Comparison of ship motion theory and experiment for mariner hull and a destroyer hull with bow modification

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NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER

Washington, D.C. 20034

ibliotheek van

e---Onderafdelin

elsbouwkunde Hogescho-OT,--Degt----nische -.173 DOCUMENTATIE

DATUM:

00' o'3 IS6

COMPARISON OF SHIP-MOTION THEORY AND EXPERIMENT

FOR MARINER HULL AND A DESTROYER HULL WITH

BOW MODIFICATION

by

N. Salvesen and W.E. Smith

Approved for public release; distribution unlimited.

SHIP PERFORMANCE DEPARTMENT

RESEARCH AND DEVELOPMENT REPORT

June 1971 Report 3337

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The Naval Ship Research and Development_{Center is a U.S. Navy center tor laboratory}

effort directed at achieving improved sea and air_{vehicles. It was formed in March 1967 by merging the} David Taylor Model Basin at Carderock, _{Maryland and the Marine Engineering Laboratory (now}

Naval Ship R & D Laboratory) at Annapolis, Maryland, The Mine Defense Laboratory (now_Naval

Ship R & D Laboratory) Panama City, Florida became part of the Center in_{November 1967.}

Naval Ship Research and Development Center

Washington, D. C. 20034 * REPORT ORIGINATOR A700 DEPARTMENT OF MATERIALS TECHNOLOGY A800 DEPARTMENT OF APPLIED SCI ENCE A900 1 SYSTEMS DEVELOPMENT OFFICE 01101

MAJOR NSRDC ORGANIZATIONAL COMPONENTS

700 SHIP ACOUSTICS DEPARTMENT 900 800 NSRDL PANAMA CITY COMMANDING OFFICER TECHNICAL DIRECTOR

-I

DEPARTMENT OF TECHNOLOGY OCEAN P710

-I

D COUNTERMEASURES DEPARTMENT OF MINE P720

--I

COUNTERMEASURES DEPARTMENT OF AIRBORNE MINE P730 ,..IDWEAPRAFRAIIENTg)capiE0DROE DEFENSE P740 NDIVWSRDC 3960/43 (340) SHIP CONCEPT

RESEARCH OFFICE PROJECT OFFICESDEVELOPMENT

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*

SHIP PERFORMANCE DEPARTMENT AVIATION DEPARTMENT A600 500 600 DEPARTMENT OF MACHINERY TECHNOLOGY STRUCTURAL MECHANICS DEPARTMENT COMPUTATION AND MATHEMATICS DEPARTMENT NSRDC CARDEROCK COMMANDER TECHNICAL DIRECTOR

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DEPARTMENT OF THE NAVY

NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER

WASHINGTON, D. C. 20034

COMPARISON OF SHIP-MOTION THEORY AND EXPERIMENT FOR MARINER HULL AND A DESTROYER HULL WITH

BOW, MODIFICATION

by

Approved for public release; distribution unlimited.

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REFERENCES TABLE OF CONTENTS EXPERIMENTAL STUDY TEST PROCEDURE ... . .. ANALYSIS OF DATA THEORETICAL STUDY LIST OF FIGURES Page ABSTRACT ADMINISTRATIVE INFORMATION ... ... ...

...

1 INTRODUCTION 1 7

COMPARISON OF EXPERIMENTAL AND THEORETICAL RESULTS 9

MARINER HULL FORM -9

DESTROYER HULL WITH AND WITHOUT BOW MODIFICATION 10

CONCLUSIONS 11

APPENDIX: LINEARITY PLOTS AND TABULATED VALUES FOR THE

TEST MODELS 23

34

Page

Figure 1 - Comparison of Experimental and Theoretical Heave and

Pitch Amplitudes for Series 60, Block 0.70 Form at

Fr= 0.30

... ... .. .. . ... . ... ... . . . 13

Figure 2 - Body Plans of Ships A and B with and without

Bow Modification ...

... ... ... ....

14

Figure 3 - Comparison of Experimental and Theoretical Heave

Amplitudes for Ships A and B 15

Figure 4 - Instrumentation for Measuring Heave, Pitch, and

Surge for Free-Running Model 16

Figure 5 - Comparison of Experimental and Theoretical Pitch and

Heave Atplitudes for Mariner Hull at Fr = 0.10 and

Fr = 0.20 16

Heave Amplitudes for Mariner Hull at Fr = 0.30 and

Fr = 0.40 17

Heave Phases for Mariner Hull at Fr = 0.10 and

Fr = 0.20 18

Heave Phases for Mariner Hull at Fr = 0.30 and

Fr = 0.40 19

.

... ...

5

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Figure 9 - Comparison of Experimental and Theoretical Pitch and Heave Amplitudes for Destroyer Hull at

Fr = 0.204

Heave Amplitudes for Destroyer Hull at Fr = 0.272

Heave Amplitudes for Destroyer Hull at Fr = 0.408

Figure 12 - Comparison

of

Experimental and Theoretical Pitch and

Heave. Phases for Destroyer Hull at Fr = 0.204

Figure 13 - Comparison of Experimental and Theoretical Fitch and

Heave Phases for Destroyer Hull at Fr = 0.272 22

Figure 14 - CoMparison of Experimental and Theoretical Pitch and

Heave Phases for Destroyer Hull at Fr 0.408 22

Figure 15 - Heave and Pitch Linearity Study for Mariner Hull at

Fr = 0.10 24

Fr= 0.20

25

Figure 17 - Heave and Pitch Linearity Study for Mariner HUH at

Fr = 0.30 26

Fr= 0,40

... ... ... . .... 27

Figure 19 - Heave and Pitch Linearity Study for Destroyer Hull at

Fr = 0.204 28

Figure 20 - Heave and Pitch Linearity Study for Destroyer Hull at

Fr = 0..272 29

Figure 21 - Heave and

Pitch

Linearity Study for Destroyer Hull at

Fr = 0.408 30

LIST OF TABLES

Table 1 - Characteristics of the Test Models

Table 2 - Numerical Values for Experimental and Theoretical Heave

and Pitch Amplitudes and Phases for Mariner Hull' 31

Table 3 - Numerical Values- for Experimental and Theoretical Heave and Pitch Amplitudes and Phases for Destroyer Hull with

Bow Modification 32

Table 4 - Numerical Values for Experimental and Theoretical Heave

and Pitch Amplitudes and Phases for Destroyer Hull

with-out Bow Modification 33

Page 20 20 21 Page 5

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'References are listed on page 34. ABSTRACT

The objective of this study was to evaluate more pre-cisely the accuracy of ship-motion strip theory for ships in

head seas. _{Theoretical and experimental results were compared}

for the Mariner hull and for a destroyer hull with and without

a bow modification. _{In view of the good agreement found, it}

was concluded that for practical design purposes, strip theory can be used to predict head-seas motions with satisfactory

accuracy provided there is adequate station representation.

ADMINISTRATIVE INFORMATION

This study Was authorized by the Naval Ship Systems Command (NAVSHIPS)

under the General Hydromechanics Research Program with funding under

Sub-project S-R009 01 01, Task 0100 And by Bureau of Ships letter Serial

1623-206 dated 19 August 1965 with funding under S-2217, Task 8543.

INTRODUCTION

. Extensive comparison studies of strip theory and experiments for

head-seas ship motions have been conducted at various laboratories during

the last decade. _{As a result of this work, strip theory can} _{now be used}

to predict head-seas ship motions with a quite satisfactory confidence

level. Strip theory has been shown to work well for common cruiser-stern

ships at low and moderate forward speeds (see, for example, Gerritsma and

Beukleman)1 _{and for high-speed destroyer hulls at low, moderate, and high}

speeds (see Smith)2 as well as for many hulls with large bulbs (see Smith and Salvesen).3

The main objective of the present investigation _{was to evaluate more} precisely the accuracy of the Frank close-fit ship-motion _{computer program.4} This computer program is based on an improved version of the original

head-seas strip theory of Korvin-Krouskovsky and Jacobs.5 _Noticeable

dis-crepancies between theory and experiments have been found for the two following cases:

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Pitch amplitudes for cruiser-stern ships at very high speeds.

Heave amplitudes for some destroyer hulls with large bow

modifi-cations.

The present study was undertaken to further investigate these two kinds of

discrepancies.

A comparison of the improved strip theory with the

Gerritsta-Beukelman study' on the Series 60, block 0.70 hull form indicated that the

theory overpredicted pitch amplitudes at very high speeds. At Froude number (Fr) 0.20 (15 knots for a 500-foot ship), the theoretical pitch was only 8 percent more than found experimentally; at Fr = 0.25 (19 knots), it was 16 percent larger, whereas at Fr = 0.30 (24 knots), it overestimated

the measured pitch by as much as 45 percent (see Figure 1 for the 0.30

Froude number case). However this discrepancy should not be interpreted as

necessarily indicating that the strip theory is inadequate for all ships at

high speeds. For example, Smith has found good agreement for high-speed

destroyer hulls up to Fr = 0.45.

It is felt that the discrepancy for the Series 60, block 0.70 hull

form at Fr = 0.30 was most likely due to an interaction between the

oscillatory motions and the large "steady-state" waves created by the hull

when operating substantially above design speed. The maximum design speed

for a 0.70-block cruiser-stern ship is about Fr = 0.24, and theory and experiment seem to agree quite well at that speed. Note that in the derivation of the strip theory, the "steady-state" wave resistance perturbation potential is assumed to be small enough to be ignored in

determining ship motions. Physically this means that the waves created by

a ship advancing at constant speed in calm water are assumed to have no

effect on ship motions. This appears to be a fairly reasonable assumption

for most displacement ships operating ,at or below their design speeds.

Comparisons between theory and experiments for head-seas motions seem to

verify this. For cruiser-stern ships with a block coefficient of 0.7.0,

quite satisfactory agreement has been found for speeds up to Fr = 0.20; with a block of 0.60, the agreement was good up to Fr = 0.25; and for

high-speed transom-stern ships with a block of about 0.50, reasonable agreement has been shown for speeds up to Fr = 0.45.

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It was felt that additional confidence in the accuracy of the strip

theory for predicting pitch amplitudes', of cruiser-stern ships at high speeds could be obtained by-conducting an additional .head-seas Model test,

using the free-running model-test technique recently developed by Smith

and Salvesen.3 The Mariner hull form was selected as a good sample of

modern.high-speed cruiser-stern ships. It has a maximum design speed of .

about Fr =0.28 and a block coefficient of 0.63. It was also decided to,

conduct a careful investigation of the nonlinearities in the motion responses

with respect to the wave height.

The prediction of head-seas mcitions for ships with large bulbs:and

extreme bow modifications has received much attention in the past few

years. By applying close.fit ship-section representation in computing the

added-mass and damping coefficients used in the strip theory, Smith2 .

showed that the maximum heave amplitude for the Davidson A form (a high-speed transom-stern hull with an extremely large bulb) was approximately

twice that of similar hull forms without bulbs. More recently, Smith and

3

Salvesen- compared theoretical and experimental results for the pitch and

heave motions of the Davidson A hull. Their experimental results showed

about the same large increase in heave amplitude due to the,bUlb as

pre-dicted by the strip theory. However, their results also indicated that

the heave response for.the Davidson A hull as markedly nonlinear with

respect to wave amplitude and that agreement between theory and experiment

for the heave, amplitudes was satisfactory only when stall amplitude waves

were used. Furthermore; their experimental investigation showed that the

heave measurements for a hull with a large bulb could easily be affected by mechanical friction when the heave-staff technique was used to measure

responses. This is attributed to the fact that the heave responses- for

hulls with large.bulbs have considerably less damping and hence a,very

sharp resonant peak compared to regular hull forms. Smith and Salvesen

concluded, therefore, that it was necessary to use a free-running model-test technique for the Davidson A form in order to obtain the most

accurate heave amplitude data and also that small amplitude waves had to

be used for this particular hull form in order to stay within the linear. response range.

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A couple of years ago, Dr. Shen Wang compared theoretical and

experi-mental ship motions for high-speed destroyers with modified bows. He

investigated the pitch and heave motions for seven destroyer hulls with and without modified bows, and found satisfactory agreement for most of the hull forms with computed results obtained by the Frank close-fit

ship-motion computer program. However the noticeable discrepancy found for

some of the forms precluded the drawing of general conclusions with respect

to the accuracy of the program as applied to hulls with large bow

modifi-cations.

The Wang study drew our attention to some unexplainable

dis-crepancies

in

the heave amplitude results for two of the hull forms.

Figure 2 shows the body plans of these two hulls as used in the computer representation; they will be referred to in this report as Ship A and

Ship B. Both ships have high,speed, transom-stern hull forms and their

hull shapes are generally quite similar except for their somewhat different

bow modifications. Comparison of theoretical and experimental heave

ampli-tudes (Figure 3) did not indicate the same degree of accuracy for these

two ships. There was practically no increase in measured heave due to the

modified bow for Ship A whereas theory predicted an increase of about

20 percent. For Ship B, on the other hand, both theory and experiment

showed an increase in heave of about 38 percent due to the Modified bow. It should be pointed out that both Ship A and Ship B had been tested in the

same model tank under the same regular-wave conditions and that the same mechanical heave-staff technique had been used for measuring responses.

Taking all of these factors into consideration, we could see no particular reasons why there were such differences between theory and

experiment for these two ships. It was decided, therefore to conduct

additional head-seas experiments for the Ship A. destroyer hull with and

without bow modification in order to further investigate these

dis-crepancies. It was felt that the most accurate test data could be obtained

by using the free-running model-test technique and by including an

experi-mental investigation of the nonlinearities in the motion responses.

Unpublished NSRDC study.

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This paper reports on the findings Of the tWo following _{model tests} in regular waves: (1) the Mariner hull and (2) the destroyer _hull,

Ship A with and without bow modification. _{Comparisons between strip theory}

and experiments are also presented.

EXPERIMENTAL STUDY

TEST PROCEDURE

The free-running technique developed by Smith and Salvesen3 was

used to test the models. _{Their characteristics are listed in Table 1.}

TABLE 1

Characteristics of the Test Models

The Mariner hull model was tested ai seven _{wave lengths (L/X = 0.50,}

0.60, 0.70, 0.80, 0.90, 1.00, an-d 1.10) for each o four Froude numbers

(Fr = 0.10, 0.20, 0.30, and 0.40). _{The destroyer hull model with bow}

modification was tested at eleven _{wave lengths (L/X = 0.57, 0.67, 0.75,}

0.80, 0.85, 0.90, 0.95, 1.00, 1.10, 1.20, and 1.30) _{for each of three}

Froude numbers (Fr = 0.204, 0.272, and 0.408)% _{The destroyer model without}

bow modification was tested at the _{same speeds but at only five wave}

lengths (L/X = 0.67, 0.80, 0.90, 1.00, and 1.10).

5

Parameter Mariner Hull

Form (Model 4906)

Ship A Destroyer Hull Form

With Mod. Bow Without Mod. Bow

Length between

per-pendiculars LBP, ft 12.69 20.00 20.b0 Beam, ft

-- --

_1.83 _2.17 _2.17 Draft at , ft _0.715 0.67 0.67 Block coefficient _0.632 _0.482 0.467 Center of buoyancy, ft _0.208* _0.008** _0.14* Center of flotation, ft 0.524* 1.37* 1.37* Radius of gyration/LBP, ft 0.250 0.265 0.255 * Aft of CD ** Forward of ₀₃

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Furthermore, in order to evaluate the linearity of the responses with respect to wave height, the Mariner hull and both f6rms of Ship A hull were tested at each wave length for wave heights ranging from 0.3 to

2.8 inches.

The tests were performed in regular waves using Carriage 2 in the 1200- x 51- x 22-foot basin with the model self-propelled and remotely

steered. Figure 4 is a sketch of the instrumentation used for measuring

heave, pitch, and surge motions. Four sonic transducers were used; two

measured pitch and heave, one measured surge, and one (not shown in the

sketch) measured wave height. One of the pitch-heave transducers (A) was

located 4 feet aft of the forward perpendicular (FP) and the other (B) was 4 feet forward of the aft perpendicular (AP). Both transmitters and

receivers were attached to the model, amd the signals were reflected by a

horizontal flat plexiglass plate. The transducer for surge had its

transmitter (C-S) at the AP and its receiver (C-M) attached to the carriage

about 4 feet aft of the model. The wave-height transducer was placed

10 feet forward of the model. The roll angle and the rudder angles were

also measured. All the data included in this report are from runs with

roll angles no larger than 2 degrees.

ANALYSIS OF DATA

One of the major difficulties in experimental seakeeping studies is

to make "clean" regular sinusoidal waves. In addition to the fundamental

wave component, other wave-length components are also present, particularly,

higher harmonic components. Therefore, in order to separate the fundamental

component from the actual wave measurement, the wave data were digitized

and then Fourier analyzed on a digital computer. Similarly, the motion

response data were Fourier analyzed to separate the responses associated with the nonfundamental wave components from the motion data and so obtain a purely sinusoidal response associated with the fundamental wave component.

Heave was also measured by an accelerometer in order to check the

accuracy of the data.

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This is similar to the approach used in obtaining the response amplitude

operators from irregular wave data. This technique proved to be very

satisfactory and resulted in a much smaller spread of the data, especially

for the pitch and heave phases.

The heave and pitch amplitudes were plotted versus wave height in

order to evaluate the linearity of response. In general, these test data

seemed to be quite linear. However, because of the rather large spread in

data, a smaller line was drawn through the test points for each case to obtain the mean values used in the comparison of experimental and

theo-retical results (see Tables 2-4 in the appendix).

(A33 4- 11) 113

where n3 is the heave displacement coefficients are dependent on both. the form:

A33 =

f

a ()

B33 j=

b() dE

C33= pg

B (E) dE

THEORETICAL STUDY

The theoretical results used in this study

the Frank close-fit ship-motion computer program.

was developed by Frank and Salvesen4 and is based .5

the linearized strip theory by Korvin-Kroukovsky

station representation. The coupled differential

heave motion are:

A

+ B

+ (A + J) + B 77) + C = F 53 3 53 3 55 5 55 5 55 5 5 and ns is frequency

Ass

B55

were all obtained from This computer program on an improved version of

with accurate close-fit equations for pitch and

+ C n = F

35 5 3

the

pitch

angle. The

and forward speed and are of

2

fE2a(E) dE 12-A33

fE2b(E) dE

C55 pg

..12B()

dE

The subscript notation for six-degree-of-freedom motion (Salvesen et al. )6

is used here with

n, j

_{referring.to surge, sway, heave, roll,}

pitch, and yaw displacement, respectively.

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A35 =-

fa()

dE - V2B33

A53 jrEa(E) dE + V2 B33

B35 =-

fEb(E)

dE V A33

B53

lEb(E)

dE - V A33

C35 =- pg

_fCB(E)

g

C53 =- pg

1B()

dE

where the integrations are over the effective length of the 8114. The wave-induced excitation force and moment are given by:

ikE

f3

(E)

e

g and

F5

f

f5 (E) eikE dE

Here

f3(E)

and f5(E) are the complex sectional exciting force and moment,

respectively. Their explicit forms are given in more detail in the report

by Frank and Salvesen.4

The two-dimensional added mass and damping coefficients a(E) and b(E) are computed ih the program either by distributing source singularities over the submerged surface of each ship section (Frank)7 or by the Lewis-form transformation using the Grim method.8

The other symbols are:

p Mass of the ship

J Mass moment of inettia of the ship in pitch

w Frequency of encounter

V Forward speed of the ship

B(E) Sectional beam"

p Mass density of the water

g Gravitational acceleration

k Wave number

It is important to note that the forward-speed contributions to the coefficients in the equations of motion differ considerably from the

speed-corrections applied in other strip theories. The added-mass cross-coupling

coefficient

A53 contains an additional forward-speed term not present in

other theories and the pitch added-mass coefficient A55 lacks a linear

speed term included in some other theories (see, for example, Gerritsma).1

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contribution to the coefficient

A55 has a rather small effect on the motion.

However, the forward-geed effect on Ass is very important and has a large

effect on the motion at high speeds in near-resonant situations. The

additional speed effect on Ass is believed to be correct for two reasons: (1) the Timman-Newman symmetry relationship9 is satisfied and (2) experi-ments by Smith2 clearly verify this speed effect.

COMPARISON OF EXPERIMENTAL AND THEORETICAL RESULTS

MARINER HULL FORM

The theoretical and experimental pitch and heave amplitudes for the

Mariner hull are shown in Figures 5 and 6. _{The experimental values are}

shown on the figures as open or solid points. _{Open symbols denote actual}

values and closed symbols the mean values obtained from the linearity plots

given in the Appendix. Tables 2-4 of the Appendix list experimental values

as well as the theoretical values computed from the Frank computer _program.

Comparing the theoretical and experimental pitch and heave, we find

that the theoretical pitch and heave both agreed well with experimental

results at the two lower Froude numbers, 0.10 and 0.20 (Figure 5). There

was also good agreement in heave at Fr = 0.30, but agreement for pitch was

less satisfactory (Figure 6); in fact, the theoretical values differed from

measured pitch by as much as 28 percent. _{Figure 6 also indicates that the}

linear strip theory was insufficient for the highest speed used (Fr = 0.40); the theory overpredicted heave by as' much as 50 percent and pitch by as much as 100 percent.

The design speed for the Mariner is about Fr = 0.28. Therefore, at

Fr = 0.30 and even more at Fr = 0.40, the Mariner hull created _{very large}

"steady-state" waves. _{The large discrepancy between theory and experiments}

at the extreme speeds is quite understandable considering that strip _theory

ignores the interaction between oscillatory motions _{and "steady-state"}

waves. Unfortunately time limitations precluded tests at speeds between

In the figures, heave is presented as the amplitude of heave divided.by

the wave amplitude, z/a and plotted against length _{between perpendiculars}

divided by wave length, L/A. The pitch is presented _{as the angle of pitch}

in radians multiplied by half of LBP and divided by wave amplitude, L/2a.

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Fr = 0.20 and Fr = 0.30. It is difficult, therefore, to draw any valid

conclusions regarding the accuracy of the strip theory as applied to the Mariner hull at the design speed, other than to state a belief that the

agreement between theory and experiment would be considerably better at the

design speed than at Fr = 0.30.

Turning to Figures 7 and 8 which give the heave and pitch phases, we note that the theory predicted both the heave and the pitch phases quite

satisfactorily for the long wave length range, but that the theoretical

phases for both heave and pitch were less than indicated by the experiment

for the shorter wave-length range. The experimental points shown in

Figures 7 and 8 are all mean values obtained from two or more test runs, and the numerical values are tabulated in Table 1 of the Appendix.

DESTROYER HULL WITH AND WITHOUT BOW MODIFICATION

The theoretical and the experimental pitch and heave amplitudes for the desttOyer h011 (Ship.A) With and Without modified bow are Shown in Figures 9, 10, and 11 for Froude numbers 0.204, 0.272, and 0:408,

respec-tively. The experimental points are those listed it Tables 3 and 4 in the

Appendix. Mean values obtained from the linearity plots Shown in the

Appendix Were used for the wave lengths with several test runs.

Comparing the heave amplitudes first, we see

in

Figures 9, 10, and

11 that-the experimental

results

Showed an increase,

in

heave of less

than 10 percent due to the modified bow whereas the theory predicted an

increase of as much as 20 percent. For-the case without bow modification,

there was good agreement between experiment and theory for heave at

Fr. = 0.204 and Fr = 0.272. (Figures 9 and 10) and fair agreement at FT = 0.408

(Figure 11).. Thus the theory predicted the heave for the bare hull quite'

well but overestimated the increase in heave for this particular bow

modification.

*-The phase angles express the lead with respect to maximum wave elevation. at_midship.

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Comparing the pitch amplitudes, which are also presented in

Figures 9, 10, and 11, we see that at the lower Froude _{numbers (0.204 and}

0.272) the theory predicted an increase in pitch of _{no more than 8 percent} due to the modified bow and only a small shift in the wave length of

maximum response at Fr = 0.408.- Thus the magnitude _{of the predicted pitch} amplitudes was practically the same as obtained _{experimentally.} _As

indicated, the bow modification had only _{a minor effect on the pitch}

amplitudes and the comparison plots show that the _{strip theory predicted}

the trend of this effect very well.

Turning to Figures 12, 13, and 14, which give the _{heave and pitch} phases, we find that the theory predicted _{a very small decrease in both}

pitch and heave phases due to the modified bow, _{only about 10 to 15 degrees}

at the wave length of maximum response

_LA

_0.9. _{The experiments showed}

practically no change in the phases due to the _{modified bow.} _Considering how little effect a 10- to 15-degree phase _{change has on the total ship} motion, the agreement between theory and _{experiment for the phase angles is}

felt to be quite acceptable. _{However, it should be pointed out that for}

the maximum speed case, Fr = 0.408, there were noticeable discrepancies

between theory and experiments (Figure 14) both for _{the heave and the pitch} phases in the short wave-length range

_LA

> 1.0.

CONCLUSIONS

This study shows that the Frank close-fit _{ship-motion computer} pro-gram predicted the pitch and heave motions with quite satisfactory _accuracy

for the Mariner hull form at speeds less than and _{possibly also equal to}

the maximum design speed (Fr :.-:. 0.28); above this speed,_ the agreement was

rather poor.

The Frank computer program predicted the _{head-seas motions with good}

accuracy for the destroyer hull form (Ship A) without the bow _modification at the three ship speeds tested (Fr _{= 0.20, 0.27, 0.41).} _{Furthermore, the}

effect of the bow modification on the pitch motions _{was satisfactorily}

predicted by the theory. _{However, for this particular bow modification,}

the theory overestimated the increase in heave _{amplitudes; it indicated an}

increase of up to 20 percent whereas experimental _{results gave less than}

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lb-percent increase, It is important

to

'note that despite this

consider-able discrepancy in the heave response, both theory And experiment predicted the sate trend, namely that the modified bow cOnfiguratioliwould increase

heave amplitude.

It has not been possible to find

any

explanation for this discrepancy

in the heave response for the destroyer with the bow Modification. We note,

however, that the agreement.between strip theory and experiment has been

found to be. quitesatisfactory for the heave amplitudes of three other

destroyer hulls with large bulbs and domes: (1) the Davidson A form (Smith

and SalVesen)3 (2) the USS SPOKANE (unpublished Work) and (3) Ship 5

(unpublished NSRDC Study

by

Wang).

fik 15-.to IS-percent etrcir in predicting heave motions May be quite

acceptable fbr most design applications as long as the trend is predicted

correctly. . It

is

felt therefore that for most practical design purposes,

the Frank Close-fit ship-motion computer program can be used to predict with

satisfactory accuracy the head-seas motions not Only of.regular hull formS

but also of hulls with large bulbous bow configurations.

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4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 -. -THEORY 1 1

I

EXPERIMENT

AO

h/A = 1/40

-A.

h/A = 1/50

"

VREEN '12" A ; I

10

WATER I i 0.4 .16: 0.61.Z, 0.8 I\ L", 110 12 0: '4

Figure 1 - Comparison of Experimental and Theoretical Heave and

Pitch Amplitudes for Series 60, Block 0.70 Form at Fr = 0.30

13

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SHIP A

WITHOUT AND WITH BOW MODIFICATION

SHIP B

WITHOUT AND WITH BOW MODIFICATION

Figur0 2 - Body Plans

Of

Ships A and B with and Without Bow

Modification

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0.2

1

0 EXPERIMENT

SHIP BAT Fr. = 0.31

}WITH

BOW MODIFICATION

WITHOUT BOW MODIFICATION 4 OA 0.8 1.0 1.2 0.4 ' OA 0.8 1.0 1.2 L/A Figure 3

Comparison of Experimental and Theoretical Heave

Amplitudes for Ships A and B

<

0

w < 1.4 1.2 1.0 OA 0.4

jp

0 o

-SHIP A AT Fr. =

0

0.27 THEORY EXPERIMENT -.- THEORY

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2.0 1 5 3.0 2.5 1.0 0.5

04--PITCH

A

TOWING CARRIAGE

Figure 4 - Instrumentation for Measuring Heave, Pitch, and Surge for Free-Running Model

Fr . 0.10 Fr . 0.20

3.5

THEORY

A 0EXPERIMENT

Aio MEAN VALUES -"Fl EXPERIMENTS - _PITCH HEAVE el .1 0.6 0.8 1.0 1.2 0 4 0.4 0.8 1.0 Li A

Figure 5 - Comparison of Experimental and Theoretical Pitch and Heave Amplitudes for Mariner Hull At Fr = 0.10 and

FT = 0.20

16

1.2

-FLAT PLATE

(22)

4.0 3.5 3.0 2.5 _s

r

E 2.0 U.' 1.5 1.0 0.5 0.4 0.6 Fr 0.30 0.8 Lilt Figure 6 - Comparison Heave Amplitudes for

0.8

L/ A

of Experimental and Theoretical Pitch and

Mariner Hull at Ft = 0.30 and Fr = 0.40

1.0 _{1.2 04} 17 0.6 Fr 0.40 THEORY

A 0

EXPERIMENT

A

e{MEAN VALUES EXPERIMENTS 1.0 1.2

(23)

-180 -225

04

Fr F '0.10

Fr = 0.20

THEORY MEAN VALUES EXPERIMENTS

1 0.8 1.0 L/A 0.8, 1.0 1.2 0.4 OAS L/ A

Figure 7 - Comparison of Experimental

and Theoretical Pitch and

Heave Phases for Mariner Hull at

Fr = .0,10 and Fr = 0.20

(24)

45 90 135 -180 225 -270 Fr = 0.30 Fr = 0.40 HEAVE THEORY

MEAN VALUES EXPERIMENTS

PITCH 0.4 0.6 0.8 1.0 1.2 04 0.6 0.8 L/ A L/ A

Figure 8 - Comparison of Experimental and Theoretical Pitch

and

Heave Phases for Mariner Hull at Fr = 0.30 and Fr

= 0.40

(25)

3.0 .23 2.0 0.5 HEAVE THEORY WITH

A

EXPERIMENT BOW ,MODIFICATION THEORY . WITHOUT

A 0 EXPERIMENT J BOW MODIFICATION

3.0 2.5 2.0 1.0 1 0 0 OA 0:8 0.8 10 1.2 14 L/A -.PITCH. THEORY

A

EXPERIMENT

--- THEORY

A 0

EXPERIMENT

/

WITH BOW MODIFICATION ) WITHOUT BOW MODIFICATION 1

Figure 9 - Comparison of Experimental and Theoretical

Figure 10 - Comparison of Experimental and Theoretical

Pitch and Heave Amplitudes for Destroyer

Hull at Fr = 0.204 Hull at Fr = 0.272 1.4 04 0:6 0.8 10 1.2 L/A

(26)

3.0 2.5 2.0 1.5 1.0 0.5 0 04 EXPERIMENT

/

HEAVE

0

THEORY THEORY 0 EXPERIMENT

A

1 WITH BOW MODIFICATION WITHOUT BOW MODIFICATION 1 0.6 0.8 10 Li A

Figure 11 - Comparison of Experimental and Theoretical Pitch andHeave Amplitudes for

Destroyer Hull at Fr = 0.408 -180 225 270 HEAVE 41 THEORY 8011 MODIFICATION EXPERIMENT WITH THEORY Li 0 EXPERIMENT /WITHOUT.-BOW MODIFICATION 1

A

****-,..

04 0.6 0.8 10 1.2 Lilt

Figure 12 - Comparison of Experimental and

Theoretical Pitch and Heave Phases for

Destroyer Hull at Fr = 0.204 1.4 -45 ^ Ill ac 0 uJ 0 Z -90 PITCH Lu'n 1.2 1.4

(27)

PITCH HEAVE THEORY

- A

EXPERIMENT WITH BOW MODIFICATION

Theoretical Pitch and HeAve, Phases for

Destroyer Hull at Fr = 0L272 +45 0 ₄₅ ₉₀ 135 180 n5 270 HEAVE THEORY 1. WITH BOW MODIFICATION

A

EXPERIMENT THEORY WITHOUT '11 A 0 EXPERIMENT B°W ON IF ICAT ION L/ A .1.2

Theoretical Pitch and Heave Phases for

Destroyer Hull at Fr =0.408

1.4!

0:8

0.6

(28)

APPENDIX

LINEARITY PLOTS AND TABULATED VALUES FOR THE TEST _MODELS

To evaluate the linearity of the _{responses with respect to wave} height, several tests were run at each wave length using wave heights from

0.3 to 2.8 inches. The heave and pitch amplitudes _{were nondimensionalized}

with respect to wave height and wave slope, respectively, and plotted

against wave height. _{The heave and pitch amplitudes from these} _{tests are}

presented in Figures 15-21 for the wave length _{cases in which four or more}

runs were performed. _{The responses seemed to be quite linear for most of}

the cases. _{However, as seen in Figure 17, nonlinearities were present in}

the heave amplitudes for the Mariner hull _{at Fr = 0.30 and wave lengths}

LA = 0.70 and L/X = 0.80. _{The test data clearly indicated that the} nondimensional heave amplitudes decreased with _{an increase in the wave}

height for these two wave lengths. _{Some slight nonlinearities also seemed}

to be present for both heave and pitch amplitudes _{of the Ship A destroyer} hull without bow modification (Figures _19b-21b). _{The nondimensional} ampli-tudes appeared to increase with an increase in _{wave height.} _{This type of} nonlinear trend is rather unusual for head-seas _motions. _{The nondimensional}

amplitudes of pitch and heave motions are usually found to decrease with an

increase in wave height for those _{cases where nonlinearities are observed.} Furthermore, it is interesting to note that data _{of Figures 20 and 21 for} the destroyer hull with bow modification did _{not seem to show any nonlinear}

trend within the range of wave heights employed. _{This was quite unexpected}

since the test data for the Davidson A form with _{the large bulb configuration}

had showed considerable nonlinearity in heave _{amplitudes with respect to}

wave height.3.

Aside from the above-mentioned nonlinearities, _{the test data}

pre-sented in this Appendix seem in general to be quite linear. _However,

be-cause of the rather large spread in the data, a mean line was drawn through the test points for each case in order, to Obtain the mean values listed in

Tables 2-4. _{These mean values were used in the comparison}

of experimental

and theoretical results. _{Values calculated by the Frank computer} _program

are also indicated in Tables 2-4.

(29)

0.8

0

L/A = 0.8 1.2 1.1 1.0 0.9

0

L/A = 0.6

Figure 15 - Heave and Pitch Linearity Study for Mariner Hull

at Fr = 0.10 93 0.9 0.8 0.7 0.7 0.6 0.5

0

7 = 0.6

0

. LAA = 0.7

0

07

0

0 -Q 0

0.4 0.8 1.2 1.6 2.0 0 0.4 0:8 1.2 1.4' 2:0

WAVE HEIGHT IN INCHES

0

L/A = 0:7

(30)

I./A = 0.8 i 1 [ 1 1

WAVE HEIGHT ININCHES

Figure 16 - Heave and Pitch

Linearity Study for Mariner

Hull at Fr = 0.20 1.3

0

0 1.2

0

1.1 Lilt = 0.7 1.3 Oa

0

12

0

1.1 I i i I 1../A = 0.8 1 0.4 0.8 1.2 1.6 2.0 1.1 1.0 0.9 1.3

c9

0

0.7

0 0 0

0

L/A

o

0

1.2 1.1

0

0.4 0.8 1,1 1.6 2.0

(31)

14 LiA = 08 I. 0 0.4 0.8 1.2 1.6 2.0 1.3 1.2

00

1.0

-o

0

1 i L/A = 0.8 1 1 I 1 0.4 0.8 1.2 1.6 2.0 1

Figure 17 - Heave and Pitch Linearity Study for Mariner Hull

at Fr = 0.30 Lilt = 0.6 1.1 1.8 1.7 1.6 1.7 1.6 1.5 1.4 L/A = 0.6

o

I

0

L A =. 0.7

0

0 0 *ay 0 I

o°

o

0

N. ..4"ok

0 44

0

1.4

00

1.2

oi

cif L/A 0.7

(32)

Figure 18 - Heave and Pitch Linearity

study

for Mariner Hull

at Fr = 0.40 a. Lu = 7 0. LIJ 1.6 1,5 1..2 1.1

0

a. 0 In Lu 0. 1.1

0

0 L/A 07 1.0 0.9 0.8 0

0

VA = 0.700

o

-0-0

0

L/). = 0.800

-0

0

so, 0 L/A = 0.8,

00

0

0.4 0 .8 1.2 1.6 2.0 0.4 0.8 1.12 11.6

(33)

0.8 0.2 0.8 0.7 0.9 0.8 0.7 0.9 014 07 0.8 0.7

6-04) L/A = 0.80

11 I---I

L/). - 1.10

P

at

28 1.0 0.9 1.0 0.9 1.0 0.9 0 0.8 a. 0.9 0.8 0.7 0.7 0.6

Figure

19a - With Bow Modification

1.1 1.0 0.9 0.9 0.8 07

-4-110

P

I _ LA.1180 I

Figure

-19b - Without Bow Modification

Figure 19 - Heave and Pitch Linearity Study for Destroyer Hull

at Fr = 0.204

JEJS__-____ L/A 0.90

1-

-0.4 0.8 1.2 1.6 2.0 2.4 2.8

L/). = 0.67 0.8 0.7 0 6 0.8 0.7 0.6 0.8 0.7 06 0.8 0.7 0.6 . a. 101 1 = 0.67 1 1

111wilr --IL--4041

0

L/). = 0.80 1 7

a

-_ _1 1./) = 0.90 1 1 -0 L/A - 1.00 1 1 0.4 0.8 1.2 1.6 2.0 2.4 2.8 0 0.4 0.8 1.2 1.6. 2.0 2.4 28 WAVE HEIGHT IN INCHES

0.4 0.8 1.2 1.6 2.0 2.4 2.8

L/A - 1.00 L/A 0.90 1.0 -11171.

-0

0.9 .= 0.80 08 L/A = 1..00

-0.8 0.9

-taio

L/). 0.90

(34)

08 0.9 0.8 0.8 1,0 4 0.9 1.0 0.9 1 1 1 0.4 0.8 1..2 1.6 2.0

Figure 20a - With Bow Modification

2.4 2.8 .29 1.2 IS L/A - 0.667 I. 1 1/A - 1.00 1 0.4 0.8 1.2 1.6 2.0 2.4 2.8

.-1)-.

L/A 0.80 a. 1 1.0 . 0.80 I 1-1.1 1 a. 4

1.0 H

we

_ 1/A 0.90 1 _0.9 L/A . 0.90 0.9

'0-44

1 I 1 1L/A = .00 1 0.8 I 1 L/A 1.00 0.4 0.8 1.2 1.6 2.0 ' 2.4 28 0.4. 0.8 1.2 1.6 .2.0 2.4 28 1.0 0.9

I*

I 1/A . 0.667 1.1 1.1 -1.0

-

-0 0.800 0. 1.1 -1 a. tu 0.9 1.1 41)

a

_ui > 1.1 1.0 L/A - 0.90 1.0 Zi 1.2 1.1 5 a: 0.9 0.8 1.0 _L/A 1.00 1 0.7 0.7 0.9

H.

1/A . 1.10 0.6

WAVE HEIGHT IN INDIES WAVE HEIGHT IN INCHES

Figure 20b - Without Bow Modification

Figure 20 - Heave and Pitch Linearity Study for Destroyer Hull at Fr = 0.272

10

(35)

1.1 1.3 1.2 1.6 1.5 1.5 1.1 1.3 1.2 7.0 0.9

Figure 21a - With Bow Modification

1/ A - 0.67 01 I

0

I 1 = 0.90 1 1 1 1 .1 L/A 1.00 I 0.1 0.8 1.2 1.6 2.0 2.4 7.8 WAVE HEIGHT IN INDIES

--1111.-0-71r-7eg

1.4

IL

1.3 . L/A = 0.67 1 OE 1 1.3 1.2

-41-1-9

-ir----

--Ir--/r--L/A = 0.80 L/A = 0.80 I

-I

1 _ 11 0 1.0 0.9

-

--Se 6

L/A = 0.90 L/A = 0.90 _ _0.7 1 0.6 = 1.00 L/A = 1.00 I i I_ _I 0.5 1 111 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 1.5

_

1.4 1.1 L/A 0.67 411° 1 I -1 1 1.3 1.7 _1.2

o

1.6 I -0.80 Q.

0

1.1 1.5 S.

;

1.1

a

0

0 0.9 - 0.8 gLs 1.3 1.0 0.9 0.7 0.6 1 -1 L/A 0.90 E. 0:7 0.5 0.3 = 1.03 1 1 1 1

0

- 411 L/A = 1.10 1 1 1 1 1 0.4 0.8 1.2 1.6 2.0 2.1 28

WAVE HEIGHT IN INCHES WAVE HEIGHT IN INCHES

Figure 21b - Without Bow Modification

Figure 21 - Heave and Pitch Linearity Study for Destroyer Hull

at Fr = 0.408

(36)

TABLE 2

Numerical Values for Experimental and Theoretical Heave and Pitch Amplitudes and Phases

for Mariner Hull

31

MODEL TEST, MEAN VALUES COMPUTED VALUES

FROUDE PITCH HEAVE PITCH HEAVE PITCH

NO. L A

/

HEAVE PITCH DIV. BY PHASE PHASE HEAVE PITCH PHASE PHASE

z/a 0L/2a WAVE IN IN z/a 0L/2a IN IN

SLOPE DEGREES DEGREES DEGREES DEGREES

0.1 0.5 -2.5 -102.3 0. 84 1.60 -1 -100 0.1 0.6 0.76 1.98 1.05 11.5 -99.8 0.78 1.88 0 -104 0.1 0.7 0.75 2.48 1.13 8.3 -112.2 0.71 2.13 1 -110 0.1 0.8 0.63 2.59 1.03 5.0 -124 0.65 2.33 2 -117 0.1 0.9 1.3 -133 0.61 2.47 4 -125 0.1 1.0 11.4 -137 0.59 2.42 2 -137 0.1 1.1 24.8 -133 0.54 2.11 -7 -151 0.2 0.5 5.1 -105.5 0.95 1.83 0 -104 0.2 0.6 14.5 -101.5 0.98 2.27 0 -113 0.2 0.7 1.03 2.70 1.23 -3.7 -130.1 1.09 2.69 -3 -125 0.2 0.8 1.21 3.06 1.22 -9.7 -145.7 1.29 3.01 -15 -141 0.2 0.9 -31.7 -165 1.35 3.08 -45 -163 0.2 1.0 -59.9 -168.9 0.95 2.59 -84 -188 0.2

Li

' -51.9 -174.4 0.43 1.80 -120 -211 0.3 0.5 -8.4 -114 1.16 2.14 0 -110 0.3 0.6 1.37 2.56 1.36 2.8 -121.5 1.48 2.73 -7 -124 0.3 0.7 1.75 2.79 1.27 -2.3 -148.3 1.96 3.36 -32 -143 0.3 0.8 1.55 2.69 1.07 -57.5 -162.7 1.92 3.62 -81 -176 0.3 0.9 -76.9 -175.4 1.00 2. 50 -125 -211 0.3 1.0 -96.9 153.9 0.39 1.49 -151 -231 0.3 1.1 =107.4 134.5 0.13 0.89 -175 -243 0.4 0.5 -6.2 -122.3 1.56 2.51 -2 -116 0.4 0.5 -32.9 -141.4 2. 34 3.52 -28 -136 0.4 0.7 1.58 2.35 1.07 -69.3 -164.2 2.57 4.34 -89 -185 0.4 0.8 1.13 2.18 0.87 -94.1 -178.7 1, 06 2.47 -140 -227 0.4 0.9 -127.1 143.3 0.41 1.38 -161 -242 0.4 1.0 -146.5 125.2 0.19 0.83 -176 -251 0.4 1.1 -138.1 134.6

(37)

TABLE 3

Numerical Values for Experimental and Theoretical

Heave and Pitch Amplitudes and Phases for

De-stroyer Hull with Bow Modification

*Mean va Ines from four or more test runs.

32

1

MODEL TEST COMPUTED VALUES

FROUDE OITCH _HEAVE _PITCH HEAVE PITCH

NO. Imi f` HEAVE PITCH DIV. BY PHASE PHASE HEAVE PITCH PHASE PHASE

z/a 0L/2a WAVE z/a 0L/2a

(Degrees)

SLOPE (Degrees) (Degrees) (Degrees)

0.204 0.57 0.84 1.79 1.00 10.3 -100.9 0.87 1.83 - 5.0 -11 3. 0 0.204 0.67 0.78' 2.09 1.00 1 O. 97 -11 2. 6* 0.87 2.08 6.0 -4 20. 0 0.204 0.75 0.78 2.36 1.00 1 9.9 -11 4. 0 0.139 2.26 6.0 -1 26. 0 0.204 0.80 0.78' 2.44' 0.97' 14.5* -121.7' 0.90 2.35 7.0 431.0 0.204 0.85 0.80 2.58 0.97 20.7 -121.7 0.92 2.43 6.0 4 36. 0 0.204 0.90 0.76* 2.54* 0.90* 21 .1* -119.4' 0.94 2.48 4.0 -1 42. 0 0:204 0.95 0.71 2.39 0.80 35.9 414.1 0.96 2.50 0.0 448.0 0.204 1.00 0.78* 2.54' 0.81' . 1 8. 8* 4 35. 9* 0.98 2.49 -5.0 4 56. 0 0.204 1 .1 0 0.73' 2.25* 0.65' 17.6' -1 42 . 5* 0.95 2.35 -1 8. 0 4 72. 0 0.204 1.20 0.66 1.92 0.51 -19.5 474.0 082 , 2.03 -35.0

4890

0.204 1.30 0.45 1.33 0.33 -17.2 176.2 0.60 1.55 -54.0 -206.0 0.272 0.57 0.89 2.02 1.13 12.8 -107.7 0.97 1.91 6.0 -117.0 0.272 0.67 0.92' 2.39' 1.14* 19.9' -110.6*. 1. 03 2. 2, 6.0 -127.0 0.272 0.75 1.00 2.75 1.17 13.2 -128.1 1.12 2.48 2.5 -136.0 0.272 0.80 1.02' 2.86' 1.14* 13.3* -131.1* 1.18 2.60 -1.0 -142.0 0.272 0.-85 1.05 2.94 1.10 19.3 -12$.8 1.24 2.68 -5.0 -150.0 0.272 0.90 1.09' 2.94* 1.04* -15.1* -137.7' 1.29 2.71 -12.0 -157.5 0.272 0.95 1.03 2.62 0.88 -4.8 -160.5 1.31 2.-70 -21.0 -167.0 &272 1.00 1.Q9' 2.67* 0.85*

-0.8'

-157.3' 1.30 2.60 -33.0 -177.0 0.272 1.10 8.80' 2.04' 0.59' -22.1* -170.5' 1.11 2,16 -58.0 -200.0 0.272 1.20 0.65 1.47 0.39 -44.7 164.5 0.73 1.62 -83.0 -218.0 0.272 1.30 0.38 0.98 0.24 -59.8 150.6 0.38 1.13 -105.0 -233.0 0;408 0.57 1.19 2.36 1.32 6.1 -124.5 1.27 2.27 4.0 -125.0 0.408 0.67 1.43' 2,85' 1.36' 0.4' -142.6' 1. 55 2.65 -5.0 -142:0 0.'408 0.75 1.64 2.95 1.25 -9.5 -158.6 1.80 2.88 -20.0 -157.0 0.408 0.80 1.70' 2.91* 1.16* -20.6* -170.4' 1.91 2.92 -34.0 -169.0 0.408 0.85 1.60 2.59 0.97 -33.9 178.0 1.94 2.87

-500

-162.0 0.408 0.90 1.39* 2.23* 0.79' -48.0* 166.9 1.80 2.63 -69.0 -197.0 0.408 0.95 1.18 1.76 0.59 -62.7 o158.5 1.53 2.30 -87.0 -210.0 0.408 1.00 0.99' 1.54' 0.49' -62.5* 157.3' 1.22 , 1.97 -104.0 -222.0 0.408 1.10 0.63' 1.11* 0.32' -81.7* 150.6* 0.66 1.31 -130.0 -240.0 0.408 1.20 0.41 0.87 0.23 -96.0 142.2 0.30 0.83 -150.0 -254.0 0.408 1.30 0.21 0.57 0.14 -108.6 127.2 _

(38)

-*Mean values from four or more test runs.

TABLE 4

Numerical Values for Experimental and Theoretical

Heave and Pitch Amplitudes and Phases for De-stroyer Hull without Bow Modification

33

MODEL TEST COMPUTED VALUES

PITCH

FROUDE HEAVE PITCH _PITCH HEAVE PITCH

NO. L/A HEAVE

z/a PITCH 0L/2a DIV. BY WAVE PHASE (Degrees) PHASE (Degrees) HEAVE

z/a 0 L9L/2a PHASE

(Degrees) ASE (Degrees) SLOPE 0.204 0.67 0.77* 2.09' 1.00* 1.7' -118.8' 0.77 2.00 6.0 -116.0 0.204 0.80 0.73' 2.41' 0.96* 14.0' -120.0' 0.75 2.20 8.0 -123.0 0.204 0.90 0.70' 2.54* 0.90* 23.2' -121.5' 0.73 2.30 9.0 -132.0 0.204 1.00 0.68* 2.36* O. 75* 27.0' -127.1* 0.72 2.28 5.0 -143.0 0.204 1.10 0.61 2.14 0.62 13.3 -148.2 0.70 2.15 -1.0 -155.0 0.272 0.67 0.89' 2.39* 1.14* 25.1* -112.4 0.90 2.16 5.0 -119.0 0.272 0.80 0.94' 2.79' 1.11* 8.6* -133.8* 0.95 2.43 4.0 -130.0 0.272 0.90 0.97' 2.83' 1.00* 13.7* -138.8' 1.00 2.53 -2.5 -144.0 0.272 1.00 0.99* 2.70' 0.86* 3.2* -154.3* 1.02 2.50 -13.0 -158.0 0.272 1.10 0.82 2.07 0.60 -22.8 -178.3 0.94 2.26 -31.0 -175.0 0.408 0.67 1.33* 2.87* 1.37* 7.0' -134.4* 1.30 2.52 0.0 -131.0 0.408 0.80 1 . 58* 3.06' 1.22* -19.6' -168. 8* 1.58 2.90 -17.0 -152.0 0.408 0.90 1.41* 2.54* 0.90' -43.2* 172.5' 1.64 2.92 -45.0 -176.0 0.408 1.00 1.00* 1.76' 0.56' -64.7' 158.5* 1.33 2.43 -83.0 -204.0 0.408 1.10 0.61 1.17 0.34 -81.7 152.0 0.73 1.58 -113.0 -227.0

(39)

REFERENCES

Gerritsma, J. and Beukelman, W., "Comparison of Calculated and Measured Heaving and Pitching Motions of Series 60, CB = 0.70 Ship Model in

Regular Longitudinal Waves," Laboratorium voor Scheepsboukunde, Delft,

Report 139 (1966).

Smith, W.E., "Computation of Pitch and Heave Motions for

Arbitrary Ship Forms," International Shipbuilding Progress, Vol. 14 (1967). Smith, W.E. and Salvesen, N., "Comparison of Ship-Motion Theory and Experiment for Destroyer with Large Bulb," Journal of Ship Research,

Vol. 14 No. 1 (1970).

Frank, W. and Salvesen, N., "The Frank Close-Fit Ship Motion

Computer Program," NSRDC Report 3289 (1970).

Korvin-Kroukovsky, B.V. and Jacobs, W.R., "Pitching and Heaving Motions of a Ship in Regular Waves," Transactions SNAME, Vol. 65 (1967).

Salvesen, N. et al., "Ship Motions and Sea Loads," Transactions

SNAME, Vol. 78 (1970).

Frank, W., "Oscillation of Cylinders in or Below the Free Surface

of Deep Fluids," NSRDC Report 2375 (1967).

Grim, O., "A Method for a More Precise Computation of Heaving and Pitching Motions Both in Smooth Water and in Waves," Third Symposium on

Naval Hydrodynamics, ONR, Washington, D.C. (1960).

Timman, R. and Newman, J.N., "The Coupled Damping Coefficients of

a Symmetric Ship," Journal of Ship Research, Vol. 5 No. 4 (1962).

(40)

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1 Prof. B.V. Korvin-Kroukovsky East Randolph, Vt. 4 Hydronautics, Inc Attn: 1 Dr. B.L. Silverstein 1 Mr. P. Eisenberg 1 Dr. H.P. Tulin 1 Cadcom, Inc 2024 West Street Annapolis, Md. 21401

Attn: Dr. John C. Geibhart

1 Hydraulic Lab

Newport News Shipbldg & DDCo

Newport News, Va

(42)

UNCLASSIFIED

Security Clas5iticatio

DOCUMENT CONTROL DATA - R & D

,Securifk classification of title, body of abstract and Indexing annotation ntlist be entered When the overall report is classified)

i ORIGINATING ACTIVITY (Corporate author)

Naval Ship Research and Development Center Washington, D.C. 20034

2a. REPORT SECURITY CLASSIFICATION NCLASSIFIED

U

2b. GROuP

3.'REPORT TITLE

' COMPARISON OF SHIP-MOTION THEORY AND EXPERIMENT FOR MARINER HULL AND A DESTROYER HULL

WITH BOW MODIFICATION 4. DESCRIPTIVE NOTES (Type of report and inclusive dates)

Final Report

15. Au THORISI (First name, middle initial, last name)

6. REPORT DATE

June 1971

7a. 707AL,. NO. OF PAGES

39 :

76. NO. OF REFS 9

fie. CONTRACT OR GRANT NO.

b. PROJECT NO. SR009 0101 '

Task 0100 d.

Be. ORIGINATOR'S REPORT NUMBER(S)

3337

gb. OTHER REPORT NOM (Any other numbers that may be assigneil thie report)

10. DISTRIBUTION STATEMENT

Approved for public release:: distribution unlimited.

I,

11. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY

Naval Ship Systems Command Washington, D.C. 20360

-13. ABSTRACT

The: objective of this study was to evaluate more precisely the accuracy of ship-motion strip theory for ships in head seas. Theoretical and experimental results were compared for the Mariner

hull and for a destroyer hull With and without

a

bow modification.

In view of the good agreement found, it was concluded that fiOr practical design purposes, strip theory can be used to.predict head-seas motions with satisfactory accuracy provided there is

adequate station representation.

.

S/N 0101-807-6801 Secunty Classificatton

(43)

UNCLASSIFIED

Security Classification

KEY WORDS LINK A LINK- B LINK C

ROLE WT ROLE ' WT ROLE WT

Ship motion Strip theory Head seas Mariner hull Destroyer hull

with bow modification without bow modification

-.

.

,

DDITT.514 73 (BACK)

UNCLASSIFIED