Report 977

¢. _ VIHEMATICS

HYDROMEGHANICS

AERODYNAMICS

STRUCTURAL MECHANICS

APPLIED

PART 2- STATISTICAL PRESENTATION OF THE MOTIONS,

SEA TESTS OF THE USCGC UNIMAK

HULL BENDING MOMENTS, AND SLAMMING PRESSURES

N.H.

FOR SHIPS OF THE AVP TYPE

by

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

ity -

STRUCTURAL MECHANICS LABORATORY -

April 1957

RESEARCH AND DEVELOPMENT REPORT

Report 977

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

TRESS OTSRUA CST oe Te SAORI RET, BY AOC ss RON OR OF le oP eR ce 1 TNR O DUG TION Beeches osetia oad seceiedeee ca sen cube else elcausa sb sL oi ac toes roe ate rece Rob terse tae wan Ielane tars Seeeree il STATISTICA BACKGROUND isi ccisciiss-secusececeosseccnsesnncsensecicsannecsrecseesccesincssteneccadeane sustecst 4 DERIVATION OF DISTRIBUTIONS OF SHIP MOTIONS AND LONGITUDINAL BENDING MOMENTS OF THE HULL..........0.::ccccceceeeseesseneeneeees 4 DESIGN AND OPERATIONAL CONDITIONS FOR WARTIME SERVICE.........--..--:c-ce0 20

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

and)|Wave; Heights. 3 c..cccscsseseeee tote <ceee ene ese reece Mont scone taneous occas uecvsusleeisn sce seauRe 20

Predictions of Ship Response to Waves for Given Conditions... 20

Prediction of Extreme Values....--..-....-.cseccssessssesseeseseereeseesteetsenscenssascaneencssersermeressemenee! 99

Design Loads for Bottom Structure to Withstand Slamming Loads..............::ceeeeee 26 DISCUSSION oe Sea taleae at a EEE NES eee eg bh ole pee ie ee 27 ING KNOWL DGMEN DES oeceeicceiensscesesccseee<sscctesccaseevss occscrsce srsuts saummmneuance tara tucssccens corsrte cote autem 28 APPENDIX A - SAMPLE OSCILLOGRAMSG..........c::cccsscccssescssensceeeeeeceseccnecesecese nme cceeeecansen ee 29 APPENDIXOB!="SAMP IGE) CAW CUIAUIONS ceceececrcrre cece eee eere ee cea seacia sete resteceteee sss sohe 35 APPENDIX C - PHOTOGRAPHIC DEFINITION OF SEA CONDITIONS................:.:.5+ 37 REERRENCE GS eiiie Le eer dhe cacncytesahesay sematuiia Stet ves deaaunseeatetar One scens ce Sea feaesscet suse 42

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LIST OF ILLUSTRATIONS

1 - Profile and Characteristics of USCGC UNIMAK (AVP10-Class Vessel) ......

2 - Distribution of Heights of Ocean Waves at Weather Station C, BOO INT Be (We Niort ANAT COXGEDM. | cocosoconpooocncoosonnosossecconadcasanectneseoansucoKeecodoonodose

3 - Distribution of Variation in Pitch Angle (Sample 1) forsUSCGCPUNIMAK.-.c:.0cccscuecesrssertasmeerars. cece het cmicecu rte Minerale emecac ame aL ea,

4 - Cumulative Distribution of Variation in Pitch Angle (Sample 1) foraWS CGCHUNIMA Ki is sot tence sae Ue 2a a dla a Avesta ei cca NeiRLe I

5 - Distribution of Variation in Pitch Angle (Sample 2) forpU SC GCLUNIMAK .c..sctsccceeteseee aerate eee gue eave aes Nc seen usa ta iar ca mee pa taheaD

6 - Cumulative Distribution of Variation in Pitch Angle (Sample 2) for WS CG GCHUNIMA KE ioe ore eee Ie ACL RERUN coe genrs ooets Syaine sb oiacs Maacebere sae

7 - Long-Term Cumulative Distribution of Pitch Angle for Wartime Service, North Atlantic Ocean ...............cccessessccccssosecessccsstcsessntsesscenssecssonsencecoes

8 - Long-Term Cumulative Distribution of Pitch Acceleration for Wartime Service, North Atlantic Ocean ..............:seseseeceesecetececceeencceeeeesseeessenes

_9 - Long-Term Cumulative Distribution of Roll Angle for Wartime Service.) North Atlantiic:Oceam ) eee ead Sato cccuealcasasdos incecoeub cb acestens

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

Amidships, for Wartime Service, North Atlantic Ocean..............:...sccsceeseesseeeees

Figure 11 - Samples of Records Taken During the Tests ...............cc:csccsesseseecceeeceeeeeseeseenees

igure. 12 >-“Wave: Photographs)... caiicmsscssscescsssetessecccdessenccassesutoalssectaeetermnaten weet ceveceece ucccrntetes

Puce, IS! =) Wave pro fl GScisioc.-tesnel eset yn costesioceict scecactuasestecudes scuceeeseumunates paneeeteasue veneceseatesscaaeees

ili.

Page

Table 1- Table 2- Table 3- Table 4- Table 5- Table 6-

Table 7-

Table 8 -

Table 9-

Table 10 -

Table 11 -

Table 12 -

LIST OF TABLES

Page

Estimated Wartime Operating Conditions .............:ccccsccsssssssssseses coscee ceeneceeceeeee sens 2g Basic Statistical Data on Pitch Angles................:.cssccssecscccesesee coececeecce ereesesenees 11 Basic Statistical Data on Pitch Accelerations. ............::.cccccccccsseeece sccccecees cesses ces 12 Basic Statistical Data on Roll Angles.............0..::ccccescssececcesecceseceesersecrmececesees 13 BasicistatisticalyDataronistresSesiscscccssceeee eee eee 14 Basic Statistical Data on Heave Accelerations ..............s:ssssesserseeeeeeseeeeseceeeeesce 15 Constants Required for Prediction of Probable Maximum Value

in a Sample from a Rayleigh Distribution, 20.00.00... cee ceceeceseecceeeeceeceeene scenes yg 16) Derivation of Predicted Distribution Pattern for Variations

in Pitch Angle for Wartime Duty in North Atlantic Ocean...............:::cscsscene Sr al - Derivation of Predicted Distribution Pattern for Variations

in Pitch Acceleration for Wartime Duty in North Atlantic Ocean..................... 17

Derivation of Predicted Distribution Pattern for Variations

in Roll Angle for Wartime Duty in North Atlantic Ocean................:::csssceeeeeeees 18 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. ............cccccesccsececesssenseeeeersreneeeseteme sees 19 Maximum Values of Ship Motion and Longitudinal Bending Moment

for Use in Design Calculations. ..................1..-ssssesecesesseessesneceesceeesesesmecsee cane nesnens 26

lv

ABSTRACT

The motions and hull-girder bending moments which a ship of the general form and size of the AVP10 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 North 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.

lpeferences 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 range. Sea states are defined in Reference 4.

Percentage of Time Operating at the Given Speed*

Ship Reporting

Sea State 2 Sea State 3 Significant Wave] Significant Wave | Significant Wave] Significant Wave Height 6 ft Height 7-9 ft Height 16 ft Height 21 ft

WAVP370 5 i i WAVP374 b L y : WAVP378 3 i J Atlantic WAVP381 x 1 I WAVP382 15.74 13.5 15.01 4. 6 17.75 14.7 35.53 32.6 WAVP383 average : average 41.2 average i average F AVP38 d a ; i Hl AVP41

ae sai ee average

WAVP370 13.9 17.8 WAVP374 J i . i WAVP378 : b Atlantic WAVP381 | 17.29 17.3 15.16 17. 0 28.53 13.8 28.89 20.0 WAVP382 average 10. average 4.9 average 9. average 34. WAVP383 d 17.6 b i AVP 38 H 50.0 J H AVP41 20.0 H

haan eee apie

WAVP370 Hy

WAVP374 fF 5 H ;

WAVP378 5 : b ,

WAVP381 5 E

WAVP382 35.17 23.0 37.95 67.9 28.54 36.6 22.58 21. 2

WAVP 383 average 20. average 4 average 25. average 24.2 AVP38 x i i ; AVP41 65.0

average average aa oe 0

WAVP370 WAVP374 I Ly D WAVP378 31.80 18.9 31.88 15.8 25.18 8.5 WAVP 381 average A average d average b WAVP 382 jo i b WAVP383 b 5 AVP38 AVP41 0

COMAIRPAC ee ae SUF Or each ship, the percentages add up to 100 percent for each sea state.

Sea State 4 Sea State 5

Ocean

ne 13.00 12.6 average 0) 11.4 38.5

Longitudinal Hull Girder Stress at Amidships

Location of Stereo Cameras

Heave Acceleration

atlGenter of Gravity Contro! Center, Recorders

Gyro, (Pitch & Roll) Pitch Accelerometer

Midship Section Modulus (for location of strain gage) 11,000 Retin” Slamming Pressure Pressure Trigger Midship Section Moment of Inertia 761 ft? Plate Strains Switch Block Coefficient 0.571 Plate Deflection

Midship Section Area Coefficient 0.972 Acceleration at Keel

Prismatic Coefficient 0.588 Strain in Keel

Waterplane Area Coefficient 0.703

Figure 1 - Profile and Characteristics of USCGC UNIMAK (AVP 10-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 weath- er ships at various locations in the Atlantic Ocean. These observations have been made at 3-hr intervals since 1947. It has been found that the 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.

Experimental Data

Probability Density

12,365 observations each of which represents a given sea state.

0 4 8 12 16 20 24 28 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 2, is the integral of the d.f. up to the value z= 2; it is equal to the

fraction of all members of the population of wave heights which have a height less than je

The dashed lines denote the limits the : a

| aN

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a Ai observed values of significant wave height which ah A nae C were obtained at intervals of 3 hours over a period

Probability of Not Exceeding Wave Height (percent)

Probability of Exceeding Wave Height (percent)

of 4% years. The position of the line was computed from the observed data.

fepresents the distribution of individual wave heights jj ‘derived from the significant wave heights represented

2 4 6 8 10 12 14 16 18 20 Wave Height, Crest to ai ee

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 pened of 44% years by U.S. Weather Bureau personnel.

Mathematically x co

P(z)= | pdeandP(zx+~)= | pde=1 {1] 0 i)

P is a function of x, and this function is designated as the cumulative distribution function (c.d.f.) of z. P(x) is numerically equal to the probability that a value chosen at random from the population-is less than z.

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

2 P(z)=1-e% /E

where E is independent of z. Thus the probability is defined by a single number* £. 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:

(log x— p)? ga. ae d (log z)

p (log z) d (log z) =

1 oV2a

where wu is the mean value of log z and o is the standard deviation of log z.

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 x2.

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 that 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 v2 = «?/E is plotted against the probability instead of plotting 2 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 2 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, together with the value E, 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 E, as building blocks in order to construct the long-term frequency distribution patterns of the ship responses to the 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 (f,), at the given heading to the sea (f,), and at the given ship speed (f,)- 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,f,f,N = (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

*Throughout this report, a variation is taken to mean the peak-to-peak variation of the variable

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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 that 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. Longuet-Higgins® has shown that the largest probable value out of N measure- ments is /E 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 Vlog, N. Table 7 gives the value of the constant by which VE 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 ft* 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

K)

7-9

7-9

4 16

5 21

5 21 = aa

21

Heading of

Waves Relative| Speed

to Ship

Quarter Head Seas

Quarter Following Seas

Following Seas

N Number of Variations per Hour

Minutes Sampled| deg?

TABLE 2

Predicted Maximum Value for

1-hr Operation

Maximum Measured Peak-to-Peak Variation

Quarter Head Seas

‘Beam Seas Quarter Following Seas Following Seas

Head Seas

Head Seas

Quarter Head Seas

Following Seas

10 587 27 1/2) 1.79 3.4 3.1 14

17 592 37_-| 2.02 3.6 3.9

10 542 29 (| 3.52 4.7 4.3 14

17 298 |_ 26 1.08 2.5 3.3 10 14

523 31 | 1.85 3.4 3.9

23 (| 1.28 2.8 2.4

aal|

14 578 30 |26.12 12.9 11.6

71/2) 517 27 1/2|47.32 17.2 18.0 10

14 583 24 56.00 18.9 15.5

71/2| 541 38 1/2(35.13 14.9 13.9 10

14 577 28 1/2)47.14 L 17.3 16.5

30 |16.78 9.9

28 1/2|20.24 10.9 9.8

10 296 29 |28.00 12.6 11.5

14 302 27 ‘(|17.2 9.9 8.8

11.8

10.8

11

*The speed is the nominal speed read from a calibration curve of propeller rpm versus knots; 7 1/2, 10, 14, and 17 knots correspond to 94, 127, 185, and 230 rpm, respectively.

Basic Statistical Data on Pitch Angles

z |

Number of Variations in Sample from Which Maximum Was Obtained

282

Predicted Maximum Peak-to-Peak Variation

Ratio Predicted Maximum to

Measured Maximum

1.00 0.90

1.16 1.03

0.99 1.06

TABLE 3

Basic Statistical Data on Pitch Accelerations

Sea |Significant} Heading of Ship N Minutes E Predicted | Maximum Measured} Number of Variations Predicted Ratio State Wave |Waves Relative| Speed | Number of|campieq|(@¢_\") Maximum Peak-to-Peak in Sample Maximum Predicted (Est'd)| Height to Ship Variations sec2) | Value for Variation from Which Peak-to-Peak| idaximum to ft Perec | ee Mos I-hr Operation rad/sec? Maximum Was Obtained | Variation |Measured Maximum Head 10 704 30 =} 0.0015 0.099 0.093 352 0.093 1.00 2 6 Seas 14 786 32 | 0.0024 0.126 0.123 419 0.121 0.99 Quarter 10 761 32 }0.0015 0.100 0.093 406 0.095 1.02 2 6 Head Seas 14 872 32 | 0.0014 0.097 0.097 465 0.093 0.960 6 Beam 10 708 29 1/2 | 0.0033 0.147 0.144 348 0.139 0.97 2 Seas 14 740 32 | 0.0033 0.148 0.140 395 0.140 1.00 Quarter Following 6 Seas 14 890 29 =| 0.0016 0.104 0.11 430 0.099 0.90 Following 6 Seas 32 | 0.00028 0.043 26 | 0.0109 0.267 3 7-9 Head 32 | 0.0161 0.327 Seas 27, (| 0.0171 0.341 Quarter 10 779 27 1/2 | 0.0022 0.121 1/9 Head Seas 17 900 37 | 0.0028 0.138 Beam ri 763 29 =| 0.0030 0.142 3 7-9 Seas 17 760 26 =| 0.0029 0.139 Quarter Following 7-9 Seas 17 696 31 | 0.001 0.081 Following Seas 17 629 23 | 0.00072 0.068 Head 14 780 30 | 0.0222 0.384 Seas 21 Head 7V/2 624 27 1/2| 0.0173 0.334 Seas 14 692 24 | 0.0308 0.450 Quarter 71/2 615 38 1/2} 0.0140 0.300 Head Seas 14 711 28 1/2} 0.0327 0.465 Beam Seas 71-2 458 0.0039 0.155 Quarter 71/2 702 0.0032 0.145 Following 10 660 0.0023 0.123 Seas 14 714 0.0023 0.123 Following 71/2 524 0.0013 0.090 0.068 288 0.085 1.25 Seas 14 470 0.0004 0.050 0.058 243 0.047 0.81

*The speed is the nominal speed read from a calibration curve of propeller rpm versus knots; ‘ 7 1/2, 10, 14, and 17 knots correspond to 94, 127, 185, and 230 rpm, respectively.

12

TABLE 4

Basic Statistical Data on Roll Angles

Sea |Significant] Heading of | ship N Minutes | E Predicted Maximum | Number of Variations | Predicted Ratio State Wave |Waves Relative! sooeq Number of Sampled| deg? | Maximum Measured in Sample Maximum Predicted (Est’d)| Height to Ship Variations Value for |Peak-to-Peak from Which Peak-to-Peak| © Maximum to

per Hour I-hr Operation) Variation |Maximum Was Obtained| Variation Measured Maximum ft knots* deg Head 10 380 10.7 9.4 190 9.96 1.06 Seas 14 362 10.4 10.5 193 9.80 0.93 Quarter

Head 13.5 13.1 219 0.99

Seas 12.4 12.2 191 0.96

Beam 10.3 10.6 191] 0.91

Seas 10.6 10.3 196 0.97

Quarter Following Seas

1.02

Quarter Following Seas 285

Following

Seas

Head

Seas

Head 7V2 369 27 V2 Seas 14 398 24 rea 8 Quarter

Head 71V2 388 38 1/2] 75.3 21.2 Seas 14 408 28 wos mn 3 neal 8

Br ae & wo wo

71/2 364

Quarter 71/2 384 ave) 4 38.8 Following 10 372 148 29.6 24.0 Seas 14 360 . 114. 25.9 21.9

Following | 71/2 Seas 14

*The speed is the nominal speed read from a calibration curve of propeller rpm versus knots; 7 1/2, 10, 14, and 17 knots correspond to 94, 127, 185, and 230 rpm, respectively.

13

TABLE 5

Basic Statistical Data on Stresses

] i i Rati Sea Significant Heading of Ship N Minutes Predicted Maximum Measured Number of Variations | Predicted , H lo State Wave Waves Relative | Speed Number of Sampled E |Maximum Value Peak-to-Peak in Sanple Maximum redicted (Est’d) Height to Ship Variations 4 for I-hr Variation from Which Peak-to-Peak Maximum to per Hour (al Operation kips/in.2 Maximum Was Obtainel| Variation | Measured Maximum 71 2 ft knots* oe kips | Head 10 670 30 0.22 1.20 1.2 335 1.13 0.94 Seas 14 784 32 0.31 1.44 15 418 1.37 0.91 Quarter | Head 10 256 37 0.21 1.08 1.2 158 1,03 0.86 Seas 14 1004 32 0.24 1.30 1.3 536 1.22 0.94 Beam 10 } 522 29.1/2 | 0.37 1.52 1.6 257 1.43 0.89 Seas 14 666 32 0.29 1.38 17 355 + 1.31 0.77 Quarter Following Seas 14 640 27 0.22 1.19 1.5 288 1.11 0.74 Following Seas 14 1.4 209 1.39 0.99 10 2.6 269 2.5 0.96 Head 3 9 ann 14 2.8 414 2.84 1.01 17 2.9 446 2.72 0.94 Quarter Head 10 0.9 396 0.81 0.90 3 7-9 Seas 17 1.0 438 0.985 + ——_ Beam 10 0.94 243 1.02 Seas 17 0.97 297 1.01 Quarter 3 Following Seas 17 1.0 237 0.905 Following 3 Seas 17 0.59 138 0.666 Head 14 3.1 384 2.64 4 16 Seas we au 3.9 265 3.96 1.02 5 21 Seas 14 4.5 318 4.48 1.00 Quarter Head 71/2 3.9 384 3.73 0.96 5 21 Seas 14 4.0 330 4.16 0.96 Beam 5 21 Seas 71/2 2.7 266 2.69 1,00 Quarter 71/2 2.0 212 2.14 0.94 Following 10 2.3 159 2.38 1.03 Seas 14 d 2.3 155 2.25 0.98 Following | 71/2 325 1.90 3.3 3.6 179 3.14 0.87 Seas 14 300 1.57 3.0 3.1 | 155 2.82 0.91 *The speed is the nominal speed read from a calibration curve of propeller rpm versus knots;

7 1/2, 10, 14, and 17 knots correspond to 94, 127, 185, and 230 rpm, respectively.

14

TABLE 6

Basic Statistical Data on Heave Accelerations

T Maximum Measured

Sea | Significant] Heading of | Ship N sina E |, ecueeea Number of Variations | Predicted Ratio State | Wave | Waves Relative| Speed | NUmbet Of | sampled aximum Value) Peak-to-Peak iniSample Maxi Feet tes (Est’d)| Height to Ship Variations for 1-hr Variation from Which Peak-to-Peak Maximum to per Hour Operation Maximum Was Obtained} Variation | Measured Maximum ft knots* | g's? gis g's Head 10 448 26 | 0.0107 0.252 0.26 239 0.251 0.97 3 7-9 Seas 14 590 32 | 0.0186 0.35 0.32 315 0.321 1.01 17 582 27__-| 0.0221 0.37 0.37 262 0.35 0.95 Head 71/2 433 27} 0.0221 0.37 0.51 197 0.341 0.67 5 21 Seas 10 518 27} 0.0272 0.41 0.41 233 0.385 0.94 14 514 24 1/2 | 0.0382 0.49 0.49 210 0.451 0.92 Quarter 71/2 466 38 1/2] 0.0182 0.33 0.29 299 0.322 1.11 5 21 Head 10 583 28 =| 0.0245 0.40 0.44 272 0.371 0.84 Seas 14 565 27 1/2 | 0.0498 0.57 0.62 259 0.525 0.85 —}—— ar Beam 5 21 Seas 71/2 433 28 | 0.0143 0.29 0.26 202 0.276 1.06 Quarter 71/2 418 32 | 0.0147 0.30 0.35 223 0.282 0.81 5 21 Following 10 552 30 | 0.0131 0.29 0.34 226 0.267 0.78 Seas 14 504 27} 0.0135 0.29 0.32 227 0.270 0.84

*The speed is the nominal speed read from a calibration curve of propeller rpm versus knots; 7 1/2, 10, 14, and 17 knots correspond to 94, 127, 185, and 230 rpm, respectively.

Let x ma:

according to Longuet-Higgins

O= log, N.

TABLE 7

Constants Required for Prediction of Probable Maximum Value in a Sample from a Rayleigh Distribution

6

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Sample

N

Size

15

Sample Size

10,000 20,000 50,000 100,000

N

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19

DESIGN AND OPERATIONAL CONDITIONS FOR WARTIME SERVICE

In the discussion of the statistical background, it was pointed out that the distribution patterns readily give the probability of exceeding any given magnitude of the motion or stress and that the distribution pattern can be utilized as a load spectrum for endurance strength calculations. In this section the methods will be applied to determine design and operational

conditions for wartime service. These determinations are based on the following assumptions.

1. The vessel will be operating in the North Atlantic Ocean. The observations of sea conditions at weather station C (52°N37°W), see Figure 2, are considered typical of conditions in the North Atlantic and are assumed to represent the conditions the ships will encounter in

service.

2. The ship operating speeds for the different sea conditions are taken to be the average

of the estimates obtained from ship’s officers of a number of ships; see Table 1.

3. All headings of the ship relative to the predominant wave direction are assumed equally likely, excepting only that seas coming approximately off the beam are considered unlikely for

combinations of high speeds and rough seas.

“‘LONG-TERM”’ DISTRIBUTIONS OF SHIP MOTION, HULL BENDING MOMENT, AND WAVE HEIGHT

The charts of Figures 7 through 10 give the probability of exceeding and of not exceed- ing any given value of stress or motion if all the motions or stresses are considered to which the vessel is subjected over a period of a number of years. For example, only 3 percent of all variations in roll angle would, on the average, exceed a value of 10 deg peak-to-peak; see Figure 9. Figure 2 gives similar data for significant* wave heights to be expected in the North Atlantic Ocean. These distributions may be considered valid up to maximum variations of 25 deg in pitch, 56 deg in roll, 0.8 rad/sec? in pitch acceleration, and 40,000 ft-tons in

bending moment.

PREDICTIONS OF SHIP RESPONSE TO WAVES FOR GIVEN CONDITIONS

It is difficult to make reliable estimates on the basis of the available data because the specification of the sea state and of the relative heading of the ship to the sea are somewhat indefinite. Nevertheless the following formulas may be used to make estimates which should be fairly good if the environmental conditions are similar to those for which measurements

were made. The most frequent magnitude of the variation will be 0.707 VE. The average magnitude

of the variation will be 0.886 VE. The significant magnitude (average of the upper third of the

*The significant wave height is used to denote a sea state. It is estimated as indicated in the footnote on page 3.

20

pecee Sie Bee

(1-P), Probability of Exceeding Pitch Angle, percent

Sa eh Ba ire ans iz

99.99 0.

Ae pee 2 OE AR 2 1

Variation in Pitch Angle, degrees Double Amplitude

ape ele |

Figure 7 - Long-Term Cumulative Distribution of Pitch Angle for Wartime Service, North Atlantic Ocean This log-normal distribution is computed on the basis of the data represented by the plotted points and it cor- responds to the following parameters (see Appendix B for calculations). Mean value of logo (variation in pitch angle) = 0.1227 Standard deviation of log, , (variation in pitch angle) = 0.3898 It is probably valid up to 25 deg.

21

o Fractiles taken from Table 9

+ | Bee He tt tt A , AMM ONNE i mueTataRLTTL) 60 raaina ane) Ame AEN 20 || :

Seoct | a : 4 : Hl, Cae ial ae il!

eee SBE,

01 0.02 0.05 0.10 0.20 0.50 1.0 Variation in Pitch Acceleration, Radians/sec2 Double Amplitude

Ee Ss s P, Probability at not Exceeding Pitch Acceleration, percent

(1-P), Probability of Exceeding Pitch Acceleration, percent

Figure 8 - Long-Term Cumulative Distribution of Pitch Acceleration for Wartime Service, North Atlantic Ocean

This log-normal distribution is computed on the basis of the data represented by the plotted points and it cor- responds to the following parameters: Mean value of 1oB19 (pitch acceleration in rad/sec”) = 2.4314

Standard deviation of log 9 (pitch acceleration in rad/sec”) = 0.4895

It is probably valid up to 0.80 rad/sec2.

waves having the largest magnitudes) will be 1.416 VE. The most probable magnitude of the largest of 50 variations will be 2.01 VE. The most probable magnitude of the largest of 500

variations will be 2.509 VE. The most probable magnitude of the largest of N variations will be (constant) VE where the value of the constant is given in Table 7. For large values of N,

the constant is approximately equal to log, N. The values of E corresponding to various combinations of sea condition, ship speed,

and heading are given in Tables 2 through 6. PREDICTION OF EXTREME VALUES

It may be desired to estimate the largest value of ship motions or hull girder stress

22

jo

99.99

lO Fractiles taken from

—+——__—+

(P), Probability of not Exceeding Roi! Angle, percent

(1—-P), Probability of Exceeding Roll Angle, percent

1 20 30 40 50 60 70 80 90 100 Roll Angle, degrees

Figure 9 - Long-Term Cumulative Distribution of Roll Angle for Wartime Service, North Atlantic Ocean

This log-normal distribution is computed on the basis of the data represented by the plotted points and it cor- responds to the following parameters:

Mean value of logi9 (variation in roll angle in degrees) = 0.4868

Standard deviation of log ig (variation in roll angle in degrees) = 0.2741

It is probably valid up to 56 deg.

that a ship structure is expected to experience in a given number of variations or over a given period of time.* The cumulative probability functions plotted in Figure 4 (Rayleigh distribu- tion) and Figures 7 through 10 (log-normal distributions) may be used to find the probability of exceeding (1-P) or of not exceeding (P) a given value of the variable.

In the preceding section a convenient formula is given for estimating the most probable

magnitude of the largest variation out of N variations; this formula is applicable only when the

*The average number of variations expected per hour of sea operation are given in Tables 8 through 11, column 8.

23

Variation in Longitudinal Bending Moment Hog to Sag, foot-tons 500 750 1000 2000 3000 4000 5000 10,000 15,000 20,000 30,000 40,000

Pe

hy ARE ZANE

99.99

99.9 99.8

LS ‘ 99

98

Bae fee Esp tale) Ped

P, Probability of not Exceeding the Stated Value

95

90

80

70

60

IES

50

(1-P), Probability of Exceeding the Stated Value

40

30

20

10

0.2 0.5 1 2 5

Variation in Stress, Main Deck, Amidships, kips/in2, Hog to Sag

Figure 10 - Long-Term Cumulative Distribution of Longitudinal Bending Moment, Amidships, for Wartime Service, North Atlantic Ocean

This log-normal distribution is computed on the basis of the data represented by the plotted points and it cor- responds to the following parameters: ~

Mean value of lo€19 (variation in stress in kips/in.2) = 1.6016

Standard deviation of log ig (variation in stress in kips/in. 2) = 0.3229

It is probably valid up to 40,000 ft-tons.

conditions of ship speed, heading, speed, and sea are steady. The following is a more general approach which may be applied to any distribution provided that its cumulative distribution function P (z) is known.

The following formula, developed in Reference 3, gives the fraction f of all samples of

24

size N [belonging to a given distribution specified by P (x)] which will have at least one value of z >, . The formula is valid only if P (z, ) has a value close to unity, that is, the 1 1

formula is designed to estimate the values which occur rarely. The formula is

-N[i- P(x, )] f=l-e A

or alternatively

oy. hip) i eG > amo weenie: where [1 —- P(z,, )] is the probability of exceeding x, in the fraction f of all samples of size N each. Knowing [1 - P(z,, di it is easy to compute the corresponding value of the variable Ema"

In order to estimate the largest values of motion and bending moments for design pur- poses we will use this formula to estimate the value om which, on the average, is exceeded by the fraction f of all similar ships during their service life. Thus f represents the risk of exceeding lms"

It will be assumed that the worst combination of operating conditions is the most severe of those listed in Tables 1 through 6, viz., a State 5 sea characterized by a significant wave height estimated to be 21 ft. The values of E specifying the corresponding Rayleigh distri- butions are listed in Table 12. Assume that the ship will be subjected to these operating con- ditions for a duration of 12 hours, experiencing V variations in this period of time, and that this situation will be repeated n times during the service life of the ship; therefore N = nV. For the Rayleigh distribution we have -x,? /E,

m

fl-P@, )l=e 1 1

Substitution in the expression for f gives: 2

1 -f=exp[-e 7] where y = ar - log, N m Table 1 of Reference 9 tabulates the values of exp [-e ”] as a function of y. Thus, for a specified risk f of exceeding 2, one may look up the corresponding value of y and then solve for the desired value of 2m from the relation

a2 = E,, ly + log, N]

ih

As an example consider the maximum value for the variation in roll angle.

From Table 12: E£,, = 176 (deg)?, V = 4600 If we take f = 0.001 and n = 10, then Reference 9 gives y = 7.0. Therefore:

ze = [176 (7.0 + 10.74)1% = 56 deg (port to starboard) 1

m

25

TABLE 12 - Maximum Values of Ship Motion and Longitudinal Bending Moment for Use in Design Calculations

All values given refer to the peak-to-peak variation.

Stress

Vv a8 2 = Boo s3 : VD mF 62 Sen = a Condition for Which the Extreme Value is Predicted Number of Variations) 2Y=zi~ | => | gee Ze BO | oo = 3 3 : in 12 Hours Saco 5 ees 2se ao aa forstety | BSE | cesu| geo | =e —_— = a PO a= a Significant | Direction | Shaft EB Conditions 3 2 s 2 2 = SEs & é Wave Height | of Seas | RPM i ie s & aj = Roll Angle 5 94 176 (deg)? 4600 39° 50° 56° Pitch Angle Ts [185 56 (deg)? 7000 2 about 25° LE ae *Roll Angle 5 94 40° *Pitch Angle 5 94 he \ Me 10° Pitch Acceleration 5 185 | 0:0327 (rad/sec2)* 8500 _ 10.54 rad/sec?| 0.78 rad/sec2| 0.77 rad/sec?| 0.8 rad/sec? Heave Acceleration 5 185 | 0.0498 (gravity unit)? 6800 0.66 g 1.0 g 1.0 g Longitudinal Bending | Moment H 185 | 85 x 10° (ft-tons)? 9500 28,000 ft-tons| 40,000 ft-tons| 33,000 ft-tons| 40,000 ft-tons Longitudinal Bending H [" 3.50 (kips/in2)2 9500 5.7 kips/in? | 8.0 kips/in2 | 6.7 kips/in? | 8.0 kips/in?

*®This is believed to be a most severe condition of simultaneous roll and pitch. The data are taken from Figure 5b of Reference 2.

**This estimate (32% is believed to be outside the range within which the statistical estimation is valid and therefore the value is discaried. {These values are nearly the largest magnitudes obtained under any conditions experienced during the tests reported in Reference 2.

QH - Quarter Following; QF - Quarter Head; H - Head

Maximum estimated values for the other variables have been computed similarly, taking

f = 0.001 and n=10. They are listed in Table 12 together with the largest values measured at any time during the rough water sea trials reported in References 2 and 6. We will take the larger of the statistically estimated and the measured values as the suggested maximum value to use for design purposes.

For some design problems, it is necessary to make an estimate of the extreme condi- tions of simultaneous pitch and roll. It is unlikely that the maximum conditions of pitch and roll listed in the last column of Table 12 will occur simultaneously. The most severe combi- nations of simultaneous roll and pitch angle, measured during the sea trials,* was 40 deg double amplitude in roll together with 10 deg double amplitude in pitch, see Table 12. It is suggested that this combination be used as an extreme condition for design purposes. Predicted extreme values should be used with caution because the method eventually breaks down by predicting too extreme a value. This occurs because, in practical application the theoretical distribution cannot be relied upon at the extreme ranges of the function. For ex- ample, the prediction of 32 deg -for the extreme value of pitch angle variation is probable unrealistic as nonlinear behavior of the pitch motion will probably set a lower limit than this.

The extreme values listed in the last column of Table 12 may be used to set an interim

upper limit to the validity of predicted extreme values.

DESIGN LOADS FOR BOTTOM STRUCTURE TO WITHSTAND SLAMMING LOADS

A detailed analysis of the loads, stresses, and deflection for the bottom plating of an

AVP vessel incident to slamming has been made by Greenspon.° On the basis of the latter

’

study and photographs of an AVP during slamming,? it is estimated that the part of the bottom structure extending from the keel to the turn of the bilge in the forward quarter length of the ship may be subjected to occasional localized slamming or pounding pressures. In some locations within this area, the pressure attains values of the order of 300 psi. For the pur- pose of design calculations, the time variation of the pressure is such that it may be assumed

to act statically. The following design loads are given as an interim recommendation:

a. For the design of bottom panels: Assume that the pressure attains a maximum value

which varies linearly from 300 psi at the bow to 30 psi at a distance of 0.25 L from the bow:

Po = 300 — 1080 a ce 0.25

where Po is the design pressure for plates, is the location of the plate measured from the bow in feet, and

Lis the length of the ship in feet.

b. For the design of transverse framing: Assume that a static uniform pressure of inten-

sity po /2 acts on the bottom over a strip one frame space in width.

c. For the design of longitudinal stiffeners or framing: Assume that a static pressure

acts on the bottom plating supported by the longitudinal equal to p,/2.

If the bottom plating is to be designed to keep the stresses within the elastic limit, then the simple formulas and tables of Reference 10 may be conveniently used for the calcula- tion of the maximum stresses and deflections in plates loaded transversely. The ultimate load for transversely loaded panels may be estimated by utilizing the simple method given by

Greenspon.!!

DISCUSSION

The data of Tables 2 through 6 furnish a basis for working up distributions of motion and hull bending moment for assigned service missions of ships of this type. In the present instance, these basic data have been utilized to predict wartime service conditions for opera- tion in the North Atlantic; the procedure for making this prediction is carried out in Tables 8 through 11, as a guide for similar analyses of other missions. It should be pointed out that the prediction for ‘‘Wartime North Atlantic’’ service is greatly influenced by the estimated operational speeds provided by the U.S. Coast Guard. Inspection of Table 1 indicates that the estimates of service operating speeds made by COMAIRPAC vary considerably from those provided by ships in service in Atlantic waters.

It should be emphasized that the sea state is a variable which is most difficult to de-

fine. In the present case, variability of the sea conditions, for a given sea state, has been

27

minimized by conducting the tests for a given sea state during one continuous time interval with the exception of the data for the State 3 Sea, for which two different time periods were required. The estimates of the sea state, as defined by the scale given in Reference 4,

were made by the Weather Bureau observers who were assigned to the USCGC UNIMAK during the trials. In order to give a more quantitative idea of the sea state, sample stereophotographs together with photogrammetric analyses thereof are reproduced in Appendix C for sea states experienced during the trials of the UNIMAK (States 2, 4, and 5).

Inasmuch as the evaluation of sea states made by ships’ officers and reported in Table 1, as well as that made by weather observers during the sea tests, depended upon visual ob- servations, one may expect reasonable agreement in the severity of the sea as defined by the sea State. In any case, no better basis for making the synthesis given in Tables 8 through 11 was available to the authors.

The general method of synthesis utilized in this report could also be applied to data obtained from model tests of ships in waves rather than from full-scale test data. This would be a more flexible arrangement in that a wider variety of conditions could economically be covered by model tests than would be feasible with full-scale tests. Furthermore, the problem of measurement would be less difficult.

The order of magnitude of the pressures measured on the USCGC UNIMAK were also experienced by a sister ship, the USCGC CASCO (formerly AVP 12), during earlier sea tests in 1951. The indications are that the measured pressures are typical of the loading to be ex-

pected in heavy seas for this type of ship.

ACKNOWLEDGMENTS

The cooperation of the Commandant, U.S. Coast Guard and the Commanders, Air Force, U.S. Pacific and U.S. Atlantic Fleets made it possible to obtain realistic operational esti- mates of the speeds and headings under which ships of the AVP class are expected to operate in service. The Naval Photographic Interpretation Center and the Naval Hydrographic Office made the analyses of stereophotographs given in Appendix C. Mr. B.M. Wigle of the Vibra-

tions Division, Taylor Model Basin, assisted in the calculations.

28

APPENDIX A SAMPLE OSCILLOGRAMS

The two oscillograms of Figure 11a indicate the variation of pressures on the bottom plating with time and the consequent strains and deflections in the plate. The response to slamming is also indicated in the oscillograms of pitch acceleration and hull girder stress amidships in Figure 11e.

The maximum peak-to-peak variations in stress measured in the keel 15 in. aft of Frame 23 were 3500 psi, associated with presently undefined higher modes of hull structure

which were excited subsequent to slamming at the bow.

29

Figure 11 - Samples of Records Taken During the Tests

fr] T Oscillogram No. 4098 | _| Estimated fundamental period of plate obtained by hitting plate and allowing it to vibrate freely. 0.1 sec. Heave Acceleration ve g Roll Angle inh at a —

‘Pitch Angle

EE

200, in/in.

Yn

ik Ini

0.015 in deflection I | Inoperative 31pin/in. I eee ft 100 psi puree Sex EP Ast cy ce | Eee a . a . Oscillogram No. 4064 0.1 sec.

| | |

Roll Angle Heave Acceleration

Pitch Angle

CU ai Wt

Inoperative

IN

8 Reference

Ig I

Figure 11a - Variation of Pressures in the Bottom Plating with Time

30

° ° ie") 4 a 0.68 Radians/Sec2 Pitch Acceleration iS re iw) nN is) i) 2 = Hull Girder Stress on Main Deck = 5000 psi Longitudinals - Amidships ey 2 (Longitudinal Flexure of Ship) 7S

nw 1S) nN. S 2 Heave Acceleration (oe) (os) [) ear

= 1 Gravity Unit

i) nN =

[e) N Nm = cf = Maximum Measured Roll Angle (Peak to Peak) a (o2) & > nN. {o) id iw)

Tz Ss ~ 50 Degrees Roll Angle

(o2} (e5) foe) (oe) ° 3° =) S [o*) (ee) fe?) m x 20 Degrees Pitch Angle nN. iw) ine) in)

Figure 11b - Oscillogram at Time of Maximum Measured Roll Angle 16 Jan 55

Maximum Roll Angle 40 deg Ships Speed

Significant Wave Ht 21 ft Relative Heading of Seas Wind Velocity 32 knots Heading of Waves Wind Direction 090 deg Heading of Ship

31

7.5 knots 135 deg 090 deg 315 deg

S 5 [e*) = o a o>) = > = a ; 2 Pitch Acceleration 0.68 Radians/Sec iw) Tw) [o) T is) ind a = = = & Hull Girder Stress on Main Deck 4-2 2 Longitudinals - Amidships 2 5000 psi = cy) (Longitudinal Flexure of Ship) fo) PJ (o) = IX) 2 Heave Acceleration = : @ ies) oF c2) . . = = 1 Gravity Unit bw) no () ° > S S) 5 fos) © fe?) (e?) = Maximum Measured Roll Angle (Peak to Peak) = 50 Degrees Roll Angle NS in) i) i) 3 — — Maximum Recorded Pitch Angle |StationD 26 October 1954 = (2) 20 Degrees Pitch Angle = J i) is) (o) fo) tad -— (o>) (o>)

Figure lic - Oscillogram at Time of Maximum Measured Pitch Angle 26 Oct 1954

Maximum Pitch Angle 18% deg Ships Speed 0.0 knots (Patent Log) Significant Wave Height 25-29 ft Relative Heading of Seas 000 deg Wind Velocity 50 knots Direction from Which Waves Come 260 deg Wind Direction 270 deg Heading of Ship * 260 deg

32

ors S = o @ an an B F 2 Pitch Acceleration 0.68 Radians/Sec = iw) iw) So [e) iw) ind = Observer Watched This Record = Maximum Measured Pitch Acceleration4at Time of Recording = : a Hull Girder Stress on Main Deck ==° 2 Longitudinals - Amidships = 00 psi (Longitudinal Flexure of Ship) a 00h. a (e) id i) S) 3 = o o : Heave Acceleration — (o)) 1 Gravity Unit > f= = ins) ine) [o} = o- = -- oS) ° = © © Maximum Measured Roll Angle (Peak to Peak) 50 Degrees Roll Angle = = in) nD in) ins) BS S z tS) S) [e*) @ (o>) z fe?) 20 Degrees Pitch Angle i= > N Lo fo} + P= J : October 26, 1955 (o>) (o>)

Figure 11d - Oscillogram at Time of Maximum Measured Pitch Acceleration 26 Oct 1954 2

Maximum Pitch Acceleration 0.77 rad/sec“ Ships Speed 0.0 knots (Patent Log) Significant Wave Height 29 ft Relative Heading of Seas 010 deg Wind Velocity 50 knots Direction from Which Waves Come 270 deg Wind Direction 270 deg Heading of Ship 260 deg

33

V|||9)|/8)| OL

Pitch Acceleration

0.68 Radians/Sec2 t +

i . Slamming Response bh oS (es) 7 5000 psi (22) Hull Girder Stress on Main Deck Maximum Stress, Amidships Longitudinals - Amidships (Bending) (Longitudinal Flexure of Ship = Heave Acceleration 1 Gravity Unit cr ~ iy [o) is) . . { = 5 Maximum Heave Acceleration S © = 50 Degrees Roll Angle

Maximum Measured Roll Angle (Peak to Peak) Ny

TO = — (o} ic) . 20 Degrees Pitch Angle (2) Ts ms a Figure 11e - Oscillogram at Time of Maximum Measured Stress and Heave Acceleration 1 Feb 1955 Maximum Stress 5900 psi Ships Speed 14.2 knots Maximum Heave Acceleration 0.55 g Relative Heading of Seas 015 deg Significant Wave Height 20 ft Direction from Which Waves Come 090deg Wind Velocity 32 knots Heading of Ship 075 deg Wind Direction 079 deg

34

APPENDIX B SAMPLE CALCULATIONS

In the derivation of the long-term distributions of ship motions and bending moments, it is necessary to fit a log-normal distribution to the truncated histograms computed in Tables 8 through 11. This requires the calculation of the mean value and the standard deviation from the truncated data. i

The method and tables of Reference 7 are applied in making these calculations as in- dicated below. In the calculations, the symbols used are: o for standard deviation, y and z for the parameters needed to enter Table IX of Reference 7, 2 being an estimate of the point of

truncation.

LONG-TERM DISTRIBUTION OF VARIATION IN PITCH ANGLE

The mean value and standard deviation of the long-term distribution of the variation in pitch angle are computed from the data given in Table 8. These data are truncated at a pitch angle of 1/2 deg (@ = 5).

log. 6 Percent of log, 6 | log. @ Measiredi | Variations 70 #10 alli from alling at End of | at Center

within Class of Class

Class Interval Interval

Variation deg x 10

—oco 0.6990 =/ 1.0000 1.3010 1.6021 1.7782 1.9031 2.0000 2.1461

2.2593 3 30.515 | 44.792

In accordance with the procedure outlined-on page 29 of Reference 7, we have:

y = 2N2?XN _ 30-515 (89.61) _ 9.6815

2(ZN2)? 2 (44.79)? z = —1.087 (from Table IX of Reference 7, corresponding to y = 0.6815) g(z2) = 0.7798 (from Table IX of Reference 7)

o = 9 = 2N® oz) - £4.79(0.7798) _ 03998 =N 89.61

35

Theoretical percentage of truncation = 13.9 percent(from Table II of Reference 7, corresponding to z = —1.087).

Mean value of =—zs = 1.087 (0.3898) = 0.4237 = @.

Mean value of A = 0.6990 + z = 0.6990 + 0.4237 = 1.1227, 6 = 13.26 Mean value of @ = antilog of 1.1227 = 13.26

Therefore the mean value of the pitch angle = 13.26 + 10 = 1.326°

The value of the variate h corresponding to a probability of 97.5 percent is 1.96 stand-

ard deviations greater than the mean value of h. Let this value be A,, .. Then h,, . =

log (097 5) = 1.1227 + 1.96 (0.3898) = 1.8867, 6,, , = 77.0. Therefore the pitch angle corres- ponding to a probability of 97.5 percent is 7.7 deg. The two sets of values of pitch angle and probability (1.326 deg, 0.50), (7.7 deg, 0.975) define the straight line in Figure 7 which represents the log-normal distribution of pitch angle.

36

APPENDIX C PHOTOGRAPHIC DEFINITION OF SEA CONDITIONS

Photographs were taken with stereo-cameras during the sea voyages at estimated State 2, 4, and 5 seas. Photogrammetric analysis results in wave profiles at various dis- tances from the centerline of the ship; see Figure 13. By use of these profiles, it is possible to obtain quantitative values of wave height and wave length which can then be treated statis- tically to determine, for example, the mean value of the one-third highest waves, commonly

referred to as the significant wave height.

37

Figure 12a - Photograph 525F, Sea State 2

Figure 12b - Photograph 551F, Sea State 4 Figure 12c - Photograph 515A, Sea State 5

Figure 12 - Wave Photographs

The stereo cameras were located 52 ft apart approximately 56 ft above the ship’s baseline.

38

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41

REFERENCES

1. Bureau of Ships letter S29-7 (442-440-330) of 21 June 1948 to David Taylor Model Basin.

2. Jasper, N.H., and Birmingham, J.T., ‘‘Sea Tests of the USCGC UNIMAK. Part 1 - General Outline of Tests and Test Results,’’ David Taylor Model Basin Report 976 (Mar 1956).

3. Jasper, N.H., ‘‘Statistical Distribution Patterns of Ocean Waves and of Wave-Induced Ship Stresses and Motions, with Engineering Applications,’’ Transactions, Society of Naval Architects and Marine Engineers (1956).

4. Hydrographic Office Publication No. 606-e (1950).

5. Greenspon, J.E., ‘‘Sea Tests of the USCGC UNIMAK. Part 3 - Pressures, Strains, and Deflections of the Bottom Plating Incident to Slamming,’’ David Taylor Model Basin Report 978 (Feb 1956).

6. Jasper, N.H., ‘‘Study of the Strains and Motion of the USCGC CASCO at Sea,”’ David Taylor Model Basin Report 781 (May 1953).

7. Hald, A., ‘‘Statistical Tables and Formulas,’’ John Wiley and Sons, Inc., New York (1952).

8. Longuet-Higgins, M.S., ‘‘On the Statistical Distribution of the Heights of Sea Waves,’’ Journal of Marine Research, Vol. XI, No. 3 (1952).

9. Probability Tables for the Analysis of Extreme-Value Data, National Bureau of Standards Applied Mathematics Series No. 22, issued July 6, 1953.

10. Greenspon, J.E., ‘‘Stresses and Deflections in Rectangular Plates Under Dynamic Lat- eral Load Based on Linear Theory,’’ David Taylor Model Basin Report 774 (Apr 1955).

11. Greenspon, J.E., ‘‘An Approximation to the Plastic Deformation of a Rectangular Plate Under Static Load with Design Applications,’’ David Taylor Model Basin Report 940 (Jun 1955).

42

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GaIWISSVTIONN (q10dea quewdojeaep pus yoivesey) ‘sjoi ‘‘sadvip ‘syduid ‘se]qey ‘snq]I “dey ‘Al “1 G6L ady ‘syooig “J°y pus sedsef “HN Aq ‘AdAL

dAY GHL AO SdIHS YO SHUNSSAYd DNINNV'IS GNV ‘SLNAW -OW DNIGNGAG TINH ‘SNOILOW GHL JO NOILVINASaYd TIVO

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4ueseid o18 SUOIpuod duneiedo jo efusI epIM ev JOAO edUeIIedxe 0} pejoedxe eq Avul sS¥]o OTdAY ©4} JO OZI8 pus wioj [v1oued 04} jo diys @ yolyM sjueWoW SuIpued Jepsts-{[ny pus’ suoNnow oy J,

GaldISSVTONN (qaodes jueudojesep pus yoisesey) ‘sjoi ‘sideip ‘sydvid ‘seyqey ‘snqq{I “dg ‘Ar “1g6T ady “syoorg “Jy pus sedsef “H°N Aq ‘Gd AL dAV GHL AO SdIHS YO SAUNSSAUd DNINNVTS GNV ‘SLNAN -OW ONIGNGG TINH “SNOILOW GHL AO NOILVINASAYd TWO -IZSILVIS - 6 LUVd “MVWINN ODOSN AHL 4O SLSAL Vas

“LL6 3424 “uysDg |apow 40]40) pang

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“Ta ‘syxoog “TJ

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98809 °S'N) MVWINA *2 uoNNqIyNSIp einsseig —

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Sulpueg — syiny diyg -g sisA]eus [eons

“BIS — UONOW — sdiyg “F sisA]eus [BONS

-81S — usIseq — sdiyg “¢ suoljip -u09 Sunviedg — (siepue}

euvjdees “s°) dAV °% usiseq — (siepue4

eueidves *S°) dAV ‘T

L80-TELSN “III

“Ty ‘syooig “II

*H wewion ‘sedsep ‘] (aeyND pieny

48809 ‘S') MWWIND *“2 uolynqii}sip einsseig —

Surwueys — sqny diys “9 sjuewou

Supueg — syiny diyg “¢ sisA]Bue [B0Ns1y

-B1S — UONOW — sdiyg *F sisAyeue [Bons

-81g — usIsog — sdiyg “¢ suontp -uoo Juysiedg — (siepue,

euvtdves “s') dAV “3 us1seq — (siepue4

euvldves *S7) dAV ‘TL

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GdaldISSVTONA (qaodes juowdojeaep pus yoivesey) ‘sjoi ‘*sideip ‘sydeid ‘soyqzy ‘snq[I “dey ‘At “1)G6T ady “syooig “T'y pus sedsef “H*N Aq ‘AdAL

dAV AHL AO SdIHS YOU SUUNSSAUd ONINNVIS ANY ‘SLNAW -OW DNIGNAG TINH “SNOILOW GHL 40 NOILVINASAYd TVD

“WLSILVIS- 6 LUVd “MVWINM OSOSN AHL AO SLSaL VuS 116 “3494 “UISDG japow sojAD] prAng

woiy *8)8p jo JUNOWB oSIv] OY} Jo UOTVeWUESeId pus ‘sIsAyTeUB ‘uO -00][09 OY UI pus s][BI4 OY) Jo Sosvyd vos4e 04] Jo Suluueyd oy} ur poXojdwe ueeq OABY SOlSIVBIS JO Spoyjoul ey, “uvEeDQ ONUEPY YYON 04} Ul STeI4y ves FuUNp MVWINN ODNOSN ey} uo epew syueu -OINSBEW GAISUE}XO UO pes’ alv BIBp CYT, “WIJ [BOI4SYeIS UI po 4ueseid oie SuOMIpuod SuNeiedo jo esuBl OpIM¥ JeAO QdUETIEdxe 0} peyoedxe og Atul sS¥]9 OTGAY 94} JO OZIS pus Wo} [e1eued EY} jo diqs ¥ yolym sjuewWOW SuIpueq Jopiis-[[nYy pus suoyow oyy,

GaIaISSVTIONN (q10de1 juewdoyeaep pus yorsesey) ‘sjoi ‘sadeip ‘sydeis ‘sejqey ‘*snq]I “dep ‘Al “21G6L ady ‘syooig “J-y puv sedsef “H*N Aq “Ad AL

dAV AHL AO SdIHS HOA SAUNSSAYd DNINNVTS GNV ‘SLNAN -OW DNIGNAY TINH ‘SNOILOW GHL AO NOILVINASAYd TIVO

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*SUONOW PUB S}TEWOUW JO SeN{BA WNWIXBUW e[qeqoid SuyeWYsSe UI esN “SUONOW PUB SJUEUIOW JO SeN[VA WNWIXeU e[qeqoid SutsuUse UI esN

10} UGAIS O18 SB[NWIOY “Seinsseid FuIWWB]S pus ‘suoyOUW [[NY ‘syueWoW SuIpueq SuTATOAUI JO} USAIS O18 SB[NWIOY “Sseinsseid SuiuMie[s pus ‘suoyow [[Ny ‘syuewoW Suipueq SuIATOAULI swe[qoid Zunwiedo pus usisep ul esn Joy digs jo odAy S14) 10} peAtiep e1¥ BBP “sz]NSel 4se] ET} swo[qoid Sunwiedo pus usisep ul esn J0J diys yo odAy S14) 10} peAliop O18 BBP ‘sz][NSeI 4507 ET} *SUONOU PUB S}TEUIOW JO SENTRA WNWIXBU e[qeqoid JuyjewWHysSe ul osn “SUOY}OW PUB SyUEWOUW JO SeN{BA WNWIXBU o[qeqoid SuNeWSe UI esN

1OJ USAID O18 SB[NWIOY “Seinsseid dulwwe]s pus ‘suoyow [[Ny ‘syuewOU SuIpueq JULA[OAUL 10J USAIS O18 SB[NWIOY ‘“Seinsseid Suiuweys pus ‘suonow [[ng ‘syuewow Suipueq SuIA[OAUI

sule;qoid Sunviedo puv usisep ul esn Joy diys jo edAéy sig} 10} peAliep o18 Byep ‘s}]NSe1 4Se7 Eq} swe]qoid Sunsiedo puv usisep ul osn Joy digs jo odAy siy} 10J pealiop o1¥ ByBp ‘Ss}]NSe] 4Se} Eq}

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