8/20/2019 Practical Bollard-Pull Estimation http://slidepdf.com/reader/full/practical-bollard-pull-estimation 1/6 Marine Technology, Vol. 24, No. 3, July 1987, pp. 220-225 Practical Bollard-Pull Estimation Y. A. Isin 1 During the preliminary design of a tugboat, the use of minicomputers can permit the designer to give a very quick estimate of propeller characteristics such as pitch-diameter ratio, expanded area ratio, revolutions per second, and the thrust and delivered horsepower for the bollard-pull condition. These estimates can be made by the use of charts derived from polynomial expressions of experimental propeller series data, for example, the Wageningen B-Screw Series. THE REASON for the existence of a tugboat is the pulling or pushing of large vessels and, hence, it follows that one of the tugboat's most important components is its propeller. Tugs operate under various conditions, that is, free running, towing at some intermediate speed, and bollard pull. Thus, when powering a tug all these conditions must be considered. Harbor tugs are designed for general operation in and around a harbor and as such specific requirements cannot be quoted, except that the tug should have a certain free-running speed and that it should have a specified minimum bollard pull. For preliminary design purposes, a well-designed propeller should develop about 15 kg (33.5 lb) of bollard-pull thrust per delivered horse- power installed. Argyriadis [1]2 has stated that for the tug L. E. Norgaard the expected bollard pull is about 15.2 kg/DHP (34 lb/DHP), for the E. F. Moran it lies between 13 and 13.6 kg/ DHP (29.1-30.4 lb/DHP) and for D. S. Simpson it is equal or close to 10 kg/DHP (22.4 lb/DHP). The design of the propeller for the bollard-pull condition is, of course, somewhat academic since tugs do not, in general, operate at this condition. It is still an important design condi- ti~n for harbor tugs as it is the simplest and most comm on one. Design for bollard pull The design of a propeller for bollard pull introduces four issues; (1) choice of the propeller's main dimensions, (2) estima- tion of the bollard pull, (3) estimation of the tug's free speed, and (4) estimation of the tug's overall towing performance. The tug's free-speed and towing performance depend on the choice of the optimum propeller for the required bollard pull and can be estimated from the hull resistance and the machinery char- acteristics (power and rpm). The choice of the propeller dimensions for bollard pull re- volves around one main criterion, that is, to install the largest- diameter propeller possible. Considerations are the tug's draft and the hull-propeller clearance. The maximum practical di- ameter of an open propeller is about 85 percent of the draft aft. The rpm of the propeller should be chosen, if possible, to keep the pitch-diameter ratio (P/D) between 0.6 and 1.25. However, the best bollard pull P/D is about 0.6. The minimum blade-area ratio should be between 0.50 and 0.55 in order to give all-around towing performance and high astern bollard pull. The area of the blade should be distributed to give fairly wide tips. In general practice, propellers fitted on single-screw tugs have three blades and those fitted on twin-screw tugs have three or four blades. 1 Senior research engineer, State University of Liege, Liege, Belgium. 2 Numbers in brackets designate References at end of paper. Original manuscript received at SNAM E headquarters July 7, 1985; revised manuscript received March 14, 1986. The bollard-pull condition is the condition during the pull operation when the tug speed is zero and the propeller advance coefficient (J) is zero: nD where VA = propeller advance speed n -- propeller revolutions per unit time D = propeller diameter The advance coefficient (J) is nondimensional and at the bol- lard-pull condition is zero as VA is zero. Also, at this condition, the wake coefficient W is zero since both the tug speed and the propeller advance speed are zero and the thrust deduction coef- ficient t can be assumed to be about 2 or 3 percent. For most tug forms the relative rotative efficiency ~R can be assumed to be about unity. Bollard-pull charts For preliminary design purposes Argyriadis [1] gives the fol- lowing equations (changed to the metric system) for the bol- lard-pull and the corresponding rpm N: KT BHP° × Tc with T c 60 X -- T(kg)=716X NoXD =20~ KQ BHP 0 ~ 1 /2 N = 60 X 6.55 × with T r = KQ N o X D ~ X Tr] The symbols are defined in the Nomenclature. The values of Tc and Tr are given in Fig. 1 as a function of the propeller pitch- diameter ratio for three- and four-bladed propellers with a disk-area ratio of 0.50. Strictly speaking, the curves apply only to propellers with airfoil shape sections from 0.5 radius to the tip. In the discussion to reference [1] both Kimon and Morgan point out that the coefficient from Fig. 1 can be strictly applied only to constant-torque installations. Morgan [1] derives the expression for bollard-pull and the corresponding rpm for both constant-power installations for three, four, and five-bladed Troost propellers with different expanded area ratios. Figures 2 and 3 reproduce here the three and four-bladed propeller data, respectively. Since these diagrams are based on open-water tests, the bollard pull tends to be overestimated by a few per- cent (up to 10 percent). These corresponding equations, in the metric system, are: 220 0 0 2 5 331618712403 0220500.3710 MARINE TECHNOLOGY
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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 :
2 2 0 0 0 2 5 3 3 1 6 1 8 7 1 2 4 0 3 0 2 2 0 5 0 0 . 3 71 0 M A R I N E T E C H N O L O G Y