Norman Hans Jasper. # Sea test of the USCGC Unimak : part 2 - statistical presentation of the motions, hull bending moments, and slamming pressures for ships of the AVP type online

. **(page 1 of 4)**

Online Library → Norman Hans Jasper → Sea test of the USCGC Unimak : part 2 - statistical presentation of the motions, hull bending moments, and slamming pressures for ships of the AVP type → online text (page 1 of 4)

Font size

HYDROMECHANICS

M.

977

rifi&r^^;^CÂ«^^

JEA TESTS OF THE USCGC UNIMAK

PART 2 - STATISTICAL PRESENTATIOK OF THE MOTIONS,

HULL BENDING MOMENTS, AND SLAMMING PRESSURES

FOR SHIPS OF THE AVP TYPE

eODYNAMICS

by

STRUCTURAL

MECHANICS

N.H. Jasper, Dr. Eng., and R.L. Brooks, CDR, USN

APPLIED

\THEMATICS

STRUCTURAL MECHANICS LABORATORY

RESEARCH AND DEVELOPMENT REPORT

m

; m

i â–¡

ir=t

rm

SEA TESTS OF THE USCGC UNIMAK

PART 2- STATISTICAL PRESENTATION OF THE MOTIONS,

HULL BENDING MOMENTS, AND SLAMMING PRESSURES

FOR SHIPS OF THE AVP TYPE

by

N.H. Jasper, Dr. Eng., and R.L. Brooks, CDR, USN

April 1957 Report 977

NS 731-037

TABLE OF CONTENTS

Page

ABSTRACT ^ 1

INTRODUCTION 1

STATISTICAL BACKGROUND 4

DERIVATION OF DISTRIBUTIONS OF SHIP MOTIONS

AND LONGITUDINAL BENDING MOMENTS OF THE HULL 7

DESIGN AND OPERATIONAL CONDITIONS FOR WARTIME SERVICE 20

Long-Term Distributions of Ship Motion, Hull Bending Moment,

and Wave Height 20

Predictions of Ship Response to Waves for Given Conditions 20

Pre^diction of Extreme Values 22

Design Loads for Bottom Structure to Withstand Slamming Loads 26

DISCUSSION 27

ACKNOWLEDGMENTS 28

APPENDIX A - SAMPLE OSCILLOGRAMS â€¢ 29

APPENDIX B - SAMPLE CALCULATIONS 35

APPENDIX C - PHOTOGRAPHIC DEFINITION OF SEA CONDITIONS 37

REFERENCES 42

LIST OF ILLUSTRATIONS

Figure 1 - Profile and Characteristics of USCGC UNIMAK (AVPlO-Class Vessel) 3

Figure 2 - Distribution of Heights of Ocean Waves at Weather Station C,

52Â° N 37Â° W, North Atlantic Ocean 5

Figure 3 - Distribution of Variation in Pitch Angle (Sample 1)

for USCGC UNIMAK 8

Figure 4 - Cumulative Distribution of Variation in Pitch Angle (Sample 1)

for USCGC UNIMAK 3

Figure 5 - Distribution of Variation in Pitch Angle (Sample 2)

for USCGC UNIMAK 9

Figure 6 - Cumulative Distribution of Variation in Pitch Angle (Sample 2)

for USCGC UNIMAK 9

Figure 7 - Long-Term Cumulative Distribution of Pitch Angle for Wartime

Service, North Atlantic Ocean 21

Figure 8 - Long-Term Cumulative Distribution of Pitch Acceleration for

Wartime Service, North Atlantic Ocean 22

Figure 9 - Long-Term Cumulative Distribution of Roll Angle for Wartime

Service, North Atlantic Ocean 23

Figure 10 - Long-Term Cumulative Distribution of Longitudinal Bending Moment,

Amidships, for Wartime Service, North Atlantic Ocean 24

Figure 11 - Samples of Records Taken During tiie Tests 30

Figure 12 - Wave Photographs 38

Figure 13 - Wave Profiles 39

LIST OF TABLES

Table 1 - Estimated Wartime Operating Conditions 2

Table 2 - Basic Statistical Data on Pitch Angles 11

Table 3 - Basic Statistical Data on Pitch Accelerations 12

Table 4 - Basic Statistical Data on Roll Angles 13

Table 5 - Basic Statistical Data on Stresses 14

Table 6 - Basic Statistical Data on Heave Accelerations 15

Table 7 - Constants Required for Prediction of Probable Maximum Value

in a Sample from a Rayleigh Distribution. , 15

Table 8 - Derivation of Predicted Distribution Pattern for Variations

in Pitch Angle for Wartime Duty in North Atlantic Ocean 16

Table 9 - Derivation of Predicted Distribution Pattern for Variations

in Pitch Acceleration for Wartime Duty in North Atlantic Ocean 17

Table 10 - Derivation of Predicted Distribution Pattern for Variations

in Roll Angle for Wartime Duty in North Atlantic Ocean 18

Table 11 - Derivation of Predicted Distribution Pattern for Variation in Hull

Stress Due to Longitudinal Bending, at the Main Deck, Amidships

for Wartime Duty in North Atlantic Ocean 19

Table 12 - Maximum Values of Ship Motion and Longitudinal Bending Moment

for Use in Design Calculations 26

ABSTRACT

The motions and hull-girder bending moments which a ship of the general

form and size of the AVPIO Class may be expected to experience over a wide range

of operating conditions are presented in statistical form. The data are based on

extensive measurements made on the USCGC UNIMAK during sea trials in the

J<forth Atlantic Ocean. The methods of statistics have been employed in the plan-

ning of the at-sea phases of the trials and in the collection, analysis, and presenta-

tion of the large amount of data. From the test results, data are derived for this

type of ship for use in design and operating problems involving bending moments,

hull motions, and slamming pressures. Formulas are given for use in estimating

probable maximum values of moments and motions.

INTRODUCTION

The Bureau of Ships initiated a long-range investigation of strains in ships at sea for

the purpose of evaluating and improving methods for the design of the ship girder and its

structural components.^ Instrumentation has been developed and installed on various types

of ships to collect information on the wave loads, stresses, and motions which ships exper-

ience in service. During the winter of 1954 and 1955, measurements were carried out on the

USCGC UNIMAK (formerly AVP31) during operation in the North Atlantic Ocean. One of the

main objectives of this work is the collection of sufficient data on ship motions and longitud-

inal hull-girder stresses to determine, by statistical methods, the frequency distributions of

these quantities for different combinations of sea conditions, ship speed, and ship heading

relative to the waves. For a complete background and general discussion of these trials, see

Reference 2.

This report presents the distributions of the motions and bending moments* to be util-

ized for design purposes. To devise these distributions, it is necessary to specify the ship

operations for which the vessel is to be designed. The term "mission" will be used here to

define the ship's assigned operational pattern. One component of this mission is the aggre-

gate of sea conditions under which the vessel must operate. It will be assumed that the ship

will operate in the North Atlantic Ocean inasmuch as this probably represents more severe

sea conditions than the vessel will actually experience and thus is on the safe side.

Accordingly, the probable speeds and headings at which these ships would be expected

to operate under wartime conditions and the fraction of time the ships would spend at each of

the various conditions were estimated by the skippers of a number of vessels of this class.

References are listed on page 42.

*The hull bending moments due to flexure in the longitudinal plane of the ship were deduced from the strain

measurements and the section modulus applicable to the strain-gage location.

TABLE 1

Estimated Wartime Operating Conditions

The data for the WAVP vessels have been developed on the basis of a detailed analysis of ships' logs. For

the AVP vessels data are based on estimates made by officers having experience in this type over a wide range

of operating conditions. Values for individual ships were evaluated for mutual consistency and then averaged for

each sea state and speed rsinge. Sea states are defined in Reference 4.

0c63n

Ship

Ship

Percentage of Time Operating at the Given Speed*

Sea State 2

Sea State 3

Sea State 4

Sea State 5

Speed

Reporting

Significant Wave

Significant Wave

Significant Wave

Significant Wave

knots

Height 6 ft

Height 7-9 ft

Height 16 ft

Height 21 ft

WAVP370

19.7

6.2

47.9

WAVP374

16.7

9.5

4.3

6.6

WAVP378

16.5

30.0

22.0

14.8

Atlantic

7

WAVP381

22.4

9.8

25.0

70.0

WAVP382

15.74

13.5

15.01 14.6

17.75 14.7

35.53

32.6

WAVP383

average

22.1

average 41.2

average 39.8

average

27.4

AVP38

10.0

10.0

10.0

10.0

AVP41

5.0

5.0

20.0

75.0

Pacific

COMAIRPAC

1

average

1

average

45

average

95

average

WAVP370

13.9

19.2

17.8

WAVP374

9.8

2.9

15.2

19.9

WAVP378

15.9

8.9

31.4

13.7

Atlantic

10

WAVP381 -

17.29

17.3

15.16 17.0

28.53 13.8

28.89

20.0

WAVP382

average

10.4

average 4.9

average 9.5

average

34.8

WAVP383

11.0

17.6

9.1

9.9

AVP38

50.0

50.0

70.0

90.0

AVP41

10.0

20.0

60.0

25.0

Pacific

COMAIRPAC

3

average

3

average

45.

average

5.

average

WAVP370

26.6

29.2

23.8

24.7

WAVP374

30.4

37.2

46.4

41.6

WAVP378

48.7

45.3

38.1

58.9

Atlantic

U

WAVP381

27.7

12.2

17.5

10.0

WAVP382

35.17

23.0

37.95 67.9

28.54 36.6

22.58

21.2

WAVP383

average

20.0

average 11.8

average 25.9

average

24.2

AVP38

40.0

40.0

20.0

AVP41

65.0

60.0

20.0

Pacific

COMAIRPAC

95.

average

95.

average

10

average

average

WAVP370

39.8

70.8

50.8

9.6

WAVP374

43.1

50.4

34.1

31.9

WAVP378

31.80

18.9

31.88 15.8

25.18 8.5

13.00

12.6

Atlantic

17

WAVP381

average

32.6

average 61.0

average 43.7

average

WAVP382

53.1

12.6

39.2

11.4

WAVP383

46.9

29.4

25.2

38.5

AVP38

AVP41

20.0

15.0

Pacific

COMAIRPAC

1

average

1

average

For each ship, the percentage

3 add up to

100 per

cent for each sea s

ate.

Longitudinal Hull Gird^

Stress at Amidships

Heave Acceleration

at Center of Gravity

Location of Stereo Cameras

Control Center, Recorders

Gyro, (Pitch & Roll)

Pitch Accelerometer

Midship Section Modulus (for location of strain

Midship Section Moment of Inertia 75X ft^

Block Coefacient 0.571

Midship Section Area Coefficient 0.972

Prismatic Coefficient 0.588

Waterplane Area Coefficient 0.703

11,000 ft-in.

Slamming Pressure

Plate Strains

Plate Deflection

Acceleration at Keel

Strain in Keel

Pressure Trigger

Switch

Figure 1 - Profile and Characteristics of USCGC UNIMAK (AVPlO-Class Vessel)

The information received from these officers is summarized in Table 1. These estimates were

primarily based on an examination of ships' logs.

The sea conditions will be specified in terms of a significant wave height.* Estimates

of the significant wave heights are made by weather observers stationed on a number of weatii-

er ships at various locations in the Atlantic Ocean. These observations have been made at

3-hr intervals since 194:7. It has been found that tlie frequency distribution of these significant

wave heights is approximately logarithmically normal.^ The Weather Bureau's observations of

significant wave heights have been utilized here to evaluate the sea conditions to be expected

in the North Atlantic Ocean.

During the at-sea phases, oscillographic recordings were made of actual variations of

roll and pitch angle, heave accelerations, and hull strains as the ship responded to wave-

induced loads. In general, 1/2-hr continuous records were taken for each combination of ship

speed, heading, and sea condition. Typical oscillograms are shown in Appendix A. Instru-

ments were located as shown in Figure 1.

The pressures incident to slamming acting on the ship's bottom were measured by

seven pressure gages installed on the UNIMAK.^ Similar but more limited data were obtained

during trials^ of a sister ship, the USCGC CASCO.

*The significant wave height was obtained by averaging the observed highest wave in each of a number of

groups of waves. Note that the term "significant height" as used here is not synonymous with the statistical

meaning of "significant" value which is defined as the average of the upper third highest values.

2r 0.1

-Experimental Data

12,365 observations each

of which feptescnts a

given sea state.

H.

12 16

Significant Wave Height, feet

Figure 2a - Distribution Function

STATISTICAL BACKGROUND

The wave heights, ship motions, and hull bending moments experienced under a given

set of conditions will be described or specified in terms of their distribution patterns or, math-

ematically speaking, their distribution functions.

For illustrative purposes, consider one of the variables, for example, wave height. All

wave heights are considered to be members of a statistical "population." The distribution

function (d,f.) of wave heights indicates the relative probability p{x) of encountering a wave

of a given height as a function of that height. Figure 2a illustrates this distribution function.

(Similar illustrations are given for the ship motions in Figures 3 through 6.) The area under

the curve up to a value x- is the integral of the d.f. up to the value x= x-; it is equal to the

fraction of all members of the population of wave heights which have a height less than x^.

10 12 14 16 IB 20

Wave Height, Crest to Tfough, feet

Figure 2b - Cumulative Distribution Function

Figure 2- Distribution of Heights of Ocean Waves at Weather Station C,

52Â° N 37Â° W, North Atlantic Ocean

This distribution is based on 12,365 observations made over a period of 4V4 years by

U.S. Weather Bureau personnel.

Mathematically

r r

P{x) = I pdx and P (a; -Â» oo) = I pdx = 1

â€¢'

[11

P is a function of x, and this function is designated as the cumulative distribution function

(c.d.f.) of X. P{x) is numerically equal to the probability that a value chosen at random from

the population- is less than x.

A discussion of the statistical methods utilized here is given in References 3 and 7.

There is considerable evidence^ to indicate that the distribution of wave heights cor-

responding to any one given sea condition is of the one-parameter type known as the Rayleigh

distribution which is defined as

P{x) ^l-e-''^/^

where E is independent of x. Thus the probability is defined by a single number* E. On the

other hand, when the heights of all waves experienced over a long period of time, say over

several years, are considered, then the evidence indicates that the logarithm of the wave

height is approximately normally distributed, that is, the two-parameter log-normal distribution

describes the situation. The log-normal distribution is defined as follows:

(logx-fi)2

1 ^

p (log x) d (log x) = â€” ^ e 2 0^ d (log x)

where u is the mean value of log x and a is the standard deviation of log x.

Reference 3 shows that these two types of distributions also describe the response of

the ship to the waves. For the sake of brevity, the distributions applicable to homogeneous

conditions of the sea, ship speed, and course will be called "short-term" distributions,

whereas the function which represents the distribution when the seas, ship speeds, and

courses are allowed to vary over a range of conditions, will be designated as "long-term"

distributions.

The distribution pattern will, at a glance, give the probability of exceeding any given

magnitude of motion or stress. It also can be applied to the prediction of the largest magni-

tude to be expected in a given number of variations. For application to design for endurance

strength, the distribution pattern can be utilized as a load spectrum. Illustration of these

applications will be given in a later section.

*E is the mean value of x .

DERIVATION OF DISTRIBUTIONS OF SHIP MOTIONS AND LONGITUDINAL

BENDING MOMENTS OF THE HULL

It will be assumed without further discussion that the short-term distribution of wave-

induced ship motions and stresses may be represented by the one-parameter Rayleigh distri-

bution and Uiat the corresponding long-term distributions are approximated by the two-

parameter log-normal distribution. Evidence to support these hypotheses is presented in Ref-

erence 3.

Typical distribution patterns of variation* in pitch angle are shown in Figures 3 through

6. In all, 129 similar sets were analyzed. Pertinent results are given in Tables 2 through 6

for variations of pitch angle, pitch acceleration, roll angle, heave acceleration, and the hull

girder stress in the main deck amidships due to bending of the ship in a longitudinal plane

normal to the deck.

It is interesting to note that all cumulative Rayleigh distributions (for example, those

shown in Figures 4 and 6) become identical if v"^ = x^fE is plotted against the probability

instead of plotting x directly. Utilizing this artifice it is necessary to know only the value of

E corresponding to a particular sea condition, ship speed, and heading in order to obtain the

probability of exceeding any value of x from a single graph (Figure 4) which is equally appli-

cable to wave heights, ship motions, and hull stresses. The values of E for various ship

operations are given in Tables 2 through 6. Table 7 gives factors which, togetiier with the

value Â£", permit making statistical predictions as discussed later.

We now proceed to utilize the short>term distributions, each of which is characterized

by a value of Â£, as building blocks in order to construct the long-term frequency distribution

patterns of the ship responses to tJie sea applicable to wartime service in the North Atlantic

Ocean. (It should be noted that the distribution patterns for other "missions" can be readily

computed from the data given in this report.) Each of these short-term distributions will be

weighted in accordance with the relative fraction of time spent at given sea state (/,)Â» ^^ ^^

given heading to the sea (/,), and at the given ship speed (/ ). For example, if tests have in-

dicated that the ship will experience N = 480 pitch variations per hour in a State 2 sea when

heading directly into the waves at a speed of 10 knots, then one may expect that n = f-Jofz^

= (0,33) (0.34) (0.125) 480 = 6.73 variations of pitch angle per hour, out of the average

number of variations per hour, can be attributed to this set of environmental conditions over

an average year's operation in the assigned mission.

These calculations are carried out in Tables 8 through 11. Each horizontal line in

these tables gives the data corresponding to a given set of environmental conditions. The

probabilities (1-P) of exceeding given values of pitch angle, etc., are computed and tabulated

in columns 10 through 18. The total number of variations per hour which, over the average

*Throu^out this report, a variation is taken to mean the peak-to-peak Tailation of the vanablck

7

)U33J3d'd-I

,, J

TTIT

M

+^f^

â– il

to

Fj-

ill

( If

lt!l

^5

- -^, - -', I

tt-^

l~

^_j

^3

â– "s

:;â– â– '

Â« - I-

-" - "â– Eii

-+â–º n*

:;a

5;:::::.::: . .. - ..

E

,. ....

niiiiii T'f-

Ifji" 1 1?

:;1

'c'

1 4

% Contid

Mill

ence Lim

:::::^...

- ^

|f|d

Â±r

- ^t

:::::::::;;: ;: :iÂ£l^

â€žJÂ»,^,-, H,, iU, 05 - ;H

(-.i

-f LLl

"â€¢â–

1

- - -â– : ':-i ^

^'IMT'-s

t.p

jilT:

:::::!

5.

s

Mmfi

iir

z

Hlij]

[â– ' :'-r

t;:

::::::::::::: ' : ::::.^^

?pi#

::::::::K

M-

b.

pr

.:q

1 -^

:: : ;^< ^5^s^5p4T-OT:i;:TT

.-.Tl

t;f

T."

...1

ffiff

::::j1 ^^^

^pM:

t:;: *

[, -. .

:-;â–

â€¢'â– :â€¢)

_ . - -s -

- Â° - - -t-

'"I V s

SI

^,ri r

5

T ^;:

â€¢t^r +

II

~1

[lllllll

::: = :;::;; |:|; 'hl'^

ttiH^

III!

+ft^T

, .M

1

-Ti

llllllllll III

â€” * â– !!'' i

ill-

ijrti:

t^'.-

-l-T-

-t+^55

^i;

11

'-t+T

<<,\

3

^1

llllllllllll III 1 â€”

â– 1 T f j

.. s

1

1

I I t

T

pyHiiiHiiii|iiii).i i 1 ii

iiiliiUllUUll.J. 1 1 1

11

LiiiliL

.^JiLi

c3 3

O

3 "3

tf H Â§

O lO g CO

2 3 -S '^E

Q ^ :;

c u

.:: 5 ^ 2i o

*. â€¢^â– a

^ fc-

3|3UV l|3)|cJ 33l33p/|U33i3d Â» d

.2 o

f^ 3 C 53

â€¢o O â€” o

4) ffl c 2 o

aÂ«Â« o o^

Â» o â€¢- S o J

O. O .2 â– " 10 3

j: o

O J3

- Â« Â° ffl Â§ S

Â«^ Â«'o^:r 3

n S Â° Â«

i-g-o Â» c

- < o a. m^ g-C

(U J3 JS J3 T3 c

tSH g-o c o

*- s c o ^

â– " J S I* I" o

* J3 J, " 4, U

" "S C "" O- .-

_

5 3

D, a

i *j 5; m M o

Si5Â§ .w-c

o o Q ""s i

^ fo a oj b/)

Iii93iad 'd - 1

luaoisd 'd

â€” E -

I I I I ^^

.2* o m

^ j3 J, c "t;

(M "-S Â° Â°

w m ^ a o

S" I" ^ CO 3

E " n > XI

â€” 'g J3 -I ^

c â– " a 4) '3

** Si 2>-

&g8^

2 ^

aiSuv i|3)!d asiilsp/iuaaiad = d

M g

i|s|

C/3 '5S "^ o

x: 0) o

I. > t-l 01

4-. ^ 3 O)

â– " o u a Â«)

â€¢Â»- (II D S N

4) s, M ""a

S -^ c 3 S

â– a " o H "

â– u ,Â«-5 <"

a f Â« 4)

^3 P- Â« â€¢?. o\

d-o â€ž ii<N

O fl) 3 "i "^

O Â« o o- u

year, will exceed each given level are obtained by summing the product of column 9 with col-

umns 10 through 18 over all environmental conditions. The last line in the table gives the

probability of exceeding any one of the given magnitudes, for the long-term distribution. The

latter values are plotted on the cumulative probability distribution charts in Figures 7 through

10.

The straight lines shown on these charts have not been drawn by eye through the plot-

ted points but have been computed directly from the percentages represented by the plotted

points under the assumption that the long-term distribution is of the log-normal type. A sample

calculation is given in Appendix B. The rather good fit of the computed line to the plotted

points indicates that this assumption is reasonable. One would expect tJiat the points corres-

ponding to the more extreme values would lie above the theoretical line because by far the

greatest contribution to the computed probability for these extreme values derives from the

more severe sea conditions. It is apparent that if data had been available for more severe

seas than State 5, the probabilities of exceeding the higher values would have been increased

whereas the plotted points representing probabilities of exceeding low or medium large values

would not have been affected to any noticeable extent.

The value of E corresponding to any short-term distribution may readily be used to pre-

dict the most probable maximum value of the motion or stress expected in any given number of

oscillations. LonguetrHiggins^ has shown that the largest probable value out of A' measure-

ments is -/fi^ times a constant if the population is of the Rayleigh type, where the constant is

a function of N only. For large values of N, the constant is nearly equal to yJlog^N. Table 7

gives the value of the constant by which ^'^must be multiplied. A comparison of predicted

and measured maximum values, utilizing this method, is given in Tables 2 through 6. There

appears to be a satisfactory agreement.

The wave-induced hull-girder stresses can be converted to the corresponding vertical

bending moments amidships by making use of the midship section modulus which is applicable

to the strain-gage location (23.8 ft above baseline, 10 ft above the location of the neutral

axis). Tests have indicated ^'^ that the deckhouse of the AVP vessel is fully effective in

resisting bending, thus resulting in a section moment of inertia of 761 ff* which corresponds

to a section modulus applicable to the strain-gage location of 11,000 ft-in^. This value of

the section modulus has been used to convert wave induced stresses to wave-induced bending

moments.

10

TABLE 2

Basic Statistical Data on Pitch Angles

Sea

Slate

(Est'd)

Significant

Wave

Height

ft

tteading of

Waves Relative

to Ship

Ship

Speed

knots*

N

Number of

Variations

per Hour

Minutes

Sampled

E

deg2

Predicted

Maximum

Value for

1-hr Operation

Maximum

Measured

Peak-to-Peak

Variation

deg

Number of Variations

in Sample

from Which

Maximum Was Obtained

Predicted

Maximum

Peak-to-Peak

Variation

Ratio

Predicted

Maximum to

Measured Maximum

2

e

Head

Seas

7-7 1/2

10

14

17

480

555

30

32

4.00

4.48

5.0

5.3

4.8

5.3

240

296

4.68

5.04

0.98

0.95

2

6

Quarter

Head

Seas

7-7 1/2

10

14

17

404

514

37

32

1.97

1.86

3.4

3.5

3.1

3.3

249

274

3.3

3.24

1.06

0.98

2

6

Beam

Seas

7-7 1/2

10

14

17

561

643

29 1/2

32

5.40

3.75

5.9

4.9

6.2

4.8

276

M.

977

rifi&r^^;^CÂ«^^

JEA TESTS OF THE USCGC UNIMAK

PART 2 - STATISTICAL PRESENTATIOK OF THE MOTIONS,

HULL BENDING MOMENTS, AND SLAMMING PRESSURES

FOR SHIPS OF THE AVP TYPE

eODYNAMICS

by

STRUCTURAL

MECHANICS

N.H. Jasper, Dr. Eng., and R.L. Brooks, CDR, USN

APPLIED

\THEMATICS

STRUCTURAL MECHANICS LABORATORY

RESEARCH AND DEVELOPMENT REPORT

m

; m

i â–¡

ir=t

rm

SEA TESTS OF THE USCGC UNIMAK

PART 2- STATISTICAL PRESENTATION OF THE MOTIONS,

HULL BENDING MOMENTS, AND SLAMMING PRESSURES

FOR SHIPS OF THE AVP TYPE

by

N.H. Jasper, Dr. Eng., and R.L. Brooks, CDR, USN

April 1957 Report 977

NS 731-037

TABLE OF CONTENTS

Page

ABSTRACT ^ 1

INTRODUCTION 1

STATISTICAL BACKGROUND 4

DERIVATION OF DISTRIBUTIONS OF SHIP MOTIONS

AND LONGITUDINAL BENDING MOMENTS OF THE HULL 7

DESIGN AND OPERATIONAL CONDITIONS FOR WARTIME SERVICE 20

Long-Term Distributions of Ship Motion, Hull Bending Moment,

and Wave Height 20

Predictions of Ship Response to Waves for Given Conditions 20

Pre^diction of Extreme Values 22

Design Loads for Bottom Structure to Withstand Slamming Loads 26

DISCUSSION 27

ACKNOWLEDGMENTS 28

APPENDIX A - SAMPLE OSCILLOGRAMS â€¢ 29

APPENDIX B - SAMPLE CALCULATIONS 35

APPENDIX C - PHOTOGRAPHIC DEFINITION OF SEA CONDITIONS 37

REFERENCES 42

LIST OF ILLUSTRATIONS

Figure 1 - Profile and Characteristics of USCGC UNIMAK (AVPlO-Class Vessel) 3

Figure 2 - Distribution of Heights of Ocean Waves at Weather Station C,

52Â° N 37Â° W, North Atlantic Ocean 5

Figure 3 - Distribution of Variation in Pitch Angle (Sample 1)

for USCGC UNIMAK 8

Figure 4 - Cumulative Distribution of Variation in Pitch Angle (Sample 1)

for USCGC UNIMAK 3

Figure 5 - Distribution of Variation in Pitch Angle (Sample 2)

for USCGC UNIMAK 9

Figure 6 - Cumulative Distribution of Variation in Pitch Angle (Sample 2)

for USCGC UNIMAK 9

Figure 7 - Long-Term Cumulative Distribution of Pitch Angle for Wartime

Service, North Atlantic Ocean 21

Figure 8 - Long-Term Cumulative Distribution of Pitch Acceleration for

Wartime Service, North Atlantic Ocean 22

Figure 9 - Long-Term Cumulative Distribution of Roll Angle for Wartime

Service, North Atlantic Ocean 23

Figure 10 - Long-Term Cumulative Distribution of Longitudinal Bending Moment,

Amidships, for Wartime Service, North Atlantic Ocean 24

Figure 11 - Samples of Records Taken During tiie Tests 30

Figure 12 - Wave Photographs 38

Figure 13 - Wave Profiles 39

LIST OF TABLES

Table 1 - Estimated Wartime Operating Conditions 2

Table 2 - Basic Statistical Data on Pitch Angles 11

Table 3 - Basic Statistical Data on Pitch Accelerations 12

Table 4 - Basic Statistical Data on Roll Angles 13

Table 5 - Basic Statistical Data on Stresses 14

Table 6 - Basic Statistical Data on Heave Accelerations 15

Table 7 - Constants Required for Prediction of Probable Maximum Value

in a Sample from a Rayleigh Distribution. , 15

Table 8 - Derivation of Predicted Distribution Pattern for Variations

in Pitch Angle for Wartime Duty in North Atlantic Ocean 16

Table 9 - Derivation of Predicted Distribution Pattern for Variations

in Pitch Acceleration for Wartime Duty in North Atlantic Ocean 17

Table 10 - Derivation of Predicted Distribution Pattern for Variations

in Roll Angle for Wartime Duty in North Atlantic Ocean 18

Table 11 - Derivation of Predicted Distribution Pattern for Variation in Hull

Stress Due to Longitudinal Bending, at the Main Deck, Amidships

for Wartime Duty in North Atlantic Ocean 19

Table 12 - Maximum Values of Ship Motion and Longitudinal Bending Moment

for Use in Design Calculations 26

ABSTRACT

The motions and hull-girder bending moments which a ship of the general

form and size of the AVPIO Class may be expected to experience over a wide range

of operating conditions are presented in statistical form. The data are based on

extensive measurements made on the USCGC UNIMAK during sea trials in the

J<forth Atlantic Ocean. The methods of statistics have been employed in the plan-

ning of the at-sea phases of the trials and in the collection, analysis, and presenta-

tion of the large amount of data. From the test results, data are derived for this

type of ship for use in design and operating problems involving bending moments,

hull motions, and slamming pressures. Formulas are given for use in estimating

probable maximum values of moments and motions.

INTRODUCTION

The Bureau of Ships initiated a long-range investigation of strains in ships at sea for

the purpose of evaluating and improving methods for the design of the ship girder and its

structural components.^ Instrumentation has been developed and installed on various types

of ships to collect information on the wave loads, stresses, and motions which ships exper-

ience in service. During the winter of 1954 and 1955, measurements were carried out on the

USCGC UNIMAK (formerly AVP31) during operation in the North Atlantic Ocean. One of the

main objectives of this work is the collection of sufficient data on ship motions and longitud-

inal hull-girder stresses to determine, by statistical methods, the frequency distributions of

these quantities for different combinations of sea conditions, ship speed, and ship heading

relative to the waves. For a complete background and general discussion of these trials, see

Reference 2.

This report presents the distributions of the motions and bending moments* to be util-

ized for design purposes. To devise these distributions, it is necessary to specify the ship

operations for which the vessel is to be designed. The term "mission" will be used here to

define the ship's assigned operational pattern. One component of this mission is the aggre-

gate of sea conditions under which the vessel must operate. It will be assumed that the ship

will operate in the North Atlantic Ocean inasmuch as this probably represents more severe

sea conditions than the vessel will actually experience and thus is on the safe side.

Accordingly, the probable speeds and headings at which these ships would be expected

to operate under wartime conditions and the fraction of time the ships would spend at each of

the various conditions were estimated by the skippers of a number of vessels of this class.

References are listed on page 42.

*The hull bending moments due to flexure in the longitudinal plane of the ship were deduced from the strain

measurements and the section modulus applicable to the strain-gage location.

TABLE 1

Estimated Wartime Operating Conditions

The data for the WAVP vessels have been developed on the basis of a detailed analysis of ships' logs. For

the AVP vessels data are based on estimates made by officers having experience in this type over a wide range

of operating conditions. Values for individual ships were evaluated for mutual consistency and then averaged for

each sea state and speed rsinge. Sea states are defined in Reference 4.

0c63n

Ship

Ship

Percentage of Time Operating at the Given Speed*

Sea State 2

Sea State 3

Sea State 4

Sea State 5

Speed

Reporting

Significant Wave

Significant Wave

Significant Wave

Significant Wave

knots

Height 6 ft

Height 7-9 ft

Height 16 ft

Height 21 ft

WAVP370

19.7

6.2

47.9

WAVP374

16.7

9.5

4.3

6.6

WAVP378

16.5

30.0

22.0

14.8

Atlantic

7

WAVP381

22.4

9.8

25.0

70.0

WAVP382

15.74

13.5

15.01 14.6

17.75 14.7

35.53

32.6

WAVP383

average

22.1

average 41.2

average 39.8

average

27.4

AVP38

10.0

10.0

10.0

10.0

AVP41

5.0

5.0

20.0

75.0

Pacific

COMAIRPAC

1

average

1

average

45

average

95

average

WAVP370

13.9

19.2

17.8

WAVP374

9.8

2.9

15.2

19.9

WAVP378

15.9

8.9

31.4

13.7

Atlantic

10

WAVP381 -

17.29

17.3

15.16 17.0

28.53 13.8

28.89

20.0

WAVP382

average

10.4

average 4.9

average 9.5

average

34.8

WAVP383

11.0

17.6

9.1

9.9

AVP38

50.0

50.0

70.0

90.0

AVP41

10.0

20.0

60.0

25.0

Pacific

COMAIRPAC

3

average

3

average

45.

average

5.

average

WAVP370

26.6

29.2

23.8

24.7

WAVP374

30.4

37.2

46.4

41.6

WAVP378

48.7

45.3

38.1

58.9

Atlantic

U

WAVP381

27.7

12.2

17.5

10.0

WAVP382

35.17

23.0

37.95 67.9

28.54 36.6

22.58

21.2

WAVP383

average

20.0

average 11.8

average 25.9

average

24.2

AVP38

40.0

40.0

20.0

AVP41

65.0

60.0

20.0

Pacific

COMAIRPAC

95.

average

95.

average

10

average

average

WAVP370

39.8

70.8

50.8

9.6

WAVP374

43.1

50.4

34.1

31.9

WAVP378

31.80

18.9

31.88 15.8

25.18 8.5

13.00

12.6

Atlantic

17

WAVP381

average

32.6

average 61.0

average 43.7

average

WAVP382

53.1

12.6

39.2

11.4

WAVP383

46.9

29.4

25.2

38.5

AVP38

AVP41

20.0

15.0

Pacific

COMAIRPAC

1

average

1

average

For each ship, the percentage

3 add up to

100 per

cent for each sea s

ate.

Longitudinal Hull Gird^

Stress at Amidships

Heave Acceleration

at Center of Gravity

Location of Stereo Cameras

Control Center, Recorders

Gyro, (Pitch & Roll)

Pitch Accelerometer

Midship Section Modulus (for location of strain

Midship Section Moment of Inertia 75X ft^

Block Coefacient 0.571

Midship Section Area Coefficient 0.972

Prismatic Coefficient 0.588

Waterplane Area Coefficient 0.703

11,000 ft-in.

Slamming Pressure

Plate Strains

Plate Deflection

Acceleration at Keel

Strain in Keel

Pressure Trigger

Switch

Figure 1 - Profile and Characteristics of USCGC UNIMAK (AVPlO-Class Vessel)

The information received from these officers is summarized in Table 1. These estimates were

primarily based on an examination of ships' logs.

The sea conditions will be specified in terms of a significant wave height.* Estimates

of the significant wave heights are made by weather observers stationed on a number of weatii-

er ships at various locations in the Atlantic Ocean. These observations have been made at

3-hr intervals since 194:7. It has been found that tlie frequency distribution of these significant

wave heights is approximately logarithmically normal.^ The Weather Bureau's observations of

significant wave heights have been utilized here to evaluate the sea conditions to be expected

in the North Atlantic Ocean.

During the at-sea phases, oscillographic recordings were made of actual variations of

roll and pitch angle, heave accelerations, and hull strains as the ship responded to wave-

induced loads. In general, 1/2-hr continuous records were taken for each combination of ship

speed, heading, and sea condition. Typical oscillograms are shown in Appendix A. Instru-

ments were located as shown in Figure 1.

The pressures incident to slamming acting on the ship's bottom were measured by

seven pressure gages installed on the UNIMAK.^ Similar but more limited data were obtained

during trials^ of a sister ship, the USCGC CASCO.

*The significant wave height was obtained by averaging the observed highest wave in each of a number of

groups of waves. Note that the term "significant height" as used here is not synonymous with the statistical

meaning of "significant" value which is defined as the average of the upper third highest values.

2r 0.1

-Experimental Data

12,365 observations each

of which feptescnts a

given sea state.

H.

12 16

Significant Wave Height, feet

Figure 2a - Distribution Function

STATISTICAL BACKGROUND

The wave heights, ship motions, and hull bending moments experienced under a given

set of conditions will be described or specified in terms of their distribution patterns or, math-

ematically speaking, their distribution functions.

For illustrative purposes, consider one of the variables, for example, wave height. All

wave heights are considered to be members of a statistical "population." The distribution

function (d,f.) of wave heights indicates the relative probability p{x) of encountering a wave

of a given height as a function of that height. Figure 2a illustrates this distribution function.

(Similar illustrations are given for the ship motions in Figures 3 through 6.) The area under

the curve up to a value x- is the integral of the d.f. up to the value x= x-; it is equal to the

fraction of all members of the population of wave heights which have a height less than x^.

10 12 14 16 IB 20

Wave Height, Crest to Tfough, feet

Figure 2b - Cumulative Distribution Function

Figure 2- Distribution of Heights of Ocean Waves at Weather Station C,

52Â° N 37Â° W, North Atlantic Ocean

This distribution is based on 12,365 observations made over a period of 4V4 years by

U.S. Weather Bureau personnel.

Mathematically

r r

P{x) = I pdx and P (a; -Â» oo) = I pdx = 1

â€¢'

[11

P is a function of x, and this function is designated as the cumulative distribution function

(c.d.f.) of X. P{x) is numerically equal to the probability that a value chosen at random from

the population- is less than x.

A discussion of the statistical methods utilized here is given in References 3 and 7.

There is considerable evidence^ to indicate that the distribution of wave heights cor-

responding to any one given sea condition is of the one-parameter type known as the Rayleigh

distribution which is defined as

P{x) ^l-e-''^/^

where E is independent of x. Thus the probability is defined by a single number* E. On the

other hand, when the heights of all waves experienced over a long period of time, say over

several years, are considered, then the evidence indicates that the logarithm of the wave

height is approximately normally distributed, that is, the two-parameter log-normal distribution

describes the situation. The log-normal distribution is defined as follows:

(logx-fi)2

1 ^

p (log x) d (log x) = â€” ^ e 2 0^ d (log x)

where u is the mean value of log x and a is the standard deviation of log x.

Reference 3 shows that these two types of distributions also describe the response of

the ship to the waves. For the sake of brevity, the distributions applicable to homogeneous

conditions of the sea, ship speed, and course will be called "short-term" distributions,

whereas the function which represents the distribution when the seas, ship speeds, and

courses are allowed to vary over a range of conditions, will be designated as "long-term"

distributions.

The distribution pattern will, at a glance, give the probability of exceeding any given

magnitude of motion or stress. It also can be applied to the prediction of the largest magni-

tude to be expected in a given number of variations. For application to design for endurance

strength, the distribution pattern can be utilized as a load spectrum. Illustration of these

applications will be given in a later section.

*E is the mean value of x .

DERIVATION OF DISTRIBUTIONS OF SHIP MOTIONS AND LONGITUDINAL

BENDING MOMENTS OF THE HULL

It will be assumed without further discussion that the short-term distribution of wave-

induced ship motions and stresses may be represented by the one-parameter Rayleigh distri-

bution and Uiat the corresponding long-term distributions are approximated by the two-

parameter log-normal distribution. Evidence to support these hypotheses is presented in Ref-

erence 3.

Typical distribution patterns of variation* in pitch angle are shown in Figures 3 through

6. In all, 129 similar sets were analyzed. Pertinent results are given in Tables 2 through 6

for variations of pitch angle, pitch acceleration, roll angle, heave acceleration, and the hull

girder stress in the main deck amidships due to bending of the ship in a longitudinal plane

normal to the deck.

It is interesting to note that all cumulative Rayleigh distributions (for example, those

shown in Figures 4 and 6) become identical if v"^ = x^fE is plotted against the probability

instead of plotting x directly. Utilizing this artifice it is necessary to know only the value of

E corresponding to a particular sea condition, ship speed, and heading in order to obtain the

probability of exceeding any value of x from a single graph (Figure 4) which is equally appli-

cable to wave heights, ship motions, and hull stresses. The values of E for various ship

operations are given in Tables 2 through 6. Table 7 gives factors which, togetiier with the

value Â£", permit making statistical predictions as discussed later.

We now proceed to utilize the short>term distributions, each of which is characterized

by a value of Â£, as building blocks in order to construct the long-term frequency distribution

patterns of the ship responses to tJie sea applicable to wartime service in the North Atlantic

Ocean. (It should be noted that the distribution patterns for other "missions" can be readily

computed from the data given in this report.) Each of these short-term distributions will be

weighted in accordance with the relative fraction of time spent at given sea state (/,)Â» ^^ ^^

given heading to the sea (/,), and at the given ship speed (/ ). For example, if tests have in-

dicated that the ship will experience N = 480 pitch variations per hour in a State 2 sea when

heading directly into the waves at a speed of 10 knots, then one may expect that n = f-Jofz^

= (0,33) (0.34) (0.125) 480 = 6.73 variations of pitch angle per hour, out of the average

number of variations per hour, can be attributed to this set of environmental conditions over

an average year's operation in the assigned mission.

These calculations are carried out in Tables 8 through 11. Each horizontal line in

these tables gives the data corresponding to a given set of environmental conditions. The

probabilities (1-P) of exceeding given values of pitch angle, etc., are computed and tabulated

in columns 10 through 18. The total number of variations per hour which, over the average

*Throu^out this report, a variation is taken to mean the peak-to-peak Tailation of the vanablck

7

)U33J3d'd-I

,, J

TTIT

M

+^f^

â– il

to

Fj-

ill

( If

lt!l

^5

- -^, - -', I

tt-^

l~

^_j

^3

â– "s

:;â– â– '

Â« - I-

-" - "â– Eii

-+â–º n*

:;a

5;:::::.::: . .. - ..

E

,. ....

niiiiii T'f-

Ifji" 1 1?

:;1

'c'

1 4

% Contid

Mill

ence Lim

:::::^...

- ^

|f|d

Â±r

- ^t

:::::::::;;: ;: :iÂ£l^

â€žJÂ»,^,-, H,, iU, 05 - ;H

(-.i

-f LLl

"â€¢â–

1

- - -â– : ':-i ^

^'IMT'-s

t.p

jilT:

:::::!

5.

s

Mmfi

iir

z

Hlij]

[â– ' :'-r

t;:

::::::::::::: ' : ::::.^^

?pi#

::::::::K

M-

b.

pr

.:q

1 -^

:: : ;^< ^5^s^5p4T-OT:i;:TT

.-.Tl

t;f

T."

...1

ffiff

::::j1 ^^^

^pM:

t:;: *

[, -. .

:-;â–

â€¢'â– :â€¢)

_ . - -s -

- Â° - - -t-

'"I V s

SI

^,ri r

5

T ^;:

â€¢t^r +

II

~1

[lllllll

::: = :;::;; |:|; 'hl'^

ttiH^

III!

+ft^T

, .M

1

-Ti

llllllllll III

â€” * â– !!'' i

ill-

ijrti:

t^'.-

-l-T-

-t+^55

^i;

11

'-t+T

<<,\

3

^1

llllllllllll III 1 â€”

â– 1 T f j

.. s

1

1

I I t

T

pyHiiiHiiii|iiii).i i 1 ii

iiiliiUllUUll.J. 1 1 1

11

LiiiliL

.^JiLi

c3 3

O

3 "3

tf H Â§

O lO g CO

2 3 -S '^E

Q ^ :;

c u

.:: 5 ^ 2i o

*. â€¢^â– a

^ fc-

3|3UV l|3)|cJ 33l33p/|U33i3d Â» d

.2 o

f^ 3 C 53

â€¢o O â€” o

4) ffl c 2 o

aÂ«Â« o o^

Â» o â€¢- S o J

O. O .2 â– " 10 3

j: o

O J3

- Â« Â° ffl Â§ S

Â«^ Â«'o^:r 3

n S Â° Â«

i-g-o Â» c

- < o a. m^ g-C

(U J3 JS J3 T3 c

tSH g-o c o

*- s c o ^

â– " J S I* I" o

* J3 J, " 4, U

" "S C "" O- .-

_

5 3

D, a

i *j 5; m M o

Si5Â§ .w-c

o o Q ""s i

^ fo a oj b/)

Iii93iad 'd - 1

luaoisd 'd

â€” E -

I I I I ^^

.2* o m

^ j3 J, c "t;

(M "-S Â° Â°

w m ^ a o

S" I" ^ CO 3

E " n > XI

â€” 'g J3 -I ^

c â– " a 4) '3

** Si 2>-

&g8^

2 ^

aiSuv i|3)!d asiilsp/iuaaiad = d

M g

i|s|

C/3 '5S "^ o

x: 0) o

I. > t-l 01

4-. ^ 3 O)

â– " o u a Â«)

â€¢Â»- (II D S N

4) s, M ""a

S -^ c 3 S

â– a " o H "

â– u ,Â«-5 <"

a f Â« 4)

^3 P- Â« â€¢?. o\

d-o â€ž ii<N

O fl) 3 "i "^

O Â« o o- u

year, will exceed each given level are obtained by summing the product of column 9 with col-

umns 10 through 18 over all environmental conditions. The last line in the table gives the

probability of exceeding any one of the given magnitudes, for the long-term distribution. The

latter values are plotted on the cumulative probability distribution charts in Figures 7 through

10.

The straight lines shown on these charts have not been drawn by eye through the plot-

ted points but have been computed directly from the percentages represented by the plotted

points under the assumption that the long-term distribution is of the log-normal type. A sample

calculation is given in Appendix B. The rather good fit of the computed line to the plotted

points indicates that this assumption is reasonable. One would expect tJiat the points corres-

ponding to the more extreme values would lie above the theoretical line because by far the

greatest contribution to the computed probability for these extreme values derives from the

more severe sea conditions. It is apparent that if data had been available for more severe

seas than State 5, the probabilities of exceeding the higher values would have been increased

whereas the plotted points representing probabilities of exceeding low or medium large values

would not have been affected to any noticeable extent.

The value of E corresponding to any short-term distribution may readily be used to pre-

dict the most probable maximum value of the motion or stress expected in any given number of

oscillations. LonguetrHiggins^ has shown that the largest probable value out of A' measure-

ments is -/fi^ times a constant if the population is of the Rayleigh type, where the constant is

a function of N only. For large values of N, the constant is nearly equal to yJlog^N. Table 7

gives the value of the constant by which ^'^must be multiplied. A comparison of predicted

and measured maximum values, utilizing this method, is given in Tables 2 through 6. There

appears to be a satisfactory agreement.

The wave-induced hull-girder stresses can be converted to the corresponding vertical

bending moments amidships by making use of the midship section modulus which is applicable

to the strain-gage location (23.8 ft above baseline, 10 ft above the location of the neutral

axis). Tests have indicated ^'^ that the deckhouse of the AVP vessel is fully effective in

resisting bending, thus resulting in a section moment of inertia of 761 ff* which corresponds

to a section modulus applicable to the strain-gage location of 11,000 ft-in^. This value of

the section modulus has been used to convert wave induced stresses to wave-induced bending

moments.

10

TABLE 2

Basic Statistical Data on Pitch Angles

Sea

Slate

(Est'd)

Significant

Wave

Height

ft

tteading of

Waves Relative

to Ship

Ship

Speed

knots*

N

Number of

Variations

per Hour

Minutes

Sampled

E

deg2

Predicted

Maximum

Value for

1-hr Operation

Maximum

Measured

Peak-to-Peak

Variation

deg

Number of Variations

in Sample

from Which

Maximum Was Obtained

Predicted

Maximum

Peak-to-Peak

Variation

Ratio

Predicted

Maximum to

Measured Maximum

2

e

Head

Seas

7-7 1/2

10

14

17

480

555

30

32

4.00

4.48

5.0

5.3

4.8

5.3

240

296

4.68

5.04

0.98

0.95

2

6

Quarter

Head

Seas

7-7 1/2

10

14

17

404

514

37

32

1.97

1.86

3.4

3.5

3.1

3.3

249

274

3.3

3.24

1.06

0.98

2

6

Beam

Seas

7-7 1/2

10

14

17

561

643

29 1/2

32

5.40

3.75

5.9

4.9

6.2

4.8

276