Anti-pitching fins in irregular seas

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REPORT Nr. 93

October 1962

SHIPBUILDING LABORATORY

-

-I

TECHNOLOGICAL UNIVERSITY .DELFT

AÑTI-PITCHIÑG FINS IN IRREGULAR SEAS

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Summary,

Selt'-propulsion seakeeeping teste with a model of the S.ris

Sixty (c 0.65), fitted with a bow anti-pitching fin (Fin E [1] )

were carried out in longitudinal regular waves and in still water, The model responsee in irregular waves, defined by Neumann's wave

spectra, are calculated as a function of the Beaufort number and

the speed.

1, Introduction.

Model experiments to compare the performance of several

anti-pitching fina in regalar

head waves have been carried out before by

the author, using a 1/5k

acule model of the Series Sixty (C»

0.65),

Resistance, pitching and heaving motion. and induced vibratione were measured in those experimente and the following items were

oon-firmed:

1),. The anti..pitohing fin, are reaarkebly effective for reducing

th. pitching motion and the resiatance at synchronous conditioù

2). 8lit. in the fine an, very efficient to reduce the induced

vi-brations and yet they do not introduce any dsadvantag. with regard to the motions and the resistance, provided that their

position and dimensions are

carefully determined,

The reaulta of teats in regular waveS are in itself not suffi..

cient to predict the general performance of the fina at seat because

of the irregular character of the water surface. The self-propulsion

testa in regular wave, are carried out over

a 1irge range of

wave-lengths (ø6 A/L..1,t/L)

to prepare transfer functions, which

could be used

to predict the performance in an irregular sea,

7m E, which showed the beet performance with regard to the motions,

resistance and

induced vibration. is

used throughout these

experi-ments. Th. motions

and propulsive responses in irregular waves are

calculated by applying the transfer functions to several

Heumannn's

wave spectra,

Sea keeping tests with the original model of the Series Sixty

(Cb - o65)

and with a odif'jed model which baa a 10% bulb were also carried out in the Dell t Towing Tank.

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-

-2-These results will be published in lhe near future.

A comparison of the three modela namely: the origInal model, the

model fitted with an anti-.itch1ng fin and the

model

with a 10% bulb

is given in this paper.

2. Exerimental procedure.

The reader is requested to refer to [i ] for tite model and the

fin particulars. The teste are carried out under the following

con-ditiona

3. Weve

itrum.

Any seaway cari be charaotarfted by a "wave sectrua" which indicates th. relative importance (wave amplitudes) of the regular

wave componsnt which produce the obrierved irregular pattern by

superposition. The wave spectrum is defined as:

C..) + tC.)

0(W)'

ir2 (w)

and has the dimension of length squared time. The integral over

_we

of the wave spectrum is generally known ea the "cumulative energy

density".

waveheight: h

a

5.6 cm h/L

R a

fo

(w )dw

Furthermore, the significant waveheight

1/3 is expressed as toi-lowS!

-3

wavelength:

A

= 1.35 a = o.6o = 1.81 a

= o8o

-

226 a

a 1.00

-

2.71 a 1.20 3.16 a 1.40 3.61 a =

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-3-The Neumann's wave spectra for the 1/5k scale are calculated and classified according to the Beaufort number and the Froude

num-ber. The

corresponding ful]. scale wind velocities and significant

ve1engths for different Beaufort numbers are as tollow for a ful.

According to the above mentioned representation, the sea state

at a fixed

point

je given by:

or:

r(t)

f

coe(t +

£(cJ)

\f[r«J)]2.

dJ

r(t) oos.)t + _{(CJ)\[2G(C41)dCA)}

According to Neumann the energie spectrum can be expressed in the following form:

i 2

Grr(CiJ) 1cjU

where g is the acceleration due to gravity

and U la the wind

velocity in

ni

per second.

k, Reav.

and pitoh energy epeota.

Tb. aseumption is made that th. sum of the responses of a ship

to a number of simple

sine waves is equal to the

response of the

ship to the sumo! thees regular wave components. The

heave

energy

peotrur is expressed aa

G

«J)A2(cJ5).G

((J)

rr e

sr. e

is known as a "Response amplitude operator" and can be obtai-ned by cross plotting the results of the model tests in regular

waves at

constant

for*ard speed and then plotting the

value of

ly developed sea:

Beaufort No. ₅ 6

6j

6 7 8

Nind velocity (knots) 19 2k 26 28.2 30 37

Vaveheight (ni)

1/3 2.1

38 k.6

5.6

6.7

11,3

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(heave amplitude/wav, amplitud.)2 agath8t the circular frequency of

Sneounter

L,.

Now the

cumulative

energy density for heave is expressed as

follows ¡

IL

-

JG(()dC.3

jA2(()G(Q5)d9j

Consequently the significant amplitude (the average amplitude of the

one-third highest motions) is expressed as:

Z11,

A similar expression holds for pitch. It should be noted, however, that the energy spectrum of heave has th. d.tuiension of (length)211ius whereas the energy spectrum of pitch has th. dimension of time.

3. Propueiona]. characteristics.

The mean increase of torque in an irregular long-created way. system which has s certain spectrum is determined as follows:

2G((J)

((.))

d(*,

where:

a

wav

spectrum

j(&j )

transfer function for

torque. r

The validity of the

above mentioned formula vMs confirmed by Gerrits-.

ma [}. Consequently, similar expressions are valid

for

the other

propulsive abaracterta tics.

6. Resulte 9f

the tets.

Th. measured values

of

torque,

thruet

and number of

r.volu-tions in still water and

in

regular

waves

are

shown

in

Fig. 1.

In

still water the t.rqu.

and

thrust for the model with the fin

are

higher than

for

the

model without

the

fin. Although the

scale efe

feats of th. model itself ari ignored in the paper, it should be

noted that the oale

of

the

model fe

1/51f, which is oertsinly too

small t. allow a experimental determination of

appendage

resistance.

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I-5-

5.-The small fin size and the low model apeed result in very low

loqal Reynolds numbers with the consequent

oeiibility of laminar

flow. This may be mo sensitit

that even minor unfairness of the

appendages will oau

separation of the flow with a corresponding

large increases in drag.

As the full-scale finst on the other hand, are in turbulent

flow, it is supposed that the tuUiaçale fin resistance in still

water will be very email.'

The dimensionless increases of torque, thrust, power and

revo-lutions in waves are shown in rig. 2 as a function of speed and the

model length Nave length ratio. The transfer Iuncione (increase

of propulsive characteristics devided by the squar, of the wave

em.-plitude) of torque, thrust, power and revolutione se the function

of the frequency of encounter are given in 1'ig, 3. The comparison

of these transfer funotiona to those of the original model ehowø a

reduction of about 50 per cent at the mad.mum values. U8ing these

transfer ftinctione and the Neumann tnve spectra, the mean increases

of the propulsive characteristics az's caloulated. They are, given in

Fig. ka and kb as a function of the Beaufort number corresponding

to the Neumann spectz'a. The values for the original model

and the

model with a 10% bulb are given in the ease ftgure. It shows that

the fin gives quite an improvemeritin the propulsive characteris.-

-tics.

The response amplitude operators for heave aM pitch are shown

In Fie. 5 and the significant motion amplitudes in a Neumann sea

are shown in fig. 6. A considerable decrease in pitch not only in

synchronous conditions in regular waves, but *leo in irregular wava

is found. The heaving motion 1.n irreuiar waves, however,, je not

re-duoed by the fine.

It should be understood that the sea state corresponding to a

Beaufort rnzmber B te a very severe condittofl. It is quite certain

that the principle of superposition wil]. not be valid for these

conditions. The ca3.culted pointe, however', are given in the vari.-

-oua fj.ures to show the trend of the cuz'Ve5.

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7,

The Suture proseet of aflti.itohin

fina

It is confirmed in this paper that anti-pitching fins are Very

valuable to improve t power characteristics and

pitch motion in

irregular waves. There are two things which have to be studied care-fully before a successful application on a full.eoala ship is pos

sible.

Fir:L1y, it

is urgently z-.quired to find a method to cope

with

the jiduced vibrations. To cut slits tn the fine, for instance1

is one possibility to solve this problem. Another way is to place the tine forward of the atem so that the impact toro., due to the

collapse of the cavities arid 3lammtn lili not be applied to the

bow sides, This method La lo favurable to deoreaae pitch motion

because of the longer arm for the

pitching moment. Secondly, it is

fl.00SRary to pay attention to the utili water performance of a mo

de]. with anti-.pitchtng fins. Although it is supposed that increase

of resistance in rtill water due to antipitching fins will b.

rm'ill, the position and the section of the fin have to be carefully

ituUied lest it uhould disturb the flow along the hull.

Finally it should be remarked that structural problema with

regard to

the

construction of the fin and its connection to the

ship are not conaiderod in this paper.

Acknowledgement.

The experiments have been carried out by the author in the

Delft hipbui1ding Laboratory under a ucholarshp of the Miriietry

of Educat±on in tht NetherlandsE

The author is deeply grateful. to

the ki.nd instruction of P-rot, Ir J. Gerritema and Ir i.C. Meijer. The author also wishes to express his great thanks to Hr W. Beukel man who has carried ot the eperim.ntal work of the seakeeping

testo of the original model of the Series Sixty and the model with

the 1O

bulb.

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V

o

-7-REFE1ENc.

1

V. Sonoda,

"Model Exper

mr,r.t

wl th Sevril

_{Ar t i -1t tc}ii}

o

Shipbuilding Lhcrt.ory, Report No. 90,

_{Techzio.ogical University}

Deif t. July 1962,

Prof.ir J. Oerritsma,

"Propulsion in )egu1az' and Irregular

duve&'.

International hiphuildiug Pzogre, 1961

P. Mandel,

"Some Rydrornamic Apect8 of

Appendage 1)e6igrt".

SNAME, November 1953.

M. St. Enia, J. P1er80r11

"On the Motions of Shipa in Conruod

oao".

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FIG.1

THRUST. TORQUE AND REVOLUTIONS IN STILL WATER AND IN REGULAR WAVES

1000_ 800 -gr .1.00 200 -STILL WATER 5/L .06 =0.6 1.0 7 _iz Vi i.' 1.6

MODEL WITH FIN E'

1- I I OES 0.8 I I 1.0 1.2 V_,tm/Sòc 1.4 1200 1000 BOO -grcm ¡ 600 -Q 400 200 -O =1.2 k/i 1.4 =1,6 1 6 - I i I 0.6 0.9 to v_L... m/55 1.2 25_ 20_ 1,5 sec1 ft lo

-

5-MODEL WITH FIN, E

I i ' I

0.6 08

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F1G.2

DIMENSIONLESS INCREASE OF TORQUE THRUST POWER AND REVOLUTIONS IN REGULÄR WAVES

3-2._ o o o Tr .pgB/L Fr _0.150 __-.___ Fr 0175 Fr oa ___.__ Fr 0225 Fr0.250

05 X,..,. 10

Vr g r2BIL O---O-- Fr r.01NO Fr. _0.250 1.5 I ' 0.5 A -1.0

/LT

u

20_ 15 10 0 o

r

2 pg r2'0/L D .______o__. Fr. 0.150 ____.--__ Fr. .0.175 N N Fr. .0.200 _________ Fr. .0225 Fr...0250 i I 0.5X 10 Pr pgr29tL V Fr. 0I50 Fr Ø175 Fr. 0.200 Fr. .0.225 F,. .0.250 T I 0.5 to 1.5 ._____.._ Fr. ..0175 Fr. 02O0 N .-____-___ N g- Fr. 0225

"r

20_ N ..c.15 -io

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6 7 9 10

w. ____.

FIG. 3

TRANSFER FUNCTIONS FOR TOROUE.THRUST .REVOLLTfONS AND POWER

0 1

I T I _I I I T

S 6 7 6 9 10

s.c

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2 600 - 'X-r Trr 00 200 -100 o 900 ex TX -FCm rr 500 '00 300 100rn Fr .0.150

-O-O- OHWIN.L NI.

WITS IH%W4ß WITH FIN E Fr.. 0.150

-o--O-

-W-6 sOo 100 o 900 - Fr. 0.176 600 700 .rc" f -Q1., 500 -oc 300 200 -100rn Fr 0.i75 WITS fl WHO WITH FW L 5 7 WINDFORCE O -O-.- HHiW U

____. WITH WHI HISS

e ex-500 'X-gr Trr 300 200

-

lx-0 FIG. 6 a

THE MEAN INCREASE OF THRUST

Fr .0.200

-o-O-WIT OHIHISS

THE MEAN INCREASE OF TORäUE

Fr50.200 o WINDFORCE 500 -500 400 gr Tri. 300 -200 Fr.0.225 - - HITS flBI&H s e___. 7. WINDFORCE ___ O 900 ex 200 ix -5 S WINDFORCE _ B 8 6 7 WINOFORCE .__ O 5 6 7 WINOFORCE B e 5 7 WINDFORCE ___ o

5.7

S 7 5 e 7

WINDFORCE o WDxFORCE o WØCFORCE

coo ex -grcm cx -

'X-ix.

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15 -5 s 5 7 e WINDFORCE B 6 7 WINOFORcE . B L- 3-1H 0 Fr .0.175 OalflM ca WITH WV. STAN Fr .0.175 6 7 WINDÇORCE B _..o...o_.. 0015M WItCH

___._ WITH WIN SINS

e 6 7 - WINOFORCE _=_ B n- 5-5

THE MEAN INCREASE OF r.p.m.

Fr .0.200

FIG. 4

cSIM ca

aTM SIN. 5MO

WITH MI

S 6 7

WINDFORCE B

THE MEAN INCREASE OF POWER

7 WBFORCE s ñrr * HP 7. - 015 -s Fr.0.225 WIPCFORCE ... B Is -s 5 7 WNDFORcE .__ B e Fr..0.225 Fr .3 250 9-e s 5 6 7 WINOFORCE -! 6WINDFORCE - B7 6 Fr. 0.150

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200 -1.50_ degree/cm 1.00 0.50 -o 2.00 1.50 -f Zo/ too -050 o--.-- F,._O.1SO __p._-_. Fr 0.115

-o

FIG. 5

RESPONSE AMPLITUDE OPERATORS 'FOR PITCH AND HEAVE

I I I I I I J

-I

I J 2 3 4 5 6 7 B 9 10' 11 12 13 14 15 W0...,. eec-1 F,. ...OI5O Fr Ot7J Fr O2OO Fr 0221 F, Q250 J J J, J I 0 1 2 3 1. 5 6 7 8 9 (A), _.. seca 10 11 'I J - 'i-12 13 14 15

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jJo

deçe.

d.ye.

4,.

Fr. .IN225

._.o.___.__ ORG HOOEL

.ac

WITH,FIN E Fr. O.225 ORO, MODEL -..,__-___ WITH FINE 10 -t s-d.y.. 5 ---. o

FI6

PITCH AND HEAVE IN IRREGULAR WAVES DEFIÑED BY 'NEUMANN SPECTRA

Fr.=0150 PITCH ORG MODEL W1TIIFW E W1PFORCELB ORO, MODEL, WITH FIN I o cm L5j ZN cm Z ID -o 5 WINOFORCE WINDFORCE_...B '6 7 WINDFORCE -B -B B?' 06 B dse. 10. o Io -Fr. =0.250

o- -W----PITCH ORO RODEL WIIHIFIII,E cm, 10 lo 5 WINDFORCE ...B 08 0150 0.175 0.200 0225 0.250 0.150 0.175 0.200' O225 0.250 Fr. Fr. lo - r.0.150 HEAVE ORO MODEL WITH FIN I 10 Fr.=O.175 PITCH 5 WINDFORCE B HEAVE Fr. =0.250

__.o____o__ ORO. MODEL

__.-..__.__ WITIIFW(

5