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E d i t o r ' s N o t e : T h i s a r t ic l e w a s o r i~ i -

n a l h y p u b l i s h e d i n t h e M a r d - 1 1 9 7 9 i s s u e

o f S u r f a c e W a r f a r e m a g a z i n e , a n d

r e p ri n t ed 8 ! t e a r s l a t er . T h e a i r t h o r , L T

b l u r V . H a l l o f t h e L I S S Power (DD

8 3 9 ) r e t i r e d f r o n t t h e n a v a l s e r v i c e i n

1979 . W e r e c e i v e n u m e r o u s r e q u e s t s f o r

c o p ie s , s o i n h o n or of : A P T H a l l ' s a r t i -

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

o r i g i n a l a r t i c l e u s i n gc o n t r i b u t i o n s

f r o m

M a r i n e S a f e t i l I n t e r n a t i o n a l . A s m o r e

S a i l o r s l r t t a 1 1 1 q u a l i f r c a t i o l l t1 S 00D, or

s t a n d w a t c h a s J u n i o r O f f i c e r o f t h e D e c k

o r J u n i o r O f f i c e r o f t h e W a t c h , w e h o p e

t o r e c e i v e m a r n f m o r e i n n o v a t i v e

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

i n g !A s t h e t e c h n i q u e s a n d

mach ines designed to aid in

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

become more num erous and sophis -

t i c a t e d , i t s e e m s a p l e a s u r e t o r e a l i z e

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

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

the exercis e of good human judg-

ment and thought, aided by rather

simple equipment of long st andin g .

T h e c o n n i n g o f f i c e r d o e s o f c o u r s e

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

even the most elementa ry man euvers .

C I C , r a d a r , a n d t h e m a n e u v e r i n g

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

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

p l a y e d . E v e r y t h i n g o n t h e b r i d g e

s e e m s t o b e c a l m , i n o r d e r , r e a d y .

P r o b a b l y i t i s . But somehow, some-

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

u n e x p e c t e d l y e n o u g h s o t h a t a n a l m o s t

i n s t a n t a ne o u s d e c i s i o n w i l l h a v e t o b e

mad e with out much outside help .

12

I t

Even if help and recommendati ons

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

t h e q u e s t i o n , i s t h i s c o r r e c t ? I s i t t h e

s a f e s t , q u i c k e s t a n d b e s t w a y ? T h e

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

m i n a t i o n d o e s n o t l e a v e t h e b r i d g e ; i t

i s t h e r e t o s t a y .

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

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

a b l e t o q u i c k l y a n d a c c u r a t e l y s n a k e

t h i s d e t e r m i n a t i o n . T h e 0 0 1 ) i s

r e q u i r e d t o s t u d y p e r t i n e n t t a c t i c a l

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

ss t i c s o f h i s o w n s h i p a n d o t h e r t y p e s ,

and man euvering board . H e i s

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

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

b e a c c e p t a b l e . T h e r e i s h o w e v e r , a

faculty which an OOD can develop

a n d u s e e f f e c t i v e l y w i t h j u s t a l i t t l e

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

www.navy . i i t i l / i i a v p i i l i b / c n o / i i 7 6

A O n e r a d i a n i s a p p r o x i m a t e l y 6 0 d e g r e e s , W e u s e t h e r a d i a n r u l e f o r s m a l l a n g l e s ( 3 0 d e g r e e s o r l e s s )

t o a p p r o x i m a t e t h e l e n g t h o f t h e s h o r t s i d e o f a t r i a n g l e b y a s s u m i n g t h e r a t i o i s 1 t o 6 0 c o m p a r e d t o t h e

l o n g s i d e .

a

s e e m t o c o n s c i o u s l y u s e . I t i s n o

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

o n a v a r i e t y o f s i m p l e r i f l e s .

When the OOD uses "thumb

r u l e s " i n m a n e u v e r i n g , l i e i s m e r e l y

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

a s p ec i f ic s i tu a t i o n . W h e n l i e e x e r -

c i s e s „ s e a m a n ' s e y e " , h e i s a l s o m a k -

i n g m a t h e m a t i c a l c a l c u l a t i o n s , b u t

o n a l e v e l b e l o w ( o r a b o v e ) t h e l e v e l

o f c o n s c i o u s f i g u r i n g . L e t ' s l o o k f o r

a min ute at one simple device :

radian m easure .

M o s t O O D ' s h a v e r u n a c r o s s t h e

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

mentary mat h courses . F e w a p p r e c i a t

i t p r o p e r l y .

What is a Rad ian?

A r a d i a n i s d e f i n e d a s t h e a n g l e

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

S1 . I r f a c e W a r f a r e

Winter 2004 Vol . 29 No .



91 k

t i l for 0

By LT John V. Hall, USN and Marine Safety Internationalthe arc subtended by an an gle of 1

degree is going to be approxi-

m a t e l y 1 / 6 0 o f t h e r a d i u s , 2

d e g r e e s , 2 / 6 0 o f t h e r a d i u s , 1 0

degrees, 1/6 of the radi us, and s o

f o r t h . For smal l an gles (30 degrees

o r l e s s ) , t h e a r c ( a ) a n d c h o r d ( c )

are approxi mat ely equal .

Simply put : f o r e v e r y a n g l e o f 1

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

t r i a n g l e t o t h e s h o r t s i d e i s 1 t o 6 0 .

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

l o n g s i d e i s 6 0 0 y a r d s , t h e n t h e s h o r

s i d e i s 1 0 y a r d s .

F o r i n s t a n c e :

Y o u s e e a f i s h i n g b o a t a b o u t t w o

m i l e s a h e a d , , 3 d e g r e e s o n y o u r s t a r -

,A Applying the radian rule here, 1 degree to 60 degrees is the some ratio as the side opposite of one

board bow. He seems to be DIW .

d e g r e e t o t h e a d j a c e n t s i d e - 10 yards to 600 yards .

How close do you come if you hold

your course?

w h e r e t h e l e n g t h o f t h e a r c e q u a l s t h e

If we round 7 . 4 t o 6 0 , w e c a n

T r u e t h i s i s a n i n s t a n t ' s w o r k o n a

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

s a y t h a t t h e l e n g t h o f t h e a r c c r e -

ma neuverin g board . But why not

r and c hord c are shown . When a = r

ated an angle of 60 degrees is g oing c o n v e r t t h a t 3 d e g r e e s t o 1 / 2 0 o f a

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

to be approximately equal to the

r a d i a n ( 3 d e g r e e s / 6 0 d e g r e e s ) , a n d

7 . 4 d e g r e e s .

radius . Consequently the length of

t h e n t a k e 1 / 2 0 o f t h e r a n g e , t h u s

4 , 000 YO ,

A W h i l e b e a r i n g d r i f t , t h e c o n s t a n t c h a n g e o f a n o b j e c t ' s b e a r i n g f r o m t h e s h i p , w i l l h e l p d e t e r m i n e i f a d a n g e r o f c o l l i s i o n e x i s t s , t h e a c t u a l r a n g e o f t h e c l o s e s t

point of approach ((PA) can be found using the radian rule .

Win ter 2004

www.navy .mil /navpalib/cno/n7 6

1



getti ng your 200 yard CPA? Too

close? Fiv e hundred yards would be

b e t t e r . W e l l , 0 0 i s 1 / 8 o f 4 0 0 0 , a n d

1 / 8 o f a r a d i a n i s w h a t ? B e t w e e n 7

and 8 d egrees . T o c l e a r h i m b y 0 0

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

a b o u t 8 d e g r e e s o f f h i s b e a r i n g s o

y o u c o m e l e f t d e g r e e s

Another raplil1Crati0ra 0f t h e r a d i a n r u l e :

While alongside during an unrep,

o n e o f o u r p r i m a r y c o n c e r n s i s k e e p -

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

s h i p . S i n c e w e r o u t i n e l y s t e e r c o u r s e s

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

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

14

A p p l y i n g t h e r a d i a n r u l e t o s p e e d v e c t o r s , w e s e e a 1 d e g r e e c o u r s e c h a n g e a t 1 3 k n o t s d u r i n g c a l m

w e a t h e r c o n d i t i o n s c a u s e s t h e s h i p t o o p e n a t 2 0 f e e t p e r m i n u t e .

A T h e A m p h i b i o u s ( o m m a n d S h i p ( r i g h t ) h a s a n o v e r a l l l e n g t h o f a p p r o x i m a t e l y 6 00 f t . A 1 d e g r e e s t a r -

b o a r d c o u r s e c h a n g e s w i n g s t h e s t e r n t o w a r d t h e g u i d e s h i p b y a t l e a s t 1 0 f e e t , t h e d e c r e a s e i n p r e s s u r e

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

would be useful to know how this

a f f e c t s t h e p o s i t i o n o f o u r s t e r n .

T h e r e a r e a l o t o f v a r i a b l e s a t w o r k

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

l a t e r a l m o v e m e n t o f t h e s t e r n ( a t l e a s t

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

r e l a t i v e l y e a s y t o d o . F o r s i m p l i c i t y ,

a s s u m e o u r s h i p i s 6 0 0 f e e t l o n g . I t

we cha nge headin g 1 d egree, and . i f

we a s s u m e t h e s h i p p i v o t s a t t h e b o w

( a " w o r s t c a s e " s c e n a r i o ) , w e a p p l y

t h e r a d i a n r u l e r a t i o o f 1 / 6 0 a n d c o n -

c l u d e t h a t t h e s t e r n m o v e s l e f t 1 0

fe e t . S i n c e w e k n o w t h a t t h e s h i p

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

www.navy . n i i l / i i.,ivpalib/cno/n76

t i l e 1 0 f o o l f i g u r e r e p r e s e n t s t h e m o s

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

e r y s h i p f o r e v e r y o n e d e g r e e o f

heading chang e .

Y 'L t raiiother applicat iora .M o s t u n r e p s a r e c o n d u c t e d a t a

s p e e d o f 1 3 k n o t s . W h e n t h e r e c e i v -

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

o r l e f t o f R o m e o C o r p e n s h e s h o u l d

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

w h a t s i d e o f t h e d e l i v e r y s h i p s h e i s

on . I t i s u s e f u l t o k n o w w h a t t h e r a t

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

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

I n t h e d i a g r a m t o t h e r i g h t , t h e t w o

s h i p ' s v e c t o r s a r e s h o w n w i t h a h e a d

i n g d i f f e r e n c e o f o n e d e g r e e . I f w e

take 1/60 of 13 knots (which happen

t o b e 1 3 0 0 f e e t p e r m i n u t e ) w e g e t

2 1 . 6 f e e t p e r m i n u t e ( f p m ) , w h i c h w e

r o u n d o f f t o 2 0 f p m . T h u s , i n t h e

a b s e n c e o f o t h e r f o r c e s , f o r e v e r y o n e

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

Romeo Corpen we open (or clos e) at

t h e r a t e o f a b o u t 2 0 f e e t p e r m i n u t e .

G e t t i n g o u t o f c l o s e

q u a r t e r s -- t h e " f i v e

degree" ma neuver :

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

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

o i le r , s a y 6 0 o r 8 0 f e e t , y o u h a v e t o

o p e n t h e d i s t a n c e q u i c k l y b e c a u s e

i n t e r a c t i v e f o r c e s a r e i n c r e a s i n g e x p o

n e n t i a l l y a n d y o u a r e r u n n i n g o u t o f

t i me You ini ti at e emergenc y break-

a w a y ; b u t y o u c a n ' t f l o o r t h e a c c e l e r -

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

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

r i v e r t h e h u l l m a y c a u s e t h e w a t e r

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

t h e r , i n c r e a s i n g c h a n c e s f o r c o l l i s i o n .

Y o u a r e s o c l o s e t h a t k y o u ' r e c o n -

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

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

N e v e r t h e l e s s , t h a t ' s w h a t y o u h a v e t

do and what's more, you have to

make a decisi ve course cha nge .

Ass ume you are to starboard of

t h e o i l e r . A s w e l e a r n e d a b o v e , f o r

Surface Warfare

Winter 2004 Vol . 29 N



(

W i n t e r 2 ( 0 4

A T h e b l i n d a r e a c r e a t e d b y a p a r t i c u l a r l y r a k i s h b o w o r l o w s u p e r s t r u c t u r e c a n b e a d a n g e r o u s r e g i o n . S m a l l b o a t s s h o u l d n e v e r d r i v e u n d e r t h e b o w .

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

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

c l o s e t h e o i l e r b y a s m u c h a s 1 0 f e e t

( f o r a 6 0 ( ) f o o t l o n g s h i p ) . A t t h e s a m e

t i m e , h o w e v e r , e a c h d e g r e e o f h e a d -

i n g c h a n g e t o t h e r i g h t a d d s a b o u t 2 0

f e e t p e r m i n u t e t o y o u r o p e n i n g v e c -

t o r . T h u s , i f y o u m a k e a c o u r s e

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

y o u r s t e r n w i l l c l o s e b y a t m o s t 0

fe e t . A t t h e s a m e t i m e y o u w i l l

a c h i e v e a n o p e n i n g r a t e o f 1 0 0 f e e t

per minute or more. I n f a c t , a s t h e

ship c omes right even th ough t he

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

s h i p , i t c l o s e s b y m u c h l e s s t h a n 0

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

e f f e c t a n d t h e s h i p t r a c k s t o t h e r i g h t .

I t i s r e c o m m e n d e d t h a t t h i s " f i v e

degree" maneuver be executed by

g i v i n g a c o u r s e o r d e r ( i . e . " H e l m ,

come righ t sma rtly to XXX . " ) v i c e a

rudder order and tha t the helmsman

be a qualified ma ster helmsman who

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

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

breaka way . You may ch oose to use

rudder orders, but th e helms ma n

may be carrying sig nifi cant am ounts

o f r u d d e r a l r e a d y t o h o l d t h e o r d e r e d

course and will know what's needed

t o e x e c u t e a s m a r t c o u r s e c h a n g e .

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

m a y b e r e t u r n i n g t o b a s e c o u r s e

b e f o r e y o u o p e n u p t o o f a r .

The Three Mi nut e an d

One Min ute Rules

Experienc ed OODs are well

v e r s e d i n t h e t h r e e m i n u t e r u l e

w h i c h s t a t e s t h a t t h e d i s t a n c e i n

y a r d s t r a v e l e d i n 3 m i n u t e s i s e q u a l

t o t h e s p e e d i n k n o t s m u l t i p l i e d

A A t a s i g n a l ' s e x e c u t i o n , a s h i p m u s t e x p e d i t i o u s l y m a n e u v e r t o s t a t i o n w h i l e m i n d i n g

s a f e t y o f n a v i g a t i o n .

www.navy.mil /navpalib/cno/n7 6

by

1Winter 2004 Vol . 29 No . 1



16

A I n t h e 2 . m i n u t e s i t t a k e s t o t u r n a t 2 0 k n o t s , t h e g u i d e w i l l t r a v e l 1 0 0 y a r d s . T h e r a t i o o f 1 0 0

y a r d s t o t h e r a n g e a t s t a t i o n i s s l i g h t l y l e s s t h a n h a l f a r a d i a n , a p p r o x i m a t e l y 2 d e g r e e s . T u r n w h e n

t h e g u i d e b e a r s 0 9 , 2 d e g r e e s g r e a t e r t h a n g u i d e ' s b e a r i n g w h e n a t s t a t i o n .

1 0 0 . Thus a s hip going 10 knots

t r a v e l s 1 0 0 0 y a r d s i n 3 m i n u t e s . F o r

slow speeds it m ay sometim es be

u s e f u l t o u s e t h e o n e M i n u t e r u l e

w h i c h i s e s s e n t i a l l y t h e t h r e e m i n u t e

r u l e d i v i d e d b y t h r e e . The one

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

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

e q u a l t o t h e s p e e d i n k n o t s m u l t i -

p l i e d b y 1 0 0 . Thus a sh ip approach-

i n g a b e r t h a t 2 k n o t s w i l l t r a v e l 2 0 0

f e e t i n o n e m i n u t e .

T h e I n v i s i b l e

Dis ta nc e Formula

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

not quick mat h . I t h a s t o b e c a l c u -

l a t e d i n a d v a n c e b u t o n c e c a l c u l a t e d

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

q u a r t e r s s i t u a t i o n s . A g ood example

o f i t s u s e i s t h e s i t u a t i o n w h e r e y o u

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

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

o b j e c t s u c h a s t h e q u a y w a l l . F rom

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

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

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

the bow which , giv en your heigh t of

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

t h e v e s s e l w i l l b e a f i x e d d is t a n c e .

Typically for CG; a n d D O G s t h i s d i s -

t a n c e i s a b o u t S 0 o r 9 0 y a r d s .

However, using the drawing and for-

mula below you can ca lculate what it

w i l l b e f o r y o u r p a r t i c u l a r s h i p . You

w i l l f i nd , t h a t d if f er e nc e s i n h e i gh t o f

e y e a n d s m a l l c h a n g e s i n s h i p ' s d r a f t

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

One of the thin gs an OOD is

e x p e c t e d t o k n o w i s , o f c o u r s e , t h e

m a n e u v e r i n g c h a r a c t e r i s t i c s , o r " t a c -

t i c a l c u r v e s " o f h i s s h i p . U s u a l l y t h i s

A I n t h e 2 . m i n u t e s i t t a k e s t o t u r n a t 2 0 k n o t s , t h e g u i d e w i l l t r a v e l 1 0 0 y a r d s . T h e r a t i o o f 1 0 0

y a r d s t o t h e r a n g e a t s t a t i o n i s s l i g h t l y l e s s t h a n h a l f a r a d i a n , a p p r o x i m a t e l y 2 d e g r e es . T u r n w h e n t h e

g u i d e b e a r s 0 9 , 2 d e g r e e s g r e a t e r t h a n g u i d e ' s b e a r i n g w h e n a t s t a t i o n .

www.navy . m i t / ;navpalib/cn o/n76

w i l l comprise a volume of fi gures

a n d g r a p h s , w h i c h c a n s c a r c e l y b e ;

mem orized . I l o w e v e r , i t i s i m p e ra °

t i v e f o r t h e U U D t o h a v e a r a t h e r

acc urate knowledge of advance,

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

i n g r a t e s f o r v a r i o u s speeds and rud-

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

m e m o r i z e f i g u r e s f o r , s a y , t e n , f i f t e e n ,

t w e n t y , a n d t w e n t y - f i v e k n o t s , t h e

s a m e r u d d e r a n g l e s , a n d 1 8 0 ' o f t u r n

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

r e a d i l y a c c e s s i b l e , p r e f e r a b l y i l l a

hand y tabulated form .

Now suppose th at . y o u a r e a c o n -

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

g u i d e , a n d y o u a r e t o l d t o t a k e s t a -

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

d e c i d e t o t u r n a n d h e a d b a c k o n t h e

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

t h r o a t " . He's maki ng 20 knots, you

a r e a t 2 , a n d s u d d e n l y t h e r e Y o u a r e

w i t h a c l o s i n g r a n g e o f n e a r l y 4

knots and a decision to make . I t i s

well to c ome prepared .

Your sta tion is 1000 yards dead

ahead of the guide, and you have

decided t o turn bac k to bas e course

at 2 kn ots with 1 degrees rudder,

s l o w i n g t o 2 0 a s y o u b e g i n t o

steadyt i p

on base course. N ow you

absolutely mus t k now how log ;

t h a t t u r n i s g o i n g t o t a k e .

S i l l f r 7 C ' i ' W n r t r z r i '

Winter 2004 Vol . 29 No . 1



F o r s a f e t y ' s s a k e y o u a r e g o i n g t o

ass ume it takes th ree minutes . I n

three min utes the guid e will

approach you by a m atter of 2000

yards, d ue to his own motion .

Therefore, when his range is 3000

yards you Will turn, and when you

hav e completed your turn an d

slowed to 20 knots, you Will b e j u s t

about 1000 yards ahead of him ,

a c t u a l l y a t r i f l e m o r e . However, if

from necessit y or choice you are

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

there is n o other way t han to make

t h e s e c a l c u l a t i o n s . CIC can do no

more and you may be lucky i f th ey

react quickly enough to do as much .

A ma neuvering board is no help . I t

will ha ve to be done in your head .

Here you are coming int o what

m i g h t b e s c r e e n s t a t i o n , 3 0 0 y a r d s

from t he guide and somewhat abaft

of his beam . H i s c o u r s e i s 0 0 0 ° ,

W1,Ite1" 2004

A T a r g e t a n g l e o f f e r s u s e f u l i n f o r m a t i o n t o q u i c k l y p l a n o r v i s u a l l y c o n f i r m t h e c o u r s e o f a c o n t a c t c a l c u l a t e d b y C I C .

speed 18 , and when on stati on he

w i l l b e a r 0 7 0' . You are coming down

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

t h e t r a c k s h o w n a t 2 0 k n o t s .

Y o u c h o s e y o u r c o u r s e , b y e y e o r

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

p l a c e d t o w a r d s t h e g u i d e ' s t r a c k b y

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

Now as y ou close him, you are again

wondering wh ere to sta rt your turn .

Begin by assum ing th at your turn

w i l l t a k e p l a c e a t a p o i n t . T h e p o i n t

chosen i s th e one you reach on c om-

p l e t i o n o f y o u r t u r n . w h e n t h e r e , y o u

h o p e t o b e o n s t a t i o n . This assump-

t i o n w i l l i n t r o d u c e e r r o r , b u t n o t

m u c h i n a s i t u a t i o n s i m i l a r t o t h i s

example . T h i s t u r n i s g o i n g t o t a k e

(you know or hav e looked i t up) 2

m i n u t e s a t 2 0 k n o t s , w i t h s t a n d a r d

rudder. Ag ain you are going to slow

t o 1 k n o t s t o w a r d s t h e e n d o f

t h e t u r n .

www.navy. rnil/navpalib/ono/n76

While you spend 2 mi nutes turn-

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

h i s t r a c k ? A b o u t 1 0 0 y a r d s , b y t h e

t h r e e m i n u t e r u l e . Those 100 yards

a r e l e s s t h a n h a l t o f your 300 yards

f i n a l r a n g e . T h e a n g l e A a b o v e i s

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

r a d i a n , s a y 2 d e g r e e s . T h e r e f o r e

w h e n t h e g u i d e b e a r s 0 0 , y o u w i l l

begin y our turn .

Now when you look a t i t objec-

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

cula te? All you used . w a s t h e

knowledge you had anyway, plus t h

r a d i a n r u l e . You make no attempt to

b e a b s o l u t e l y p r e c i s e . You used sev-

e r a l a p p r o x i m a t i o n s , f o r s i m p l i c i t y ' s

sake . P r o b a b l y y o u t u r n e d a l i t t l e

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

a t e l y o n c o m i n g o u t o f y o u r t u r n .

What gav e your mental ca lculat ions

t h e i r v a l u e W a s t h e f a c t t h a t y o u

knew you would come out quit e

c l o s e t o s t a t i o n .

Winter 2004 Vol . 29 No . 1

1



At the moment you began your

t u r n , t h e s i t u a t i o n l o o k e d l i k e t h i s :

You turned with th e guide at a

range of 3000 yards . With your turn-

i n g d i a m e t e r o f 1 1 0 y a r d s , t h e a n g l e

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

r a d i a n , s a y 2 d e g r e e s . The distance

f r o m C t o I ' w a s t h e r e f o r e o n l y 2 7 0 0

yards . I f y o u r t u r n h a d , i n f a c t t a k e n

3 mi nutes, as you assumed, you

would h ave ended up only 700 yards

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

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

you 300 yards behind st ation . T h a t

extra half min ute you allowed for

the turn s erved to compensa te for

300 yards, inasmuch as half a m inute

r e p r e s e n t e d v e r y c l o s e t o 3 0 0 y a r d s

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

h i s t r a c k .

1 8

A T o t h e o b s e r v e r o n t h e b o w , t h e n o r t h f a c e o f P i e r 1 i s " O P E N " , A i s t h e " D I S T A N C E T O " P i e r 1 , B i s t h e o f f s e t o f t h e b o w " F R O M" t h e f a c e o f P i e r 1 , a n d ( i s t h e

o f f s e t o f t h e p o r t s i d e " T O " t h e e n d o f P i e r 1 . T o t h e o b s e r v e r o n t h e s t e r n , t h e s o u t h f a c e o f P i e r 1 i s " O P E N " , t h e n o r t h f a c e o f P i e r 1 i s " C L O S E D " , t h e s t e r n " H A S

S W I N G C L E A RA N C E " o n b u o y T , o r t h e s w i n g c l e a r a n c e o n b u o y T i s d i s t a n c e D .

How do most OOD's f ig ure recip-

r o c a l b e a r i n g s ? A q u i c k g l a n c e a t t h e

man euvering hoard is no doubt easi-

e s t a n d s u r e s t . B u t i f y o u w a n t t o d o

i t i n y o u r h e a d , d o y o u t r y t o a d d o r

s u b t r a c t 1 8 0 d e g r e e s ? T h i s c a n

become awkward, and c an lead to

e r r o r s . Why not add 200" and th en

s u b t r a c t 2 0 , o r c o n v e r s e l y s u b t r a c t

2 0 0 a n d a d d 2 0 ? T h i s i s o f c o u r s e

extremely sim ple, but h ave all OOD's

t h o u g h t o f i t ?

F e w O O D ' s r e a l i z e t a r g e t a n g l e s ,

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

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

a c o n t a c t ' s c o u r s e .

T h e c o n t a c t b e a r s 1 6 8 ' . T h e r e c i p -

r o c a l i s 3 4 8 ' , t h e c o n t a c t i s 2 0 d e g r e e s

on the st arboard bow. Contact course

3 4 8 ° m i n u s 2 0 e q u a l s 3 2 8 " . T h e s o l u -

t i o n i s f o u n d i n a n i n s t a n t , a n d i f

www.navy.mil /navpalih/cno/n7 6

y o u r e s t i m a t e w a s g o o d , w i l l b e b e t -

ter than CIC's, which ma y not be

ava ilable an yway for two or

th ree min utes .

V i s u a l i z i n g r e l a t i o n s h i p s i s a l a r g e

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

you determi ne conta ct course, CPA,

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

help you commun ica te better.

C o n n i n g o f f i c e r s o f t e n r e l y o n

r e p o r t s f r o m t h e f o c ' s l e a n d f a n t a i l t o

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

ment . T h i s i s o n l y u s e f u l i f e v e r y o n e

is speaking the same languag e . T h e

drawing below suggests s everal t erms

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

ful in communicating between the

b r i d g e a n d v a r i o u s l o o k o u t s .

Surfac e Warfare

Win ter 2004 Vol . 29 No . 1



Doubling the Angle onthe Bow (A ClassicDR tool)

Another application of basi c

trigonometry can be useful in

obtain ing ai l estim ated positi on

from a single land mark . S h o o t t h e

bearing to a fi xed object an d record

the difference between your head-

ing and the bearing (angle on the

bow) . Mai nta in course and con-

t i n u e t o s h o o t b e a r i n g s t o t h e

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

t w i c e w h a t i t w a s a t t h e f i r s t b e a r -

i n g . A t t h a t p o i n t , y o u r d i s t a n c e

f r o m t h e f i x e d o b j e c t i s e q u a l t o t h e

dis tan ce traveled between the two

bearing s . The bearing and di stanc e

thus obtained can be plotted as an

estimated positi on .

Wliit cl" 2004

A R u n n i n g f i x e s c a n b e e s p e c i a l l y u s e f u l w h e n v i s u a l b e a r i n g s a r e o n l y a v a i l a b l e o n o n e s i d e o f t h e s h i p .

I t w o u l d b e i m p o s s i b l e t o e x h a u s t

the situations in which an OOD

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

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

man euvering problems . T h e v a r i e t y

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

i s a l s o e nd l e s s . I b e l i e v e , h o w e v e r ,

t h a t i t i s a p p r o p r i a t e t o s t r e s s t h a t

t h i s t y p e o f t h i n k i n g , a n d m e n t a l

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

cal part of an OOD's continuous and

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

meet any si tuation which may a rise .

The radian rule and the three

m i n u t e r u l e a r e e x c e l l e n t a i d s t o a n

OOD in the execution of hi s con-

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

T h e i r u s e i s f o r a s s i s t i n g i n m a k i n g

rapid and accurate maneuvering

d e c i s i o n s . T h e f o l l o w i n g t e s t r e p r e -

sents applications of mathematics

www.navy.mi l /navpalib/cno/ n76

tha t OOD's should be able to do

( s a n s c a l u c u l a t o r s ) .

( T h e t e s t i s n o t i n c l u d e d h e r e -

g o o n l i n e t o

wy v . n a ~ ~ s e a . navy . m 1 l / swm<ra r , i n e

and download the test and

0 v a r i a t i o n s ! )

1

Win ter 2004 Vol . 29 No . 1

ood quick math

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