The Choice of the Propeller

The Choice of the Propeller' By J. D. v a n M a n e n 2

in this paper the four main requirements for a propeller are dealt with. These require* ments concern efficiency, cavitation, propeller-excited forces and stopping abilities. In a propeller diagram the characteristic efficiency curves for different conditions are explained. A comparison of the optimum efficiencies for various types of propulsors is given, and the applications on a 130,000-dwt tanker are considered. Cavitation-inception curves both for a specific propeller and for systematic propeller series are discussed. Predicted torque and thrust fluctuations, based on model*test data, and the results of measurements on the full-size ship are compared. Finally a quasi-steady testing technique, developed to analyze different types of stopping maneuvers, is described.

IN this paper an a t t e m p t is made to explain in an instructive way the results of applied research in the propulsion of ships. In particular it is hoped that it will be instructive to those who are active in the field of ship design. The main requirements for a ship propeller are: 1 High efficiency. 2 %linimum danger of cavitation erosion. 3 2~/[inimum propeller-excited vibratory forces. 4 Good stopping abilities. 5 Favorable interaction with the rudder, to improve maneuverability. 6 Dependability--minimum vulnerability. 7 Low initial and maintenance costs. In the following sections the author has restricted himself to a discussion of the requirements mentioned under points 1 through 4. There are two important diagrams, with the aid of which insight into nearly every propulsion problem can be obtained. These are: (a) The diagram giving the relation between the thrust coefficient Kr and torque coefficient KQ and the advance ratio J of the propulsor is shown in Fig. i. (b) The velocity and force diagram of a screw-blade element is shown in Fig. 2. Results such as those given in Fig. 1 were obtained from an "open-water test" of a given screw model. In such tests the screw model is driven from behind. The propulsion motor and the measuring apparatus are housed in a boat which is a considerable distance behind the screw model and is connected to the carriage of the towing tank. In this manner the thrust T and the torque Q can be measured for constant values of rotative speed n and varying advance speed Va without the x Lecture held at a Seminar of The Royal Institute of Engineers, Delft, The Netherlands, 1965. 2 Assistant Director, Netherlands Ship ~[odel Basin, Wageningen, The Netherlands. 158

T

KT=

K

Q

~

~°'°----q Q"O--SrZ

KT

~P=~

3

j

Va

" o-5

0,6F g

"

KI ~ 0,2

. . . . . . . . . .

0

0.2

0.4

0,5

0,8

l.O

12

--j

Fig. t

Relation between thrust coefficient K~, torque coefficient

KQ and advance coefficient J of propeller

influence of the ship t h a t ultimately is to be driven by the propeller. As a rule, thrust and torque are given in nondimensional form T K T

=

"

p(nD)2D

T 2

q I![Q --

p(nD) 2D2D

pD4n 2

Q

(thrust coefScient)

pD~n 2

(torque coefficient)

where p = mass density of fluid a measure of rotative speed of screw D 2 = a measure of screw-disk area nD=

These thrust and torque coefficients are plotted as a function of the advance coefficient J, which is the ratio between the speed of advance Va and the rotative speed nD.

%/lost design problems can be solved for a particular MARINE TECHNOLOGY

' f id

X

[dT i

~,

/c. - ~ / .~:,:-x/~i~ -/

rr/2

~ ,

........

j

,

;va

!

P/{ dQi

dO

Fig. 2

w

r

1

Force and velocity diagram of screw-blade element~at radius r 5

1

-Bp

10

15

20

30

40

50

60

t,0

Fig. 4 Bp -- ~ diagram

......

0,E

a,

o.a.

11.8 " " "

~\\\x \~\!/_~/\ \a \ .~/ 1

O.t £

1.1

"A',,. / 0,2

\.*/ \ ~ / -

1.3

/

0.9

% &2

0.4

0.6

0.8

1.0

1.2

1.4

t

1.6

J 0.7

Fig. 3 KT-KQ-Jdiagram 0,5 5

screw using a diagram such as Fig. 1. If, for instance, for the screw concerned, the speed of advance Va and the rotative speed n are known, then the thrust and torque can be read off, or, with known Va and Q the rotative speed n can be found. Thus, when two out of the four quantities Va, n, T and Q are given, the other two can be determined from the diagram. In Fig. 2 the force and velocity diagram of a screwblade element at a certain radius r is given. The thrusting action of the screw induces velocities in the fluid. The magnitude of these induced velocities depends on the screw loading. If the speed of advance Va (or ship speed Vs) is decreased, while the rotative speed is held constant, the screw loading will increase and the induced velocities will increase at a rate proportional to the increase in lift force dL and the effective angle of attack OZl.

The induced velocities G, which are, to a good approximation, at right angles to the resultant incoming velocity V, can be resolved into axial and tangential components c~ and c~. At the screw disk the induced velocities are one-half of their ultimate values far behind the screw. IlK the diagram, Fig. 2, the following symbols are indicated: c~ror 7rnd = tangential speed of blade element at radius r dD~ = profile drag of blade element APRIL 1966

-Bp

10

15

20

30

40

50

60

Fig. 5 Characteristic curves in a B~-3 diagram

dT~, dQ.; = thrust and torque force of blade element without influence of profile drag

dT, d(2 = thrust and torque force including influence fl 3~

of profile drag = hydrodynamic pitch angle uncorrected for induced velocities = hydrodynamic pitch angle corrected for induced velocities

This force and velocity diagram forms the basis for the lifting-line theory for ship propellers. This theory will be treated in greater detail in the section "Cavitation of the Screw-Blade Sections." This diagram is also helpful when analyzing propulsion problems using quasi-steady considerations, see also subsequent sections. Efficiency of the Propeller

An important source of data for screw design are the results of open-water tests with systematical screw series. A systematic screw series consists of a number of screw

models, in which only the pitch ratio P/D is varied. All other characteristic dimensions, including diameter D, number of blades z, blade-area ratio Ao/A, blade planform, form of blade sections, blade thicknesses and hub159

Table

1

T r a n s f o r m a t i o n o f the

K~

-

-

KQ

-

-

J

Diagram

Into B~-6 D i a g r a m

KQ

,S

3

200

0.506

210

0.482

j2s

~D=0.6

0.8

1.0

0.182

0.0100

00234

00398

0.161

0.0108

0.0244

0.0410

Bp 1.2

1.4

0.6

08

1.0

1.2

1.4

0.0612 0.0840

18.2

27.8

36.3

45,0

52.3

0.0624

0.0854

21.3

32.1

41.5

51.3

60,0

36.7

47.3

58.1

679

220

0460

0.144

0.0115

0.0254

0.0420

0.0636

0.0868

24.7

230

0.440

0.128

0.0122

0.0262

00430

0.0647

00879

28.4

4 1 . 7 53.4

65.5

76.4

240

0.422

0116

0.0128

0.0269

0.0438

0.0656

0.0890

32.4

4 7 . 0 60.0

73.4

85.5

250

0.405

0.104

0.0134

0.0275

00446

00666

0.0900

36.7

52.3 67.0

81.8

95.2

260

0.390

0095

0.0138

0.0282

0.0453

0.0672

0.0909

41.0

5 8 . 4 74.1

90.3

1050

270

0.375

0.086

00143

0.0287

0.0460

0.0680

0.09t7

45.9

65.1

82.4

100.2 116.3

280

0.362

0.079

0.0148

0.0292

0.0466

0.0687

00924

51.0

71.7

90.6

110.0 127.6

79.3 I00.0

121.1 140,5

8 6 , 4 108.8 131.6 152,5

290

0.349

0.072

0.0152

0.0297

0.0472

0.0693

0.0932

56.7

300

0.339

0.066

0.0156

0.0301

0.0477

00698

0.0937

62.2

j = 101.277

8p=33.08\/ ~

5

diameter ratio dh/D are fixed for this series. The results of open-water tests for such a screw series are given in the Kr-KQ-J diagrams, Fig. 3. The propeller efficiency ~ can be expressed in terms of these nondimensionM coefficients as follows: TVa K~. J ~ - 2~rQn - KQ 2~r By interpolation in the K~.-I£~-J diagram of a screw series most problems, which arise when designing or analyzing screw propellers, can be solved. Tile most widely encountered design problem is t h a t where the speed of advance of the fluid into the screw disk Va, the power to be absorbed by the screw P and the number of revolutions n are given. The diameter D is to be chosen so t h a t the greatest efficiency can be obtained. This is done as follows: By choosing discrete values of the diameter D, the corresponding values of the advance ratio J and the torque eoettlcient K¢ can be calculated. From the K~KQ-J diagram, Fig. 3, the corresponding pitch ratios P / D and the efficiency ~; can be read off for each diameter chosen. Plotting the values of ~ as a function of the diameter will allow the diameter leading to the o p t i m u m etficieney to be chosen. I n order to simplify this frequent design problem, the K~-KQ-J diagrams can be transformed into another diagram, from which the o p t i m u m diameter D can be read off directly when the speed of advance Va, the power P and the rotative speed n are given. For this purpose a design coel~cient B,~ has been formed from the torque coefficient K¢ and the advance ratio J in such a way t h a t the screw diameter is eliminated:

B~ 160

-

NPV~ - 33.08 (ICQ'~V~

Va2V~

\ j; ]

I n the coefficient B~, N is the number of revolutions per minute, the power P is in horsepower and the speed of advance Fa is in knots (1 knot = 0.5144 m / s e e = 1.689

fps). I n the usual diagram, the design eoelficient ]3~, is the base and a new speed ratio 5 is used. This speed ratio is defined as ND Va

101.27 J

in which D = screw diameter in feet. The manner in which the Ks-K~-J diagrsbm is transformed into the B,j-8 diagram is shown in Table 1. Fig. 4 gives an example of a B~-5 diagram for a particular screw series. In Fig. 5 some characteristic curves in the Bp-5 diagram are shown: (a) O p t i m u m ~,, for P / D = eonst. This curve goes through the points where the tangents to the curves of equal efficiency (vp = const) are horizontal ( P / D = const). The o p t i m u m ~,,-values correspond to the peaks of the ~h~-curves in ;he K~,-Ke-J diagram, Fig. 3. (b) O p t i m u m r,~, for J = const. This curve goes through the points of contact between the curves of 3 = const and those for s~ = const. These o p t i m u m s~values coincide with those on the envelope of the efficiency curve in the K,r-KQ-J diagram, Fig. 3. (c) O p t i m u m ~ for the most favorable diameter D. This curve connecbs the points of contact between the curves of ss = const and their vertical tangents (Bp = const; P, N and Va are given). (d) O1)timum v,, for the most f~vorable number of revolutions N. This is the locus of the points of contact between the curves of constant efficiency (,~ = eonst) and MARINE

TECHNOLOGY

P COASTERS . . . .

TWIN-SC.REW SINGLE SCREW SHIPS i CARGO SHIPS .

TANKERS

0,80

TRAWLERS

_

PROPELLERS

' 060

SERIES 4 - 7 0 '

B

I

~

-

o,Ts

Vs

- -

SHP

I ~ ~)O.7,00m

I

.1s.8 k ° . - -

~

=27720hp

I

~-_. 3",~

,~ D, 6 7 4 m

~

~

tl\

[NNRR

!

i

0 t')

i

60\ SECT'ON.~ 40 B0 /~ ~/~n

80~/V-SHAPEO\

/30~0

~ o,~,,y I

I

8~ I U-SI'4APEDSECTION Fig. 18

FIGURES INDICATE TFtE BLADE ANGLES IN DEGREES

]Fig. 17

Thrust eccentricity calculated by Stuntz, Pien, Hinterthan, and Ficken

J diagram as proposed by Schuster [11 ] may give a qualitative picture of the forces generated by a screw in a circumferentially nonuniform flow field. For every 5 or 10 deg of the circumference an instantaneous examination of the blade is made. The axial wake velocities are regarded as constant at each blade position. With the aid of the open-water characteristics (K~-KQ-J diagram) of the particular screw, the time history of the thrust and torque can be found. The path of the center of the thrust will be symmetrical with regard to the longitudinal centerplane of the ship when the tangential wake velocities are neglected. This path will be swept z-times every revolution for a z-bladed propeller. Usually the region of maximum wake velocity above the propeller axis will be broader (thicker) than that below the propeller shaft. The closed path on which the center of thrust is moving will lie mostly above the propeller axis. When the tangential wake velocities are included, the rotative speed of the screw blades will be smaller when entering the peak of the wake and larger when leaving this peak. This will cause a shift of the path of the center of thrust to starboard for a screw that rotates clockwise and to port for a screw that rotates counterclockwise. The shape of the sections in the ships afterbody has a pronounced influence on the position and form of this path, Fig. 17. Because of this eccentric position of the thrust, horizontal and vertical bending moments are created in the propeller shaft. 166

Coordinates, elastic deformations and forces

Looking more closely at the variation of torque, it is obvious t h a t a dynamic-force pattern is created in the propeller shaft in way of the propeller because of the circumfereni;ial inequality of the wake and, hence, the torque-generating Force. These horizontal and vertical transverse forces and bending moments have to be absorbed mainly by the sterntube and the sternpost. The forces and moments acting on the propeller working in the flow field behind the ship can be divided into six components: Axial. Thrust and torque. Transverse. A transverse force, because of the circumferential inequality of the torque force (unbalance of torque) ; a vertical bending moment due to the thrust eccentricity. Vertical. A vertical force and a horizontal bending moment for the same reasons as stated in the foregoing, see Fig. 18. The experimentM determin'~tion of the thrust and torque fluctuations of a screw model behind a model of a single-screw ship was carried out successfully for the first time by Krohn and Wereldsma [12]. T h e y carried out their measurements of the hydrodynamic forces created by the propeller using a measuring shaft of very great stiffness. M a n y systematic and individual experiments have been done using the apparatus of Krohn and Wereldsma [13,14]. The systematic experiments give information about the influence of number of blades, the shape of the afterbody and the position of the propeller shaft. The frequencies of the periodic force fluctuations due to the propeller running in the flow field behind the ship, will be equal to the number of revolutions of the propeller times the number of blades (the blade frequency) or a multiple thereof. Regarding the influence of the nmnber of blades, the characteristic difference between propellers with even and odd numbers of' blades must be mentioned. MARINE TECHNOLOGY

TORQUE VARIATIONS

F\ ,,,/~,,,

)

i4A

VERTICAL BENDING MOMENT(propetter

,i\"

!'

::/0 v "...i

~.../

~/

I

I

0°

.*20

I

180° Propeller

~

i

270°

position

A

v

HORIZONTAL

,

LO ,

P~

BENDING

ii

i

oo

oo0

i

0°

)

,

18o.

,70.

,,'o.

z., Z-5

"7~ t /~f,~\.(-'~,'/ I / f ' t f ! ~'

.-5\1 .10

MOMENT

o.=t25

Ii//~ !

,o

v--v-

.

360

8

THRUST VARIATIONS

,..15~

v

",._.1

1

90°

wlwgh~ududed)

!,,/!,

',!/ \ /

0°

Z=6

1 / I', /i ~,~ '.,_," .J

-~.,. 9I

I//'

i

i

180° 270° PropetEer position 8

i

360°

Fig. 19 Effect of number of blades on dynamic propeller forces, excited in "behind" condition Table 4

Formulas A p p r o x i m a t i n g

Transverse Forces a n d

Bending Moments,

Excited by Propeller ( 1 5 - K n o t Tanker) FORMULAE APPROXIMATING THE TRANSVERSE FORCES AND BENDING MOMENTS EXCITED BY APROPELLER (15KNOTS TANKER) 1) HORIZONTAL TRANSVERSE

:/FyO'7D/ = 0 . 1 2 , 0 . 0 7 3

FORCE

-

-

SIN(4~3+80 °)

Z,4)

LTz g e m j

2) VERTICAL TRANSVERSE

FORCE

=0.12+ 0.150 SIN (513÷ 101 ° )

ZI 5)

:r]/Fx'O7D/=006.0.076 SJN (413.126 °)

Z= 4)

[Tz gem j =006,0130

3) HORIZONTAL BENDING MOMENT

4) VERTICAL BENDING

MOMENT

:[ Tx ]=0.007, 0008 LFz gem 0.7DJ

:[

-Ty

APRIL 1966

( Z = '5)

SIN (413+147 ° )

(Z=4)

=0.007-0019

SIN (513+159 °)

(Z= 5)

]oo.o32-o.o12

S~N(4~,.130°~

CZ- 4>

=0032+0053

SIN (513 +155 °)

( Z = "5)

IFz gem 0.7D]

For a screw propeller with an even number of blades, the fluctuating forces of two opposite blades will give rise to a larger total thrust and torque amplitude because two blades pass simultaneously the stern and its associated peaks in wake velocities. The transverse force and bending moment of one blade will be compensated more or less by those of the opposite one. For propellers with an odd number of blades, the blades will pass, alternatingly, the upper and lower wake peak. The total thrust and torque fluctuations will thus be smaller than for an even-bladed propeller. For an odd number of blades the transverse forces and bending moments, the favorable mutual compensation experienced by the even-bladed propeller will not occur. Fig. 19

SIN ( 5 p , 2 0 1 o)

gives an illustration of results of measurements on 47 5and 6-bladed screw models in the wake of a ship model. A statistical investigation of the experimental data on thrust and torque fluctuations of some 40 different ship models, tested at the N S M B , leads to the following conclusions: 1 No systematic relation can be found to exist between the amplitudes of the force fluctuations and the principal ship-shape parameters such as block coefficient, prismatic coefficient and screw diameter-ship length ratio. 2 For prismatic coefficients of the afterbody between 0.73 and 0.79 it was ascertained for 4-bladed propellers t h a t with a probability of about 80 percent the following results will be obtained: The amplitude of the 167

Table 5

~z lz*~z

td:z

*~z

*~z

symbol

Coefficient

Hydrodynamic moment of inertia

+ ; z C z =rz

1i

]

measured

17 6 10_~ kgmsec21 i i

Hydrodynamic torsional damping

0.86 10 .2 kgm I

Hydrodynamic

mass

32"10-2

Hydrodynamic axial damping

2,7

kg sec m

F Acceleration

Velocity

coupling

coupling

~]

=

14 10 -3 kg sec 2

=~

023

kg sec

L~J LL~J Fig. 20

Scheme of coupled differential equations of screw shaftthrustblock system

first harmonic 4 of the torque fluctuation will be 6 ~ percent of the mean total torque, the amplitude of the first harmonic of the thrust fluctuations will be 10 percent of the mean total thrust, and the amplitudes of the higher harmonics will be substantiMly lower. And likewise for a 5-bladed propeller: The amplitudes of the first and second harmonics of the torque fluctuations will be, respectively, 1 ~ and 1 percent of the total torque, and the amplitudes of the first and second harmonics of the thrust fluctuations will be, respectively, 2 and lJ/~ percent of the total thrust. Deviations from these indications larger than 2 percent absolute do not occur. 3 Fine-ended vessels, which includes most fast ships, can have substantially greater force fluctuations. In Table 4 a review of the formulas which approximate the transverse forces and moments generated by a 4-bladed and a 5-bladed propeller behind a 15-knot tanker is given. For the loading of the shaft in the vertical direction besides the hydrodynamic forces the weight of the propeller hag to be taken into account. The mean value of the propeller-generated transverse forces can be neglected compared to the propeller weight from a viewpoint of static shaft loading. The static bending moment, lifts the propeller up and reduces the deflection of the sterntube. Reckoning has to be held, however, with a large bending moment in the shaft in way of the screw plane. Comparing the dynamic behavior of a 4-bladed and 5-bladed propeller, it is noted that: (a) The fluctuations in the transverse force of the 54 The first harmonic has the blade frequency. 168

Initial speed

kn

10,1

11.7

13.3

14.6

Speed at which tugs assist effectively in braking and keep the ship on course

kn

7

8

9

10

Reach at 20 R,RM. ahead before tug assis:ance becomes km effective

3.1

2.9

2.6

2,3

Reach at 50 R.R~". astern and 40 tons extra braking force km exerted by tugs

0.9

1.1

1.4

1.7

km

4.0

4.0

4.0

40

Head

m

Stopping Maneuvers for a lO0,O00-dwt Tanker for Headreach of 4 km (2.5 miles)

reach

bladed propeller (although unimportant) are twice as large as those for the 4-bladed propeller. (b) The fluctuations in bending moment are much higher for a 5-bladed than for a 4-blMed propeller. Realizing that the ship designer generally has at hand effective and relatively cheap means of avoiding axial shaft vibrations (torque and thrust) and thai; he has to reduce the excitation of horizontal hull vibrations to a minimum, the 5-bladed propeller is to be regarded as an unfavorable propeller compared to a 4-bladed one. From results of recent systematic tests with, among others, the Wageningen B-Series it could be deduced that a 6-bladed propeller has about 3 percent less efficiency than the comparable 4-bladed propeller [4]. The smaller screw diameter, the larger screw clearances and the very favorable pattern of the fluctuating forces (see Fig. 19) are, however, distin,% advantages, justifying tlhe application of 6-bladed propellers for single-screw ships. The propeller shift and the ship's stern are not infinitely stiff. Thu~, because of the described force patterns, elastic deformations will occur. The torsion and the axial displacement of the screw owing to the elastic shaft give rise to hydrodynamic coupling between tl'~e axial dynamic screw forces (thrust) and the dynamic torsion forces (torque). The deflections ,of the propeller shaft due to the bending moments create gyroscopic phenomena at the propeller. A certain volume of water follows the unsteady movements of the screw blades, manifesting itself as an added lnaSS.

The unsteady character of the screw loading will'induce in the screw race helicoidal trailing vortex patterns, varying periodically [n strength, see Fig. 10. The energy, carried away by this vortex system causes hydrodynamic damping. All the hydrodynamic quantities of the screw as a source of' vibration are summed up now. If it were possible to calculate or determine experimentMly these hydrodynamic quantities, then it would be possible to predict the expected stresses in the stern construction and in the propeller shaft resulting from the unsteady forces of the ship propeller. Fig. 20 gives the :~cheme of coupled differential equations of the screw-shaft-thrustblock system. MARINE TECHNOLOGY

FI,~ * ¢~PIEEE

~!~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i!i~i~i~i~i~i~i~!~i~i~i~i¸II~!i~i~i~i !~i~i~i~i~!~ii~!i!i~iii,'i!~ii;!i~!~i i~!i i i i i i li~i i i !ili!i !¸ii ~i i i~ii!i!~i iii!i~i~i ~i ~!ii i i ~!i~i !~!~!i!~ii !i !!~ii !i ~i i i!i ~i~i!~ii~i~i i!!~ii!!ii i i !i!i!~ii!i~i~i~i i~i i !!i!~ii i ~i!i!!!!~i~!ii ~i i!~i~i~i~i!~ii!i ~!!~ii i i i i ~i!i~i~i i~i i~i i i i~i i ~i i~i~!ii ~ Fig. 21

P r o p e l l e r exciter for d e t e r m i n a t i o n o f coefficients for h y d r o d y n a m i c mass a n d d a m p i n g a n d h y d r o d y n a m i c coupling between thrust and torque vibrations

,5 i

TORQUE VARIATION

l

THRUST VARIATION

Fig. 20 the values for a model of a specific single-screw cargo ship, as measured by Wereldsma, are given [15]. The results of Wereldsma's prediction of the torque and thrust fluctuations based on model-test data and the results of measurements on the full-size ship are compared in Fig. 22. The good correlation between prediction and measurement indicates that a new area of ship-model testing has been opened as a service for the shipbuilding and ship operating industry.

0

5

'1 . 5

g o

I 0°

"Jl 45 °

•

MEASURED - FULL SIZE ....

Stopping of Ships

90 ° 135 ° PropH[er position e

180 °

SHIP

PREDICTION DERIVED FROM MOOELTEST-RESULTS

Fig. 2 2 C o r r e l a t i o n of m e a s u r e m e n t s o n full size a n d p r e d i c t i o n of t o r q u e a n d t h r u s t variations, b a s e d o n model-test results

The hydrodynamic mass and damping and the hydrodynamic coupling between thrust and torque vibrations have to be determined for the prediction of the stresses in a given shaft configuration. Wereldsma has developed a propeller exciter, Fig. 21, to evaluate the coefficients appearing in the left-hand side of the equations. With this exciter a given axial or torsional vibration can be imposed on a model screw at a certain load KT or K~ and at a certain advance ratio J. In the column at the right in APRIL 1966

With the aid of the quasi-steady velocities and forces diagram acting on a screw-blade section an insight can be gained into the force pattern around the screw during stopping, Fig. 23. When the rotative speed of the screw is reduced the angle of attack, and, hence, the thrust, will decrease from that at full-ahead power (phase 1). At about 70 percent of the normal ahead number of revolutions the thrust will become zero and the screw turns freely (phase 2). As the RPM is further reduced, a negative angle of attack will result in negative lift and thrust. A further reduction in RPM leads to such large negative angle of attack that flow separation on the screw blades will occur with an accompanied loss in lift. This separation starts at about 30 percent of the RPM ahead (phase 3). The decreasing lift causes a decrease in braking force 169

0

r

f

(T)

I

fuU power

. ~lOO

tugs

w turning stack

v.

t

I $Lo~vty~|stern

make flmgt

'i --*50

i

--m0

±50

®

L

RPk~ OF THE PROPELLER : !.50 1

zOlO +100

0

÷50

.S,O

I

R "P 141 IN */=

-tO0 I

e:

z

®

i

12

I

L i SPEED REOUCTION

•

14- i9

.9:

knots I

I

i 3

1

----HEAO

Fig.

SPEED OF SHIP

2 5

2

REACH

~ 6-4 knols

__

i 5

6

7

~'% j i~ 8

IN k m

Headreach :for a 1 0 0 , 0 0 0 - d w t tanker; initial speed 14 knots

® v,~0 Fig. 23 Relation between thrust and R P M at a constant ship speed. Force and velocity diagrams for blade element of screw

dv dv d s dv K : m . a = m ~ - = m ~ - ~ - = m ~d~ V

d s = rn KV--dv vi

in w h i c h

S : Head

reach

m

A= D i s p l a c e m e n t

g = Gravitational v i = Initial vt= Terminal

K = Braking

Fig. 24

ton acceleration

speed speed

force

msec-

2

m.sec- 1 m see -1 ton

Integral for calculation of headreach of ships

until such time as the separation or profile drag become large enough to predominate and the braking force again increases (phase 4). The continued increase of profile drag with the astern operation of the propeller will further increase the braking fores (phase 5). At a high number of astern revolutions the probability of cavitation and of drawing air into the propeller increases. The occurrence of one of these m a y cause a decrease in braking force. The typical S-characteristic, describing the thrust between 100 percent R P M ahead and 100 percent R P M astern operation, was described for the first time by T h a u [16]. For the propeller alone, this curve can be determined for quasi-steady operation, when the openwater screw characteristics are available for the ahead and astern running condition [17]. These quasi-steady considerations are at the same time the basis for a method for calculating the headreaeh. I n Fig. 24 an integral is derived calculating the headreach from the basic law of dynamics, t h a t Force = mass X acceleration 170

The hydrodynamic added mass has been taken into account by tile use of a faetor 1.05. The values of tee ratio V/K can be determined from a model test for each speed V at different rotative speeds. For a given ship displacement the braking force K call be calculated for any combination of speed V and the rotalive speed, and the integral :for the headreach can be determined. The ratio between displacement and power A/SHP, or as written in the integral of Fig. 24, the r,~tio A/K, is very important for the length of the headreaeh. A large displacement propelled b y a relatively small power will give a long headreach (large value of the ratio A/SHP, tankers). A low value for the ratio A/SHP, as for in-stance for destroyers and tugboats, will give a very short headreach. Analysis for a m a x i m u m allowable headreaeh of 4 k m (2.5 miles) were made for a 100,000-dwt tanker at different initial speeds, with the assumption thai, tugs would assist in the stopping maneuver. Table 5 is a review of this analysis. The only possible maneuw~r is the one starting from an i>itial speed of 10.1 knots. When braking from 10.1 to 7 knots with a rotative speed of 20 rpm, the distance covered is 3.1 k m (2 miles). At. 7 knots the tugs take hold and exert an extra braking force of 40 tons. The rotative speed becomes 50 r p m astern and the tanker stops after another 0.9 k m (0.6 mile). Operations requiring tugs to ntske fast at speeds greater than 7 knots nmst be considered a very risky undertaking. For a m a x i m u m allowable headreach of zi k m the initi~d speed of the 100,000-to> tanker may, hence, not exceed 10.1 knots. These conclusions are based on model tests. I t m a y be possible, due to a conservative interpretation of the scale effect, t h a t these results are somewhat pessimistic. Owing to the lack of sufi%ient data from full-scale tests, a correction of the data in Table 5 for scale effects is not possible. I n Fig. 25 the c~dculation of stopping of a 100,000-ton tanker is given for an initial speed of 14 knots. The different phases into which the whole maneuver can be divided are indicated. An essential part of th.e maneuver MARINE TI'CHNOLOGY

is the fact that the screw is to be stopped when the speed reaches 6 knots and the tugs make fast. Otherwise the vessel will loose steerageway. Finally, it may be noted that data and testing methods as treated in this review are important resources needed in the choice of the type of propeller and the determination of its dimensions for a given application. References

1 L. Troost, "Open Water Test Series with Modern Propeller Forms," Trans. NECI, 1950-51. 2 W. P. A. van Lammeren, L. Troost, and J. G. Koning, Resistance, Propulsion and Steering of Ships, The Technical Publishing Company, H. Stare, Haarlem, 1948. 3 J . D . van Manen, "Fundamentals of Ship Resistance and Propulsion, Part B, Propulsion," International Shipbuilding Progress, 1957. 4 J . D . van Manen, "A Review of Research Activities at the Netherlands Ship Model Basin," International Shipbuilding Progress, 1963. 5 A.J. Taehmindji and W. B. Morgan, "The Design and Estimated Performance of a Series of SupercavRating Propellers," Second Symposium on Naval Hydrodynamics, Washington, 1958 (1960). 6 J. D. van Manen, "Ergebnisse systematischer Versuche mit Propellern mit armb~hernd senkrecht stehender Achse," Jahrbuch STG, 1963; Schip en We'll, 1964. 7 J . B . Hadler, W. B. Morgan, and K. A. Meyers, "Advanced Propeller Propulsion for High-Powered Single-Screw Ships," Trans. SNAME, vol. 72, 1964, pp. 231-293. 8 I. It. Abbott, A. E. yon Doenhoff, and L. S. Stivers, "Summary of Airfoil Data," NACA Report 824, 1945. 9 L.C. Burrill and A. Emerson, ':Propeller Cavita-

APRIL 1966

tion: Further Tests on 16 in. Propeller Models in the King's College Cavitation Tunnel," Trans. NECI, 196263 ; International Shipbuilding Progress, 1963. 10 J. D. van Manen, "Dutch die Schraube erregte Sehiffssehwingungen," Schiffstechnilc, 1965; Schip en We~f, 1965. 11 S. Schuster, "Propeller in Non-Uniform WakeCollection of Existing Work," Tenth ITTC, London, England, 1963, Report of Propulsion Committee, Appendix 7. 12 J. Krohn and P~. Wereldsma, "Comparative Model Tests on Dynamic Propeller Forces," International Shipbuilding Progress, 1960. 13 (a) J. Krohn, "Ueber den Einflusz der Propellerbelastung bei verschiedener Hintersehiffsform auf die Sehub- und Drehmomentsehwankungen am Modell," Sch~i~ und Hafen, 1958. (b) J. Krohn, "Ueber den Einflusz des Propellerdurchmessers auf die Schub- und Drehmomentschwankungen am Modell," Sch~stechnih, 1959. 14 J. D. van Manen and R. Wereldsma, "Propeller Excited Vibratory Forces in the Shaft of a Single Screw Tanker," International Shipbuilding Progress, 1960. 15 (a) R. Wereldsma, "Dynamic Behaviour of Ship Propellers," Doctor's Thesis, Technological University, Delft, 1965; Publication No. 255 of the NSMB. (b) R. Wereldsma, "Experiments on Vibrating Propeller Models," International Shipbuilding Progress, 1965. 16 W. E. Thau, "Propellers and Propelling Machinery. Maneuvering Characteristics During Stopping and Reversing," Trans. SNAME, 1937. 17 It. F. Nordstr6m, "Screw Propeller Characteristics," Meddelanden Statens Skeppsprovningsanstalt No. 9, 1948.

171