Notes on ship model testing in transient waves

DEPARTMENT OF THE NAVY

NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER WASHINGTON, D. C. 20007

NOTES ON SHIP MODEL TESTING IN TRAN ENT WAVES

by

Alvin Gersten

and

Robert J. JohnsOn

Thjs document has been approved for public release and sale; its

distri-bution is unlimited.

TABLE OF CONTENT

DETAILS OF TRANSIENT WAVE PROGRAMS AND. TRANSFER FUNCTION OF

WAVEMAKER

VARIATION OF TRANSIENT WAVE TRANSFORMS WITH TANK LOCATION COMPARISON OF TRANSFER FUNCTIONS OBTAINED IN SEVERAL TRANSIENT WAVE SYSTEMS AND IN REGULAR WAVES

EFFECT OF SAMPLING RATE ON TRANSFORMS

REFERENCES

LIST, OF FIGURES

Page

- Body Plan of Series 60, Cb = 0.60 Parent 5

- Impulse TOwing Strut 6

- Time Histories of Waveaker Control Signals 9

- Spectra of Wavemaker Control Signals . . . . 11

- Transient Wave Height Spectra for Programs A, B, and C Obtained by Averaging Results at Several Locations in

the Taflk ,. 13

- Normalized Transfer Function of Hydraulic Actuator

Wavemakér System 14

- Time Histories of Waves from Program A at Several

Locations in Tank . . 16

Spectra for Transient Waves Measured at Several Distances

fromWavemaker . 17

Sample of Strip Chart Records Obtained during Tests with

the Model . . 21

Figure 10 - ComparisOns of Transient Wave Spectra Derived from

Measurements Made on the Carriage. and in the Far

Field 22 ii Page Figure 1 Figure .2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 . ABSTRACT 1 ADMINISTRATIVE INFORMATION 1 INTRODUCTION . 1

DESCRIPTION OF MODEL AND TEST EQUIPMENT 3

TEST PROGRAM AND PROCEDURE .

. .: 8 10 12 24 38 42

Table 1. - Particulars of Series 60, 0.60 Block Coefficient Parent Form

1]1

Page 26 28 30 32.

Figure .l Comparison of. MOtion Transfer Functions Obtained frOm

'tests in Transient and Regular Waves at Zero Speed

Figure 12 - Comparison of Motion Transfer Functions Obtaine4 from Tests in Tiansient and Regular Waves at a Froude Number of 0.15

Figure 13 - Comparison of Motion Transfer Functions Obtained from Tests in Transient and Regular Waves a a Froude

Number of 0.25

Figure 14 - Comparison of Motion Transfer Functions Obtained from Tests in Transient and Regular Waves at a Froude Number of 0.30

Figure 15 - Comparison of Motion Transfer Functions Obtained from Tests in Transient and Regular Waves at a FrOude

Number of 0.35

Figure 16 - Fourier Transform of a Rectangular Pulse as Computed on the IBM 7090 Digital Computer

Figure 17 - Effect of Sampling Rate on the Accuracy of Transient

Wave Transforms

34

37

ABSTRACT:

Ship model eperiments Were conducted to evaluate the accuracy of motion transfer functions obtained by means Of the transient wave technique Since such an evaluation was especially needed for higher ship speeds, Froude numbers up to 0.35 were investigated. Also studied as the

feasi-bility of measuring the incoming wave train far ahead of the

model, where distortion of the fOrcing function by

mode],-generated waves cannot occur. Further, in the interest of

reducing computer usage time, the effect of sampling rate on the analysis of analog signals obtained during transient

wave tests 'was examined. Results: are also presented which

demonstrate a need for smoothing the Y'raw" spectra obtained

from the coinpuation of Fourier transformations, in order to

provide consistently usefUl' transfer functions.

ADMINISTRATIVE INFORMATION

The study reported herein is part of an extensive development pro-.

gram requested by the Naval Ship Systems command in. letter. Serial 341B-.l16

of 1 August 1963. It was funded under Task 0100 of Project S-R009 .01 01..

INTRODUCTION

1*

in. l9.64 Davis and Zarnick introduced to the field of seaworthiness

they concept of employing transient water waves in the towing tank to Obtain

the frequency response . thracteristics of ship motions. Their principal

goal was to. reduce the number of tests required to characterize a model

from that necessary. .when testing in. regular. (periodic) waves. Since a

transient. wave train contains energy distributed 'over a wide range of fre-quencies, a single run in transient waves can 'permit. definition of the en-tire frequency response; jn contrast, only one point on the. response function

(at a single frequency) js. btained by making a pass through regular waves. They developed the testing and analysis techniques for transient head waves

by conducting .model ,eperiments on Mariner,' Series 60., and aircraft carrier

*

forms at Froude. numbers (F) rangingfrom 0 t.o 0.14. The transfer functions

of

pitch and heave were found to agree closely with those obtained from

regular wave tests

The data obtained in regular waves were utilized as a standard for accuracy since the inputs and responses are not compressed into a short time period and the data superimposed, aS- in the -case of a transient input.

Accurate resolution

of

transient signals into their frequency components places stringent demands-on the recordingand-analysis.systems. _Especially

good agreement was found in the heave to pitch ratio derived from records

obtainedin the two types of wave systems. This was because obtaining this ratio does not require measurement of the wave forcing function _Accurate delineation of the waves exciting the model proved to be difficult _since

measurements of the wavôs. cOming-from ahead were corrupted by waves

gen-erated by the pitching and heaving model and by some reflections from the

beach directly opposite the wavémaker. It was also believed that

non-linearities might be associaté.- with the water dynamics and/or the wave

measurement. - -

-Davis and Zarnick also provided an original contribution to the

general field of linear systems analysis in that they proposed and _justified the utilization of transient excitations which are a linear frequency

sweep rather thai those which approximate an impulse. _{There are several}

advantages to their proposal. --First,- when the _{transient is lengthened, the}

severe concentration Of information over a short time span is relaxed aid.

so, therefore, is the- Jrequ-irement for extremely piec1se iñStithtientation-:

In addition, the very high: frequency content 'of--an

_impulse

_{is'not' present}

and so the .model is not vibrated at its structural natural. frequency. Such.

structural vibration would, in turn, excite traflducers.at their _natural

-frequencies.

_an

introduce "noise", into the meäsu'ed signals. _{A third}

ad-vantage is. the avoidance, of. nonlinear model 'and water behavioi that can

occur with a-high-wave. _{And-finally; -the difficul-trequ.irement of meeting}

the waves exactly at their point of coalescence is obviated.

-The purpose of this paper is -to report _{some recent findings on}

test-ing in transient waves. _{The present writers have conducted -experiments on}

than have been investigated heretofore, so tha the accuracy of the

transient technique:could be checked thore extensively. As mentioned above,

Reference 1 reported difficulty i'n measuring the wave forcing function 'undistOrted by nibdel-generated waves, even when the wave p±obê' ià.'thounted

on the carriage approximately 15 ft forward of the bow of the model The

present study :evaluated -'the practicability of measuring the waves fa a],ead

of the model.. This approach was considered since wave theory indicates

that the magnitu4e of he wave transform is independent of 'where the

theasurethent is ijiade along the direction Of w.Ve travel. 'Motion transfè±

-functions obtained by utilizing wave records made ditectly .ahead of the

model are compared with those in the far field

*

Another area investigated

is the effect of iampling rate, on the calculation of Fourier transforms

for the type'of zimhist.oy gererated by traflsient wave tests.

DESCRIPTION OF MODEL AND TEST EQUIPMENT

The rnodel,used- for this study was a Series '60,: Block 0.60 form. Table 1 lists the particulars of this vessel., and Figure l.shows the body

plan. .

The model was towed and guided by the "impulse towing' strut". (ITS).

shown in Figure 2.. This apparatus is designed to permit model-responses

in five degrees' of freedom (yaw is completely restrained) and-the

appli-cation. of atow force at the., center of gravity. Restoring forces in:surge

and sway are provided by springs. All restraints on the model due to

tow-ing and guidance can be measured;- heave, surge, ad sway' forces are sensed by differential reluctance. block gages, and 'yaw restraint by a

strain-gaged flexure. Since towing gear inertias and frictions are included in

the force measurement., corrections: for..their effect on the motions can be

made. Unrealist-ically large surging motion occurs f the frequency of wave

encounter is -close to the natural frequency in, surge of-. the vibratory

system consisting of model, towing gear, and springs. Because of

cross-coupling between motions, the pitch and heave become erratic.

Sonic-type wave probes were used since they do not physically contact

the water surface.

3

TABLE ].

Particulars of Series 60, 0.60 Block Coefficient Parent Form

In the present series of tests, the surge spring stiffness was quite

small,*

and so the natural period in surge was appreciably longer than the

longest period of wave encounter. As a result, the surge was kept within

proper bounds, and pitch and heave, uncorrected for restraints, were in good agreement with results obtained previously at this Center and at other

towing tanks. It should be noted that the present results for both

tran-sient and regular wave tests are not corrected for restraints since the corrections do not appear to be significant for head seas. This is es-pecially true here because our principal goal is not the accurate

character-ization of the motions of a ship but rather the comparison of two test

pro-cedures (transient wave and regular wave) both of which were executed with

the same towing apparatus. The sway and yaw restraints during these head

seas tests were extremely small as was the heave restraint due to heave

staff friction and inertia. The motions were measured by means of

film-type potentiometers. The pitch and roll potentiometers are driven by gears

*The

spring constant for each of the two surge springs was 7 lb/in, this yielded a total restoring force of 14 lb/in, at the point of-spring

attachment. _{The effective spring constant at the model,- however, was only}

3.5 lb/in.

4

Item Model Ship

Length. between perpendiculars (LBP) ft 10.0 400.0

Beam, ft 1.33 53.33

Draft, ft 0.53 2i.33

Displacement 266.3 lb FW7,807.0 Ltons SW

Longitudinal center of buoyancy

aft of as percent of LBP . 5

'

1 5 Distance of vertical center of

gravity below waterline, ft 04 1 76

Radius of gyration 0.25 LBP 0.25 LBP

i4.

A

11111

&

fiIi1FIIIIIII

Li111II'

liii

16

_III

%II1IIIII 1111

6

7/

loj/J

BUTT 0.25 0.25 BUTT -. 0.075 0.075

Figure 1 Body Plan of Series 60, C = 0.60 Parent

1 .5OWL 1.25 WL 1 .00WL 0. 75WL 0.50WL 0.25WL 0.075WL

Mounting Plate on Carriage Upper Gimbal Assembly

/

Sway Axis Note: Length 121_ltl to

of Gimbals with Heave Staff in Mid-Position

IrI

Spring for Surge Restoring Force

IIi

Upper Section

Lower Section

Figure 2 - Impulse Towing Strut

Surge Axis ..-Heave Staff

ii

Yaw Flexure

-Ii']

FI.

ILthiI

Pitch Axis Roll Axis 6 Ball Bearings

Surge Force Gage

Side Force Gage Heave Force Gage

U-4

w

Lower Gimbal Assembly

mounted on the shafts of the lower gimbal, whereas the surge and sway

p0-tentiometers are activated by the shafts of a gimbal .supporting the top of

the tubular strut. Utilization of the ITS simplifies the conduct of a,test

(as compared to the effort required to test a more freely runnthg model)

because no propulsion and steering systems need be installed and operated.

The experiments were carried out at this Center. in the Harold B.

Saunders Maneuvering and Seakeeping Basin (MASK); it is a rectangular tank

360 ft long by 240 ft wide by 20 ft deep. The facility is equipped with a

bank of eight electrohydraulic servosystems which control the flow of air to domes along the shorter side of the tank. The air travels through the domes, impinges on the water surface, and causes the formation of waves which progress away from the source. Regular waves can be generated by employing the electrical signal from a sine-wave generator to drive the

-sCrvosystöms. If long-crested transient or random waves are desired,

signals from magnetic tape programs are employed to control the

servO-systems. Fixed-bar trpe, cohcrete wave absorbers are installed along the

wall opposite the wavemaker. These aborb approximately 95 percent of the

incident wave energy for the range of wavelengths of primary interest, äl-though there is some variation in absorptivity which is dependent upon wave

steepness.

The transducer signals were amplified and, recorded on three devices:

a Sanboth strip chart recorder, analog magnetic tape, and digitalmagnetic

tape. Ahalog to digital conversion was performed by a digital data

ac-quisition system (DIDAS) during the course of each run. The signals to be digitized were not affected by either alternative recording device but were transmitted directly to DIDAS where they were passed through a l0-cps low-pass filter andthen sampled. This was done because of the desirability of bypassing the analog tape recorder which is less accurate than the DIDAS

system. DIDAS can digitize an analog signal at various rates up to 6000

points/sec For a majority of the analyses performed in this investigation, a sampling rate of 125 samples/channel/sec was used. This selection was

.2

based on the finding of Smith and Cummins that the above rate should be

used to achieve, a maximum difference of 1 percent between the "exact"

spectrum (based on a sampling rate of 6000/channel/sec) and the approximate

spectrum. Computation of the transforms and transfer functions was

per-formed on the IBM 7090 digital computer. 7

TEST PROGRAM AND PROCEDURE

Experiments were.first conducted in regu]ar head waves to obtain the

motion transfer functions by meafls of a tried and proven method. These

results were needed to provide a basis for evaluating the reliability of

the transient technique:. Wave length to ship length ratios ranging from

0.75 to 2.0 were utilized in increments of 0.25. The spee4s investigated

corresponded to Froude numbers (F) ranging from 0 to 0.35 in inqements of

0.05. As is often the case when tests are run in regular waves, lack of

funds and time precluded taking data over a wider range of frequencies and

for.a closer frequency spacing.

*

Three different wave programs were used for the transient wave tests.

All of these are comprised of a frequency. sweep which is a linear function

of total elapsed time and which starts at high frequencies (short waves) and proceeds towards low frequencies (long waves). The highest frequency is nominally 1.0 cps since this is usually the highest frequency of

im-portance for seaworthiness model tests. A linear frequency sweep leads to

coalescence of the waves at one point in the tank.; that is, the later

generated long waves catch up to the short ones, and they all merge to form

one large wave. _{As discussed previously, each run was conducted so as to}

avoid a meeting of waves and model at the point of wave coalescence. It can be seen in Figure 3 that one of the wavemaker control programs consists of a signal which has constant amplitude for all frequencies; the other two

initially decrease in amplitude as the frequency is decreased, and then

in-crease in amplitude with further dein-crease in frequency. _{The manipulation}

of amplitudes was performed to produce a water wave system which is

character-ized by a flat spectrum for the frequency range of interest. _{This is}

de-sirable because it helps maintain a good. signal-to-noise ratio in the

measured responses. It was known that the frequency response of the

wave-maker was not flat and, in fact, reached a peak. in the 0.4- to 0.5-cps

fre-quency range.3 Since the spectrum of the control signal is multiplied by the frequency response .f the linear system (wavemaker) through which

* .

.

These programs were developed by Davis and Zarnick.

0 .1 4J 0

I,

$

I'S

4

V

4Sec.ul

1.1-Program C _Time

Figure 3 - Time Histories of Wavemaker Control Signals

Program B 4 I 0

ii

I Program A S I p a

the signal passes, it was attempted to provide a control signal with a transform magnitude inversely proportional to the magnitude of the

wave-maker transfer function.

During the model tests in transient waves, one sonic wave probe was

'attached to the carriage, at a point 21 ft directly forward of the model

center of gravity, and traveled down the tank with the model. .A second probe was attached to the bridge which spans the basin and supports the

carriage. This stationary probe was 'lOcated at a point 94 ft from the

wavemaker dome and approximately 15 ft. off the line of travel of the model.

The model speeds investigated were the same as specified above for the

tests in regular waves. After the first waves were emitted from the

wave-maker, the model was accelerated in calm water to the desired speed; it then passed through the wave train and proëeeded in calm water again. When wave measurements were made along the centerline of the tank to determine

the variation of the wave transform with distance from the wavemaker, two sonic probes were mounte4 40 ft apart on the carriage; by locating the

carriage at two points in the basin, it was possible to make records 132,,

172, 222, and 262 ft from the wavemaker. No attempt was made to measure

the waves closer than. 132 ft from the source because the longer waves

(maximum wave length was 120 ft) may nothave formed completely at those

locations.

DETAILS OF TRANSIENT WAVE PROGRAMS AND TRANSFER FUNCTION OF WAVEMAKER

The magnitude of the Fourier transfo±m of the wavemaker control

signals is given in Figure 4. The spectra reveal quite clearly that the

signal for Program A is constant in amplitude whereas the signal for Program C has a decided minimum amplitude at approximately 0.45 cps. _It should be noted for future reference that even when the spectrum js flat, as in Figure 4a, a jaggedness is superposed on the principal shape.

In Reference 3, Davis presents. the transfer functionM the 'MASK wavemaker which was obtained by the generation and measurement of regular

waves. _{This frequency response function was used iii the process Of making}

up the control signals. To ascertain the shape of the wave spectra

1.0 0.8 .0.6 0.4 0.2 0 Figure 4a Figure 4b Frequency in cycles/sec Figure 4c

Figure 4 - Spectra of Wavemaker Control Signals

11 Program B A

j/\

1

JSp1tng

_---62.

s Semplee 125 Samples Samples Per I Rate Per Per Second Second Second I I J .1 - Program C 1.0 0.8 0.6 0.4 0.2 0 1.0 0.8 0.6 0.4 0.2

generated by Programs A, B, and C, wave measurements were made at several

locations in the basin, and. average, spectra were computed (see Figure 5).

Amplitude adjustment in the Program C control signal to achieve a flat wave spectrum was, to a large degree, successful; however, there is some room

for further improvement. Where no attempt is made to account for the

wave-maker frequency response, as:in Program A, the wave spectrum is relatively

narrow band and has a pronounced peak. To provide an additional measure

of the wavemaker transfer function., the contLrol signal transforms were divided into those of the water' waves for corresponding wave programs and

frequencies. The three transfer' functions obtained differed somewhat (these

are not presented here), but it must be remembered that the wave transforms themselves are averages and vary with distance from the wavemaker. An

'average wavemaker frequency response function is plotted in Figure 6. To

some extent, this function was different in shape from the one obtained in regular waves; however, it did peak at approximately the same frequency

(0.4 cps from transient waves, as compared to 0.45 cps from regular wave.$).

Because of the distinct maximum and minimum in the transfer function, it requires 5.5 times as large an excitation to generate the same wave height

at 0.9 cps as at 0.4 cps.

VARIATION OF TRANSIENT WAVE TRANSFORMS WITh TANK LOCATION

According to linearized wave theory, the magnitude ofthe'wave trans-form should be invariant if the time history of a transient wave packet is measured at various points along its direction of travel. Supposedly, the energy content of the waves is not altered as they progress away from the'

wave, source. The phase of the trarsforni does, of course, change; it lags

by where w is the: frequènçy of a particular wave component,

x is the distance between measuring poLits, and' g; is the acceleration due

to gravity. If indeed, the magnitude of the wave transform were constant,

*

This was necessarybecause. the spectra vaxywith location of the wave

train in the tank. See the next section for details.

Figure 5a Program B Figure 5b 13

Frequency in cycles/sec

Figure 5c

Figure 5 - Transient Wave Height Spectra for Programs A, B, and C Obtaine4 by

Averaging Results at. Several Locations in the Tank

;omc

1.0

0.8

0.6

0.4

0.2

1.0

0.8

0.6

0.4

0.2

0 Program A

//

0

0.8

0.6

0.4

0.2

0

1.0 0.8 0.6 0.4 0.2 0 0 0.2 14 L

3 Ft. - 16 In. Dome Configuration Measured Sept 1966

04

06

08

1.0

12

1.4

Frequency in cycles/sec

Figure 6 - Normalized Transfer Function of Hydraulic Actuator Wavemaker System

it would be possible to measure the wave input at a great distance forward of the model, away from the influence of model-generated waves, and to use the transform of this uncorrupted time function to compute motion transfer

functions.

As a check on this hypothesis, measurements of the t-ransient waves

were made at several locations in the tank along the direction of wave

travel. It can be seen from the samples of the records presented in Figure

7 that the time histories vary considerably with tank location. At 132 ft from the wavemaker, the waves are almost coalesced. _{Gradually, the longer} waves overtake the shorter ones and produce a dispersed wave pattern at

262 ft. Although the wave transfOrms for a particular program (see Figure

8) do notdife

_{as much as the time functions, they are certainly not}

constant. _{Among the.characteristics eyident in Figure 8 is a tendency for}

the wave amplitudes at frequencies close to that _{of maxiflium amplitude to}

increase with distance from the waveinaker.

One possible explanation for this is as follows. _{It is known that}

wave energy is propagated towards the sides of the tank by the waveinaking

units at both ends of the wavemaker bank. _{When reflected back toward the} center of the basin, this energy would not be detected by _{a transducer} located on the longitudinal centerline of the tank and _{close to the point} of wave origin, but it cold impinge. on _{a probe farther away from the wave}

source. _{The.waves reflected by the long beach and the dome of the long}

bank of wavemakers may besüfficiently high (especiai-ly _{since the dome} tends to act as a resonator) to cause the seemingly anomalous increase of wave amplitude (shown in Figure 8) by superposing on the _{waves traveling}

directly down-tank. _{The differences in wave amplitude at the low and high}

frequency ends of the spectra are not as pronounced as they are near the peaks; however, there is an indication in Figure 8c _{that the energy at the} high frequencies tends to decrease with _{istance from te wavemaker. Waves} propagating through a fluid and not acted upon by outside forces, such as wind, will normally lose energy because _{of visóous dissipation.}

A further examination of the practicability _{of utilizing far-field} wave measurements for computing motion transfer functions _{was implemented} by mounting a fixed wave probe 94 ft from _{the wavemaker and 15 ft off the}

)IUB.L Ut SUOt3O T19AQS

'

ui2o.i

woj;

SOABM

O SQtIO3SH 9WU - L

uoivaszd 30

3UTUAUOO 103

UJfl UT P3T4B uaaq Aq Sp10O1 OABM a9j

°°N

aj3S aWfl.<

ll UIhffiWWfflIHlIWi Ill IIHllI 1lltIllIWIllI1i flU.11llhIIII1ll1llhlII!ItUIl llflDflhIii$HfflJ

OIdIIOUIBHIIIIIIII VIII WIIIE

I III _!IIi

-UT c1

t

ak ru

.; ... --n- - --n--ii h4...,.. ... .. ,. I-J,.. I I

I________

iL'

IVNII UnIIiiIIIfflIIIIIIII illi IhiiTIImIik thIIIIlINIIIhtttI1IUIIIVIVhI'llI Vi -;ii i IWIi I "N--.!IVVI -UT

'cz

1O)WWOAM W013 ia zzz IV . Ii . j

9Itr I

ii II II I 1111 II I II JIIIII I 1aBWeAeM tU013 ZLT uT

cz

T

I.r:.c:!.- 1=

1ff g-.--:a.--r

1avwaeLt w013

iJIir IllIlImlin -HI UHIIIP'. ...,. ,3II --. ., .--.--.. .. - nU-.-.- --iii

Figure 8 - Spectra for Transient Waves Measured at Several

- Distances from Wavemaker

17 / - -- 172 Ft. from Wavemaker Wavernaker Wavemaker 222. Ft. fran 262 Ft.. froni

/I

f

Ii

(I\:

--I , - - -- -..

.--

- - -,

J/

V

'-J

0.4 0.8

₁₂

1.6 Frequency -th cyCles/sec Figure 8a - Program A 6 U 1.I

J4

2

132 Ft. from Wavemake 172 Ft. from WäveTnaker 0.8 Frequency in cycles/sec

Figure 81 - Program B

18

6 4 0 0 19 I. '132 rt. from Wavernaker 172 Ft. from Wavernaker 222 Ft. from Wàvemaker 262 Ft. ftOm Jaemaker

-J

7v)\\I\.

/

L

-04

08

12

1.6

Frequency in cyclés/sèc

Figure 8c - Program C

tank centerline and a second probe on the towing carriage 21 ft forward of

the model center of gravity. Here again, the wave records,obta-ined at the

two locations are different (see Figure 9,) not only because of the spatial

separation of the transducers but also because one measurement (far field)

was made at.. the wave frequency while the other (carriage) includes the

Doppler shift on frequencies due to motion of the transducer (so-called

frequency of encounter The digitized wave records from the. fixed

probe were used to compute Fourier transforms in the wave fre4uehcy domain. These were then converted to the frequency of eicounter domain4 by

calcu-lating f from . . .

e

2.

= 2r f

e g

where f is the. wave frequency and v is"the. model. speed, and multiplying the ordinates of the spectrum. by the Jacobian.

1

i/l - 4cL

e 2rrfv

where = - e The modified ordinates were then plotted at the

fre-e g .. -.,

-quency of enc'ounterderived from the applicable wave fre4uency. Figure 10

compares the converted transforms with those obtained from the moving

probe. It can be seen that although they are in fairly good agreement and

have the same general..shape., the differences in detail are by no means

negligible. The curves in Figures lOb-lOd are for speeds at which no

model-generated waves should reach the wave probe. Nevertheless, the

dis-agreement between the two. curves in each of these figures is the same

order of magnitude as the disparity between the curves in Figure lOa; at

that speed, according to Reference 1,. significant wave energy can reach

the probe from the model. This would indicate that there is, in general,

no increase in accuracy to be obtained by measuring the wave forcing

function far away from the model to avoid model-generated waves. However,

for certain types of tests (e.g., those carried out with a radio-controlled

model in which signals are telemetered to shore) there may be no platform.

moving with the model on which a wave probe could bö mounted, and it may

T3POW

93

42TM

SSQj

dtl2S

S1ø3j

pouqo

ur1np

O QtdWBS 6

in2j

u

paps

uaaq

seti

aqoid

pT;-1e;

eu wo

poe.2

aôt

aq

:eoN

J 1.4. I T T IIll111H11hIHI111IlIlHfIirlx:lrIIluI!IIIkJlIl:I11flvrIlIflhIIIIlI11l11VIflhIWHHul11rn11lUlH11ThqIlIllThIIIfl III l.!1PIU U.11111111 . Iii 1 VU 'I 'II v.111111 III

II

4. . L 1111 I . HWIHtlHItHlVI

-

Iu IHImIIII5!HIIflhJ11

IlHIVl

1111IB11H111111II1I -. WF J11i1lI I1D1M1II

IHP'11W'

1hI11l11P11th11114lfltflll ILfflhIll)qr I ulll,ItmuLIIturnIIIuI11mnhIIn

T

1111 3 rt1l11ISlIIII.l 1...1101011 k.l1II11110tll1Il1fllF1lLIt1llhIlfihlI11 iB0ILlQIll ill

III

110U11III S S1VIS1nAHhlluIIiII1ISWvILl11lVbiIIIIfl1lTllhjllhIfflhIIS11 'IS011UUii15iI0IUiIIDIWIB5l11ffiJHflIIlIl11J11hI5Ill1111

T

lIiiIlIiII1illIlIIIl11II1IflIllIlIIlIIlt11I1flIUIIItt0I11 11IS!011III'lII1IlI1Vl9l11aIIEUfl1U'lt0IIllhIllISm11hIHIlllL11J1JS

aqolj

a2st.z13

2UI 40W !tIIIIFUIHIIIIl1!IIIIIIIJ0iV11II1I1ilIllISfl1I1IHIlI1UIH1I11hj11Iffll11jlI11IH -

ut

ç --

qT

H ASM II iI Ml I I! III 11r ,I,,.ltflIIII .IIImII: III,IIIIII.IIIIilIIIIrnII.IuHIIImIIIlII.uIIlvh.vvw.IjtII:II,wmfflIwIntm4..u3.lrnr..,ItItmItm till HIilflItmI 1 ilhhIlill UIlItIhltI mtmI

I

10 '1l'I1h 111111 IIIII II. IlIHlIIllIIIil dill 11lIIIlVIIII ..l11HIIIfllIlIIIVh

T5.11

-' - Fl 1

5I!

5Iqq1IflIIj1 111111111511 L I11I'lI1'UIIIIl'lIIhII11Hll1 VIOl SVBIH1Ul11V11ll11HflSIIVIVIflIfl5fl11SH5Hfl55ffljffl I 1 I I 5! '1111 SI hIlilill IlIVIlIlIlIlIHI I IgflSWIII1lIIIHStl1lISlIHflIfl1fflIVIlIIVIl0flI11IIfllIII511 VIII I 1 .1 0I1III! Ill I lI'IIUIIIlIIIlHffiI VIuSrIltII.IzlVIst9nVIIII11umVwsISimoSlloIVI a S

III I III III Li,IVllIUIhilhlIIVhIVlO1111NIISVI0IIIIl5 115t IITIILIT11111I5I 11511111 I F' dl m 0V z UT

" 111111111111101 I4IIIIUIIIIIHJIIIIfl .IllIHHJIl1IH .L V JIHISE!

Ili

4 I allIllill I 1111111 IIIIIIP1IIIUHIIIIIIIIIIP6,1I uPIIIIIhIilIlIIflIWI11ilV11H0IHP SflhIVt I ..iIII'II II11I1ftJIIifflSVIIlflV11l110mIl99tSIIVIVSS10I5JI11lI0II0u11III1IIh11i

-

u11155 I k Iii I i IiiIl,lh 51111 IIIPlh I DIII' ii IllS 11111 'III ID 1111111 1111I11,'MIIIID'U1111191111I1 11111111151I5111 1115155

IllII

IVIIFI IS 11" 10 0III111J1 'II "i,15111 1111111 IIDIIIL' 1111111 ' 111101 911101111111 IIIlPiiIIll!lIIIll 'S

'

11.50511111 511 15lflh1lIIIItVI15'd5VI11I11uJHfl511I!Ih II l I I !I11'I'i 111111111 Iii .5IIIklIIIllIIIIIIDmV5I11IVJ11ljIflV511II9I5 1101111111111 0 11Sl1I1I11I1 l'1111flI111115IIIVIIIHII11h1V5I11hIII5IIt11IlIjI11ffih110jIlIIIHII 1111-hI I I l 101 111111II1111 I I SIll '1111111111111115111111111111111111 fl II11'I T'11101lIpF'IIOSV11IIHIIIIIVVIII11IHIIIISVIVVS11IMIHIIIVIV 11&W1l'lT111I I ,- dç F P P II 11191111111 ii' IUIIIIIIIIPIIIIIOIHOSI 011111 r liii II' Si it I .W' tllD'IIIIOIOIH111111ISVIIIHSVVIIIIHIIRVVSIII11MV11 t-& 11111

ut

111 11111 II 'II lIlII1111,5Il5d-,11 II .'I V-I 4.Ir IIO1III1111111UIOHIHVIII11IHDI11III,11115h15115J1_ill1.,51.!IHI I 511111110111 I

'III IIIIIDII1IIIIIIIIIIIIIII1I1 PUID'IIIII _dlip IIIIISIIIIIIIIIIIIIIIIIIIII!I 11 _I'19111111

.1,0 JI1IIIIDVIIIVIIIIIIDIIIVIIIUIIJ 1I11111111I1111111111111111111h101111111111151111 OIl . I P 1 I_I l 11111 Ill 9111IIW'ilIlIIIIVIIIIIII 111111111110 Ii iLlIllIl III 1 lU I -1' liIIiIIIVllIIIIlIlD II11JLIIOIIII1IIIIIIIIVO 5115I11t1115V111111I11111111110h1111111h111h1IV10111111111111111011111 '11,1

Ill

r I'd Ill 1111 ?UIlIiILIIIIISII OIl11VAlh9IIITlf.vtflfflOI r'llttlIllhIn IllDIlHJh4ftlllI11l0llV15llHlfflOIflfflI15rhlIHIfllfllIIIflIl11h1lfl1l11hIflOIUS11SIIVII15 I I II 1111111 Oh 1111111111111111111 III .111511,15 .1 1 1 01111 1111111111 IRIk"dfflhIh 'W01lII1" .11111101 i I, IDI1P.1lIiil*I1111111111h1111OIJI,mIS0I1111I11hIIVnSOF51l1511j11l111lI11115fl11fllfl0511 I III 10511I1101111110115151111111111151111IIIW

}

!IIIIIDSIIIDL, IlI.IIIIIIIIV01I,11101111111111 11111111111 1' T I1D1VIIIIPIIIIVII 'IVIi011rI11IIOIIIIIOI111111IS11IIIOIOOIOI1MIIIMII11 II I 1 I 1 1111111 l.IHlIVHl11Illirulr 10 VflI11,lI"I155I?' . rr'IJIV1i I11IIIL51IVOIPIIIDIIIIIVIHIIDVIIDIDDIIIIIIOIU

1.l3td 55i!lI...IIlIFi!i5.IIIPpl..:hliI!IIfflIIiIIiIDP!IHII9I!!!Dff

ü'55"5I

I IIiiihh -l'=- Z

I

2ap

Iz

IIllIIIII1Il1ilIIll111hIliJI S 1 3 HIUS'l11I11VUU1VlIIIII 1 . IIUIIIIIIIIHIflhIIIIIli I I111111111111151111111II111111h111111!i IIIIIIiIllI11IIh.i11I' 1 Ii 3OO T

t

I I

L1OtS

qtaH

aABM

Figure 10 Comparisons of Transient Wave Spectra Derived from Measurements Made on the Carriage and in the Far-Field

0.6 00 3.0 2.4 0.6 0 0 -0.4 0.8 1.2

Frequency 'in cycles/sec

Figure lOa -' Wave Probe Speed = 0 Knots,IProgram A 1.. -S. 22 2.0 .1': Moving Carriage Probe Stationary' Far-Field Probe -1L

Ai

I:

:1

16

0.4

08

12

Frequency in cycles/sec

4

00 _0.4 0.8 1.2

23

2Q

0 0.4 0 8 1.2 i.6 2.0

Frequency ii. cycles/sec

Figure lOd -_ Wave. Probe -Speed = 3.72 Knots,

Program B ____I'_ .

I

-I -Carriage -Moving Stationary Far-Field -Próbé Probe. -. --

f\j.

- . ..-Il-I-. . :- . \ 1.8

Figure lOc - Wave Probe Spee4 _{= 2.65 KnOts,}

Program B U U -a

_I,..

I',

U '-I -I E o _0.6 a a

I'

I'

I, -I ' I

therefore be necessary to make wave measurements far ahead of the model. The results presented above and in the next section of this report Show that reasonably accurate motion trnfer functions can be obtained from

such measurements.

COMPARISON OF TRANSFER FUNCTIONS QBTAINED IN SEVERAL TRANSIENT WAVE SYSTEMS AND IN REGULAR WAVES

The motion transfer functions obtained from tests in transient waves

for Froude numbers of 0, 0.15, 0.25,, 0.30, and0.35 are plotted in Figures 11 through 15; these figures also include the response data for regular

waves. _{Because new procedures for processing transient signals had been}

developed just prior to th analysis required by this study, the records provided served as "guinea pigs" for the debugging process. As a result,

errors appeared in several of the computations of transfej' function

magni-tude and/or phase. Since the system frequency response is independent Of

the excitation used, costly reanalysis of the records was avoided by pre-senting, where necessary, the response magnitude obtained by means of one wave program along with the phase obtained by means of a different pro-gram (e.g., see Figure 14).

Several types of evaluations can be made from these figures. First,

by comparing the response functions derived in the transient and regular wave systems, we can determine the accuracy of the transient wave technique

(data obtained in regular waves are used as a standard for accuracy of the

analysis). In addition, we can check the consistency of the _response

functions obtained with different transient wave programs _{Finally, we can} examine the agreement between the magnitude of transfer functions derived from far-field wave measurements and those made directly _{ahead of the}

model.. Utilization of a fixed, far-field wave transducer makes it extremely

difficult to determine the phase between the forcing function (waves) and

the responses since it is necessary to know the position _{of the model}

relative to the wave probe at all times. Only with this. information

available is it possible to compute the phase of a motion relative to a wave crest (or trough) located on some station along the hull. _{For this} reason, phase data for the fixed probe are not presented in Figures 11

1rough 15,.

If we compare the magnitude of the transient wave responses which

were computed by utilizing the wave transforms from. the oving probe (solid

line) with the regular wave data, we find that the agreement is fairly good in those cases where the solid line is relatively smooth (e.g., for pitch and heave in Figure 12a). Where the transient wave response function.

is jagged, as for pitch and heave in Figure 14a, the blackened circles

repi'esenting regular wave data fall within, or adjacent to, the band

de-fined by the trajgbt-line segments. Naturally, in the latter case, it is

difficult to make a definitive judgment on accuracy; nevertheless, the

results do look encouraging. The correspondence between transient-wave and

regular-wave phase data follows the same geneTal trend exhibited by the magnitudes, although the plots for the former tend to be reasonably smooth throughout the speed range and permit a comparison to be made more easily. In summary it can be stated that acceptable motion transfer functions

(both magnitude and phase) can be obtained from model tests conducted in head transient waves over a wide range of speeds.

The transfer functions obtained from tests in, different transient

wave systems differ mainly in detail, that is, all the short straight-line

segments do not superpose (see Figures 11 and '12 for magnitudes and

Figures 11 and 13 for phases), 'but for the most part, the large-scale trends

are in agreement. There are occasional large differences (for example,

the heave plot of Figure l2a at a frequency of approximately 0.95 cps and

the pitch-wave phase plot of Figure 13b at approximately 1.0 cps)., but these would become less significant if mean, srnOdth curves were faired

through the jagged ones shown. The motion frequency responses derived from

far-field transient wave measurements compare satisfactorily with the regu-lar wave data, indicating that this method does produce usable results.: However, 'there is no obvious'improvement in accuracy over the response magnitudes computed from wave, measurements made with a moving probe mounted directly forward of the model.

Even a cursory examination of the transforms and transfer functions

presented in this paper.reveals the existence of an all, too conunon jagged

shape. _{The jaggedness is characteristic of the type of transient signal}

being processed rather than

an

artifact introduced by the digital analysis.

Figure 11 - Comparison of Motion Transfer Functions Obtained from Tësts in Transient and Rgu1ar Waves at Zero Speed

3.2 2.4 1.6

I.

0.8!I!

V 1.2 U (0 S

a

0.8 U 0.4 0 1.6 -00 U S '-I .5 0.8 0.4 0 F' 0 2 0 4 0 6 0.8 1.0 Frequency in cycles/sec

Figure ha - Magnitude of Transfer Functions

26

'S I

J,I'

Program A

Moving Carriage Probe

-- Program A

Stationary Far-Field Probe

Program C,

'Moving Carriage Probe

'.rl DR '1 CD CD tn CD o h '-3

Ii

n

p

CR iH CD - 5 n 0 I-'.

o

CR

Phase of Maximum Upward Heave Referred to Maximum Bow Up Pitch in degrees Phase of Maximum Upward Heave Referred to Wave Crest at LCG in degrees

U'

Phase of Maximum Bow Up Pitch RefErred to Wave Crest at LCG in degrees

o

U'

'0 0

rt

Figure 12 - Comparison of Motion Transfer Fuflctions Obtained from

Tests in Transient and Regular Waves at a Froude Number of 0.15 2.0 1.6

.1

0

O4

06

0.8

1.0

.1.2

1 4

Frequency in cycles/sec

Figure 12a Magiitde of Transfer Functions

.28

Program A,

Moving Carriage Probe

Program A,

Stationary Far-Field Probe

Program C,

Moving Carriage Probe a Regular Javes 4.0 bO '- 2.4 U (0 1.6 U ij

0.8

0

0

Phase of Maximum. Upward-Heave. Referred to Wave Crest at LCG- in degrees -0.0

0

o

Phase of Maximum Upward Heave Referred to Maximum Bow Up Pitch in degrees Phase of Maximum: Bow Up Pitch Referred to Wave Crest at LCG in degrees

Figure 13 Comparison of Motion Transfer Functions Obtained from Tests in Transient and Regular Waves at a Froude Number

of 0.25 4.0 0 .0 1.6 1.2 0.8 0.4 0 .0 0.4 0.6 0.8 1.0 1.2 1.4 '1.6 Frequency in cycles/sec

Figure 13a Magn:itude of Transfer Futictions

30 Program C, Movtng Carriage probe Program C, Stationary Far-Field Probe Regular Waves

(D

0. OO

Ii

Phase of Maximum Upward Heave Referred t9 Wave Crest at LCG in degrees

Phase of Maximum Upward Heave Referred tO Maximum Bow Up Pitch in degrees

I.-. '0 0th.

0

a' 0'

0

Phase of Maximum Bow Up Pitch Ref erred to Wave Crest at LCG in degrees

0\

vi

0

m

lUll

-I WW I-

0

CD ..< C)

-C)

r

m1.-. C) 0 U) '.0

0

U'

Figure 14 - coarison of Motion Transfer Functions Obtained from Tests in Transient and Regular Waves at a Froude

Number of 0.30

0.4

0

0.4 0.6 0.8 1.0 1.2 1.4 1.6

Frequency in cycles/sec

Figure 14a - Magnitude of Transfer Functions

32 Program C, MOving Carriage Probe - Program c, Stationary Far-Field Probe Regular Waves

Phase of Maximum Upward Heave Referred to Wave Crest at LCC in degrees

Phase of Maximum Upward Heave Referred to Maximum

Bow Up Pitch n degrees

I-00

.

0

La -U, 0-Ui I-' La

0

0

U' Phase of Maximum Bow Up Pitch Referred

to WaVe Crest at LCG in degrees

.1:- D-Ui Ui

-0

U' '0

0

- 1' ID Pt

_CDQO Cia) -'ID I

-r

-Figure 15 - Comparison of Motion Transfer Functions Obtained from Tests in Transient and Regular Waves at a Froude

Ntithber of 0.35 40 -C 3.2 S 2.4 U S C g 1.6 S U -'-I 0 2.8 2.4 2.0 1.6 1.2 0.8 o.4 0 1.. 6 1.2 0.8 0.4 0- T-0.4 0.6 0.8 1 0 1.2 1 4 1.6 Frequency Ln cycles/sec

Figure iSa . Magnitude of Transfer Functions

34 -- Program B, Moving Carriage Probe Program B, Stationary Far-Field Probe Regular Waves

r1 _I-I.

c '1 CD 1)1 CD

0

'1 In CD

9

rP '-I. 0 In,

Phase of Maximum Upward Heave Referred

Phase of Maximum Upward

to Wave Crest at LCG in Degrees

Heave Referred'to Maximum Bow Up Pitch In derees

0'

0

U'

'.0

0

U,

-Phase of Maximum how Up Pitch Referred to Wave Crest at LCG in degrees

'.0

0

vi 0

Ui

0

Ui '.0

0

fit,

This was demonstrated by utilizing the existing computer programs to obtain the transform of a rectangular pulse; the result (Figure 16) is obviously

quite smooth. The irregularity present in the other transforms is probably

caused by the fact that their associated time histories are comprised of

single cycles of sine functions joined end tO end. It is known that the

transform of a single cycle of a sine wave is a curve which has its largest peak close to the frequency of the sine wave, with secondary peaks (which

are by no means insignificant) at. higher and lower frequencies. If many

single cycles of sine waved with di.féren;t frequencies are joined to form a continuous signal and the transform' of this function is computed, the

secondary peaks associated with each sine wave will superpose on those of

the neighboring sine functions. Thespectral ordinates tabulated by the

digital computer will, in effect., result from addition of thQse individual

ordinates contributed by each sine wave Occurring at the same frequency.

The net ordinates associated, with the secondary peak's will generally not,

blen4 with the ordinates falling near the fundamental frequencies of the

sine waves to fOrm a smooth curve.

Methods are presently being investigated' for smoothing the "raw"

spectra obtained from.the computation of Fourier transforms.. One approach

under consideration is to convolve the spectrum with an. appropriate filter

which smooths the Fourier coefficients by an averaging process. A form of this averaging, which is known as Hanning, is given below

Ak = (l/4)ak ₁ + (l/2)ak + (l/4)akl

'Bk = (l/4)bkl + (l/2)bk

_"4k+l

where aK and bk are the coefficients of the real and imaginary parts of the

raw spectrum and Ak and Bk are the smoothed coefficients.

*A

Hanning-type smoothing process is almost always used 'in the numerical

calculation of energy density spectra from random signals.

+2 10 0 0 0 C 0 0 0 0 C 0 0 0 0 0 0 0 00000000000 000000 000 CoCa0 C .-o00000o000000o oO

24

04

08

L.2 1.6.

20

Frequency in cycles/Sec

Figure 16 Fourier Transform of a Rectangular Pulse as

Computed on the IBM 7090 Digital Computer

37

InpUt

Ideally, when the transfer function of a linear response is being

calculated., the jaggedness present in the transforms of input and response

should divide out. Actual experience reveals that such cancellation does

not occur because these irregularities fluctuate rapidly and are of large

amplitude. An appropriate method of smoothing the raw amplitude spectra

must be incorporated in the analysis in order to make the transfer functions obtained during transient wave tests useful for the objective prediction of ship response in a random seaway (the ultimate goal).

EFFECT OF SAMPLING RATEON TRANSFORMS

in order to employ digital computers in the analysis of transient signals, a continuous time history must be represented by discrete values of the function at finite time intervals apart. The sampling rate should be high enough to permit the computation of transforms with an accuracy

that is no greater than require4 for the user's purposes; excessively high sampling rates result in a waste of computer time. According to the Shannon sampling theorem, 2f samples/sec suffice to represent perfectly time

function containing only frequency.components below f cps. This theorem is

often difficult to apply because most empirical data do not have ,.a clearly determinable upper frequency bound.

An alternative method of arriving at an appropriate sampling rate is

a "cut and try" approach. First, an extremely high digitizing rate is used

to compute a transfQrrn which is to be the standard for accuracy. Then, the

digitizing rate is decreased. in discrete steps until the difference between

the standard and the approximation has reached what is considered to be the

maximum acceptable limit. This method was used by Smith and Cuxnmins2 when

computing transforms of records obtained during force pulse tests. They **

I _{determined that a sampling rate of 125/sec was needed to produce a}

*The

rigid body responses of a sh.ip model to force and moment impulses were being studied.

**

All sampling rates given are on.a per channel basis.

transform with a maximum error of 1 percent (the standard was based on a digitizing rate of 6000 samples/sec). In keeping with their findings, the sampling rate used for computing the transforms presented thus far in this

report is 125/sec.

As a check on whether a lower sampling rate would yield satisfactory results in the analysis of records from transient wave experiments, such analyses were performed after digitizing the signals at rates which, in some cases, were as low as 1.25 samples/sec. Figure 4 shows how the

trans-form of the wavemaker conrol signals is affected by decreasing the samp-.

ling rate to 62.5 and 25/sec. It should be recalled that the highest

frequency sine wave programmed into the controlsignal was 1.0 cps. Higher frequencies could, however, be present in the signal because of distortion of the Sine functions (harmonic content) or electronic noise. The only

change in the spectra which can be resolved in Figure4 occurs at the low frequency end where the energy content is quite small, and so the effect is

insignificant.

The wave records were sampled at even lower rates with no

deerio-ration in the transforms. The plots in Figure 17a are the transform of

waves generated in the basin by PrQgram A and measured at zero speed. If harmonic content is neglected, the highest frequency in the time function

should be close to 1.0 cps. The figure clearly shows that the sampling rate coul4 be decreased to 5/sec without causing an appreciable change in

the spectrum. Similar plots are presented in Figure l7b, here the

measure-ment was made at a forward speed of 3.72 knots (corresponding to F 0.35

for the model) so that the upper frequency limit in the signal was greater

than that associated with Figure l7a. As a result, the minimum sampling

rate that could be Utilized without altering the spectrum was -increased to 6.25/sec.

Thus, this brief investigation into the effect of sampling rate on the analysis of analog signals obtained during transient wave tests mdi-cates that in most cases, these signals can be digitized at a rate of approximately 10 samples/sec without causing-a significant error in the

computed spectra. If spurious signals are filtered out, it should be

necessary to increase the sampling rate above 10/sec only when the fre-quencies of wave encounter are significantly higher than the values reported

herein.

o

_'4-I

0

'5

i-i 0.8

I-I

-Figure 17 - Effect of Sampling Rate on the Accuracy of Transient Wave Transforms 2.4

2.0

0.4

2.5 Samples Per Second

- - - 5 Samples Per Second

125 Samples Per Second

0 2 04 0.6 0.8 1.0 12 14 1.6 18 Frequency in cycles/sec

/ 1.2 1.0 0.2 0 ..-5.0 Samples - --6.25 Samples 125.0 Samples Per Second Per Second Per Second

-h

.2 0.4 0.6 08 10 12 1.4 1.6 ₁₈ Frequency in cycles/sec

Figure iTh - Wave Probe Speed = 3.72 Knots, Program A

C) 4' 0.8 a' 0.6 0.4

The curves in Figure 17 reveal that when the sampling rate is de-creased to the point where significant changes in the spectra begin to appear, these differences occur at the high frequency end of the spectra. Usually, when this "folding" or aliasing of the spectrum about occurs, it

is characterized by an increase in the spectral ordinates. This is due to

the inability of the discrete sampled. values to adequately represent the

higher frequencies in the record, and.the energy associated with these high frequencies is attributed to lower ones. In Figure 17, however, the aliased spectra are lower than the true spectra, at leas. up to the

highest frequency analyzed. Additional studies of sampling rate effects

will be conducted in the future to provide more comparisons of spectra,

especially at higher frequencies than showfl ii Figure 17, so that this apparent anomaly can be explained.

REFERENCES

Davis, M.C., an7 Zarnick, Ernest E., "Testing Ship Models in

Transient Waves," Fifth Symposium On Naval Hydrodynamics., Bergen, Norway

(Sep 10-12, .1964).

Smith, W..E. and Cummins, W.E., "FOrce Pulse Testing of Ship

Models Progress Report," Fifth Symposium on Naval Hydrodynamics, Bergen,

Norway (Sep 10-12, 1964).

Davis, M.C., "Simulation Of a Long-Crested Gaussian Seaway,"

David Taylor Model Basin Report 1755 (Apr 1964)

St. Denis, M. and. Pierson, W.J., Jr., "On The Motions of Ships In Confused Seas," Society of Naval Architects. and Marine Engineers Transactions, Vol. 61, pp 280-357 (1953).

Copies 3 NAVSHIPSYSCOM 2 Ships 2052 1 Ships 0341 6 NAVSEC 2 Sec 6110 2 Sec 6122 2 Sec 6115 2 CHONR 1 Code 438 .1 Cod8 466

1 ONR, New York 1 ONR, Pasadena 1 ONR, Chicago 1 ONR, Boston 1 ONR, London 1. NMDL 1 NAVUWRES 1 NOL 1 CDR, NUWC 1 CDR, NWC 1 NRL 1 D.L., SIT 1 Dr. J. Breslin

DIR,. DEF R&E'

Dir, Exptl Nay Tank, Univ of Mich, Ann Arbor

1. Dir, Inst for Fluid Dyn

Appi Math, Univ of Md

1 Dir,, Scripps Inst of Ocean,

Univ of Calif

1 Dir, WHOI, Woods Hole 1 Dir, ORL, Penn State

1 CO, USNROTC NAVADMINU, MIT

1 Dir, St. Anthony Falls

Hydrau Lab,, Univ Of Minnesota,, Minneapolis

INITIAL DISTRIBUTION

43

Copies

1 ,. Dir, Fluid Mech Lab, Univ of

Cal..f,, Berkeley

1 'James. Forrestal Res Ctr,

Princeton Attn: Mr. Maurice

H. Smith, .Asst to Dir

2

NNSDDCo.

I Asst Nay Arch

1, Dir, Hydra Lab

20 CDR, DDC '

1 . MARAD(Res. Dev.Sec)

1'. Catholic Univ., Mechanical

Engineering Dept, School

of Eng Arch

1 prof J R Paul hng Cbllege'of Eng, Univ of

Calif, Berkeley

NYU, Dept Of Oceanography ..Metèoro1or

1 Dr. W.J. Pierson, Jr.

1 Mr. R. Jôhson

2 ' DIR, SPO

1 Genelal Dynamics Corp.

Electric BOat Div

1 bceanics,, Inc., Technical

Industrial Park

1 Westinghouse Electric Corp,

Annapolis, Md

Attn Mr. M.S. Macovsky 1 .SNAME

Attn: Panel. H-7

1 Dir, Natl BuStand 1 Dir, APL/JHU

1 . Dir, Fluid Mech Lab,

Columbia Univ, New'York, N.Y..

1 Dir, Hydra Lab, Univ of

Colorado

Copies

1 Dir, Hydra Res Lab, thiiv of Conn,

Storrs, Conn

I Dir, RObinson Hydra Lab, Ohio

St thliV, Colunibüs, Ohio 1 Admin, Webb Inst of Nay .Aith,

Glen COve

2 Dir Iowa. Inst of Hydrau Res,

St Univer of IOwa, Iowa City

1 Dr. L Landweber

1 Dir, Hydra Lab, Penn State Univ,

University Park,: Pa.

1 Dir, Hydra Lab, Univ of.Wisconsin

1 Dir, Hydra Lab, Univ of Washington.

1 SAHL/Univ of: 1i

1 Dir of Res, The Tech Inst,

:Noihwestern Univ

- Evanston, Ui.

1. Dr. M.L. Aibertson, Head of

Fluid Mech Res, Dept of Civil

Engr, Colorado St Univ

Fort Collins:, Cob.

1 MIT, Dept of NA. ME

1 _{Lockheed Missiles} Space Co

Swmyvaie, Ca.if

1 Hydronautics, Laurel, Md.

UNCLASSIFIED - Security Classification

FORM 1473

(PAGE 1) I NOV 65 I S/N 0101.807-6801 UNCLASSIFIED Security Classification

-- ---

---'DOCUMENT CONTROL DATA - R & D

-(Security classification of title body of abstract and indexing annotation must be entered when the overall report is classIfied)

I ORIGINATINGACTIVITY (Coipórata authär,)

-Naval Ship Research P Development Center

-Washington, D.C. 20007 - -

-Zà.REPORT SECURITY CLASSIFICATION

UNCLASSIFIED

2b. GROUP

- 3. REPORT TITLE -

-NOTES ON SHIP MODEL TESTING IN TRANSIENT WAVES

4. DESCRIPTIVE NOTES (Dype of report and inclusive dates)

Research and Development -

-5. AUTHOR(S) (First name,middie Initial, last name) -

-Alvin Gersten and Robert J. Johnson

6. REPORT DATE ,.

April 1969 ---

-7a. TOTAL NO. OF PAGES 47

7b. NO. OF FS 4

Ba. CONTRACT OR GRANT NO.

b. PROJECT NO. _{S-R009 01 01}

Task 0100

a. .

-9a.-ORIGINATORS REPORT NUMBER(S) -

-2960

Sb. OTHER REPORT NO(S) (Any oth'.iriumbers that may be assigned this report)

10. DISTRIBUTION STATEMENT -

-This documefit has been approved for public release and sale; its distribution is unlimited.

II. SUPPLEMENTARY NOTES

--Development of Testing Techniques

12. SPONSORING MILITARY ACTIVITY _{-; --}

-NaVal Ship Systems Command

13. ABSTRACT

-Ship model experiments were conducted to evaluate the accuracy of motion transfer functions obtained by means of

the transient wave technique-. Since such an evaluation was

especially needed for higher ship speeds, Froude numbers up

to 0.35 were investigated. Also studied was the feasibility

of measuring the incoming wave train far ahead -of the model,

-where distortion Of the forcing function by model-generated

waves cannot occur. Further, in the interest of reducing'

computer usage time, the effect of sampling rate on the

- analysis of- analog signals obtained during transient wave

tests was examined. Results are also presented which

demon-strate" a need for smoothing the "raw" spectra obtained from

the computation of Fourier transformations, in order to provide consistently useful transfer functions.

DDFORM 1473 (BACK)

_{NOV 65 I} (PAGE 2) UNCLASSIFIED Security Classification UNCLASSIFIED Security Classification GPO 872-586 14

KEY WORDS LINK A LINK S LINK C

ROLE WT ROLE W ROLE WT

Ship Motions Seaworthiness Ship Models Transient Waves