Wave propagation in the tenth-scale model of the maneuvering basin, Part I: Long-crested regular waves

-AR .1-1E-F

-... . f " Tid 1111 I1YDROMEHANICS

0

AERODYNAMICS '0 STRUCTURAL MECHANICS 0 1 APPLIED I A., P I 11111 _ Lzb.

v.

Scl

Aittikun,4-1:c

iet

tectiaLc-te

j

"

Delft

WAVE PROPAGATION IN THE TENTH-SCALE MODEL OF THE MANEUVERING BASIN

PART 1 LONG-CRESTED REGULAR WAVES

by

Wilbur Marks

HYDROMECHANICS LABORATORY RESEARCH AND DEVELOPMENT REPORT

WAVE PROPAGATION IN THE TENTH-SCALE MODEL OF THE MANEUVERING BASIN

PART I LONG-CRESTED REGULAR WAVES

by

Wilbur Marks

TABLE OF CONTENTS Page ABSTRACT...-. -., INTRODUCTION _ MANEUVERING BASIN.--PHYSICAL PROPERTIES WAVE-GENERATING SYSTEM

LONG-CRESTED REGULAR WAVES 8

BALANCING THE WAVEMAKERS , Li. ' 8

SPATIAL DISTRIBUTION OF WAVE FIELDS --..,...., ... ..._____ .-, . ,..., ,.;: 12

A =40 Ft (Figures 7a, 7b, 7c) J .., , 13 A = 30 Ft (Figures 7d, 7e 7f) . , . . ; 13 X = 20 Ft (Figures 7g, 7b Ti)

,

... - 13 A --. 10i Ft. (Figures 7j, 7k)..---.. ,..- . - i .-. ., . % .. . 20 X = 5 Ft 20 Summary 20

TEMPORAL DISTRIBUTION OF WAVE HEIGHTS - 2_1,

MISCELLANEOUS PHENOMENA ,, , - 26

HIGH-FREQUENCY SIDE RERADIATION . 26

EFFECT OF VARIABLE DEPTH al 4 El 26

REMOVAL OF BARRIER A .. t - 7 : .4 .1 32

EFFECTIVENESS OF WAVE ABSORBER 32

APPENDIX BASIC DATA ON BALANCING THE WAVEMAKER 35

REFERENCES' .

-

38 3 4 5 ' - . CONCLUSIONS,:... ... ... ... - - 32 1 1

LIST OF ILLUSTRATIONS

Page

Figure 1 Tenth-Scale Model of Maneuvering Basin 3

Figure 2 1:120-Scale Model of Rotating Arm and Maneuvering Basin 4

Figure 3 Plan and Elevation of Maneuvering Bridge

Figure 4 General Arrangement of Wavemakers 7

Figure 5 Waves Produced by a Single Wavemaker 11

Figure 6 Diagram of the Observation Points in the Tank 14

Figure 7 Contour Diagrams of Wave Field 14-19

Figure 8 Wave Profiles Recorded at 40, 140, and 240 Ft Down-Tank, in Front

of Wavemaker V During 30-Minute Test Periods 22-24

Figure 9 Long-Crested Sinusoidal Waves Covering Entire Range of Wave Lengths

and Assorted Wave Heights 25

Figure 10 Reradiation of Wave Energy from Side Barriers 27

Figure 11 Propagation of Waves of Variable Depth 29

Figure 12 Propagation of Long-Crested Waves, Long Barrier Removed 31

LIST OF TABLES

Table 1 Experimental Test Conditions (Prototype Scale)

Spatial Distribution 12

Table 2 Experimental Test Conditions (Prototype Scale)

Temporal Distribution 21

Table 3 Blower and Trimmer Valve Settings Required for Specified

Wave Heights and Wave Lengths 36-37

ABSTRACT

A quantitative study was made of long-crested regular waves in the

tenth-scale model of the Taylor Model Basin maneuvering basin. The eight

wave-makers which constitute one short side of the basin were "balanced" to produce

uniform sinusoidal waves. The nature of the wave field, in time and space, was

investigated for a variety of wave lengths and wave heights. It is demonstrated

that a sufficiently large area of the tank remains homogeneously stationary to

satisfy most test conditions. The observance of high-frequency reradiation from

the sidewalls of the tank is discussed and remedial measures, based on

experi-mentation, are suggested. It is shown that variable depth and removal of one side barrier do not materially affect wave propagation in the range of wave lengths

and wave heights tested. The wave-absorbing beach was found to be highly

effective.

INTRODUCTION

Many parameters of ship model performance are more profitably studied under the action

of waves than in still water. Heretofore, such testing has been accomplished by adapting the traditional long narrow test channel to wave production; that is, a wavemaker is installed

at one end of the tank and a beach at the other. This, however, leaves something to be

de-sired. Although the long narrow channel is ideal for still-water tests, where ship's heading

is of no consequence, it restricts tests in waves to head seas and following seas and to zero

speed of advance in beam seas. The desire to conduct model tests in different relative

head-ings of model to waves (that is, oblique seas) has led to the concept of the rectangular tank.*

This type of facility permits oblique-sea testing by two alternative methods:

The path of travel of the ship model is restricted to a fixed line with respect to the

boundaries of the tank, whereas the direction of wave propogation relative to the same

bound-aries may be varied in certain ways; or

The direction of wave propagation is always the same whereas the path of travel of the

ship model along a line may be altered with each test.

Implicit in the above is the possibility of embodiment in a particular facility of both methods 1 and 2. Such is the case in the TMB maneuvering basin.

One possible disadvantage of the rectangular tank should be noted. Because of the

necessity for wavemaking facilities along one or two sides of the tank, it will in general be

much shorter than the long narrow channel. There is then the chance that for certain speeds

The value of oblique-sea testing is that methods exist which enable ship motions, in

any degree of freedom, to be computed from such tests.' _{strong reason for reproducing}

the seaway in the laboratory is that the model tank can be _{an analog computer that gives}

pre-cise answers to ship behavior problems. Most wavemakers produce, at least in principle, sinusoidal waves. Sinusoidal conditions, although unrealistic, are easily reproducible, and coupled with the fact that the sine wave is a mathematically well-behaved forcing function, its desirability as an initial test condition is evident.

The sine wave, moreover, is the key to the complexity of the sea surface, for recently

it has been proved analytically that the seaway can be considered to be composed of _a

multi-plicity of independent sinusoidal components combined in random phase.2 The idea of

cre-ating an irregular sea surface is not incompatible with known wave-genercre-ating techniques. Indeed, at least one institution has conducted extensive tests in long-crested irregular seas.3 The extension of our knowledge on the direction of travel of ocean waves4 emphasizes the

superiority of the rectangular tank for reproducing the seaway in the laboratory; the narrow

tank is, of necessity, restricted to propagating waves in one direction.

Generally in a rectangular towing facility equipped for generating waves some of the following phenomena may be produced:

long-crested oblique regular waves, long-crested oblique irregular waves,

short-crested oblique irregular waves.

At this time there are several institutions which have in operation, or are building,

rectangular tanks.5 One such facility is the TMB maneuvering basin;6 a one-tenth scale

model (Figure 1) has been successfully operating for over a year.

The function of the one-tenth scale model is to provide information on the basic nature

of the prototype. It is hoped that extensive tests will demonstrate: how well the facility can

produce the wave fields listed above; what, if any, modifications are indicated; how to set up programs for the propagation of different sea conditions; etc. The investigation of waves in the tenth-scale model will follow the sequence of steps listed below, and the results of these

experiments will be reported as they are completed:

long-crested regular waves,

properties of individual wavemakers and simple combinations thereof, long-crested irregular waves,

short-crested waves.

This particular order is dictated by expedience rather than by logic.

'References are listed on page 38.

2

A

Figure 1 Tenth-Scale Model of Maneuvering Basin

This report presents the results of the first part of the investigation, that of long-crested regular waves. The nature of these waves was studied both as a function of space and as a function of time. The following aspects are treated in the text:

balancing wavemakers,

spatial distribution of wave field, temporal stationarity of wave heights,

interference wave pattern due to reradiation from side barriers,

effect on wave propagation of differential depth, effect on wave propagation of removal of side barrier, effectiveness of wave absorber (beach).

MANEUVERING BASIN

Fundamentally, the technique of oblique-sea testing in the maneuvering basin, is pre-dicated on the change in ship heading for constant wave direction. It is possible to generate oblique waves as well, and this will be done when generation of a particular sea state

4 1. '2. 3.

4,

5.

Figure 2a

Figure 2b

Figure 2 1:120-Scale Model of Rotating Arm and Maneuvering Basin

warrants it. All testing herein described relates, therefore, to waves whose direction of travel

is perpendicular to the plane of the wavemaker. All tests were made in the tenth-scale model, of course, but it will be convenient to think of the dimensions in terms of the prototype scale. The use of the prototype frame of reference will enable the reader to visualize more clearly what is expected in the maneuvering basin.

PHYSICAL PROPERTIES

The basic inside dimensions of the maneuvering basin are 360 ft by 240 ft by 20 ft. One section, about 50 ft wide and extending the length of the tank, is 35 ft deep and is designed

to accommodate submerged models. One wall of the basin is equipped with thirteen pneumatic

wave generators, the adjacent wall with eight, and opposite the banks of wavemakers are fixed

4

bar-type concrete wave absorbers. Figure 2 shows a 1:120-scale model of the maneuvering basin in its planned housing.

A steel bridge spans the basin and is capable to being rotated through an angle of

45 deg (Figure 3). Mounted under the bridge is the towing carriage which travels the length

of the bridge. If head seas be designated by 0 deg and following seas by 180 deg, the short

bank of wavemakers affords test conditions in the range 0 45 deg and 135 180 deg and,

the long bank of wavemakers provides information in the range 45 135 deg. Since all ships

are symmetrical about their longitudinal axes, it is sufficient to test in only 180 deg of

rela-tive direction. More detailed information on the mechanical and electrical aspects of all the

features in the maneuvering basin is available in the literature.6

WAVE-GENERATING SYSTEM

The mechanism for wave generation is the pneumatic wavemaker, of which eight units

each 25 ft long extend along one short side of the tank; thirteen like units occupy an

adja-cent side.

The principle of pneumatic wave generation can be understood byconsidering a tank

of water with a partition near one end that extends across the tankbut not to the bottom. If

the water surface inside the partition is depressed, the pressure is transmitted, by Pascal's

law, to the water on the opposite side of the partition and the water surface nearest the

parti-tion is raised. This disturbance will then travel the length of the tank. The height of the

wave is a function of the magnitude of the initial force applied to the confined surface, and the

length of the wave is determined by the length of time the initial force is applied. The length of the wave is also affected by the distance of the partition from the bottom, because this

dictates the nature of the transmission of pressure in the large fluid chamber.

In practice, a dome forms an enclosed air chamber near one wall of the tank. A blower

motor forces air into the dome, thereby creating a difference of pressure between the water

surfaces inside and outside the dome. The blower-motor speed is a control of wave height

because it controls the amount of air flowing into the dome per unit of time, which in turn

dic-tates the magnitude of the force on the free surface. This force is proportional to the wave

height. A valve system permits the air to enter the dome when it is drawn from the atmosphere,

and forces the air into the atmosphere when it is drawn from the dome. Furthermore, the

fre-quency of oscillation f of the valves determines the wave length A generated through the

formula

VAVgUdtflflp 3 p _' _ /14.. \ \ \ \

\

\

\

\ ?JAN 1133LIVILING 643,1 \ I/ .as

11111`116. Aar PARICWrOlt Ar_OZ.VARIF

- --+

Figure 3

Plan and Elevation of Maneuvering Bridge

.144C.,CMQ . \

\

_\

\ \ ...dr \ 4,111 i 5 \

\5

\

11 Ell

Elk

L 1$ I2'.2f. 4 -I ,rder 401 SIdnd Jproe fel [no I. .5 d , 0 Shp, (55, too alM) 10 22. VO/ve " Or,ve un, PLan of Wa vernakers cf.,- El /13-O. VIrd L/n, .ach Inching Mot Miler Cede_ 0 /3 /2 1 0 Sprocket Jos d 1.90.1 PLAN 9ync9rono.. Volve Oro.. 2Cnsm,35,./', ShCO, Figure 4

General Arrangement of Wavemakers

(ii. l0090) 4 3 I dt

Wave length is also restricted by the geometry of the basin. Since the celerity of a

wave is given by

2 gA 27Th

c = tanh

277 A

where h is the depth to the bottom, it is seen that for deep-water waves, the celerity is a func-tion of wave length (frequency)alone whereas for shallow-water waves the celerity is only

depth dependent. The transition from deep to shallow water occurs approximately at h = A/2.

Therefore, in a tank 20 ft deep, waves longer than 40 ft cannot be generated and still behave

as deep-water waves. The lower limit of wave-length generation is around 5 ft. Shorter waves

become unstable soon after they are produced.

Although the dome is common to all the wavemakers, it is divided into separate

compart-ments 25 ft long, each with its own valve and blower system. This means that the individual wavemakers are essentially independent of each other. If separate instruction programs are

given to the wavemakers twenty-one possible sources of wave energy are provided. Figure 4 shows the general arrangement of the wavemakers in the maneuvering basin.

The wave-generating system, as stated, is designed to produce waves from 5 ft to 40 ft in length and up to 24 in. in height. If models are to be tested in the wave-length range be-tween half the ship length and twice the ship length, then the basin will accomodate

models from 10 ft to 20 ft. This presupposes that the wavemakers can produce the idealized

sinusoidal waves through the entire range of lengths and heights and no other adverse situa-tions are encountered.

LONG-CRESTED REGULAR WAVES

Perhaps the most difficult type of wave field to be produced in the maneuvering basin is the regular long-crested sinusoidal wave of constant height and length. It is paradoxical that this system, which purports to surpass the traditional long channel in achieving realism, should find it difficult to produce the sine wave, the basic feature of the standard towing tank. Yet when it is considered that eight wavemakers, with slightly different physical characteris-tics (due to manufacturing tolerances), are required to work together harmoniously as a uniform

line source, some difficulties can be expected.

BALANCING THE WAVEMAKERS

In this set of experiments only the short bank of wavemakers was used. It was inter-esting to find that radial waves were being produced at the larger wave lengths by individual wavemakers operating alone. Each element is 25 ft long, by no means a point source; yet for all wave lengths exceeding one-half the length of the unit generator, curved wave crests are an obvious feature of the wave field produced by a single wavemaker (Figure 5a). A proper

combination of point sources acts as a line source and produces a wave front or plane

sin-usoidal wave. In the case of the short waves (less than one-half the length of the unit

gener-ator), the output of a single vvavemaker appears as a plane wave in the middle, bounded by

partially circular waves due to diffraction from the ends of the wavemaker (Figure 5b). In

effect then, consider this short wave as a line source of finite length such that the ends, act-ing as point sources, produce the partially circular effect observed. The diffraction effects at the ends are cancelled by the waves generated on both sides; the net result is a plane wave which spans the tank. Discrepancies occur at the side walls of the tank where the diffracted

energy from the end wavemakers may be reflected and/or reradiated back into the wave field

as it travels down the basin. This matter will be more fully discussed (page 26).

At the outset there was no knowledge on the behavior characteristics of the wavemakers when operated in unison. A basic assumption in the experimental approach to this is that the greatest probability of achieving the desired long-crested sinusoidal wave will be realized

if it can be ascertained that immediately after generation the wave has a constant height along

its crest for any given wave length. This balancing of the wavemakers was essentially

car-ried out on a trial and error basis. Eight wave probes were arranged in a line across the tank 15 ft (prototype scale) from the short bank; each probe was placed in line with the center of a wavemaker and was assumed to measure the waves from that wavemaker. For each wave length

tested the output of each wavemaker was adjusted until all the probes recorded approximately the same height. The wave height was then considered to be invariant along the crest.

The entire bank of wavemakers is operated on line shaft control; that is, a single drive system controls the wave length produced by each unit so that with little difficulty the wave

length may be held constant for the bank. The height of the wave is controlled in twoways:

(1) the blower-motor speed, and (2) the trimming valves. The blower-motor speed governs the volume of air admitted to the system per unit time, and the trimming valves in turn permit

pas-sage of any part of the allowable volume of air into the wavemaker dome. To produce a de-sired wave, the frequency control is set for the given wave length, and the blower-motor speed

and trimming-valve angle are adjusted at a given height. It was found that in the range of

exper-imental interest the relationship between wave height and blower-motor speed is linear. For a given wave length and blower-motor speed the height also varies linearly as a function of

trimming-valve angle.

The balancing and testing program was carried out for a discrete number ofwaves

rang-ing in length from 5 ft to 40 ft, and for various heights, resultrang-ing in a wide band of_{wave slopes}

(Table 1).

The balancing tests are made as follows: generate the desired wave length,

choose any blower-motor speed,

record the wave heights at the eight stations,

*

1-fr" 1.

a

10 ,1 Figure 5a

The wave length is long compared to the length of the wavemaker.N

1

PSD-66791

-1

Figure 5b

The wave length is short compared to the length of the wavemaker.

Figure 5 Waves Produced by a Single Wavemaker

TABLE 1

Experimental Test Conditions (Prototype Scale) Spatial Distribution

select the wave height which occurs most frequently (this is arbitrary) and adjust the trimming angles in an effort to achieve this value at each recording station,

repeat steps (2) to (4) for a range of

blower-motor speeds that will produce the

de-sired slopes,

repeat steps (1) to (5) for all the wave lengths in Table 1.

This technique, although admittedly crude, resulted in the propagation of

sinusoi-dal waves wherein the variation in height _along

the entire length of crest never exceeded

+ 10 percent of the mean wave height, and was

never less than + 2.5 percent of the mean wave

height. It may be added that other methods

used in attempts to balance the wavemakers were far less productive. The purpose of

bal-ancing the wavemakers is essentially to

pro-vide a set of numbers for which the

experi-menter may reproduce waves of a specified

nature with a given degree of accuracy. Since balancing is fundamentally related to the phy-sical properties of the individual wavemakers, the data collected in the one-tenth scale model

are not applicable to the prototype maneuvering

basin. However, to keep intact, as a unit, the

12

Nave Length

ft

Nave Height

in. 'ave Slope

27.0 1/18 22.5 1/21 40 12.0 1/40 9.6 1/50 30.0 1/12 27.5 1/13 30 12.5 1/29 9.5 1/38 6.7 1/54 27.0 1/11 22.5 1/13 25 17.0 1/13 11.0 1/27 5.0 1/60 22.0 1/11 17.4 1/14 20 15.0 1/16 9.3 1/24 4.5 1/53 5.6 1/21 10 3.4 1/35 2.4 1/49 5 1.5 1.1 1/40 1/53

information gathered in this facility, the results of the balancing tests are included as an appendix to this paper.

SPATIAL DISTRIBUTION OF WAVE FIELD

Once the wavemakers are balanced, the conditions for wave generation are fixed. In

order to measure the wave field over the entire extent of the tank, the eight _{wave probes}

were moved systematically down the tank to each of six positions (Figure 6). Fifty-six points were used as observation stations and, in accordance with the schedule in Table 1, a total

of 1344 measurements of wave height were obtained.

For each wave length and wave height a contour surface of_{wave height was drawn.}

Figure 7 is a selection of such contour diagrams. These were assembled to illustrate

,4;

,51.

some of the dominant features of the wave field. In order to facilitate the reading of the

dia-grams, some basic information will be helpful. The contours represent curves of constant wave height (inches) and the contour interval is given by the difference, in the value of any two adjacent contours. The gradient (or density) of the contours is a measure of the variation of wave height, the tighter the gradient the greater the variation. A tight gradient in the hor-izontal direction (across the page) is typified by close-knit vertical lines (Figure 7a, right and left sides of the tank) and indicates great variation in wave height across the tank at those places. Similarly, a tight gradient in the vertical direction (up and down the page)

(Figure 7k, bottom) signifies severe changes in wave height down the tank (away from the

wavemakers). To the left of the contour diagram is a tabulation of average wave height (h)

across the tank at that position.

The various contour diagrams reveal some rather interesting aspects of the different wave fields.

= 40 Ft (Figures 7a, 7b, 7c)

The contours indicate little change in height down the center of the tank, with a varia-tion of 5 to 10 percent in the average height measured across the tank. There is a tight gradient near the long bank of wavemakers which shows a definite decrease in height from the center of the basin to the right side. A similar situation, though not so severe, exists

adja-cent to the long barrier in front of the beach, on the left side. In general, the main part of the tank is free for testing at A = 40 ft and all wave heights. The difficulties encountered at the sides are understood and will be discussed on page 26. Corrective measures will also be

recommended.

= 30 Ft (Figures 7d, 7e, 7f)

The average variation at different points in the tank is as much as 15 percent. Yet there is no definite pattern in the down-tank direction but rather a semblance of homogeneity in the almost random scattering of wave heights in the main part of the tank. The tight gra-dients along the sides are greatly relaxed and tend to diminish with decreasing wave height. Indeed, for A = 30 ft, h = 6.7 in. (Figure 7f) the gradient adjacent to the barrier is no longer

evident.

= 20 Ft (Figures 7g, 7h, 7i)

The gradient adjacent to the barrier is gone and the gradient adjacent to the long bank of wavemakers is greatly reduced. There is, however, a general decrease of average wave height down the tank, and in one case (Figure 7g) the decrease exceeds 25 percent between

stations 90 and 140 ft. This tight down-tank gradient depends on one set of points (at sta-tion 90 ft) and bears checking. The general decrease in wave height may to some extent be

290 240 190 140 90 40 1.50 Beach 1 1 I 1

Li

MIIIL

T/ BI If

I

Wovemaker 300 250 200 150 100 50 25.60 Figure 7

Contour Diagrams of Wave Field

26.59

I

26.90. 27.03

Beach

Figure 6

Diagram of the Observation Points in the Tank

Figure 7a

ii

1 I I 0 200 150 100 50 feet 1 1 i 1 I 1 i 1 in =I YE

7 IV

in II

I

Wave maker 50 200 150 100 feet A= 40 feet h27 inches 350 350 300 250 200 a, 150 100 50

0-12.98 _I. 13.18 13.36 i 3.03 13,29 113.00 11.95 200 -150 100 feet "kin MI In 7" Mt

aa.0

Waveniaker _{Figure 'lb} Figure 70 1 200 150 100 50 feet r it I

t)

_ Wavernaker A= 40 feet hr 1 2 inches A= 40 feet hr 9.6 inches // 7 1 I 350 300 250 200 \-150 100 350 300 250 200 100 50 0 Beach 10.84 10.80 10.84 I 10.24 10.35 9.94 9.47 /3 /2 /2 /3 /5 2 50 /2 0

28,22 27.23 co 29.14 26.56 28.69 27.60 31.25 A. 30 feet h. 30 inches 200 150 100 feet I I ME IL Ill

vJV

Wovemaker _{Figure 7d} 3 4 50 0 J I I III IC 1 13.62 200 1162 _c 150 I 11.39 13.91 11.70 12.84 12.34 200 A= 30 feet /2 13 /4 h12.5 inches /5 4 3 1 I 1 150 100 50 feet /2 1/ /G /2 1 1 1 I 1 1 1 1 =1 VII SE -S7 TZ 111 It 1

Woverna her _{Figure 7e}

350

r7z-

-250 200

A. 30

(

1 1 L__ I 1 MIL ILII Id 7

I/

RI III

I

We verna ke r Wavemaker X. 20 feet h= 22 inches 350 350 Beach 300 19 300 18.22 /4 /5 18 /6 /6 250 250 16.45 /6 /5 200 200 )3 17.03 /7 150 /6 150 15.01 81 17 19 20 00

iT

100 2/ 50 22 50 23 23 22.01 0 200 150 100 feet 0 1 I I 1 1 MI %/It VI. It ET III II

I

Figure 7f Figure 7g 1 1 1 50 200 150 100 feet feet h =6.7inches. 22,36

11.96 10.68 _{12.25 14.95} 200 /2

/4

-A.= 20 feet h =15 inches Beach /3 /2 150 100 feet /5 I 1

II

I 1 I I

ME=

L

irI

Wavemoker Figure 7h 350 300 50 50 0 8.94 9.85 A. 20 feet h .9 845 inches Beach /0 8 - 100 9 9

)10

I. [ 1 1 200 150 100 50 feet 1 1 1 1 I 1 1 1 MI 3IL IL Y Ili III Il

I

Wovemo her Figure 7i

350 300 250

200

150

50

t

8.08 7.30 6,25

350 -- 300 250 200 1.84 co 150 1.46 100

50

1.30 1.10 0.84 0.90 2.44 0 200 1.5 1 4 7 I 1 1 200 150 1 1 1 1 100 feet I I 50 1 I

ME Nll_31-1-am

Ir T A, 10 feet 11=2.44 inches 350 Beach 300 /.0 1.0 1.0 /.5 250 1.5 0.9 200 1.0 150 1.5 100 07 1.0 50 2.0 1 150 100 50 feet 0 I I I

I1

I 1 1IL 371 Tir 1111 It

I

Wa vema ker Wavemoker Figure 7j Figure 7k feet 5.64 inches

attributed to the increased prominence of surface tension at the lower wave lengths. If this is the case, much better results may be expected in the prototype.

X JO Ft (Figures 7j, 7k)

The down-tank gradient is very tight in the first 40 ft, where the wave height decreases by over 50 percent. Thereafter, the situation appears to stabilize and the wave field

in the main part of the tank is quite good, on the whole. This situation cannot be attributed wholly to surface tention, since there is no uniform decline in the wave height. The difficulty

seems to stem from the physical properties of the wavemakers, and the phenomenon seems

most evident at shorter wave lengths. The ideal wavemaker is one that will impart to the water particles the correct velocities that result in the appropriate orbital motions for the desired

wave. It has been showns that horizontal energizing of the water is sufficient to create proper

waves almost immediately. This is so because the wavemaker supplies a wall against which the vertical motions can orient themselves. In the case of vertical energizing (pneumatic wavemakers), only the free surface is available as an aid to proper arrangement of the orbital motions. In this case, the formation of the wave may take somewhat longer. This is offered

only as a possible explanation for the tight gradient in the first 40-ft down tank. If it is

found, in the prototype, that the same phenomenon persists, it will be quite sufficient for test purposes to establish that regular waves do exist beyond 40 ft from the wavemakers.

X = 5 Ft

For the shortest wave length there was a two-fold difficulty: (1) surface tension was

quite pronounced in damping out the waves, (2) the recording equipment, at maximum

sensi-tivity, was unable to detect any appreciable change in water level as the waves went by the probes. This was alsodue to surface tension on the capacitance probes. There is every rea-son to expect much better results in the prototype.

Summary

The spatial characteristics of wave height can be listed as follows:

Relatively large areas exist where the wave height does not vary more than 10 percent. Testing may be conducted at all wave lengths in these regions.

Tight gradients along the sides observed at longer wave lengths tend to distort the waves in the main part of the tank. This is due to the resonating characteristics of the don-re

on the long bank of wavemakers. Experiments showed that additional bracing of the dome

changed its mode of vibration and greatly reduced the reradiation effects.

Tight gradients in the first 50 to 100 ft become prominent for the shorter wave lengths. These are believed to be due partially to surface tension (which attenuates the wave height),

and partially to the properties of the wave-generating system (which requires a certain length of tank to establish the proper veloc-ity distribution in the orbit of the waves). This condition will receive close scrutiny in

the prototype.

4. Surface tension greatly affects the

propagation of short waves. This will not be the case in the prototype.

In general, there is, with respect to the overall dimensions of the basin,

reason-able area for model testing at all wave

lengths and wave heights. In these areas

the wave heights will not vary more than

10 percent. It is believed that these areas

will be increased in the prototype to the ex-tent that the test space will be limited by fac-tors other than the nature of the wave field.

TEMPORAL DISTRIBUTION OF WAVE HEIGHTS

successful tank test requires a uniform wave field over the entire extent of the work-ing area. Also, the wave field must remain reasonably stationary for the duration of the longest

test planned. To determine whether this latter condition prevails, waves were recorded for

periods equivalent to approximately 30 minutes of running time in the prototype at three

sta-tions down-tank in line with the central wavemaker. These test condista-tions appear in Table 2.

No wave condition was maintained absolutely stationary over the entire test period. At

stations 40 ft and 140 ft the waves remained steady for several minutes at a time. At 240 ft

the wave field began to deteriorate after a short time. This was mostpronounced for the

shorter wave lengths. Figure 8 illustrates the nature of the wave profiles as a function of time

and space.

The highest and longest wave tested was A = 40 ft, h = 27 in. (Figure 8a). At

sta-tion 40 ft the profile is smooth but not sinusoidal. At 140 ftthe profile is somewhat trochoidal,

and at 240 ft it is reasonably sinusoidal. The three groups of waves which comprise the sample

for each station were made at intervals of 15 minutes. The group on the left shows a maximum

height variation of about 10 percent. This group differs in mean height from the following group

by about 12.5 percent. The same difference results from comparison of group 2 and group 3.

At stations 140 ft and 240 ft the same situation resulted for A= 20 ft and h = 10 in. (Figure 8b),

the wave height decreased down-tank in the manner described by the contour diagram (Figure 7i).

The profiles are not so smooth as those for A 40 ft but they are more sinusoidal near the

TABLE 2

Experimental Test Conditions (Prototype Scale) Temporal Distribution Station ft Wave Length ft Wave Height in. Slope 40 27 1/18 40 20 10 1/24 10 25 1/50 40 27 1/18 140 20 10 1/24 10 25 1/50 40 27 1/18 240 20 10 1/24 10 25 1/50 A =

(ra)l

40i feet from Wavemokers

(b) 140 feet (c) 240 feet

Figure ,8

Wave Profiles Recorded at 40, 140, and 240 Ft Down-Tank

in Front dr

Wavemaker V During 30-Minute Test Periods

Figure 8a+, X -a-- 40 Feet. bt--s 27

Incheu-4111111ENEEEEMINEEEEEEEMINEEEPEINEERIONMEEEEEEEN::];iliffFillUdEil EEL REEEFEINEIYMEmoramwarnaimmmommosammL' INVINEERIEINEREEEELNE.ErnillEINEEEEEEMEr

,11111M.ESEOCIEMIElliEMEMEERIEWEEMENEEEMIENINEEEEEEEEtirl:

ElliallHEMEEEIFIERNMEEMBliflIalllEMEEINEEEEEEEEE1111::::

MLISIVENIEVISINEIVEMEMEDEEHEIMEREFAEHEENEIHREINFAME::: IEEE@ iTIMPIENNE 11111AINEEMEEEEnEEEMIM

IMMEEMBIONEWEEN

41EIEEIIIIIEEEEE'ThEEK.VREPNEEEEEEEEEPMEERNEEEEEIMERIE

-!::11111111121EEENINE:i :-4;EINEEENIIIIIIIIIMEIEEN1110211 :HEEEEENEMIEMENIENEWEI

:::11111111MICE

MEEEEEICEIMESEEMEEM H-;1010111EffigiNNIIIM MEELIZENIFEIEEMEE :7i

47111111111E'Etil.:: 17"E11111111 3110111111:;,. 111EMENIF" IIMEEMIN

EME:.L

EEES.1:;::

MN

'--25

NMI _lURU IRE 1.15 2 IRE 1-10.2 IMP ENE

-0 MEI 2.8 sec 2,8 seconds

__-anommiumorsocninimminuurammeradi

liffifilffilittElErtlEiliffillinMill

.11111111111411111111111111111111111111111111111111

OEM

111111MEN 79111::. .11111MEIMIVIENNEENIENIE;::: 11111111111111§11111EINNEEE. - EMS - 25 ' UUU 11111Era -20.

glillE11111111110VERIMEN111PIII

41111111111illinlEVNIER11111111111/ EMINEEIA MINEMEMIE ISM

111111111111EMEREEI:::

..:1111111gENIMIEEELINEEff -111112D: -15 2. - NNW -10.2

141111411111,BREILIZIElf111/11111111111 LIE II1EMEMWEVERTMIECTIFFAIIIINEPAINWINAIIIIIIIIPA'1111. iiiii!EIEElm'EMEEEME111111111111EEMENEMEERI,.111-:

INEMEINE ;,,7mmialamme OBIEMENIEMINIONINSEIREINE::: NEEEERIMENNEEEEMIEICEEL -5 MIND' -0 =MEW Aineommuramommorommffinomuisinimmun Eau--1111ME..

-111111111AME11111E wEriminumenwirminammatimattiiiiiisiii.rimirtititsmonimmiinilor- IAINIERELERIVENEEMENEIFIEVERINEOMEIETNEEEEEEEENIEMINERMEISNIEEEEEMENEMEN51

-25

10111111011 011111111.1 -20v,

111111111111ENtilEHE OWEIPIERREEMINEENEEEMIEEEZEINEEEEEMEIMMELINEEEEMERIENIEENI _{1E11111111E V MEM}

MINEERINIIRIEEEEEMENIEREMINECIEEEEENEIN1111111EEENEEDIMINEME120110.-11111111WilleilanEll VIIIMEREEMEEINEEEEEESIMENEMINENEEEEINIMMINEEEDIVEMEEEREEMINI

EMOTE -15 .2 OMEN 1111,2 -10 .2 Emus _.alm -5

lEMIEVERIEMES IMEERVAMEEMEEEINEEEMEENEEViiiEEEEMEEEMEEIREELEINEMEEEEE EdiliENIENIENEEFAINEENEEEEEEEMEMEEENEERIEEEEEEEREEEERIEMEMIEMEEEEENEEE

11111154111111111111111

-0

Figure 8b = A 20 Feet, h 1011ricMs. :'iimAMEMMEMMEMEMMEMEMMMEMMUMEMMMMMEEMMEEMMIAMANNEMITEEM

Ma,

Emmisummmmummemm

Pm=

mumommummommmummammemmmmanemmmmmimmmmammommommitimm IINEMEMMMEMEMMEIROMMEMMUMMINIMOMMMMMEMEMMENOMMMMMAMMMM WOMMUMPAMMOIMMINMEMMEMEMMIIMMOMMINEMEMMEIMMOMEMMUMMME EIMMNMEWMEMMEIMMMOOMMEUMMEMMEMORIAMEMEMEMBOMPSMOIMEME

MMEMMEMMOMMEMMIIMMME

MMMIMMEM MMIEMME67/

1MMIIMMEM AEMMEMOIM

M_

AIEMBIMNEMM fuAMEMEMII 141MEM@MM

Mg=

FitEMMOMM t; MM MrA EgM AGIV ,1MM

11119MEMM MEIMEEET MMENIMM WORM@

ATAMEME TIROMMEIM

-MMEMEM

EM*: -ENV: rt alL4muMMUNEMMENAMEMMOMME

masimmommamemm

MMMIMMCMOIMMEM

UMW

MMMEMMMUMMUMMIMM MMIMMUMMOMMEM

MEM=

MMMAMMMIMMUMMIMM MMIMMEMMOMMMM WUNIMM MMOMMML IMMUML MOIMMMIMMEMMMOMMMIMMM MN MN

=MIMI

mmmommommin

UMMIUMMOMOMIMMMO

1 mm rIIMMMKAMEMMUMM

=BROM=

M MM MNP2MMMMOMMIMMOMWAMM = =

aagaioa' aitiasimal allumanammosamalawanummeammaima

.lammlifigmilitsgm EIMMOMOMMIIIIMMEIRMIMUM MIIIMINSIIIIMMM1011111111111111 10_1 _ 111111111111111111fiMMIIPIRM 19111111@WOMPOIRMNIONMNIIININIMIONIIIPSIEL A INAMENION1111151111110111111WIRNMFAMOMPI/ONZTAIMMENIIFINFIRMILIFAIRilliirlrl 111111ArnIMMI&MIEMMitl11111MM hAMMMIIIIIINMOYMINIIIII1411111.111MINIIIIMM0111 1:11 PHE p.HHInffIHIilm III RI I n unnun:, lir iil 9...911 P9 ;;

111111111111111MENIMMIERNIMIIIIIIMUMI:Willii MEM 2;MMMEINIMIEREIMINEIRINNEERMIU: 11911111111115M/1111111V1111111111141N111111111M

RIF01411-P111,11n

-11511i111111141120111i1MEIMIMMillillbil24114MMINNIMMINMIIit!

'''

'

-ffisihiAillEMMMEIMMIO11111111111 IIMEIRMEMMI21111111111111111111111111 IMMitiMMEMOIME1111111111111V 7ff1MIONLIIIIMEEEMBP70111:': M

Figure 8c

A=,10 Feet, h = 2.$ filches

qailat MT;

r-MEM

MkMMIT AMMO 4111MEM LIMON :EMMINW MEM MM

WC,

M MEMEIMCMEMMEMEMW MMMEAMMEMMEMEN M MEMMEMMEF MMIIMMOMMEM MM MERMEN EMMEN 4 P, rrA' ITU

T,MOMMEMMMEMMEMOMMEMMEMEMEMMMEMM NE111131011111MMMMOMMIMORIEMMOIMMMMOMMINDE i:"11111111,11110111TINTIVITINPLIMRTERINIMITAIPINIEM121111f

_{,7aimainciaranizaikonwasaaammaamarkania:::}

11111111111111111111MMMIRMMOMMME11111111111111111111111111MMERIE

MIIMMEEMMIIIMMMIMIIIMMEIMMM111

:111111111111M111411111111MIMINMERIMMMMIIIIV LIIIN1111111111111111111E111111111111111111111011111111111ft

chwamtraurtiminomminrwirrmf

:7inbasaitismaassimanitaiiiimmurai,:

sr. ....Aril/Affill111MNPVIWalrillliPini :::111111111111111111111110110111111111111111MIEMIN::: _{-11111111111111111111111111111111111111111111111":::} 1111i1111211110111111111114;1111iM1174:::: 1 I II/111111111101112111111 ,MINIIIIIIME1=111111111111111111111111111:::::::' LI WI MI IPA :1111111111111111 AMAIN 11 El &ASA

II

fi .1 ...

"aliagnikatmatiliiiamman

::::11111111M@IIIIMMIMMIN111111111111111111111111111111111111111111111111 7:11111111110NEFFIVIDEETTVErillrfrrthrlITMITITITM 1111 Ti11111 111L1111111111111111 .rommem. T1'1111 . 1

Figure 9a A.= 40 Feet, h -= 2.7 Inches, h/A= 1/50 Figure 9b 25 Feet, h= 5.0 Inches, h/A. -= 1/60

Figure 9c = 10 Feet, h= 3.4 Inches, h/A= 1/35 Figure 9d =5 Feet, h 1.1 Inch, h/A.= 1/53

Figure 9 Long-Crested Sinusoidal Waves Covering Entire Range of Wave Lengths

and Assorted Wave Heights

PSD-67033

L.--

=

wavemakers (40 ft). The height variation with time is less than that for the longer waves,

being on the order of 7 to 8 percent over a 30 minute sampling _period.

The shortest and lowest wave measured is A = 10 ft, h = 2.5 in. (Figure 8c). Even at

this low height and short length, the waves attain their sinusoidal _{shape during the down-tank}

journey, although the height is somewhat reduced with distance _{from the source. On the whole}

the temporal picture is encouraging. The middle range of waves is smooth and regular and has

the best record of constancy, with less than 10 percent variation for 30_{minutes of recording.}

The longest and highest waves are smooth-profiled though _{not regular until half the length of}

the basin has been traversed. Over a recording period of 30 minutes, the wave heights do not vary more than 15 percent. The smallest waves defy examination because of the fundamental crudity of the sensing and recording system. Again, it is expected that this difficulty will be

remedied in the prototype, where the 10-ft waves will be relatively long. _{Figure 9 shows some}

examples of the propagation of regular long-crested waves.

MISCELLANEOUS PHENOMENA

There are other problems related to the physical nature of the facility which_{may affect}

the propagation of long waves in the tank. Some of these have already been _{mentioned and}

require further discussion; others are essentially new.

HIGH-FREQUENCY SIDE RERADIATION

It has been observed that shortly after the wave generators are activated, high-frequency

wavelets appear to emanate from the sides of the tank. This is best illustrated in Figure 10.

At the outset (Figure 10a), the waves are free of any supplementary disturbance _{on the surface}

except at the corners, where some activity is evident. By the time the waves have traveled

two-thirds the length of the tank (Figure 10b) the superimposed high-frequency_{waves are}

evi-dent. In due time the waves travel the length of the tank (Figure 10c), the primary_{wave form}

is somewhat masked, and after several minutes (Figure 10d) the_{wave field appears quite}

mud-dled. It is noted that such activity is more pronounced on the side with the long bank of

wave-makers. It was suggested that the dome of the long bank of wavemakers acted _{as a resonator}

which reradiated waves at a length equal to the width of the dome. When a barrier was placed

in front of the dome, the situation was greatly alleviated. _{It has been recommended to the}

lab-oratory liaison officer that a barrier of this sort be incorporated into the plans of the prototype

and that the barrier in front of the long beach be more rigidly reinforced.

EFFECT OF VARIABLE DEPTH

The basin, as mentioned, is 20 ft deep with a narrow channel 35 ft deep running parallel and adjacent to the long bank of wavemakers. The question arose as to the effect of this

var-iable depth on the propagation of surface _{waves. The variable depth was modeled in the tank,}

(Text continued on page 32.) 26

111

6

":.1.,P=7

-Figure ;106'=;IGbfiefation of Initial Waves

..;i7woo :die .ANI

Hi 11

IMP

"4.

Figure 10c The First Wave Reaches

the Absorbing Beach

FrWraitliTitt"$

AM, .ralit17

Figure 10 Reradiation of Wave Energy from Side Barriers

The wave is 20i ft long and 22 in. high With a slope of 1/11.

Ti

c

Figure 10b The Waves Reach the

Three-Quarter Mark

1-47,4

' ir

PSD-67034

I !-,J" AL, 4 0 er Al!, . J Figure 1,1a 2 28

1 °.n k-' _ Et If II fl II 1.,11 , Figure i11DB Li

/4

-

I 30 11 Figure 12a V PSD-66843 1111

11

0 01

Figure 12b

Figure 12 PrOpagation of Long-Crested Waves,, Long Barrier Removed

11}

m

and waves with lengths proportional to 40 ft (Figure 11a) and 30 ft (Figure 11b) were produced.

As the waves pass over the shallow portion (center) they appear to be discontinuous, but this

is an illusion of refraction due to the photographic-optical system. When the _{waves emerge}

in deep water down-tank they are definitely continuous, which indicates that the variable depth has no measurable effect on the surface waves.

REMOVAL OF BARRIER

If tests in cross seas are desired, both banks of wavemakers must be utilized. In that case the long barrier must be removed. What happens to the waves is illustrated in Figure 12. The longest waves are refracted onto the beach (Figure 12b) whereas the shortest waves are apparently insensitive to the beach. Waves in the intermediate length range are proportionately affected. However, it is clear that the interference with the wave train does not extend far into the tank and will certainly not seriously reduce the working area.

EFFECTIVENESS OF WAVE ABSORBER

The effectiveness of the wave absorber is really a measure of the settling-out time of the wave system; that is, how long does it take the basin to calm itself? Long high waves, short small waves, and intermediate waves were used in this test. A stop watch measured the length of time it took the basin to quiet down after the last wave was incident on the beach. For the worst condition, the settling-out time was 12 minutes (prototype); 6 minutes was the

average time. It is expected that the same order of magnitude will apply to the prototype.

CONCLUSIONS

The material covered in this report results from a lengthy investigation of the wave fields produced by a number of waves of different length and height. Where the results were not immediately evident they were summarized at the end of the individual sections. The conclu-sions which follow are based on the collected data and are extended where possible to refer

to the prototype.

Balancing the wavemakers is the primary task in the production of long-crested waves.

This is related to the physical properties of the individual wavemakers and must be done

sep-arately for each wave-generating system.

When balancing the wavemakers the test section should be as close to the wavemakers as possible, to insure the generation of the desired wave.

The spatial distribution of wave heights indicates that sufficient working area is avail-able for most tests, once the disturbing effects due to the side wall are removed.

Little can be said of the short wave lengths because it was not possible to examine

32 '3.

them. This difficulty stems from scale effects which are peculiar only to the one-tenth scale

model.

The temporal distribution indicates that quasi-stationary conditions, on the order of 5 minutes in the prototype, may be expected. This should be sufficient to carry out most tests.

Reradiation effects from the sides of the tank can be reduced by placing a bulkhead

in front of the wave bank not in use and by reinforcing the bulkheads in front of the beaches.

(Or see 8 below.)

Variable depth in the tank appears to have no effect on the surface waves.

The removal of Offside barrier has little effect on the wave field so the side barrier

may be removed in long-crested wave tests.

It is expected that settling-out time-will not generally exceed 12 minutes.

In general, models must be between 10 and 20 ft long for tests in wave lengths equal to half the ship length and twice the ship length.

This report is not intended to supplant ti similar test program in the prototypebut is

intended rather as a guide for the proper orders of magnitude which may be expected, and as an indication of inherent difficulties which may or may not be remedied.

5.,

[6.

7.,

APPENDIX

BASIC DATA ON BALANCING THE WAVEMAKER

Table 3 given in this appendix describes the adjustment required to produce waves with certain lengths and heights in the tenth-scale model of the maneuvering basin. It is

understood that these numbers are not applicable to the prototype. It is also understood that

these numbers are not unique because there is an infinite number of combinations of blower-motor speed and trimming-valve angle that will yield the desired wave height for a particular wave length.

TABLE 3 - Blower and Trimmer Valve Settings Required for Specified Wave Heights and Wave Lengths Height in. Trimming Angle Percent Deviation from Mean Height in. Trimming A ogle Percent Deviation from Mean Height in. Trimming Angle Percent Deviation from Mean Height in. Trimming Angle Percent Deviation from Mean A = 40 ft, 11=27 in., Slope 1/18 A =40 ft, h= 22.5 in., Slope 1/21 A =40 ft, It = 12 in., Slope 1/40 A =

40 ft, It= 10 in., Slope 1/50

Blower Setting 6 Blower Setting 5 Blower Setting 4 Blower Setting 3 26.8 51 -0.8 22.4 52 -0.5 12.28 47 +2.8 9.71 46 +2.6 26.8 62 -0.3 22.8 61 +1.3 11.50 53 -3.8 9.56 56 +1.2 27.7 60.5 +2:4 23.4 61.5 +4.0 12.15 49 +1.6 9.47 50 0 26.4 59 -2.3 223 57 +1.0 11.91 49 -0.4 9.40 52 -0.3 27.2 63 +0.6 22.8 63 +1.3 11.69 49 -2.1 9.12 51 -3.6 27.1 56 +0.25 223 56 -0.9 12.66 48 +5.9 10.06 49 +5.2 26.9 62.5 -0.5 21.8 62.5 -3.2 11.60 53 -3.0 9.12 54 -3.6 27.3 56 +1.0 22.2 56 -1.3 11.86 49 -0.8 9.33 50 -1.4 h=27.03 in, A=22.55 in. h = 11.95 in. 71.= 9.47 in. A = 30 ft, h= 30 in., Slope 1/12 A = 3011, h= 27.5 in., Slope 1/13 A =3011, h= 12.5 in., Slope 1/29 A 3011, h= 9.5 in., Slope 1/38 Blower Setting 6 Blower Setting 5 Blower Setting 4 Blower Setting 3 34.05 64 +9.0 28.39 64 +4.7 13.00 43 +1.2 9.13 43 -2.0 29.75 71 -4.8 26.30 72 -3.4 12.90 51 +0.5 9.42 51 +1.1 31.90 68 +1.1 27.12 66 0 12.40 48 -3.4 9.00 48 -3.4 30.95 70 -1.0 26.59 72 -2:0 13.06 50 +1.7 9.51 50 +2.1 29.74 70 -4.8 25.69 72 -5.6 12,96 41 +1.0 9.26 46 -0.6 31.20 70 -0.2 25.95 73 -4.4 12:96 51 +1.0 9.58 51 +2:8 30.00 71 -4.0 27.75 74 42.3 12.94 49 +0.7 9.41 49 +1.0 32.42 64 +3.8 29.30 64 +8.0 12;54 46 -2.4 9.30 46 -0.2 h= 31.25 in. 4= 27. 2 in. h= 12.84 in. h= 9.32 in.

A=30 ft, h= 7 in., Slope 1/54

A=25 ft, '5=27 in., Slope 1/11

A=25 ft, h= 22.5 in., Slope 1/13

A= 25 ft, h= 17 in., Slope 1/18 Blower Setting 2 Blower Setting 6 Blower Setting 4 Blower Setting 3 6.68 43 -0.7 28.31 60 +4.7 22:78 49 -2:1 16.42 48 -2.2 6.98 51 +3.8 27.10 72 +0.3 22.00 56 -1.4 16.63 57 -0.9 6.54 48 -2.8 26.60 70 -1.5 21.03 54 -5.8 16.41 53 -2.2 6.98 50 +3.8 27.32 70 +1.2 22.35 56 +0.2 16.30 55 -2.9 6.48 46 -3.6 21.15 72 +0.5 21.93 53 -1.7 17.00 54 +1.3 6.70 51 -0.3 26.09 75 -3.5 22.95 59 +2,8 16.92 60 +0.8 6.95 49 +3.3 25.59 72 -5.4 21.85 53 -2:0 17.04 52 +1.5 6.48 46 -3.7 28.00 69 +3.6 23.58 50 +5.6 17.50 51 +4.2 it= 6.72 in. ir =27.02 in. h =22.31 in. h= 16.78 in. I I

Wavemaker Height tn. Trimming Angle Percent Deviation from Mean Height in Trimming Angle Percent Deviation from Mean Height IA. Trimming Angle Percent Deviation from Mean Height in. Trimming Angle Percent Deviation from Mean X =25 ft, h= 1 in., Slope 1/27 X=25 ft, h= 5 in., Slope 1/60 A= 20 ft, h= 22 in., Slope 1/11 X =20 ft, h= 17 in., Slope 1/14 Blower Setting 2 Blower Setting 1.5 Blower Setting 6 Blower Setting 5 1 10.90 47 -2,1 5.06 49 +0.4 21.38 53 -2.9 16.60 53 -1.5 II 11.03 56 -0.9 479 55 -5.0 22,61 61 +2.7 18.20 61 +7.9 III 10.78 53 -3.2 5.09 57 +0.9 21.00 59 -4.5 17.84 59 +5.8 IV 11.11 55 -0.2 5.10 60 +1.2 22.90 60 +4.0 16.73 60 -0.8 V 11.07 54 -0.5 4.91 53 -2:7 22.30 58 +1.4 16.55 58 -1.9 VI 11.54 62 +3.6 5.12 59 +1.5 23.06 67 +4.7 16.60 67 -1.5 VII 11.11 51 +0.2 5.18 52 +2.7 21.22 59 -3.5 16.35 59 -3.0 VIII 11.50 50 +3.3 5.11 49 +1.3 21.58 53.5 -2:0 16.00 53.5 -5.1 h= 11.13 in. h= 5.045 in. h= 22.01 in. 4=16.86 in. X= 20 ft, h= 15 in., Slope 1/16 X= 20 ft, h= 10 in., Slope 1/24 A = 20 ft, h= 4.5 in., Slope 1/53 X= 10 ft, h = 6 in., Slope 1/21 Blower Setting 4 Blower Setting 3 Blower Setting 1.4 Blower Setting 3 I 15.00 53 +0.3 10.35 55 +4.8 4.47 52 -1.1 7,10 53 +3.1 II 15.00 61 +0.3 9.54 61 -3.4 4.47 63 -1.1 7.10 61 +3.1 III 15.00 59 +0.3 9.75 60 -1.3 4.49 59 -0.6 6.92 59 +0.5 IV 14.62 60 -2:2 9.72 62 -1.7 4.44 55 -1.7 6.77 60 -1.7 V 14.15 58 -5.3 9.88 57 0 4.83 56 +7.0 6.92 58 +0.5 VI 15.41 67 +3.1 9.32 65 -5.4 4.46 66 -1.3 6.70 67 -2.7 VII 14.94 59 -0.1 9.88 59 0 4.47 59 -1.1 6.88 59 -0.2 VIII 15.50 53.5 +3.6 10.32 54.5 +4.4 4.50 53.5 -0.4 6.69 53.5 -2.8 Ta= 14.95 in. h = 9.845 in. h = 4.52 in. h= 6.885 in. X =10 ft, h= 3 in., Slope 1/35 X = 10 ft, h = 2 in., Slope 1/49 X= 5 ft, h = 1.5 in., Slope 1/40 X= 5 ft, h= 1 in. Blower Setting 5 Blower Setting 4 Blower Setting 3 Blower Setting 2 I 3.37 22 -2.0 2.37 23 -2.9 1.545 51 +3.0 1.087 51 II 3.49 31 +1.5 2.415 31 -1.0 1.535 60 +2.3 1.093 60 -3.4 III 3.53 31 +2.7 2:59 33 +6.1 1.480 62 -1.4 1.057 62 -6.5 IV 3.57 30 +3.8 2:44 29 0 1.447 61 -3.5 1.170 61 +3.5 V 3.39 25 -1.5 233 23 -4.5 1.558 55 +3.8 1.157 55 +2,4 VI 3.42 32.5 -0.6 2.59 34 +6.1 1.410 64 -6.0 1.068 64 -5.5 VII 3.30 25.5 -4.0 2,30 23 -5.8 1.440 56 -4.0 1.200 56 +6.2 VIII 3.43 20 -0.3 2.50 21 +2:5 1.596 50 +6.3 1.212 50 +7,2 4=3.44 in. 4=244 in. h= 1.50 in. h= 1.13 in. 1 -3.8 I

REFERENCES

Marks, Wilbur, "On the Prediction of Full-Scale Ship Performance from Model Tests,"

Symposium on the Behaviour of Ships in a Seaway, Wageningen, Holland (Sep 1957).

Pierson, W.J., Jr., "Wind Generated Gravity Waves," Advances in Geophysics, Vol. _2,

pp. 93-178 (1955).

Lewis, E.V., "Irregular Waves in Model Tanks," Experimental Towing Tank, Stevens

Institute of Technology, Proceedings First Conference on Ships and Waves (Nov _1954).

Marks, Wilbur and Pierson, W.J.,Jr., "The Directional Spectrum of a Wind Generated

Sea," Paper presented at 38th Annual Meeting, American Geophysical Union, Washington, D. C. (Apr 1957).

Marks, Wilbur, "On the Status of Complex Wave Generation in Model Tanks," David

Taylor Model Basin Report nu (Jul 1956).

Brownell, W.F., "A Rotating Arm and Maneuvering Basin," David Taylor Model Basin Report 1053 (Jul 1956).

Brownell, W.F., et al., "A 51 Ft. Pneumatic Wavemaker and a Wave Absorber," David Taylor Model Basin Report 1054 (Aug 1956).

Kennard, E.H., "Generation of Surface Waves by a Moving Partition," Quarterly of Applied Mathematics, Vol. 7, No. 3, pp. 303-312 (Oct 1949).

INITIAL DISTRIBUTION

3 9

Copies Copies Copies

It CHPUSHIPS, Library (Code 312)

5 Tech Library

1 Prof. C.W. Prohaska, Danish Model Basin,

Hjortekaer, Denmark

1 Director, Royal Institute of Tech,

Stockholm, Sweden

1 Tech Asst to Chief (Code 106)

1 Res&Dev Program Plan (Code 320)

1 Sci&Res (Code 442)

1 Mr. W.P. Walker, Orr, Wm. Denny&Bros, Ltd,

Dumbarton, Scotland

1 Dr. H. Edstrand, Statens Skeppsprovningsanstalt,

Goteborg C, Sweden 2

1

CHONR, Mach Br (Code 438) DIR, USNRL

1 Dr. F.H. Todd, Supt of Ship Div, NPL,

Teddington, England

1 Chief, Hydro Res, Escher Wyss Lab,

Zurich, Switzerland

1 CDR, USNOL

1 Mr. P.R. Crewe, Chief Erg!, Saunders-Roe, Ltd,

Isle of Wight, England

1 DIR, Istanbul Model Duper Tank, Turkish

Shipbuilding&Res Inst, Istanbul, Turkey

1 CDR, USNOTS, Pasadena, Calif.

1 Prof. L.C. Burrill, Prof. of Nay Arch, Univ of 1 Prof. S. Silovic, Shipbuilding Run Inst.

1 CO&DIP, USNUSL, New London, Conn.

Durham, Kings College, Newcastle-on-Tyne 1,

England

Zagreb, Yugoslavia

1 Dr. E.V. Teller, Skipsbygging, Norges

1 CO, USNUOS, Newport R.I. 1 Supt, Ship Model Exper Tank, Vickers-Armstrong Tekniske Hogskole, Tronheim, Norway

II DIR, USNEES, Annapolis, Md.

Ltd, St. Albans, Harts, England

1 CO, USNMDL, Panama City, Fla.

9 USN Attache, London, England

1 D1R, Towing Tank, Convair Div of General

Dynamics Corp, San Diego, Calif.

RADM Roger E.M. Braid, Dir, Bassin d'Essais, des Carenes, Paris, France

1 DIR, Buyer Naval Tank, Univ of Mich,

Ann Arbor, Mich.

Prof. J.J. Rahola, Finland Inst of Tech,

Helsinki, Finland

1 DIR, Garfield Thomas ,iater Tunnel, ORL,

University Park, Pa.

It Dr. H.W.F. Lerbs, flit, Hamburg Model Basin, Hamburg, Germany

1 DIR, Hydra Lab, NNSB&DCCo.,

Newport News, va.

1 DIR, Versuchsanstalt ffir Wasserbau und

Schifbau, Berlin 87, Germany

1 Head, Dept of NAME, MIT, Cambridge, Mass.

1 Prof. Dr. !rig. Allis di Bella, Dir, hist of Nay

Arch, Univ of Genoa, Genoa, Italy

1 DIR, Ship Model Towing Tank, MIT,

Cambridge, Mass. 1

Pres. log. U. Pugliese, Instituto Naz per Studi ed Esp. di Arch, Nay, Rome, Italy

1 DIR, ETT, SIT, Hoboken, N.J.

1 DIR, Towing Tank, U.S. Nan Academy,

Annapolis, Md.

Prof. D. Volker, Indian Int of Tech, Kharagour,

West Bengal, India

1 Chief, Meguro Model Basin, Transportation

1 DIR, Hydra Model Basin, Univ of Calif,

Richmond, Calif.

Tech Res Int, Tokyo, Japan

1 D1R, Exper Tank, Mitsubishi Shipbuilding 1 DIR, Robinson Model Basin, Webb Int of Tech,

Glen Cove, L.I., N.Y.

&Engin Co., Ltd, Nagasaki, Japan

1 OinC, Postgrad School, 'Hebb Inst of Tech,

Glen Cove, L.I., N.Y.

1 Mr. Taboo Ito, Ministry of Transportation,

Shipbuilding Section, Tokyo, Japan

1 Prof. W.P.A. van Lammeren, Netherlands 1 Chief, Nall Hydra Lab, US Natl BuStand Ship Model Basin, Wageningen., Netherlands

1 Hydro Lab, CIT, Pasadena, Calif. 1

DIR, DeVoorst Hydr Lab, Emmeloord, Netherlands

1 DIR, Fluid Much Lab, Univ of Calif,

Berkeley, Calif.

e 1 Dr. J. Cerritsma, Univ of Tech, Shipbuilding Lab,

Delft, Netherlands

1

1

DIR., Hydra Lab, Carnegie Inst of Tech, Pittsburgh, Pa,

DIR, Hydra Lab, Colo St Univ, Ft Collins, Colo,

Prof. J.K. Lunde, Dir, Statens Skipsmodelltanken, Trondheim, Norway

Dir, Kryloff Shipbuilding Res Int, Leningrad,

Russia

1 DIR, Iowa Inst of Hydra Res, Iowa City, Ia.

1 MR, AEW, Haslar, England

1 DIR, St Anthony Falls Hydra Lab, Univ of Minn,

Minneapolis, Minn. 1 Dr. J.F.C. Conn, Prof of Nay Arch, Univ of Glasgow,

Glasgow 01-2, Scotland

1 Dr. L. Kretschmer, Schiffbautechnische

Versuchsanstalt, Vienna XX, Austria 1 Mr. J. M. Ferguson, Supt of Doper Tank, John

Brown&Co, Ltd, Glasgow, Scotland.

1 Dr. A. Andreoni, Tech Res Int, Doper Tank,

So Paulo, Brazil 1 Dr. Manuel Lopez Acevedo, Canal de Experiencias

Hidrodinamicas, Madrid, Spain

1 DIR, Model Testing Basin, Natl Res Council,

Ottawa, Canada 1 Mr. L. Pehrsson, Chief of Cavitation Tunnel,