Tug propulsion - wake, thrust deduction, and r.p.m.

Summary

The variation of the wake coefficient _{and the thrust} deduction coefficient with the speed, the advance number, and the thrust load coefficient has been determined on the basis of model experiments published by different authors. An attempt was made to diminish the._{experimentajl} in-accuracy. The result is applicable for preliminary _dèsign of tugs.

A diagram for determination of the dependence of the wake and thrust deduction coefficient on the block coeffi-cient for tugs is giveñ.

Finally the question of the _{most suitable nimmber of} re-voluticrns arid the propeller diameter is discussed.

Oelv non-shrouded propellers are mentioned Introduction

For the preliminary design of tugs, knowledge

of the wake and thrust _{deduction coefficient at a}

low rate of speed and at a high thrust load is often necessary. _{In the literature contradicting}

details are' found abOut these quantities, e.g. in some _cases it 'is stated that the wake _{coefficient has nearly the} same value under free-running conditions _{as under}

towing at low speed. _{In othêr cases it is stated} that the wake increases ündér towing conditions, and elsewhere it 'is mentioned that it assumes the value O at the bollard. trial. _{In this paper it has} been attempted to clear up this confusing picture.

As regards the thrust deduction _{coefficient, the} various statements _{are more concordant, huf still} the unreliability of the determination of the thrust deduction coefficient is great.

For a long time it has been _{realised that for}

hydrodynamic reasons the diameter of the propeller should be as great as possible. An increase of the

diameter of the propeller by _{22 0/0 will cause a}

dec±ease of 13 0/0 to 17 o/o _{of the horsepower} ne-cessary under towing conditions.

O)

Professor, Dr. techn., Shipbuilding _Department, Dan-marks Tekniske Højskole.

TUG PROPULSION

WAKE, THRUST DEDUCTION. 'AND _R.P.M.

By

Sv. Aa. Harvald*)

V

nD (2)

can be inserted in equation (1), n being the num-Equation (1) then becomes

ber of revolutions and D the diameter _{of propeller.}

J Je

w -

₍₃₎

J

Cönse4uently the wake can be determined by

the use of a propeller diagram in which curves of the propeller behind the ship _{are plotted (propeller}

experiment IV, Fig 1) in addition

_{to the}

cor-responding usual curves of the _{open water} experi-melits _{(propeller experiment I, Fig. 1). Such a}

diagram is given in Fig. 2. For the ten tugs of

which Mr. C. D. Roach in the _{paper «Tugboat}

Design» [5J has given the _{results of the model}

experiments, the' KT, KQ, and _{K cuPies have}

'been calculated. As the calculation _{is based on the} The variation of_{wake with the advance number}

The effective wake coefficiènt _{is determined by} the ship propeller acting as a wake measurer and a wake integrator, the effective velocity _{of wake} being defined as the difference between the velo-city of propulsion (y) and that _{velocity (ve) which} in a homogeneous field would enable the propeller

at this definite number of _{revolutions to create a}

thrust or to absorb _{a torqueequal to that present.} Dividing the two velocities of wake thus found by the velocity of propulsion, two wake coefficients are ' obtained, determined by thrust identity _'and by torque identity respectively. _{Thus the wake co} efficient is expressed by:

t.'i.

5COEpSOU1kUnd

ARCHLEF

Technische Hogeschool

REPRINTED FROM Deift

,,EUROPEAN SHIPBUILDING"

NO.3-1963

V - Ve w

V (1)

If the revolutions of the propeller _{are kept} con-stant, the advance number

publishèd faired curves, the uncertainty of the

cal-culations ii rather considerable, but at any rate

the figure gives an idea of the position in the dia-gram of the curves for tug's running free

KT and K0 are

defined, by

T

_{and IC =}

Q

T _{p n2 D4} p n2 D5

respectively, where T is the thrtist of the propeller Q the torque in shaft, p the mass per unit volume,

n the number of revolutions, and D the diameter

of the propeller.

Further, KR is inserted and defined by

R KR _{= p n2' D4}

R being the ship resistance. The abscissa is

V

advance number J = _nD

On the K0 curves the pitch ratio (PID) of the

propellers is given in brackets next to the model number.

The blade area ratio of thetugpropellerhas an

average value of 0.456. Therefore, the curves from

Wagenmgen B 4-45 have been put in for

com-parison. The figures of the open water experiments are iii some degtee equal to those from Wagenin-gen.

It can therefore be

assumed that if the Wageningen propeller diagrams are used in preli-minary design of tugs, reasonable results will be obtained.

Though the idea of performing propeller

ex-periìnents with the propeller behind the ship is not

of recent date (e.g. it is prescribed on page 166

in [2]), few experimental results have been pub-lirhed. In the «Tug Propulsion Investigation» [4], Parker and Dawson give the rèsuitsof experiments in such a form that propeller diagrams of the

pro-peller working in open water, as well as for the

propeller behind the ship, can easily be

construct-ed. This has been done in Fig. 8, where the KT

curves and the } curves for four propellers have been drawn in. The length of the tug is 100 ft and the dia'méter and the pitch ratio of the four pro-pellers are

P 157, D = 950 ft.,

.PÏD = 0.980 P 160, D = 10.25 ft., P/D = 0.818

P 158, D = 9.00 ft., PfD =

0.560

P 159, D = 7.80 ft., PID =

0.511

The blade area ratio ..edfrom

0.50 to 0.55.

It will be observed that the KT curves for the

propeller in open water and the propeller behind

the ship do not intersect at J = 0. The same

ap-plies to the curves. The viay in which these

curves intersect is of the greatest importance to the

Fig. 1. Propeller experiments I, H, III and IV.

magnitude of the wake coefficiènt when towing

at low speed. This question will be discussed fur-ther below.

Fig. 4 indicates the pÉobable run:f the curves at small values of J. In the first three instances, the curves are assuine4 to be: approximated by straight lines, in the last case by parabolas.

Case A:

w=

J - Je

(6)

As will be seen, w assumes a,fixed value pendent of the J-value.

Case B:

As y approaches Vi, w will approach the value 1.00' As y approaches 0:

W-- +

Case C:

w becomes O if y = y2. As y approaches 0:

w

w=1

Fig. 2.

CaseD:

If the parabolas _{are termed by} y p' x

and y = p2x

(pi > P2) the fóllowing formula will be obtained:

n

V = X _{and Ve =}

i

n

1!

V P2 (9) ,O

curves for 10 tugs. P/D of the propellers is stated in brackets.

Thus w is constant.

It will be seen that

_{even i:iegligible variations}

of the position of the _{points of intersection mean}

considerable variations of the value _{of the wake} coefficient.

_{This value can vaty from}

_{- oc to}

+ co, which cannot be correct.

In Fig. S the _{KT curve for a propeller behind}

the ship intersects the KT curve fOr. a propellei

in open water at _{a negative advance number. At}

J O the, thrust of propeller

_{is greater for the}

propeller behind the ship than for _{the propeller}

in open water, and this is. due to the influence of the rudder. At the Statens _{Skeppsprovningsanstalt,} Gothenburg, Sweden,' open water propeller

experi-X X.

I

:2 ° EE RUN NI1G NG PROP LSION T's TESTS

ai

::

' TX7Q9,.

Fig. 3. KT, KR, and K0 curves of four tug propellers.

ments have been carried out [3], where different rudders have been placed behind the propeller as shown in Fig. 1, sketches II and III. The propeller

diagram is rendered in Fig. 5 where the

thick-ness ratio of the rudder (tu) is given for the

dif-ferent rudders. The curves for KT and K0 from

a series of self propulsión experiments with a model

of a tanker are shown in the same diagram. The

tanker model was fitted with different rudders.

For tugs similar conditibns can be assumed. [t is. evident that the mode of operationof the propeller is altered if a rudder'isplaced in the propeller race. Firstly, the propeller will work in the wake field

of the rudder and secondly, the rotation in the

propeller race will be altered. The presence of the wake causes a change in the slope of the KT and

K0 curves, (curve No. II,

Fig. 1). The altered

rotation causes the KT curves as well as the K0 curves to be raised, (curve No. III, Fig. 1). The turning as well as the displacing of the curves de-pends- on the type and sie of rudder (see Fig. 5). If the total displacement was caused by the waké

of the rudder the wake

coefficient, originating from the rudder, would have to have values up to

0.10, which is not probable (page 159 in [2]).

Therefore, it can be assumed that the alteration of

¡-SELF. PROPULSION rESTS ,-OPEN RArER TESTS

4

1k

2, 2, 3

Fig. 4. K curves for values of J near zero.

the conditions of rotation causes the displacement of the curves. Consequelitly examining the variation

of the wake coefficient with the advance

nüm-ber, a correction for the rotation

shôuld be

pr-formed by. displacing the curves for «propeller in the open» to intersect the corresponding curves

for «propeller behind the ship» at a

value for. J = 0. This justifies the assumption that the curves

can generally be approximated by straight lines

when J is approaching zero, as shown in Fig. 4,

part A, and that the wake coeffiçient is

approach-ing a fixed value determined by the slope of the

lines.

-Fig. 5. The influence of the rüdder on- the- KT id curves. ¿E P.157 a' P156 'L I -O RU p 3, ,R5 r FREE-RUNN)NU -.V7,KN(TOWROP.PUL).,&. (BRLLARO -- j SlOP

--BEHOlD j rOw-ROPE PULL) ----PROPULSION -_Th PULL)

-L-

I-- P157 -l58 U

r---1 , SSPA. POPELL - NpP H S?

-I PLATE

.,,.

-- -UDR 'II 0.09 ,,, --RI/ODE ---.3 OPEN RUD WATER _CO S ESTS PLEOLED ' AFTBO a2 PROPLLER - _{LP PROULSION} rs .1

-III

1111111

.Li!II

PIPI.

!1P-'s

.1

I

Fig. 6. The variation of wake with advance number for tugs.

As is known, the wake coefficient can be split up into three components

W Wp +Wfr + W (10)

w, Wf± ,and w being the potential, the friction,

and the wave, wake coefficient respectively. When the speed is tending towards 0, w will also tend

to 0, w will be constant, and the variation of

Wir is assumed to be rater negligible. For this

reason also it is natural tö expect the curves to

.:intersect at J. = 0, as shown in Fig. 4, part A.

5

In Fig. 6 is shown the variation of the wake

coefficient of a tug with the advance number ap plying the cönentional as well as the new method.

Using the conventional method equation (10)

- should be altered to

W = Wp + _{Wfr ± w}

+

Wrot ...(11)

where Wrot denotes the apparent alteration of the

wake coefficient due to the alteration of the

ro-tation in the propeller race.

The apparent àlteration Wrot can assume values of abotit 0.05 when running free, and it is included

in .the effective wake coefficient determined by

the conventional _{KT or KQ identity. For tugs,} therefore, it must be expected that the conventional wake coefficient is approaching w 1.00, as

approaches its maximum value, and that itassumes

the value + oo at the advance number _{J 0.}

The variation of thrust deduction with the advance number

Regarding the variation of the thrust. dduction with the advance number pinion differs less than on the question of wake. In most cases the thrust

deductión coefficient varies from about 0.20 _at

self-propulsion' to aboUt 0.04 at the bilard trial

condition (see Fig. 7). The thrust deduction

co-efficient is determined by

KT (12)

Fig. 7. The variation of thrust deduction with the advance number.

wT

.40 CONL'ENTJCNAL METH XI.

-430

\\\

.759 ._'rP156P 157 P160

\

. L.. I OW .... Q -, wr PROPOSED ME THOD Q_10 O - 0,7 0.2 03 64 0,5 0.6 -0.6

t

0.25

,.

..-

_..

Y= . O.0ë554 .

I--//

Ii 1:3163-x . ß20 .. _ .

i'

. /

/_

/

::

.58P60/57

0 . 0.2 o. _{Q8_}

where KT is the propeller thrust coefficient and KR is defined by

R KR _{= p n2 D4}

when running free,, and

R±P

KR

_{= pn2D4}

under towing conditions.

p is the mass per unit volume, n the number of

revolutions, D the diameter of propeller, R the ship resistance, and P is the tow-rope pull. The

curves, Fig. 3, have been used for the

deter-mination of t.

As will be seen from Fig. 7, the thrust deduction coeffiçient is gradually increasing from about 0.04

at the bollard trial to about 0.22 running free,

while at the samé time the thrust load coefficient is decieasing. The làwer the speed, when running

free, the higher the thrust deduòtión coefficient seems to be, Even so, the uncertainty of the

de-termination of the thrust deduction is very great.

If the KT and K

curves are approximated by

two straight lines, as shown in Fig. 8, A and B,

or by two parabolas; Fig. 8 C, hyperbola-shaped

curves (Fig. 8 D) are obtained for the variation .f

t with the advance number J. Further, it could

be assumed that the KT and

KR curves were intersecting on the abscissa which would mean

that t would converge to a fiied value determined

by the slopes of the tangents to the curvés at the

point of intersection. It is impossible at present

to give a physical explanaon of the variation of

the thrust deduction. It is also impossible to

as-D

î

io J

certain, from the existing experimental c]ata

whether the KT and KR curves intersect. Supposing a ship towed at a speed y, with the

engine making such number of revolutions that T

and KT are equal to 0, then the tow-rope pull P is equal to R + S (R is the ship resistance at

the-speed y and S is the suction). This leads. to

R(R+S)

S

KR _{p n2 D4 p n2 D4}

As suction will occur it will be seen that

KTKR

_(16)'

approaches co as. KT approaches 0, and that KT

assumes the value i for KR = 0

In addition to the curves resulting from the

experiments, two hyperbolas have been put irito. the diagram, Fig. 7. These hyperbolas have been

determined, so that they pass through t = 0.0375

at J = O and t = 1.0, where K

is supposed to

assume the value 0. Naturally, no complete

ac-cordance can be expected, due to the shapes of

the-KT and K curves.

The variation of the wake and thrust deduction.

coefficients with the block coefficient and the B/L-ratio

The dingram, Fig. 9, hats been based on pub-. lished data from model experiments. The daa.. used are partly those previously mentioned and.

paitly those from the «Wake of Mérchant Ship».. [2].

othetical variation of thrust deduction coefficient with load. Fig.8. H

Fig. 9. Variation of thrust deduction coefficient and wake .coefficient with block coefficient and length-breadth ratio

for tugs.

Fig. 10. PHP - RPM diagram for tugs.

7-The examined tugs are arranged according _to

the block coefficient 8, and a _{mean curve drawn}

for B/L = 0.265 and D/L = 0.086 (L, B, and D

being the length, the breadth, and propeller dia-meter respectively). The mean values of the wake

coefficient within the field of experiment have been marked by a dot, whilst therange of variation

is indicated by a vertical line (published values

are used, complete agreement with Fig. 2 cannot be expected). Since the available experimental

material is rather limited, arrangements according

to B/L and DIL have not been possible, and

therefore the curve for different values of B/L is inserted, using the results from the wake and thrust

deduction diagrams in the «Wake of Merchant

Ships» [2]. For a deviation in D/L of ± 0.01 from standard, a correction of 0.01 on w for this type of ship is suggested.

Number of revolutions

Of ten a decision has to be made to select a

num-ber of revolutions for a preliminary tug design.

Good conditions are necessary both for the bollard

trial, in towing, and when running free. The

im-portance of the number of revolutions is illustrated in the paper by Parker and Dawson [4]. The result is given in Fig. 10, where the horsepower PHP is

OJO D/LOO6 j 1x1 84 -

----r7I ii0___

-f-r

920 1X6 1X7 xl0 I

---I

h---t--

-

--0.30 1X3 84 I ,.._-_

__

-L-h-

TX I 7/17

-0.25

--X9

,___

--015 020 _.__._.-, 52

--p.265 '25 _-

' _1

)IFkERIOIG

---.-i__ -056 ô TX4 '5107 0.45 4cox*rcrJN;o3, F/tOM jO.SO TANO1RD . X1 0.46 FO 0.52 °,'L 0.5'

-.

II..

I /

h

I J,,,, /y-px A ---CONSTANT

CONSTANT TOW R0'PE PULL. PROPELL& THRUST.

CONSTANT SPEED, /UVOTS

PRE&RUNN/NG PRO.ULS/ÒN

-L

trONS _1q15 TONS / -II

//

±

Pj.0?14

kg 1016 kg j

-j A ,,,/,

p12/

/

/

/

/

1000

T

/

/

,g.o,

/

/

/

_zo,d

[

,//,12

r

_Vòsi,,6

"6'V

v//,opf4

:°

A

/

d

.7'

7 H

- l5-r

:

-500 250 ₃₀₀ 4 PPN

i,-indicated as function of the number Of revolútions

(RPM) of a tug, tested with thrée different

pro-pellers Curves for constant thrust of propeller (T)

for,: constant tóv-ropé pull (P), and for constant

velocity (y) haye been inserted together with the curves from the self-propuliôn tests.

As will be seen, an alteration of the diameter of

the propeller from 7.8 ft. to 9.5 ft. (i.e. by about 22 o/o) causes a decrease in the horsepower

neces-sary for free running at a fixed speed of about

300/o. When towing at a speed of 7 knots, this

alteration of the diameter causes a decrease of

necessary horsepower of about 17 e/o. At the bol-lard trial the decrease is still less, only about 13 o/o. It is interesting to compare these values, with the transmission efficiencies of the systems in

general use for tug propulsion (see f. ex. page 372 in [1]). The transmission losses can be from 3o/o

to 15 °/o according to the system chosen. In other wOrds at the preliminary design stage it is just as important to choose a suitable transmission sy'stem a suitable diameter of the propeller andthereby the number of revolutions of the propeller. Procedure for preparation of a horsepower-diagram for a preliminary design

The resistance of the tug is to be determined,

e.g. by the use of diagrams in appendix 3 in

«Modern 'Tug Design» [1].

The diameter of propeller is chosen as great

as possible.

A propulsion machinery 'and a transmission

system are chosen. Thereby the RPM is deter-mined

Either the demand on the tow-rope pull,

gener-ally at the bollard trial, or the demand on the

free-running speed will determine the

remain-ing data for the propeller, i. e. the 'pitch ratio P/D is either determined at J = O or by J =

nD'

where Ve iS fixed at Ve = V (1 w).

The wake coefficients are fóünd from the

dia-grams, Fig. 9 and Fig. 6. Thé frictional wake

coefficient 'of the tug model is bigger than that of the tug, but on account of the big D/L ratio the différence will be only about 0.02. There-fore it is suggested that in calculations of this kind the scale effect of. w be disregarded.'. For a propeller diagram the' Wageningen diagram B-4 is suggested. The blade area ratIo is estim-ated at a'bout 0.455.

5;

and I(

crves for propeller behind the

ship 'are to be prepared, assuming that

a) KT and KQ at J = O are 1.025 times the

values for' the propeller ¡ri open water.

8-b) j

, where w is assumed to1vary

i

w

as shown at the top of. Fig. 6. This is the

conventional method. If the K.1-

and K0

open water curves are displaced by the

values 0.025 KT and 0.025 KQ respectively

(KT and K0 for J = 0), w may hé assiimed constant according to the proposed meçhod. The curve for the thrust load coefficient.

a.

=

p v2-D2

T

8'KT

, . _J2

(17)

is to 'be drawn on the propeller diagram

(tor-responding to the KT curve for a propeller

behind the ship).

The PHP curve 'for the free-running cond!ion is to be determinecj in the following. order as ,shown by the flow diagram below.

..

(18).

where the value to the right of the arrow can

be determined once the.value to the left of the arrow is known.

The curves corresponding to the constant speed

V and varying tow-rope pull are determiied.

V and J are chosen arbitrarily. Thus the follpw-ing flow diagram shows the order of calculation V and J n

-(9)

The PHP - RPM diagram is now drawn (see

Fig. 10).,

Such' a PHP - RPM diagram gives the

ship-owners all the particulars required for forming an opinion about the performarices of the proposed.

tug under various conditions, and the possibilty

of deciding whether the suggested propulsion

machinery is sintable for the tug or not, as the HPRPM curves for the machin'ery can easily

added to the diagram

REFERENCES

Argyriadis, Doros A.: «Modern. Tug Design with Particular Emphasis on Propeller Design, Ma-neuverability, and Endurance», SNAME 17, p. 362.

Earvaid, - Sverid Aage: «Wake of Merchant Ships'>, Copenhagen 1950.

LAndgren H., a±id taf f of SSPA: «The Influence

'of Propeller Clearance and Rudder upon the

PTOpuISive Characteristics", Meddelanden frn Stajtens Skeppsprovningsanstait, nr. 33, 1955. I

Parker, M. N., and Dawson, James: «Tug Pro-pulsion Investigation'>, TRINA 1962, p. 237. Roach, C. D.: «Tugboat Design», SNA1VIE' 1954. p. 593.