Practical Bollard-Pull Estimation

8/20/2019 Practical Bollard-Pull Estimation

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Mar ine Techno logy , Vo l . 24 , No . 3 , Ju l y 1987 , pp . 22 0-2 25

Pract ical Bol lard-Pul l Est imat ion

Y . A . I s in 1

During the pr e l i m i na r y de s i gn of a t u g b o a t, t h e u s e o f m i n i c o m p u t e r s c a n p e r m i t t h e d e s i g n e r t o g ive a v e r y

qu ick es t imate o f

pr op e l l e r c ha r a c te r i s t i c s s uc h a s p i tc h -d i a me te r r a t io , e x pa nde d a r e a r a t io , r e v o l u t ions pe r

second, and t h e t h r u s t a n d d e l iv e r e d h o r s e p o w e r f o r t h e b o l l a rd - p u ll c o n d i ti o n . T h e s e e s t i m a t e s c a n b e m a d e

by the use o f char ts der i ved f rom p o l y n o m i a l e x p r e s s i o n s o f e x p e r i m e n t a l p r o p e l l e r s e r i e s d a t a , f o r

e x a mp l e , t h e W a g e n in g e n B - Sc r e w S e r i e s .

T H E R E A SO N fo r t h e e x i s t e n c e o f a t u g b o a t i s t h e p u l l i n g o r

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

t u g b o a t ' s m o s t i m p o r t a n t c o m p o n e n t s i s it s p ro p e l l e r. T u g s

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

a t s o m e i n t e r m e d i a t e s p e e d , a n d b o l l a r d p ul l. T h u s , w h e n

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

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

a n d a s s u ch s p e c i fi c r e q u i r e m e n t s c a n n o t b e q u o t e d , e x c e p t t h a t

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

s h o u l d h a v e a s p e c i fi e d m i n i m u m b o l l a r d p ul l. F o r p r e l i m i n a r y

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

a b o u t 1 5 k g ( 3 3. 5 lb ) o f b o l l a r d - p u l l t h r u s t p e r d e l i v e r e d h o r s e -

p o w e r i n s t a l l e d . A r g y r i a d i s [ 1 ] 2 h a s s t a t e d t h a t f o r t h e t u g L . E .

N o r g a a r d t h e e x p e c t e d b o l l a r d p u l l is a b o u t 1 5 .2 k g / D H P ( 34

l b / D H P ) , f o r th e E . F . M o r a n i t l ie s b e t w e e n 1 3 a n d 1 3 .6 k g /

D H P ( 2 9. 1- 3 0. 4 l b / D H P ) a n d f o r D . S . S i m p s o n i t i s e q u a l o r

c l o s e t o 1 0 k g / D H P ( 22 .4 l b / D H P ) .

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

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

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

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

D e s i g n f o r b o l l a r d p u l l

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

i s s u es ; (1 ) c h o i ce o f t h e p r o p e l l e r ' s m a i n d i m e n s i o n s , ( 2 ) e s t i m a -

t i o n o f t h e b o l l a r d p u l l , (3 ) e s t i m a t i o n o f t h e t u g ' s f r e e s p e e d ,

a n d ( 4) e s t i m a t i o n o f t h e t u g ' s o v e r a l l t o w i n g p e r f o r m a n c e . T h e

t u g ' s f re e - s p e e d a n d t o w i n g p e r f o r m a n c e d e p e n d o n t h e c h o ic e

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

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

a c t e r i s t i c s (p o w e r a n d r p m ) .

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

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

d i a m e t e r p r o p e l l e r p o s s ib l e . C o n s i d e r a t i o n s a r e t h e t u g ' s d r a f t

a n d t h e h u l l - p r o p e l le r c l e a ra n c e . T h e m a x i m u m p r a c t i c a l d i -

a m e t e r o f a n o p e n p r o p e l l e r i s a b o u t 8 5 p e r c e n t o f t h e d r a f t a f t .

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

t h e p i t c h - d i a m e t e r r a t io ( P / D ) b e t w e e n 0 . 6 a n d 1 .2 5 . H o w e v e r ,

t h e b e s t b o l l a r d p u l l P / D i s a b o u t 0 .6 . T h e m i n i m u m b l a d e - a r e a

r a t i o s h o u l d b e b e t w e e n 0 . 5 0 a n d 0 . 55 i n o r d e r t o g i v e a l l - a r o u n d

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

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

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

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

f o u r b l a d e s .

1 Senior research engineer , S ta te Un ivers i ty of Liege , Liege , Belgium.

2 Num be r s i n b r a c ke t s de s i gna t e Re f e r e nce s a t e nd o f pa pe r .

Or i g i na l ma nu s c r i p t r e c e ive d a t SN AM E he a dqua r t e r s J u l y 7 , 1985 ;

revised manu scr ip t rece ived Ma rch 14, 1986.

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

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

c o e f f i c i e n t ( J ) i s z e r o :

n D

w h e r e

VA = p r o p e l l e r a d v a n c e s p e e d

n - - p r o p e l l e r r e v o l u t i o n s p e r u n i t t i m e

D = p r o p e l l e r d i a m e t e r

T h e a d v a n c e c o e f f i c ie n t (J ) i s n o n d i m e n s i o n a l a n d a t t h e b o l -

l a r d - p u l l c o n d i t i o n i s z e r o a s VA i s z e r o . A l s o , a t t h i s c o n d i t i o n ,

t h e w a k e c o e f f i c i e n t W is z e r o s in c e b o t h t h e t u g s p e e d a n d t h e

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

f i c i e n t t c a n b e a s s u m e d t o b e a b o u t 2 o r 3 p e r c e n t . F o r m o s t t u g

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

a b o u t u n i ty .

B o l l a r d - p u l l c h a r t s

F o r p r e l i m i n a r y d e s i g n p u r p o s e s A r g y r i a d i s [ 1] g i v e s t h e f o l -

l o w i n g e q u a t i o n s ( c h a n g e d t o t h e m e t r i c s y s t e m ) f o r t h e b o l -

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

K T

B H P ° × Tc w i t h T c 6 0 X - -

T ( k g ) = 7 1 6 X N o X D = 2 0 ~ K Q

B H P 0 ~ 1 /2

N = 60 X 6 . 55 × w i t h T r = K Q

N o X D ~ X Tr ]

T h e s y m b o l s ar e d e f i n e d in t h e N o m e n c l a t u r e . T h e v a l u e s o f Tc

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

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

d i s k - a r e a r a t i o o f 0. 50 . S t r i c t l y s p e a k i n g , t h e c u r v e s a p p l y o n l y

t o p r o p e l l e r s w i t h a i r f o i l s h a p e s e c t i o n s f r o m 0 . 5 r a d i u s t o t h e

t i p .

I n t h e d i s c u s s i o n to r e f e r e n ce [1 ] b o t h K i m o n a n d M o r g a n

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

o n l y t o c o n s t a n t - t o r q u e i n s t a l l a t i o n s . M o r g a n [1 ] d e r i v e s t h e

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

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

T r o o s t p r o p e l l e rs w i t h d i f f e re n t e x p a n d e d a r e a r a t i o s . F ig u r e s 2

a n d 3 r e p r o d u c e h e r e t h e t h r e e a n d f o u r - b l a d e d p r o p e l l e r d a t a ,

r e s p e c ti v e l y . S i n c e t h e s e d i a g r a m s a r e b a s e d o n o p e n - w a t e r

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

c e n t ( u p t o 1 0 p e r c e n t ) .

T h e s e c o r r e s p o n d i n g e q u a t i o n s , i n t h e m e t r i c s y s t e m , a r e :

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A p = p r o j e c t e d a r e a o f p r o p e l l e r b l a d e s , m 2

B H P = b r a k e h o r s e p o w e r a t b o l la r d p u l l

D H P 0 = d e l i v e r e d h o r s e p o w e r a t d e s i g n s p e e d

( m a x i m u m p o w e r)

E A R = e x p a n d e d a r e a r a ti o =

A E / A o

E A R 0 = m i n i m u m e x p a n d e d a r e a r a ti o fo r f r e e

B H P 0 = b r a k e h o r s e p o w e r a t d e s i g n s p e e d

( m a x i m u m p o w e r )

C = C a ld w e l l ' s c a v i t a t i o n c o e f f i c i e n t

C Z AR = e x p a n d e d a r e a r a t i o c o e f f i c i e n t

= 0 . 6 7 . ~ ( C T L S ' 8 ~

C N = p r o p e l l e r r o t a t i o n a l c o e f f i c i e n t

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= t ~ p 1 /2 ) K p Z/~

D = p r o p e l l e r d i a m e te r , m

D H P = d e l i v e r e d h o r s e p o w e r a t b o ll a r d p u l l

c a v i t a t i o n se r v i c e

J = p r o p e l l e r a d v a n c e c o e f f i c i e n t

= V a / n D

K 0 = t o r q u e c o e f f i c i e n t

Q / p n 2 D 5

K r = th r u s t c o e f f i c i e n t

= T / p n 2 D 4

N = p r o p e l l e r r o t a t i o n a l sp e e d ( r p m ) a t

b o l l a r d p u l l

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s i g n s p e e d

n = p r o p e l l e r r o t a t i o n a l sp e e d ( r p s ) a t b o l -

l a r d p u l l

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~ R = p r o p e l l e r r e l a t i v e r o t a t i v e e f f i c i e n c y

P = p r o p e l l e r p i t c h ( m )

P / D = p r o p e l l e r p i t c h - d i a m e t e r r a t io

p = A p / A E

Q = p r o p e l l e r t o r q u e ( k g X m )

75

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S H P = s h a f t h o r s e p o w e r

T = p r o p e l l e r t h r u s t ( k g ) a t b o l l a r d c o n d i -

t i o n

= p n 2D 4 • K T

t = t h r u s t d e d u c t i o n c o e f f i c i e n t

T c = p r o p e l l e r t o r q u e - th r u s t c o e f f i c i e n t s

r a t i o

6 0 K T K r

- - o r - -

20.7r KQ KQ

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= K 0

V = t u g s p e e d , m / s

V a = p r o p e l l e r s p e e d o f a d v a n c e , m / s

=v(1-w)

V t i p = p r o p e l l e r t ip s p e e d , m / s

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F i g u r e s 2 a n d 3 s h o w t h a t t h e t w o m a j o r f a c t o r s a f f e c t i n g t h e

b o l l a r d p u l l o f a tu g a r e t h e p r o p e l l e r d i a m e t e r D a n d t h e

h o r s e p o w e r D H P d e l i v e r e d b y t h e e n g in e . O t h e r b o l l a r d - p u l l

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

b a s i c d e f i n i t i o n s o f KT, KQ, a n d Q a n d t h e p o l y n o m i a l e x p r e s -

s i o n s fo r t h e W a g e n i n g e n B - S c r e w S e r i e s [ 3] .

CT CN

G E A R c h a r t s

A t b o l l a r d p u l l, t h e r e l a t i o n s h i p b e t w e e n t h r u s t T , p r o p e l l e r

d i a m e t e r D , a n d e n g i n e d e l i v e r e d h o r s e p o w e r D H P c a n e a s il y

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

d e f i n i t i o n s o f t h e t h r u s t c o e f f i c i e n t KT, t h e t o r q u e c o e f f i c i e n t

K Q , a n d t h e e n g i n e d e l i v e r e d h o r s e p o w e r D H P . T h u s b y d e f i n i -

t i o n

K T =T~,KQpn2D - p n 2 ~ a n d D H P - 2~nQ75

t h e n

T = C T x ( D H P X

D ) 2/3

(1)

w h e r e

\2/3

= 75 pt /2) X KT

CT ~ KQ2/a

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

t h e p r o p e l l e r d i a m e t e r D f r o m t h e e x p r e s s io n s f o r KT, KQ a n d

T . T h u s

D H P 2

n = CN x T5/2 (2)

w h e r e

CN = 75 X

CT3/2 KT

2~r KQ

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f u n c t i o n s o f t h e c o e f f i c i e n ts K T a n d KQ a n d t h e y c a n e a s i l y b e

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

v a l u es o f p i t c h - d i a m e t e r r a t io P / D a n d o f e x p a n d e d a r e a r a t io

E A R .

T h e v a l ue o f E A R t o a v o i d c a v i t a t i o n t h r u s t b r e a k d o w n a n d

e r o s i o n h a s b e e n d e r i v e d b y C a l d w e l l [ 2 ] f r o m a n a n a l y s i s o f

B u r r i l l ' s c a v i t a t i o n c h a r t a s s u m i n g a p p r o x i m a t e l y 2 1/.2 p e r c e n t

b a c k ( s u c t i o n s i d e ) c a v i t a t i o n . T h e f o r m u l a i s g i v e n b y

(DH P/A~ ) 2/3

E A R 0 = C x

T h i s e q u a t i o n c a n b e w r i t t e n a s f o ll o w s

E A R 0 = [ ~ . 4 - C3/2. DHP 12 / 5

D 2 p O r - n - D ) l ° 8 J

w h e r e

p = p r o p e l l e r p r o j e c t e d a r e a - e x p a n d e d a r e a r a t i o

= Ap/AE =

1.067 - 0 .229

P / D

B y s u b s t i t u t i n g t h e e x p r e s s i o n s f o r n a n d D f o r t h e W a g e n i n g e n

B - S c r e w S e r i e s , E A R o c a n b e w r i t t e n i n t h e f o l lo w i n g f or m :

2 2 2 M A R I N E T E C H N O L O G Y



where

EA Ro = CEAR X (D~HTP)°768

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28 8

c o . 6 ( 6 T 1 ' 8 4 8 ~

CEAR=0 . 67×\

The value of the coeffi cien t C varies betw een 0.15 and 0.2. The lB.0

values of

GEAR ca n

be computed for the values of C T and CN for

given values of

P / D

and EAR.

Curves of

C T, C N,

and

GEAR,

develope d from the approp riate 16.8

propeller charts, can be plotted as functions of P / D and EAR

and used to give a quick estimat ion of the prope ller main di-

mensions for a given DHP and required bollard pull. Such

curves have been derived from the Wageningen B-Screw Series ,4.8

polynomi al expressions for three and f our-bladed pro pellers [3]

and are shown in Figs. 4, 5 ( a , b , e ) , and 6 ( a , b , c ) . Figure 4, CEAR

versus T/DHP, gives the minimum values of EAR to avoid

cavit ation thru st breakdown and erosion and Fig. 5 or Fig. 6 can ,2.8

be used to determine the dia meter D, revolutions per second n,

and

P / D

for the selec ted EAR f rom Fig. 4.

These figures and the equations for T versus C T and n versus re. e

C N can be used in different ways to determine the propeller

main characteristics for the required bollard pull at a given

DHP or the bollard pull and DH P for the chosen propeller. The

designer can obtain an opt imu m propelle r after some iterations. 8.8

One simple example, treated in the Appendix, shows how to

obtain by using these diagrams a quick estima te of the propell er

characteristics for a given DHP and required t hrust at bollard

pull.

C o n c l u s i o n

As can be seen from the exam ple trea ted in the Appendix, the

CT CN

G E A R

bollard-pull charts can be used to give a good

estimate of the propeller characteristics. Moreover, these data

should be adequate for preliminary design purposes.

When utilizing the new diagrams, the designer must keep in

mind that some corrections should be introduced, such as cor-

rections for Reynolds number and hull interference effects

(thrust-deduction factor and wake fraction). Without these cor-

rections, the values obtained from the chart may be overesti-

mated by a few percent. For preliminary design purposes, the

designer can decrease this over-estimation by decreasing the

calculated propeller diameter by 0.5 to 1 percent.

The C T, C N, CEARbollard-pull charts present ed in this paper

are derived from the polynomial expressions of

K T

and

K Q

for

the Wageningen open-water B-Screw Series for a Reynolds

numb er of 2 × 106. Corrections for other Rey nold' s numbers are

given in reference [3].

R e f e r e n c e s

1 Argyriadis, D. A., Modern Tug Design, with Particular Emphasis

on Propeller Design, Maneuverability, and Endurance,

T r a n s .

SNAME, Vol. 65, 1957, pp. 362-444.

2 Wood, J. N., C a l d w e l l' s S c r e w T u g D e s i g n , Hutchinson Publish-

ing Co., London, 1969.

3 Oosterveld, M. W. C., Fur ther Computer Analysed Data of Wa-

geningen B-Screw Series, Netherland Ship Model Basin Publicat ion

No. 479; also, I n t e r n a t i o n a l S h i p b u i l d i n g P r o g r e s s , Vol. 22, No. 251,

July 1975.

Appendix

E x a m p l e o f a p p l ic a t i o n

Estimate the three-bladed Wageningen B-Series propeller character-

istics

D , P / D ,

EAR and its rpm N for

:EAR mnmum for cavitation

free service

.S .6 .l .8 .9 1. 1.1

I l [

6 8 I0

CEAR

Fig . 4

• Available delivered horsepower at bollard (DHP) = 600 hp

• Reques ted thrust a t bollard (T) = 9300 kg

a. without any restriction on D

b. with D -- 2.6 m only

Case

a

With no restriction on D and N, the best propeller can be defined by

taking P / D = 0.5 to 0.6 and EAR = 0.5 to 0.7, if possible, to give all-

round towing performance and high astern bollard pull.

--From Fig. 4

T

DH~ = 15.5 -~ CEAR= 4.85

EAR = 0.6

--F rom Fig. 5(a)

EAR = 0.6

- - - , P /D = 0.52

CEA = 4.85

--From Figs. 5(b) and 5(c)

P / D =

0.52

C T =

70.56

EAR = 0.6 CN = 7.73 X 104

Then for

Thus we obtain

C T =

70.56, equation (1) gives D = 2.52 m

C N = 7.73 X 104, equation (2) gives N = 200

rpm.

D = 2.52 m Z = 3 blades

P / D = 0.52 N = 200 rpm

EAR = O.6

Case b

In this case, it is necessary to introduce D = 2.6 m in equation (1) to

compute

CT:

J U L Y 1 9 8 7 2 2 3



1.2

I.I

1 . 8

B.9

B . 8

8.7

B.6

B.S

8 4

P / ~

EAR

.5 .7 .9 1.1

I I I | I I I

4 4 . 5 5 5 . 5 6 6 . 5

CEkR

F i g . 5 ( a )

1.2

I . I

1 . 8

8 . 9

8 . 8

8 . 7

@.6

8 . S

9 4

Z-3

P / l ) p ~

Z-3

1

I . I I 8 . 9 8 . 8 8 . 7 8 . e 8 . 5

I i i I

S , 6 8 6 5 78

F i g . 5 ( b )

I

C l

1 .2

I . I

1 . 8

8 . 9

8 . 8 i

8 . 7

8 . 6

8 . S

8 . 4

I . i

I o . g

f I

5 6

F i g . 5 ( c )

E A R

G . 6 8 . 7 6 . 6

I

8

Z-3

8 . $

I

C~.IO 4

- - F r o m e q u a t i o n ( 1 )

T = 9 . 3 0 0 k g

D H P = 6 0 0 h p - * C T = 6 9 . 2

D = 2 . 6 m

- - F r o m F i g . 5 ( b )

C T = 6 9 . 2

- - P / D = 0 . 4 4 2

E A R = 0 . 6

C T = 6 9 . 2

- - P / D = 0 . 4 9 2

E A R = 0 . 7

- - F r o m F i g . 5 ( a )

E A R = 0 . 6

P / D = 0 . 4 4 2 - * C E AR = 4 . 5 8

E A R = 0 . 7

P / D = 0 . 4 9 2 - * C E AR = 4 . 7 3

- - F r o m F i g . 4

= 4 . 5 8

C E A R = 4 . 7 3 - -~ m i n i m u m E A R - - 0 . 5 5 - 0 . 6

( f o r c a v i t a t i o n )

I f w e a s s u m e E A R = 0 . 6 a n d w i t h P / D = 0 . 4 4 2 :

- - F r o m F i g . 5 ( c )

E A R = 0 .6

P / D = 0 . 4 4 2 - - * C N = 8 . 0 6 × 1 0 4

T h e n f o r C N = 8 . 0 6 × 1 0 4, e q u a t i o n ( 2 ) g i v e s N - - 2 0 8 r p m . T h u s w e

o b t a i n

D = 2 . 6 m ( g i v e n ) Z = 3 b l a d e s

P / D = 0 . 4 4 2 N = 2 0 8 r p m

E A R = 0 . 6

2 2 4 M A R I N E T E C H N O L O G Y



P/O

1.2

1 1

1 . 8

8 . 9

8 . 8

8.7

8 . 6

e.s

9 . 4

E A R

Z , 4

.7 .9 1.1

I I I I I I I

4 4.5 5 5.5 6 6.5 CEXR

F i g . 6 ( a )

P/D

1.2

I . I

t . 8

8 . 9

9 . 8

8 . 7

8 6

8 . S

8.4

I . I

E A R

0 . 9 8 . 8 8 . 7 9 . 6 0 . 5

I I

68

6S

F i g . 6 ( b )

70

Z=4

CT

hese calculat ions can be checked from the T c and T r curves given in

Figs. 2 and 3. P / 0

Case a 1.2

For D

=

2.52 m, from the Wageni ngen B-Screw Series polynomial

computa t ion:

P / D = 0.52 -* K T = 0.1995 T ¢ = 10.9 I. t

EAR = 0.6

Z = 3 blad es K Q = 0.018 3 T r = 0.018 3

1.8

Th en for DHP = 600 hp -~ N = 199.5 ~ 200 rpm

T = 9313.7 kg

C a s e b 9.9

For D = 2.6, from the Wa genin gen B-Screw Series polynomial com-

p u t a t i o n

P / D = 0.442 -~ K T = 0.1636 Tc = 11.7 e. 8

EAR = 0.6 K Q = 0.014 T r = 0.014

Z = 3 blad es

8.7

Then for DH P = 600 hp -* N = 207 rpm

T = 9336 kg

These resul ts are similar to those obtained from the CT , CN , CEAR

bollard -pull chart ; the observed small differences ar ise from the preci- 6.8

sion of the CT , CN , GEAR dia gra ms of Figs. 4 an d 5.

M e t r i c C o n v e r s i o n F a c t o r s

lm = 3 .28f t

1 kg = 2.20 lb

1 kW = 1.34 hp

e.S

e . 4

I . I I

I I

5 6

F i g . 6 ( c )

~AA

8 . g e . 8

I

7

Z . 4

0.7 8.8 9.5

t J

8 CN.10-4

JULY 1987 2 2 5

Documents

Practical Bollard-Pull Estimation