Progress report on determination of forces and moments exerted by waves on a restrained ship model

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EXPERIMENTAL TOWING TANK

TCSC

STEVENS INSTITUTE OF TECHNOLOGY

HOEOKEN. NEW JERSE'Y

_Delli

LR No.

₅₂₅

Progress Report on Determinaticn of Forces and Morents

Exerted by Waves on a Restrained Ship Model

(SNAME Purchase Order

1397,

ETT Project

_lIilj5)

Prepared for Presentation at H-7 Panel Meeting ofJanuary 21, l95L

by

B. V. Korvin-Kroukovsky

Sunnary

In this progress report the work accomplished to date on the in-vestigatn of forces and moments exerted by waves on a restrained ship

is described. It is sho that pitching moments appear to be quite

regular, and tend to increase in intensity with shipts speed. The

heaving forces are very irregular and also increase with speed and

exhibit certain changes of phase.

A suggestion is made that more useful results can be achieved

within the scope of the present investigation by curtailing further

expriinental work and by doing instead mori analytical investigation

of the effect of the above peculiarities on ship motions.

Introduction

1b. y. Schpowknd

/0

The objective of this investigation is to determine exper.inental1y

the forces and moments exerted by regular sea waves on a ship model

re-strained from pitching and heaving motions. The theoretical foundation and significance of these measurements is presented in Reference 1, which was distributed to miibers of the H-7 (seakeeping qualities) panel at its

meeting of 26 October 1953. Briefly, it is shown that the entire force and moment experienced by a ship in a seaway can be considered as the sum

of forces and moments occuring due to ship oscillation in smooth water

and those exerted by waves on a restrained ship. These latter then can be used as flexcitinghl functions in the usual forn of inhomogeneous equations of forced motion.

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Model, Apparatus and Conditions of Test

The model, constructed of wood, is that of DB Series 60, 0.60

Block coefficient, the particulars of which are:

Length b.p. 5 ft. O

in0

Breadth 3 in.

Shear tlgtandardft _{See body plan}

-Fiare 'ean" Fig. i

Draft (even keel) 3.20 in.

Displacement 33.27

lbs0

The model was ballast ed to float on an even keel at LWL and to have

the longitudinal radius of rration (in air) of .25 of the length between perpendiculars.

The model was attached to two spring dynamometers capable of measuring vertical forces at 25 and

.75

of its length, or 1.25 feet forward and aft

of midship sections. A third spring dynamometer measured the horizontal

drag force. This dyrainometer was attached to the model at LWL. Each dynamometer had the maximmi deflection not exceeding O.o1.o" so that the

change of model position was quite negligible as compared to wave height

or slope. The stiffness of the dynamoirteter springs was such that natural periods of vibration (with model iii water) were from 0.08 o 0.12 sec.

Since the periods of wave encounter ranged from 0.60 to 0.97 sec., the

effects of natural frequencies on the final readings were negligible0

DefleCtiOris of dynamometers were picked up by Shaevitz induction gauges, the signal was amplified and was f irially recorded on the photo-sensitive tape of a gaivononeter. A sample of the tape record is reproduced in actual

size on Figure 2. In reading the tape, a smooth curve was sketched by hand

eliirtinating the high frequency "noise" oscillations, and the ordinates of this curve were measured.

The dynamometer was initially constructed several years ago for a

certain research for the Office of Naval Researoh, and required a relatively simple adaptation for present tests. Originally it was thought that it would be necessary to use a small model in order not to exceed the capacity

of this dynamoineter. However, the recommendations as to wave heights to be used in all wave tests - Ref. 2 - have recently reduced the recommended

wave heights and it was found possible to use the model of ₅ foot length, i.e. the size commonly used at DThIB and at ETT Tank No. 1.

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-2-The wave height was measured simultaneously with forces by means of

the wire resistance gauge.

This consists of a pair of thin vertical wires

connection so that the current passed from one wire to another through

water.

The resistance to the current was recorded on the galvanometer.

The calIbration was made by raising or lowering the wire in still water

and recording the change of resistance.

The galvanometer reading was

f ound to be very nearly linear within the wave height used.

The wires

were mounted in line with the front perpendicular to the side of the

model centerline on the towing carriage and moved through water at the

speed of the model.

Program of Tests

The present progress report gives the description of the preliminary

group of tests conducted originally in order to check the instrumentation

and the method of operac.ion.

Ce wave size only was used, nominally equal

to the length between perpendiculars, i.e.

feet, and nominally l.

inches

high, i.e. x/L = i and X/H = Lo.

Actual wave dimensions as read from

*)The period of wave encounter ifl seconds.

The heaving forces at the front and rear dynamometers, the drag force

and the wave profile were recorded.

A photograph of the wave profile at a

side of the hull was taken and a mark on the recording tape indicated the

instant at wnich it was made.

The algebraic sum of forces recorded by

front and rear dynamometers gave the heaving force, and the algebraic

difference times the distance of dynaniometer attachments from midship

section gave the pitching moment.

Actually two or three runs were made at each speed, and the record

least distorted by noise, and corresponding to the most interesting

photograph was chosen for analysis.

LRS2

-3-records differed a little from these nominal discussions.

6 model speeds

were used as follows:

of.p.s.

vK/\/Lft

= o

0.97

1.07

u 7? =

0.80 l.L7

t' T? ti 0. 7

2.26

7'

" .6

0.67

2.92

3.32

't 7? 77

.8

t? 9

o.61

0. 8

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Prior to taking measurements of model forces, several runs weiSe iliade

to check the form and size of waves and to calibrate the resistance wire wave height gauge at rest and in motion. For this purpose, the gauge record obtained on the galvonometer tape was compared with the photograph

of the wave at a grid. Figures 3 and ì show the comparison of these

re-cords with each other and with theoretical wave profile. Under "theoretical"

here is meant the theory of wave of finite height with second order term,

which gives the profile hardly distinguishable from trochoidal.

The wave recorded by resistance wire gauge conforms well to the

theoretical wave profile. Th grid photograph discloses the existence of harmonics apparently generated at the edge of the grid plate meeting

the waves, but generally confirms the readings of the resistance gauge.

The grid was always stationary, but the resistance wire gauge was moving

with the carriage.

Results of Tests

To this date only four record tapes were read: at zero speed,

2.26

f.p.s. and two records at 3.32 ft/sec. The data obtained are shown

on Figures

_5,

7 and 5. The upper plot of each figure gives the positions of crests and troughs of undisturbed waves as they move along the length of

a ship. The other diagrams give heaving force, pitching moment and surging

force. The general appearance of the model at 3.32 ft/sec. is given on the photograph of Fig. 9, and Fig. 10 gives the enlargement of the actual size

used for measuring wave heights. Figure 11 gives the comparison of the wave at the side of a ship with undistorted sea waves and with the still water wave superposed onto undistorted sea waves.

The above material represents essentially the raw test data put in

the form convenient for comparison and examination. No detail analysis was made as yet to permit a thorough discussion of the various features of this data or of their signifIcance in determining the motions of a

ship, and only a few general comments can be offered at this time.

0f all data taken, the pitching moment appears to show the greatest

regularity. The maxima and minima occur with wave crests and troughs instantaneously located very near to 25% and _75% of the ship' s length, or with the

point

of maximum wave slope very close to the midship section. While the form of tank waves conforms closely to the theoretical form of

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Li-waves of finite he±ght (or trochoidal) and the wave period is quite uniform, there are observed fluctuations in the wave height. In

re-porting test data it is convenient therefore to define the pItching

mnent coefficient as

i/M

thZ,(

()

II

where M is the observed absolute value of maximum or minimum of pitching

moment in foot pounds

L

Displacement in pounts

L - Length between perpendiculars in feet

H - Wave height in feet -

Tr*tt-

7 (re4t

X - Wave length in feet

( H/X) is the maximum slope o a wave.

The wave height H in the present case cari be taken as the height measured from the wave trougíi or crest preceeding the particular peak

of the pitching moment to the one following it. The analysis of the-data

available on this basis gives the following results:

Run 11, zero speed - one crest and one trough, mean Cm = 0.260

Run 2L,

2.26 f.p.s.- u

.3li,

.292,

.322,

mean Cm 0.298

.263

Run

30, 3.32 f.p.s.-

Cm =

.283, .298, .335,

mean C =

.302

.268, .328

Run

32, 3.32 f.p.s.-

C = .295,

.317, .2i2,

mean Cm =

_.277

255

Eliminating two abnormally low points for mean C - .303

3.32

f.p.s.

i the Froude-Kr±loff hypothesis used heretofore by almost all

in-vestigators of ship motions, the forces and moments are assumed to be

caused only by the changes of displacement and the changes of pressure

gradient in undisturbed waves due to orbItal motion of water particles.

Under this assumption the forces and moments are independent of ship's

speed. D reality, the presence of a hull modifies the orbital motion

of water particles in the wave since they are now deflected and are

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forced to flow around the hull.

This in

turn modifies fluid velocities and pressures and makes them dependent on the speed of the ship. This

phenomenon is demonstrated by the increase of Cm witn speed as shown above.

The mathematical solution of such water flow in waves in the presence of a

hull has recently been published by Havelock - Ref. 2 - for a particular

case of a submerged elongated spheroid, and the change of the pitching

moment in waves of x/L = i from zero speed to VK/vLf of .90 is shown

to be of the saine order of magnitude - roughly about 20%. Havelock's

work ±ndicates that the amount and nature (increase or decrease) of the

change will depend on the wave length ratio x/L.

In the above discussion only the oscillatory amplitude of the pitching

moment was considered. In addition, there is a change of the mean moment

which on a free ship would cause a change of the mean trim around which

oscillations occur. These mean moments acting on the model were observed

to be:

u f0p.s + .10 foot-pounds

2.26 f.p.s. - .o8

3.32

f.p.s. - .2L and -.32 foot pounds

The drag forces (or surging forces) follow in regularity next to pitching

moment. They are exactly in phase With pitching moments and exhibit their maxima and minima at the same time. The form of the curve of surging force, however, unlike the curve of the pitching moment, deviates markedly

from the form of the wave which caused it. The mean values of the drag

due to waves were found to be:

O f.p.s. mean drag = .02 lbs.

2.26 f.p.s. t? _.l _lbs.

3.32 f.p.s. = .2 and .27 lbs.

The drag of the present model in smooth water is found from Ref. 8

to be .107 and .22 pounds at 2.26 and 3.32 f.p.s. respectively. Deducting

these figures, the added drag due to l." high waves acting on a restrained

model is found to be .0Li3 and .03 lbs. Deducting the smooth water drag from the drag of pitching and heaving model in l.25' waves given

in

Ref.

5,

gives the added drag as .1OC) and .090 pounds. If it is assumed that the

added drag is proportional to wave height, then the drag due to waves

acting on the restrained ship is seen to be about

1/3

of the total, and drag due to pitching and heaving about 2/Y of the total.

Id-25

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-6-The difference between the added wave drag of .0li3 and .03 pounds

can be considered to be well within the experimental error and the added

wave drag can be taken as independent of speed. This conclusion is in

accord with the theoretical calculat.Lons of Havelock (Ref. 3).

The heaving force appears to be extremely irregular and its form

deviates markedly from the form of the wave which caused it. In writing

the equations of motions for a ship it has been customary to indicate the

forcing functions on the right hand side as a simple harmonic function.

In reality even for a pitching moment it probably has to be written as

the sum of the first and second hax,nonics corresponding to the form of

simple sea wave. It appears that for the heaving force it has to be written as a more extended sum of several harmonics. The analysis of the

harionic content of heaving force curves, however, has not been made yet.

The only significant features, apart from irregularity, which can be

commented on are the change of phase and of amplitude with the change

of speed from zero to 2.26 or 3.32 ft.p.s. The maximum amplitude of the

force increases from the mean of l'os. at zero speed to the mean of

±l.0 at 2.2e and 3.32 f.p.s. This variation again is in accord with

Havelock's findings of Ref. 2, and represents the deviation from the

Froude-Kriloff hypothesis.

The heaving force is usually assumed to be at its maximum or minimum

when the wave crest or trough is at midship point, i.e. it is taken to be

900 _{in phase to the pitching moment.} A marked deviation from this is found on the record for zero speed on Fig. . The maxima or minima occur

consistently with the wave crest or trough about l% of ship length aft

of midship section, which represents an increase of pitch to heave phase

from 900 to

lLi5°.

At 2.26 and 3.32 f.p.s. this peculiarity seems to disappear.

The significance of the above heave phase shifts and of the irregularity of heave curves cannot be evaluated until computations are made of the

coupled pitch-heave motion.

Suggestion as to Further Activity

The test program initially contemplated for this investigation,and

approved by the H-7 panel of the SNAE, considered tests at three speeds

corresponding to V/Vt of 0, o.hL and 0.89 (or alternatively v/VL

= o.t

and 0.8),

at five wave lengths of x/L =

.7,

1.0, l.2, 1. and 1.7. The preliminary

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tests described in the present report were undertaken primárily in order

to check the instrumentation and the test procedure to be employed, and

to obtain a general idea of the action of forces and moments in relation

to the waves.

The test data at 6 speeds were obtained at x/L

1, but

the present progress report includes the data of only three of these

speeds, for which test tapes were read by this date.

A rather sudden

change of behavior of forces and moments is observed from O speed to the

next speed read at 2.26 ft/sec.

Better information as to tte nature of

the changes will become available when the tapes for speeds of 1.07 and

l.L7 f.2.s. are read.

Likewise the change from 2.26 to 3.32 f.p.s. is

too small in view of Havelock!s work cited.

It may have been shown to

be so small due to the accidental scatter of observation data.

This

question aguln will be answered when t.he available tes for the

inter-mediate speeds are read.

These observations point to the fact that the

specification of three speeds

in

the original test program was not practical,

and a series of tests at smaller speed intervals are necessary.

On the

other hand, the tests and reduction of the data were found to be more

laborious than expected and therefore it is not considered practical or

expedient to suggest the enlargiient of the program.

_{Instead, it is}

suggested to curtail the test program in favor of a more thorou-i coverage

of a smaller program.

To be specific, it is suggested that tank tests

already conducted on the preJJininary program at six speeds at

one wave

length be accepted as sufficient fthe present, and that the remaining

funds be directed to a more complete analysis of this data as further

described below.

Under the "analyss' above is meant the trial application of

ex-peru.mentally founo. exctng functions to the ecations of ship motion

n

order to determine the effect of observed peculiarities of these functions.

it has been already nentioned that pitching moments exhibited

_{a fair}

regularity, and therefore the uncoupled pitching motion can be expected

to be correspondingly regular.

_{The crucial quat ions, theréfore, is to}

what extent this pitching motion is modified by coupling with the heaving

motion caused by irrugular heaving forces.

The analysis will consist,

therefore, in comparing the pitching motion due to observed pitching

moments alone with the pitching motion resulting from the two node

pitch-heave oscillation with the observed irregular heaving forces.

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-8-

-9-The limited financing of the present investigation does not permit

a general thorough investigation of ship motions, and will require the

use of drastic simplifying assumptions in the setup of equations. In

line with previous theoretical work - such as References 3 and ¿ - these

will be assumed to be linear, although the computational work of

References and 6 shows that large deviations from linearity can be

expected. The virtual masses will be assumed to be such as to give

the observed natural frequencie in pitch and heave, and the damping

coefficients will be suitably estimated. The stress will be put. entirely

on the effect of the coupling of pitch and heave and on the form of

forcing functions. On the basis of the aircraft experience, it will be assumed that the effect of surging on pitcning motion is negligible

and only the effect of coupled neaving on pitching motion will be

in-vestigated. The observed exciting functions will be approximated by

summations of simple harmonic functions.

The investigations of the behavior of the DThIB Series 60 models in

waves is distributed between D113, IT and ETT, and parallel work is

also believed to be done at Newport News. Conceivably it will be desired

to describe all these investigations in a single paper. It is believed that in such an eventuality the theoretically slanted research at ETT,

in the inodif led form suggested above, will blend best with the experimental

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Ref erenc es

3. V. Korvin-Kroukovsky, "Forces and Moments Imposed on aSh1p by

Waves," ETT Note No. 2)49, September 1953.

Ivllnutes of the meeting of the H-7 panel of the SNAE held on 26 October 1953 at Hoboken,

N.J0

Thomas H. Havelock, "The Forces on a Submerged Bor Moving Under

Waves," Institution of Naval Architects, Transactions January 195)4.

)4. G. Weinblum and M. St. Denis, "On the Motions of Ships at Sea,"

Transactions SNAME, 1950.

M. St. Denis, "On SustaThed Sea Speed," Transactions SNAME, 1951.

H. L. Hazen and P0 T. Nims, "Calculation of Motion and Stresses of

a Pitching and Heaving Ship," SNAME Vol. 118, ₁₉₎₁₀ _{pp. 9)4-113.} Adm±ralty Ship Welding Committee Report No. 118, "s.S. Ocean Vulcan