Screw propeller dynamic forces and moments

(1)

Lab.

y.

Scheepsbouwkuniie

A1IC.

1982

H1LF

Technische Hogeschool

Deift

Screw-propeller dynamic forces and moments

A. V u e i n i c - Superina)

Introduction

It can be stated that during the last years the apDlication of theoretic approaches onto propeller design is becoming very frequent and, at the sa-me tisa-me, theories and sa-methods are found in order to analyse the action of manufactured propellers.

Analysis are not just related to the optimization of propulsion efficisncies, but they are applied to indicate and compute parameters of impor

-tance for the propulsion system and the hull construction.

The method of computing the propeller dynamic forces can be recognized as quasi-stationary or instationary.

In the work, here presented, two quasi-stationary methods based on model series open-water test results were applied, one worked out by the author (i), and the other by Vedeler, (2)

The third used quasi-stationary method was also proposed by Vedeler, (3),on basis cl' Burrills theoretic-empiric approach.

In this research the computer program of Vedeler-Burril method worked out by the Brodaraki Institute in Zagreb was used.

Sparenberg, (6) , applied in 196o. the tbreedìmensional integral equation

of motion to the propeller action in a homogeneous flow to get the uflknown propeller load from the known velocity distribution along the blade surface.

Later on Shiori and Tsakonas,

₍₇₎

,Hanaoka, (6), and Verbrugh, (9), widened

his work by taking into account the inhomogeneity of the propeller inflow. Further development of those methods by the introductions of rotative supplements, of viscosity and cavitation phenomena will give surely better comprehension of the propeller action and more suitable and. practical re-sul t s.

As this work is concerned, here was applied the Sparenberg's theory progra-med at the Ietherlands Ship Model Basin at Wagerinigen for subcavitating propellers with blades of zero rake working in instationary wake flow.

The worked out comparison of quasi-stationary and instationary method compu-ted results can be used. as a qualitative indication of their reliability.

Ship and. propellers characteristics

The work ol' a propeller family designed to act in the non-homogeneous wake flow of a single screwed tanker is analysed.

(2)

The tanker is a ship of 225

000

tDW, which at trials reaches a speed of

V=

16,5

kn when tbe1engine is delivering 4o

000

hp at shaft number of

revo-lutions n = 90 znin

The ship length is L= 327.64 ni and she has a block coefficient of

= 0.841.

She is the prototype of slow running ships having a Froue s

number of F = 0.150.

At the begiflning two propellers were analysed one nu.mbered. il, a

W.B.5.6o

serie propeller, while the other one, No. 0209, was designed by lifting line method for wake-adapted. propellers, fig. i and 2. Here are also ana-lysed. two series of optiniwn wake-adapted propellers designed. for the sanie tanker: one vas designed by variation of the number of blades and. the other by variation of the shaft number of revolutions.

The tanker wake field

This research program comprehends the variations of blade and propeller dynamic forces and moments caused by the inhomogeneity of the inflow into the suboavitating propellers.

The inliomogeneity is related to the model nominal wake measured fie].d.,figs.

3, 4 and

5.

The applied, mean disk wake resulted from radial and circumferential nican

wake computation, fig. 6 and

_7,

with a value of Wap =

_0.4415

for Da.8.76o in.

Mean disk circumferential wake variations applied. in the openwater results methods are presented. on fig. 7. Harmonic analysis was used to approxime.te the measured nominal disk wake field for the lifting line and lifting

surface methods.

Intake angles pulsations

The nominal wake field analysis makes clear that a non-homogeneous field is present at a given mean axial water velocity at the propeller disk.

Due to its turning around the axis, the propeller sensation of the wake

field, related to the period of 2Tt , is therefore periodically unsteady.

An interesting indicative analysis can be worked off in order to find out which are the oscillations of the hyd.rodynamic pitch angle of a straight lifting line placed. at different angular positions in such a wake flow. The oscillations can be calculated for the mean values in relations to the entire lifting line length and/or for the values to each radius, and. ac-cording to the two-dimensional approach for axial perturbations only, or, for the summed up axial and. tangential perturhtLnu.

dimensionally intake angle variations can be decomposed into

Schifistechnik Bd. 27 - 1980 170

(3)

mark "at" relates to zial + tangential influence,

"a" relates to axial influence,

"t" relates to tangential influence.

Figs. 8 and. 9 relate to the presentation of local intake velocity diagrams for nonhomogeneous flow at propeller disks of single and. side-screwed. ships. The mean bydrodynamic pitch angle of the lifting line can be calculated, at the mean radius r, where the mean axial wake velocity is working at

tari

v/2T nr

while the variations of this angle are for axial perturbations only:

tari»

=(v /vHcnj3

ar a a

and. for the summed up axial-tangential perturbations:

tan

v/( 22Tnr

_{+ Vt)}

L(2n r)I2Tnr+ V1)l.(V/v)tQn

_pQ

(6)

Such analysis was worked. out for the tanker wake flow at different advance coefficients J.

The basic values for the calculation of mean axial intake angle variations are presented on table 5-l.

Table 5-1 Basic data for intake angle pulsation calculation

J

0.264 _0.366 0.440 _0.653 Va/V 0.5585 0.5585 0.5585 0.5585 a

(ms)

3.195 4.746 6.146 8.498

V (ms)

5.721 8.498 1i.oc4 15.216 r (m) 3.26° 3.26e 3.26° 3.26o 2Jf n(s ₎ _8.7588 _9.4243 _lo.1o34 _9.4228 Pa (d.gs.) 6.3845 8.7810 lo.5697 15.4606

(4)

The intake angle variations are: -33 a 'a a and/or at at$

-(8)

The values y and v were given on fig.

_7.

The calculation results are given on fig. 10.

In order to get an insight into the influence of the tangential mean

volo-city inclusion into calculations an analysis of the mean

W.S WOl'

-ked. out for the tanker and a container ship at relative propeller coe-fficients of advance. The results are given on fig. li.

Influence of tanentja1 wake velocitiws inclusion into calculations

Blade and. propeller dynamical forces and moments due to wake inhomogeneity

were calculated, according to coordinate systems presented on figs. 12 and.

13 by unsteady lifting surface theory integration method for propeller W.B.

5.60 at J = 0.366 to harmonic j-t = 6, what is equal to ji- = Z + 1.

Examples cf resulting blade force and moment circumferential variations

are given on figs. 14 and 15, while figs. 16 and. 17 relate to propeller

values.

From these figures, where the continued line relates to axial velocity variations only, while the dash line includes tangential velocity varia

-tions it can be seen that the influence of the tangential wake velocity on forces and moments data appears to be quite small.

The small resulting differences between the two cases computed by lifting surface theoretical approach seem much more reliable than those quite high ones computed by quasi-steady methods, both open water data and. lifting line approaches, see figs. 18 and 19. The better adequacy of unsteady lif-ting surface method. results, with and without tangential velocity inclu-sion, in relation to quasi-steady results is supported. by the analysis of intake velocity angle pulsations presented. in part 4, fig. 11.

6.

Coniparison of Quasi-stationary and instationary theories

re suits

6.1. Blades and propellers additional steady load coefficients

One particular difference between the results computed by the quasi-statio-nary method and. those gotten by the instatioquasi-statio-nary one is in the fact that the used instationary method is giving additional steady loads due to wake

(7)

(5)

-inhoinogeneity, which do not possibly come out from quasi-stationary approa-ches,

These additional the order:

for blade loads:

thru.s t turning moment tangential force radial force bending moment torsional moment

for propeller loads:

thist

o turning moment

horizontal transverse force

loads were evaluated, for the .B. 5.60 propeller to be of

¿O.03 ET ¿O.O3 EQ ¿O.lO EF AC.40 BF F y1 vertical transverse force F zi horizontal transversa moment Q yl vertical transverse moment 0.C5 _BQ

L,1Q

BQ, O.4O T

L0.4C

Q

¿1.9O

F

LO.90

F z2ï1.40 Q y ¿ìO.6O z

Note:

The

-value means the amplitude between the relative mam'um and.

minimum value

The foregoing proportionalities remained constant when the mean disk advance coefficient was variated, which means that the additional stea&y parts were becoming bigger, a.s were the amplitudes of the oscillating d,ynamic forces and. moments, with the increasing of the mean disk advance coefficient. A plausible interpretation of the presence of these additional steady parts

can 'be searched into the possibility that the instationary method is by itself correcting the volumetric computed input value of the mean disk wake, by taking into account the local wake values at each radius and. at each angle of the propeller disk.

As it is presented all the additional values were positive in this case. Br o BQ o BF to EF ro to BQ T

(6)

Schiffstechnik Bd. 27 - 1980 174

-6.2 Blades and. propellers oscillating load, coefficients

Values of oscillating blade thruste an moments calculated by unsteady

lif-ting surface theory to )-' = 6 for propcller To.l have been plotted. on

figs. 18 and. 19 in order to show the differences in loada achieved by the worked out methods.

It can be seen that the circumferential function of these loada, a1thou rorked. out by axial-tangential wake inclusion is closer to the open-water data method which is not including tangential wake velocity and it is closer just at the transversal angle positions where the tangential wake velocity is not zero.

The lowering of the curves picks gotten by lifting surface calculations

pro-ves that a surface senses at each moment a. mean wake disturbance which is

always lower than the iaaximum one occurring at a strai&at or curved lifting line, because a surface senses the mean radial and circumferential wake while a line senses just the mean radial wake related. to the position angle. Propeller oscillating forces and. moments coefficients are given on figs. 2oa, 2ob and. 2oc for the characteristica]. angular region 2l/Z for propeller

No. 11 at J =

0e366.

Propeller thrust and. torque coefficients are worked.

out without the steady contribution due to inhomogeneity as they are not present in the results of quasi-steady methods. The results relates to

values tofu

6.

Further on it was found. that optimum propellers wor.dng at lower load coefficients have in reality bigger variations of d.ynanrLc coefficients

cau-sed. by wake in.homogeneity while hia loaded propellers do work at smaller

amplitudes of d.ynat.c force and moment coefficients variations. This oocu-renco is connected with the fact that load coefficients are decreasing with the increasing of advance velocity coefficients.

7.

Influence of blade frequency variation on results

The instationary surface method was used. to analyse the influence of blade freqiency variation. This method was applied to three blade numbers:

z = 4,5 and 6 running at 90 mm'4; then to z = 5 with four shaft speeds:

u = 8o, 9o, loo and 110 min'4

It resulted in the blade frequency region, (zn), from 380 to

550 min'

All the dynamically changing values are nond.imensionally given on tables and diagrams in relation to the relative steady values. Only for the pro-peller transverse values the author decided to propose the proportions to "QJD = quotient of torque by diameter" for forces and. the proportions to

"TD product of thrust and diameter" for moments.

This way of coefficients computation is resulting from the fact that

transverse forces are mainly depending upon propeller turning moment while transverse moments depend upon propeller thrust.

Coefficients of additional blade and. propeller steady loads are given on figs. 21 and. 22.

(7)

Coefficients of the maximal oscillations or amplitudes for the unstead.y

loads were integrated to the wake harmonic _lu = z + i and. are presented on

figs. 23, 24 and 25 for blades and. on figs. 26, 27 and 28 for propellers.

7.1

Some considerations

It can be generally stated that the increasing of blade frequency would decrease dynamic forces and moments arriplitudes coefficients.

7,1.1. Additional steady coefficients. First it can be stated that blades

and propellers have the saine values of additional axial loads coefficients, fig.21. Resulting propeller steady transverse force and. moment coefficients are the same in the horizontal and in the vertical direction, fig.22.

7.1.2. Unsteady coefficients. Amplitudes of blade unsteady force and

mo-ment oscillations are bigger than those of the propeller.

It can be generally stated that the increasing of blade frequency caused by the incrsasec. shaft speed at constant number of blades will always cau-se the decreacau-se of dynamical loads anrplitud.e for the blades and for the propeller.

This cannot be said wnen the blade frequency is increasing 'because of the increasing of the number of blades when a single - screwed ship is concer-ned. Having such a ship a mirrorwise wake field, the frequency of her wake field. is even. This fact makes the functions of the load coefficients to be periodical with maximum and. uiinimu.m values: the maximum axial and the minimum transverse loads values are reached with even blades numbers, while the inverse case takes place with uneven blades numbers. Prom these calcu-lations it cari be stated that by blade frequency increasing the amplitudes, governed by number of blades variation follow the decreasing limiting

functions of maximum and miuimu.m values.

8. Conclusions

- Circumferential and. tangential inhomogeneity of the wake field is increa-sing the mean disk intake velocity angle at advance coefficìent increaincrea-sing. - The used. quasi-stationary methods, by open-water ddta and by lifting line

theory, give bigger differences between the blade axial loads coefficients computed without and those computed with the inclusion of tangen -tial wake velocities than the instationary lifting surface method. - The instationary lifting surface method gives additional axial steady

loads which are not resulting from quasi - stationary methods.

This fact is maybe showing that the mean disk axial wake computed by volumetric method was not the riit mean value.

- Quasi-stationary and instationary method show that the increasing of the advance coefficient is increasing the additional steady and the unsteady

(8)

loads coefficients due to wake inhomogeneity.

It can be concluded that optimum propellers, at lower load coefficients, have in practice bigger dynamic oscillations caused by wake inhomogeneity than the high loaded propellers.

- Increasing of biais frequency means decreasing of dynamic load. coeffi-cients when it is caused by increasing of shaft speed.

The number of blactes are interfering with the frequency of the wake field. As alrea&y resulted from experiments, the even wake frequency at the cen-tral placed propeller disk makes this function periodical: maximum axial and. minimum transverse loads coefficients are reached. with even numbers of blades, and inverse. It can be concluded that the amplitudes of the periodic function depending on number of blades follow the decreasing limiting functions of maximum and minimum values at increasing blade frequency.

Nomenclature

A amplitude at each harmonic

A , A1 amplitude at zero and first harmonic

AE/A expanded area ratio of blades

BQ, BQr

3F , BF r t BT C n D propeller diameter

, F propeller transverse forces

J advance coefficient (yap/nD)

j

y /nD

a a

J advance coefficients due to y and y

at a t

L ship s length at sea level

n shaft number of revolutions

P blade pitch

Q propeller turning moment

propeller transverse moments

R propeller radius

r radial coordinate

r propeller average lift radius

blade bending moment, blade torsional moment blade radial force, blade tangential force blade turting moment, blade thrust

hull block coefficient related to

(9)

-T propeller thrust

V, V, V

a r t V

V ,V

ar ri' ti' V

V ,V

ap _rp tp

local axial, radial and tangential wake velocities components

mean axial, radial and tangential wake velocities com-oonents at each radius

mean disc axial, radial and tangential wake veloci-ties components

Va y v mean spanwise axial, radial and. tangential wake

ve-locities components at each transversal angle of position V V

-v

aw a ap V

y

-v

arw ar ap V

ships speed

w wake coefficient z number cf blades x r/R

°a'

t' at additional intake velocity angles due to axial,

tan-gential and axial + tantan-gential wake disturbance mean disc hyd.rodynamical angle

mean spanwise hydrodynamical angle in axial unhomogeneous flow at each

mean spanwise hydrodinaniical angle in axial + tangential unhomogeneous flow at each

ideal hydrodynamical angle

mean hydrodynamical angle for side screw ships

ri propeller efficiency

angular coordinate on disc plane

W

shaft angular velocity

index before load signs means amplitude ina.ex on top of signs means poriodicity

ind.eks for steady transversal forces, wich occure at » = i

o _{indeks for additional steady axial forces, which}

(10)

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FLAU MODEL 'IO.O P/1 5 6/0dB o' p/S 9O''.L/,,l,,S o S - 1740 B/B - 4370 Po 4454 - 7440 Jo - ESSES A. -31 2015 .' A. - # 2 -01*1.11M/ 0. /.,LUSR ES .047 7.10 075/. ASAs - 00/9 AIA, -5,o.,4. - 2 IU.J PA,41/,oH .A50A5 PPA005JR .,Oo,.-ps/oh o IAOA. ip PIMMs* PBAlR)R P*r*.IM.d.4 0/01 O' E.0 0/14.01.. 7/Od 4411. No.**. .1 N. PRORTILER MODEL o 0203 , SI//p ....OA N. N. ₂ S,/. Also I.. 40 Schiffstechnik Bd. 27 - 1980 178

(11)

-- o lTr I 435 4O 22 5 cx,o/

e

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tc,ke,-;;:-=

I/I

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--(Foe 3600_ jg

/,

/ 1 ) d

r,bt0r,

of tgo'o/

Q ke - -t fe os .i ec r,,

t do

¡or D

9042 '-'im

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0 315

I

-\

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/

o2g --O7 o c9 o.95_._ -f .14 904-2 mm

22Y 0

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0-cJ,slih,uto of ,-od'o/ WQ4O

180 -180e ç/Jo

,f-he/ pcsrfo,,

=0 øt lied

bostor,

o.

r,9 4

0=0e cit liee/ bos,1c,p, ,t:., ₃ 1.0 05

/

I.-/ I.-/

/

1/ /1 /1 /

f

--I I C 45 l5 27f / ds t.-, b,?.-, -S,,i9/e -CPCL/Cd do2,

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31

2 70 90 o b 3G0 Ø

Co-3o

0. --0

Heq.c.irfr,,er,t

!c" D 3042mm

(12)

5ingle - 5creved ton/c-er

5h/p

Ilean wake velocity at each

radius in tIle axial /angen/ia/

and radial direction

(13)

-9 C

0,8

-0

5ing(e - 5crewed tanker

Qr 8760m

Circurnfere ria/ pu/saior

of nominal wa/ce

in Ihe

axial

1-angential and rod/al

d/rection

C 1800 11-t V

0 5585

Fig

7 70° 2 900 1800 2700

_360°

(14)

f

i

_{w r}

A1/ 'P,cJ 7?./

Cy'

Jn?Lae water ve(oc/jies due

f3 A/Oke

/)hOfrQ9,7/jy Ìor

/f)/C

w r

'7f/C) /

oÌ

infaJe

xiater ve1oc,'tis

'-

t-4ç

ìt1

.r

ed

Schiffstechnik Bd. 27 - 1980 182

-D

(30L iY3 _aw

8

inside

turning propellers

Outside

turning prope/Ìer5

(15)

00

0

9Q0 1800

liaDo

270°

PU/Sat/or)

of screw mear? intake

velocity angle clue to ox ial wake

0 8. 760 m

Fig IO

360°

Q

(16)

o -*3° 2° + 4° - 20 30 40 50

Influence o

/

//

_/7'

¡r

f80°

9QO

tan en fiai ve/o

270°

on intak-e angle

ity

Schiff stechnik Bd. 27 1980 184

-/80°

270°

tcynker

container

5h ip

Pu/at;on of .screw mean intake

velocity angle due to ax/a! and

a-iò1 - tange nt,ol wake var/at/on

360°

-

-37= 036G

37: 0,853

tanker

L7 876Dm

container 5r 6,68Gm

(17)

z

zf

Composition of blade load

t.

propel/er load

Q

8Qr

-y

F. 12

Coordinate

system and notations used

(18)

Woke on1;-;bj»,,, 7ô b/od %'O$t

7 7. a$c

(i'./J 5Se 6' harmcp,,)

Wøke

t0 Wade

or f.Q34

(7// ?

harmc,,v)

(19)

-/44.10

4O4

O)

hàÍiL4

90 \ to ,brofrei' . 03CC

(j/

4ope//9ro

Wa4re

7; òroft//r rorqt#t

ar

(

U la-6)

(20)

5a

-[8T7 _LBTJqD 0/ \ Vede/e 8T / . -øurr,/i t -/ I ₇ o e /i,,e) o sTcdy)

4.

o 7 +

/

0/

IO O . / t -i--, 0

i

G -J \0o Q

/

G 0/ Q

/

..

0,

/-+

\

-4 4 4-o.

//c

-f'o

arl

ZIO?

o/

o,4,esc' L'cr

1,-17/

- o'e 7jst

est d?,

35 .

Pe//,-A6

y. o.

-/l(WeC0)

Q,,

F,9 f8

.

G, SO" I I

-

-4'.fO , Vm I

-.

_I8a]

L

112 -'4 ø .-:

/

-,

(..

-i

4 13/

-

:

.

-1

.\

N

-'

--4-.

N ,,

-4

--=

TH

-- -i

'.7

OR 1' i

w.

I

-0

qtj /Q?Q Fk.c Tor

ct,,ri Q1

pd.sha/t

/.-om obe, _ap,o'

Pr-ape//e,- A4,.kí7-/.i3.6o)

7=a3

I 7ê..t n,e7od,

-2---'.

/

r

90 270

--F

/9 --

....-"

180

(21)

q2-ci

Q 01 o 2 'Z 001 - Q02 - Q O3

;

7T/z 21T/z

-

IT/z

/

\\

/

-/-

N

_/

1/

-Q2--

Author

- Vede/er

8urrí//

Sparenberg r19 2Q17

PROPEL LEP

/ VO. 217/z

Fig 2O7

Fi.2Qc

t'z/(TD)

Q / (TO)

rl'

/

----\

002 QQ! o 7T/z

- qui

- q02 Q03 o

- 0/

(22)

-003 0.02 - 0.01 o 0.03 0.02 0.0/ o t 300 Tw 7 87 2w

8Qo. io

a

- BQ

Coefficients of blade adthhona/

.

-400

n rrnin

J

Cae ffiients of propel/er and blade

additional steady thrust and turning

moments

harmonic O

I

I-500 800 Fig, 21 0.09- 0.08 -Fy1 Q/O -Q/L7 0,O7. 0.06- 005-Qzj

Qyf

004-- 002- 00 1- o TO TQ

(o)

o- - - -o--- e

Coefficients

of

propel/er steady

transverse force and moments

harmon,

/

Fig 22

steady bending moments harmonic O

- f(n)z=5

0.10 z

n90min1

5

-- f/z) n= SOm,n

[(n)

-- [(z)

500 300 400

znrmin -l]_

(23)

f 0.5 _{¿1 8T} 5T 0

15

BT f0

BT

0.5

flaximum amp Laudes of blade thrusJ

coefficients

(1,1/ // = z

I)

I

-f(n) z

5

--f(z), n=90min

BT 4 87_ o max, 87

8r

- -.

300 400

500

600 zn (m'n'J

1.0 0,5 ¿t 8Q Ba 0 1.5

to

80

05 A

Ilaximum ampLitudes of 6/ade

moment

coefficients

/ t////(=z il)

_f(n),z=5

--fiz),

n,

90 min L' &Q

+

80 oß

8Q min. 8Q

-maxj i

23 Fig 24

500

600

400

Zn (minJ

300

(24)

10 _0.5 _{¿ 8Qt} BOt 0

15 a 5

1'1o.imum arnpLde

of blade

beridincj moment coefficients

till /1 r

i)

s-ffn)Zr5

-- f(z),

nr90m,n1

¿8Qt ÇQt o 8 t max. 8Q min 8Q 300 400 500 600

Zr) (mir'J

F,. 25

Propel/er ¿/rust and sliaf f

torcjue amp/if ocies coeffìient1s a Z o 300 400 500 600

zr?[min 'J

i9. 26

012-

'b0

11.7

-0-

o.04

002-\

\

o

f(n),

zr 5 n-.90m,r1

I o

-

--[(z),

\

T'

Q .

\

-\

o

8Q t ôQt 1.0

(25)

DIG - o Fy

_a/o

A Fy

a/o

0.10

-/

0.0&

/

_/

/

_/

006-.-/

_/

V.

004-

002-o

Propel/er transverse forces amplitudes

coefficients

(ti/I

/J r

i)

fTh) zr5

--[(z) nr9Omip1

AFy

0Arz

Q/O I Q/O 0.02-o

Propeller transverse moments

amplitudes coefficients

(ti/I /

z# I)

_f(n), zr5

_--f(z),

r9O miri

Qz TQ TO

ay

-TO Qz 00G-TO 004

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Fig 27

Fig 28

900 /,iQQ

500

600

300

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500

600

Zn(mlri -z-n [miri J

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Literature

(i) Vuini6, A. "Theoretical Fundamental Researches on Dynamical

and. Propeller Loadings Caused. by Unsteady

Inflow", University of Rijeka,

_1975.

Ved.eler, B. "On Marine Propeller Forces in Calm Water and.

Waves and. the Strength of Propeller Shaft Systems in Single Screw Ships": Det Norake Ventas Report 68 - 12 - M, l96.

Burnil, L.C. "Calculation of Marine Propeller Performance

Characteristics": Trans.of the North East Coast Institution of Engineers and. Shipbuild.era, V31.

60, 1944.

Ritger, P.D. and. Breslin, J.P., " Theory o' the Quasysteady and.

Unsteady Thrust and. Torque of a Propeller in a

Ship Wake" : David Taylor Report

686, SIT,1958.

Tsakonas, S. and. Jacobs, W.R., "Theoretical Calculations of

Vibrato-ry Thrust and. Torque and. Comparisons with Bipe-ri. mental Measurements":

Stevens Institute of Technolo, Davidson

Labora-tory Report No.

827,

February

_1961.

Sparenberg, J.A. "Application of Lifting Surface Theory to Ship

Screws" : International Shipbuilding Progress,

No.

_67,

Vol.

_7,

March

1960.

Shiori, J. and. Tsakonas, S., "Three-Dimentional Approach to the Gust

Problem for a Screw Propeller":

Davidson Laboratory Report

940, SIT, 1963,

Journal of Ship Research, Vol.

7, No. 4,

April

1964.

Hanaoka, T., "Introduction to the Nonuniform Hydrodinamics

Concerning

a

Screw Propeller" ¡ Yournal of the

Society of Naval Architects of Japan, No.109 and. "On the Integral Equation Concerning an Oscilla-ting Screw Propeller by LifOscilla-ting Line Theory": ibid., No. 110.

Verbrugh, P. "Unsteady Lifting Surface Theory for Ship Screws":

Report No.

_68-036-AB

of the Netherlands Ship Mo

-dei Basin, April

1968.

(lo) Sntved.t, T. "Propeller Induced Exitation Forcest' :Det Norske

Ventas, Publication No.

74,

January

_1971.

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-Some of the gentlemen, who are not only interested but render

compe-titive aid in the editing of this periodical made some comments to

the paper of Prof. Vudini&.

Besides they mean that it would be of interest to have more details

on the problems of pressure distribution on the blades,of the phase

position, of the loading of the leading edge, of vortex geometry and

differences between nominal and effective wake areas in connection

with scale effects. Problems of modern measuring technics and/or

cavi-tation would also have been of interest.

Perhaps it would be useful to take into account the induced velocities

also for moderate duty screws. The comparison of the results of

quasi-stationary and non quasi-stationary theory as desribed in chapter 5 and 6

are not to be accomplished, at least by using fig. 18 and 19.

Concer-fling section 6 in which has been said that the non stationary theory

gives higher medium sized (resp. stationary) stresses of propeller

blades than quasi stationary theory it is proposed to examine this with

the used calculating methods once again. The induction of neglected

free longitudinal vortexes has an inverse effect in quasi-stationary

theory. It's well known too, that a propeller gives a lower K,, value

in an inhomogeneous wake as if it would be operated on homogeieous

influx along with the suitable wake factor averaged over the propellers

disk plane. Perhaps it would be useful for a not so competent readers

to explain the Fig. 14, 15, 16 and 17 a little bit more.

Red.

Authors reply

In this paper are not discussed the theoretical principles of the used

methods of calculation, as they are given in the original works listed

in the literature at the end of it. There are given in a short review

the numerical results from my thesis, where are these methods discussed

in respect to the problems of pressure distribution, phases etc.Anyway

there are not included results of actual force and moment measurements

neither on models nor on ships. Nominal wake values measured on ship

models were used. The designed propeller family

is expected to work

free of cavitation, as cavitation is not taken in account. Cavitation

will surely enlarge the force and moment variations.

In respect to the inclusion into calculation of the induced velocities,

that is surely important when design of screw propellers is worked out

while it cannot be said the same for the analysis of the work of

geome-trically given propellers, what is here the case. My and Vedeler's

quasi-stationary methods are based on open water propeller KT and K

values and they are not expected to include induced velocities. The

Burrill's lifting line and Sparenberg's lifting surface theory are

worked out for optimum conditions so here is given one example of what

is obtained by their use.

I agree with you that figs. 18 and 19 are just a little contribution

to the comparation of results gotten by different methods but I found

myself limited by the range of an article. These are problems of wide

discussions.

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