * c a r r i e d o u t f o r t w o r a d i i of g y r a t i o n , fc„„/Lj,p = 0.233 a n d kyy/Lpp = 0.259, t o show t h e i n f l u e n c e o f t h i s p a r a m e t e r o n t h e m o t i o n c h a r a c t e r i s t i c s . T h e s h i p v a l u e s l i e w i t h i n t h i s range. T h e results w i t h r e g a r d t o m o t i o n a m p l i t u d e s a n d phases are s h o w n i n F i g . 3 f o r c o m p a r i s o n w i t h t h e m o d e l e x p e r i m e n t s a n d t h e f u l l -scale tests. M A R C H 1 9 6 7
7
^0 Z Zb
/
— ƒ — V - s h i p s p e e d
wave- E = EjCos(kXo+ujt) t.o.v. X o y ^ z ^
E =EjCos(ü)e t) to.v. x y z , x = o heave - z = z j cos(u)e t + E z ^ )
pitch - e= ejcos(u)ei + E e ^ )
Fig. 4 Definition of wave and motions
Discussion
T h e agreement b e t w e e n m o d e l e x p e r i m e n t a n d calcu-l a t i o n , b o t h w i t h r e g a r d t o a m p calcu-l i t u d e s a n d phases, is good. T h e o n l y d i f f e r e n c e of a n y significance occurs i n t h e h e a v i n g m o t i o n b e t w e e n t h e w a v e - l e n g t h r a t i o s of
L/\ = 1.1 t o L / X = 1.4. T h i s d i f f e r e n c e is also
sup-p o r t e d b y c o m m e r c i a l m o d e l tests o n t h e same shisup-p f o r m . I t s h o u l d be observed, however, t h a t i n t h i s range t h e m o d e l t e s t a n d f u l l - s c a l e results check p a r t i c u l a r l y w e l l . W h i l e t h e e x p e r i m e n t does n o t p r o v i d e d i r e c t evidence as t o t h e reason f o r t h i s difference, t h e e x p e r i m e n t a l re-sults are i n e v e r y case so s t r o n g l y l i n e a r as t o p r a c t i c a l l y e l i m i n a t e lack of l i n e a r i t y as a p r o b a b l e cause. T h i s s m a l l d i f f e r e n c e does n o t occur f o r p i t c h .
T h e f u l l - s c a l e r e s u l t s as expected show m o r e scatter t h a n t h e m o d e l tests. T h i s s c a t t e r increases w i t h i n creasing w a v e l e n g t h a n d m a y be p a r t l y due t o a b r o a d -e n i n g of s t a t i s t i c a l confid-enc-e l i m i t s f o r t h -e long-er w a v -e c o m p o n e n t s associated w i t h t h e r e l a t i v e l y s h o r t w a v e records a n d t h e longer w a v e periods. I t is of interest t o n o t e t h a t t h e t r a n s f o r m a t i o n of t h e w a v e h e i g h t f r o m b u o y t o ship l o c a t i o n is t h e o n l y step of a n otherwise d e t e r m i n i s t i c e x p e r i m e n t i n w h i c h s t a t i s t i c a l m e t h o d s are e m p l o y e d . O t h e r possible sources of error are t h e u n c e r t a i n t y i n t h e f r e q u e n c y t r a n s f o r m a t i o n of t h e w a v e s p e c t r u m o w i n g t o b u o y d r i f t a n d errors i n t h e ship speed l o g , a n d d i r e c t i o n a l spread of t h e seaway itself. W h i l e t h e r e are differences b e t w e e n f u l l - s c a l e a n d m o d e l results, t h e agreement as a w h o l e is v e r y g o o d a n d t h e r e are n o differences w h i c h exceed t h e possible m e a s u r e m e n t e r r o r .
A n i m p o r t a n t c o n s i d e r a t i o n , h o w e v e r , is t h e tran.s-f o r m a t i o n used t o a p p r o x i m a t e t h e ship cross sections, since t h e accuracy of t h e c o m p u t a t i o n is p a r t i c u l a r l y sensitive t o errors i n t h e cross-section t r a n s f o r m a t i o n . F o r t h i s p a r t i c u l a r s h i p t h e L e w i s or t w o - c o e f f i c i e n t t r a n f s f o r m a t i o n p r o v i d e s an excellent fit f o r each section. T h i s , however, is g e n e r a l l y n o t t r u e f o r a r b i t r a r y ship
cross sections, a n d f o r m a n y ships a greater n u m b e r of coefficients w i l l be r e q u i r e d t o o b t a i n t h e r e q u i r e d a p -p r o x i m a t i o n . C o n c l u s i o n s T h e use of m o d i f i e d s t r i p t h e o r y f o r t h e c o m p u t a t i o n of s h i p m o t i o n s i n p i t c h a n d heave is confirniecl b y t h i s c o m p a r i s o n of f u l l - s c a l e , m o d e l , a n d c o m p u t e d results. A d i r e c t c o r r e l a r y of t h i s c o n f i r m a t i o n is t h e desired v a l i d a t i o n o f F r o u d e scaling f o r g e o m e t r i c a l l y s i m i l a r ship f o r m s o v e r a b r o a d r a n g e of speeds a n d w a v e l e n g t h s . I t f u r t h e r c o n f i r m s p r e v i o u s e x p e r i m e n t a l re-s u l t re-s w h i c h re-show t h a t m o t i o n l i n e a r i t y ire-s q u i t e g o o d . T h e v a r i a t i o n o f t h e m o t i o n s w i t h changes i n t h e r a d i u s o f g y r a t i o n (mass m o m e n t o f i n e r t i a i n p i t c h ) is s m a l l b u t p r e d i c t a b l e f r o m m o d i f i e d s t r i p t h e o r y . A g r e e m e n t b e t w e e n t h e m e a s u r e d a n d c o m p u t e d m o -t i o n s is s u f f i c i e n -t l y good, especially i n p i -t c h , as -t o sugges-t t h e p o s s i b i l i t y of a n extension of s t r i p - t h e o r y m e t h o d s t o i n c l u d e t h e c o m p u t a t i o n of b e n d i n g m o m e n t s . A c k n o w l e d g m e n t s T h i s w o r k was possible t h r o u g h t h e c o o p e r a t i o n of t h e R o y a l N e t h e r l a n d s N a v y . P a r t i c u l a r a p p r e c i a t i o n is expressed f o r t h e w i l l i n g assistance of t h e o f f i c e r s a n d crew o f H M Groningen. T i m e l y c o m p l e t i o n of t h e p r o j e c t was m a d e possible b y t h e e n t h u s i a s t i c assistance of t h e S h i p b u i l d i n g L a b o r a -t o r y S -t a f f . T h e excellent p r o g r a m m i n g a n d m a c h i n e c o m p u t a t i o n assistance p r o v i d e d b y t h e W i s k u n d i g e D i e n s t ( C o m -p u t e r D e -p a r t m e n t ) is g r a t e f u l l y a c k n o w l e d g e d . References 1 V . G . Szebehely, M . D . Bledsoe, a n d G . P . S t e f u n , "Scale E f f e c t s i n S e a w o r t h i n e s s , " D a v i d T a y l o r M o d e l B a s i n R e p o r t N o . 1070, W a s h i n g t o n , D . C., 195G. 2 J . G e r r i t s m a , " S e a w o r t h i n e s s T e s t s w i t h T h r e e G e o m e t r i c a l S i m i l a r S h i p A'lodels," S y m p o s i u m o n t h e B e h a v i o u r of Ships i n a Seaway, W a g e n i n g e n , T h e N e t h e r l a n d s , 1957. 3 H . J . S. C a n h a n , D . E . C a r t w r i g h t , G . J . G o o d -r i c h , a n d N . H o g b e n , "Seakeeping T -r i a l s o n O W S
Weather Reporter," Transaclions of the Royal Institute of Naval Architects, E n g l a n d , 1962. 4 M . D . Bledsoe, 0 . Bussemaker, a n d W . E . C u m -m i n s , " S e a k e e p i n g T r i a l s o n T h r e e D u t c h D e s t r o y e r s , " T E A N S . S N A M E , 1960. 5 F . U r s e l l , " O n t h e H e a v i n g M o t i o n o f a C i r c u l a r C y l i n d e r o n t h e S u r f a c e of a F l u i d , " Quarterly Journal of
Mechanics aiid Applied Mathematics, v o l . 2, P a r t 2, 1949.
6 F . T a s a i , " O n t h e D a m p i n g F o r c e a n d A d d e d M a s s o f Ships H e a v i n g and P i t c h i n g , " Report of Research
Institute for Applied Mechanics, K y u s h u U n i v e r s i t y ,
J a p a n , 1 9 6 0 .
7 W . R . P o r t e r , "Pressure D i s t r i b u t i o n , A d d e d M a s s a n d D a m p i n g C o e f f i c i e n t s f o r C y l i n d e r s O s c i l l a t i n g i n a
{Continued on page 27)
J a n u a r i 1967 R A P P O R T N r . 1 6 8 0 0 / 8 2 9 8 / S B
F U L L SCALE DESTROYER iMOTION MEASUREMENTS
b y • J . G E R R I T S M A a n d W . E . S M I T H
M I N I S T E R I E V A N D E F E N S I E ( M A R I N E )
H O O F D A F D E L I N G M A T E R I E E L
B U R E A U S C F I E E P S B O U W
T O R E N S T R A A T 172 - ' s - G R A V E N H A G E
N E D E R L A N D
P R E F A C E T h i s r e p o r t is t h e f i r s t r e s u l t o f f u l l scale s e a k e e p i n g t r i a l s w h i c h w e r e c o n d u c t e d i n t h e N o r t h A t l a n t i c i n J a n u a r y 1965 w i t h t h e N e t h e r l a n d s s u b c h a s e r " G r o n i n g e n " . D u r i n g these t r i a l s p i t c h , h e a v e a n d r o l l m o t i o n s w e r e m e a s u r e d as w e l l as s h a f t t o r q u e a n d s h a f t r . p . m . T h e seastate has b e e n m e a s u r e d b y a f r e e f l o a t i n g \ y a v e b u o y . T h e t r i a l s w e r e p r e p a r e d a n d p e r f o r m e d w i t h t h e assistance o f t h e L a b o r a t o r i u m v o o r . S c h e e p s b o u w k u n d e o f t h e T e c h n i s c h e H o g e s c h o o l a t D e l f t , t h e A'^erificatie \ ' a n R i j k s z e e e n L u c h t v a a r t -i n s t r u m e n t e n a n d t h e R -i j k s w e r f a t d e n H e l d e r . T h e s h i p m o t i o n i n h e a d seas has b e e n a n a l y s e d b y t h e L a b o r a -t o r i u m v o o r S c h c e p s b o u w L u n d e o f -t h e T e c h n i s c h e H o g e s c h o o l a t D e l f t . T h e p u r p o s e o f t h i s analysis w a s t h e d e r i v a t i o n o f t h e p i t c h a n d h e a v e response f u n c t i o n o f t h e s h i p f r o m t h e m e a s u r e d m o t i o n s a n d w a v e e l e v a t i o n a t sea. T h e s e response f u n c t i o n s w e r e c o m p a r e d w i t h t h e v a l u e s d e r i v e d f r o m m o d e l t e s t s i n r e g u l a r w a v e s a n d f r o m c o m p u t e r c a l c u l a t i o n s a c c o r d i n g t o a s t r i p t h e o r y Avhich i n c l u d e s t h e e f f e c t o f f o r w a r d speed. T h e a g r e e m e n t b e t w e e n t h e o r y a n d e x p e r i m e n t s p r o v e d t o be s u f f i c i e n t l y g o o d . P r o f . i r . J . G E R R I T S M A a n d his s t a f f are c o n g r a t u l a t e d w i t h t h e succes o f these e x p e r i m e n t s . H i s c o o p e r a t i o n a n d w i U i n g n e s s t o issue t h i s r e p o r t ' as a p u l ^ l i c a t i o n o f B u r e a u ScheepsbouVv o f t h e M i n i s t e r i e v a n D e f e n s i e ( m a r i n e ) are h i g h l y a p p r e c i a t e d . I r . K . DE M U X T E R H o o f d v a n h e t b u r e a u S c h e e p s b o u w
C O N T E N T S p a g e S u m m a r y 5 1 I n t r o d u c t i o n 5 2 F u l l Scale M o t i o n t r i a l s 6 3 ^ v l o d e l tests • • 7 4 C a l c u l a t i o n s 7 5 D i s c u s s i o n . 8 6 C o n c l u s i o n 9 7 A c k n o w l e d g e m e n t 9 R e f e r e n c e s ; . 9 N o m e n c l a t i u ' e 10
F U L L S C A L E D E S T R O Y E R M O T I O N M E A S U R E M E N T S *
b y
J . G E R R I T S M A * * a n d W . E . S M I T H * * *
Summary
T h e results of f u l l destroyer raotion tests i n head seas are presented. A comparison is made between motion respc obtamed f r o m f u l l scale tests, model experiments and computer calculations.
.•Agreement is satisfactory. • 1 I n t r o d u c t i o n A c a r e f u l c o r r e l a t i o n b e t w e e n f u l l scale s h i p m o t i o n responses a n d those o b t a i n e d f r o m m o d e l e x p e r i m e n t s has l o n g b e e n c o n s i d e r e d a n a r e a o f c o n -s i d e r a b l e i n t e r e -s t b y -s e a k e e p i n g re-searcher-s. T h i s v i e w is also expressed i n t h e r e c o m m e n d a t i o n s o f t l i e I n t e r n a t i o n a l T o w i n g 7 ' a n k C o n -f e r e n c e 1 9 6 3 : " A c c u r a t e F u l l Scale D a t a u n d e r C o n d i t i o n s S u i t a b l e f o r A n a l y s i s to be U s e d f o r C o r r e l a t i o n w i t h M o d e l T e s t s " . M o t i o n tests c o n d u c t e d w i t h g e o m e t r i c a l l y s i m i l a r m o d e l s o f d i f i e r e n t sizes i n r e g i d a r lono-c r e s t e d h e a d wa\-es h a v e n o t s h o w n a m e a s u r a b l e scale e f f e c t [ 1 , 2 ] . T h e r a n g e o f size c o n s i d e r e d i n [ 1 , 2 ] is, h o w e v e r , t o o r e s t r i c t e d t o p r o v i d e c o n -c l u s i v e a n s w e r s i n this r e s p e -c t . F u l l s-cale results
With t h e r e s u l t i n g scale r a t i o s o f 4 0 t o 1 o r g r e a t e r , c o u l d r e v e a l a n y s i g n i f i c a n t scale e f f e c t s i f p r e s e n t . S u c h a c o m p a r i s o n s h o u l d p r ó \ i d e s t r o t i g s u p p o r t f o r t h e e x p l a n a t i o n t h a t t h e m o t i o n g e n e r a t e d s u r f a c e w a v e s a c c o u n t f o r t h e g r e a t e s t p a r t o f t h e e n e r g y d i s s i p a t e d , a n d t h a t o t h e r sources s u c h as v i s c o u s d a m p i n g a n d b o u n d a r y l a y e r e f f e c t s , w h i c h c o u l d c a u s e scale e f f e c t s , are q u i t e s m a l l . T h e a c c u r a c y o f t h e f u l l scale m e a s u r e m e n t is o b v i o u s l y a m a j o r f a c t o r i n d e t e r m i n i n g t h e v a l i d i t y o f t h e c o r r e l a t i o n . T h i s i m m e d i a t e l y i m p o s e s m a j o r r e s t r i c t i o n s o n t h e test c o n d i t i o n s a n d m e a s u r e m e n t s . T h e s e a w a y e n c o u n t e r e d m u s t be o n e t h a t c a n be m e a s u r e d a n d a n a l y s e d , i.e. v i r t u a l l y a u n i d i r e c t i o n a l s e a w a y . T h i s c o n d i t i o n is also necessary f o r t h e a c c u r a t e d e t e r m i n a -t i o n o f m o -t i o n responses w h i c h a r e -themselves a f u n c t i o n o f s h i p h e a d i n g r e l a t i v e t o t h e sea. H e a v e a n d p i t c h d i s p l a c e m e n t s c a n be easily m e a s u r e d w i t h s u f f i c i e n t a c c u r a c y b u t d i e measure¬ * Report no. 142, Shipbuilding Laboratory, Delft. ** I'rofessor in Naval Architecture. Shipbuilding
Labora-tory, Delft.
* * * Physicist David 'I'aylor Afodel Bu.sin, Washington, working at Shipbuilding Laboratory, Delft.
m e n t o f e v e n a u n i - d i r e c t i o n a l w a v e a n d t h e phase r e l a t i o n s b e t w e e n t h e m o t i o n a n d t h e w a v e is m u c h n i o r e d i f f i c u l t . T h e p h a s e o f t h e m o t i o n c a n be d e t e r m i n e d o n l y w i t h a w a v e r e c o r d e r w h o s e p o s i t i o n is k n o \ v n r e l a t i v e to t h e s h i p , s u c h as t h e s h i p b o r n e w a v e r e c o r d e r . T h e s e d o n o t w o r k s a t i s f a c t o r i l y a t h i g h e r speeds since t h e w a v e a m p l i t u d e n e a r t h e s h i p is s e r i o u s l y m o d i f i e d b y t h e a d v a n c i n g s h i p . A c o m b i n a t i o n o f s h i p b o r n e w a v e m e t e r a n d f r e e floating b u o y was used i n t h e W e a t h e r R e -p o r t e r t r i a l s [ 3 ] . T h e wa\-es w e r e m e a s u r e d a t a l o c a t i o n r e m o t e f r o m t h e s h i p u s i n g a b u o y a n d n e a r t h e s h i p w i t h a s h i p b o r n e i n s t r u m e n t . I f t h e w a v e s p e c t r u m is a s s u m e d t o be s t a t i o n a r y b o t h i n space a n d t i m e , a n a n a l y s i s o f t h e b u o y i n f o r -m a t i o n p r o v i d e s t h e w a v e a -m p l i t u d e s p e c t r u -m a n d t h e s h i p b o r n e d a t a p r o v i d e the phase spec-t r u m . F u r t h e r c o m p l i c a t i o n s arise f r o m t h e d i r e c t i o n a l s p r e a d o f t l i e wa^•e s p e c t r a , as discussed i n t h e analysis o f t h e "Weather R e p o r t e r t r i a l s . I n a l o n g c r e s t e d s e a w a y , w h e r e t h e d i r e c t i o n a l s p r e a d is v e r y s m a l l , a s i m p l e , f r e e floating b u o y w h i c h m e a s u r e s o n l y t h e v e r t i c a l d i s p l a c e m e n t o f t h e sea s u r f a c e c a n be e m p l o y e d f o r t h e d e t e r m i n a t i o n o f t h e w a v e s p e c t r u m . S u c h a seastate is v e r y u n u s u a l a n d is s e l d o m a v a i l a b l e d u r i n g t h e t i m e o f s e a k e e p i n g t r i a l s . I n v i e w o f t h e a b o v e r e s t r i c -t i o n s , -t h e d i f l i c u l -t y o f s u c h a f u l l scale c o r r e l a -t i o n test i n w a v e s is r e a d i l y a p p a r e n t . H o w e v e r , c o n -firmation o f t h e e q u i v a l e n c e b e t w e e n f u l l scale a n d m o d e l tests a n d c a l c u l a t i o n results is o f s u c h i m -p o r t a n c e t o b o t h t h e d e s i g n e r a n d o w n e r t h a t t h e tests w e r e a t t e m p t e d e v e n t h o u g h t h e p r o b a b i l i t y o f success was s m a l l . T h e f u l l scale tests w e r e c o n d u c t e d a b o a r d t h e d e s t r o y e r H . M . " G r o n i n g e n " o f t h e R o y a l N e t h e r -l a n d s N a v y . T h i s t y p e o f s h i p was se-lected because o f t h e vast a m o u n t o f s e a k e e p i n g d a t a a l r e a d y a v a f l a b l e f r o m p r e v i o u s tests. A s h i p o f t l i i s class
w a s p r e v i o u s l y tested i n t h e U n i t e d States R o y a l N e t h e r l a n d s N a v y s e a k e e p i n g c o m p a r i s o n t r i a l s . M o t i o n s w e r e c o m p a r e d i n \ ' a r i o u s sea c o n d i t i o n s a n d t h e results w e r e r e p o r t e d i n [ 4 ] ( 1 9 6 0 ) . I n J a n u a r y 1965 a series o f m o t i o n a n d p r o p u l s i o n tests w e r e p e r f o r m e d f o r a wide r a n g e o f f o r w a r d speed. T h e s e t r i a l s w e r e also used t o c o m p a r e t h e p e r f o r m a n c e o f t h r e e d i f f e r e n t types o f f l o a t i n g w a v e h e i g h t m e t e r s . T h i s p a p e r presents s o m e o f t h e results o f t h e h e a d sea m o t i o n tests.
A l t h o u g h c o r r e l a t i o n b e t w e e n m o d e l tests, f u l l scale tests a n d c a l c u l a t e d results was n o t t h e o r i g i n a l o b j e c t o f t h i s t r i a l , t h e results are t h o u g h t to be s u f f i c i e n t l y i n t e r e s t i n g t o be i n c l u d e d i n t h i s p a p e r . 2 F u l l S c a l e M o t i o n , t r i a l s T h e f u l l scale m o t i o n t r i a l s with t h e R o y a l N e t h e r -l a n d s N a v y d e s t r o y e r H . M . " G r o n i n g e n " w e r e c a r r i e d o u t d u r i n g t l i e p e r i o d J a n u a r y 1 9 - 2 1 , 1965 i n t h e sea areas t o t h e west o f M a r o c c o a n d P o r t u -g a l . A l i n e s p l a n o f this F r i c s l a n d - c l a s s vessel is g i v e n i n F i g u r e 1 a n d the m a i n c h a r a c t e r i s t i c s are s u m m a r i z e d i n T a b l e 1. Table 1 M a i n characteristics of ship Table 2 T r i a l conditions Date 1965 Area W i n d speed W i n d direction \Vave height Wave direction Period of waves (estimation) Mean displace-ment 19Jan. R u n 1-7 36=28'N 10"15'\V 7-9 m/s 290= 3 m 305''-315° 10-13 s 2978 t 20 Jan. Run 11-15 34'00'X 9=57'\V 7-5 m/s 310" 2.5-3 m 310° 10-14s 2931 t 21 Jan. Run 19 36° 7'N lO'-lO'W 4 m 3 340^-320^ 4 in 345° 11-13 s 2870 t T a b l e 2 s u m m a r i z e s t h e p e r t i n e n t t r i a l c o n d i t i o n s . T h e r a d i u s o f g y r a t i o n g i v e n i n T a b l e 1 is f o r t h e s h i p i n a f u l l d e s i g n l o a d c o n d i t i o n . T h e m e a n v a l u e d u r i n g t h e t r i a l s is e s t i m a t e d a t 27 m o r .24-Lpp, since f u e l h a d b e e n c o n s u m e d f r o m t h e m i d s h i p t a n k s d u r i n g t h e tests. I t a p p e a r s t h a t e v e n l a r g e r v a l u e s f o r t h e r a d i u s o f g y r a t i o n m a y o c c u r w h e n t h e s h i p is i n a l i g h t c o n d i t i o n . A l l t e s t i n g was d o n e o n a course e q u a l t o t h e m e a n o f t h e o b s e r v e d d i r e c t i o n o f w a v e p r o p a g a -t i o n as g i v e n i n T a b l e 2. T h e sea s-ta-te a p p e a r e d f r o m v i s u a l o b s e r v a t i o n , t o be f a i r l y l o n g c r e s t e d a n d u n i d i r e c t i o n a l . T h i s f a c t was f u r t h e r s u b -s t a n t i a t e d b y t h e a l m o -s t c o m p l e t e ab-sence o f r o l l d u i i n g t h e test r u n s . T h e r a n g e o f speeds c o v e r e d d u r i n g t h e t e s t i n g was Fn = .18 t o F,,. = . 4 4 . H e a v e a c c e l e r a t i o n a n d p i t c h a n d r o l l d i s p l a c e -m e n t w e r e r e c o r d e d as a f u n c t i o n o f t i -m e d u r i n g e a c h test. A - v e r t i c a l r e f e r e n c e d g y r o s c o p e w-as used f o r t h e r o l l a n d p i t c h m e a s u r e m e n t s , a n d a g y r o s t a b i l i z e d a c c e l e r o m e t e r was used f o r t h e h e a v e m e a s u r e m e n t s . T h e h e a v e a c c e l e r a t i o n s i g n a l was d o u b l e i n t e g r a t e d , a n d hea\'e d i s p l a c e m i c n t also w a s r e c o r d e d . A f r e e floating w a v e b u o y * w a s used t o m e a s u r e t h e v e r t i c a l a c c e l e r a t i o n o f t h e sea s u r f a c e . T h e b u o y t r a n s d u c e r was a p e n d u l u m s t a b i l i z e d a c c e l e r o m e t e r . T h e a c c e l e r o m e t e r a n d p e n d u l u m w e r e sus-p e n d e d a t t h e c e n t r e o f a s sus-p h e r e filled w i t h a d a m p i n g lic[uicl. T h e p e n d u l u m a n d a c c e l e r o -m e t e r w e r e d e s i g n e d t o be o n l y s l i g h t l y b u o y a n t i n t h e l i q u i d , t h e r e b y o b t a i n i n g a v e r y s m a l l r e s t o r i n g m o m e n t a n d a l o n g n a t u r a l p e r i o d . T h e t i l t e r r o r i n t h e a c c e l e r o m e t e r is, t h e r e f o r e , esti-m a t e d to be s esti-m a l l . A h i g h pass e l e c t r o n i c filter was used i n t h e a c c e l e r o m e t e r c h a n n e l t o e l i m i n a t e f r o m t h e i n t e g r a t o r a n y s t e a d y o f f s e t o r d r i f t c o m -p o n e n t s . T h e f r e q u e n c y res-ponse o f t h i s filter w a s s u c h t h a t f o r a w a v e p e r i o d o f 2 0 seconds t h e s i g n a l a m p l i t u d e was a t t e n u a t e d 1 0 % . A l l d a t a was r e c o r d e d o n a 14 c h a n n e l F M m a g n e t i c t a p e r e c o r d e r . T h e d a t a a n a l y s i s w a s a c c o m -p l i s h e d b y d i g i t i z i n g a l l signals a n d r e c o r d i n g t h e m o n p u n c h e d p a p e r t a p e . T h e a n a l y s i s w a s p e r f o r m e d b y a s t a n d a r d d i g i t a l c o m p u t e r . T h e s p e c t r a f o r p i t c h , h e a v e a n d w a v e h e i g h t as d e t e r m i n e d b y t h e c o m p u t e r are s h o w n i n F i g u r e 2. A l l s p e c t r a are p r e s e n t e d as a f u n c t i o n o f f r e c j u e n c y . o f e n c o u n t e r oje. F o r ease o f r e f e r e n c e a n d a d d i t i o n a l scale p r o p o r t i o n a l t o LjA is i n c l u d e d .
* Manufactured by Datawell N . V . Haarlem^ Netherlands.
Length overall 116.00 m
Length between perpendiculars • 112.40 m
Breadth 11.74 m
M a x i m u m draught 4.01 m Design displacement i n seawater 3070 t
Blocf; cocfFxien: 0.563
Midship coefficient 0.827 Waterplane coefficient 0.801 Longitudinal radius of gyration : 0.233/,^,,= 26.2 m (design condition;
Longitudinal moment of inertia of
T h e d u r a t i o n o f e a c h r u n was 15 m i n u t e s , a n d i n v i e w o f the l o n g w a v e l e n g t h s e n c o u n t e r e d t h i s is c o n s i d e r e d t o be s o m e w h a t s h o r t f o r s t a t i s t i c a l p u r p o s e s . T h e c o m p u t e d o n e t h i r d h i g h e s t ' v a l u e s o f t h e w a v e h e i g h t s are l a r g e r t h a n t h e m e a n o b s e r v e d w a v e h e i g h t s as gi\-en i n T a b l e 2. T h e w a v e h e i g h t e s t i m a t i o n b y eye p r o v e d t o be d i f f i c u l t because o f t h e s m a l l slope o f the d o n i i n a n t l o n g w a v e s . T h e a m p l i t u d e c h a r a c t e r i s t i c s o f h e a v e a n d p i t c h w e r e c a l c u l a t e d f r o m t h e r e c o r d e d w a v e a n d m o t i o n s p e c t r a , t h u s : Table 3 Model test conditions
Oa F o r p i t c h t h e d i m e n s i o n l e s s response ^ is t h e n f o u n d w i t h : kCa •V tOe
=
0) - a n d : k of"-g I n F i g u r e 3 t h e a m p l i t u d e c h a r a c t e r i s t i c s are p l o t t e d o n a base o f w a \ ' e l e n g t h r a t i o L!?.. 3 M o d e l t e s t sA scale r a t i o o f 4 0 t o 1 was selected f o r t h e m o d e l e x p e r i m e n t s , w i t h a r e s u l t a n t m o d e l l e n g t h o f 2 . 8 1 m . T h e m o d e l was b a l l a s t e d t o t h e d e s i g n l o a d w a t e r l i n e a n d \\'as ' o p e r a t e d w i t h a r a d i u s o f g y r a t i o n o f .25Loa o r .259Lpp. T h i s r a d i u s o f g y r a t i o n was selected since a p r e v i o u s c o m m e r c i a l test scries h a d b e e n r u n a t the s m a l l e r r a d i u s
.233Lpp a n d i t was c o n s i d e r e d d e s i r a b l e t o • i n -v e s t i g a t e the e f l e c t s o f t h e r a d i u s -v a r i a t i o n s w h i c h o c c u r as l o a d c o n d i t i o n s c h a n g e . T h e u n p o w e r e d m o d e l was c o n n e c t e d t o a t o w i n g a p p a r a t u s w h i c h was so a r r a n g e d as t o r e s t r i c t a l l m o d e s o f m o t i o n e x c e p t p i t c h a n d h e a v e . A l l t e s t i n g was d o n e i n r e g u l a r l o n g c r e s t e d h e a d w a v e s w i t h a p e a k t o p e a k h e i g h t o f a p p r o x i m a t e l y Lppj4:Q. T h e w a v e h e i g h t s w e r e r e d u c e d a t f r e -q u e n c i e s n e a r r e s o n a n c e t o p r e v e n t t h e m o d e l f r o m s h i p p i n g -water. T h e w a \ ' e l e n g t h s w e r e v a r i e d f r o m Lj?. = .5 t o Ll/. = 2 . 0 . T e s t i n g w a s d o n e f o r a r a n g e o f F r o u d e n u m b e r s f r o m F„ = .15 t o . 5 5 . T e s t c o n d i t i o n s w e r e as s h o w n i n T a b l e 3. P i t c i i , hea\'e a n d wa\-e d i s p l a c e m e n t s w e r e r e c o r d e d f o r e a c h test. T h e p i t c h a n d h e a v e d i s -p l a c e m e n t s w e r e sensed b y m i c r o - t o r q u e r o t a r y p o t e n t i o m e t e r s m o u n t e d as p a r t o f t h e t o w i n g a p p a r a t u s . T h e t o w i n g s t r u t a n d m o t i o n t r a n s -d u c e r s -were a r r a n g e -d so t h a t t h e r e s t r a i n t f o r c e s i n h e a v e a n d p i t c h w e r e n e g h g i b l e . Speed F„ = .15, .25, .35, .45, .55 Wave lengtii ratio L/?. = .500, .555, .625,. 714, .833,
1.000,1.250,1.670,2.000 Wave heiglit ratio 2t„/Z. = 1/40
T h e w a v e h e i g h t was sensed b y a resistance w i r e p r o b e l o c a t e d 4 m f o r w a r d o f t h e m o d e l c e n t r e o f g r a v i t y a n d d i r e c t l y a h e a d o f t h e m o d e l A l l d a t a w a s r e c o r d e d s i m u l t a n e o u s l y o n a m u l t i - c h a n n e l s t r i p c h a r t r e c o r d e r . M o t i o n i n f o r m a t i o n was r e c o r d e d o n l y a f t e r t h e c a r r i a g e a n d m o d e l h a d b e e n r u n n i n g a t a c o n s t a n t speed f o r a s u f f i c i e n t l e n g t h o f t i m e t o i n s u r e s t e a d y state c o n d i t i o n s . T h e i n f o r m a t i o n r e c o r d e d was a n a l y s e d m a n u a l -l y b y a v e r a g i n g t h e v a -l u e s . f o r t e n c o n s e c u t i v e cycles o f m o t i o n . F o r t h e w a v e h e i g h t m e a s u r e -m e n t t h e phases r e l a t i \ - e t o t h e -m o t i o n s w e r e a d j u s t e d to c o m p e n s a t e f o r t h e d i s t a n c e b e t w e e n t h e wa\-e p r o b e l o c a t i o n a n d t h e m o d e l c e n t r e o f g r a v i t y . T h e m e a s u r e d a m p l i t u d e a n d p h a s e c h a r a c t e r i s t i c s f o r speeds c o r r e s p o n d i n g t o t h e f u l l scale t r i a l c o n d i t i o n s w e r e olDtained b y i n t e r -p o l a t i o n . T h e y are -p l o t t e d i n F i g u r e 3. 4 C a l c u l a t i o n s T h e m o t i o n s o f t h e s h i p w e r e c o m p u t e d as a f u n c t i o n o f w a v e l e n g t h f o r t h e v a r i o u s speeds c o n s i d e r e d i n t h e f u l l scale tests. T h i s c o m p u t a t i o n is a c c o m p l i s h e d b y : 1. e v a l u a t i n g t h e t w o - d i m e n s i o n a l d a m p i n g a n d a d d e d mass a t v a r i o u s l o c a t i o n s a l o n g t h e s h i p b y m e t h o d s f r o m [ 5 , 6, 7 ] , 2. a p p l y i n g a m o d i f i e d f o r m o f s t r i p t h e o r y [ 8 , 9, 10] t o o b t a i n t h e c o e f f i c i e n t s o f t h e e q u a -t i o n s o f m o -t i o n , 3. a d e t e r m i n a t i o n o f t h e e x c i t i n g forces (so-c a l l e d r i g h t - h a n d side o f t h e e q u a t i o n ) a n d 4. t h e s o l u t i o n o f t h e c o u p l e d d i f f e r e n t i a l e q u a -t i o n s o f m o -t i o n . T h e e q u a t i o n s o f m o t i o n f o r h e a v e a n d p i t c h a r e : ggVz = F lyyQ = M
(1)
w h e r e : z a n d 0 are t h e h e a v e a n d p i t c h d i s p l a c e m e n t s , F a n d M are the_ t o t a l f o r c e a n d m o m e n t a c t i n g o n t h e s h i p . i ^ a n d A / e a c h are d e c o m p o s e d i n t h r e e p a r t s w h i c h a r c e v a l u a t e d b y i n t e g r a t i n g t h e c r o s s - s e c t i o n a l v a l u e s o\'er t h e l e n g t h o f t h e s h i p :M=^ ~l\Fi'+F2'+Fs')xbdxb (2) T h e c r o s s - s e c t i o n a l v a l u e s are f o u n d b y u s i n g t h e s t r i p t h e o r y , t a k i n g i n t o a c c o u n t t h e e f f e c t s o f f o r w a r d s p e e d . F o r a r i g h t h a n d c o o r d i n a t e s y s t e m (see F i g u r e 4 f o r d e f i n i t i o n o f w a v e a n d s h i p m o t i o n s ) t h e f o l l o w i n g expressions f o r F' c a n b e f o u n d : Fl' = -2egy,„{z-Xb6-l:*) F2' = -N'{z-XbÖ+VO-C*) Fs' = ~^^{m'{z~XbÓ+V6~C*)} (3) o r : F,' = ^m'{z-XbÖ + 2VÓ.--C*) + dm' + V~-{z-Xb&^VO~C*) dXb w h e r e : V t h e f o r w a r d speed o f t h e s h i p jw t h e h a l f w i d t h o f t h e w a t e r l i n e m' t h e s e c i o n a l a d d e d mass N' t h e s e c t i o n a l d a m p i n g c o e f l i c i e n t a n d : = C ( l - 7 I'y.e'^^dzb) T t h e d r a u g h t o f a s e c t i o n C t h e \ - e r t i c a l d i s p l a c e m e n t o f t h e w a t e r s u r f a c e T h e e x p r e s s i o n f o r 4"* n i a y be w r i t t e n i n t h e f o l l o w i n g f o r m : w h e r e T* is d e t e r m i n e d f r o m : 1 k • T* = - -Ig I yoe'-^dzb) A n u m e r i c a l a n a l y s i s s h o w e d t h a t T* is a p p r o x i -m a t e l y e q u a l t o t h e -m e a n d r a f t f o r f u l l cross-s e c t i o n cross-s : t h u cross-s : T* i=ü , w h e r e is t h e cross-section a r e a . 2yw T h e e q u a t i o n s o f m o t i o n are u s u a l l y w r i t t e n i n t h e f o r m o f t w o c o u p l e d s e c o n d o r d e r d i f f e r e n t i a l e q u a t i o n s w i t h f r e q u e n c y d e p e n d e n t c o e f f i c i e n t s , n a m e l y : {a + o\')z + hz + cz~-dd-ed-gO = FaCOs{(0et + S,,^) (A+Iyy) ë + BÓ + Cd-Dz-Ez-Gz F r o m ( 1 ) , ( 2 ) a n d ( 3 ) i t f o l l o w s t h a t a = ƒ m'dxb ' L d = ƒ m'xbdxb b = j N'dxb L e = \N'xbdxb~ Vm c = QgAw g = Qg^v)— Vb A = f rn'xb'dxb D = / m'Xbdxb L L B = /" N'xb^dxb E = IN'xbdxb+Vm L = oglw-VE G = QgSw a n d : Fa cos £^., /- cos kXb , -y . ~-= + 2 ^ 0 / Jio e dxi Qa Sin E/;. L s m k.Vb , cos kxb s i n k.Vft -co{vi + kV) f m' e~'-'^' "7 7'" dxb + f Ar/ AT- s m kXb , j cos kxb Ma cos s^i^ Ca s i n E^j. ' _ J., cosA-.Vó -"Qg JtoXbe . , dXb -r L s m KXb L Sin kXb f sin kxb , L cos kxb L cos kXb
I n these expressions t h e s e c t i o n a l a d d e d mass a n d t h e s e c t i o n a l d a m p i n g c o e f f i c i e n t N' a c c o r d i n g t o T a s a i ' s m e t h o d , w e r e used [ 6 ] . I n t h i s m e t h o d t h e cross-sections o f t h e s h i p are a p p r o x i m a t e d o n l y b y a t w o c o e f f i c i e n t t r a n s f o r m a t i o n o f t h e u n i t c i r c l e . T h e c a l c u l a t i o n s w e r e c a r r i e d o u t f o r t w o r a d i i o f g y r a t i o n : kyyjLpp = .233 a n d kyyjLpp = . 2 5 9 , t o s h o w t h e i n f l u e n c e o f t h i s p a r a -m e t e r o n t h e -m o t i o n c h a r a c t e r i s t i c s . T h e s h i p v a l u e s l i e w i t h i n t h i s r a n g e . T h e r e s u l t s w i t h r e g a r d t o m o t i o n a m p l i t u d e s a n d phases are s h o w n i n F i g u r e 3 f o r c o m p a r i s o n w i t h t h e m o d e l ex-p e r i m e n t s a n d t h e f u f l scale tests. 5 D i s c u s s i o n s T h e a g r e e m e n t b e t w e e n m o d e l e x p e r i m e n t a n d c a l c u l a t i o n , b o t h w i t h r e g a r d to a m p l i t u d e s a n d phases, is g o o d . T h e o n l y d i f f e r e n c e o f a n y s i g n i f i
-c a n -c e o -c -c u r s i n t h e h e a v i n g m o t i o n b e t w e e n t h e w a v e l e n g t h r a t i o s o f Z / / = 1.4 t o Lj). = 1.1. T h i s d i f f e r e n c e is also s u p p o r t e d b y c o m m e r c i a l m o d e l tests o n t h e s a m e s h i p f o r m . I t s h o u l d be o b s e r v e d , h o w e \ e r , t h a t i n t h i s r a n g e t h e m o d e l test a n d f u l l scale r e s u l t s c h e c k p a r t i c u l a r l y w e l l . W h i l e t h e e x p e r i m e n t does n o t p r o v i d e d i r e c t e v i d e n c e as t o t h e r e a s o n f o r t h i s d i f f e r e n c e , t h e e x p e r i m e n t a l r e s u l t s a r e i n e v e r y case so s t r o n g l y l i n e a r as t o p r a c t i c a l l y e l i m i n a t e l a c k o f l i n e a r i t y as a p r o b a b l e cause. T h i s s m a l l d i f f e r e n c e does n o t o c c u r f o r p i t c h . T h e f l i l l scale r e s u l t s as e x p e c t e d s h o w m o r e s c a t t e r t h a n t h e m o d e l tests, T h i s s c a t t e r increases w i t h i n c r e a s i n g w a v e l e n g t h a n d m a y be p a r t l y d u e t o a b r o a d e n i n g o f s t a t i s t i c a l c o n f i d e n c e l i m i t s f o r t h e l o n g e r w a v e c o m p o n e n t s associated ^ v i t h t h e r e l a t i v e l y s h o r t w a v e r e c o r d s a n d t h e l o n g e r w a v e p e r i o d s . I t is o f i n t e r e s t t o n o t e t h a t t h e t r a n s f o r m a t i o n o f t h e wa\-e h e i g h t f r o m b u o y t o s h i p l o c a t i o n is t h e o n l y step o f a n o t h e r w i s e d e t e r m i n i s t i c e x p e r i m e n t i n w h i c h s t a t i s t i c a l m e t h o d s are e m p l o y e d . O t h e r possible sources o f e r r o r are t h e u n c e r t a i n t y i n t h e f r e q u e n c y t r a n s f o r m a t i o n o f t h e w a \ e s p e c t r u m d u e t o b u o y d r i f t a n d e r r o r s i n t h e s h i p speed l o g , a n d d i r e c t i o n a l s p r e a d o f t h e sea^vay i t s e l f W h i l e t h e r e a r e d i f f e r e n c e s b e t w e e n f u l l scale a n d m o d e l results, t h e a g r e e m e n t as a w h o l e is v e r y g o o d a n d t h e r e a r e n o d i f f e r e n c e s w h i c h e x c e e d t h e possible m e a s u r e m e n t e r r o r . A n i m p o r t a n t c o n s i d e r a t i o n , hoNvever, is t h e t r a n s f o r m a t i o n used t o a p p r o x i m a t e the s h i p cross sections s i n c e the a c c u r a c y o f the- c o m p u t a t i o n is p a r t i c u l a r l y s e n s i t i v e t o errors i n t h e cross s e c t i o n t r a n s f o r m a t i o n . F o r t h i s p a r t i c u l a r s h i p t h e L e w i s o r t^vo c o e f f i c i e n t t r a n s f o r m a t i o n p r o v i d e s a n e x c e l l e n t fit f o r e a c h s e c t i o n . T h i s , h o w e v e r , is g e n e r a l l y n o t t r u e f o r a r b i t r a r y s h i p cross sections a n d f o r m a n y s h i p s a g r e a t e r n u m b e r o f c o e f f i c i e n t s \\'\\\ be r e q u i r e d t o o b t a i n r e q u i r e d a p p r o x i -m a t i o n , 6 C o n c l u s i o n s T h e use o f m o d i f i e d s t r i p t h e o r y l o r t h e c o m p u t a t i o n o f s h i p m o t i o n s i n p i t c h a n d h e a v e is c o n -firmed b y t h i s c o m p a r i s o n o f f u l l scale, m o d e l a n d c o m p u t e d results, A d i r e c t c o r r e l a r y o f t h i s c o n -firmation is t h e d e s i r e d \ a l i d a t i o n o f F r o u d e s c a l i n g f o r g e o m e t r i c a l l y s i m i l a r s h i p f o r m s o v e r a b r o a d r a n g e o f speeds a n d w a v e l e n g t h s . I t f u r t h e r c o n f i r m s p r e v i o u s e x p e r i m e n t a l results w l i i c h s h o w t h a t m o t i o n l i n e a r i t y is q u i t e g o o d . T h e v a r i a t i o n o f t h e m o t i o n s w i t h c h a n g e s i n t h e r a d i u s o f g y r a t i o n (mass m o m e n t o f i n e r t i a i n p i t c h ) is s m a l l b u t p r e d i c t a b l e f r o m m o d i f i e d s t r i p t h e o r y . A g r e e m e n t b e t w e e n t h e m e a s u r e d a n d c o m -p u t e d m o t i o n s is s u f f i c i e n t l y g o o d , e s -p e c i a l l y i n p i t c h , as t o suggest t h e p o s s i b i l i t y o f a n e x t e n s i o n o f s t r i p t h e o r y m e t h o d s t o i n c l u d e t h e c o m -p u t a t i o n o f b e n d i n g m o m e n t s . 7 A c k n o w l e d g e m e n t T h i s w o r k was possible t h r o u g h t h e c o o p e r a t i o n o f t h e R o y a l N e t h e r l a n d s N a v y . P a r t i c u l a r a p p r e -c i a t i o n is expressed f o r t h e w i l l i n g assistan-ce o f t h e - O f f i c e r s a n d c r e w o f H . M . G r o n i n g e n . T i m e l y c o m p l e t i o n o f t h e p r o j e c t was m a d e possible b y t h e e n t h i o u s i a s t i c assistance o f t h e S h i p b u i l d i n g f ^ a b o r a t o r ) ' S t a f l ^ T h e e x c e l l e n t p r o g r a m m i n g a n d m a c h i n e c o m -p u t a t i o n assistance -p r o v i d e d b y t h e ^ V i s k u n d i g e D i e n s t ( C o m p u t e r D e p a r t m e n t ) is g r c a t f u l l y a c k n o w l e d g e d . R e f e r e n c e s
1. V . G. .SZEDEHELY, M . D. BLEDSOE, G. P. STEEUX,
".Scale Effects in Seaworthiness", David Taylor Model Basin Report No, 1070, 1956.
2. J. GERRITSMA, "Seaworthiness Tests with Three Geo-metrical Similar Ship Models", Symposium on the Behaviour of Siiips in a Seaway, AVageningen 1957.
3. H . J . S. CANH.^N, D. E. C.\RT\vRiGHT, G.J. GOODRICH,
N . HoGBEN, "Seakeeping Trials on O.W.S, \Veather Reporter", Transactions Royal Institute of Naval Architects 1962.
4. Jlf. D . BI.EDSOE, O. BUSSEM.\KER, VV, E, CUM.MINS,
"Sea-keeping Trials on Three Dutch Destroxers", Trans-actions Society of Naval .Architects and Afarine Engineers, 1960.
5. F. URSELL, " O n the Heaving M o t i o n of a Circular Gvlinder on the Surface o f a F l u i d " , Quarterlv Jour-nal Mech. and Applied' M a t h . V o l . t f PT 2 1949. 6. F, TASAI, " O n the Damping Force and Added Mass of Ships Heaving and Pitching", Report of Research institute for .'Applied Mechanics, Kvusliu University 1960.
7. \V, R. PORTER, "Pressure Distribution, Added Mass and Damping Coefficients for Cylinders Oscillating in a Free Surface", University of Caliibrnia, fnstitute of Engineering Research, Series 82, 1960.
8. B. V , KORVIN-KROUKOVSKY, \V, R. JACOBS, "Pitching
and Heaving Motions of a Ship in Regular Waves", Transactions Society of Naval Architects and Afarine Engineers, 1957.
9. Y . WATAN.ABE, " O n the Theory of Pitch and Heate o f a Ship", Technologv Reports o f t h e Kyushu Univei'sity, V o l . 31, 1958 I Translation Y. Sonoda 1963~.,
10. J. GERRITSMA, W. BEUKEL.\I,\.N, "Distribution of the
Hs'drodynainic Forces on a f-Iea\irig and Pitching Sliip Model in .Still Water", international .Ship-building Progress 1964,
N O M E N C L A T U R E
abcdeg 1 Coefficients of tlie equations of motion for
A BCD EG Jhea.ve and pitcli A^u Area of waterplane Aj. Area of cross-section Cb Block coefficient
F T o t a l force on sliip
Fl, F^', F,' Sectional liydromeciianical forces Fg . Wave force amplitude on restrained ship
V
VgLp
Froude number
Wave number
g Acceleration due to gravity
Longitudinal moment of inertia of waterplane area w i t h respect to the j ' ^ axis
rj,,, Real moment of inertia of ship
271 ' - 1
. Length over all
Ljjp Length between perpendiculars
M T o t a l moment on ship
Mg . ^Vave moment amplitude on restrained ship
m T o t a l added mass for heave m' Sectional added mass
A''' Sectional damping coefficient
S Spectral density
5'^, Statical moment of waterplane area / T i m e
T Draught of ship
V. Speed of ship
•^•(ijj'ii! ~b Right-handed bod\' axis system
y„{x) H a l f w i d t h of designed waterline
2 Heave displacement
Zg Heave amplitude
£ Phase angle between the motions (forces, moments) and the waves
J fnstantaneous wave elevation Wave amplitude 0 Pitch angle Qg Pitch amplitude A Wave lengtii Q Density of water V Displacement volume CO Circuiar frequency
M O D E L 1 7 0 0 ^
RUN 13 ' RUN 15 F n = . 3 6 V=11.79rT/sec = .U V = U . 9 9 m s e c 9 5 3 2 1.5 1.0 0.75 9 5 3 2 1.5 ^0
V L V L
— RUN 19 Fn = . 2 8 ' • V= 9.22 m sec 0 0.5 1.0 1.5 2.0 Ol)^ ^ sec-'' 1 1 1 1 1 1 t I _ J 9 7 5 3 2 1.5 1.0V L
RUN 1 Fn = .18 V=11.68 K n . 0,5 H E A V E H E A V E P H A S E P I T C H P H A S E
O FULL SCALE TRIAL • MODEL EXP. k ^ y L . 0 259
CALCULATION k ^ V L . 0 . 2 5 9 CALCULATION l< ^ , y L . 0 23t
I 1
0.5 1.0 1.5 2.0
RUN 11 RUN 19 RUN 4
Fn = .18 V=11.68Kn. Fn = .28 V=17.92 Kn. F n = .31 V = 20.22 Kn. _ 0.5 _ 3 6 0 H E A V E H E A V E P H A S E P I T C H P H A S E O F U L L S C A L E T R I A L • M O D E L E X P , / L . O 259 C A L C U L A T I O N it^^^Lm02'" . - CALCULATION f / L . 0 , 2 0.5 1.0 L A -1.5 2.0 0,5 H E A V E P I T C H H E A V E P H A S E
FULL SCALE TRIAL MODEL EXP k ^ y L i 0 , 2 • CALCULATION k ^ ^ L . 0 259 • CALCULATION k ^ ^ ^ L . 0 , 2 3 t - 1 _ 0.5 1.0 L A -1.5 2.0 ^ . ^ 0.5 - 1 8 0 H E A V E ° o
^
" O T O A O ^ 1 1 ~ -P I T C H o 0 \ , O . oV° \
1 1 H E A V E P H A S E•
1 , P I T C H P H A S E J \ \ \ \O FUlU SCALE TRIAL \ \ • MODEL EXP, k ^ ^ A . 0 , 2 5 3 Ï - CALCULATION k V L »0 259 \ CALCULATION k J J J ^ L . 0.334 V.
1 1 1
0 0.5 1.5 2.0
V - s h i p s p e e d C - w a v e c e l e r i t y w a v e - £ = ( ^^0"*"^*^) ^ ^^iCos{{i)Q t ) h e a v e - z = cos (oJ e t + E z ^ ) p i t c h - e = e a c o s ( o j e t + G g ^ ) t.o.v. X O Y O Z Q t.o.v. x y z , x = o COp= (JÜ + - ^ X Xo
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