A study of propeller action in the behind conditions

ARCHE7-

Lab. v. Scheepsbouwkunde

Technische Houschool

Reprinted from aEUROPEAN SHIPBUILL/INGD NO. 1, 1960, VOL. 1960

Norwegian Ship Model Experiment Tank Publication No. 60, May 1960

S. Bern. Hegland Flekkefjord

Delft

A STUDY OF PROPELLER ACTION IN THE BEHIND CONDITIONS

By

A STUDY OF PROPELLER ACTION IN THE BEHIND CONDITIONS

Introduction.

The main purpose of the propeller is to

con-vert the torque of the engine into thrust with the highest possible efficiency. In the past,

therefore, the propeller action has been studied

mainly from the point of view of efficiency, and this approach will undoubtedly continue

in the future. But, as the difference of the

pro-peller action in free-running condition and

when placed behind a ship can frequently give

rise to trouble with the propeller itself, the shafting, the rudder and the hull, it is

neces-sary to pay some attention to the

problem

from angles not directly concerned with

effi-ciency. This seems to be of increasing

import-ance, as the power transmitted by one single screw has been steadily increasing during the

past years, and it is not certain that the

maxi-mum limit has been reached yet. It is expected

that all sorts of trouble which come into

exi-stence with propellers with low power will be

intensified when the power transmitted is

in-creased, and it is also expected that some new

kinds of trouble may appear if nothing _has been done to prevent it. But, as it is always

necessary to expect

trouble and to know

something about the reason for it before any

preventive action can be taken, any

investiga-tion which can explain or clarify details con-cerned with the propeller action behind a hull

may be of great practical value.

The different sorts of trouble which occur

in connection with the propeller action may be classified under the following headings:

1. Trouble with the propeller itself.

Cavitation.

Vibration of propeller blades.

Cracking or bending of propeller blades.

2. Trouble with the tailshaft and bearings due

to:

Torsional vibrations.

Lateral vibrations (Transverse

vibra-tions).

Axial vibrations (Longitudinal

vibra-tions)

Bending forces due to asymmetric

loading of the propeller.

By Mayne Letveit, Os/o.

Hull vibrations. Rudder vibrations.

Owing to the variations both in velocity and

direction of the flow entering the propeller, the torque absorbed and the thrust delivered by a single propeller blade will vary with the

angular position of the blade. Furthermore, the

presence of the rudder and some parts of the hull in the vicinity of the propeller may, apart

from the influence on the magnitude and

direc-tion of the wake, have some influence on the local propeller loading. Disregarding the rea-sons for the torque and thrust variations we may express the circumferential torque and

thrust variation for one propeller blade as

d Q

d

r (so) (1) and d T

= f2

(co)

... (2)

d

To be able to predict the most unfavourable

conditions as far as cavitation and bending or

cracking of one propeller blade is concerned, it

is of great importance to know the functions

f1 (co) and f2 (p), and if these functions are

known the total torque and thrust variation of

the propeller as a whole may be calculated and

the magnitude of the alternating bending mo-ment acting upon the propeller shafting may be found approximately. If f1 () and f2 (97) are merely functions of the distribution of

wake velocity and direction in the basic flow,

the functions f1 (9) and f2 (0 may be

deter-mined if the distribution of wake velocity and

direction is known. Such calculations have been

carried out by several authors [1], [2], [3],

[5], [6]. Pitot-tube measurements of the wake

distribution, in full scale and in model scale [4] have shown that there are some scale ef-fects upon the wake distribution, and it is

therefore preferable, if possible, to carry out

experimental work to determine the functions

fi (r) and f2 (9) in full scale. But as full scale measurements are much more expensive and in many cases unpractical or impossible to

2

F (cp) = fAc,

f (cp + 2 zTc)

..

(4)

z=1

Using (3) and (4) we get:

00 2z7s [an sin (n z= n=1 2 zrc bn cos(n cp + ₍₅₎

For a three-bladed propeller we then have:

00

F (cp) --=3A0 [an sin (ncp LTr) 3 n=1 4rc 2,c an sin (ncp

3)

an sin (np) bn cos (ncp 477

bn cos (up bn cos (n?)]

For any value of n which is not a multiple

of three the sum of the components

2rc 47s

an sin (mp ± ) an sin (ncp )

2Tr

+ an sin (ncp) bn cos (ncp ) bn cos

4Tc

(np ± bn cos (ncp)

becomes zero, and for a three-bladed propeller we therefore have:

F (40) = 3A0 + 3a3 sin 3 so 3a6 sin 6ç

+ 3a0 sin 9q, +

...

+ 3133 cos 3s0 + 31)6 cos 6s0 + 31)0 cos 9s0 +

-Therefore the harmonic components of or-ders other than a multiple of three may have any value without altering the total thrust or torque variations for a three-bladed propeller. For four- and five-bladed propellers it is pos-sible to show in a similar way that only the

harmonic components whose orders are a

mul-tiple of four or five can influence the total thrust and torque variation of the propeller.

We may then conclude that only the harmonic

component of f(f) whose orders are multiples of Z can be studied by measuring the total thrust or torque variation of a Z-bladed pro-peller, and it is impossible to draw any

con-clusion about the harmonic components of f (r)

of orders other than a multiple of Z from

such measurements. This is an important

con-clusion since we may expect the f (so) to contain

carry out, the investigations in most cases have to be based upon model experiments.

We shall then consider first the different kinds Of experiments which it is possible to carry out in a ship model tank and what the

results might tell us.

The different types of experiments may be

listed as below:

Measurements of the thrust and torque variations for actual model propellers in

behind conditions.

Measurements of the bending moment on

the tailshaft.

Measurements of the stresses on one

pro-peller blade.

Measurements of the thrust, torque and

bending moment variations for a one-bladed

propeller.

Measurements of the velocity and pressure

distribution in the flow behind the model with and without the propeller working. Measurements of the resulting thrust and torque variations for a propeller can be car-ried out quite easily with the aid of modern

electrical equipment, but as the influence of the different blades will partly cancel each

other out, any conclusion about thrust and tor-que variations for one separate blade can hardly be drawn from such experiments. This is easily

shown by splitting up the functions f1 (r) and

f2 (so) into harmonic sine and cosine components,

and adding together the influence of the

dif-ferent blades, and thus obtaining an expression

for the total thrust or torque variation for the propeller. According to Fourier, any function

which repeats itself periodically can be expres-sed as a series of sine and cosine components, then

CO

f (9) --= Ao + (an sin ncp bn cos ncp)

n=1

or alternatively

00

f cp) = Ao [An sin (n cp ± On)] (3)

n=1

when the mutual interference between the

different propeller blades is neglected, then the

total thrust or torque variation for a Z-bladed

propeller is: 27c 4Tc F (y) =-- f (q)

z)

(cp

)

2 Z7C f (q)

a fairly big first and second order harmonic component and smaller harmonic components of higher orders. Therefore, a small percentage

change in f (,), if it takes place in the Z order

harmonic component only, may produce a con-siderably greater change in F (99 for a Z-bladed

propeller, but will not produce any change in F (v) for propellers with blade numbers other than Z (or a multiple of Z). Thus it is clear that measurements of thrust or torque varia-tions for the whole propeller are unsuited to

give complete information about f1 (f) and Ng)).

Measurements of the bending moments on the tailshaft can be carried out by means of

electric strain gauges, and such measurements

are carried out in full scale in the U.S.A. [2],

[5] and [6], and similar tests can easily be carried out in model scale. When the bending moment due to the weight of the propeller is disregarded, the variation of the bending mo-ment an the tailshaft about any axis may be

expressed as a function of the angular position of the propeller: G (cp) = z2rc z2rc [g

(p ) sin (f1

) . (6) where g (y) = f2(p) a

and is the angle between the axis and the

first blade and a is the distance from the pro-peller centre to the centroid of the thrust for one blade in one special angular position. If

G (c) is known it is very difficult, if not

impos-sible, to determine from this alone the func-tion g (F) and if g (r) was actually known it might be difficult to find the function f2

dT

since bath and a are functions of the

angu-dcp

lar position of the propeller.

The latter difficulty also arises when the

stresses on one blade are measured. Such mea-surements have been carried out by Dorey [7]

and Bunyan [27] and can undoubtedly give very valuable results especially when carried

out in full scale.

By measuring the thrust, torque and bending

moment on the tailshaft for a one-bladed

pro-peller it is possible to determine the functions

fi (v), f2 (v) and g (0 by disregarding the mu-tual interference between the different blades

of an actual propeller.

There must be a relation between the

pres-sure and velocity changes which take place in

the propeller slip-stream due to the propeller action and the propeller thrust force, and this

z=1

relation is expressed by the momentum theory.

It is therefore possible to relate the pressure

and velocity "changes in the slip-stream to the

propeller thrust. By this method it is possible

to obtain an approximation to f2 (so) and it may

also be possible to elucidate the propeller ac-tion somewhat further. Such measurements

have been carried out for the propeller in free-running and behind condition by H. Voigt [8],

[9].

This investigation was to begin with mainly

an investigation of the rudder action for

rud-ders working in the slip-stream on single-screw ships. (The results of the rudder tests are given

in [10]). To obtain information about the

velocity and pressure distribution in the slip-stream behind the propeller at about the po-sition where the rudder is normally placed, some pitot tube measurements of the velocity

and pressure were carried out. Apart from the

results which were needed for the rudder

in-vestigations it seemed to be possible to analyse

the results in a way which might give some valuable information about the propeller

ac-tion. Therefore the test programme in this

spe-cial section was somewhat enlarged, and it became a separate subject. Although carried

out in a very simple way and with very simple

apparatus, the information gained from the tests can tell us quite a lot about the propeller action behind a single-screw hull. Because of the simple apparatus and test procedure the results must be considered as approximations only, but nevertheless these results may in

some respects tell. us more about the function

f2 (r) than many direct measurements of the variation of the forces and moments acting

upon the whale propeller.

The momentum theory of propellers.

A complete description of the momentum theory is given by Glauert [11], and only a

short résumé of this theory, and how it can be used to relate the pressure and velocity changes

in the slip-stream of the propeller to the

pro-peller thrust force, will be given here.

If the friction in the fluid is neglected and

the propeller is considered as an actuator disk

capable of imparting an axial velocity to the fluid in the slip-stream and sustaining a reac-tive thrust, and if the thrust is uniformly di-stributed across the disk area then we may

write:

where

T = thrust.

F1 = the area of the slip-stream p = density of the fluid

Vi = velocity in the slip-stream

vo = velocity through undisturbed fluid. If the thrust is not uniformly distributed across

the disk then we have

T = Spvi - vo) dF. (8)

or

T = f fpvi (vi - vo) dr rdr. (8)

where r and 97 describe the actual spot on the disk in cylindrical coordinates. The integration has to be carried out over an area greater than

the cross-section of the slip-stream, but this

area is unlimited since outside the slip-stream

(vi - vo) = 0.

For actual screw propellers there will always be some rotation of the slip-stream. To extend

the theory to include the effects of this

rota-tional motion, it is necessary to modify the

qualities of the actuator disk by assuming that

it also is able to impart a rotational velocity component to the fluid while the axial (and

radial) components remain unaltered.

The mass of fluid which in unit time passes

through an annular element of the slip-stream

between r and (r + dr) is

p V 27r rdr

and if the angular velocity of this fluid is wi then the torque of the corresponding annular

element of the propeller is

dQ = 27r p vi 0,11'3 dr ₍₉₎

and the total torque of the propeller

Q = 127rpvicuirs dr (10)

Due to the rotation of the slip-stream, some pressure changes take place and this has to be

taken into account in the expression for the thrust. If these pressure changes are denoted

4

Main particulars of the models tested.

by AP, then we have

T = If [p vi

- vo) + AP] dr rdr . (11)

If the velocity and pressure changes which take place due to the propeller action have been determined, these changes are related to

the thrust of the propeller by equation (11) and

if the variations of f [pvi (vi - vo) + AP] rdr with 9, are considered, this then is an

expres-sion for f2 (r), which is the circumferential

thrust distribution for a propeller blade. Measurements of the pressure and velocity distribution behind two models with and

without propellers.

The models.

The measurements were carried out behind two models of tankers of about 24,000 tons deadweight. The main particulars of the

mo-dels are given below.

The lines of both models are conventional.

Model A is an ordinary wax model whilst model

B is a wooden model built for special purposes.

Further details of model «B» and propeller

«II» are given in [10] (Model «B» is identical with M 297 and propeller «II» is identical with

P 177). Turbulence was stimulated on both

models. For model B the stimulation was of the usual trip-wire type whilst two fret-saw blades were used on model «A».

Test arrangement.

The measurements of the pressure and

velo-city changes in the slip-stream were carried out by means of a simple pitot tube, which

could be placed at any decided position behind

the models. A sketch of the test arrangement is shown in Fig. 1. The pitot tube a is fixed to

the carriage by means of two transverse beams

b which also serve as guides for the frame which carries the pitot tube. The whole stand

Model «A»

Scale model ship 1 : 24 1.: 22

Length of model LLwL m 7.280 8.340

Breath of model B 1.016 1.109

Draught of model dLWL .405 .436

Block coefficient CB .761 .745

Prismatic coefficient Cp .769 .756

Midship section coefficient Co .989 .985 Waterline coefficient CLwr,

LINVL

L.C.B. in per cent of LLvvi, forward of

.846 +.50 .834 +3.29 2 Model propeller II Number of blades Z 4 4

Model propeller diameter D m .224 .259

Pitch ratio r/R = 0.7 .818 .791

Figs. 1 & 2.

with the pitot tube can then be moved trans-versely along the guides. On the frame which carries the pitot tube another vertical guide

with a caster c is placed. Thus it is possible to

move the pitot tube along two axes which are perpendicular to each other, and it is possible

to place the pitot tube and thus carry out

measurements of the velocity and pressure in

any position in a plane normal to the propeller axis. On the upper beam is fixed a dial d which is always kept in the same position in relation

to the towing carriage and on the rod e which

carries the pitot tube is fixed an index f which shows on the dial the position of the pitot tube in relation to the propeller. The adjustment of the dial in relation to the propeller was carried

out for the models at rest, but the changes of trim under way were measured and in the cases where the change of trim was greater

than 1.0 mm (in model scale) the measurements

were corrected for this difference. All the

measurements, both for towing and propulsion

tests, were carried out in the same plane in

relation to the model, but the distance A (Fig.

1) from the centre of the propeller boss to the

tip of the pitot tube was not the same for both models. The distance A for the two models is:

Model

aA»

«AD/D

gAD aBx.

The submerged vertical part of the pitot

tube is covered with a streamlined brass

mantle. The bore at the tip of the pitot tube is 4 mm and the split g (Fig. 1) is 0.7 mm. The

distance from the tip to the split is 36 mm and

the external diameter of the horizontal part of

the pitot tube is

13.0 mm. The pressure is

measured by an ordinary water tube

manome-ter. If the difference in water level under way and at rest is hs for the manometer tube nected to the split and hd for the tube con-nected to the bore, then the local velocity of

water in relation to the pitot tube is:

v = ko Vhd - hs =-- lc() VAli

It is then assumed that the flow direction is

parallel to the horizontal part of the pitot tube.

The difference in static pressure for the sy-stem at rest and under way is y hs where y is the specific weight of the fluid in the

mano-meter tube.

For this pitot tube ko = 0.141 when v is

measured in m/sec. and h in mm. This value is,

strictly speaking, valid only when the flow direction is parallel to the horizontal part of the pitot tube. If the flow assumes an angle

a with this direction and v is the total velocity,

see Fig. 2, then the connection between the

velocity and the pressure change is

v = k VAh.

where km as a rule is different from ko.

If ko, kik°, k1 may be called a reduction factor and is a function of the flow angle a.

The curve for k1 as a function of a, Fig. 3, has been obtained by experiments, and it is evident from the curve that as long as a is a small angle the value of k1 is very little different from 1.0.

For angles less than a < 15° - 20° the

dif-ference between ko and koc is so small that we

may consider the pitot tube to be registering the total velocity if ko is used throughout. In the actual tests with the pitot tube behind the model the flow direction in relation to the pitot tube has not been measured, but as the

angle of flow hardly exceeds 20° in any of the tests, it may be assumed that the velocity found

by the formula v = ko VAh is the total

velo-city.

5 240 mm 300 mm

Test conditions.

Both models have' been tested in loaded con-ditions. During the'propulsion tests model «BD

was towed with a force corresponding to the

relative difference in friction resistance for the model and the ship according to Frou.de. Thus

the results for this model will correspond to the trial-trip, smooth-Weather conditions for

this ship.

Model «AD was tested without any correction

for the difference in frictional resistance. This

loading Condition of the propeller will then

correspond to a condition. a little worse than

average sea conditions. Other particulars of the test conditions are given below:

Test conditions for the Models.

6

The executicrn of the tests.

To determine the pressure and velocity

con-ditions behind the models in the best possible

way by means of the pitot-tube, measurements

of the pressure and velocity were carried out in different positions in the wake. For each series of towing or propulsion tests where the flow conditions were determined,

measure-ments were carried out on at least 130 different spots. The sequence of the measurements has,

as a rule, been that the spots with the same angular position but at a different distance from the propeller centre were taken next to

each other.

Spots on 16 different radia were examined

and the radial distances between the spots were usually 20 mm. Plots for Ah were set up during

the tests and in the cases where any

irregular-ity of the Ah curves were found, new

measure-ments at radial distances of 10 mm were

car-ried out.

During the tests without propeller the mo-dels were kept in a fixed position in relation

to the carriage, but during the propulsion tests

the models were allowed, within very close limits, to move slightly in the longitudinal

di-rection in relation to the carriage. The

revolu-tions of the propeller were then regulated so that the speed of the propelled model was

exactly the speed of the towing carriage. In the

cases where the models were towed with a force equal to the relative difference in

fric-tion between the model and the ship, this force

was transmitted to the model through a towing

rope in the usual way.

The speed and revolutions were registered during all tests, but the thrust and the torque

were not measured during any of the tests with

the pitot tube. The change of trim aft was occasionally measured during each series of

tests.

The models were not equipped with rudders during these tests

As the purpose of these investigations was to relate the velocity and pressure changes which take place in the wake, due to the pro-peller action, to the propro-peller forces, it is of great importance that nothing which might alter the pressure or velocity conditions is placed between the propeller and the position

where the measurements are taken. As the load distribution of an ordinary untwisted rudder in the slip-stream of a propeller is not

symmetri-cal in any case, and as there will always for zero lift for the rudder as a whole, be some local lift at the different rudder sections, the rudder will always introduce some changes into the pressure and velocity distribution in the slip-stream behind a propeller. To relate the pressure and velocity distribution behind the rudder to the propeller forces the effect of

the rudder action has to be taken into account.

If it is possible to account for this effect, the rudder introduces a new uncertainty into the calculations and thus reduces the value of the results. It was therefore decided to carry out the tests without rudder. Measurements of the torque variations by means of electric equip-ment were carried out for model cA» with three- and four-bladed propellers with and without rudder to determine the influence of the rudder and the clearance between the

rud-der and the propeller. These tests are described and discussed in a special section.

Presentation of test results.

To be able to form a notion of what is really

happening in the slip-stream it is important to be able to present the results in such a way that they clearly show how the pressure and

velocity conditions change from spot to spot in the slip-stream. This may be obtained if charts

with curves for constant values of a velocity function and of a pressure function are

pre-pared.

To do this the pressure and velocity

condi-tions have to be examined at such a large

num-ber of spots that it is impossible to carry out the necessary number Of measurements with

Model speed in/sec. 1.335 1.500 Model propeller revolutions

pr. sec. 9.60 8.09

V/ YELva, (knots Iffeet) .53 .56

CONTOURS FOR CONSTANT W. MODEL.A" NAKED MILL.= RUDDER

CONTOURS FOR CONSTANT A vi

MODEL.e NAKED MILL , NO RUDDER

PROPEL L ER .1.

Figs. 3 & 4.

Figs. 5 SZ 6.

IIMIXE_RPLAPIL

CONTOURS FOR CONSTANT

NODEL A. MANED NULL. NO RUDDER

PROPELLER

/

\

/

/1

/ I I 0

CONTOURS FOR CONSTANT A It, MODELW, HARED NULL , NO RUDDER.

PROPE L L E R-17

a single pitot tube during one single run with the model. As the speed of the carriage can hardly be kept exactly constant during such a

series of runs, it is important to be able to

pre-sent the result in such a way that the errors arising from the small variations in the speed of the carriage can be eliminated. The results will therefore be given for the tests without

propeller as Taylor wake fraction:

vo = v (1 - wo). (13)

where v is the speed of the model, and in a

similar way for the tests with propeller:

= v (1 -

...

(14)

and for the increase in velocity due to the pro-peller action we have:

vi - vo = Av = (wo - wi) v

Awv

(15)

The different velocities and the velocity

changes expressed as wo, w1 and Aw are thus presented in a non-dimensional form.

There was a marked change in the static pressure distribution behind the models with and without the propeller working. The static

pressure (corrected for the difference in height)

behind the model without propeller Po was nearly constant across the examined area, but this was not the case when the propeller was working. The pressure change due to the

pro-peller action AP is then

AP = P1 - Po.

and this can be expressed in non-dimensional

form as

P1 - Po

Ape = (16)

p v2

where AP0 is a non-dimensional pressure

coef-ficient.

As one value of APc has to be based upon

two different runs, with and without propeller, it is necessary to ignore the variations in model

speed during the series in this case, but as the speed variations have always been less than 1/2 per cent this omission seems to be

per-missible.

The total thrust of the propeller (Equation

(11) ) can then be expressed by the non-dimen-sional coefficients as

T =

pv2 55 [(1 - w1) w + APc] ,dr- rd' (17)

Then, if we introduce the dimensionless thrust

coefficient ; as

Tc = [(1 - w1) Aw APc] (18)

pv

the total thrust can be expressed as

T = ffAT dr rdy, = pv2 f f Tc dr - rdso

Fig. 7.

For both models, charts showing the variation

of wo, w1, Aw, AP0 and Tc have been prepared.

These charts for model A are shown in Figs. 3-7. The charts showing the variations of wo

and Tc for model B are shown in Figs. 8 and 9.

From the figures it is evident that the velo-city, pressure and thrust distributions in the

propeller slip-stream are not symmetrical

about the ship's plane of symmetry.

If the upper starboard propeller quadrant is called the first quadrant and the lower star-board is called the second quadrant and the lower and upper port quadrants are called the

third and fourth, then for both models there are

zones in the fourth quadrants near the centre

of the propeller plane where the pressures and the velocities in the slip-streams are low, which also means zones of low Tc values. These zones

indicate the position of the boss vortex of the

propellers

in the plane examined.

During

some of the tests a fluorescent substance has been put on the propeller boss and thus the

boss vortex of the propeller has been visualized.

Unfortunately we were not able to take any

photograph of the boss vortex behind the

pro-peller, but it was quite evident that

immedia-tely after the vortex had left the boss it moved

over to port, and further aft it seemed to

con-tinue parallel with the propeller axis, but some distance away from it. The reason for the boss vortex moving away from the propeller centre

CONTOURS FOR CONSTANT Tc.

NIODEL:1-,NANED- NULL NO RUDDER. PROPELLER-1:

3

10

:PROPELLERPLAK

00_

must be the existence of some pressure

differ-ences between the different zones in the

pro-peller slip-stream. From the Tc charts it is

evident that more thrust is delivered by the

starboard side than by the port side of the

pro-peller. The reason for this will be discussed

later.

It is shown by different authors that one half of the total velocity increase given to the water

in the slip-stream by the propeller is imparted to the fluid in the propeller plane or in front

of it. The energy which corresponds to the other half of the velocity increase is present immediately behind the propeller plane as a positive pressure increase. If there is a differ-ence between the local propeller loading for

the different zones in the propeller plane, there

will also be a pressure difference between these zones in the slip-stream immediately behind the propeller. This consideration can fully explain the observed movement of the

boss vortex.

The charts for w1 Aw, APc and Tc for the two models tested are very similar. The main difference between the two sets of charts are the differences due to the difference in

pro-peller loading for the two cases.

Analysis of the measured pressure and velocity changes in the slip-stream.

From the measured pressure and velocity

distribution behind the models with and

with-out the propeller working it is possible to determine approximately the centre of the propeller thrust in relation to the propeller centre and the function f2 (f). The total thrust

and the position of the thrust centre was

deter-mined by integration of the Tc-curves for the two models. As expected the total thrust

found in this way is somewhat higher than the

thrust measured directly by the propeller

dy-namometer. In the table below both the thrust

found by integration of the Tc-curves and the thrust measured directly are given for both

models.

Comparison of thrust found by integration of the T curves and measured thrust.

Thrust found by integration of the Tc Curves. -Thrust measured by the

propeller dynamometer

Per, cent difference

Model «AD Model «Bo 5.80 kg 5.70 kg 4.85 kg 5.10 kg 19.5 Vo 11.8 Vo

CONTOURS FOR CONSTANTWa _{CONTOURS FOR CONSTANT}

Tc.

MODEL -Er NAKED NULL NO RUDDER

MODEL B NAKED HULL, NO RUDDER PROPELLER

To try to explain the relatively big difference

between the thrust determined from the

pres-sure and velocity meapres-surements and the thrust

measured by the propeller dynamometer, the rotation of the propeller slip-stream has to be

taken into account. Because of the very simple

apparatus used for the pressure and velocity

measurements, it is impossible to draw any

conclusion from the measurements about the

angular velocities in the slip-stream, but as the

propeller torque is measured by the propeller

dynamometer in separate tests, it is possible by means of the momentum theory and by making some assumptions to determine an approximate

mean value for the angular velocities in the

slip-stream.

From Equation (10) we have

Q = 5 27rpvi wj r3 dr. (10)

If the values for v1 and w1 are now assumed to

be constant across the slip-stream then we

have

Q = 1/2 P Vi wi R14. (10a)

where R1 is

the radius of the slipstream.

If half the axial velocity increase imparted to the propeller slip-stream is imparted in front

of the propeller disk and the other half behind it, then Equation (7) can be re-written thus:

vi =

v02 + 2T

and the expression for R1 becomes

10

R1 = R

-Vvi+vo

2v1

Both Equations (19) and (20) are based upon the assumption that the rotational velocity is small compared with the axial velocity and

that the pressure term in Equation (11) can be neglected. As we only want to get an

approxi-mate value for wi, the approximations made

may be justified. Using the mean nominal wake

fractions found by integration of Fig. 3 and

Fig. 8 we obtain for Model cAD col = 4.93 rad/

sec. and for Model «BD 031 = 3.43 radisec.

Now, if an annular element of radius r = 0.7 R of the slip-stream is regarded as repre-sentative for the whole propeller slip-stream,

then it is possible to determine to what degree

the use of the vectorial sum of the axial and rotational velocity, instead of the axial velo-city alone, will influence the value for the thrust determined from the velocity and

pres-sure meapres-surements.

Using Equation (7) we can now write

AT = F1p krit - VO) - V1 (V1 VO)]

where = 1/(wiri)2 + v12

and AT is the increase in calculated thrust when

v1' is used instead of vi

AT v1' (v1' - vo) - v1 (v1 - VO)

Or .. (21)

(vi - Vo)

For r1 = 0.7 R the calculation has been carried

out and the results are:

m/sec. v1 m/sec. v,' m/sec.

PT in per cent of T

From these considerations it may be con-cluded that it is impossible to explain the ob-served differences between the thrust

deter-mined from the velocity and pressure measure-ments and the thrust measured by the propeller

dynamometer by the rotation of the propeller

slip-stream alone.

Other possible explanations of the

differen-ces may be:

The thrust measured by the propeller dy-namometer is not the total thrust but the total thrust less the propeller's own resi-stance. Therefore, the thrust measured by the propeller dynamometer will always be less than the total thrust of the propeller taking into account the propeller's own

resistance.

In some cases zones with small negative values of w were found outside the

slip-stream. These small negative values of Aw have not been taken into account since their numerical values never exceeded 0.005. Some small, local inaccuracy may have been

introduced by the fairing of the curves for

constant velocity and pressure.

Due to the constancy of angular momentum

the rotational velocity will have a relatively

stronger influence upon the measured resultant

velocity in zones where the axial velocity 's

small than in zones where the axial velocity is high. This has the effect, in a small degree, of

evening out the fluctation of the course of the

f2 (co) curves determined from the Tc charts.

A similar effect will come into existence be-cause of the measurements of pressure and

velocity having been carried out some distance

from the propeller plane, and at this distance some of the high energy water in the zones of the slip-stream which correspond to the high load zones of the propeller will flow over to

zones where the energy content in the water is less, thus making the apparent circumferential

Model aA.» Model «Bx,

0.890 1.110 1.785 1.765 1.827 1.792 7.2 6.8

.... (19)

.. (20)

Fig. 10.

load distribution of the propeller more even. It is impossible to predict what kind of influ-ence, if any, the exclusion of the -small

nega-tive Aw values, the propeller's own resistance

and the inaccuracy of fairing will have upon the circumferential load distribution of the

propeller, but as these influences are believed to be small, it may be concluded that the

fluc-tuations in the circumferential load distribu-tion of the propeller found from the velocity

and pressure measurements are somewhat less

than the actual fluctuations if these had been

measured directly on the propeller itself. When considering Fig. 7 and Fig. 9, we shall not expect the centre ,of the propeller thrust to

be exactly in the propeller centre. The centre of the propeller thrust has been determined from Fig. 7 and Fig. 9 for both the models. In both cases the position for the centre of the thrust is in the first quadrant of the propeller

circle. The positions are (see also Fig. 10):

IfliffERENCF P051170&

Model Model

aAo oBo Angular positiorr of thrust centre 0 52.6° 55.6°

Eccentricity in per cent of propeller

diameter 1.78 3.17

It may be of interest to compare these

find-ings with the positions for the centre of thrust

which Jasper and Rupp [2] have found from measurements on a full-scale T-2 tanker. The values for the angle 0 found vary from about 15° to about 55° and the eccentricity varies from about 3% to about 6% of the propeller

diameter. Both these investigations and the in-vestigation made by Jasper and Rupp confirm

that there is some eccentricity of the centre of thrust of the propeller and that this centre

is in the first quadrant for ships in loaded

con-dition.

As mentioned above there will always be a

flow of water from the zones in the slip-stream which corresponds to the most heavily-loaded zones of the propeller to the zones which

cor-respond to a lighter degree of loading. In our

case this means that there will be a flow of

wa-ter from the first quadrant towards the fourth,

second and third quadrants and this will result

in an apparent reduction of the eccentricity and an increase in the angle 0. When this is taken into account there will be better agree-ment between these investigations and Jasper and Rupp's investigation than is apparent at

first glance.

It is evident from the Tc charts and from the

position of the centre of the thrust of the pro-peller determined from the charts or from [2] that the propeller loading is not symmetrical about the plane of symmetry of the ship. As the rate of power transmitted by one single screw is steadily increasing, it is increasingly

important to be able to explain the true reasons for the thrust and torque variations of the

pro-peller. In some of the works concerned with

these phenomena [12], [13] only the variations

of the axial wake fraction are taken into ac-count, and curves for the thrust and torque variations which are symmetrical about the

ship's centre plane have been produced. It is

evident from the above consideration that cur-ves for thrust and torque variations determined

on this basis must be considered as first

ap-proximations only.

From the Tc charts, Fig. 7 and 9, the circum-ferential thrust variation can be obtained. From Equation (18) we have

T = pv2 55 Tc r dr dr. . (18)

dT

= PV2 5 T

Therefore, if Tc is plotted to a base of r, the

moment about an axis through the propeller centre, and normal to the radius of the area

under the Tc curve is an expression for the

re-lative magnitude of the thrust in the angular

position considered. The Tc curves to a base of

r have been integrated and thrust variation

for both of the models with the corresponding propellers have been determined. Fig. 11 shows

dT

the variation of

dr dT for the two models.

Or dr. (22)

is the mean value for

dTfor the whole

dTidT

Th

propeller plane. e is an expression

so cis°

for the f2 (9) function -for a one-bladed

pro-peller if the propro-peller blade can be considered as a single line. As mentioned, the velocity and pressure conditions behind the propeller will be

more even the further aft the velocity and

pressure measurements have been carried out.

As there is some distance from the propeller plane to the plane where the measurements have been carried out, we must expect the

f2 (so) curve determined from the pressure and

velocity measurements in the propeller

slip-stream to be somewhat more even than a f2 (99

curve 'determined at the propeller either by direct measurements or by pressure and

velo-city measurements in the slip-stream. With this background it may be somewhat astonishing to find the big fluctuations in the circumferential thrust variation curves for the two models

de-termined from the velocity pressure measure-ments in the propeller slip-streams.

If the

thrust variations of a propeller of a

single-screw ship have fluctuations even bigger than shown in Fig. 11, this will greatly influence the

stresses in a propeller blade and ought to be

taken into account in propeller strength

calcu-lations. Furthermore, it is of interest to know

the magnitude of the thrust variations for cavi-tation calculations and cavicavi-tation tests. L8vstad [26] has mentioned some cavitation tests car-ried out with the propeller working behind the

after-body of a ship model. In these tests the

cavitation started when the propeller blade was in the upper vertical position, reached its maximum about 20 degrees after and disap-peared after about 40 degrees. When the pro-peller blade was in its lower position, a slight starting cavitation was observed. As the cavi-tation will first take place when the propeller blade is in an angular position where the pro-peller loading is high, the cavitation tests re-ported by Lovstad confirm that the propeller loading is highest in the first quadrant. The

conclusions which can be drawn from Lovstad's

tests are thus in agreement with the conclu-sions which can be drawn from Fig. 11, but it

is impossible to draw any conclusion from

Loy-stad's tests about the magnitude of the

-fluctua-tions in the circumferential propeller load

distribution. To be able to find out whether the

12 .A'It it' 00 00 0 70 810 SO 100 ISO I do /30 20 OR 80 SO

CROSS P170,TueE MEASUREMENTS

CALCULATED' ,,Jk 7 CALCULATED Vu 02 ANGULAR POSITION 9 Fig. 11. /8 225. 70. MODECEI;PROPEUER..7%.

NAKED NULL , NO RUDDER

225* 270. .15. 30

NUDELY, PROPELLERr

NAKED NULL NO RUDDER.

fluctuations in the propeller loading,

deter-mined from the velocity and pressure measure-ments, are likely to be correct or not, a

theore-tical calculation of the thrust variations for

the propeller sections r/11 = 0.7 and r/R 0.9

have been carried out for both the propellers.

The calculations are based on some assumptions

and the results are shown in Fig. 11. A

descrip-tion of the calculadescrip-tion and of the assumpdescrip-tions

made is given in the next section.

Theoretical calculations of the thrust

varia-ticms. :

There are in general several possible expla-nations for the observed thrust and torque variations of a propeller working behind and

in the neighbourhood of the hull and its

appen-dages. The importance of each of the sources may be different in different cases depending upon the actual conditions, but in most cases the most important reasons for the thrust and

torque variations may be as listed below.

The non-uniformity of axial velocity

com-ponents in the wake.

The angularity of the flow entering the

propeller plane.

45. 90. US. /80.

ANDuLAR 70siliON

FROM 7810,TUDE ME05000EMENTS

CALCULATED 7/17 07

(ALMA TED 7'u -09

.70

Figs. 12 & 13.

The influence upon the working conditions

of the propeller of the hull and its appen-dages which are placed in the immediate

neighbourhood of the propeller.

Influence of the free surface, especially

when the propeller blades are breaking the

surface.

Many investigations have been carried out to clarify the influence of the non-uniformity of the flow conditions in the wake upon the

propulsive efficiency [1], [14], [15], [16], [17] and [18], and some works deal with the

influ-ence of the hull and appendages [14], [28],

and others with the influence of the free

sur-face [20], [21]. Despite the enormous amount

of work carried out in this special field, the

reasons for the thrust and torque variations are far from completely explained. It is at present hardly possible to carry out a complete

theore-tical calculation of the thrust variation of the propeller taking all possible sources of thrust

variation into account. The aim of this chapter

is by theoretical considerations to show

whether the thrust variation of the propellers determined from the pressure and velocity

measurements is likely to be correct or not. For this purpose an approximate calculation based

upon. some assumptions might be sufficient. Attention has been drawn to points 1. and 2. in the above list and the influence of all other possible sources of the thrust variations have been disregarded. If only the variations in the

axial velocity components have to be taken into

account, then we will get a thrust variation which is symmetrical about the centre plane of the ship, but if there are some vertical and

transverse velocity components in the flow entering the propeller, these velocity compo-nents will produce a thrust variation which is not symmetrical about the centre plane of the ship. The influence of a variation in the axial velocity on the flow conditions at a propeller blade section of radius r is shown in Fig. 12. If angular velocity of the propeller (0 is

con-stant and the flow is perpendicular to the

pro-peller plane, the lift of the blade element be-tween the radius r and (r + dr) is determined by the angle (43 - 8). For lift coefficients less than the maximum for the propeller blade section we find that, for a non-cavitating

pro-peller, the bigger the angle (.13 - /3) the,greater

the lift or thrust producted by the blade sec-tion, and therefore the greater the wake the

heavier the propeller loading, which is a well-known fact.

If the influence of the propeller action is ignored, the flow conditions at the propeller plane must be symmetrical about the plane of

symmetry of the ship. Therefore, if we compare

the flow conditions at a spot in the propeller plane on the port side of the centre plane of

the ship with the flow conditions at the

corres-ponding spot on the starboard side, we will find the same axial velocity and the same

angularity. Instead of dealing directly with the angularity of the flow, we may decompose the

resultant velocity into an axial, a vertical and

a transverse velocity component and deal with

the influence of the vertical and transverse

velocity components upon the propeller action

instead of the angularity. If corresponding

spots on starboard and port side in the

pro-peller plane are considered, then the magnitude

of the vertical velocity component vy and the

transverse velocity component vx must be the same, but the influence of vx and v y upon the working conditions of the propeller will not be

the same. If vxy is the resultant of vx and vy

and vxyt is the component of v is

normal to the propeller radius at the spot con-sidered, then we find that in the first quadrant,

i. e. the upper starboard quadrant, the direc-tion of vxyt will be against the direcdirec-tion of rotation for a right-handed propeller and in the fourth quadrant the direction of vxyt will

be with the direction of rotation of the

propel-ler. In the first quadrant the effective angular

velocity of the propeller will be higher -than (0

and in the fourth quadrant less than (0. The

influence of vxyt upon the flow condition at a

blade section of radius r in the first and fourth

quadrant for a right-hand turning propeller is

shown in Fig. 13. It is evident from the figure

that in the first quadrant vxyt will increase

the effective value of or and decrease the angle

both of which mean an increase in the pro-peller loading, but in the fourth quadrant the

opposite tendency is found. The influence of

the velocity components vx and vy upon the

working 'condition

of the propeller in the

second and third quadrants depends upon the

angular position of the propeller blade and on the relative magnitude of the velocity

compo-nents vx and

_v'

No measurements of the

velo-Y

city components vx and vy for the models «AD and «BD were carried out, but, proceeding from the measurements of the angularity of the flow

entering the propeller plane given in [2], [6], [9], [22], the magnitude of the velocity com-ponents vx and vy for bath models art r/R =

0.7 and r/R = 0.9 has been assumed to vary as shown in Fig. 14. vx is taken as positive when the direction is towards the ship centre plane and v y is positive upwards, and as the

variations of vx and v y with these signs must

be symmetrical about the centre plane of the

ship, only the variations for one side of the pro-peller plane has been shown in the figures. The variations of the axial wake components have been assumed to be as shown in Fig. 3 for

mo-del «AD and in Fig. 8 for momo-del «BD. Proceding

from the above-mentioned assumptions, the thrust of a propeller blade section at r/R = 0.7 and r/R = 0.9 for propeller «ID behind model «AD and propeller «IID behind model «BD have been calculated for six different

angular positions of the propeller blade. The

calculations follow the method described by Hill [23].

The .spots and curves for calculated thrust

variation for r/R = 0.7 and r/R = 0.9 are

shown in Fig. 11, together with the thrust va-riations determined from the pressure and

velocity measurements. Both the curves for

the thrust variation determined from the

pres-sure and velocity meapres-surements and the cur-ves based upon theoretical calculations and

assumed flow directions at the propeller plane show mainly the same properties. It may, then,

be concluded that the greater part of the fluc-tuations in the circumferential thrust distri-bution of a propeller are due to the variations

in the nominal wake and the angularity of the flow entering the propeller plane, but evidently. 14

02

02

0.1

Fig. 14.

there will also be some influence from the magnitude of clearance between the propeller and the stern frame and the rudder.

The agreement between the thrust variation curves determined from the pitot tube mea-surements and the curves based upon calcula-tions and assumed flow direccalcula-tions at the pro-peller plane is as good as could be expected

taking into account the roughness of the

assumptions made for the theoretical calcula-tions and also that the calculacalcula-tions have been

carried out for two different 'values of r/R only.

Therefore, despite the simple apparatus used for the pitot tube measurements, the curves for the thrust variations based upon the mea-sured pressure and velocity changes in the

slip-stream of the propellers behind the models seem to be good approximations to the correct

curves for the circumferential thrust

distribu-tion or to the funcdistribu-tion f2 (v).

Harmonic analysis of the thrust-variation

curves.

When the mutual interferences of the pro-peller blades are neglected, the thrust varia-tions for the propeller as a whole are simply

the sum of z thrust distribution curves for one

propeller blade (f2 () curves) taking into ac-count the phase differences between the-pro-peller blades. It has been shown that only the

I ;41.0.9

----

I--I no en SD 0° 120. do° leo. /p.Ø7

Arlfab

/

0° 30. 00° 90° 120° 150° 780° MO° 200° 270° 240° 210° 330. 900° 270° 240 210

*) Stress-measurements from [27].

n z harmonic components of f2 (co) will

influ-ence the thrust variations for a Z-bladed pro-peller as a whole. It is therefore of interest

to break down the circumferential thrust

varia-tion curves into harmonic components. If the

thrust distribution for a one-bladed propeller

is expressed as:

dT

= Ao + A1 sin (so+ +

dcp

A2 sin (2f + (D2) + + An sin (nr + 43n),

An/A0 is an expression of the importance of

the n-harmonic component. The harmonic

ana-dT

lysis of the -curve has been carried out

dq)

using 24 ordinates and the scheme described

by Manley [24]. The magnitude of the

differ-ent harmonic components is expressed as

An/A0 in the above table.

The results of stress measurements on a

pro-peller blade, carried out on board a T-2 tanker

by Bunyan [27], are included for comparison.

From the above table it is evident that the

trend is the same for results of Bunyan's stress

measurements and the results from the pitot tube measurements.

From the figures we may conclude that

generally the more blades a propeller has the less is the thrust variation for the propeller as a whole. This also agrees with our general

experience. Owing to some possible small

inaccuracy in the fairing of the curves neces-sary to produce the thrust distribution curves

and other uncertainties previously mentioned,

the accuracy of the An values cannot be ex-pected to be better than ± 2.0 per cent of Ao. The difference between A4 and A5 for model <do> is therefore within the limits of accuracy

and thus it may be wrong to conclude that for model <A» a four-bladed propeller will pro-duce less thrust variation than a five-bladed

propeller.

An/Ao

Direct measurements of the torque variations for a three- and four-bladed propeller behind

model «AA.

To extend the investigations reported and to make some measurements which could possibly

serve as a control of the correctness of the findings from the pressure and velocity

mea-surements in the propeller slip-stream, a series

of direct torque variation measurements for two different propellers on model gA» were carried out. The instrumentation used for the tests was mainly the same as described by H. Christensen [25], but some further

improve-ments were made. The strain gauge torque

dy-namometer was replaced by a new specially designed torque dynamometer, and the Brush

amplifier replaced by a new amplifier designed

in connection with the new torque

dynamo-meter. The remaining part of the

instrumenta-tion was the same as described and used by

Christensen [25], but the time calibration-base

was adjusted to 200 cycles/second instead of as

previously 500 cycles/second. With the

impro-vements made, the amplification is constant and the phase shift is a linear ftmetion of the frequency for all the harmonic components

within the practical range.

If the propeller is given a single knock when

the propeller is mounted on the shafting sys-tem of the model and the model is floating at the desired draught and with the instrument-ation ready for test, the shafting system with the propeller will vibrate for a while with its

natural frequency. By having these vibrations transmitted to the oscilloscope and photograph-ing the display, it is possible to determine the

natural frequency for torsional vibrations for

the system (with one special propeller) at rest. The natural frequencies for torsional vibrations for the system with propeller gID and propeller «III» determined in this way are:

Natural frequency for torsional vibra-tions in the shafting system with the

propeller submerged 200 cycles/second 193 cycles/second 15 n 1 I 2 3 4 5 6 7 8 I

910

Model «Ax. , 1.85 .192 .059 .037 . .048 .031 I .035 .021 ; .021 .016 Model «B» I .263 .213 .103 , .099 .043 .035 .013 .023 .010 .006 T-2 tanker *) 1 .300 .178 .008 I .077 .061 .050 .049 .065 . .037 .036 Number of blades Propeller no. «I» 4 3

If the moments of inertia of the entrained water of the propellers are equal both for the propellers vibrating at rest and for the

pro-pellers:working, then with a maximum 12

revo-lutions per second for the model propellers, only the harmonic components of the torque

variations of an order higher than 16 (referring to the propeller revolutions) can possibly come -into resonance with the natural frequencies of the shafting. In this case, therefore, the

instru-mentation can be used to study the torque variations of the propellers if the harmonic components of an order higher than three or four times the blade number are regarded as unimportant. As the test results do not show any marked evidence of vibrations of such a high order, the instrumentation can be

con-sidered as well suited to our purposes.

The main purposes of the torque-variation

measurements were:

To carry out torque variation measurements

for the propellers under conditions similar

to the test condition for the pitot-tube

mea-surements. The results of the torque

varia-tion measurements could then be compared

directly with the findings from the pitot-tube measurements and thus be used as a guide towards determining the correctness

of these.

To make a comparison of the torque

varia-tiOns for a three- and four-bladed

propel-ler under. similar conditions.

To study the influence of the amount of clearance between propeller and rudder

upon the torque variations of the propellers. Measurements of the torque variations were carried out as described on model «AD

equip-ped with propeller a. and «MD. Tests were

run at two different speeds, and with two different rudders and without rudder (as for

the pitot-tube tests). All tests were run with

the model self-propelled without any correc-tion for the relative difference in the

frictio-nal resistance for model and ship.

The outline of the propeller apparatus of

model qA» with the two propellers and the two

rudders is shown in Fig. 15. Both the rudders

are ordinary streamlined balance rudders

with thickness about 17 per cent of the chord. The main particulars of propeller «MD are:

16

Diameter 227.5 mm

Number of blades 3

Pitch ratio at r/R = 0.7

.853

Expanded blade area ratio .427

ATOCEL

Fig. 15. STERN ARRANGEMENT

The results of the torque-variation mea-surements are shown in Fig. 16 for the four-bladed propeller (propeller «ID) and in Fig.

17 for the three-bladed propeller. The torque

variations are expressed as the actual torque Q of the propeller in a particular angular

po-sition over the mean torque Q of the. propeller. By increasing the speed of the model and thus

the loading of

the propeller, the absolute

magnitude of the torque variations increase, but Q/-Q seems to be almost the same for the two speeds. When the clearance between the propeller and the rudder is not too small, the influence of the rudder upon the torque varia-tions of the propeller seems to be small (Rud-der 1), but when the clearance between the

rudder and the propeller becomes small

(Rudder 2) then the presence of the rudder increases the magnitude of the torque

varia-tions of the propeller.

When the torque variation curves for the four-bladed propeller (Fig. 16) are compared with the corresponding curves for the three-bladed propeller (Fig. 17) it is evident that

for the three-bladed propeller the second order

harmonic component (referred to the blade

frequency) is much more pronounced than for the four-bladed propeller.

Strictly speaking, the different harmonic

components of the torque variations cannot be

directly compared with the corresponding

harmonic components of the thrust variations determined from the pitot-tube tests, because

the thrust variations for the propeller as a

whole will not be identical with the torque variations. But it is to be expected that the torque variations and the thrust variations of' the propeller will show very similar trends.

The torque variation curves have been split into harmonic components using the usual

twelve ordinate rule. If f (so) is either the

tor-que or the thrust variation of the propeller and if 97 is the angle of rotation of the propeller,

then we can express the torque or the thrust variation curves of the propeller as:

f (99 = AO + A1 sin + /31)

+ A2 sin (2v + P2) +

+ An sin (n +

)

An/A0 is then an expression for the relative importance of the n-harmonic component of f (i0). A comparison of the magnitude of

har-monic components expressed as An/A0 for the

torque and the thrust variations is shown in

the table below.

Taking into account all possible sources of inaccuracies and differences between the two

types of measurements, the agreement between

the torque variation measurements and the

results from the pitot-tube tests is satisfactory.

The torque variation measurements are thus to some degree a confirmation of the results of the pitot-tube tests.

Some tests with fins on the hull in front of the

propeller.

The investigations so far reported show that

the angularity of flow in the water entering the propeller influences the load distribution of the propeller to a large extent. Therefore, if it is possible to control the direction of the

flow entering the propeller plane by means of

fins on the hull in front of the propeller, it

should be possible, to some degree, to control

the circumferential load distribution

of the

propeller by means of fins. We should expect that if it were possible to obtain a more even load distribution for the propeller, this would result in a better propulsive efficiency. How-ever, in most cases it will be required that the

placing of the fins should not lead to a poorer. propulsive efficiency.

Tests with one and two fins placed on the hull in front of the propeller were carried out to try to find what kind of influence such fins

would have upon the propulsive efficiency and

the load distribution of the propeller. Model

«AD was chosen for these tests because this

model is a wax one and thus allows easy

mounting and dismounting of the fins without

destroying the model. The fins were made of

wood (teak) and cast into the wax model. Fig. 18 shows the form and the position of the fins.

From Fig. 11 it is evident that to obtain a

more even circumferential load distribution of

the propeller, the propeller loading has to be

increased between 210 degrees and 320 degrees.

Furthermore the loading ought to be reduced

between 340 degrees and 80 degrees. To clarify how the fins influenced the working condition of the propeller and the load distribution of the propeller, some preliminary tests were carried

out with one fin in the first quadrant and

another in the third quadrant of the propeller plane. Both of the fins were placed

horizon-tally. Some pitot-tube measurements were

carried out and analysed and showed that only

the fin in the third quadrant influenced the

An/A0

*) See table on page 16.

17

n = 1 - Z = (blade

frequency n = 2 - Z

1

Number Model Torque From the Torque- From the

Propeller of

blades Rudder speedm/ sec. variationmeasure-_ments pitot-tubetests *)

variation measure-ments pitot-tube tests *) L33 0.051 0.037 0.015 0.021 I 4 No. rudder Mean of1.57 0.059 0.024 both speeds 0.055 0.019 1.33 0.059 0.020 I 4 1 1.57 0.047 0.020 Mean 0.053 0.020 1.33 0.088 0.027 I 4 2 , 1.57 Mean 0.0770,083 0.026 0.027 III 3 No. 1.34 1.57 0.047 I 0.024 0.059 0.043 , 0.030 0.031 rudder , Mean 0.035 0.036 1.34 0.033 0.035 III 3 1 1.57 0.033 0.032 Mean 0.033 0.033 1.34 0.062 0.077 III . 3 2 1.57 0.039 , 0.047 Mean 0.050 0.062

18

RUDDER

RUDDER Y

ANGULAR POSITION OF PROPELLER

ANGULAR POSITION OF PROPELLER

mODEL-A , PROPELLERT V T.57 Fig. 16. Fig. 18. MODEL!',4-, PROPELLERr V 1.33 flYsec. RUDDER 1: RUDDER

-2-AORAMEMENT OF DIE ONO.

load distribution in the desired way. The upper

starboard fin (the fin in the first quadrant) was therefore removed and some new tests with only the lower port fin on the hull were carried out. The test results indicated that a slight inclination of the fin might give better

results. Accordingly the fin was given an

inclination of 2.15 degrees as shown in Fig. 18,

and a series of pitot-tube tests were run both with and without propeller. The results of

these tests are- presented as charts with curves

for constant wo, w1 and Tc in Figs. 19-21.

1.10

105 ZOO

.95

2

ANGULAR POSITION OF PROPELLER

RUDO R T UDD

wirHour RUDDER

2 ANGULAR POSITIONorPROPELLER

Fig. 17.

MODEL "A", PROPELLER-1r V 134 flkiee.

MODEL le,

PROPELLER-DI-V. 1.57 m/sec.

Similar tests were also carried out with two fins, symmetrically placed on the port and

starboard sides of the hull. The results of the

tests are shown in Figs. 22-24. The circum-ferential thrust distribution of the propeller in the two cases was found from the pitot-tube measurements, and the results are shown in

Fig. 25 together with the circumferential thrust

distribution curve for the propeller without

fins on the hull.

The charts Figs. 19-24 compared with the charts Figs. 3-7 show that it is possible, by means of fills, to alter both the distribution of the wake behind the hull and the thrust distri-bution over the propeller plane. It is also

possible to alter the circumferential thrust

distribution of the propeller, but the tests

carried out are too few to draw any conclusion about how far it is possible fully to control the

circumferential load distribution of the pro-peller by means of fins on the hull in front of the propeller. However, the tests indicate that

it is, at least to some degree, possible to control the load distribution of the propeller by means

of fins, but a series of tests with systematic variations of the form and location of the fins have to be carried out before it is possible to predict the best form and location of the fins.

ERFLARE7

Fig. 21.

CONTIVRS FOR CONSTANT k

MODECA. WM ONE FIN

PROPELLER,' NO RUDDER.

In addition to the pitot-tube tests, ordinary

resistance and propulsion tests have been made with the model, with and without the fins. The

results of the resistance tests are given in Fig.

26. As expected, the model resistance increases

slightly with the introduction of the fins, and the increase in resistance caused by one fin is

Figs. 19 & 20.

CONFORM FOR 05571147 VI;

MODEL,. WIN CRE SIRECRP KW ADE

NMI OP INELIMITION 0 OR 270. FROPELLERV, AO RAWER.

roughly the half of the resistance increase

caused by two fins placed symmetrically.

The propulsion tests were run with a con-stant speed of the model (v =1.345 m/sec.) and with variable propeller loading. The pro-peller loading is controlled by the towing force transmitted to the model from the carri-age. Normally this towing force is used to

compensate for the relative difference in fric-tion resistance for the ship and the model, but

as the pull can be given any magnitude and

made positive or negative at will, it can also be used to control the propeller loading. The

con-dition «zero per cent overloath Means the

condition for the model which corresponds to

the predicted ship resistance according to

Froude (no roughness allowance). x per cent overload means that the sum of the model resistance and the pull is x per cent higher than for zero per cent overload. The variation of the propulsive efficiency Tr with the

pro-peller loading for the model without fins, with one fin on the port side and with two fins sym-metrically placed, is shown in Fig. 27.

.1( )) Rv

nir =

2 ir n Q where x = per=

centage overload.

R = resistance corresponding to smooth

ship resistance (kg)

20

CONTOURS FOR CONSTANT We MODEL 'A WITH TWO SYMMETRICAL FINS ANGLE OF INCLINATION OF THE FINS 215.

NO RUDDER.

30

x10

y 30

Figs. 22 & 23.

CONTOURS FOR CONSTANT VA MODEL "A WITH TWO SYMMETRICAL FINS ANGLE. OF INCLINATION OF THE FINS VS. PRCIPELLER7; NO RUDDER.

fin placed either on the port or on the star-board side of the model would be nearly the same in both cases, but this is clearly enough not the case. To be able to explain, or at least

find some possible reasons for the differences in the propulsive efficiency, the wake fraction

and the thrust

deduction factor determined

from the tests with and without fins in front of the propeller, we have to go back to the nominal wake distribution behind the model and the load distribution of the propeller. If Fig. 19 and Fig. 22 are examined and compared

with Fig. 3, we find that the introduction of the fins on the hull has produced a change in the distribution of the nominal wake, and the actual nominal wake fraction may also have

been altered. The changes in the nominal wake

distribution caused by two fins placed sym-metrically are, as must be expected, the same on both sides of the model and the nominal wake distribution is in this case symmetrical about the centre plane of the model and prac-tically the same as the wake distribution on

the port side in the case with only one fin

placed on the model in front of the propeller.

If the increase in effective wake'

caused by two fins placed-symmetric'ally On the

model speed (m/sec.)

.n = number of revolutions per second

for the model propeller

Q = torque of the model propeller

(kgm)

In the calculations of 7pr the resistance R for the model without fins has been used in all

cases both with and without fins. Thus the

to-tal influence of the fins upon the propulsive efficiency is included in 7T. Therefore when Fig. 27 shows higher 7pr for the model with

one fin on the port side this means that a real improvement in the propulsion of the model

has been obtained.

From the propulsion tests with and without

fins' the effective wake fraction wT, the

thrust-deduction factor r

and the relative rotative

efficiency 7iR have been determined using

thrust-identity. The' resultsof the analysis are shown in Fig. 28. In these calculations the

resistance of the model in the actual condition, with or without fins, has been used.

Without knowing anything about the cir-cumferential load distribution of a propeller working behind a hull, we might at the very

first

suppose that the

influence upon the