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HYDROMECHANICS



M.



977



rifi&r^^;^C«^^




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 □

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 • 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,

52° N 37° 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,
52° N 37° 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; -» oo) = I pdx = 1
•'



[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) = — ^ 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 £", 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 £, 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 (/,)» ^^ ^^
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



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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


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Online LibraryNorman Hans JasperSea 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)