Davidson K S M.turning Steering of .1944.TRANS

8/10/2019 Davidson K S M.turning Steering of .1944.TRANS

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On the Turn ing and Steer ing of Sh ips

B Y K E N N E T H S . I X{ . D A V I D S O N , / ~ E M B E R 1

S h i p s h a v e b e e n t u r n e d a n d s t e e r e d w i t h r e a s o n -

a b l e s u c c e ss fo r c e n t u ri e s . Y e t , a s r e c e n t l y a s

1 9 23 , S i r A r t h u r J o h n s r e f e r r e d t o t h e s t u d y o f

t u r n i n g a n d s t e e r i n g a s " a g e n e r a l l y n e g l e c te d

p o r t i o n o f n a v a l a r c h i t e c t u r e " [ 1] . 2 T o b e s u r e ,

t h e l i t e r a t u r e o n t h e s e s u b j e c t s h a s b e e n a u g -

m e n t e d i n t h e t w e n t y y e a r s s i n c e 1 9 2 3, [ 2] [3 ] [6 ]

[ 11 ] a n d o t h e r s . T h e f a c t r e m a i n s , h o w e v e r , t h a t

i t h a s n o t y e t b e c o m e p o s si b le t o p r e d i c t t u r n i n g

a n d s t e e r i n g c h a r a c t e r i s t i c s w i t h a s s u r a n c e i n t h e

p r e l i m i n a r y d e s i g n s t a g e .

T h e s i t u a t i o n i s n o t u n l i k e t h a t w h i c h w o u l d

e x i s t w i t h r e g a r d t o r e s i s t a n c e a n d e f f e c ti v e h o r s e -

p o w e r e s t i m a t e s , i f c o d i f ie d e x p e r i m e n t a l r e s u l t s

l i k e t h o s e f o r T a y l o r ' s S t a n d a r d S e r i e s o f h u l l

f o r m s [ 4] h a d n e v e r b e e n w o r k e d o u t . T h e S t a n d -

a r d S e r ie s d a t a p r o v i d e a c o o r d i n a t e d f r a m e w o r k

o f q u a n t i t a t i v e i n f o r m a t i o n o n re s i s t a n c e w h i c h

b r i n g s o u t c l e a r l y t h e r e l a t i v e i n f lu e n c e o f t h e p r i n -

c i p al g o v e r n i n g v a r i a b l e s , a n d f r o m w h i c h r e l i a b le

e s t i m a t e s c a n b e m a d e fo r n e w d es i gn s . L a c k i n g

a c o r r e s p o n d i n g f r a m e w o r k o f q u a n t i t a t i v e i n -

f o r m a t i o n o n t u r n i n g a n d s t e e r i n g , t h e d e s i g n e r

f i n d s h i m s e l f i n a p o s i t i o n w h e r e , a s o n e n a v a l

a r c h i t e c t p u t i t r e c e n t l y , " I t i s o n e t h i n g t o p r o -

g r e ss f r o m o n e d e s i g n t o t h e n e x t , o n t h e b a s i s o f

a c c u m u l a t e d e x p e r i e n c e , a n d q u i t e a n o t h e r t o ' h i t

i t o n t h e n o s e ' e v e r y t i m e . "

1 Professor of Mechanic al Enginee ring and Director of Experi-

mental Towing Tank, S tevens Ins t i tu te of Technology, Hoboken,

N. J . ; Consul ta nt wi th David W. Taylor Model Bas in , Uni ted S tates

Navy Department ; Member , Subcommit tee on Seaplanes , Nat ional

Advisory Commit tee for Aeronaut ics .

Dr. Da vids on was born in Buffalo, N. Y. , on Februa ry 9, 1898.

He received the degree of Bachelor of Science in Mechanical Engi-

neer ing from the Massachuset t s Ins t i tu te of Technology in 1920.

In 1918, he was a Second Lieutenant, Pilot , in the Army Air Service.

From 1923 to 1929, he was engaged by the Crosby Steam Gage and

Valve Company as a research engineer and then as chief engineer.

In 1929 he came to Stevens, and in 1935 became the Director of the

Experimental Towing Tank. In 1944, he was awarded an honorary

degree of Doctor of Science by Stevens Insti tute of Technology.

Dr. Da vidson i s the author of numerous technical papers including,

" 'Some Experimental S tudies of the Sai l ing Yacht , " Transactions of

The Society of Naval Architects and Marine Engineers, 1936, for

which he won the first award of the Captain Joseph H. Linnard Prize

and he cont r ibuted the chapter on "Res i s tance and Powering" to

the book "Princip les of Naval Archi tecture. " He i s a member of The

Society of Naval Archi tect s and Marine Engineers , the Ins t i tu te of

the Aeronautical Sciences, and The American Society of Mechanical

Engineers.

2 Numbe rs in bracke ts design ate references l isted at the end of the

paper. No att emp t has been made to prepare a complete bibliog-

raphy on the subject , the references being essentially indicative of

avai lable mater ial.

T h i s p a p e r m a k e s n o p r e t e n s e o f p r o v i d i n g d e -

s i g n i n f o r m a t i o n . I t is e s s e n t i a l l y a p r o g r e s s r e-

p o r t o n m e t h o d s o f a t t a c k , d e a l i n g f i r st w i t h

b r o a d c o n c e p t s i n a n a t t e m p t t o g a i n p e r s p e ct i v e

o n t h e s co p e o f t h e p r o b l e m s i n v o l v e d , a n d

s e c o n d w i t h a n a l y t i c a l a n d e x p e r i m e n t a l p r o -

c e d u r e s a i m e d a t s i m p l i f y i n g a c o m p r e h e n s i v e

a t t a c k .

A t t e n t i o n i s c e n t e r e d l a r g e l y o n t h e i n f l u e n c e

o f t h e h u ll . T h i s is d o n e , n o t w i t h a n y t h o u g h t

t h a t t h e r u d d e r i s o f s e c o n d a r y i m p o r t a n c e i n f ix -

i n g t h e t u r n i n g a n d s t e e r i n g c h a r a c t e r i s t i c s , b u t

b e c a u s e ( 1) t h e r u d d e r i s b a s i c a l ly a n a p p e n d a g e ,

t h e d e s i g n o f w h i c h i s n e c e s s a r i ly g o v e r n e d b y t h e

j o b i t h a s t o d o , t h a t i s , b y t h e c h a r a c t e r i s ti c s o f

t h e h u l l t o w h i c h i t is a p p l i e d ; ( 2 ) a g o o d d e a l o f

r e l i a b l e i n f o r m a t i o n o n r u d d e r c h a r a c t e r i s t i c s i s

a l r e ad y av a i l ab l e , [ 2 ] [ 10] [ 11] an d o t he r s , , wh er ea s .

r e l a t i v e l y l i tt l e s y s t e m a t i c w o r k h a s b e e n d o n e o n

h u l l c h a r a c t e r i s t i c s . I n e f f e c t , t h e p o i n t o f v i e w is

a d o p t e d t h a t a b e t t e r k n o w l e d g e o f h u l l a c t i o n is a

p r e r e q u i s i t e t o a b e t t e r u n d e r s t a n d i n g o f r u d d e r

a c t i o n a n d , u l t i m a t e l y , o f i n t e r f e r e n c e e ff e c ts b e -

t w e e n h u l l , r u d d e r a n d p r o p e l le r s .

GEN ERAL CHARACTERISTICS OF THE TURN ING

MANEUVER

T h e g e n e ra l fe a t u r e s o f t h e t u r n i n g m a n e u v e r

a r e w e ll k n o w n . F i g . 1 r e f e r s t o t h e c o n v e n t i o n a l

m a n e u v e r o r d i n a r i l y u s e d f o r r e fe r e n c e p u rp o s e s ,

i n w h i c h ( 1 ) t h e s h i p a p p r o a c h e s o n a s t r a i g h t

c o u r s e a t a u n i f o r m s p e e d , w i t h f i x e d t h r o t t l e s e t -

t i n g s w h i c h a r e n o t a l t e r e d d u r i n g t h e m a n e u v e r ,

( 2) t h e m a n e u v e r i s c o n s i d e r e d t o b e g i n w i t h e x e -

c u t i o n o f t h e o r d e r t o l a y t h e r u d d e r , ( 3 ) t h e r u d d e r

i s l a id t o a p r e s c r i b e d a n g l e a t t h e m a x i m u m r a t e

p r o v i d e d b y t h e s t e e r in g e n g i n e a n d i s n o t s u b s e -

q u e n t l y a lt e r e d d u r i n g t h e m a n e u v e r . W i t h t h e s e

r e s t ri c t io n s , i t h a s b e e n f o u n d t h a t f o r p r a c t i c a l l y

a l l t y p e s o f s e a g o i n g v e s s e l s :

( a ) A s u b s t a n t i a l l y s t e a d y s t a t e o f t u r n i n g

m o t i o n c a n b e e x p e c t e d t o e s t a b l i sh i t s el f, r o u g h l y

w i t h i n t h e f i rs t q u a d r a n t o f t h e t u r n , t h e s h i p

287


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3/38

ON THE TUR NIN G AND STEE RIN G OF SHIPS 289

80Bcmk

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Ficjhfer

Tra mspo r+ Sh ip

AirpI~ne Airplane

5Bamk

Ce .n-~rif:uojal Ac ce l. .09 ~ O.04oj-

t.)

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C a ) ( b )

No+e:

Forces Propo~+~om(xl +o Accelerc~fions

L = 4 0 F ~ . L = I 0 0 F t. L = 4 0 0 F + ,

v : 4 o o M . ~ . H . v : Z O O M .~ . H. V : I ~ K + s .

v/TE : ss (v i~ K~o+~) 7 E: ~ 4 (v i~ K~o+~) 7V[ = 0.8

% - 9 o y ~ s 4 o /~ = 3

FIG. 2.- -~OMPARATIVE 1V~INIMUM TURNING CIRCLES OF AIRPLANES AND SHIPS, SHOWING THE GREAT EFFECT OF SPEED

ON THE I~ESULTANT ACCELERATION IN TURNING

swinging thereafter at constant angular velocity

about a fixed center, at a uniform turning speed

less than the approach speed.

(b) A trans ient phase occurs at the start, dur-

ing which the instant aneous turning radius dimin-

ishes from infinity to the steady-turning value and

the instantaneous speed diminishes from the ap-

proach to the steady-turning value.

Fig. 1 has been drawn with some care to show to

scale a typical minimum-diameter turn (with

maximum rudder angle) for a normal seagoing

vessel having good turning characteristics by

present-day standards. The term "good" is ap-

plied to these characteristics primarily because the

tactical diameter is only three times the length

of the ship

(T D /L

= 3), and this figure is rare ly

bettered in practice at the present time. Mini-

mum tactical diameter is a simple criterion by

which to compare the turning characteristics of

different vessels, and has been used widely for th e

purpose. Bu t the question natu rall y arises of

whether a tactical diameter of three lengths con-

stitutes really good turning, or whether it repre-

sents simply a mean of what has been accomplished

so far. This is rather a basic question, which de-

serves some attention.

The possibility suggests itself of getting a some-

what broade r view of the ques tion by comparing the

minimum turning circles of ships with t hose of air-

planes (Fig. 2). Airplanes and ships differ radically

in their overall configurations. Yet both are free

bodies moving through fluids, and, in general, have

to be turned as expeditiously as possible. Withou t

looking into the matter, it could easily be ima-

gined tha t airplanes might be found to have better

turnin g characteristics than ships. This, however,

is not the case. Airplanes have to tu rn in much

larger circles than ships--measured in terms of

length--sim ply because of the limitation imposed

by the permissible centrifugal force. In airplanes,

the centrifugal force caused by the high speed may

easily exceed the force of grav ity by a large mar-

gin, making heavy banking necessary--as also in

racing automobiles or even racing bicycles. In


4/38

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5/38

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FIG. ~ : . - -TURNI NG ~HARACTERISTICS AND ~PEED RECOVERY

The turnin g plots have proportions in accordance with the mean curves of Fig. 3; the speed recovery plots are computed.

N o t e :

(1) The turns shown represen t a geometric progression in tactical diameter, each turn being half again as large as the preceding turn.

(2) Spots show successive positions of the ship at uniform time inter vals equal to the time required to tra vel 2 ship lengths at V a / ' ~ / L = 1 .

(3) Steady- turning speed is assumed after the third time interval.

(4) Central angles show relative rates of change of heading in steady turning.

(5) Auxiliary speed-recovery plots show relative distances required for regain of speed (dotted portions ), and relati ve distances run in four time intervals after centering rudder (tot al length of

lines).

t ~


6/38


s h i p s, o n t h e o t h e r h a n d , w h i c h b y c o m p a r i s o n

t r a v e l a t l o w s p e e d s f o r t h e i r l e n g t h s , t h e c e n t r i f u -

g a l f o r c e d o e s n o t e x c e e d a f e w p e r c e n t o f t h e

w e i g h t , a s m a y b e s e e n i n F i g . 2. T h u s t h e a i r -

p l a n e d e s i g n e r n e e d n o t s t r i v e f o r v e r y s h o r t t u r n -

i n g , s i n c e c e n t r i f u g a l f o r c e w il l g o v e r n i n a n y c a s e ,

w h e r e a s t h e s h i p d e s i g n e r i s n o t g o v e r n e d b y t h i s

l i m i t a t i o n a n d s t i l l h o l d s t h e i n i t i a t i v e .

A m o r e p r o m i s i n g a p p r o a c h t o t h e q u e s t i o n o f

w h a t c o n s t i t u t e s r e a l l y g o o d t u r n i n g i n a s h i p c a n

b e m a d e , b e g i n n i n g w i t h a s o m e w h a t m o r e d e -

t a i l e d c o n s i d e r a t i o n o f F i g . 1 . T h e t a c t i c a l d i a m -

e t e r t h e r e s h o w n i s t h r e e l e n g t h s

(TD,/L

= 3) ,

a s p r e v i o u s l y n o te d . B u t , t h e sp e e d r e d u c t i o n is

l a r g e ( I ~ / V a = 0 . 5S ) , a n d t h e t r a n s i e n t p h a s e o f

t h e t u r n i n g p a t h i s l o n g ( A / T D = 0 . 9 9 ) . Ob -

v i o u s l y , a l e s se r s p e e d r e d u c t i o n a n d a s h o r t e r a d -

v a n c e w o u l d b e d e s i ra b l e i m p r o v e m e n t s - - i f t h e y

c o u l d b e o b t a i n e d . I t is t h e r e f o r e o f i n t e r e s t t o

l o o k i n t o t h e v a r i a t i o n o f t h e s e t w o a d d i t i o n a l

c h a r a c t e r i s t i c s o f t h e t u r n , a n d i n t o t h e i r f u n c -

t i o n a l c o n n e c t i o n ( if a n y ) w i t h t h e r a t i o o f t a c t i c a l

d i a m e t e r t o l e n g t h .

T h e c h a r t s o f F i g . 3 w e r e p r e p a r e d w i t h t h e s e

e n d s i n v i ew . T h e y s h o w d a t a d e d u c e d fr o m th e

t a c t i c a l t r i a ls o f a n u m b e r o f s hi p s a n d m o d e l s r e p -

r e s e n t i n g a v a r i e t y o f t y p e s o f a c t u a l s e a g o i n g

v e s s e l s o f g e n e r a l l y n o r m a l d es i g n . T h e r e i s a

s e p a r a t e c h a r t f o r e a c h o f t h e t w o r a t i o s m e n -

t i o n e d i n th e p r e c e d i n g p a r a g r a p h ,

s p e e d r e d u c t io n . . . . . . . . . . . . . . . . V J V~,

a d v a n c e t o t a c ti c a l d i a m e t e r . . . . . A / T D ,

a n d o n e f o r t h e l e s s i m p o r t a n t r a t i o

t r a n s f e r t o t a c t i c a l d i a m e t e r . . . . . T/TD.

A l l o f t h e c h a r t s a r e p l o t t e d t o t h e s a m e s c a l e o f

a b s c i s s a e; n a m e l y , th e r a t io

t a c t i c a l d i a m e t e r to l e n g t h . . . . . . TD/L .

T h e w i d e l a te r a l s p r e a d o f t h e c h a r t s i s d u e m a i n l y

t o t h e f a c t t h a t d a t a a r e g i v e n f o r t h r e e r u d d e r

a n g l e s , u s u a l l y 3 5 , 2 5 a n d 1 5 d e g r e e s , a n d t h e s e a r e

n a t u r a l l y d i s t r i b u t e d a c r o s s t h e c h a r t s s i n c e , i n

a n y g i v e n c a s e, a r e d u c t i o n o f r u d d e r a n g l e r e s u l t s

i n a n i n c r e a s e o f t a c t i c a l d i a m e t e r . A l s o , t h e

d i f f e r e n t d e s i g n s s h o w n h a v e d i f f e r e n t m i n i m u m

r a t i o s of t a c t i c a l d i a m e t e r t o . l e n g t h ( a t m a x i m u m

r u d d e r a n g l e ) , a n d i n m a n y c a s e s d a t a a r e g i v e n

f o r t w o o r m o r e s p e e d - l e n g t h r a t io s . T h u s t h e

c h a r t s d o n o t i n a n y w a y i n d i c a t e t h e r e l a t i o n s h i p

b e t w e e n t a c t i c a l d i a m e t e r a n d r u d d e r a n g l e f o r

i n d i v i d u a l d e si g n s ; t h e y m e r e l y c o m p a r e t h e

v a r i o u s o t h e r f a c t o r s i n v o l v e d i n t u r n i n g , o n t h e

b a s i s o f t a c t i c a l d i a m e t e r .

I t w i l l b e s e e n t h a t t h e f o r m o f p l o t t i n g i n v o l v e s

o n l y d i m e n s i o n l e s s r a t i o s , s o t h a t d i f f e r e n c e s o f

a b s o l u t e s i ze , w h e t h e r o f s h i p o r t u r n , a r e e l i m -

i n a t e d , a n d t h e se v e r a l c h a r a c t e r i s ti c s a r e c o m -

p a r e d o n a p u r e l y g e o m e t r i c b a s i s. A s p e e d r a t i o

m a y n o t o r d i n a r i ly b e t h o u g h t o f a s a m a t t e r o f

g e o m e t r y ; i n t h i s i n s t an c e , h o w e v e r , i n t e r e s t

c e n t e r s n o t s o m u c h i n t h e r e l a ti v e s p e e d s t h e m -

s e lv e s a s in t h e r e l a t i v e d i s ta n c e s t r a v e r s e d a l o n g

t h e p a t h i n e q u a l t i m e i n t e r v a l s ( t h e r e l a t i v e d i s -

t a n c e s b e t w e e n t h e s u c c e s s i v e p o s i t i o n s i n F i g . 1 ,

f o r e x a m p l e ) , a n d t h e s e a r e c l e a r l y a m a t t e r o f

g e o m e t r y .

I t i s a p p a r e n t a t o n c e t h a t F i g . 3 ef f e ct s r e a s o n -

a b l y g o o d c o rr e l a t io n o f t h e t e s t d a t a , a n d t h u s i n -

d i c a t e s g e n e r a l f u n c t i o n a l r e l a t i o n s h i p s t o a f a i r l y

g o o d f ir s t a p p r o x i m a t i o n . I t is t r u e , o f c o u r s e ,

t h a t t h e s c a t t e r o f i n d i v i d u a l p o i n t s f r o m t h e

m e a n c u r v es d r a w n t h r o u g h t h e m is o f t en a s m u c h

a s 10 p e r c e n t , a n d i n s o m e c a se s m o r e . B u t t h i s

i s s c a r c e l y s u r p r i s i n g i n v i e w o f t h e v a r i e t y o f t h e

d e s ig n s i n c lu d e d , a n d t h e f a c t t h a t t h e p o i n t s r e p -

r e s e n t t e s t s a t v a r i o u s r u d d e r a n g l e s a n d s p e e d -

l e n g t h r a t i o s , p l o t t e d w i t h o u t r e g a r d t o t h e v a l u e s

o f t h e s e v a r ia b l e s . I f t h e r e is a n y t h i n g s u r p r i si n g

a b o u t t h e c h a r t s , i t w o u l d s e e m t o b e t h a t t h e

s c a t t e r is n o t g r e a t e r t h a n i t is . A s a m a t t e r o f

f a c t , h o w e v e r , d i s c r e p a n c i e s i n t u r n i n g c h a r a c t e r -

i s t i c s o f t h e o r d e r o f 1 0 p e r c e n t a r e w e l l w i t h i n

t o l e r a b le l i m i t s f o r m o s t p r a c t i c a l p u r p o s e s , s o t h a t

t h e m e a n c u r v e s m a y b e s a i d t o p r o v i d e a r e a s o n -

a b l y g o o d p i c t u r e o f t h e i n t e r r e l a t i o n s h i p o f t h e

s e v e r a l r a t i o s f o r t h e a v e r a g e s e a g o i n g v e s s e l o f

g e n e r a l l y n o r m a l d e s i g n .

I t a p p e a r s , t h e n , t h a t f o r n o r m a l s e a g o i n g v e s -

s e l s , t h e s p e e d r e d u c t i o n i n t u r n i n g ( l / ~ / V ~ ) a n d

t h e r e l a t iv e l e n g t h o f t h e a d v a n c e

(A /TD)

a r e

g o v e r n e d p r i m a r i l y b y t h e r a t i o o f t a c t i c a l d i a m -

e t e r t o l e n g t h

(TD/L) ,

a n d a r e n o t m a t e r i a l l y

a f f e c t e d b y d i f f e r e n c e s o f d e s i g n w i t h i n t h e l i m i t s

o f w h a t m a y b e c a ll e d n o r m a l d e s ig n i n g . T h u s

t h e l a r g e s p e e d r e d u c t i o n s h o w n b y F i g . 1 ( t o

a b o u t 6 0 p e r c e n t o f t h e a p p r o a c h s p e e d ) a n d t h e

c o n s i d e r ab l e l e n g t h o f t h e a d v a n c e ( a b o u t e q u a l t o

t h e t a c t i c a l d i a m e t e r ) h a v e t o b e c o n s i d e r e d t h e

m o r e o r l e s s i n e v i t a b l e c o n s e q u e n c e s o f r e d u c i n g

t h e t a c t i c a l d i a m e t e r t o t h r e e l e n g t h s , w h i l e F i g .

3 sh o w s c l e a r l y t h a t f u r t h e r r e d u c t i o n o f t h e t a c t i-

c a l d i a m e t e r b e c o m e s i n c r e a s i n g l y c o s t l y i n r e -

s p e c t t o b o t h s p e e d r e d u c t i o n a n d a d v a n c e . I t i s

t h e r e f o r e n a t u r a l t o e n q u i r e w h e t h e r , u n d e r t h e s e

c i r c u m s t a n c e s , f u r t h e r r e d u c t i o n o f th e t a c t i c a l

d i a m e t e r w o u l d b e w o r t h w h i l e , e v e n a s s u m i n g i t

p o s s i b l e .

F i g . 4 h e l p s t o t h r o w a d d i t i o n a l l i g h t o n t h i s

m a t t e r b y g i v i n g a v i s u a l i m p r e s s i o n o f a se r ie s o f

t u r n s c o r r e s p o n d i n g i n t h e i r p r o p o r t i o n s t o t h e


7/38

O N T H E T U R N I N G A N D S T E E R I N G O F S H I P S 2 9 3

m e a n c u r v e s o f F i g . 3. T h e s e r ie s c o m p r i s e s a

g e o m e t r i c p ro g r e s s io n i n t h e v a l u e o f t h e r a t i o o f

t a c t i c a l d i a m e t e r t o l e n g t h b e g i n n i n g w i t h a m i n i -

m u m o f t w o - - i n o t h e r w o r d s , w i t h a v a l u e w e ll

b e l o w t h e m i n i m u m o r d i n a r i l y r e a c h e d i n a c t u a l

s h ip s a t t h e p r e s e n t t im e . I t w i ll b e s ee n t h a t a s

t h i s r a t i o d i m i n i s h e s t h e r e i s p r o g r e s s i v e i m p r o v e -

m e n t , a ll t h e w a y d o w n t o t h e t w o - l e n g t h t u r n , n o t

o n l y in t h e t a c t i c a l d i a m e t e r i ts e l f, b u t a l s o i n

( a ) t h e a d v a n c e ( i ts e l f, n o t i n t h e r a t i o A /T D ) ,

( b ) t h e t o t a l a n g l e s w u n g t h r o u g h i n a g i v e n

t o t a l t i m e f ro m " e x e c u t e , "

( c) t h e t i m e r a t e o f c h a n g e o f a n g le ( h e a d i n g ) i n

s t e a d y t u r n i n g .

I n t h e s e re s p e c t s , t h e n , a m i n i m u m t u r n o f t w o

l e n g t h s w o u l d o b v i o u s l y b e s u p e r i o r t o . o n e o f

t h r e e l e n g t h s ( a s su m i n g , o f c o u r s e, t h a t i n c i d e n t a l

q u e s t i o n s s u c h a s e x c e s s iv e h e e l o r v i b r a t i o n d i d

n o t b e c o m e p r o m i n e n t ) .

I n r e s p e c t t o t h e s p e e d r e d u c t i o n , t h e t w o -

l e n g t h t u r n a p p e a r s a t f i r s t s i g h t t o b e d i s t i n c t l y

i n f e ri o r t o t h e t h r e e - l e n g t h t u r n . H e r e t h e d i ff e r-

e n c e i s l a r g e w h e n e x p r e s s e d i n t h e f o r m u s e d i n

F i g . 3 ; n a m e l y , V J Va = 0 . 3 9 f o r a t w o - l e n g t h

t u r n , a s o p p o s e d t o Vt/I~ = 0 . 5 8 f o r a t h r e e -

l e n g t h t u r n - - p r a c t i c a l l y i n t h e r a t i o o f 2 t o 3 .

B u t , a s h a s a l r e a d y b e e n e m p h a s i z e d , r e l a t i v e

s p e e d s a r e n o t i n t h e m s e l v e s o f m u c h i n t e r e s t ; o f

m u c h m o r e i m p o r t a n c e a r e t h e r e l a t i v e o v e r a l l

d i s t a n c e s c o v e r e d i n e q u a l t i m e in t e r v a l s . I n t h e

p r e s e n t i n s t a n c e , a g o o d i n d e x s h o u l d b e t h e r e l a -

t i v e d i s t a n c e s r u n o n s t r a i g h t c o u r s e d u r i n g t h e

p e r i o d o f s p e e d r e c o v e r y , s u p p o s i n g t h e r u d d e r t o

b e c e n t e r e d a f t e r t h e s h i p h a s t u r n e d f a r e n o u g h

t o b r i n g a b o u t t h e e n t i r e r e d u c t i o n t o s t e a d y -

t u r n i n g s p e e d , a n d t h e t h r o t t l e s e t t i n g s t o r e m a i n

u n a l t e r e d . T h e s e re l a t i v e d i s t a n c e s c a n b e es ti -

m a t e d w i t h s u f f ic i e n t a c c u r a c y f o r t h e p r e s e n t p u r -

p o s e b y a s s u m i n g t h a t t h e p o r t i o n o f t h e t h r u s t

t h a t h a s b e e n w o r k i n g a g a i n s t t h e i n c r e a s e o f

d r a g d u e t o t u r n i n g b e c o m e s a v a i la b l e t o a c c e l e r a t e

. t h e s h i p t o i ts o r i g i n a l a p p r o a c h s p e e d , a n d g o i n g

t h r o u g h m u c h t h e s a m e p r o c e s s a s i s d i s c u s s e d

l a t e r f o r t h e c o m p u t a t i o n o f s p e e d re d u c t i o n .

T h e r e s u l t s o f e s t i m a t e s m a d e i n t h i s w a y , o n

t h e b a s i s o f t h e m e a n c u r v e o f r e l a t i v e r e s is t a n c e s

i n F ig . 7 , a r e s h o w n i n F i g . 4 b y a u x i l i a r y p l o t s

p l a c e d a d j a c e n t t o t h.a c o r r e s p o n d i n g tu r n i n g p a t h

p l o t s. T h e a u x i l i a r y p l o t s i n d i c a t e d i s t a n c e s r u n

i n s u c c es s iv e t i m e i n t e r v a l s e q u a l t o t h e t i m e i n t e r -

v a l s u s e d o n t h e t u r n i n g p a t h p l o t s, a n d b r i n g o u t

t h e i m p o r t a n t f a c t t h a t d i ff e r en c e s i n t h e o v e r a l l

d i s t a n c e r u n i n a g i v e n o v e r a l l t i m e a r e n o t m u c h

m o r e t h a n o n e s h ip - le n g t h e v e n w h e n t h e t w o

e x t r e m e t u r n s a r e c o m p a r e d , a n d l e ss t h a n h a l f a

s h i p - l e n g t h w h e n t h r e e - l e n g t h a n d t w o - l e n g t h

t u r n s a r e c o m p a r e d . I t i s c l e ar , t h e n , t h a t w h i l e

t h e g r e a t e r s p e e d r e d u c t i o n o f a tw o - l e n g t h t u r n i s

a d m i t t e d l y a d i s a d v a n t a g e , i t s u l t i m a t e e f f e c t i s

n o t v e r y g r e a t b e c a u s e o f t h e r a p i d i t y w i t h w h i c h

s p e e d i s r e g a i n e d .

O n e o t h e r p o i n t m a y b e m e n t i o n e d i n c o m p a r -

i n g t h r e e - l e n g t h a n d tw o - l e n g t h t u r n s ; n a m e l y ,

t h e r e l a t i v e c e n t r i f u g a l f o r c e s d e v e l o p e d . I f t h e

s p e e d r e d u c t i o n s w e r e t h e s a m e , t h e c e n t r i f u g a l

f o r c e w o u l d o b v i o u s l y b e a b o u t 5 0 p e r c e n t

g r e a t e r in t h e s m a l l e r t u r n . O n a c c o u n t o f t h e

m u c h g r e a t e r s p e e d r e d u c t i o n , h o w e v e r , t h e

s m a l l e r t u r n i s a c t u a l l y f o u n d t o d e v e l o p l e ss ~

c e n t r i f u g a l fo r c e w i t h t h e s a m e a p p r o a c h s p e e d .

O n t h e w h o l e , t h e r e f o r e , t h e c h a r a c t e r i s t i c s o f

a t w o - l e n g t h t u r n a p p e a r t o b e s u p e r i o r t o t h e

c h a r a c t e r i s ti c s o f a t h r e e - l e n g t h t u r n . A n d i t

s h o u l d n o t b e f o r g o t t e n t h a t t h e m e r e a v a i l a b i l i t y

o f a t w o - l e n g th m i n i m u m t u r n w o u l d n o t m a k e i ts

u s e m a n d a t o r y - - t h e m a x i m u m r u d d e r a n g le is

o r d i n a r i l y e m p l o y e d o n l y in e m e r g e n c i e s .

I t m i g h t b e a r g u e d t h a t , i f a t w o - l e n g t h t u r n i s

s u p e r i o r t o a t h r e e - l e n g t h t u r n , a t u r n o f l es s th a n

t w o l e n g t h s m i g h t b e e v e n m o r e d e s i ra b l e . H o w -

e v e r , i n s p i te o f t h e g e n e r a l r a p i d i t y o f s p e ed r e -

c o v e r y a l re a d y n o t e d , t h e s p e e d r e d u c t i o n i t se l f

m u s t o b v i o u s l y b e c o m e p r o h i b i t i v e l y g r e a t if t h e

t a c t i c a l d i a m e t e r i s r e d u c e d f a r e n o u g h . H e n c e ,

b e a r i n g i n m i n d t h a t f e w e x i s ti n g v e ss e ls c a n t u r n

i n l es s t h a n a b o u t t h r e e l e n g t h s , a t a c t i c a l d ia m -

e t e r o f t w o l e n g t h s c e r t a i n l y s e e m s a c c e p t a b l e

a s a p r a c t i c a l m i n i m u m t o w o r k t o w a r d , a t l e a s t

f o r t h e p r e s e n t . P a r e n t h e t i c a l l y , i t m a y b e m e n -

t i o n e d t h a t t h e m i n i m u m t u r n i n g c i r c le s e v e n o f

a u t o m o b i l e s a r e n o t o r d i n a r i l y l es s t h a n a b o u t

t w i c e t h e o v e r a l l le n g t h ( o r t h r e e t i m e s t h e w h e e l -

b a s e ) .

I t h a s b e e n e m p h a s i z e d t h r o u g h o u t t h e f o r e -

g o i n g d i s c u s s i o n o f g e n e r a l i z a t i o n s r e g a r d i n g t h e

g e o m e t r i c c h a r a c t e r i s t i c s o f t h e c o n v e n t i o n a l

t u r n t h a t t h e c h a r t s o f F i g . 3 a r e b a s e d o n t h e

e x p e r i m e n t a l e v i d e n c e o f n o r m a l s e a g o i n g v e ss e ls

o n l y . T h i s m e a n s t h a t s p e c i a l t y p e s , s u c h as tu g s ,

t r a w l e r s a n d t h e l i k e , h a v e n o t b e e n i n c l u d e d .

T h e t e r m " n o r m a l s e a g o i n g v e s s e l " is u se d , h o w -

e v e r , i n a f a i r l y b r o a d s e n s e , t o i n c l u d e a n y v e s s e l

w h i c h w o u l d o b v i o u s l y b e s o c l as s if ie d , w i t h o u t

r e g a r d t o d i f f e r e n c e s o f d e s i g n d e ta i l s . T h u s

F i g . 3 i n c l u d e s d a t a f o r s in g l e , t w i n a n d q u a d -

r u p l e - s c re w v e s s el s , h a v i n g v a r i o u s d i s p l a c e m e n t -

l e n g t h r a t i o s a n d d i f f e r i n g d e s i g n s o f s t e r n , w i t h

a n d w i t h o u t d e a d w o o d , a n d f i t t e d w i t h b a l a n c e d

o r u n b a l a n c e d r u d d e r s . U n d e r t h e s e c i r c u m -

s t a n c e s , t h e r e l a t i v e l y g o o d c o r r e l a t i o n o f t h e

g e o m e t r i c d a t a a f f o r d e d b y F i g . 3 i m p l ie s a c e r t a i n

b r o a d s i m i l a r i t y a m o n g a l l n o r m a l s e a g o i n g v e s -

sels.

I t d o e s n o t r e q u i r e m u c h s t r e t c h o f t h e i m a -


8/38


i

i

- < . . .. . L e n g f h , L . . . . .

L " x I

i ) "~ I

) , i

( a )

5 h i p

o ,

d _ 3

J - f i tc , s s Y a c h f

( c)

S f a r C l e~ s s

Y o c h +

i / / i j I ~

I

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. . . . . .

L e n g f h , L

(d)

T r a n s p o - + M r p l a n e

F i t ; . ,~ .- - T & ' P I C A L H U L L F O R M S

S h o w i n g d i a g r a m m a t i c a l l y a p r o g r e s s i o n f r o n t t h e t m i f o r m d r a f t o f t h e n o r m a l s e a g o i n g v e s s e l t o t h e s e p a r a t e w i n g a n d t a i l o f t h e a i r p l a n e

g i n a t i o n t o e x p l a i n t h i s b r o a d s in f i l a ri t y . W h e n

v i e w e d i n s u f f i c ie n t p e r s p e c t i v e , t h e d e s i g n s o f a l l

n o r m a l s e a g o i n g v e s s e l s a r e , a f t e r a l l , v e r y m u c h

a l ik e . F i g . 5 ( a ) is a t y p i c a l e x a m p l e o f t h e g e n e r a l

t y p e o f d e s i g n t o w h i c h p r a c t i c a l l y a l l s e a g o i n g

v e s s e l s c o n f o r m . T h e k ee l i s s t r a i g h t a n d g e n e r -

a l ly p a r a l le l w i t h t h e w a t e r s u r f a c e , t h e l o a d w a t e r -

l i n e i s s h a r p l y p o i n t e d a t t h e b o w a n d u s u a l l y

p o i n t e d a t b o t h e n d s , a n d t h e s i d e s a r e r o u g h l y

v e r t i c a l i n w a y o f t h e l o a d w a t e rl i n e . T h e d r a f t i s

a r o u n d ~ 0 t o }~ 0 o f t h e l e n g th , a n d t h e b e a m

a r o u n d ]/{ t o } '~ 0 o f t h e l e n g t h . I t w i l l b e s e e n t h a t

t h e e x t r e m e v a r i a t i o n s o f t h e s e d i m e n s i o n r a t i o s

r e s u l t i n v a r i a t i o n s o f f o r m w h i c h , in a b r o a d

s e n s e , a r e o n l y t r if l i n g . T h e r e a r e n o d if f e r e n c e s

b e t w e e n v a r i o u s s h i p f o r m s w h i c h r e m o t e l y a p -

p r o a c h i n m a g n i t u d e t h e d i f fe r e n ce s b e t w e e n a n

a v e r a g e s h i p f o r m a n d t h e f o r m s o f t h e J - c l a s s

s a i l i n g y a c h t i n F i g . 5 ( b ) , t h e S t a r - c l a s s s a i l i n g

y a c h t i n F i g . 5 ( c ) , o r t h e t r a n s p o r t a i r p l a n e i n

F i g . 5 ( d ) .

I t i s n o t c o n t e n d e d t h a t s e a g o in g v e s se l s s h o u l d

b e m a d e t o l o o k li k e s a i l b o a t s o r a i r p l a n e s . T h e i r

p r e s e n t f o r m i s d i c t a t e d b y m a n y c o n s i d e r a t i o n s ,

m o s t o f w h i c h a r e o f n e c e s s i ty w e i g h t e d m o r e

h e a v i l y th a n t h e t u r n i n g c h a ra c t e r is t i c s. I t is

m e r e l y p o i n t e d o u t t h a t , g i v e n t h e i r p r e s e n t

g e n e r a l s i m i l a r i t y o f f o r m , c e r t a i n c o n s e q u e n c e s

w i t h r e s p e c t t o t h e t u r n i n g c h a r a c t e r i s t i c s , s u c h a s

t h o s e s h o w n b y F i g s . 3 a n d 4 , a r e m o r e o r l e s s

i n e v i t a b l e .

I t m a y b e s h o w n , fo r i n s ta n c e , t h a t t h e c o n s i st -"

e n c y i n th e s p e e d r e d u c t i o n d a t a o f F i g . 8 r e -

f le e t s d i r e c t l y a u n i f o r m i t y o f p i v o t p o i n t l o c a t i o n

w h i c h s e e m s t o b e c h a r a c t e r i s t i c o f s h i p f o r m s .

T h e p i v o t p o i n t i s a s s o c ia t e d w i t h s t e a d y t u r n i n g ,

a n d i s t h a t p o i n t o n t h e a x i s o f s y m m e t r y o f th e

v e s se l a t w h i c h a l i n e d r a w n h o r i z o n t a l l y a n d a t

r i g h t a n g l e s t o t h e a x i s w i l l p a ~ s t h r o u g h t h e c e n t e r

o f t h e s t e a d y - t u r n i n g c ir c l e. V a r i o u s o b s e r v e r s

h a v e n o t e d t h e m a r k e d t e n d e n c y f o r t h e p i v o t

p o i n t t o f a l l a t s o m e t h i n g l i k e ]/~ o f t h e l e n g t h

a h e a d o f t h e c e n t e r o f g r a v i t y [ 2 ], a n d t h i s a v e r -

a g e l o c a t i o n i s f a i r l y w e l l c o n f i rl m e d b y t h e t e s t s o n

w h i c h F i g . 3 i s b a s e d .

N o w , r e f e r r i n g t o F ig . 6 , m a d n o t i n g t h a t i n


9/38

O N T H E T U R N I N G A N D S T E E R I N G O F S H I P S 2 95

DrcLcj Cornponenf , ~ C e nf r, fu ~ o l Force,Mv~/r

(M vVr) s i= ~ \

Prop el ler ~ Pafh of C.G.

j ,

- - p i v o + p o i n +

M = M a s s 1 I

FIG. 6.- -DR AG COMPONENT OF CENTRIFUGAL FORCE IN

~TI~ADY TURNING

s t e a d y t u r n i n g t h e r e i s n o u n b a l a n c e d r o t a t i n g

c o u p l e ( t h e s h i p n o t b e i n g s u b j e c t t o a n g u l a r

a c c e l e r a t i o n ) , i t w i l l b e s e e n t h a t , o t h e r t h i n g s b e -

i n g e q u a l, t h e l o c a t io n o f t h e p i v o t p o i n t d e t e r -

m i n e s th e m a g n i t u d e o f t h e d r a g c o m p o n e n t o f

t h e c e n t r i f u g a l f o r c e , b y d e t e r m i n i n g t h e m a g n i -

t u d e o f t h e d r i f t a n g l e a t t h e c e n t e r o f g r a v i t y .

S i n c e t h i s d r a g c o m p o n e n t c o n s t i t u t e s a d e d u c -

t i o n f r o m t h e a v a i l a b l e p r o p e l l e r t h r u s t , i t r e-

d u c e s t h e s p e e d o f t h e s h ip , a n d a n y c h a n g e i n i t s

m a g n i t u d e w i ll a lt e r t h e a m o u n t o f t h e s p e e d r e -

d u c t i o n .

T h e p o s s i b i l i t y s u g g e s t s i t s e lf , t h e n , o f c a l c u l a t -

i n g t h e s p e e d r e d u c t i o n a s a f u n c t i o n o f t h e d i -

a m e t e r - l e n g t h r a t io . T h e s p e e d r e d u c t i o n s h o u l d

n o t b e m a t e r i a l l y a f f e c t e d b y d i f f e r e n c e s o f d i s -

p l a c e m e n t - l e n g t h r a t i o s i n c e t h e c e n t r i f u g a l f o r c e

i s d i r e c t l y p r o p o r t i o n a l t o d i s p l a c e m e n t a n d b o t h

r e s i s t a n c e a n d t h r u s t o r d i n a r i l y v a r y a p p r o x i -

m a t e l y i n p r o p o r t i o n t o t h e d is p l a c e m e n t . A s a

m a t t e r o f f a c t , t h e c u r v e o n t h e s p e e d - r e d u c t i o n

c h a r t o f F i g . 3 i s a c o m p u t e d c u r v e , a n d n o t s i m p l y

a m e a n c u r v e d r a w n t h r o u g h t h e p o i n t s . I t is

b a s e d o n ( 1) c e n t r i f u g a l f o r c e c o m p o n e n t s d e t e r -

m i n e d a s in F i g . 6 , w i t h a v e r a g e p i v o t p o i n t l o c a -

t i o n s f r o m t e s t d a t a , ( 2) t h e m e a n c u r v e o f r e l a-

t i v e r e s i s t a n c e s p e r t o n s h o w n i n F i g . 7 , a n d ( 3 )

o n e o r o t h e r o f t h e a s s u m p t i o n s , t h a t a n y i n -

c r e a s e d t h r u s t a t t r i b u t a b l e t o g r e a t e r p r o p e l l e r

s li p a t re d u c e d s h i p s p e e d s ( t h e t h r o t t l e s r e m a i n i n g

u n c h a n g e d ) i s a p p r o x i m a t e l y o f f s et b y i n c r e a s e d

d r a g o f th e h u l l a n d r u d d e r c a u s e d b y t h e t u r n i n g ,

o r t h a t t h e s e t w o s e c o n d a r y f o r c e s a r e n e g l i g i b l e

i n m a g n i t u d e . T h e g e n e r al a g r e e m e n t b e tw e e n

t h e c o m p u t e d c u r v e a n d t h e o b s e r v e d p o i n t s i s

e v i d e n c e o f t h e r e a s o n a b l e n e s s o f t h i s p r o c e d u r e ,

a n d o f t h e r o u g h l y f i x e d p o s i t i o n o f t h e p i v o t

p o i n t .

I t s e e m s p r o b a b l e t h a t s o m e r o u g h l y p a r a l l e l -

a n a l y t i c a l t r e a t m e n t c o u l d b e " w o r k ed o u t t o a c -

c o u n t f o r t h e s h a p e o f t h e c u r v e o f a d v a n c e t o

t a c t i c a l d i a m e t e r i n F i g . 3; t h i s h a s n o t y e t b e e n

a t t e m p t e d .

LATERAL FORCES IN STEADY TURNING

I t m u s t b e e m p h a s i z e d o n ce m o r e t h a t n o t h i n g

w h i c h h a s b e e n s a i d s o f a r i s t o b e c o n s t r u e d a s

i m p l y i n g t h a t a l l n o r m a l s e a g o i n g v e s se l s c a n t u r n

i n m i n i m u m c i r c l e s c o r r e s p o n d i n g t o t h e s a m e

r a t i o o f t a c t i c a l d i a m e t e r t o l e n g t h . F a r f r o m i t.

M a n y p r e s e n t - d a y s h i p s h a v e n f i n i m u m t a c t i c a l

d i a m e t e r s a s l a r g e a s f o u r o r f i v e l e n g t h s o r e v e n

l a rg e r , s o t h a t t h e r e i s p l e n t y o f r o o m f o r i m p r o v e -

m e n t i f a l l s h i p s a r e t o b e p u t o n a p a r w i t h t h e

b e t t e r c u r r e n t s h ip s , a n d s ti ll m o r e r o o m f o r i m -

p r o v e m e n t i f m i n i m u m t u r n s o f th e o r d e r o f t w o

l e n g t h s a r e t o b e r e a l i z e d .

A s t r i k i n g i l l u s t r a t i o n o f t h e d i f f e r e n c e s w h i c h

e x i s t t o d a y b e t w e e n a c t u a l d e s i g n s i s a f f o r d e d b y

F i g . 8 , w h i c h is a n e x t r a c t f r o m F i g . 3 . H e r e a r e

t w o m o d e l s o f e x i s t i n g s h i p s , d e s i g n a t e d A a n d B ,

t h e s e c o n d of w h i c h , w i t h t h e s a m e m a x i m u m

r u d d e r a n g l e a s t h e f i r s t ( 3 5 d e g r e e s ) , h a s a m i n i -

m u m d i a m e t e r -l e n g t h r a t io m o r e t h a n t w i ce a s

l a r g e - - 6 . 0 as o p p o s e d t o 2 .4 . W h e n b o t h a r e

t u r n e d i n c i rc l es c o r r e s p o n d i n g t o t h e s a m e d i -

a m e t e r - l e n g t h r a t io , t h e g e o m e t r i c a s p e c t s o f t h e

t u r n s a r e s e e n t o b e v e r y n e a r l y t h e s a m e , a s w o u l d

b e e x p e c t e d f r o m p r e v i o u s d i s c u ss i o n; v e r y d i ff e r-

e n t r u d d e r a n g l e s a r e r e q u i r e d , h o w e v e r , t o p r o -

d u c e t h e s a m e d i a m e t e r - l e n g t h r a t i o s .

T h e d i ff e re n ce b e t w e e n t h e m i n i m u m d i a m e t e r -

l e n g t h r a t i o s o f t h e s e t w o s h i p s o b v i o u s l y c a n n o t

b e a c c o u n t e d f o r b y a d if f e re n c e i n t h e m a x i m u m

r u d d e r a n g l e s , s i n c e t h e s e a r e t h e s a m e ( 3 5 d e -

g r e es ) . N o r c a n i t b e a t t r i b u t e d t o a d i ff e r en c e

i n t h e r e l a t i v e r u d d e r a r e a s a l o n e , s i n c e , e x p r e s s e d

a s fr a c t i o n s o f th e l a t e r a l p l a n e a r e a s , t h e r u d d e r

a r e a s a r e n o t f a r f r o m t h e s a m e . T h e s e f r a c t i o n s

a r e 0 . 0 2 5 f o r s h i p A a n d 0 . 0 2 3 f o r s h i p B , a d i f fe r -

e n c e o f 9 p e r c e n t i n r e l a ti v e r u d d e r a r e a t o b e s u r e ,

b u t a d i f f e r e n c e o f o n l y 0 . 2 p e r c e n t o f t h e r e s p e c -

t i v e l a t e r a l p l a n e a re a s . E v i d e n t l y , t h e n , o t h e r

f a c t o r s m u s t c o n t r i b u t e h e a v i l y t o t h e o v e r a l l

r e s u lt . T h e m o s t o b v i o u s a r e th e h u l l f o r m , t o -

g e t h e r w i t h a n y m u t u a l i n t e ra c t io n s b e t w e e n t h e

h u l l, t h e r u d d e r a n d t h e p r o p e l l er s .

T h e r e i s n o t h i n g v e r y s u r p r is i n g , o r e s s e n t i a ll y


10/38

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T o n a t T D / L =

I I

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F I G , 7 .- -I %{ ET HO D O F C O M P U T I N G S P E E D R E D U C T I O N I N T U R N I N G ; U S E D F O R M E A N

C U R V E F OR F I G . 3

Typical curves of straight-course hull resistance and drag component of centrifugal force

Resistance curves are for Standard Series hulls, as follows:

Displacement- Beam- Prismat ic Normal Speed-

Ships Length Ratio Draft Ratio Coefficient Length Ratio

I 60 2.5 0.60 1.2

II 100 2.5 0.65 1. (I

III 170 2.5 0.70 0.8

Drag curves are based on pivot point locations from test data . Drag curves are parabolas,

since centrifugal force varies as I:% If total propeller thrust is assumed to remain constan t

during tu rning, and straight-course hull resistances are assumed to apply, then the drag

component of centrifugal force reduces the th rus t available for forward speed. As an ex-

ample, a ship having the mean resistance curve indicated has a steady-turning speed 71

per cent of its normal speed, when turning in a steady circle with TD/L = 4.

new, in this conclusion; 35 degrees has come to

be genera lly adopted as about the maxi mum

practicable rudder angle, and the rudder areas of

normal seagoing vessels are rarely made as small

as 0.015 or as large as 0.030 of the lateral plane

areas. ~ Hence, the compar atively large differences

in the min imu m ratio of tact ical diameter to length

which are f r equentl y found must necessari ly be

put down to the hull design, or to the arra ngem ent

of the appendages (i.e., interference effects),

rather than to the rudder alone.

The comparativ e analysis in Fig. 9 of certain

tests of the same models used for Fig. 8 brings out

forcefully the relative influe nce of the hull s in

this instance. These models are admittedly

somewhat extreme examples, inasmuch as model

A turns very well and model B quite poorly.

Both, however, are models of existing ships;

they are properly referred to as normal seagoing

types, an d they are in no sense freaks. As a

matter of fact , both have the same type of stern,

moderate deadwood and spade-type rndders well


11/38

O N T H E T U R N I N G A N D S T E E R I N G O F S H I P S 2 9 7

> 0.6

0.5 /

O.4

I . I

1.0

c~ 0.9

~. 0.8

0.'7

0.6

0.5

O.1

,.-., 0 .6 o

0.4

Z 3

. . . , . . , , ~ ~ . . .. .- . -~ - ~ "

/ - , . ,

. / , o

R u d d e r

Ang le

~ M o d e l A

I0

o

A n g l e H o d e t B

o f o

I

4 5 6 7 8 9

T D / L

lO 11 IZ

Fl a. 8.- -TU RNING PATH PROPORTIONS FOR MODELS A AND ]3 (EXTRACT FROM FIG. 3)

15

IS

s e p a r a t e d fr o m t h e d e a d w o o d . I n g e n e r a l, t h e y

m a y b e s a i d t o b e q u i t e s im i l a r in r e s p e c t t o p a r e n t

h u l l f o r m : t h e m o s t o b v i o u s d i f fe r e n c e s a r e in

t h e d i s p l a c e m e n t - l e n g t h a n d b e a m - d r a f t r a t i o s ;

t h a t i s , i n m a t t e r s o f h u l l p r o p o r t i o n s . T h e

a n a l y s i s i s m a d e a t t h e s a m e r a t i o o f s t e a d y -

t u r n i n g d i a m e t e r t o le n g t h , f o r t h e s a m e a p p r o a c h

s p e e d - l e n g t h r a t io , a n d o n t h e b a s i s o f m o d e l s o f

v e r y n e a r l y t h e s a m e l e n g t h . D i r e c t c o m p a r i s o n

i s t h e r e f o r e p o s s ib l e a t e a c h s t e p .

F r o m t h e p a r t i c u l a r s o f t h e t w o m o d e l s , l i s t e d

b e l o w t h e f o r c e d i a g r a m s , i t w i l l b e s e e n t h a t

m o d e l A h a s r o u g h l y tw o a n d o n e - h a l f t i m e s t h e

d i s p l a c e m e n t ( h e n c e d i s p l a c e m e n t - l e n g t h r a t io )

o f m o d e l B , b u t , b e c a u s e o f i ts g r e a t e r b e a m - d r a f t

r a t io , r e l a t i v e l y l i t tl e m o r e l a t e r a l p l a n e a r e a o f

h u l l ( 2 7 p e r c e n t ) ; t h e r u d d e r a r e a s d i f f e r , a s

p r e v i o u s l y n o t e d , b y o n l y 0 . 2 p e r c e n t o f th e

r e s p e c t i v e l a t e r a l p l a n e a r e a s .

F r o m t h e t e s t d a t a g i v e n , i t w i l l b e s e e n t h a t

w i d e l y d i f f e ri n g r u d d e r a n g l e s ( 6 d e g r e e s f o r m o d e l

A a n d 3 5 d e g re e s fo r m o d e l B ) a r e n e e d e d t o p r o -

d u c e t h e c o m m o n r a t i o o f tu r n i n g d i a m e t e r t o

l e n g t h ( 5. 9) s e l e c te d f o r s t u d y , a n d t h a t w i d e l y

d i f fe r i n g l a t e r a l r u d d e r - f o r c e c o m p o n e n t s w e r e

o b s e r v e d u n d e r t h e s e c o n d i t i o n s , t h is f o r c e c o m -

p o n e n t b e i n g p r a c t i c a l l y z e r o f o r m o d e l A ( a c t u -

a l l y s l i g h t ly n e g a t i v e ) . T h e l a te r a l r u d d e r - f o r c e

c o m p o n e n t i s th e l a t e r al f o r c e t r a n s m i t t e d t h r o u g h

t h e r u d d e r s t o c k w h i l e t h e s e l f - p ro p e l le d m o d e l

i s t u r n i n g f r e e l y i n s t e a d y m o t i o n , a s m e a s u r e d b y

a s p ec i al d y n a m o m e t e r m o u n t e d i n t h e m o d e l .

T h e p i v o t p o i n t p o s i t i o n s , a s d e d u c e d f r o m t h e

k i n e m a t i c t e s t d a t a , a r e i n b o t h c a s e s s o m e w h a t

f o r w a r d o f t h e p r e v i o u s l y m e n t i o n e d m e a n p o s i-

t i o n o f 1/~ o f t h e l e n g t h a h e a d o f t h e c e n t e r o f

g r a v i t y , b u t d o n o t d i f f e r g r e a t l y f r o m e a c h O t h er .

T h e a n a l y s i s a s a w h o l e i s c o n f i n e d t o l a t e r a l

( a t h w a r t s h i p s ) f o r c e c o m p o n e n t s . T h e fi r st s t e p

i s t o d e t e r m i n e t h e h u l l f o r c e c o m p o n e n t , o r " l a -

t e r a l r e s i s t a n c e " o f t h e h u l l . T h i s is r e a d i l y

d o n e , s i n c e , i n s t e a d y t u r n i n g , t h e h u l l f o r c e c o m -

p o n e n t m u s t b e e q u a l a n d o p p o s i t e t o t h e r e s u l t a n t

o f t h e r u d d e r f o rc e c o m p o n e n t ( in t h i s c a s e m e a s -

u r e d ) a n d t h e c e n t r i fu g a l f o r c e c o m p o n e n t " ( e x -

a c t l y d e t e r m i n e d b y t h e s p e e d , t u r n i n g r a d i u s a n d

d i s p la c e m e n t ) ; t h e r e s u l t a n t m o m e n t a b o u t t h e

c e n t e r o f g r a v i t y i s z e r o. T h e p r o c e d u r e i s t h e

s a m e a s t h a t a d o p t e d b y H o v g a a r d s o m e y e a rs

a g o [ 5 ] , e x c e p t t h a t m e a s u r e d v a l u e s o f t h e r u d d e r

f o r ce c o m p o n e n t a r e s u b s t i tu t e d f o r e s ti m a t e d

v a l u e s, a n d t h e c o m p u t e d h u l l f o r c e c o m p o n e n t s

s h o u l d t h e r e f o r e b e c o r r e s p o n d i n g l y m o r e r e l i a bl e .

R e f e r r i n g t o t h e r e s u l ts o f t h i s s t e p , a s s h o w n


12/38


13/38

O N T H E T U R N I N G A N D S T E E R I N G O F S H I P S

2 9 9

(b')

Y a w

( a )

S + e c t d y - T u r n [ n o

D/ L =3

F I G . 1 0 . - - M O T I O N O F H U L L I N S T I~ A D T U R N I N G A N D I N Y A W

i

i n t h e d i a g r a m s , i t is o b v i o u s l y n o e x a g g e r a t i o n t o

s a y t h a t :

M o d e l A t u r n s i n s p i te o f it s r u d d e r ,

M o d e l B i s f o r c e d a r o u n d b y i t s r u d d e r .

T h e d i f f er e n c e i s c l e a r l y a t t r i b u t a b l e t o t h e d i ff e r-

i n g p o s i t i o n s ( i. e ., c e n t e r s o f p r e s s u r e ) o f t h e h u l l -

f o r c e c o m p o n e n t s , a n d n o t a t a l l to t h e i r d i f f e r in g

m a g n i t u d e s . T h e f a c t t h a t t h e h u l l f o r c e c e n t e r i s

s o m e 1 3 p e r c e n t o f t h e l e n g t h a b a f t t h e c e n t e r o f

g r a v i t y i n m o d e l ] 3 m e a n s t h a t t h e r u d d e r f o r c e

h a s t o b e a b o u t 4 0 p e r c e n t o f t h e c e n t r i f u g a l

f o r c e ; t h e f a c t t h a t t h e h u l l f o r c e i s p r a c t i c a l l y

a t t h e c e n t e r o f g r a v i t y i n m o d e l A ( a c t u a l l y

s l ig h t l y a h e a d ) m e a n s t h a t t h e r u d d e r f o rc e c a n

b e p r a c t i c a l l y z e r o ( a c t u a l l y s l i g h t l y n e g a t i v e ) ,

e v e n t h o u g h t h e c e n t r i f u g a l fo r c e is w e l l o v e r

t w i c e a s l a r g e a s i n m o d e l ] 3 .

F r o m t h i s e v i d e n c e , t h e g e n e r a l c o n c l u s io n is

i n e s c a p a b le t h a t t h e h u l l f o r m , t h r o u g h i ts c o n t r o l

o v e r t h e h u l l -f o r c e c e n t e r , p l a y s a n e x t r e m e l y i m -

p o r t a n t p a r t i n f ix i n g t h e s t e a d y - t u r n i n g c h a r -

a c t e r i s t i c s , a n d c a n i n n o s e n s e b e c o n s i d e r e d

s e c o n d a r y i n i m p o r t a n c e t o th e r u d d e r. T h i s

c o n c l u s i o n i s e m p h a s i z e d b e c a u s e , o n t h e w h o l e ,

i n th e s t u d y o f t u r n i n g o v e r a p e r i o d o f y e a r s m o r e

a t t e n t i o n s e e m s t o h a v e b e e n d e v o t e d t o r u d d e r s

a s s u c h t h a n t o h u ll s a s s u c h , e v e n t h o u g h t h e

r u d d e r i s b a s i c a l l y a n a p p e n d a g e .

I t i s i n t e r e s ti n g t o c a r r y t h e a n a l y s i s o f t h e h u l l

f o r c es s o m e w h a t f a r t h e r . I n p a r t i c u l a r , t h e

q u e s t i o n a r i s es o f a c c o u n t i n g f o r t h e o b s e r v e d f a c t

t h a t m o d e l A d e v e l o p s so m e 6 5 p e r c e n t m o r e

l a t e r a l h u l l -f o r c e c o m p o n e n t t h a n m o d e l B , w i t h

m u c h t h e s a m e p i v o t p o i n t l o c a t i o n a n d h e n c e

w i t h m u c h t h e s a m e d r i f t a n g le s a t a l l c o r r e s p o n d -

i n g l o n g i t u d i n a l p o i n t s . O n e f a c t o r i s , o f c o u r s e ,

t h e g r e a t e r l a t e r a l p l a n e a r e a o f m o d e l

A ;

t h i s

s u g g e s ts d i v i d i n g t h e h u l l - f o r c e c o m p o n e n t s b y

t h e r e s p e c t i v e l a te r a l p l a n e a r e a s , f o r c o m p a r a t i v e

p u r p o s e s . F r o m t h i s i t i s a n a t u r a l s t e p t o d iv i d e

t h e m a l s o b y t h e d y n a m i c p r e s s u r e

(p/2 )v 2,

t o

p r o d u c e a d i m e n s i o n l e s s c o e f f i c i e n t f o r t h e h u l l

f o r c e w h i c h h a s t h e s a m e f o r m a s t h e l i f t co -

e f f i c i en t o f an a i r f o i l .

T h e u s e o f " l i f t c o e f f i c i e n t s " t o d e f i n e c r o s s

f o r c e s o n h y d r o d y n a m i c o r a e r o d y n a m i c b o d i e s

o t h e r t h a n a i rf o il s h a s b e c o m e a c o m m o n p l a c e i n

r e c e n t y e a rs . T h e i r u s e i n t h e p r e s e n t in s t a n c e

w o u l d n o t c a l l f o r sp e c i a l c o m m e n t , t h e n , w e r e

i t n o t f o r t h e c u r v i l i n e a r m o t i o n o f t h e h u l l .

L i f t c o e f f i c ie n t s a r e o r d i n a r i l y a s s o c i a t e d w i t h

" a n g l e s o f a t t a c k " w h i c h , i n r e c ti l i n e a r m o t i o n ,

a r e fi x e d t h r o u g h o u t t h e l e n g t h o f t h e b o d y , a s i n

F i g . 1 0 ( b ) . F o r t h e c a s e i n p o i n t , b e c a u s e o f t h e

c u r v i l i n e a r m o t i o n , t h e a n g l e o f a t t a c k v a r i e s

t h r o u g h o u t t h e l e n g t h , t h e v a r i a t i o n b e i n g c o n -

s i d e r a b le w h e n t h e r a t i o o f tu r n i n g d i a m e t e r t o

l e n g t h is s m a l l , a s i n F i g . 1 0 ( a ) . T h i s d i f f e r e n c e

m a y c a u s e a c e r t a in c o m p l i c a t i o n o f t h o u g h t , b u t

i t i s n o t a c t u a l l y v e r y s e r io u s , f i r s t b e c a u s e i t d o e s

n o t a f f e c t t h e c o m p u t a t i o n o f t h e c o e f fi c ie n t i ts e l f,

a n d s e c o n d b e c a u s e t h e c o m p u t e d c o e f f ic i e nt c a n


14/38

3 0 0

O N T H E T U R N I N G A N D S T E E R I N G O F S H I P S

Mocte l A

O. IZ L--~

2.33 Lb.

(ss),o.~o

Lb.

I . ]

3 Lb.

. . . .

D/L = 2.3

i

I

0.05 L-->-

i

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