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c'3868

SHIP RESEARCH AND DEVELOPMENT CENTERBethesda, Maryland 20034

AN

z< RESPONSE PREDICTIONS OF HELICOPTER LANDING PLATFORM

FOR THE USS BELKNAP (DLG-26) AND

USS GARCIA (DE-1040)-CLASS DESTROYERSz

by

Wilia G Myes ndLIBRARYCC > Susan Lee Bales

Grant A. Rossignol 200LA.

a.U. S. MAVAL ACADEMAZ00

< LU APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED

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0SHIP PERFORMANCE DEPARTMENT

O0 RESEARCH AND DEVELOPMENT REPORTwU)

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July 1973 Report 3868

KE

The Naval Ship Research and Development Center is a U. S. Navy center for laboratoryeffort directed at achieving improved sea and air vehicles. It was formed in March 1967 bymerging the David Taylor Model Basin at Carderock, Maryland with the Marine EngineeringLaboratory at Annapolis, Maryland.

Naval Ship Research and Development Center

Bethesda, Md. 20034

MAJOR NSRDC ORGANIZATIONAL COMPONENTS

NSRDC

COMMANDER00

"*REPORT ORIGINATOR TECHNICAL DIRECTOR01

OFFICER-IN-CHARGE OFFICER-IN-CHARGE

CREOK05 ANPLS 04

SYSTEMS

DEVELOPMENTDEPARTMENT

iI

* AVIATION ANDSHIP PERFORMANCE SURFACE EFFECTS

DEPARTMENT 1

STRUCTURES COMPUTATIONDEPARTMENT AND MATHEMATICS

17 DEPARTMENT18

SHIP ACOUSTICS PROPULSION AND

DEPARTMENT AUXILIARY SYSTEMS19 DEPARTMENT 2

MATERIALS CENTRAL

DEPARTMENT INSTRUMENTATION28 DEPARTMENT

29

NDW-NSRDC 3960/144 (REV. 8/71)GPO 917-872

DEPARTMENTOF THE NAVY

NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER

BETHESDA, MARYLAND 20034

RESPONSE PREDICTIONS OF HELICOPTER LANDING PLATFORM

FOR THE USS BELKNAP (DLG-26) AND

USS GARCIA (DE-1040)-CLASS DESTROYERS

by

Susan Lee BalesWilliam G. Meyers and

Grant A. Rossignol

APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED

July 1973 Report 3868

TABLE OF CONTENTS

Page

ABSTRACT .......................................................... I

ADMINISTRATIVE INFORMATION ............. ..................... I

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . I

SHIP PARTICULARS ....................... ........................... 2

PREDICTION OF SHIP RESPONSES IN REGULAR WAVES .......... ............. 3

GENERAL DESCRIPTION ...................... ........................ 3

ROLL RESPONSE ....................... ........................... 4

SURGE, SWAY, AND YAW IN QUARTERING AND FOLLOWING WAVES .... ....... 5

PREDICTION OF SHIP-RESPONSE STATISTICS IN IRREGULAR SEAS ..... ......... 6

GENERAL DESCRIPTION ...................... ........................ 6

FREQUENCY-RESPONSE FUNCTIONS AT AN ARBITRARY POINT ...... ......... 8

IRREGULAR SEA REPRESENTATION ................. ................... 9

SPECTRAL CLOSURE ................ ......................... .. 10

RESULTS .................................................... ..... 11

DATA BASE OF PLATFORM RESPONSES FOR USS BELKNAP (DLG-26) AND

USS GARCIA (DE-1040) .-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-. 11

LANDING PLATFORM AND SHIP-RESPONSE LEVELS ....... ............. .. 12

EVALUATION OF DATA .................. ........................ 12

CONCLUDING REMARKS .................. ......................... .. 14

APPENDIX A - PROBABILITY OF OCCURRENCE .......... ................ 41

APPENDIX B - ROLL REDUCTION OF USS GARCIA (DE-1040) BY ACTIVE STABILIZING

FINS ................... ........................... .. 43

APPENDIX C - SUMMARIES OF INVESTIGATIONS ......... ............... .. 47

REFERENCES .......................... .............................. 90

LIST OF FIGURES

Page

Figure I Computer Fit of USS BELKNAP (DLG-26) Body Plan............16

Figure 2- Computer Fit of USS GARCIA (DE-1040) Body Plan ..... ........... .. 17

Figure 3 - Location and Size of Bilge Keels on BELKNAP and GARCIA and Location of Fin

on GARCIA ................. .......................... .. 18

Figure 4 -- Stabilizing Fin for GARCIA ..................... 19

Figure 5 - Location and Size of Helicopter Landing Platform on BELKNAP and Location ofPoints for which Responses Were Predicted ............ ............... 20

Figure 6 - Location and Size of Helicopter Landing Platform on GARCIA and Location ofPoints for which Responses Were Predicted ........ ............... .. 21

Figure 7 - Right-Handed Coordinate System for Response Predictions ..... .......... 22

Figure 8 - Incident-Wave Directions with Respect to Ship ........ .............. .. 23

Figure 9 - Comparison of Measured and Predicted Roll Response in Regular Beam Waves for a

Destroyer Hull ................. ......................... .. 24

Figure 10 - Percentage Differences Between Roll Predictions at Wave Steepnesses 1/80 and 1/50

and 1/80 and 1/110 for the USS BELKNAP (DLG-26) in Irregular Seas ... ..... 25

Figure 11 - Pierson and Moskowitz Sea Spectra for Significant Wave Heights of 4, 10, 16,and 20 Feet ................. .......................... .. 26

Figure 12 - Typical Response Spectrum and its Components for Vertical Displacement of

Point 5 on BELKNAP for Significant Wave Height of 10 Feet and Ship Speed of

20 Knots ....................... ........................... 27

Figure 13 - Comparison of Highest Expected Longitudinal Displacement, Single Amplitudes, in

100 Cycles for Origin of BELKNAP and Point 5 with Significant Wave Height

of 10 Feet .................. .......................... 28

Figure 14 - Comparison of Highest Expected Lateral Displacement, Single Amplitudes, in

100 Cycles for Origin of BELKNAP and Point 5 with Significant Wave Height

of 10 Feet ........................ .................. 29

Figure J5 - Comparison of Highest Expected Vertical Displacement, Single Amplitudes, in

100 Cycles for Origin of BELKNAP and Point 5 with Significant Wave Heightof 10 Feet . . ................... ....................... .. 30

Figure 16 - Comparison of Highest Expected Roll, Single Amplitudes, in 100 Cycles forI BELKNAP and GARCIA with Significant Wave Height of 10 Feet .. ....... .. 31

Figure 17 - Comparison of Highest Expected Pitch, Single Amplitudes, in 100 Cycles for

BELKNAP and GARCIA with Significant Wave Height of 10 Feet .. ....... .. 32

Figure 18 - Comparison of Highest Expected Longitudinal Velocity, Single Amplitudes, in100 Cycles for BELKNAP and GARCIA with Significant Wave Height of10 Feet .................... ........................... .. 33

Figure 19 - Comparison of Highest Expected Lateral Velocity, Single Amplitudes, in

100 Cycles for BELKNAP and GARCIA with Significant Wave Height

of 10 Feet .................. .......................... 34

iii

Page

Figure 20 - Comparison of Highest Expected Vertical Velocity, Single Amplitudes, in100 Cycles for BELKNAP and GARCIA with Significant Wave Height of10 Feet .................. .......................... 35

Figure 21 - Comparison of Highest Expected Vertical Velocity, Single Amplitudes, in100 Cycles for BELKNAP and GARCIA at Point 5 and 20 Knots ...... .. 36

Figure 22 - The Probability P of X Exceeding b, Given a .... ............. .. 37

Figure 23 - Nondimensional Roll-Decay Coefficient of GARCIA ... ........... .. 38

Figure 24 - Percentage of Roll Reduction for Stabilized GARCIA and ExperimentalComparison with Two Other Ships ........ ................. .. 38

Figure 25 - Comparison of Highest Expected Roll, Single Amplitudes, in N Cycles for

GARCIA with and without Roll Reduction for 30 Knots and a 120-DegreeHeading Angle ............... ........................ .. 39

LIST OF TABLES

Table 1 - Ship Particulars ............... .......................... 2

Table 2 - Location of Helicopter Landing-Platform Points for which ResponsesWere Predicted ................ .......................... 3

Table 3 - Single Amplitude Statistical Constants for a Fully Developed Wind-Generated Sea ...................... ........................ 7

Table 4 - Definition of State of Sea. ........... .................... .. 10

Table 5 - Description of Data-Base Presentation .............. ................ 11

Table 6 - BELKNAP, Origin, Root-Mean-Square Surge Response, Single Amplitudes .... 48

Table 7 - BELKNAP, Origin, Root-Mean-Square Sway Response, Single Amplitudes .... 49

Table 8 - BELKNAP, Origin, Root-Mean-Square Heave Response, Single Amplitudes .... 50

Table 9 - BELKNAP, Origin, Root-Mean-Square Roll Response, Single Amplitudes .... 51

Table 10 - BELKNAP, Origin, Root-Mean-Square Pitch Response, Single Amplitudes .... 52

Table 11 - BELKNAP, Origin, Root-Mean-Square Yaw Response, Single Amplitudes .. .. 53 5

Table 12 - BELKNAP, Point 1, Root-Mean-Square Longitudinal Response, SingleAmplitudes .................. ........................ 54

Table 13 - BELKNAP, Point 1, Root-Mean-Square Lateral Response, SingleAmplitudes ................ ......................... .. 55

Table 14 - BELKNAP, Point 1, Root-Mean-Square Vertical Response, SingleAmplitudes .................. ........................ 56

iv

Page

Table 15 - B!ELKNAP, Point 2, Root-Mean-Squarc Longitudinal Response,Single Amplitudes .............. ....................... .. 57

Table 16 -- BELKNAP, Point 2, Root-Mean-Square Lateral Response, Single Amplitudes .... 58

Table 17 - BELKNAP, Point 2, Root-Mean-Square Vertical Response,Single Amplitudes .............. ....................... .. 59

Table 18 - BELKNAP, Point 3, Root-Mean-Square Longitudinal Response,Single Amplitudes .............. ....................... .. 60

Table 19 - BELKNAP, Point 3, Root-Mean-Square Lateral Response, SingleAmplitudes .................. ......................... 61

Table 20 - BELKNAP, Point 3, Root-Mean-Square Vertical Response, SingleAmplitudes .................. ......................... 62


Table 22 - BELKNAP, Point 4, Root-Mean-Square Lateral Response, SingleAmplitudes ................. . ...... ............... 64

Table 23 - BELKNAP, Point 4, Root-Mean-Square Vertical Response, SingleAmplitudes .................. ......................... 65


Table 25 - BELKNAP, Point 5, Root-Mean-Square Lateral Response, Single

Amplitudes .................. ......................... .. 67

Table 26 - BELKNAP, Point 5, Root-Mean-Square Vertical Response, SingleAmplitudes .................. ......................... .. 68

Table 27 - GARCIA, Origin, Root-Mean-Square Surge Response, SingleAmplitudes .................. ......................... .. 69

Table 28 - GARCIA, Origin, Root-Mean-Square Sway Response, SingleAmplitudes .................. ......................... .. 70

Table 29 - GARCIA, Origin, Root-Mean-Square Heave Response, SingleAmplitudes .................. ......................... .. 71

Table 30 - GARCIA, Origin, Root-Mean-Square Roll Response, SingleAmplitudes .................. ......................... .. 72

Table 31 - GARCIA, Origin, Root-Mean-Square Pitch Response, SingleAmplitudes .................. ......................... .. 73

Table 32 - GARCIA, Origin, Root-Mean-Square Yaw Response, SingleAmplitudes .................. ......................... .. 74

Table 33 - GARCIA, Point 1, Root-Mean-Square Longitudinal Response, SingleAmplitudes .................. ......................... .. 75

Table 34 - GARCIA, Point 1, Root-Mean-Square Lateral Response, SingleAmplitudes .................. ......................... .. 76

V

Page

Table 35 - GARCIA, Point 1, Root-Mean-Square Vertical Response, SingleAmplitudes .................. ......................... 77

Table 36 - GARCIA, Point 2, Root-Mean-Square Longitudinal ResponseSingle Amplitudes ............... ....................... .. 78

Table 37 - GARCIA, Point 2, Root-Mean-Square Lateral Response, SingleAmplitudes ................ ......................... .. 79

Table 38 - GARCIA, Point 2, Root-Mean-Square Vertical Response, SingleAmplitudes ................ ......................... .. 80

Table 39 - GARCIA, Point 3, Root-Mean-Square Longitudinal Response,Single Amplitudes .-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-..-.-.-.- . .- 81

Table 40 - GARCIA, Point 3, Root-Mean-Square Lateral Response, SingleAmplitudes .-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- . 82

Table 41 - GARCIA, Point 3, Root-Mean-Square Vertical Response,Single Amplitudes .-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- . 83

Table 42 - GARCIA, Point 4, Root-Mean-Square Longitudinal Response,Single Amplitudes .-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- . 84


Table 44 - GARCIA, Point 4, Root-Mean-Square Vertical Response, SingleAmplitudes ................ .......................... 86

Table 45 - GARCIA, Point 5, Root-Mean-Square Longitudinal Response,Single Amplitudes .-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- . 87


Table 47 - GARCIA, Point 5, Root-Me-an-Square Vertical Response, SingleAmplitudes .-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-... 89

vi

NOTATION

AF. Fin planform area per side of ship

AjA Added mass coefficient

a1 Geometric aspect ratio of fin

BL Molded baseline

B A Damping coefficient

b Highest (response) amplitude

CG Center of gravity

CL Longitudinal centerline

C'k Hydrostatic restoring coefficient

DWL Designed load waterline

dICLIdJ3 Slope of lift-coefficient curve

FP Forward perpendicular

F. Exciting force and moment

GM Transverse metacentric height

g Acceleration due to gravity or 32.1725 ft/sec2

KG Height of center of gravity above baseline

kl, k2 , k 3 Fin control-system gains

LCG Longitudinal position of the center of gravity

LA Lateral displacement

L0 Longitudinal displacement

LV Vertical displacement

Lpp Length between perpendiculars of ship

Mik Generalized mass component of ship system

N Number of cycles of response

vii

n Nondimensional roll-decay coefficient

R(t) Ship response to a sinusoidal excitation

RA(CO) Amplitude of ship response to a sinusoidal excitation-frequency-response function

RF Distance from roll axis to center of pressure of fin

RI Restoring force

RL (cw), RA (w), R_ (w) Ship lateral displacement, velocity, and acceleration amplitudes-frequency.response functions

RLo(w), R; (c), Ro (cw) Ship longitudinal displacement, velocity, and acceleration amplitudes-frequency-response functions

RL V(), RL v(cw), RL'v (w) Ship vertical displacement, velocity, and acceleration amplitudes-

frequency-response functions

SR(wO), SR~(w), SR'(o) Ship displacement, velocity, and acceleration spectral densities

SR(w), SR(oE), SR(oE) Ship displacement, velocity, and acceleration spectral densities in theencountered wave domain

S(CO) Pierson-Moskowitz spectral density ordinates

t Time variable

V Ship speed

x*, y*, z* Coordinates of any point measured from the origin of the coordinatesystem of Figure 7

X, XA Surge and surge amplitude

Y' YA Sway and sway amplitude

z, ZA Heave and heave amplitude

Fin angle

Ship displacement

e Phase angle associated with response R

•'A Wave amplitude-single amplitude

Height of wave from trough to crest-double amplitude

viii

Significant wave height--average of one-third highest

'w/Xk Wave steepness

0, 0A Pitch and pitch amplitude

Xk Wavelength

pl Heading angle of ship with respect to wave direction

p Mass density of water, 1.99 slugs/ft3

a02 Variance of ship response

OR 2, OR 2, OR Variances of ship displacement, velocity, and acceleration

2 2' 2

0.2,.2,a2 Variances of ship lateral displacement, velocity, and accelerationGLA 0i LA L LA

OL 21 GE. Variances of ship longitudinal displacement, velocity, and acceleration

2 V 2a . 2 Variances of ship vertical displacement, velocity, and acceleration

01 OA Roll and roll amplitude

01s/0u Roll-reduction factor-ratio of stabilized to unstabilized roll

ý' 4 A Yaw and yaw amplitude

Cw Wave frequency

COE Wave encounter frequency

Natural or resonant frequency of roll

ix

ABSTRACT

Motion-response predictions of the helicopter landing platform for the USS BELKNAP(DLG-26) and USS GARCIA (DE-1040)-Class destroyers are presented. Predictions have beenobtained by a computer-implemented procedure, which calculates response statistics at anarbitrary point on a ship in long-crested, irregular seas. The procedure is based on ship-motion theories in the state of the art. Results are presented for several ship speeds, states ofsea, and ship headings-ranging from head to following waves. Existing envelopes of heli-copter operations are discussed, and suggestions have been made, based upon the results ofthis study, for the listed new operational envelopes in higher states of seas:

1. Responses other than roll, e.g., vertical response at the landing platform, must beconsidered,

2. Quartering sea landings may be safer than bow sea landings,3. To increase safety of operations, BELKNAP should be stabilized in roll.

ADMINISTRATIVE INFORMATION

The work reported herein was authorized and funded by Naval Undersea Research and Development

Center Work Request 2-0210 and by Naval Ship Systems Command Task S-F34 421 007, WorkUnit

1-1568-302.

INTRODUCTION

The purpose of this investigation is to predict responses of helicopter landing platforms on the USS

BELKNAP (DLG-26) and the USS GARCIA (DE-1040)-Class destroyers in irregular long-crested seas. Com-

putations are based upon ship motion theories in the state of the art, implemented on the CDC 6700

digital computer system. Results permit the study of platform-motion levels required for development of

standard landing, tiedown, and takeoff techniques for the light airborne multipurpose system (LAMPS)

helicopter.

Previous development of computer programs expedited the completion of this task. The computer

program, developed by the Center' for ship motions and sea loads, provided response data for each ship in2regular waves. The Center computer program for irregular sea-response predictions was used to extend the

1Salvesen, N. et al., "Ship Motions and Sea Loads," Transactions of the Society of Naval Architects and MarineEngineers, Vol. 78, pp. 250-287 (1970). A complete listing of references is given on page 90.

2Meyers, W.G. and S.L. Bales, "Manual: NSRDC Irregular Sea Response-Prediction Computer Program," NSRDC Report4011 (1973).

regular wave data to irregular sea-response statistics for points along the ship. This report presents a data

base of landing platform-response predictions-displacement, velocity, and acceleration-for

1. Ship headings of 180, 150, 120, 90, 60, 30 and 0 deg with respect to waves

2. Ship speeds of 10, 20, and 30 knots

3. Significant wave heights of 4, 10, 16, and 20 ft.

SHIP PARTICULARS

Table 1 presents the most important particulars of the two ships. Figures 1 and 2 give the body

plans for each ship class. Figure 3 describes the bilge keels of each ship as well as the fin locations on

TABLE 1 - SHIP PARTICULARS

Ship Particulars USS BELKNAP USS GARCIA

(DLG-26) (DE-l1040)

Length Between Perpendiculars in Feet 524 390

Maximum Beam in Feet 54.4 43.7

Draft at Midship in Feet 18.8 14.5

Displacement in Long Tons 7800 3408

KG in Feet 19.75 16

GM in Feet 5.3 4.5

LCG from Forward Perpendicular in Feet 268.29 193.73

Roll Radius of Gyration as Percentageof Maximum Beam 35.15 35.13

Pitch Radius of Gyration as Percentageof Lpp 25.0 24.7

Yaw Radius of Gyration as Percentageof Lpp 25.0 24.7

Natural Heave Period in Seconds 6.7 5.88

Natural Roll Period in Seconds 9.93 8.90

Natural Pitch Period in Seconds 6.4 5.52

GARCIA, while Figure 4 describes the planform of the pair of active fins fitted to GARCIA.

Figures 5 and 6 give the location of the landing platform on each ship. Response predictions were

made for the following five points on the landing platforms.

2

1. On the longitudinal centerline of the ship, at the forward edge of the platform

2. On the longitudinal centerline of the ship, at the center of the platform

3. On the longitudinal centerline of the ship, at the after edge of the platform

4. At a point displaced laterally from the center of the platform, halfway to the port edge

5. At a point above the center of the platform deck, coincidental with the center of gravity of alanded and secured LAMPS helicopter

The five points (x*, y*, z*) are measured from the origin of the coordinate system used in the calcu-

lation procedure. By definition, the origin is taken to be the intersection of the longitudinal centerline of

the waterplane section with the transverse plane through the center of gravity. The coordinate system is

arranged so that x* is positive aft, y* is positive to starboard, and z* is positive upward. The coordinates

of the points are given in Table 2, along with measurements corresponding to the distance of each point

from the forward perpendicular (FP), longitudinal centerline (CL), and baseline (BL).

TABLE 2 - LOCATION OF HELICOPTER LANDING-PLATFORMPOINTS FOR WHICH RESPONSES WERE PREDICTED

Distance From -

X* y z* FP CL BLShip Point ft ft ft ft ft ft

USS BELKNAP 1 108.71 0 19.70 377.00 0 38.50(DLG-26) 2 131.67 0 20.90 399.95 0 39.70

3 154.63 0 20.95 422.90 0 39.754 131.67 -10.38 20.90 399.95 -10.38 47.705 131.67 0 28.90 399.95 0 47.70

USS GARCIA 1 140.17 0 16.00 333.90 0 30.50(DE-1040) 2 158.47 0 16.49 352.20 0 31.00

3 176.77 0 16.54 370.50 0 31.004 158.47 - 7.3 16.49 352.20 - 7.3 31.005 158.47 0 24.49 352.20 0 39.00

PREDICTION OF SHIP RESPONSES IN REGULAR WAVES

GENERAL DESCRIPTION

The initial step in the computational procedure is to obtain regular wave responses of the ship at the

origin by execution of the Center computer program for ship motions and sea loads; see Reference 1.

When the program is applied, ship responses are computed to a sinusoidal excitation or regular wave

----,of unit amplitude for a given frequency of wave encounter wE, ship speed V, and heading angle to the wave

3

direction M, so that

R(t) = RA cos (wEt - e) (1)

where t is the time variable, and RA and e are the response amplitude or frequency-response function andphase, respectively. The phase angle expresses the lag with respect to maximum wave elevation at the

origin. The frequency of wave encounter is taken as

Wo2 V(2

w 2 2

woE=Iw -ocospja (2)g

where co is wave frequency, and g is the acceleration due to gravity, i.e., 32.1725 ft/sec2 .

Response amplitudes and phases are computed by the program for all six degrees of freedom, i.e.,

surge x, sway y, heave z, roll 0, pitch 0, and yaw 4'. Figure 7 shows the positive direction for thesedegrees of freedom while Figure 8 gives ship-heading angle with respect to wave direction a.

ROLL RESPONSE

It is known that regular wave-roll responses can vary nonlinearly with wave steepness near the natural

roll frequency. Figure 9a, from unpublished experimental work at the Center, shows that measured roll in

beam waves is most nonlinear at zero speed and becomes fairly linear at Froude numbers 0.15, 0.30, and

0.46. However, roll predicted by using the theory given in Reference 1 is nonlinear at all speeds. The

figure was based on data for the destroyer USS DEALEY (DE-1006) with a GM comparable to values used

in this investigation for BELKNAP and GARCIA.

It has been shown that the discrepancies between measured and predicted roll in Figure 9a are due to

differences between the actual and the computed roll-damping coefficients. The figure shows that the best

agreement for all steepnesses occurs at the lowest ship speed, Froude number 0.15. However, at the higher

speeds, experiment and theory appear to agree best at higher wave steepnesses, for instance, X/ý" ratios of

50 to 110. Figure 9b, also adapted from unpublished experiments done at the Center, compares measured

and predicted roll at wave steepnesses of 1/50, 1/90, and 1/200 as functions of wave-to-ship-length ratio.

The three solid-line curves represent the theoretical predictions of each steepness. The barred lines, e.g., I,

represent experimental values. The lower bar corresponds to the 1/50 case and the upper to the 1/200

case. The overall agreement between experiment and theory appears best at a wave steepness near 1/80.

Because the nonlinear roll predictions do not agree satisfactorily with the generally observed linear

behavior of roll motion for nonzero speeds, roll is treated as a linear response by computing transfer

functions for one selected value of wave steepness, i.e., - 1/80. This value has been chosen after

careful study of data typified by Figure 9, to best achieve agreement between the results of prediction and

experiment for nonzero speeds.

4

It is interesting to note variations in the irregular sea-roll predictions when the wave steepness is

varied for the regular wave prediction. Figure 10 shows such a comparison for BELKNAP for beam and

bow seas. Roll predictions for two other wave steepnesses, 1/50 and 1/110, are compared with predictions

for the 1/80 case. The data are shown as percentage differences in the root-mean-square roll with the 1/80

steepness data taken as the base. It is seen that the greatest difference, about 11 percent, is for the 1/50

steepness. The 1/110 case shows less than 8 percent of difference. In quartering seas, differences in the

roll predictions can be expected to be about the same as with beam, bow seas. Thus, the variation in

irregular sea-roll predictions, at speed, where roll is treated as a linear ship response is seen to be relatively

small with changes in wave slope.

SURGE, SWAY, AND YAW IN QUARTERINGAND FOLLOWING WAVES

Reference 1 and data obtained from model experiments at the Center indicate that there is reasonable

agreement between theory and experiment in head, bow, beam, quartering, and following seas for regular

wave predictions of heave, pitch, and roll. Further, sway and yaw appear to be reasonably well predicted

in all but quartering waves and surge in all but quartering and following waves; sway and yaw are zero in

following waves.

The theory fails for these particular conditions because of overpredicted responses at zero wave-

encounter frequency at higher ship speeds. The equations of motion for surge, heave, and pitch are

coupled as also are the equations for sway, roll, and yaw. The equations for surge, sway, and yaw do not

possess hydrostatic restoring coefficients C. and an illustration of breakdown in the theory for zero wave-

encounter frequency is given in the following text for a simplified equation of motion for any response R1,

i.e., one-degree-of-freedom equation.

Consider

(M1 k + Aik) R''+ Bik R + Cik Ri = F.eEi t (3)

where M is a generalized mass component

Alk, BIk are the added mass and damping coefficients

F. is the wave-excitation amplitude.

Equation (3) possesses a solution

R = IRI.e'CJEt (4)

where

5

F.I2.1 = 1/2 (5)

(Cjk)2- 2 [c - (Bk + (M)W

which becomes

RiI = (6)

[2(B/.k)2 WE

2 + M Jk2 W.E4] 1/2

[2' k

when the hydrostatic restoring coefficient is zero. The damping coefficient B/k tends to zero with wave

encounter frequency WE in quartering and following waves, and IRIl becomes very large, which is not con-

sistent with experimental measurements for surge, sway, and yaw amplitude responses.

For BELKNAP and GARCIA, the theory indicates that the problem of zero encounter frequency

arises at 20 and 30 knots for surge, sway, and yaw at p = 30 and 60 deg and for surge at p = 0 deg. Thus,

no data have been presented for these conditions.

PREDICTION OF SHIP-RESPONSE STATISTICS IN IRREGULAR SEAS

GENERAL DESCRIPTION

The ship responses to long-crested, irregular waves are found by summing the ship responses to regular

waves for all frequencies. This application of the principle of superposition to ship motion predictions was

first proposed by St. Denis and Pierson 3 and is now a widely accepted and proven procedure.

The ship motion spectral density is given by

SR(C) = [RA(w)] 2 .S .(C) (7)

where S(W) is the irregular sea spectral density, and [RA (W)] 2 is the response amplitude operator,

making use of

3 St. Denis, M. and W.J. Pierson, "On the Motion of Ships in Confused Seas," Transactions of The Society of Naval

Architects and Marine Engineers, Vol. 61, pp. 280-237 (1953).

6

' S (Wc1'" ) ,d col., = ,sit¢ (0 (! W (8)•

The integration of SR( W) over the frequency range, i.e.,

OR 2= f SIR?(C) d( (W)

can be shown to be the same as the variance of consecutive, equally spaced samples from an irregular sea time

history of the motion response. Such time-history samples tend to follow a normal or Gaussian distribution,

while peak-to-peak variations or amplitudes will tend to be approximated bya Rayleigh distribution. By

integration of the Rayleigh probability density function (Appendix A) the probability of occurrence of a

given response amplitude may be found. Table 3 gives a summary of the constants which relate the root-

mean-square value of the response oR to particular amplitudes. For example, the highest expected ampli-

tude in 10 cycles of response is 2.15 oR, etc. By the definition given in Table 3 and in Appendix A, any

statistic not listed may be determined.

TABLE 3 - SINGLE AMPLITUDE STATISTICAL CONSTANTS FOR A FULLY

DEVELOPED WIND-GENERATED SEA

Single Amplitude Statistics

Root-Mean-Square Amplitude 1.00

Average Amplitude 1.25

Average of Highest One-Third Amplitudes 2.00

Highest Expected Response Amplitude in 10 Cycles 2.15

Average of Highest One-Tenth Amplitudes 2.55

Highest Expected Amplitude in Indicated Cycles of

Response -

30 2.61

50 2.80

100 3.03

200 3.25

1000 3.72

Note: a 2 is statistical variance of time history; N is number of

1/2cycles; CONSTANT is , t 2 n N) , where CONSTANT relates ato the highest expected amplitude in N cycles.

7

In a manner similar to that previously described, the spectral density of ship-response velocity SR, and

its variance aR 2 respectively, are found by

2SR(co) = [WE (W) R A (C.)I 'Sý (w) (10)

and

cR2 f S 1 (w)dw (11)0

Likewise, the spectral density of ship-response acceleration S' and variance oR2 respectively, are

given by

SR(W)= WE(W)12 'RA(W)2 S. (w) (12)

and

OR2 f S'(cw) dw (13)0

The same single amplitude statistics (Table 3) which apply to the variances of linear and angular dis-

placement motion also apply to the variances of velocity and acceleration. In general, for the acceleration

responses in surge, sway, and heave, a" is divided by 32.1725 ft/sec 2 to provide the value in g's.

It should be noted that because GARCIA is fitted with fins, a special step is required in the calcu-

lation procedure. The unstabilized roll responses in regular waves are reduced by the factors derived in

Appendix B to obtain the stabilized-roll responses. These stabilized-roll responses are then used in

Equation (7) to determine the spectral density of stabilized-roll response.

Equations (7) through (13) refer to responses predicted at the origin of the coordinate system. They

may be used to predict responses at any other point on the ship.

FREQUENCY-RESPONSE FUNCTIONS ATAN ARBITRARY POINT

The longitudinal, lateral, and vertical displacements Lo, LA, and LV, respectively, at a point (x*, y*,

z*) are expressed as

8

LO=x--y sin + +z*sin 0+x*(cos ,+cos0) 2x*

"LA =.-v - z* sin + x* sin , +,y* (cos + cos ti) - 2y* (14)

LV =z-x*sin0+y*sin O+z*(cosO+cosO) - 2z*

where the displacements are functions of frequency and time. If small angles are assumed, Equations (14)

reduce to

Lo = x - y* 4' + z* 0

LA =y-z*O+x* x0 (15)

LV = z - x*0+y* 4

In this form it is straightforward to derive the frequency-response functions RLO (C), RLA (co), and RL V(Cw)

by calculating real and imaginary parts of Lo, LA, and LV for a given frequency and by using the approach

already described to obtain required variance values OL2, OL 2, and ar 20 A LV

Frequency-response functions of velocity and acceleration are obtained from the frequency-responsefunctions of displacement by taking the product with oE(cw) and [CjE(W)22, r,; 2

, respectively; hec 'lo 0

etc. As before, acceleration responses, o" 2 etc., are divided by 32.1725 ft/sec 2 to provide the value in* g's.

IRREGULAR SEA REPRESENTATION

The long-crested seaway is analytically represented by the spectral density ordinates of Pierson and

Moskowitz

ag2 exp F 4ag2 ] ft2 xsec (16)where cw is the wave frequency in radians per second, a = 0.0081, g = 32.1725 ft/sec 2, and (•)1/3 is the

significant wave height in feet.

Equation (16) represents the energy of a fully developed, wind-generated sea, and values used for this

investigation for (fw)1/3 = 4, 10, 16, and 20 ft are given in Figure 11. Table 4 shows the corresponding

wind velocities and Center scale for states of sea.

9

TABLE 4 - DEFINITION OF STATE OF SEA

Significant Wave Height Wind Velocity Centerft knots State of Sea Scale

4 14.70 3

10 23.25 5

16 29.41 6

20 32.88 6

SPECTRAL CLOSURE

Accuracy of the calculation of response variance UR2, described previously, relies heavily on proper

calculation of the areas under each response spectrum. If the values of SR(w) approach zero at high and

low frequencies, spectral closure is attained. For this case the area is well defined and, thus, will be

accurately calculated. It has been found that the area is still well defined if the response values of spectral

density at the lower and higher ends of the curve are less than 10 percent of the spectral value of maximum

response.

Further, the response spectrum closes properly if the product of the response-amplitude operator and

the spectral ordinate of the wave closes. This means that it is not necessary for the response-amplitude

operator to close as long as the wave spectrum closes and vice versa. Figure 12 illustrates a case when the

curve of the response-amplitude operator is open at the low-frequency end; yet, the response spectrum is

closed.

For this investigation, the response spectrum was forced to closure at the high-frequency end. Regu-

lar wave responses were computed for ratios of wave-to-ship length N/ LPP from 4.2 to 0.1. To ensureproper closure, response-amplitude operators were set to zero for a wave-to-ship-length ratio of 0.05. This

value is a conservative choice on the basis of previous experimental and theoretical investigations.

10

RESULTS

DATA BASE OF PLATFORM RESPONSES FORUSS BELKNAP (DLG-26) AND USS GARCIA(DE-1040)

Table 5 summarizes the information given in Tables 6 to 47 in Appendix C, which give the results ofthe investigation. Each table presents the predictions of root-mean-square value for displacements,velocities, and accelerations for a given response for heading angles p = 180 (head), 150, 120, 90, 60, 30,and 0 (following) deg: ship speeds V = 10, 20, and 30 knots; and significant wave heights G,•) 1/3 =4, 10,16, and 20 ft.

TABLE 5 - DESCRIPTION OF DATA-BASE PRESENTATION

Table Numbers* Response/Direction Location

6, 27 Surge

7, 28 Sway

8, 29 Heave Origin

9, 30 Roll

10, 31 Pitch

11, 32 Yaw

12, 33 Longitudinal

13, 34 Lateral Point 1

14, 35 Vertical

15, 36 Longitudinal


17, 38 Vertical

18, 39 Longitudinal


20, 41 Vertical

21, 42 Longitudinal


23, 44 Vertical

24, 45 Longitudinal


26, 47 Vertical

Tables 6 through 26 refer to BELKNAP; Tables 27 through 47iefer to GARCIA.

11

The dimensions of the root-mean-square values are as given within Tables 6 to 47. Hyphenated

spaces indicate a condition for which theory fails to predict reliable values, e.g., surge, sway, yaw-quartering,

following seas.

As described previously, other single amplitude statistics or probabilities of occurrence may be

determined from the root-mean-square values. Values for the highest response in 100 cycles of response,

shown in Figures 13 through 21, are derived directly from Tables 6 through 47 by using Table 3.

LANDING PLATFORM AND SHIP-RESPONSELEVELS

Suppose the highest of 100 amplitudes of response is required to investigate, for example, impact-

force tolerances of LAMPS landing gear. The highest of 100 values is obtained from given root-mean-

square values by using Table 3, i.e., 3.03 oR. There are many ways to cross plot these data in studying

the response levels and trends of the two ships.

As an example, it is of interest to compare the motions predicted at the LCG, waterplane, CL inter-

section of the ship with those at the CG of the landed helicopter, i.e., Point 5, for a State 5 sea.

Figures 13 through 15 show displacements in the longitudinal, lateral, and vertical directions for these

points at 10, 20, and 30 knots and significant wave height of 10 feet.

Another interesting comparison is that between selected motions for each ship for all headings and

speeds. Figures 16 and 17 show the highest roll and pitch angles, respectively, expected in 100 cycles for

both ships. It can be seen that roll is worse for BELKNAP, while pitch is worse for GARCIA. Figures 18

through 20 compare longitudinal, lateral, and vertical velocities at CG, i.e., Point 5, of a helicopter that has

landed on each ship.

Another useful cross plot is the comparison between the motions of the two ships in different states

of sea for a given speed. Figure 21 shows the vertical velocity at CG of the landed helicopter for each ship

in all four states of sea at 20 knots. It is apparent that the vertical velocity of GARCIA is higher for

y > 90 deg than is that for BELKNAP in each state of sea.

EVALUATION OF DATA

Experiments conducted by the Naval Air Test Center (Patuxent, Md.) have shown the compatibility

of LAMPS helicopter operations with BELKNAP and smaller GARCIA-Class destroyers. References 4

4 Kizer, G.R. and G.D. Carico, "Final Report Navy Evaluation of the Helicopter Hauldown System," Naval Air TestCenter Technical Report FT-20R-69 (Mar 1969).

12

through 7 discuss the experiments conducted on these or similar ships with LAMPS or similar helicopters.

Having established compatibility between ship and helicopter, it is most desirable to establish consistent

landing, tiedown, and takeoff techniques. The same references present ship-motion envelopes for helicopter

operations from data already collected. The data base presented in this report can be used to reevaluate

the envelopes of existing ship motions for which, in general, only roll motion is considered and to develop

new operational envelopes for other ship motions and states of sea.

For example, in low states of sea, such as a State 3 sea, the referenced experimental results indicate

that heave and pitch motions are not of significant importance to landing-platform operations. Indeed,

Tables 8, 10, 29, and 31 show very small pitch and heave magnitudes for a significant wave height of 4 ft.

Likewise, roll responses are of small magnitudes. To land in such conditions, the helicopter will usually

hover above the deck until a near level attitude ± 3 deg of roll is approached. Usually, the roll frequency

is small enough for the helicopter to land in the time that the deck is nearly level. This landing technique

reduces the possibility of landing out of the landing circle as well as of applying asymmetrical loads on the

landing gear. It is important for the helicopter to set down within the landing circle and land nearly level

because it might otherwise damage either itself or the adjacent superstructure of the ship; perhaps even

worse, it might slip off the side of the ship. Further, it is important that only symmetrical loads be in-

duced on the landing gear to avoid damage to the landing gear.

The existing ship-motion envelopes for helicopter operations consider roll angle only, although

Reference 7 does give valid motion envelopes to 5 deg of pitch angle. Tables 9 and 30 show smaller roll

angles in bow seas than in beam and quartering seas for the low state of sea. This substantiates the fact

that References 4 through 7 generally state that landings require less pilot effort and are thus more safe in

bow seas.

Though such an investigation is not reported, References 4 through 7 imply that any significant in-

crease in heave and pitch with increase in state of sea may effect helicopter operations. For a given heading,

Tables 8, 10, 29, and 31 do show a relatively large increase in heave response, while pitch response in-

creases somewhat less dramatically when state of sea is increased. Also, roll response, as presented in

Tables 9 and 30, increases rather significantly at the higher states of sea. One way to investigate the

relative importance of each of the three responses-heave, roll, and pitch-in any state of sea is through

vertical response predicted for points on the landing platform of each ship. It is shown in Equation (15)

that the vertical response is dependent on each of these three responses. As can be expected, Tables 17

and 38 show small values for the vertical response at the centers of the landing platforms at the low state

5 Parkinson, R. et al., "Final Report Evaluation of the DE-1052 Class Destroyer for HH-2D Helicopter Operations,"Naval Air Test Center Technical Report FT-4R-71 (Feb 1971).

6 Parkinson, R. and G. Hurley, "Fifth Interim Report, LAMPS Support and Monitor (Evaluation of the DE-1040-ClassDestroyer for HH-2D Helicopter Operations)," Naval Air Test Center Technical Report FT-41R-71 (May 1971).

7 Lineback, H.W. and-A.B. Hill, "First Interim Report Helicopter/VSTOL Compatibility Program (DLG-26/SH-2DDynamic Interface Flight Envelope)," Naval Air Test Center Report of Test Results FT-91R-71 (Dec 1971).

13

of sea. However at the higher states of sea the vertical responses are of much greater magnitude. Such

vertical responses may be used to study loads on the helicopter landing gear and on the helicopter hauldown

systems.

Knowledge of ship heading for minimum response levels is important to helicopter operations.

Generally, the responses are smallest in bow seas at lower states of sea; hence, it is considered safest to

land in bow seas for low states of sea. But as states of sea and, thus, responses increase, the tables may

show smaller responses in quartering than in bow seas. For example, the vertical displacement at the plat-

form center of BELKNAP is slightly less at 30 deg and 10 knots than at 150 deg and 10 knots for States 5,

6, and high 6 seas; see Table 17. Perhaps of more significance, the corresponding vertical velocities are

much less in all quartering sea headings than in bow seas. Thus, when considering vertical and roll

responses, it appears that landings to be made in high states of sea are safest when the ship is in quartering

seas.

In general, origin responses for BELKNAP are of less magnitude than those for GARCIA, except

for the case of roll response in which GARCIA is stabilized, and BELKNAP is not. Further, when con-

sidering higher state of sea responses, predicted at corresponding points on each ship landing platform, it

is found that longitudinal and vertical responses of the BELKNAP class are less than those of the GARCIA

class, while the lateral responses of the stabilized GARCIA are less than those for BELKNAP. Thus, if

safer helicopter operations are required of the BELKNAP-Class, especially in higher states of sea, the

response data imply that the ship should be stabilized in roll.

CONCLUDING REMARKS

The computational procedure described in this report has been applied to obtain response pre-

dictions for the helicopter landing platforms of two destroyer classes. From consideration of these pre-

dictions, the following conclusions may be drawn.

I. Predicted response trends are consistent with observed helicopter operations in low states of sea.

2. Responses other than roll, e.g., vertical response of the landing platform, must be considered todevelop ship motion envelopes for helicopter operations in high states of sea. Predicted responsesmay be used to determine these envelopes for helicopter landing, tiedown, and takeoff operationson the two destroyer classes within a range from States 3 to 6 seas and from 10 to 30 knots.

3. Helicopter operations in high states of sea may be safer in quartering than in bow seas as certainresponse magnitudes, e.g., vertical velocity of the landing platform, are less in quartering seas.

4. To expedite increased safety for helicopter operations in higher states of sea, the BELKNAP(DLG-26) class should be stabilized in roll.

The seaway applied in this calculation procedure is that of a fully developed, unidirectional, wind-

generated sea. Consideration is presently being given to develop more realistic representations of the seaway.

Such representations can include components of swell and have the form of a short-crested seaway with

two parameters.

14

The computational method which has been developed and used in this investigation may be applied

to many other problems besides the one described herein, e.g., requiring the spectral responses or the

spectral loads at any point on a ship operating in a seaway. For example, the method may be used to

predict the vertical displacement, velocity, and acceleration experienced on the bridge in beam seas in a

State 7 sea. Further, it is believed that the described method will be of use to both the naval architect

who must design ships for optimum seaworthiness and the engineer who must modify and study existing

ships in an effort to extend the operational efficiency and capability of the fleet.

It should be emphasized that the choice of a specific wave steepness, i.e., , = 1/80, to compute

roll-transfer functions is solely to obtain best agreement between theoretical prediction and experimental

data. It is not meant to typify actual sea-wave steepness.

15

o

'1I IV

-------- .,,

----------

- -- -- -4 -4,' 4

- - - - - - - - - -- - - - - - -- - - - - - -- -

- - - - - - - - - - --- -

- - C4 P-4

v)

--

4 M

16 4

4 4 4 ---- 0~~-16

0... .. 0. .

S. . . • , , • • ',- -,

S-.. ... . .. .• _ .; . ;: : -- .' • r -- * ' "-. ,,_,, ,

--------- -------- .

w UmSee/ 4 4. ... 0

w .

cn

17

14 C1

41C4 CO '-4

-W - ý - 4 l)

CL

Kn -I Io

caa !ii)N 4

r-4

.4l.

aC C

00

18

S550

20.6'

Bilge Keel

CL

Stabilizing Fin

4.0' -9.5"

Trailing Leading

8.0' Edge Edge

Planform Area, AF 32 Square feetSpan 8 Feet

Aspect Ratio, ag 2

Figure 4 - Stabilizing Fin for GARCIA

19

U

Cý00

-14

C14

C;

(U

cz CLW

Cf) Cl)

tn

7;E-4 =

0 '1)z N

7ý

.2u0

Lr). I -00CY)

cqU') LO

rL4 C14

P4

lp cn

O's LnCl)

20

r-4

PL CC

CfC

C c4

*I-4 c.1-0

C.~ .21

CL

Az

HEAVE

YA yROLL SWAY

SWAY

xSURGE

HEAVE

__4__- 7- DWL

SURGE

PITCH

Figure 7 - Right-Handed Coordinate System for Response Predictions

22

HEAD

0C

00

00

UO

0 04

C).

C-4)

0 C0

00

0

0

23

0 0 C1

0 00

0 r-0.

.0

C) W

P.,:

C4 0E-4

00 a ' C ,P4 Z

C-4 F- V

C)C

o 0

0.cz'

NON

0 -4 0C

o H 0

0 0 l

v Hnla lou 0

N x. c

24

16 _ I = 1/50DLG-26 _w/A__ 1/110

0 V = 0 KNOTS''/*• = 20 FEET

[-0

14 m ]V =20 KNOTS

" "" /• V =30 KNOTS

12

z z 10

00zz 8

S--4

• 6-

~E4

2

180 150 120 90

HEADING ANGLE, •, DEGREES

Figure 10 - Percentage Differences Between Roll Predictions at Wave Steepnesses 1/80and 1/50 and 1/80 and 1/110 for the USS BELKNAP (DLG-26) in Irregular Seas

25

80

70w /3 20 FEET

70

z

60

14 503

0 40

1300

m4

0Ez0

H 20-

10-/-

0

0.0 0.5 1.0 1.5 2.0

WAVE FREQUENCY, w, RADIANS PER SECOND

Figure 11 - Pierson and Moskowitz Sea Spectra for SignificantWave Heights of 4, 10, 16, and 20 Feet

26

16

W)I/3 =0 FEET

•HcIo 12

nU,

4- &

0

&4 POINT 5, DLG-26

V = 20 KNOTS1.5 = 120 DEGREES

04 C 0.w ZH

ý-

4.4 DLG-26 -- POINT 5

10 FEET ORIGIN0 V = 10 KNOTS

4.0 Ej V = 20 KNOTS -

0A v = 30 KNOTS

.3.6

z3.2

. 2.8

z

z2.4 0

C-,

0. 8•o. 4

0.0

180 150 120 90 .0 30

HEADING ANGLE, 4, DEGREES

Figure 13 - Comparison of Highest Expected Longitudinal Displacement,Single Amplitudes, in 100 Cycles for Origin of BELKNAP and Point 5

with Significant Wave Height of 10 Feet

28

DLG-26 -- POINT 5

-- ) = 10 FEET ORIGIN0 V 10 KNOTS

i0 Q V = 20 KNOTS/• V = 30 KNOTS

F4

S9

U8 -7/

0

180 150 120 90 60 30 0

HIEADING ANGLE, uDEGREES

Figure 14 - Comparison of Highest Expected Lateral Displacement, SingleAmplitudes, in 100 Cycles for Origin of BELKNAP and Point 5 with

Significant Wave Height of 10 Feet

29

TI II8,8 - DLG-26 -- POINT 5

() 10 FEET ORIGIN0 V 10 KNOTS

8.o 0 V =20 KNOTS

14 V= 30 KNOTS

L3 7.2

zoC

H 6.4

Z 5.c

4.0

M 3.2

C

2.4

o 1.6

0.8

0.0 I I I I180 150 120 90 60 30 0

HEADING ANGLE, i, DEGREES

Figure 15 - Comparison of Highest Expected Vertical Displacement, SingleAmplitudes, in 100 Cycles for Origin of BELKNAP and Point 5 with


30

I III i44 - (aw)1/3 - 10 FEET- DLG-26

SDE- 1040ORIGIN

O V - 10 KNOTS40 ol V " 20 KNOTS

V =30 KNOTS

S36 -

32

zH 28 -

• 24 -

*-4

* 20

16

12

8/

4

0180 150 120 90 60 30 0

HEADING ANGLE, j, DEGREES

Figure 16 - Comparison of Highest Expected Roll, Single Amplitudes,in 100 Cycles for BELKNAP and GARCIA with Significant

Wave Height of 10 Feet

31

I I

8.8 -(w)I/= 10 FEET -- DLG-26

- DE- 1040ORIGIN 0 V = 10 KNOTS

9.0 -- 0 V = 20 KNOTS

A V = 30 KNOTS

n 7.2

0

0 6.402

z

H

j 5.6

4.8

4.0

U

z

P 3.2C)W

; 2.4

1.6

0.8

0.0 I I180 150 120 90 60 30 0

HEADING ANGLE, g, DEGREES

Figure 17 - Comparison of Highest Expected Pitch, Single Amplitudes, in100 Cycles for BELKNAP and GARCIA with Significant


32

2.2 () 10 FEET DLG-26

POINT 5 - DE-1040

0 V = 10 KNOTS0

2.0 r3 V = 20 KNOTSV = 30 KNOTS

S1.8

1.600

'~1.4

0

'-4

1.2

1l.0 •>P-4

• 0.4 .-

° /

0.2

0.0

180 150 120 90 60 300

HEADING ANGLE, DEGREES

Figure 18 - Comparison of Highest Expected Longitudinal Velocity, Single

Amplitudes, in 100 Cycles for BELKNAP and GARCIA with Significant


33

I I

8.8 1- 0 FEET DLG-26

POINT 5 - DE- 1040

0 V = 10 KNOTSz8.0

8 V = 20 KNOTSV = 30 KNOTS

H7.2

6.4U

C0 1

5.6

'-4

• 4.8

z 4 .0

3.2

" 2 . 4H

m 1.6

0.8

0.0180 150 120 90 60 30 0

HEADING ANGLE, •, DEGREES

Figure 19 - Comparison of Highest Expected Lateral Velocity, SingleAmplitudes, in 100 Cycles for BELKNAP and GARCIA with


34

8.8 - -10 FEET DLG-26-DE-1040

I V = 10 KNOTS

8.0 0 V = 20 KNOTS

0• V = 30 KNOTS

S7.2

U3 6.4

U

5.6

S4.8

Z 4.0 /

S3.2

S2.4

• 1.6

= 0.8 -

0.0

180 150 120 90 60 30 0

HEADING ANGLE, i, DEGREES

Figure 20 - Comparison of Highest Expected Vertical Velocity, Single

Amplitudes, in 100 Cycles for BELKNAP and GARCIA withSignificant Wave Height of 10 Feet

35

22 V = 20 KNOTS

POINT 5 - DLG-26

- DE-1040

z 0 (7w)11 4 FEETu 200 -~ =10 FEET

~~q) ~- 16 FEET18 = 20 FEET18 n

U 1600

14H

< 12

Z

H10

8

6

0

180 150 120 90 60 300

HEADING ANGLE, DEGREES

Figure 21 -Comparison of Highest Expected Vertical Velocity, SingleAmplitudes, in 100 Cycles for BELKNAP and GARCIA at

Point 5 and 20 Knots

36

RALIHASRBT

0

- -0005 ---- ----

0.1a

Fi0.205TePoailt fX xedn b ie

374

t , - I I" i I • 1 I

z .16

P4 .14

10

O .12

o .08

• .06

mi .04

0 .02z

0 I I I.I...ILL. III I .5 10 15 20 25 30

SHIP SPEED, V, KNOTS

Figure 23 - Nondimensional Roll-Decay Coefficient of GARCIA

i I i I ! '

90

80

o 70U-..

! 6050

0

W 40

zW 30

S20 A, DE-1040

10(E) DE-1052

1-- - PG-100

0 i I 1 1

5 10 15 20 25 30

SHIP SPEED, V, KNOTS

Figure 24 - Percentage of Roll Reduction for Stabilized GARCIA and

Experimental Comparison with Two Other Ships

38

16 DE- 1040 1 -T'70

V = 30 KNOTS N = I 0010/

120 DEGREES N 0 N

S14 WITHOUT ROLL/REDUCTION/ /

,-____WITH ROLL /f,

CI/IS12 RDCTO

z IN /N10 = 1° / I

H /'-' III

X//

flllSI~N = 10

0 4 8 12 16 20 24

SIGNIFICANT WAVE HEIGHT ,(w)/ FEETW /32

Figure 25 - Comparison of Highest Expected Roll, Single Amplitudes,in N Cycles for GARCIA with and without Roll Reduction for

30 Knots and a 120-Degree Heading Angle

39

APPENDIX A

PROBABILITY OF OCCURRENCE

The probability of occurrence of a particular response, i.e., displacement, velocity, or acceleration,

over a long period of time can be determined from the area of the corresponding response spectra. The

peak-to-peak double amplitudes of response, and hence the single amplitudes, are assumed to be very nearly

distributed with a Rayleigh probability density function, which is given by

fexp2 exp for0 b, i.e., P(X > b) by

P(X > b) = - F(b) = exp I (19)2oa

The Rayleigh distribution is plotted in Figure 22 against b/a. Thus, the probability of X exceeding a

specific b can be read directly from the curve. For example, consider the vertical velocity of Point 5 on

BELKNAP with a heading of 120 deg, 30 knots, and a State 5 sea; see Figure 20. The highest value in 100

cycles is 7.30 ft/see. The corresponding root mean square or oaL value is 2.41 ft/sec. To determine theV

probability of exceeding 6 ft/sec over a long period look up the ratio of 6 to 2.41 or 2.49, which corresponds

to 0.046 on the vertical scale of Figure 22. Thus the probability of exceeding 6 ft/sec is 0.046 or 4.6 per-

cent.

There is another use of Figure 22 that should be mentioned. Suppose, for the case described pre-

viously, it is desirable to know what vertical velocity b will be exceeded with a probability of 0.001 over a

long period. In Figure 22, P = 0.001 yields b/o = 3.72. Therefore, b = 8.96 ft/sec.

It is appropriate to make further comment about the single amplitude statistics in Table 3. Consider a

large number N of values, each with equal probability I/N of being the maximum or highest value. From

Equation (19)

41

b =v'2 oa[ Vn 1/P]"2

(20)

or b = /T2-o [ F n N] 1/2

Equation (20) means that b is the highest value most likely to occur in N values. This definition is exactly

that of Table 3.

A few words of warning are necessary. There is no upper limit on the highest response b that can be

predicted by Equation (20). That is, as N becomes large, b becomes large. Therefore, Equation (20), and

hence the definition in Table 3, is best applied for small values of N.

Reference 8 gives additional procedures for developing response statistics.

8 Pierson, W.J., Jr. et al., "Practical Methods for Observing and Forecasting Ocean Waves by Means of Wave Spectra andStatistics," U.S. Navy Hydrographic Office Publication 603 (1955).

42

APPENDIX B

ROLL REDUCTION OF USS GARCIA (DE-1040) BY ACTIVE STABILIZING FINS

Th1e linear tIheory of J.I. Conolly 9 has been used to predict the reduction in roll due to a pair of

active l'ins fitted to GARCIA. To apply the Conolly theory, it is necessary to obtain an expression for1/0,,1 the ratio of stabilized to unstabilized roll, as a function of the ship and fin particulars. As not all

of the required particulars are known, certain quantities must be assumed or estimated from existing data.

It is assumed that the fini-control system seeks to completely oppose the roll angle imposed by the

wave on the ship. The system regulating the fin angle is described by

f3=k, 0+k 2 +k 3 (21)

where for opposed control

k 3

k2 2n wog

and

kI o (22)

k2 2n

where kl, k), and k3 are the control characteristics of the system

is the roll angle

Wo• is the natural frequency of roll in radians per second and

n is the roll-decay coefficient.

The ratio of stabilized-to-unstabilized roll amplitude may be estimated by

SF R (dCL)= V 2 1 '(23)(g u ~~2 A G'-'M \df

9 Conolly, J.E., "Rolling and its Stabilization by Active Fins," Quarterly Transactions of The Royal Institution of NavalArchitects, Vol. 3, No. 1, pp. 21-48 (1969).

43

where p is the mass density of water, 1.99 slugs/ft3

V is ship speed in feet per second

A is ship displacement in pounds

Gs is metacentric height in feet

RF is distance from the center of pressure of the fin to the roll axis in feet

AF is fin area per side of ship in square feet

dCL/d 3 is slope of lift-coefficient curve per radian of fin angle.

From Figure 4, AF = 32 ft 2 , and RF = 20.6 ft. From Table 1, A = 3408 long tons, G"M = 4.5 ft, and

w = 0.7 rad/sec. To apply Equation (23), it remains to determine values for dCL/d3O, n, and k 2 .

It is assumed that the fin-lift coefficient C. is linearly proportional to the fin angle 0, so that the

slope of the lift-coefficient curve is1 0

dCL -1C( ag) [ ag) + 4 + 1.8 (24)

= 3.6 per radian of fin angle

where ag is the geometric aspect ratio.

To obtain an estimate for the roll-decay coefficients of GARCIA, it is assumed that they can be cal-

culated from those measured full scale for the USS BRUMBY (DE-1044) by the relationship

rt10 4 0 A 10 4 4 1044(25)

111044 A 10 4 0 WO/t 1040

where the subscripts 1040 and 1044 refer to the ships. 9 Figure 23 gives the resulting decay coefficients as

a function of ship speed. The values for the particular speeds under consideration are as follows:

Ship Speed Decay Coefficient,knots n

10 0.069

20 0.145

30 0.131

10 Whicker, L.F. and L.F. Fehlner, "Free-Stream Characteristics of a Family of Low-Aspect-Ratio, All-Movable Control

Surfaces for Application to Ship Design," David Taylor Model Basin Report 933 (Dec 1958).

44

It remains only to find a value for k 2. Reference 9 gives 4.2 and 6.6 for ship systems of two specific

destroyer types. It seems reasonable, therefore, to put k2 = 5. It will be shown later from both model

and full-scale experiments that this value gives a roll reduction of the right order of magnitude.

Using ship speeds corresponding to 10, 20, and 30 knots, Equation 23 yields

Ship Speed 0 /0 Percentage Rollknots Reduction

10 0.4595 54

20 0.3087 69

30 0.1521 85

where the percentage of roll reduction is merely 100 (1-Os/ku) percent.

These numbers are representative of the type of roll reduction experienced by ships fitted with active

fins as may be seen from Figure 24, which gives the percentage of roll reduction for GARCIA together with

experimental results for two other ships. The diamonds represent the percentage of roll reduction observed

during full-scale trials by the Center onboard a patrol gun boat 154 ft in length, having a Froude correction

factor to speed of 1.59. The circles represent the percentage of roll reduction measured during tests by the

Center of a USS KNOX (DE-1052)-Class model, 415 ft in length, having a fin-control system dependent on

angle and velocity of roll and a corresponding Froude correction factor of 0.97. This implies that using the

previously given equations, based on linear roll theory with k2 = 5, gives an estimate of roll reduction which

is compatible with data both from model and full-scale tests for ships of similar characteristics to those of

GARCIA.

In comparing roll angles for the unstabilized GARCIA with those estimated for the ship fitted with

fins, Figure 25 shows significant values against wave height at 30 knots and a 120-deg heading angle. Single

amplitudes are shown for the highest wave in 10, 30, and 100 cycles of response. The figure expresses the

dramatic difference in unstabilized and stabilized roll angles.

45

APPENDIX CSUMMARIES OF INVESTIGATIONS

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