Isin_Y_A.Practical_Bollard-Pu.Jul.1987.MT.pdf

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 t h a t the tug should have a certain free-running speed and t h a t 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 horsepower installed. Argyriadis [1] 2 has stated t h a t 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/ D H P (29.1-30.4 lb/DHP) and for D. S. Simpson it is equal or close to 10 k g / D H P (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 conditi~n for harbor tugs as it is the simplest and most common 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) estimation 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 characteristics (power and rpm). The choice of the propeller dimensions for bollard pull revolves around one main criterion, that is, to install the largestdiameter propeller possible. Considerations are the tug's draft and the hull-propeller clearance. The maximum practical diameter 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 SNAME headquarters July 7, 1985; revised manuscript received March 14, 1986.

220

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 bollard-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 coefficient 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 following equations (changed to the metric system) for the bollard-pull and the corresponding r p m N: T(kg)=716X

BHP° × Tc with T c 60 X -KT NoXD =20~ KQ

N = 60 X 6.55 ×

BHP 0

~1/2

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 pitchdiameter 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 r p m 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 percent (up to 10 percent). These corresponding equations, in the metric system, are:

0025-331618712403-0220500.3710

MARINE TECHNOLOGY

).I0

12

).09

Ii

3.08

o

0.07 c¢

g O.O&

~9

o-

0.05

O.Ot.

0.0]

0.6

0.7

O.R Plt

0.9 ch/Dio.me

1.0 t or

I.I

1.2

1.3

0.02 1.(.

Rotlo

Fig. 1

Nomenclature AE = A0 = Ap = BHP = BHP0 =

expanded area of propeller blades, m 2 disk area of propeller, m z (=7rD2/4) projected area of propeller blades, m 2 brake horsepower at bollard pull brake horsepower at design speed (maximum power) C = Caldwell's cavitation coefficient CZAR = expanded area ratio coefficient = 0.67. ~

(CTLS'8~

CN = propeller rotational coefficient _ 7 5 . C r a / z _K_r 27r KQ CT = thrust coefficient / 75 \2/3 KT= t ~ p1/2) " KpZ/~ D = propeller diameter, m DHP = delivered horsepower at bollard pull

JULY 1987

DHP0 = delivered horsepower at design speed (maximum power) EAR = expanded area ratio = AE/Ao EAR0 = m i n i m u m expanded area ratio for free cavitation service J = propeller advance coefficient = Va/n" D K 0 = torque coefficient Q/pn2D 5 =

K r = thrust coefficient = T/pn2D 4 N = propeller rotational speed (rpm) at bollard pull No = propeller rotational speed (rpm) at design speed n = propeller rotational speed (rps) at bollard pull = N/60 ~R = propeller relative rotative efficiency P = propeller pitch (m) P / D = propeller pitch-diameter ratio p = Ap/AE

Q = propeller torque (kg X m) -

75 DHP 27rn

O = mass density of water (kg X s2/m 4) SHP = shaft horsepower T = propeller thrust (kg) at bollard condition = pn2D 4 • KT t = thrust deduction coefficient Tc = propeller torque-thrust coefficients ratio 60 KT Kr -or-20.7r KQ KQ Tr = propeller torque coefficient = K 0

V = tug speed, m / s Va = propeller speed of advance, m / s

=v(1-w) propeller tip speed, m / s = Tr.n.D w = wake coefficient

Vti p =

221

I

0.13 Troost

I ~--

B

Series

/L O.tZ

/% I

11

~

5 ~°

i

Troost

13

~'Tc

~

G I0 _ _ ~ ~

o.osg o.o,~ /

#

4

0.04

t. m: }J

0.03

//.]

0.02

0.5

06

O.']

0.9 l.O I.I I.?_ Pitch/Oiam~ier Rat;o

0.8

1.3

fo.sb~ __

o~

00s i

0.03 ~'Tr

o.ol 1,4

0.6 0.7

4

Blades

0,8 0.9 1.0 t.I I.?~ P~tch/O;arneler Ra{{o

0.02 13

0.01 I,q

Fig. 3

- - f o r constant torque

6.85 X

0,04

7/

Fig. 2

N = 60 x

0.08

_ _ 0 . 0 7

0.5

T (kg) = 716 x

o.ogY

o~ L

0.05 ~

O.ll 0.10

6

5

/

EAR

/

2

o o~

__

/0.13

Series

0.12

II ~

o.,o

g~ 7

B

IZl

0.11

y

-~-o.3~--~.y

0.14

/

where DHP o X Tc N O x D with Tc ~1/2

DHP o

N o X D 5 X Tr]

with

KT KQ

T r =

CT

=

\2/3

75 pt/2)

~

The revolutions per second n can be obtained by eliminating the propeller diameter D from the expressions for KT, KQ and T. Thus

KQ

- - a n d for constant power T(kg)=716X

DHP 2

n = CN x T5/2

DHP 0 X Tc

(2)

where

NXD X

N = 60 X 0.114

X KT KQ2/a

CN = 75 X CT3/2 KT

D H P ° ~1/3 D ~ X T~]

2~r

Figures 2 and 3 show that the two major factors affecting the bollard pull of a tug are the propeller diameter D and the horsepower D H P delivered by the engine. Other bollard-pull charts for constant-power installation can be derived from the basic definitions of KT, KQ, and Q and the polynomial expressions for the Wageningen B-Screw Series [3].

At bollard-pull, where J = 0, the values of CT and CN are functions of the coefficients KT and KQ and they can easily be computed from any chosen propeller series charts for different values of pitch-diameter ratio P / D and of expanded area ratio EAR. The value of EAR to avoid cavitation thrust breakdown and erosion has been derived by Caldwell [2] from an analysis of Burrill's cavitation chart assuming approximately 21/.2percent back (suction side) cavitation. The formula is given by

CT, CN, GEAR c h a r t s

EAR 0 = C x

At bollard pull, the relationship between thrust T, propeller diameter D, and engine delivered horsepower D H P can easily be derived by eliminating the revolutions per second n from the definitions of the thrust coefficient KT, the torque coefficient KQ, and the engine delivered horsepower DHP. Thus by definition

KQ

(DHP/A~) 2/3

This equation can be written as follows EAR0 = [ ~ .

4- C3/2. D H P 12/5 D 2" p " Or- n - D)l°8J

where

K T =T~,KQpn2D 4 -pn2~and

D H P - 2~nQ75

p = propeller projected area - expanded area ratio = Ap/AE = 1.067 - 0.229 P/D

then T = C T x (DHP X D) 2/3

222

(1)

By substituting the expressions for n and D for the Wageningen B-Screw Series, EARo can be written in the following form: MARINE TECHNOLOGY

T/{~P

EARo = CEAR X (D~HTP)°768

(3)

where

:EAR minimum for cavitation free service-

.S

28.8

co.6

.6

.l

.8

.9

1.

1.1

(6T1'848~

CEAR=0.67×\] The value of the coefficient C varies between 0.15 and 0.2. The values of GEAR c a n be computed for the values of CT and CN for given values of P / D and EAR. Curves of CT, CN, and GEAR, developed from the appropriate propeller charts, can be plotted as functions of P / D and E A R and used to give a quick estimation of the propeller main dimensions for a given D H P and required bollard pull. Such curves have been derived from the Wageningen B-Screw Series polynomial expressions for three and four-bladed propellers [3] and are shown in Figs. 4, 5(a,b,e), and 6(a,b,c). Figure 4, CEAR versus T / D H P , gives the minimum values of E A R to avoid cavitation thrust breakdown and erosion and Fig. 5 or Fig. 6 can be used to determine the diameter D, revolutions per second n, and P / D for the selected E A R from Fig. 4. These figures and the equations for T versus CT and n versus CN can be used in different ways to determine the propeller main characteristics for the required bollard pull at a given D H P or the bollard pull and D H P for the chosen propeller. Th e designer can obtain an optimum propeller after some iterations. One simple example, treated in the Appendix, shows how to obtain by using these diagrams a quick estimate of the propeller characteristics for a given D H P and required thrust at bollard pull.

lB.0

16.8

,4.8

,2.8

re. e

8.8

I 6

l 8

! I0

[

CEAR

Fig. 4

Conclusion As can be seen from the example treated in the Appendix, the

CT, CN, GEAR 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 corrections for Reynolds number and hull interference effects (thrust-deduction factor and wake fraction). Without these corrections, the values obtained from the chart may be overestimated 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. T he CT, CN, CEARbollard-pull charts presented in this paper are derived from the polynomial expressions of K T and KQ for the Wageningen open-water B-Screw Series for a Reynolds number of 2 × 106. Corrections for other Reynold's numbers are given in reference [3].

• Available delivered horsepower at bollard (DHP) = 600 hp • Requested thrust at 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 allround towing performance and high astern bollard pull. --From Fig. 4 T DH~ = 15.5 -~ CEAR= 4.85 EAR = 0.6 --From Fig. 5(a) EAR = 0.6 ---, P/D = 0.52 CEAa = 4.85

References 1 Argyriadis, D. A., "Modern Tug Design, with Particular Emphasis on Propeller Design, Maneuverability, and Endurance," Trans. SNAME, Vol. 65, 1957, pp. 362-444. 2 Wood, J. N., Caldwell's Screw Tug Design, Hutchinson Publishing Co., London, 1969. 3 Oosterveld, M. W. C., "Further Computer Analysed Data of Wageningen B-Screw Series," Netherland Ship Model Basin Publication No. 479; also, International Shipbuilding Progress, Vol. 22, No. 251, July 1975.

--From Figs. 5(b) and 5(c) P/D = 0.52 EAR = 0.6

CT = 70.56 CN = 7.73 X 104

Then for C T = 70.56, equation (1) gives D = 2.52 m CN = 7.73 X 104, equation (2) gives N = 200 rpm.

Thus we obtain D = 2.52 m P/D = 0.52 EAR = O.6

Appendix Example of application Estimate the three-bladed Wageningen B-Series propeller characteristics D, P/D, EAR and its rpm N for JULY 1987

Z = 3 blades N = 200 rpm

Case b In this case, it is necessary to introduce D = 2.6 m in equation (1) to compute CT: 223

P/l)

p~

1Z-3

.5

1.2

.7

.9

Z-3 1.1

1.2

I.I

I.I

1.8

1.8

B.9

8.9 EAR

B.8

8.8

8.7

8.7

B.6

@.6

B.S

8.S

8.4

9.4

I.I I 4

I 4.5

I 5

| 5.5

I 6

I 6.5

I

I

8.9

I

CEkR

8.8

i S,$

8.e 8.5

i 68

Fig. 5 ( a )

8.7

I 65

I

78

Cl

Fig. 5 ( b )

P/~

Z-3

--From

e q u a t i o n (1) T = 9.300 kg DHP=600hp D=2.6m

1.2

--From

-*

C T=69.2

F i g . 5(b)

I.I

C T = 69.2 E A R = 0.6 1.8

CT = 69.2 E A R = 0.7

8.9

--From

EAR

--" P / D = 0 . 4 4 2

--" P / D = 0 . 4 9 2

Fig. 5(a) E A R = 0.6 P / D = 0 . 4 4 2 - * CEAR = 4 . 5 8

8.8i

E A R = 0.7 P / D = 0 . 4 9 2 - * CEAR = 4 . 7 3 --From

8.7

Fig. 4 = 4.58 CEAR = 4.73 --~ m i n i m u m E A R - - 0 . 5 5 - 0.6 (for cavitation)

8.6

I f w e a s s u m e E A R = 0.6 a n d w i t h P / D = 0.442: 8.S

--From

E A R = 0.6 P / D = 0 . 4 4 2 --* C N = 8.06 × 104

8.4

I.i

I

o.g

f

I

5

6

Fig. 5 ( c )

224

Fig. 5(c)

G.6

8.7

6.6

I 8

8.$

I C~.IO "4

T h e n f o r C N = 8 . 0 6 × 104, 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 obtain D = 2.6 m ( g i v e n ) P/D = 0.442 E A R = 0.6

Z = 3 blades N = 208 rpm

MARINE

TECHNOLOGY

P/D

P/O

Z=4

Z,4 .7

1.2

.9

1.2

1.1

I.I

1,1

t.8

1.8

EAR

8.9

EAR

8.9

9.8

8.8

8.7

8.7

86

8.6

8.S

e.s

8.4

9.4

0.9

I.I

I

4

I

I

I

I

I

4.5

5

5.5

6

6.5

68

CEXR

9.6

I

I

6S

70

0.5

!

CT

Fig. 6 ( b )

T h e s e calculations can be checked from t h e Tc a n d Tr curves given in Figs. 2 a n d 3. Case a For D = 2.52 m, from th e W a g e n i n g e n B-Screw Series p o l y n o m i a l computation:

P / D = 0.52 -* K T = 0.1995

8.7

I

Fig. 6 ( a )

E A R = 0.6 Z = 3 b l a d e s KQ = 0.0183

8.8

T¢ = 10.9

Z.4 P/0 1.2

I. t

T r = 0.0183 1.8

T h e n for D H P = 600 hp -~ N = 199.5 ~ 200 r p m T = 9313.7 kg Case b

9.9

~AA

For D = 2.6, from t h e W a g e n i n g e n B-Screw Series p o l y n o m i a l computation

P / D = 0.442 -~ K T = 0.1636 E A R = 0.6 KQ = 0.014 Z = 3 blades

Tc = 11.7

e. 8

T r = 0.014

T h e n for D H P = 600 h p -* N = 207 r p m T = 9336 kg T h e s e r esults are s i m i l a r to those o b t a i n e d from the CT, CN, CEAR b o l l a r d - p u l l chart; t h e observed s m a l l differences arise from t h e precision of t h e CT, CN, GEAR d i a g r a m s of Figs. 4 a n d 5.

8.7

6.8

e.S

e.4

Metric Conversion Factors lm = 3.28ft 1 kg = 2.20 lb 1 k W = 1.34 hp

JULY 1987

I.I

I

8.g

e.8

0.7

I

I

I

t

5

6

7

8

8.8 9.5

J CN.10-4

Fig. 6 ( c )

225