Propeller profiles

(1)

DEPARTMEIVT OF IVA VAL ARCHITECTURE

OF GEIVOA

UIVIVERSITY, ITALY

Propellers

Profiles

BY

Prof. Ing. ALELO

DL BELLA

EDITION IN ITALIAN, BYBRIANO, GENOA 1947

EDITION IN ENGLISH.

BY PUBBLICAZIONI SCIENTIFICHE D'INGEGNERIA GENOA 1962

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(i)

PROPELLERS PROFILFS

Nowadays

the projected. area of the propeller, that is the starting point for designing a propeller , is

found

in _{rather longsorne way, viz,} _{a profile of the} pro-jected area of the required shape is designed, and. then ,

using a planiineter, and. by trial and.

_{error, same}

is

altered.

till

it encompasses the requested area.

This paper is presenting a method by

_{which, for}

a given shape of the

blade

_{to be used, for the} _number _of blades, and. for the projected area ratio, it

is

_possible

to quickly design the outline, _{mathematically fairecì} _{up ,}

and

according to the requested. data.

A) In a short paper presented. to the 1941 Meeting at Rome Ship Model Basin, we have shown that, _{if we indicate by} R _{the radius of the propeller, and. by}

k,

a, m, n,four

numbers, the equation

y/R

-

k (-a

+

)m

(i

with the conditions

o

<

n

<1

(2)

_i__

m-an

_<1

2

mn

represents the profiles of the projected areas

of a pro

peller having its

_{maximum breadth}

_{somewhere between R/2} and. R

X \fl

ru ZL

(3)

3

- The first 27 profiles may be used. for merchant ships and. not for warships, since the latter require propellers hay

ing high projected area ratio.

- The types 1, 15, 28, cannot be used. _{neither for}

merchant, nor for warships, because, having a large part

of their area near the origin, they would require _too long hubs, unless they were not retouched just near the

hub.

- The types _{14, 27, 29,} _{..., owing to their limited area} near the origin, have sections of attachment too short, and. therefore they cannot be used for lack of solidity. However they can well be coupled to other types of pro-files: for instance, designing nr.43 as a leading edge, and nr.69 as a trailing edge, a well known blade _shape is obtained (fig.4).

- As ordinary propeller profiles for warships, the most suited are nrs. 43, 44, 45, and. since there is no reason why same should not be used. for merchant _ships, it can be said. that they meet all practical needs.

B) Nr. k contained in the (i) is used to increase _{the va-.}

lue of the ordinate y and. therefore to increase the

area of the profile according to a linear law, without shifting the maximum or flexus point of same profils.For instance, if we refer to profile nr.75, having ( table

Q1) m = 1,4

and n = 0,8 , with the resulting equa-tion:

y/a = k

1x1,4

(1

1)0,8

R1

by giving to k the values 0,4 , 1, 2, 3, the four d. signed profiles are obtained.

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- r _{the radius of the hub,}

-w

thearea oaco,

-Q

thearea oabco,

- a

the angle of the leading edge of the _blade,

- y the number of blades.

It is usu_

ly called projected a-rea (Ap) of the propel

1er the area Q - W mili

tiplied. by the number of blades; in Italy is called _t the ratio

of the area Ap to the

crown of radiuses R and

r:

Ap

v(Q_w)

()

(i2) itR2[1_()2J

In case there is no hub,

f becomes:

vQ

=

which, compared with the (4), gives

r 21

"w

[i

- ()

It is now easy to show that practically

(6)

cp

=

r

In fact, usually is _{= 0,14} ₄ _0,20;

name ly, as an average, _{= 0,17 ;} _{so, the (5') gives:}

(5,)

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rea is carried out as follows:

ist Case.

If V _{is the number of blades, thus the area} _of

the blade, without the hub, for the

₍₅₎

and. (6) is:

7t R2

V

and that of the profile is:

A=f=

Chosen, using the tables, the prefered _outline,

viz, chosen m and

n , we have determined I , and for the (3) and (8), we have

ltft

= 2V I

which, substituted with m and n in the (1), gives the equation by which it is possible to draw the profile.

In order to make drawing easier, the table _Q2 ves the solution of the equation

Y

for values of = 0,1 to

0,9

and for values of X = 0,2 to 2

For instance, given = 0,4 and. X = 0,9,

the table gives Y

= 0,438

(6)

A =k I

R

A=k

IR2

it follows: A

pA

p k e U e

IR2

'VI

e

e e

A

k i

I

IR

i+p

VI

u u

By substituting in the (i) these values of

k and the corresponding values of m and n , the e-quations of the two profiles are obtained.

F) NUMERICAL EXAMPLIS

ist Case. Design the projected outline of a symmetrical propeller blade, having (fig.2):

V=

3 0,4

We choose type 38 having

m=i,5

n=0,4

1=0,223

k

mai

From

₍₉₎

we have:

k=

2 VI

7t _0,4

0,937

2x3x0,223 =

(7)

From (io) we have: f IL t it

xO,45

ke ₌

_{2 vi}

₌ _{2 x 4 z 0,265} = 0,665 e lt it

xO,45

k =

=1,51

u 2 V I 2 z 4 z 0,117 u

The equations of the two outlines are:

z Ye/R = 0,655 - (i _- _R = 1,51

(1)2

(i

x\0,7

R'

We therefore have: Flg. 3 11

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ing edge nr.69 having respectively

m =0,9

m =2,0

e u

n =0,5

n =0,7

e u I = 0,285 I = 0,117 e u k

=1,5

k

_=2,67

ema

umax

As p

= i 2 , using (ii) we have:

i i 2 it . 0,60

k=

= e

i+p

"I

2x2

_3x0,285

=1,2

e k i

it

i 't . 0,60 = 2,43

u

i+p

vi

2x2

3x0,117

u Ye/R = 1,2 (x/R)0'9 (1 - /R)0'5

y/R

= 2,43 (x/R)2 (i - x/R)°'7 LELDING EDGE x/R = 0,1 0,2 0,4 0,6 0,8 0,9 (x/R)°'9 = 0,126 _0,235 _0,438 _0,631 _0,818 0,909 (i - x/R) = 0,9 0,8 0,6 _0,4 0,2 0,1 (i - _{x/R)0'5= 0,949} _0,894 _0,775 _0,632 _0,447 _0,316 Ye/'R = 0,141 0,251 0,407 0,480 0,439 0,345

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N°m

n I k N° m n I k

N°m

n

I'

1 0,3 0,2 0,626 0,4 29 0,6 0,4 0,396 1,0 57 1,3

0,60,197

2,00 2 0,4 0,2 577 0,4 30 0,7 0,4 365 1,0 58 1,4

0,6

185 2,01

3 0,5

0,2 527 0,4 31 0,8 0,4 340 1,0 59 1,5

0,6

174 2,02

4 O6

0,2 491 0,4 32 0,9 0,4 317 1,0 EIJ 2,0

0,6

133 2,08 5 0,7 0,2 459 0,4 33 1,0 0,4 297 1,0 61 0,8 0,7 0,255 2,20

6 0,8

0,2 428 0,4 34 1,1 0,4 279 1,0 62 0,9 0,7 235 2,26 7 0,9 0,2 402 0,4 35 1,2 0,4 263 1,0 63 1,0 0,7 217 2,32 8 1,0 0,2 379 0,4 36 1,3 0,4 249 1,0 64 1,1 0,7 202 2,36 9 1,1 0,2 359 0,4 37 1,4 0,4 235 1,0 65 1,2 0,7 189 2,41 10 1,2 0,2 340 0,4 38 1,5 0,4 223 1,0 66 1,3 0,7 177 2,45 11 1,3 0,2 323 0,4 39 2,0 0,4 176 1,0 67 1,4 0,7 165 2,48 12 1,4 0,2 307 0,4 40 0,6 0,5 0,359 1,5 68 1,5 0,7 155 2,51 13 1,5 0,2 293 0,4 41 0,7 0,5 330 1,5 69 2,0 0,7 117 2,67 14 2,0 0,2 236 0,4 42 0,8 0,5 306 1,5 70 0,9 0,8 0,215 2,

15 0,4

0,3 0,518

0,6

43 0,9

0,5 285 1,5 71 1,0 0,8 198 2,69

16 0,5

093 475 0,6 44 1,0 0,5 265 1,5 72 1,1 0,8 183 2,78 17

0,6

0,3 440 0,6 45 1,1 0,5 249 1,5 73 1,2 0,8 171 2,85 18 0,7 0,3 409

0,6

46 1,2 0,5 233 1,5 74 1,3 0,8 159 2,93 19 0,8 0,3 381

0,6

47 193 0,5 220 1,5 75 1,4 0,8 149 3,00 20 0,9 0,3 357 0,6 48 1,4 0,5 208 1,5 76 1,5 0,8 140 3,06 21 1,0 0,3 335

0,6

49 1,5 0,5 197 1,5 77 2,0 0,8 104 3,32 22 1,1 0,3 316 0,6 50 2,0 0,5 153 1,5 78 1,0 0,9 0,181 3,00 23 1,1 0,3 298 0,6 51 0,7 0,6 0,302 1, 79 1,1 0,9 167 3,13 24 1,3 0,3 283 0,6 52 0,8 0,6 279 1,86 1,2 0,9 155 3,25 25 1,4 0,3 269

0,6

53 0,9

0,6

259 1,92 81 1,3 0,9 144 3,35 26 1,5 0,3 255 0,6 54 1,0

0,6

240 1,95 82 1,4 0,9 135 3,45 27 2,0 0,3 205 0,6 55 1,1 0,6 225 1,97 83 1,5 0,9 127 3,55

28 0,5

0,4 0,430 1,0 56 1,2 0,6 210 1,99 84 2,0 0,9 0,934 4,00 E,X

TABLE

Q2 E, 0,1 0,2 0,4 0,6 0,8 0,9 E, _0,1 0,2 0,4 0,6 0,8 0,9

X - 0,2

0,631

0,725 0,833 0,903 0,9560,979 X,i,o

100 200 oo o

ao

9oo 0,3 501 617 7&) 858 935 969 1,1 079 170 365 570 782 891 0,4 398 525 693 815 915 959 1,2 063 145 333 542 765 881 095 316 447 632 775 894 949 1,3 CEO 123 304 515 748 872

0,6

251 381 577 736 875 939

1,4040'

105 277 489 732 863 097 200 324 527 699 855 929 1,5 032 089 253 465 716 854 0,8 158 276

4)

665 836 919 2,0 010 040 1ff) 3ff) 640 810 0,9 126 235 438 631 818 909

TABLE Q1

15

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4 0,4 k 7

0,4 - k

0,4 0,4 k 5 6 8 9

(11)

0,4 k 13 0,4 k 16 0,6 - 0,4 k 11 0,4 k 14 0,4 k 17 0,6 - 0,4 e k 2 12 0,4 k 15 0,6 - 0,4 k 18

0,6 - 0,4

k

(12)

0,6 - 0,4

k 22

0,6 - 0,4 - k

25

0,6 0,4

-0,6 - 0,4

k 23

0,6

0,4 k 24

0,6 - 0,4 - k

27

0,6-0,4

k

(13)

28

I - 0,4

k 31 29

I - 0,4

k 32

I - 0,4

k 35

I - 0,4

k 4 30 32 36

i - 0,4

k - 0,4 k

I - 0,4

k

(14)

I - 0,4

k

1,5 - i - 0,4

k 43 41

1,5 - I - 0,4

k 44 45

(15)

46 1,5 - 0,4 k 49 1,5 - 0,4 s k 52 53 1,5 - 0,4 k 1,5 - 0,4 k 51

1,9 - I - 0,4

k 4? 48

1,8 - I - 0,4 k

1,5 - 0,4 k

(16)

1,9 - I - 0,4

k

2 - I - 0,4 - k

61

1,9-I-0,4-k

2-1-0,4-k

2 - I - 0,4

k

2,1 - 1,5 - 0,4

k 58 59 2,3-1,5-1.4D,4 s k 2,3-1,5-1.-0,4

(17)

2,3..iDS1-O,4 . k

2,-2-1-0,4 . k

2,41,510,4 - k

8 2,7.21..0,4 s k 2,8-2-1-0,4 k 54 66 67 69 2,7-2,1-1,5-1-0,4 k 2,5.1,5..t.O,4 . k 2,5-1,5.1-0,4 - k 71 72

(18)

2,8-2-1-0,4 . k 76 3,1-2-10,4 s k 3,2-2-1.0,4 77 78 3-2,6-1-1,04 - k 3,4.2, 6-1..0,4 3-2-1_0,4 . k 79 81

(19)

3,4 - 2 - I - 0,4

k 83

84