On propeller scale effects

MEDDELANDEN

FRAN

STATENS SKEPPSPROVNINGSANSTALT

(PUBLICATIONS OF THE SWEDISH STATE SHIPBUILDING EXPERIMENTAL TANK)

Nr 28 _{GOTEBORG 1954}

ON PROPELLER SCALE

EFFECTS

BY

H. F. NORDSTROM, HANS EDSTRAND AND HANS LINDGREN

GUMPERTS FORLAG GOTEBORG

1. Introduction

Publication No. 91) of the Swedish State

Shipbuild-ing E xperim ent al Tank dealt with the results of a

system-atic series of experiments with model propellers in open water. In the course of these experiments, one of the propellers, P38, was

used for an investigation of scale effect, i. e. the effect on the

characteristics produced by variations in REYNOLDS number. The present paper is concerned with an extension of the above scale effect investigations, using two of the model propellers which were employed in the previous tests and had different pitch ratios but otherwise the same dimensions. The experimental results were compared with those obtained previously with Propeller P38.

In addition, tests were made with an entirely new series of model propellers, comprising four geometrically similar models of different sizes. The purpose of these tests was the same as that of the previous investigations, i. e. to determine the influence of scale effects on the results of open water propeller tests and thereby the minimum value

of REYNOLDS number which may be considered permissible for such

tests.

Experiments with the object of determining this minimum value have already been carried out by GEBERS, KEMPF, KEARY, DE SANTIS

and VAN LA1VIMEREN,2) amongst others. The problem was closely

discussed at the Fifth International Conference

of Ship Tank Superintendents

in London 1948.

However, the Sixth International Conference

re-commended that new experiments should be conducted in order to obtain further information on this problem.

In the course of the present investigations, open water tests were also carried out with one propeller in conjunction with turbulence stimulators. In addition, some tests were conducted with another propeller with sand coverings of different degrees of coarseness

Screw Propeller Characteristics by H. F. NORDSTROM.

The results obtained from these experiments are summarised in Scale Effect of a Screw Propeller by G. S. BAKER, Trans. I. N. A., Vol. 94, 1952.

applied to the blades, in order to determine the influence of blade

surface roughness. The results of both these additional series of

tests are given in this paper, the roughness tests being dealt with in Appendix 1.

2., Symbols'

The symbols have been chosen in accordance with the recommendations made

bythe Sixth International Conference of Ship Tank

Super-intendents,

Propeller Dimensions D = propeller diameter

P = propeller pitch Ao propeller disc area

Ad, developed blade area

-= maximum blade thickness referred to centre of propeller

E, = blade width at 0.7 D12

Kinematic and Dynamic Symbols and Ratios

v = speed of advance

= propeller thrust Q = propeller torque

= rate of revolution (revs, per unit time)

= density of water (102.0 kg ,sec.2/m4 for fresh watery

= kinematic viscosity of water 1 V v2 + (0.7 Dn)2

R n REYNOLDS number

=,. temperature of water in °C)

Din tensionless' Coefficients, and Ratios

= pitch ratio. Ad

= disc area ratio Ao

blade thickness ratio

T thrust coefficient e D4 '7,2 = T = = 4

K Q = D 2" torque Coefficient p 5 n

J

advance coefficient Dn

KT J

_{= propeller efficiency in open water} KQ 2

The model is referred to in all instances, in this paper. Metric units are used throughout (1 metre = 3.281 ft.)

3. Model Propellers Tested

Eight model propellers have been investigated. The main parti-culars of these propellers are given in Table I (page 26), together with the dimensions of Propeller P38. The latter propeller (see

Intro-duction) was used previously in a similar investigation and the

results are used for comparison in this paper. Outlines of the three propellers used in the earlier tests, P36, P38 and P40, are given in Fig. 4 in Publ. No. 9. Outlines of the new propellers, P541P544, are shown in Fig. 1. Propeller P467, which was tested in conjunction with various turbulence stimulators, was employed previously in a

Fig.. 1. 5 II 1 Propeller No 'P54/ P542 P54,3 P544, I 13 mm /50 ll 200 !

250

300

Propeller No. P64 "IN - .eV%AGIVA.. -.1"firegare, 92 /287 103.0 773 R=2.5.9 ,Dimensions in mm "Pig. 2.

systematic investigation described in Publ. No. 22.1) The blade form, shape of sections, blade thickness ratio, pitch variation, rake

etc. of this propeller were chosen to conform with Professor TROOST'S

B. 4.40 Series.2) Finally, Propeller P64, which was tested with

different sand coverings on the blades, is illustrated in .Fig. 2.

4. Testing Particulars

The open water tests were carried out in accordance with the

usual practice at the Tank of maintaining the revolutions constant, or as nearly constant as possible, and varying the advance coefficient, J, by varying the speed of advance.

Each propeller was run at a number of different revolutions. The

range of REYNOLDS number was thus varied for each propeller within

the limits imposed by the revolutions and velocity and the capacity of the experimental apparatus employed. In the case of the series P541P544 (the same forth in four different sizes) the REYNOLDS number also varied on account of the variations in diameter.,

The tests were carried out using the ordinary apparatus for open water propeller tests. This apparatus is described in Publ. No. 9

(see Introduction). Two different dynamometers were employed,

_ Pilch P- /978

I). Model Tests on the Optimum Diameter for Propdlers by HANS EDSTRAND.

2) Open Water Test Series with Modern Propeller Forms by L. TROOST, Trans. N. E. Coast Inst. of Engineers and Shipbuilders, Vol. 67, 1951.

7 one being of GEBERS' design capable of measuring torque values of up to 40 cmkg and thrust values of up to 12-13 kg, while the other was of the KEMPF type with torque and thrust capacities of 100 cmkg and 20 kg respectively. The latter instrument was only used in some of the tests with Propellers P543 and P544 (see Figs. 11 and 12).

As mentioned previously, Propeller P467 was tested in conjunction with turbulence stimulators. Two different types of stimulator were used, one a horizontal grid and the other a vertical grid.

The horizontal grid consisted of three piano wires, 1 mm in dia-meter, stretched horizontally in a vertical plane at right-angles to the direction of motion and 300 mm ahead of the propeller. The middle wire was level with the centre of the propeller shaft, while the other two wires were spaced D/4 above and below the middle

one. The wires were attached to two vertical streamlined struts,

which projected down into the water from the carriage at each side; these struts were placed at such distance apart that the disturbance caused by them could be considered as having no effect upon the conditions at the propeller under test.

The vertical grid consisted of three rods, each 3 mm in diameter.

These were also placed in a vertical plane at right-angles to the

direction of motion and 300 mm ahead of the propeller. The rods were fixed to the carriage and projected vertically into the water to a depth of about 30 mm below the lowest point of the propeller disc. The centre rod was in a vertical plane through the centre of the propeller shaft, while the other two rods were spaced D/4 on

each side of the centre one.

As stated in the introduction, the effects of blade surface roughness were investigated with Propeller P64. The different degrees of rough-ness were achieved by applying Alumdum grinding sand of various grain sizes. The propeller blades were first covered with a thin layer of quick-drying shellac, after which sand of the appropriate grain size was applied; any excess sand was blown off after the shellac had dried.

This method cannot be regarded as ideal since, in the case of the smaller grain sizes at least, it was not possible to avoid laying several

layers of sand one over another. These tests with sand covered blades are, however, of secondary importance to the other experiments described herein. The results are given in Appendix 1, in spite of the aforementioned imperfection in the method, because they provide

material for an interesting comparison which is described in Appendix 2.

In all the tests described herein, the centre of the propeller shaft was at a depth equal to the diameter of the propeller in question.

5. Results

The measured values of thrust, torque, revolutions and speed have been converted to the dimensionless numbers KT, KQ, 7)0,

and J

and they are given in the usual manner in the form of curves of the first three on a base of J. The water temperatures and the

Propeller No. PJ6 D= 250mm P/D=060 3 2 Fig. 3.

1111PMEI

MR41111111111

1111M111111111

MN I

11111

ION

II

111

/0 K7. /00K, n ,,-/Jo n P.O . - Z3 0.3 - 3.. rj.rec. r/3.. ,/aite. r/3er. t-12.6-C R,- 3.2- 3, -10" R,,- 36 - 3.7. R- 2.5- 2.e R,- 2/ /0" R= 1.3/06 Op. /0' /0' /0' g 01 03 0.* 0.5 Oe 07 V On 70 60 4,0 30 20 /0 0 H 1-12.4-C

-Fig. 4,

limits within which REYNOLDS number varied in the tests in question

are also given on these curves,.

The results obtained with Propellers P36, P38 and P40 are given

in this way in Figs. 3-5, As mentioned already, Propeller P38

had been tested at an earlier date and the results applying to this propeller are also to be found in Pub!. No. 9. In Figs. 3 and 5, full lines have been drawn through the values representing the revolutions

which would be about normal for routine tests at the Tank with

propellers of corresponding dimensions. Similar curves are included 9 Propeller No. P38 D= 250mm P/D= loo B' t- *6- - 2.5. /0" January /943 n S. 7 - 3. - 10 s /as = /0" 26 - 2.9. /0' Octotie,--,1947 eO' n 6.9 R= 2/ - 2s- /Or 101/r cr n ,fter. "C 100/f Q 17 3.* r/rec. =/a - - /Or BO 70 60' 4 0 30 20 /0 0 -, 8.6 -6 - /0' 0 0, 0.2 3 0.5 06 07 0, /.0 60

10Kr Propeller No, P40 100K _{0 =250 mm P/D =140}

-- 7o r66.

t /2.0 °C. R,,- 9 - 2.4 10s n = n 4.'ft.,4 fv+se. 1-12.2°C 1.3 - 4 17 -/a 9 _{C n} =3.6 r/6. j Rn° 10 - I/

11161111

NM I

'MI El

WM IIIIIII

1

Fl IEEE

El NEU

I

0.2 0 6 06 08 Li

al

1.4 Ls On Fig. 5.

in Fig. 4, but the propeller in question, P38, was tested at normal revolutions on two different occasions, namely January 1943 and October 1947, and the temperature of the tank water varied consider-ably. Full lines have been drawn through the points obtained from the earlier tests, when the lower temperature prevailed, and dotted

curves through the points from the

later tests at the higher

temperature.

It is evident from the results in Figs. 3-5 that, as the revolutions fall below normal, the effect on the characteristics soon becomes

apparent. The normal revolutions used in routine tests are thus

a 7 6 3 2 60 70 60 50 40 30 2C /0 5 0

I

BO 60 20 Propeller- No P 3c5 0- 250 rnrn P/D - ao

it

I 4 ./-0.f 1 0 I 04 1 -i I 11 1 f, 1 _ _ '1 0 143 ''() a a I! 11 - - a li 1 1 , . Os Is 2 25 35 Fig. 6.

fairly close to the critical value which determines the minimum

value of REYNOLDS number (see Introduction),

The results in Fig. 4, including those obtained at the normal

revolutions ,(n = 8.5.r/sec.), show certain differences at the lower temperature. It should be mentioned that this temperature, 11.8° C, is exceptionally low and only occurred during the wartime winters when fuel for central heating was scarce in Sweden. Furthermore, there was an interval of nearly five years between the two series of tests. It is therefore considered that the differences between the

two sets of results can be wholly or partly attributed to external factors such as differences in the condition of the measuring

apparatus, etc.

The experimental results shown in Figs. 3-5 . are illustrated in another form in Figs. 68. Efficiency values were lifted from Figs.

-3-5 at constant values of the advance coefficient, J, and plotted

to a base of REYNOLDS number. The curves in these diagrams clearly indicate the minimum value of REYNOLDS number for this

40

.60 20 80' 40 40 '20 80' 0.8 Propeller No. P38

0-250mm P/D

too' Propeller No P40 ,D 2,50 mrn P/0- /. 40 /.8 2o .3.5 2.2 J- 0-9 -_ . 4---

, aim

, k ._ P as ,., 4 ..0 Diffel-ent remparaturt.) %, d

;

I , ; 1.1 J - /.2 /1 _IMINf

NeP2

=

11111511 1. 0 . 0.8

1.1

MT

II ! t. k5' 1 1 1 1 1 ., 1 1 , , I 1 , 3 2' Fig. '7. 40 1.2 7 / I 0

Propeller No. P54I D=150 may 13 ?.% 1 , , . 1 11

11/11/.;ir

'''''

1 , 1

A

a

_\

,

1...

II

in

1 ; I 1 , \ 1

A

MI

Aall

numusqiii

israiri__-Ilm.

mh...._

,

I

irks

, \i 0 ., v8.5 -2.4- 2 6 10 I n = /St /0)4. = /2. eC R,, = 2.o- 2.2- '/O s I001(a. n = 0.1 ,/retc. R,,- 1.3 - Zs /0' 0 v' 0.2 03' 0. 0.s O 07 0 V9 iv

= -

_on Fig. 9. 7 6 5 4 I. BO 70. 60 30' 20 /0 -50 2 0

'-0--- n- / 4 s ."/..r.,-. } , n =a

e/

/arc. t. 12./ .0 P4- .53 - 34. n = , /.../.pre. 1 _{R- 2.5- 2,, /0'} . n . 9./ 'Arc. t. /2.4.0 -..- n. 70 ,-/.... I-12.2r R,,- le - / e f /00A' a 6 Propellor No. P542 D= 200 mm 0 2 -- 2.2.

Propeller No P543 D= 250mm Fig. 11. 15

Nam

waig a

am

minatem.

mini

mu

a

Amossi m

,m

₁

MSS

&hersTypo Dynconomolor

A II ./1.2 R,=4.0-4. 4 /0 '

Kempf Typo Dynamo/mole, ....Al.} n= 54 ',loc. I 42.0 = °C R, 33- 3.7

'

71=16.2 ,....- t. /Se *c R,..,. 65- 67 /0' o n=7* ',lora' A _If=/4.2 'vs.,. R,= 5.6.,-6./ /0 '

n= 6* 'Age. I-12.4 t'' P= 2.3- 2.o /0'

, n=//o .-,o.c. R,=4.3- 4.0 = S 4 "yore. R,= 2.o /0" 10/6. _{_.}

n

,..- 3.. n/.... I-12.o V R. 42 - 14 02 0.3 0 0.2 0.2 07 Ca Op J = _{D n} ao g 70 60 7 6 5 4 3 2 40 30 20 /0 0 0 . 50

A

2.7-

2.e-Propeller No P544 D = 300 mrn

&hers Type Dynennometon

a n = 8.2}1./2. oC° R,,= 43 - 46 /0 c

-o-

0- 6s -ft.7.J R,,= 3.3 - 3.7. /0f o n . 50 r/s..r. 1=12.4 *L."' R,,. 2.6- 2.7. 10" n = 3.4 r/3.c. 1.12.0°C R,,= is - 1.9 - 10' Fig. 12.

M1

mill

INN

_oreim

_a

WA

'MEE

I

'1E1

Kemp/ Type Dynamo'''.9ter

Er 0= 10.9 r/sec. I- /54 °C R,,= 62 - 6.7 n=96 nts.e. 1= /56°C R,,= 54 - 5.8 /0' 10 14",.. 100 /, 0 02 0.5 0. 07 06 Op 1.0 4, 7 6 5 4 3 2 70 60 50 40 30 20 /0 0 -

--

-I 0'

BO 00 40 I I"

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% 1 % \c'' 4 h OS 1

t

17 Pr-opener No P544 D=300'mm Propellor No P543 0=2,50mm = Propeller Na P,542 0-200mm Propeller Na P54/ 0=1,50mm 2 3 4 6 R;70-4-Fig 13.

type of propeller. An interesting feature of Figs. 6-8 is the tendency

for the minimum REYNOLDS number to alter with pitch ratio.

A propeller of this type with la low pitch ratio, such as P/D = 0.60, thus apparently requires to be run at a high REYNOLDS number in order to ensure that the characteristics should be independent of that number.

It is also evident from Fig. 7 that the aforementioned values obtained at the normal revolutions at the lower water temperature

do not conform to. the general pattern of the other results. This can possibly be said to confirm the contention that these results were influenced by external factors such as differences in the

condition of the apparatus.

Figs. 9-12 show the experimental results obtained with

Pro-pellers P541P544. As before, full lines have been drawn through the values obtained at the revolutions which would be normal for

20

A

.7

7

Propeller No. P467

-0- Without Turbulence DIMCI

l'AtIe.}. = Hanson/a/ Gr 11. 9.4 0 a

Il

111

41...-..

._wholileillik

_FL

im

IMIIME ill

Mi

M 111611110111

NM

ERNI

MI

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ME

Id

10K, 1001/. Vertical Grid

Without Turbulence ()ewe* Harisonta/ 'Vertical Grid t= /5/ t. 14.e 3.* r/sea 1 = l -R t= 5./ V 24 24 10' 04 - It" 10' " 02 03 a. 0 0 7 Os " n Fig. 14.

routine tests with propellers of corresponding dimensions. Cross curves were lifted from these figures and they are shown in Fig. 13,

where it will be seen that there is close agreement between the

results from the different sized propellers.

The results of the tests on Propeller P467 with different turbulence stimulating devices (see previous Section) are illustrated in Fig. 14. From an assessment of these results, it seems probable that these devices did in fact stimulate turbulence, particularly at the lower of the two speeds of rotation investigated. On the other hand, the

fact that the values of KT, KQ and no increase with increasing

It 2 1 BO 70 50 40 20 /0 0-id .0 0.s 60 30 3 0

3 2 u 0.s _ V .7= 17 Fig. 15,. 0 0.9 19 J-values at the higher revolutions was probably caused by the wake from the turbulence stimulators. Moreover, it is probable that this effect became more pronounced as the speed of advance increased5 i. e. as the value of J increased,

Appendix 1 Influence of Roughness

In the course of the open water experiments described above, some similar tests were carried out with Propeller P64 with the blades covered with sand. As mentioned in Section 4 above,

Alumdum grinding sand of various grain sizes was used for this Propeller No. P64 4 ---',...-). I 'I I I --''' 1 I 1 - ' ...::Y1., '0-...-

' \

'',... --.1"-...., I 11., A-1 . `a 1 1 II ' - ---. ",.. -N '''''--..,,,,,, --... I I --4, 1 1 1 . . 6--., '-..,.., Z \NN I 'N'.,.. V

\

.... ' ,, 1 I II N ' /..' //' /I,cLe' It(N.s.. I. \ '' \ 6\ , I , , '_iiNN'll 41q,\., , , , ... , , , ,,

,

1 1 . ..., .3.-_,c., ,.... kt,

,Smooh5 Sur face

Rough Surface ( Alunclum 320)

t=/.5.3

Rough Surface (Alcooduro ) tI` /4=rt-I. Ro 32 '10s Rough Surface (A/mordant 110 )

Rough Surface (Aluendum 60) /01(7. 4 100Kg 0 6. 07 0 8 0 03 80 2 % 70 dO 50 40 30 20 /0 02 0.

--0-10 KT

4

3

2

Smooth Surface

Face Rough (Aliondum /20)

0 0 Propeller No. P64 t= /53.1 5.. ft 2 'Vs.', I. /4. °C R,. 3.0 - 3.2 105 I- /4.8 eo z 70 60 50 40 30 20 /0

Size of sand grains in mm

II

Imat

,

masililinlingl

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1111-

.,

raill

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I

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A.

, , Alumdum 60 0.45 Alumdum 120 0.20 Alumdum 180 0.11 Alumdum 320 0.03

Back Rough Alcondum /20)

Both Side., Rough ( Alumduer /20)

O., 02 0* Os 06 07 0.6 0,

- _{0 r,}

Fig. 16.

purpose. This sand is rather sharp and pointed in character and it

is therefore not entirely suitable, but it was chosen mainly on

account of the fact that it is readily obtainable in different grades

of coarseness.

Four different grades of sand, as given in the following table,

were used in the tests.

=

/OK,

I00/7'a

Smooth Surface

o

o Face Rough ,4/conduto 320)1

9.2 Bock Rough ,4/0onclum 320) I

Both Si-dos Rough (A/umonon 320) j

70 60 40 20 /0 21 Propeller No. P64 02 03 04 0, 06 07 08 09 Jr _n Fig. IT

The above grain sizes are mean values obtained by measuring the greatest dimensions of some representative grains of each quality under a microscope.

The method of applying the sand to the propeller blades has been described in Section 4 above.

The results of the open water tests on Propeller P64, both with and without the sand coverings of different grain sizes, are given in Fig. 15. Figs. 16 and 17 show a comparison between the different results obtained with sand on the face, back and on both sides of

the propeller respectively. Alumdum 120 was used for the tests referred to in Fig. 16 and Alumdum 320 for those referred to in

Fig. 17. t. /6:3 '0 /Or 7" /4.0 V R,,- 2.9- 3.0 /Or /-= /42 °C t 4.8 °C P,, 3o- 3.2 /0' eo z % R,,= -I 0

I

0 3 0 30

It is evident from Figs. 15-17 that the grain size has a marked effect upon the results. It must, however, be pointed out that the roughness produced by the coarser sands, Alumdum 60 and 120, was rather excessive.

Appendix 2 Correlation with Plate Friction Resistance

In concluding these investigations, the experimental results have been analysed on the basis of LERBS' method, which involves the so called equivalent profile?) The latter is a particular blade section which is regarded as being representative of the whole propeller and the propeller characteristics, KT, KQ and 2) 0, are thus considered to apply also to this section.

In the case of a propeller with an optimum efficiency distribution, the efficiency is the same at all sections and any convenient section can be taken as the equivalent profile.

On the other hand, when the efficiency distribution is not optimum,

the position of the equivalent profile is governed by the CD/CL

distribution (drag-lift distribution). LERBS investigated this factor and found that the average position of the equivalent profile is at about 0.75 when the CD/CL distribution is variable.

Using the open water test results, drag and lift curves for the

equivalent profile can be plotted to a base of angle of attack. The

frictional resistance of this section is then calculated from the

minimum value of the drag: this in turn is converted to the

corresponding frictional resistance of a smooth plate, by correcting for the form resistance of the section. The latter correction is given by LERBS.

By comparing the friction values so obtained with, for example, the SCHOENRERR line for smooth plate friction in turbulent flow, it is possible to deduce whether full turbulence existed in the tests in

question.

Such a comparison has been made in Figs. 18 and 19. In these figures, the results refer to an equivalent section at 0.75

' so that ') On the E f fects of Scale and Roughness on Free Running Propellers by HERMANN

Propeller No. P544 D'= 300 mm Propeller No., P543 D = 250 ram

' Propeller No. P542 D = 200 mm c1/a3 Propeller No. P54/ D = /50 mm

,/5 5 v2+ (0.757ED n)2 REYNOLDS number R:, = .1_{0.75 =}12 V' d Frictional coefficient C e/2 /0.75 7cD dr v2

Where R1 = frictional force,

10.75D = chord length at 1175 TD1

r = radius of blade element

(Note. There is a small difference between R... and the A, previously

used.)

Fig. 18 shows, the results obtained from the similar propellers P 541

P 544. The analysis of these results indicates that they are all

affected by laminar flow, even at the highest REYNOLDS number

tested (1? 105). GAwN1) has made an analogous analysis of

23

9 Effect of Pitch and Blade Width on Propeller Performance by R. W.. L.. GAW/4, Trans. I. N. A., Vol. 95, 1953.

-9 '`'kf

\

0 ₇ 2.Sch

-4-cnher, I 1-.rec I _ _ II 4 2 5 G 7 8, 9 A26 R= /;75 11,v (075 710n) 2 Fig. fs. /0 3 +

-= 7

o {./iihout Turbulence DevteqPrqpeller No. P 467 0- Ver/leo/ Grief a Smooth Propeller No. P 64 Rough (Alcune/um 320) C, 15 #'0 5 laS 10,73_ II 4/2 (0.75 770/7)2 V Fig. 19.

the test results from a TROOST series (propellers with aerofoil sections).

The agreement between the frictional coefficients calculated from the TROOST series and the present propellers P 541P 544 is rather good. On the other hand, the GAWN analysis of some other propeller series (with circular back sections) shows a different tendency. The

differences can 'certainly be explained by the different types of sections used.

Referring to Section 5, it is remarkable that fully turbulent flow

does not occur according to LERBS' method of analysis above

the minimum values of REYNOLDS number for no scale effect on no

(See Fig. 13).

The conclusion that these minimum values are reliable,. i. e. the values for no at constant J are constant also at higher values of

Rn, is perhaps precipitate. It may also be that mixed laminar-tur-bulent flow has a very small influence upon the scale effect above these minimum values or that LERBS' method does not give a reliable indication of the occurrence of laminar flow. Further investigations up to higher values of REYNOLDS number may give information about these questions.

5 6 7 /0' - ] --...m. \ IIP"

\

_\

2Schoenherr Curve \_°,,, N 1, 0- '--,-d 1 _ 1 'I 1 1 1 I 0 4 9

f

Coeff/c/ent 0.6 as 0. 4. 0 2 0.i Propeller- Na P64

0

Stnea//7 Surface

Rough Surface (A/umdum .320)

-- -0-- - Rough Surface (A/ulna/urn /80) Drog Coolrclent

25 "C. C>"----__a_,.. ..-..._ -13.. ---- a _.-IS, _ . ..., .. .. .."" . 13' 0 -2 2 Ang/ed A//ack Fig. 20.

The dotted mean curve in Fig. 18 has also been plotted for

comparison in Fig. 19. Some values referring to Propellers P467 and P64, taken from Figs. 14 and 15, are also shown.

LERBS assumed in the aforementioned paper that the lift coefficient

of a propeller is independent of the surface roughness within reason-able limits. The method for correcting for surface roughness, which is given in LERBS' paper, is based on this assumption.

Some lift and drag curves have been plotted in Fig. 20. The values were based on the results of tests with Propeller P64 with different sand coverings and were calculated from the values given in Fig. 15. The results shown in Fig. 20 verify LERBS' assumption, but the proviso roughness within reasonable limits is evidently necessary.

0 024/ 0.020 0 0/6 0,2 a aoe 0004 -3 I '

According to the latter diagram, the lift coefficient is not affected by a sand covering of Alumdum 320 (see p. 20) but is affected by

Alumdum 180.

Table I

Mean value of the pitch.

Max. value of the pitch.

Propeller Model No. Unit P36 P38 P40 P541 P542 P543 P544 P467 P64 D mm 250.0 250.0 250.0 150.0 200.0 250.0 300.0 252.0 257.3 P mm 150.0') 250.0') 350.01) 135.0 180.0 225.0 270.0 216.72) 197.82) P 0.60 1.00 1.40 0.90 0.86 0.77 D Number of blades 4 3 4 4 Ad % 45 41 40 47 A, t D of io 5.0 5.0 4.5 4.3 Rake degrees 12.5 0 15.0 9.2

Pitch . Variable Constant Variable

2)

1

. .. . .

. . ..,... . ..