On the principle of the substitute propeller

November l95

l3.9l

IPijçipke

af

jte PopeU

(i) Total Propulsive EfficIency _e

PHP P

Ve

(a) EhP

ïi-t) x

Tx

x lt

X _eh

p _p

p

lw

= eb efficiency of the "behind" Propeller

p

in the inhomogenous wake flow of mean velocity V V5 (i-") when absorbing a power P at n revolutions per second

(torque Q).

e efficiency of this propeller in

homo-p, P

geneous flow of transport velocity Ve when producing the same thrust T at the

same n, but at a sliahtly different

torque Q. It therefore absorbs a sliqhtiy different power P'. The ratio

is named relative rotative

Q P

eff!ciency" and is mostly somewhat greater than one for good single

screw hull forms.

Xe

xe

P p l-w p h r

13-791

On the Principle of the

Substitute Propeller November 1955

(c) et

El-IP RV e x e- e l-t

P

p X

_er

1w

_er

It is postulated that the propeller at its normal place in the wake behind the hull ('normau' propeller N.P.) is an A-propeller, that is a propeller of giver. (maximum) diameter D,

operating to produce a thrust T at a number of revolutions = n, such that its open water efficiency e at speed Ve V5

(i-s')

is optimum. The Apropel1er has a definite characteristic in the Wageningen B-Series diagrams. Ali A-propellers of equal disc-area ratio are located on a line of constant K.Q C,, irrespective of their J'value.

A tentative description of a Substitute Propeller (S.P. ) would be a propeller operating in homogeneous flow far behind the hull, producing a thrust T equal to the ship resistance R at a speed of

advance equal to the ship speed V5

(to which R

is correlated), at the same number of revolutions n whIch !s optimum for the N,P, This is a propeller working at a given velue of B = C, n

R°5

Vs

A large number of propellers of different de3cription as to dia-meter, pitch ratio, and propeller efficiency will fulfill this requirement.

Our first assumption is that among all these propellers there

l3.'9l

the Principle of the

Substitute propeller -3- November 1955

propulsive efficiency e' RV5. ThIs particular SP will then absorb the sane P as the NP. in open water Depending on its

actual dace in the B-dia m, it will have a

definite

value of

and we o3erve that in geíerai its dianeter D' will Vs

have a value different from D, and that its K'Q will be different from K0 of the since for same Q' and n, D is not equal to D.

O.ir second

ssuription is that in certain cases the S.P. selected

under the first assumption will be1on to the family of A-propellers as discussed under (2), which implies that K' C1. Since

KQ Q' _{= C P' in such case the torque coefficient}

pn2D

D

of the S.P. will be equal to K of the N.P, Since

2 2 Q

pn D

by definition i:' n and under our first assuntion P P' the diameter cf the P. will he equal

to

D and its trque

equal to

Q'. This is the case

of the "Afamily S,P." or A-SP,

Therefore the Â-S.P, is defined as the open water propeller operating far behind the hull n

undist.bed flow

at a speed cf advance V and a number of revolutions n. absorbing the same por

13- 791

the rincipJ.e of

tha

Substitute Propeller -.4- tcvember 1955

P' as the open water N.P, and havina tt'e same dIameter D. It

produces a tDrust T' equal to the ship's resistance R at ship speed

VS,

It belongs to

the KQ

C1 family of A-propellers.

(7) In the particular case that the A-S,P. :"uld be representative for a certain combination cf hull form and A-propeller, its open-water efficiency e

_S

ir the B ciaqram of the B-Series,

sp

P u

in accordance ;ith assumption (4), will be equal to the nominal propulsion efficiency e' of this combination The total propulsive efficiency et is then found by multiplying ep

evt

by er (Eq. c, sub, i). For er the value 1,02 of the Series 60 has

been assumed in the paper,

Denotinq l02

e1, we have e'p = et, and values of e'p as a simple function of J' are

nD

given by Eq. 32 - 34 of the paper. No previous estimate of w and

t

is required and the use cf the B-series charts

becomes

redundant

for the case of the A-S,P,

For other combinations cf hull form and A-propeller,

e' of the ¡,-SP. will be unequal to their particular value of et

and a S.P of dicrr.eter D' different from D, and therefore not be-longing to the A-propeller family, vi11 be representative for these combinations.

13 791

On the Principle of the

Substitute PrDpeller -5-

Noveer 1955

It is demonstrated in the paper fro.n analysis of Series 60 that the A-S.?. is representative for very good corbinat1ons of present-day hull forms and A-propellers. Therefore the A-S.P. can perfor!r as a good yardstick for propulsive efficiency and for the purpose of estiratng e. In pre1ininay desien. If it is

found that e < e'

the propulsive efficiency in sich case will be inferior to the !standard!1 value. In the opposite case it will

be superior to the "standard' vsìue. However, it should be realized that the final answer as to quality is found in the lowest possible value of PHP EH and that a high value of et may be associated

et

with a relatively

high

value of EHP.

When charts of propellers different from the B-Series are used,

e' for the A-S,P. can be found by drawing a curve of K

PS u

R and defining the point of 'iighest open water efficiency pV52 t

e' on this curve We then make use of e 1q02 e'r. to serve as

Sp p

a yardstick for or for estImating purposes of P P. For the e'

p

definition of the optimum number of revolutions In this particular chart (since the value of as found only applies to optimum n).

13

,791

i

the Principle of the

Substitute Propeller

November

1955

we have to establish the ':alue of KQ at the point of maximum efficiency on the K,curve. From a ____

= 5O P

, n can

pn2 D5 jpn3 t

be solved.

(io) In accordance with Eq (c) sub. (1), l'=t

ec

1-wÇ

In (7)it

is stated that for the

case

of the ASP

its e

C.t'

For

this case 1-t _e'Sp. Since and e, can be expressed as functions

lw

of the advance-coefficients J and J making use of Eq. (29-31) of the paper, and since J

V5(1w)

J'(1w), we can express t

nD

as a simple function of J' and w (See Eq. 39 and 40 cf the paper. ) The value of t thus found as a function of w, n, D, and V applies

strictly to the case of the A-S.P., but cari be used conveniently as a yardstick-value for t as found in the nodel basin test of a given design