Distribution of hydrodynamic forces along the length of a shipmodel in waves

I9(cO.

Ui) Vossuas, G.: "Sorne ApplicaI of the Slender Itody Theory", Thesis, Dclfl 1962.

17) J(HPS1r4., W. P. A. atiti WouttsiAN, J. J.: "Comptilci:

Mcthods for the Dctcrminution of Ship Behaviour". To

I. INTRODUCTION

In this report a short summary is given of forced

oscillation lest results for heaving and pitching motions

in still vater and ih results of exciting force measure-ments on a restrained ship model in regular longitudinal

waves.

The tests vere carried out with a segmented 2.26

meter polyester ship model of the Series SixtyC,1=O.70, parent forni.

The main particulars of the model arc given in

Table 1.

Table I. Main particulars ofship model

£LCCTROiC SfRAO IPASCA?OR RAMTtPI

STP;N OAUGE OrNaHOiTtR MOOiJtAI(D

CAtAtE

SCOTCA VOtE V,

Fig. I. Principle of mechanical oscillator and electronic circuit

?itz-r I(4L4

APPEDIX V

DISTRIBUTION OF HYDRODYNAMIC FORCES ALONG THE LENGTH OF A, SHIP MODEL IN WAVES

by J.. GERRITSMA (Dell t Technological Univ.)

be published.

18) Funi. Il. and OuAWMEA, Y.: "Calculation on the

Heav-ing and PitchHeav-ing of Ships by the Strip Method", Journal

of tite Society of Naval Architects of Japan,

N 118.

1965.

The modòl consisted of seven separate segments, each. of which was connected by means of a force

dynamo-meter to a continuous strong box girder

above the model, as shown in Fig. 1.

The segmented model was used for the oscillation

tests as well as for the restrained-model test in waves;

The two experiments were also carried out with a

non-segmented model to compare the sum of the section

carried out with a non-segmented model to compare

the sum of the section results With the measured total

forces and moments.

This was done to check the

ac-curacy of the experiments and to detect possible paras-tic effects of the gaps between adjacent segments.

2. DIsTRIBUTION OF DAMPING AND ADDED MAss

2.1. Experiments

With a forced harmonic heaving experiment the

in-phase and quadrature components of the forces on

each segment could be measured and consequently the

damping coefficient and the added mass of each

seg-ment could be measured and consequently the damping coefficient and the added mass of each segment could

PO SAO VER

VV

AN PtVflE P 0E MOStE A TOR

lAIE GR AT 0E

IN PHASE COi0NEIlT QUAORATOEC COEPOPOS:

Length between perpendiculars 2.258 rn

Length on the waterline 2.296 m

Breadth 0.322 m

Draught 0.129 m

Volume of displacement 0.0657ni3

Block coefficient 0.700

Waterplane arca 0.572 rn2

Longitudinal moment of inertiúof waterplane area 0. 1685m1

L.C.B. forward

L/2

0.011 m

Centre ofeffortofwaterplanc area, aft

Lf2

0.038 m

Service speed, approx. P=0.20

1c6 SlAKIFPlNCi SISSlO1

be determined.

With a pure pitching experiment the added mass cross_coupling_and the damping cross-coupling cocflici-ents were found for each segment. For the whole model the saine procedure was followed and for this case the

following equations are given to show the method of

computation.

Heave: (a -I- pv)z

+ b + cz= F,

(w! -I- (r)

D-j-E-l-Gz=

M, sin (w!+

Pitch:

(A + I)Ò+BO+ C(i=M sin

(w! + )

dö---eô+gO-- F,

sin (wl±Ö)

For a forced heaving motion z= z,L siI w! it follows'

that: b , a cza - F, cOS (y Z,,w Z,,w_ <1 .)

E=

M,sinß

D=

gz±M,cosß

ZaCI) ZaW2

Similar expressions arc valid for the forced pitching

motion experiment, from which A, , d and e can be

de-termined. The determination of the damping

coeffici-ents b and B and the damping cross-coupling

cocflìci-ents e and E. is straight forward: for agiven frequency

the coefficients are proportional to the quadrature

coni-ponents of the measured force or moments for unit amplitude of motion. For the, determination of the added mass a, the added mass moment of inertia A .and the added mass cross-coupling coefficients (d and D)

it is necessary to know the restoring force and moment

coefficients e and C and the statical cross-coupling

coef-ficients g and G. In this analysis the values for c,C,

g and G for zero speed and .frequency are used').

For each of the seven segments of the ship model,

similar expressions as (1) are valid. As only forces

and no moments were measured only the force

equa-tions for the segments remain. For each segment the

coefficients as determined by the forced oscillation ex-periment, were divided by the segment length to arrive

at mean, cross sectional vaIues Assuming that the dis-tribution of the cross-sectional values is continuous over

the length of the ship these distributions could then be determined as shown in Fig. 2.

The distribution of a',, b', d' 'and e' over the length of

the ship model is shown in the Figs. 2a, b and e for zero

speed, F=.15 and F,,=.30. The

coefficients for the

whole ship model are shown in the Figs. 3a and 3b.

lt was found that the sums of the segmentresults agree

very well with results for the whole model.

2.2. Calculation

The cross-sectional values of thc.coellicients and the

corresponding coefficients for the whole model were

calculated with a modified strip theory taking into

ac-count the chiect of forward secd. In the calculations

the cross-sectional added mass ¡n' and the cross-sec-tional damping coefficient N' according to Tasai's

method is tiscd'. I n this method the cross-sections of

the ship are approximated by only a two coefficient transi orination of the unît circle. lt is shown in i ) that:

b'=N' V

(IX, . dx,

The cross-sectional coefficient a' is equal to the

cross-sectional value o the add' ed mass m'and d' is the

mo-ment of this value with respect tothe centre of gravity.

The coefficients l'or' the whole ship as drived 'in 1)

are sumnnrizcd in Table 2. 'For ease of comparison

with the experimental values, the statical restoring force

coefficients and cross coupling coefficients are taken

as their zero speed values. For harmonic motions with frequency ai this gives the second terms in the

expres-sions 'for A and (I.

Table 2. Coefficients for the whole ship

a =J ,?I'(lX, i, =J N'dx, c=pgA A = J

Ld +

D =J N',vb2dx, C=pgI I. r Vi (/=.) ,,z.t',d.v, + --e J N'.v,d.v, - t'ai g=pgS1, D _{J L1.v5d5} E =J N'v,d.r, + t'ai G =pgS.

In Figs. 2a, b and e the experimental distributions of

the coefficients a', b', e' and d' arc'compared with the

theoretical results. Except for a few cases where the

frequency of oscillation 'is very low, the agreement is

statisfactory. in the Figs'. 3a and b the calculated cocí-ficients for the whole ship model are compared with

the' measured values For frequencies 'above w=5 or

IL

_{the agreement is' satisfactory in ail cases.}

Of special interest is tile comparison of the

cross-'coupling cocflicients e and. E which arc important in

cal-culations 'of the ship motions in waves. Fig. 4 shows

these coefficients on a base of forwardspeed for, various

fre4uencies. From the strip theory it follows that:

E= J'N'xrdxt + Vin

e

=

J' N'x,dx, -

Vin.

Titus for a symmetrical ship these cross-coupling

o. -o. E a a E -s _______ EXPERIMENT CALCULATION i 2 3

i

J

i i 2 o .2 -o 3

iThJ 6

f7

Fn: O

Fig. 2a. Distribution of a, b, d and e over the length ofthe shipmodel

,-i--:i

ilL

IIIÏL

i

:IiIi

Iii 11:

it1

=.dIsec

II

L

Ii

Iir

Muu

A:1IL

DL

PJIIIL

Ììi1i'

iiip,'

4

V

r-11111

t.

o A

11MW10

2I5

AI'PENDIX 351

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2 lT i o E o 20 lo o 20 lo

IL

35R 0 1.0 0.5 o 05 .1

.l71Tf

6 1

1

'h i 2 SI,\KIlllNC, SESSiON 2l3lh-ti+ EXPERIMENT CALCULATION 5 o -5 _10 5 o -5 _10 5 o -5 _10 _1 3 5 I

61 71

Fn= .15

Fig. 2b. Distribtition of a, b, d and e over the length of the shiprnodcl

/

\

-I F

-JÌaI

...J1N! nriTVd/sec d/sec

k

r. d/sec

rrì

/

IIuI

,,

w.4 .d/sec s'

i1ii

w= 6 rod/sec

I-l'i'

II!i

,dlI!i

i!

i:T0

uII

weOrod/S /

/

/

' , s'

L

W6 rod/se.

"Pill

_A

-risi

rodec _.A odec

₄

-I!iIlI

i 1.0

0.5 o _0.s

213

6 7 2 0 o ¿ 2 E o 2 0 6 20 10 O 20 10 o 20 10 E 20 10 o 20 10 o 1.0 0.5 o - 0.5 1.0 05 o

E o £

2

'i111i12

Ii I

5 j 6 , .1

'I-ÏT2L LiïiiII

o L, o ¿ S'_S APPENDIX E 20 10 o 20 10 o 20 10 20 10 o 20 10 EXPERIMENT CALCULATION o -5 _10 5 o -5 _10 5 o -5 10 5 o -s _lo

1213ITh1s

Fn= .30'

Fig. 2e. Distribution of a, b, d and a over the length of the shipmodcl

"lip,

_IlILil

tiII

I

I

Iii. liii

I!ïiïIi

Ii4øip

w4

;1I!

ì

1jUl11!

rod/.c

i !IIP

ii

4

iI

-g.i.i

Ì.!iiI

w.10' rad.c A

A4

r-I!iIIU

rad/sec 10 0.5 0 _o s 1.0 0.5 o _05 10 05 o E 1.0 os o .0.5 1.0 0.5 0

SlAKlIPlNC SlSSION g 8 7 E 01 (n DI -x 5 3 0 01 -x Fn.QISi.30 N AT UR At FOR H0 REOUENCY VE

This is in agreement with a result found by Timman and Newman5). The calculated values according to the strip theory are in very close agreement with the experimental

values.

3. DIsTRIBtiTI0N ot EXCITING FORCES

3.1. Experiment

The forces on each of the seven segments of the strained model in longitudinal regular waves were

re-corded on an Uy recorder and analysed manually for

amplitude and phase. For each segment the phase was

determined with respect to the wave motion at the

mid-ship section and the final results arc presented as the

4

in-phase and quadrature components of the force ampli-tude for each section.

These experiments were not carried out with zero

forward speed. However, the influence of speed on the total exciting fòrccs is small and the considered speed

range seems suflicient for studying the speed effect on

the force distribution over the ship length.

In Figs. 5a and b the measured distribution of the in-phase and quadrature components of the exciting force

is given for F= OiS and F= 0.30 as a function of

wave length ratio.

In all cases the wave height was

1/40 L73,,.

The influence of speed is quite small but

the distribution of the in-phase force shifts slightly

for-.30 ///o NATURAL FOR HEA(E FREOUENCV-.. .Fn...30 'I

V

---o w VI h 2 w (n 8 2 û -1 2 -3 o Fn. VS

,

.15 o í0 _/30 Io 15 lo 15 EXPERIMENT w CALCULATION

Fig. 3a. Comparison of the calculated values of a, b, D and E with the experiments

2.0 1.5 1J w w

E to

CT, 4 0.5 2

ward with increasing speed. .

Fig. 6 shows the total

wae force and moment amplitudes in

dimcnsionlcss

forni also for F,,= 0.1 5 and F,, = 0.30. In this Figure

the sums of the segment results arc compared with the measured total forces.

3.2. Calculation

The total force and moment follòwfroni:

=

J' (F,. -- F,,..+ F,1)d.r6= F,, cos (wet +

M

=

J' (F,.,+F..2 + F:3)XbdXb

= Ma COS(wet + £.ue)

lo 8 7 where:

c=c(i

____J'ybe_kzbdzs)

yw

_-r

5 5

e with the experiments

where the F"s are the cross-sectional values of the

wave forces and o, c

arc the phases of force and

moment with

respect to the wave at

the midship

section.

From strip theory it follows that:

F., = 2pgy,1,Ç"

;.,=

= rnht*

(It'

'

(IX6 ç

(3)

Fn.Q.IS.3O

--I, 1 30

.J

o1II\

RIM

i,

i

.3O t t 5'

St

-.15 'I NATURAL FOR PITC FREOUENCV .ik k 0.25 is 'Fn..30 is \

'

', .15 _ I -o APPENDIX 361 w w 5 10 15 u)

-w-

_{- EXPERIMENT} w CALCULATION

Fig. 3b. Comparison of the calculatcd values o A, B, d and

5 lo 15 ( ) lo 15 2 o -X -1

362 SFAKl'!'llNG SISSI()N

and:

,, cos(kx,, + u,i,1)the wave surface;

y0,the half width of a section at the waterline, ,n'thc cross-sectional acldcd mass,

N'thc cross-sectional damping coefficient.

u o 8 6 4 2 o -2 -L -6 -8 6 1. 2 o -2 -4 -6 -8 -io 6 I. 2 o -2 -1. -6 -8 -lo 6 ¿ 2 o -2 -1. -6 -8 -lo By sLui)stituting:

C = CUS (kv,, -I. (i),i)

in the expressions (3) the cross sectional values for the

exciting forces cai be found easily. The integration

according to (2) gives tile total values for the whole ship.

In Figs. 5a and b the calculated distributions, of the exciting force components arc compared with the

ex-perimental values. _{In this case tile agreement is}

satis-factory except for very small wave length ratio's.

The calculated total force and moment anipiitudes as weil as the phases c, aild are compared with the

experimental values in Fig. 6. The nagnitude of the

so-called Smith clTcct caused by the difference of and C* and the dynamic terms F,02and F, is demonstrated

by comparison with calculations in which these effects

were omitted. Fig. 6 shows that the contributions to

tile exciting forces and moments arc significant and

should not be omitted in a 'cilculation. The effect òf

forward speed 011 the force and moment amplitudes s very small and therefore the graphs in Fig. 6 are given on a base of wave length ratio rather than on a base of

frequency of encounter.

4. NOMENCLATURE

AIJCDEG Coefficient of tile equations of

mo-a b c cl

cg

tion for heave and pitch.

A,0

Arca of waterplane.

C,, Blòck coefficient.,

F,, Wave force amplitude on restrained

ship.

F,0 Wave force on restrained ship.

Cross-sectional wave force

on re-strained Silip.

F,,

V

Froude number.

Acceleration due to gravity.

Longitudinal moment of

inertia of waterpiane area with respect to

the Yy axis.

Real moment of inertia of ship.

Wave number.

Length between perpendiculars. Wave moment amplitude on restrained

ship.

Wave moment on restrained ship.

Total added mass for heave.

Sectional added mass. Sectional damping coeflicient. Statical moment of waterplane area.

g 1W M0, nl

'n,

N' SW I I I o o o s W 6 rad/sec e adec lO,radIsec s W 12,radJsec: 0.1 0.2 0.3 JEXPERIMENT E,e CALCULATED

Fig. 4. Damping cross-coupling coefficient as a function of forward speed

o

2

EXPERIMENT

CALCULATION Fn .15

Fig. 5a. Distribution of in-phase and 90 degrees out of phase wave forces along the length of the restrained model

I 2

3 iri

lo

- EXPERIMENT

----CALCULATION

Fn . 30

Fig. 5b. Distribution of in-phase and 90 degrees out of phase wave forces along the length of the restrained model

II!II

Pi

lEi

_-,

IA

I1Ii!

_ì!I1i

Ii

!1P1i

1iIiI

ihii

:rA

iMJI

vi

iIìI

f

)I

I O 0.t o 2 10 12 1.4 _o w C w 2 t6 o 2 1.8 O -L 2

4a6

O 2 o 2 o 2 o 2 o

:}

o

t

- 2 n o LL o 0.8 o 2 1.0 2 t2 o F 1.4 J C w 1.6 APPENDIX 363 o 2 OE 0.8 1.0 12 1.4 16 1.0 0.8 1.0 12 1.6 1.8

SIAKEEl'lNG Sl.SSION

Time.

Draught of ship.

Spccd ol ship.

Right-handed body axis system.

Half width of dcsigncd waterline.

Heave displacement.

1-leave amplitude.

Phase angle between

the motions

(forces, moments) and the waves.

Lfl 1.0 -9 .7 t .5

Ill,

I

I.

tOtS tO 1.2 1.0 .0 .6 AIL 0 I O 5L to

Ix

I i I I I tOtSI.0 1.2 1.0 'VI I-5 .6 _l80 Fn..15 leo In 90 o w 00 01. loo _180 Fn. 30 C Ca (i ¿la A f) V i,) to D

II

I toto to A/L

-Instantaneous wave elevation.

\Vavc amplitude.

Pitch angle.

Pitch amplitude.

Wave length.

Density of water.

Displacement volunic.

Circular frequency.

Circular frequency of encounter.

t2 to

to

EXPERIMENTj SUM 0F SECTIONS

O WHOLE MODEL

CALCULATIONS

CALCULATIONS WITHOUT DYNAMIC EFFECTS

CALCULATIONS WITHOUT DYNAMIC EFFECTS AND SMITH EFFECT

Fig. 6. Total wave force and moment on the restrained shiprnodet

..90 X w -leo I I I to to to i.z 1.0 .0

--5., REFERENCES

I) J. ('iiRRlTsMA and W. B,uKEIMAN: "The Distribution of the Hydrodynamic Forces on a I-leaving and Pitching Ship Model in Still Watcr". Paper presented at the Fifth Symposium of Naval Hydrodynamics, Bergen, Norway,

1964. international Shipbuilding Progress, 1964.

2)' II. V. KoRVEÑKRoUKOVSKY and W R. JAcolls: "l'itehing

and Heaving Motions of a Ship in Regular Waves".

Transactions Society ol Naval Architects and Marine

The following iccommcndation was made by the

Tcnth International Towing Tank Confcrcnce:

"5-8 The

Conference requests (lie Co,n,nitlee lo

nakc rCCO,fl,fle?idatiOfls lo tite

¡liii 1.T.T.C.

regarding standard sea speclra lo be USC(l ill 'predicting ship behavior in waves. . ."

Accordingly the subject of standard spectra has been

considered at all' of the subsequent meetings of the

Sea-Significant 60 W° Height Feet Meters 50 40 30

* Modifed by NPI Information to Convert Hobserved to Hsignilicont Q Wind Speed (Meters! Second) _1A 5 10 15 I I I i

III

I I t I I t t

10

APPENDIX, VI

iNTERIM STANDARD SEA SPECTRA

1y E. V. Liwis

(Webb. 1,1st. of Naval Architecture)

and R. H. COMPTON

206

WIa

peed_C l0__.gfl* , Obser' _051q1ct j'1_obs.W0e 20 Wind Speed 1Knots) Fig. 1 ÏÏ,3=3.2808 (h23-F027Hb,) Cur4 Engineers, 1957.

Y. Wirmull:

'SOis the Theory of Pitch and Heave of a Ship'. Technology Reports of the Kyushu Uniyersity,

Vol. 31, 195K. (Translation Sonada 1963).

F. TAsAI: "On the Damping and Added Mass of Ships 1-leaving and Pitching". Report of Research institute for Applied Mechanics, Kyushu University, 1960.

R.. TIMsIAN and J. N. NEwMAN: "The Coupled Damping Coefficient of a Symmetric Ship". Journal of Ship Re-search 1962.

keeping Committee.

The Committee has concluded that there are still

in-sufficient data on ocean wave spectra to permit the

adoption of a fixed standard for general use. However,

it was finally agreed that the Committee would put

for-ward a proposal for an interim standard based on the

Pierson-Moskowitz formulation

(1), för ideal

fully-developed seas.

il

CooS'° è 4" APPENDIX - 365 20 25 30 40 50 -14 -12