Further analysis of slamming from the SS WOLVERINE STATE

(1)

SSC-255

FURTHER ANALYSIS OF

_SLAMMING

DATA FROM THE S. S. WOLVERINE STATE

This document has been approved for

public release and sale; its

distribution is unlimited.

SHIP STRUCTURE COMMITTEE

4 DEC. 1q79

Lab.

y. Scheepsbouwkund

ARCHIEF

Technische Hogeschoo

(2)

SHIP STRUCTURE COMMITIEE

AN INTERAGENCY ADVISORY COMMITTEE DEDICATED TO IMPROVING

THE STRUCTURE OF SHIPS

MEMBER AGENCIES ADDRESS CORRESPONDENCE TO

Unted States Coast Guard Secretory

Nouai Seo Systems Command Shp Structure Committee

Mlitory Seahft Command U.S. Coast Guord Headquarters

MariNee Admnistration Washington, D.C. 20590

Amercon Bureau of Shippng

SR-203

1 .JMN 19/6

This report describes the analysis of the data collected

in an earlier instrumentation program on the WOLVERINE STATE. That

project, reported in SSC-210, Analysis of

Slarnniing Data from tho

S.S. WOLVERINE STATE, involved the measurement of impact pressures

and strains with only a limited analysis of the data. This effort

undertook a more sophisticated analysis and has extended the

significant information.

Your comments and suggestions on this report or other

structural problem areas will be most welcome.

W. M. Benkert

Rear Admiral, U.S. Coast Guard Chairman, Ship Structure Committee

(3)

SSC-255 Final Report

on

Project SR-203, 'Slamming Data Analysis'

FURTHER ANALYSIS OF SLAMMING DATA FROM THE S.S. WOLVERINE STATE

by

J. W. Wheaton

Teledyne Materials Research

under

Department of the Navy Naval Ship Engineering Center Contract No. NSSC-N00024-72-C-5047

This docwnent has been approved for public release

and sale; its distribution is unlimited.

U. S. Coast Guard Headquarters

---BibIiotheek van de

ifdeling Scheepsboow- en Scheepvaartkunde

Technische Rogeschool, Deift

DOCUMENTATE :

0k JU' 1980

(4)

AB STRACT

The pressure, acceleration, and hull bending

stress

data from the full-scale slamming measurements on

the S.S.

WOLVERINE STATE were analyzed in detail to

provide additional

information on frequency of occurrence, elapsed time between

slams, correlation with environmental conditions,

pressure-velocity relationship, correlation with

midship transient

stress, and pressure-location-time distribution. Seventeen

separate measurements were made on a group of 26 severe

slams to provide a data base for the investigation and data

from more than 1,000 slams which

occurred over approximately

49 hours of slamming during 3 different voyages were used in

establishing the correlation with environmental conditions.

A number of statistical correlations were examined, and

pressure-velocity measurements provided additional data for

comparison with model results.

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-il-CONTENTS

Page No.

Introduction

i

Elapsed Time and Frequency of Occurrence

i Correlation with Environmental Conditions

11 Pressure-Velocity Relationship

18 Correlation with Midship Transient Stress

21 Pressure-Location-Time Distribution

25 Results and Conclusions

25 References

27 Appendix - Detailed Measurements from 26 Slams,

28 Voyage 288W3

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Title

Slamming Transducer Cabling, S.S. WOLVERINE STATE Location of Slamming Damage on S.S. WOLVERINE STATE and

Two Sister Ships; Locations of Pressure Transducers Analog Data Format

Frequency of Occurrence of Slams, Voyage 263W2 Interval

12 (240-Second Groups)

Frequency of Occurrence of Slams, Voyage 263W2 Interval

Frequency of Occurrence of Slams, Voyage 277W2, Interval

2 (First Third)

2 (Second Third)

2 (Third Third)

Probability Density of Time Between Slams S.S. WOLVERINE STATE, 263W2 Interval 12 Beaufort 6 Fwd Draft 16.5 feet

LIST OF FIGURES

-iv-11 Probability Density of Time Between Slams S.S. WOLVERINE 8

STATE, 277W2 Interval 2 Beaufort 7/9 Fwd Draft 18.5 feet

12 Slamming History, 263W2, Interval 12

13 Slamming History, 277W2, Intervals 2-5 13

14 Slamming History, 288W3, Intervals 56-58 14

15 Relative Velocity vs. Distance 2 C

16 Pressure vs. Relative Velocity, HP2 22

17 Computed "k" vs. Station, S.S. WOLVERINE STATE 22

18 Histogram of VREL, LP21 and HP2 22

Fiqure lA lB 2 3 4 5 6 7 8 g 10 Page 2 2 3 6 6 6 7 7 7 8 8

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LIST OF FIGURES (Concluded)

Figure _Title

19 _{Acceleration Phase vs. Transient Stress}

Voyage 288W3

20 _{Midship Transient Stress}

vs. Transient Acceleration

21 _{HP2 Transient Pressure vs. Transient}

Acceleration 22

Amplitude-Time Distribution, Slam 12 23

Amplitude-Time Distribution, Slam 23

24

Pressure-Location-Time Distribution, Slam 12

25

Pressure-Location-Time Distribution, _{Slam 23}

Page No. 23 23 23 26 26 26 26

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LIST OF TABLES

Table Title Page No.

I Pressure Transducer Locations

3

II Basic Data, Elapsed Time and Frequency of Occurrence

4

III Frequency of Occurrence Analysis, Voyage 263W2, 9

Interval 12

IV Frequency of Occurrence Analysis, Voyage 277W2, 9

Interval 2

V Elapsed Time Analysis, Voyages 263W2 and 277W2

10

VI Multiple Regression Analysis, Environmental 16-17

Correlation

VII Pressure and Relative Velocity Data 20

VIII Acceleratìon Phase Data 24

(9)

-vi-The SHIP STRUCTURE COMMITTEE is constituted to prosecute a research

program to improve _{the hull structures of ships by}

an extension of knowledge

pertaining to design, materials and methods _{of fabrication.}

RADM W. M. Benkert, USCG

Chief, Office of Merchant Marine _Safety

U.S. Coast Guard Headquarters

Mr. P. M. Palermo

Asst. for Structures

Naval Ship Engineering Center

Naval

Sea

Systems Command

Mr. K. Morland

Vice President

American Bureau of Shipping

Mr. C. Pohier - Member

Mr. J. B. O'Brien - Contract Administrator

Mr. G. Sorkin - Member

U.S. COAST GUARD

LCDR E. A. Chazal - Secretary

CAPT D. J. Linde - Member

LCDR D. L. Folsom - Member CDR W. M. Devlin - M em be r MARITIME ADMINISTRATION Mr. J. Nachtsheim _{- Chairman} Mr. F. Dashnai - Member Mr. F. Seibold - Member Mr. R. K. Kiss - Member

MILITARY SEALIFT COMMAND

Mr. D. Stein - Member

Mr. T. W. Chapman - Member

Mr. A. B. Stavovy - Member

Mr. J. G. Tuttle - Member

NATIONAL ACADEMY OF SCIENCES SHIP RESEARCH COMMITTEE

Mr. R. W. Rumke _{- Liaison}

SHIP STRUCTURE COMMITTEE

SHIP STRUCTURE SUBCOMMITTEE

The SHIP STRUCTURE SUBCOMMITTEE acts for the Ship Structure Committee

on technical matters by providing technical _{coordinatìon for}

the determination

of goals and objectives of the program, and by evaluating arid interpreting _the

results in terms of ship structural

design, construction and operation.

NAVAL _SEA _{SYSTEMS COMMAND}

AMERICAN BUREAU OF SHIPPING Mr. M. Pitkin

Asst. Administrator for Commercial Development Maritime Administration Mr. C. J. Whitestone

Maintenance & Repair Officer Military Sealift Command

Mr. S. G. Stiansen - Member

Mr. I. L. Stern - Member

SOCIETY OF NAVAL ARCHITECTS & MARINE ENGINEERS

Mr. A. B. Stavovy - Liaison

WELDING RESEARCH COUNCIL Mr. K. H. Koopman - Liaison

INTERNATIONAL SHIP STRUCTURES CONGRESS

Prof. J. H. Evans - Liaison

U.S. COAST GUARD ACADEMY CAPT C. R. Thompson - Liaison

STATE UNIV. OF N.Y. MARITIME COLLEGE Mr. W. R. Porter - Liaison

AMERICAN IRON & STEEl INSTITUTE

Mr. R. H. Sterne _{- Licison}

(10)

(11)

INTRODUCTION

This report presents additional analyses _{of slamming pressures, accelerations,}

and midship longitudinal vertical bending _{stresses acquired during a program of}

data acquisition aboard the States Marine Line ship S.S. WOLVERINE STATE. _The

prin-cipal objective was to gather full-scale

data for comparison with model data and

theory reported by M. K. Ochi.l _{The first report on the full-scale}

work was

pub-lished by the Ship Structure Committee

as SSC-210, "Analysis of Slamming Data from

the S.S. WOLVERINE STATE."2 _{This previous report presented the}

results of the

ini-tial analyses, and also described the data acquisition system in detail. The

present report extends the previous _{analyses by considering more slams in greater}

detail, and by examining statistically slams from rough weather portions _{of three}

voyages.

Data were acquired by a set of transducers to measure midship bending _stress,

bow and stern accelerations, and

bottom pressures from 7 out of an array of 20

pres-sure transducers located on the bottom plating

along the keel from the Forepeak to

Frame 54. _{Transducer locations are shown in Figure}

1 _{and Table I.} _{The data}

acquisi-tion system was unmanned, operating

automatically on either a timed basis (one-half

hour out of every four)

or in response to high stresses or low pressure at the bow

(indicating emergence).

Reels of magnetic tape were returned

to the laboratory on a routine basis _for

data analysis. _{Processing involved reproduction of}

the stress signals on an

oscil-lograph for a "quick-look", and then _{automatic processing to obtain certain}

statis-tical parameters relating stress variations and environmental _conditions. _The

pres-sure data were analyzed using expanded oscillograph

records, with scale factors

determined by suoerimposed calibration _signals.

Figure 2 shows the form of the

analog data.

More details concerning the operational aspects of the program are contained in Reference 2.

These data were obtained from

a single C4-S-35 vessel, and the _{relationships}

developed in this report

are directly applicable only to this particular _{hull shape.}

Comparisons can be made, however, _{to models and vessels of other}

shapes by

con-sidering the differences involved.

ELAPSED TIME AND FREQUENCY OF OCCURRENCE The first item statistically examined

was the elapsed time between and fre-quency of occurrence of slams.

The intent was to develop more full-scale data for

comparison with the theory and data presented by Ochi in Reference 1, and to

supple-ment data previously presented in _{Reference 2.}

A. _{Frequency of Occurrence}

Ochi's conclusion from model _{tests, that slamming may be considered to be}

a sequence of events occurring in time following

(12)

AO

a pressure cell

b cable to pressure cell

in Forepeak Tank

e cable to 6 pressure

cells in No. i DT sod FPT

10

Figure lA

Slamming Transducer Cabling, S.S. WOLVERINE STATE

25 20 15 10 5

e tables to 16 pressure cells h,l cables from signal

condi-i, No. 2 DB tioner to instruisent room

f pressare cell signal conditioning

units (7 channels) j,k terminal boxes in

instru-Figure lB

Location od Sianxing isnage on2.S. WOlVERINE STATE and Two SIster Skips;Locations of Fressure Transducers

-2-Array of Four on a Single Plating Pamel

o tp, o-So psis SP, O-350 psig Nunber of Fusais Re-plsccd (Esel, A & ï Scrubs). 3 Vessela MO'9 6Fb SIPS LP22 Sf2 F521 1.521 (277) i (288) .LO00 _'1 JranktP g 30-terisSnal junction bon

a 100-tornirai junction box

Li

L

Looat.ion of Slamming Daotage no

(13)

ZERO 1 Minute rl CALIBRATiON 1 Minute TABLE I

PRESSURE TRANSDUCER MOUNTING LOCATIONS

Figure 2

Analog Data Format

Calibration lit uce

I

Li

DATA 30 Minutas Locatir Number in Tank In Bottom Plate Between Fraises Distance. Aft of Frame Off Center Vertical Keel Distance Aft from Bow

1 //1 D.T. FK-i 16-17 11' aft FR.16 il" P 4].' 5'

2 #1 DT. _FK-1 _21-22 _{11" aft FR.2l} 11" P _{52' 8"} 3 #1 D.T. FK-2 26--27 11' aft FR.26 11" P _63'll" 4 //1 D.T. FK-2 29-30 11" aft FR.29 11" P _{70' 8"} 5 //1 D.T. FK-2 31-32 11" aft FR.31 11" P _{75' 2"} 6 #2 D.B. FK-3 34-35 11' aft FR.34 9" S 82' 5" 7 #2 D.B. FK-3 37-38 11" aft FR.37 11" S _89'll" 8 #2 i).B. 1K-3 40-41 6" aft FR.40 11' S _{97' 0"} 9 #2 0.5. FK-3 40-41 24" aft FR.40 _{ii" S} _{98' 6"} 10 112 D.B. FK-4 45-46 11" aft FR.45 11" s _io'ii" 11 #2 D.B. FK-4 49-50 11" aft FR.49 _{9" S} _119'll" 12 _{#2 0.3.} _FK-4 56-55 11" aft FR.54 11" 5 _{132' 5"} 13 #1 D.T. A-8 31-32 11" aft FR.3l 41" P 75' 2" 14 #1 D.T. Â-8 31-32 11" aft FR.31 65" P _{75' 2"} 15 //1 D.T. Â-8 31-32 11" aft FR.3l 41" S _{75' 2"} 16 #2 D.B. A-9 _40-41 _{6" aft FR.40} 30" S 97' 0" 17 #2 D.B. A-9 40-41 24" aft FR.40 30' S _{98' 6"} 18 #2 D.B. A-9 40-41 24" aft FR.40 69" 5 98' 6" 19 #2 D.B. B-6 40-41 24" aft FR.40 105' S 98' 6" 20 #2 D.B. A-9 40-41 24" aft FR.40 69" P 98' 6"

21 Forepeak A-3 8-9 11" aft FR.8 11" P 24' 8"

22 #1 D.T. FK-1 23-24 11" aft FR.23 _{11" P} _{57' 2"}

23 #2 D.B. FK-3 43-44 _{11" aft FR.43} _{ii" S}

104'll'

(14)

E E E

u

§ E E E E E E E E

(15)

previously by a sample of 47 observations _{from full-scale data (Voyage 288W3,}

Interval* 57) reported in _{Reference 2.}

Additional analysis of the other _two

voy-ages was undertaken in order to establish if

the frequency of occurrence of

slam-ming was different from a deeper draft (277W2, Interval 2), _{or for few occurrences}

of slamming (263W2, Interval 12). _{In addition, the}

_time

intervals were increased

because of the lower density of slamming, _{and in one case a long record}

was

divided into thirds in an attempt to restrict the analysis to _{periods of constant}

environmental conditions.

The results of these analyses _{are shown in Figures 3 through 9.}

The

com-parison of the theoretical Poisson

distribution with the experimental _{data for}

263W2-l2 is somewhat better for _{the 100-second analysis (Figure 4)}

than for the

240-second interval (Figure 3), but both have rather wide separations in _the

1-and 2-number-of-slams regions compared with previous results in References 1 1-and

2, and the fit is _{poor as measured by the Chi-squared}

test. Figure 3 is based on analysis of 133 slams over sixty-four

240-second intervals, and Figure 4 _{is based}

on the same number of slams over _{one hundred fifty-two 100-second intervals.}

The

basic data are presented in Table _{II, and the data for Figures}

3 and 6 are

pre-sented in Tables III and IV, _{respectively.}

The last part of Interval 2, _{Voyage 277W2 was also analyzed}

in 240- and

100-second groups for the entire

run (Figures 5 and 6), and then was divided into three separate parts for re-analysis

at 100-second groups (Figures _{7, 8, and 9).}

The fit appears to improve with

the subdivision into thirds, especially in the

final third (Figure 9). _{It was hoped that additional}

environmental data could be

obtained from the ship's logbooks _{to establish headings, speeds,}

and sea states

for the subdivided parts of Interval _{2, but the logbooks could}

not be located.

B. _{Elapsed Time Between Slams}

The same basic data from

voyages 263W2 and 277W2 were used to _develop

(see Table V) the elapsed time information for comparison _{with previous results.}

Figures 10 and 11 are plots of the probability density _{of the time between slams,}

showing a comparison of experimental _{data and a theoretical Rayleigh}

distribution

truncated at the pitching period, _{7 seconds.}

In both cases the probability _density

difference between the first and

second groups appeared unusually _large. _{The data}

were re-examined to determine if the _{tolerance on the time}

measurements could have

caused this result (by causing _{too many borderline points}

to be counted one way or

the other). _{It was found that it would require}

a measurement tolerance of 4 seconds to result in any change in

distribution of data between _{the first and}

second time intervals in Figure 11. _{The basic data of Table}

II were measured to an accuracy of +1 second.

To determine if the apparent

differences between the theoretical and

actual distributions were significant, the Chi-squared _{test was used.}

The

ex-pected values are shown in Table _{V as} _n'".

Applying the standard _Chi-squared

test, it was found that while the _{data from 263W2 (Figure 10)}

demonstrated a poor fit to the theoretical distribution,

the data from 277W2 _{was a probable fit} at the 5% level.

*An "interval" _{of data is a nominal 30-minute}

sample recorded every four _hours,

with calibration signals _{at the beginning.}

All of the intervals _{of data}

con-sidered here, however,

were approximately four hours in _{length because the tape}

(16)

1 2 3 4 5

Theoretical X

Actual

Number of Slams is 240-Second Groups

Figure 3

Frequency of Occurrence of Slams Voyage 23VW2 Interval 17

(240-Second Groups)

1 2 3

Number of Siano in 240-Second Group Figure 5

Frequency of Occurrence of Slams Voyage 27yw2,lntersoi 2 240-Second Groups -6-0.5 0.4 n n a 0.2 0.1 2 3 4

Number of Slams i 100-Second Groups

FIgure 4

Frequency of Occurrence of Slams Voyage 263W2, Interval 12

(17)

0.5

0.4

O

0 1 2 3

Number of Slams in 100-Second Croup

ligure 6

Frequency of Occurrence of diamo

Vevsge$77W2. Int,rV,t 1 2 100-Second Oronpa Theoreticl N k Actual N 1 2 3

Number of Slants in 100-Second Group tigure 8

Frequency of Occurrence of Slams

Vorige .i7W2. cierval 2

Second li, rd

-0 1 ¿ 3

Number of Slums in 100-Second Group Figure 2

requeney of Occurrence of Slams Voyagc 277142, interval 2 First Third 0.5 -0.4 u u 0.3 o u. 0.2 0.1 N N t Theoretical Actual '

x

0.5 - _Thoteldcsi Actual 0.4 u 0.3 u. 0.2

-L

t. 0.1 -o r

(18)

t' e. 0.3 00 k .0 0 5 0 0.2 _S 0.0 \\ 0 i 2 3

Bomber of Siano in 100-SecondStoop

Figure 9

Frequency of Occurrence of Slams

Voyafe 271t7, SotemoS 2 Ihir,) Third 0.9 0.) 0.0 10.5 0 0.0 0.3 0.2 o.) o coperimeatal D00 0 Theoretical Distribotlon '0.-e00087 t-7) f(t) 0.00375 57 10) 157 207 2 7 30) 3') 403 0,7 500 9100 ScOot,, 01,00 - Satoodo -8-+" Expori.ocntat Data Figure 10

Probability Density of Tine Between Siamo

SS WOLVERINE STATE263W2 Interval 12

Beaufort 6 Fwd Sraft 17.5'

+" Thcorp000ai LllOOPib00100

IC,,) -0.009 -0.0091,-7)

Figure ii

Probability Deosity of Tic Between Slams

SS WOLVLRINE STATE 27'/W2 Interval 2

Beaufort 7/9 S'Vi Draft 18.5'

7 217 207 357 4)) 097 507 SIll 107

Tino. 0tocm, Slanm-Scpnods

0.9 0.6 o-0 0.5 Theoretical ) X 0.7 g i.í t Actual

(19)

-TABLE III

FREQUENCY-OF-OCCURRENCE ANALYS IS, 263W2, _{INTERVAL 12}

(Figure 3)

Ar A

133 slams

Theoretical: P = - e » where A = expected value,

2.08

r!

groups

TABLE IV

FREQUENCY-OF-OCCURRENCE ANALYSIS, _{277W2, INTERVAL 2}

(Figure 6)

r

Theoretical: P = -'--- C_A

where A = expected value, slams

= 0.853

r!

64 groups No. Slams per

240-Sec. Group (r)

No. 240-Sec. Croups

with r Slams _{Distribution,}Theoretical

Percent Experimental Distribution, Percent 0 ₂₁ 12.5 _32.8 1 ₁₁ 26.0 _17.2 2 9 _27.0 14.1 3 7 _18.7 10.9 4 ₈ 9.7 _12.5 5 4 _4.1 6.25 6 0 _1.4 0.0 7 ₂ 0.4 _3.1 8 ₁ 0.1 _1.6 9 ₁ 0.0 _1.6 64

No. Slams per

240-Sec. Croup

(r)

No. 100-Sec. Groups

with r Slams

_Distribution

Theoretical

Percent Experimental

Distribution,

Percent 0 ₃₅ 42.6 _51.5 1 ₁₇ 36.3 _25.0 2 ₈ 15.5 _11.8 3 ₇ 4.4 _10.3 4 ₁ 0.9 _1.5 68

(20)

TABLE V ELAPSED TIME ABALYSIS

(Figures 10 and il)

-lo-Voyage 263W2, Interval 12 Voyage 277W2, Interval 2

n

n 70.N

AT, Sec. n n 7O N AT, Sec. n

n' 7-77 83 60.7 0.00898 7-57 25 3.0 0.00877 78-147 15 32.3 0.00162 58-107 6 12.1 0.00210 148-217 11 17.2 0.00119 108-157 4 7.9 0.00140 218-287 9 9.2 0.00097 158-207 10 5.5 0.00350 288-357 4 4.4 0.00043 208-257 1 3.3 0.00035 358-427 4 2.6 0.00043 258-307 8 2.1 0.00280 428-497 1 1.4 0.00011 308-357 2 1.4 0.00070 498-567 1 0.7 0.00011 358-407 0 0.9 0.0 568-637 2 0.4 0.00022 408-457 1 0.6 0.00035 638-707 2 0.2 0.00022 458-500 0 0.4 0.0 -N (t-7) -N (t-7) f(t) = Ne -f(t) = Ne S

-= 0.0086 15,177-520 0.009 N5 _6762-136 7 0.00900 7 0.0086 77 0.00479 10 0.0085 147 0.00255 20 0.0078 217 0.00136 50 0.0060 357 0.00043 100 0.0039 497 0.00011 200 0.0016 300 0.0007 400 0.0003 500 0.0001

n' expected number ri' expected number

= 21.1 d.f. = 4 X2 = 7.83 d.f. = 3

(21)

The same test was on Ochi _{'s model results (Reference 1,}

Figures 12 and 14),

confirming the good fit of the model data.

The probable explanation for the _{results of the}

elapsed-time--between-slams analysis is the fact that the

7-second pitching period of the ship can

cause, in a wave system with encounter periods

in the same range, _{a number of}

sequential slams at 7-second _intervals.

This reasoning can also be applied to the frequency-of-occurrence

data, since repeated slams due to a pitching resonance with the wave system imply that the Poisson distribution may not be

applicable. In Ochi's model tests3, the _{encounter period was 9.2 seconds.}

III. _{CORRELATION WITH ENVIRONMENTAL}

CONDITIONS

The correlation of slamming _{incidence with environmental}

conditions, sea

state, heading, speed, and forward _{draft was accomplished by counting both the}

number of slams and the maximum

pressure from HP2 for sequential _20-minute

in-tervals for all three _{voyages under consideration.}

For each interval, the sea

state, relative heading, ship speed, and draft were noted _{from the logbook data}

(see Appendix B, SSC-2l0). _{These data are plotted in}

Figures 12, 13, and 14.

Note that observed sea states should _{be used with caution.}

For example, Reference 3, p. _{17, refers to a typical design}

case of Sea State 7 in the North

Atlantic, giving a significant _{wave height of 30.2 feet, and using}

the

Pierson-Moskowitz wave spectrum for _{a 40.5-kt wind.}

Logbook data used in the _present

full-scale study (Appendix B, _{Reference 2) rarely show}

wave or swell heights greater

than 20 feet, even at Sea State _9.

Figures 12, 13, and 14 show

graphically the changes in the rate of slamming and in the maximum HP2

pressure as changes occurred in the _{other variables.}

For

example, Figure 12 shows the events during Voyage 263W2 _{on June 4, 1966.} _The

WOLVERINE STATE was westbound in the North Atlantic near latitude _{50°N, longitude}

l7°W, with a forward draft of _{17.5 feet (molded design}

draft is 30 feet). _Recorded

Interval 9 began just before _{logbook Index 80 at 0024}

GMT, with a sea state

equiva-lent to Beaufort 5.

Engine RPM was 81.5, which is close to the maximum found in

the logbook for calm conditions. _{Relative heading}

was 32°, determined by taking the difference between the Course (270°)

and the true wave direction (SW x W, or about

238°).

Slamming began about 0320, and _{RPM was decreased in two}

steps to 65 RPM. _At 0423 logbook Index 81 _{reported Sea State 6, and}

true wave direction WSW, for a

relative heading of 22 degrees. _{The slamming rate increased}

rapidly during the next few hours, and at 0820,

just before Index 82, RPM was reduced to 60, with sea

state reported as 7. At the same time true

wave direction changed to West, and Course was 264°, for

a relative heading of 6 degrees. _{These conditions continued}

throughout the day, with slamming

rate averaging about 10 every 20 minutes, and maximum HP2 pressures averaging

between 30 and 40 psi, with _{two excursions}

exceed-ing 50 psi. _{Sea state gradually decreased}

as did slamming rate, and at 1725 _RPM

was increased to 65. _{True wave direction}

was reported as W x N at 2048, _{for a}

relative heading of 16 degrees _{with Course now 265 degrees.}

There was a temporary increase in slamming rate and maximum pressures, but

sea state decreased to 5 and

RPM was advanced in several _{steps back to the full}

throttle value of 80 RPM as

(22)

80 70 60 40 o rO 20 lo O 9 (15)

Maximum HP2 pressure transient during 20-minute period

Relative Headin 30 degrees o o a .0

z

No. of slamE each 20-rninut period 5 6

+

7 4e 6 IrJil 6

4i

5 Reported Sea State

(14.5)

4- RPM

Reported Average Speed, knots (12) 10 Sunrise 0505 -12-(10 Fwd Draft 17.5' (est.) Position: 50.5°N, 17.4°W Figure 12

Slamming History, 263W2, Intervals 9-14

Y X Sunset 2114 14

t

'f

t

$

80 81 82 83 84 85 -r o cj-) -r

o

CMT -r c-J June 4, 1966

o

o -r

o

c-J 51.& 56.

(23)

o u 30 ai E z25 20 15 10 * Interval 3 73 Logbook Index r' Sunset ('4 --2 037 (-'J X X Relative Heading Sunrise 0822 74 75 7 ° _GMT C O

_rj

March 24,19670 -Figure 13

Slamming History, 277W2, Intervals 2-5 6 No. of slams each 20-minute period

J

9 7 4

Reported Sea State 80-full throttle 75 70-(J

1)__RePorted kverage

Speed, knots (9) 65

_(RPM

60 -Fwd Draft 18.5 feet o o Position: 46 N, 37 W 55 50 I) (6) (6) (I;45 Q) Q) u _{"Maxjmum HP2 pressure} transient

Q) _{during 20-minute period}

S

E

(24)

35-(J) X 56 interval '

t

Logbook Index 161 Sunset _Q r, H 57 8 -14-9

1

58

t

162 Q

o

GMT o April 3, 1967 Figure 14

Slamming History, 288W3, Intervals 56-58

o No. f 20 each 20-m jnt E o z 10 60 50 - 40 -RPM (5) Reported Average Speed, knots

Reported Sea State

Fwd Draft 16.5' Position: 41.5°N, 60.5°W

(2)

Maximum HP2 pressure transient during 20-minute period

(2) Hei

3t ve

I-i ad1112 dE grec

t

163 Sunrise

o

0744>

u-'

o

(25)

Lack of maximum pressure data for several _{20-minute periods during Interval}

10 is the result of the fact that several slams _{occurred, as defined by the dual}

criteria of bow emergence and midship transient _{stress ("whipping), but there}

were no measurable transient pressures on HP2. _{This situation also occurred at}

several times during Voyage 277W2.

The information on RPM changes is also quite detailed in Figure 13 (277W2)

because the mates on watch made notes in the data logbook each time there was a

change in RPM. _{It is obvious that a reduction in RPM had}

a significant effect on

the rate of slamming, even though the _{reported sea state increased from 7 to 9}

dur-ing this period. _{Despite the reduction in speed to about 6}

knots, there was still

an occasional slam of significant pressure _{on transducer HP2.}

Figure 14 (288W3) is not quite so detailed. _{It indicates an average RPM of}

about 50 for about 11 hours, under sea states of 8 and 9; in general, worse

con-ditions than the portion of 277W2 examined _above. _{Average number of slams in 20}

minutes is also higher. _{The results for 263W2 (Figure 12)}

are quite similar to

those of 277W2, in that there appears _{to be a definite correlation between the}

number of slams and both RPM and relative _heading.

In order to determine more accurately _{the degree to which sea state, RPM,}

relative heading, and draft are correlated with slamming incidence, _{a multIple}

linear regression analysis was performed for a set of independent variables _and

a dependent variable. _{From the data in Figures 12, 13, and 14}

"number of slams"

was assigned as the dependent variable for

Selection 1, and "maximum HP2 pressure" was assigned for Selection 2.

The results of the regression analysis are shown in

Table VI-A for the three _{voyages separately, and in Table VI-B for all}

three com-bined.

The regression analysis results _{may be interpreted by examining the "t" values}

with respect to the degrees-of-freedom _involved.

A relatively high "t" value

with respect to the value tabulated _{in statistical tables for}

the confidence level

assumed indicates that the regression _{coefficient in question is highly}

unlikely to

be zero. _{An examination of the data in Table}

VI-A reveals that there is a strong

correlation between the number of slams in a 20-minute period and _{the maximum}

pres-sure during that period, as would be expected.

The sign of the regression coeffi-cients and the value of "t" for the

independent variables 3 (sea state), 4 (RPM),

and 5 (relative heading) confirm what Figures 12, 13, and 14 _{have already revealed.}

For example, in Figure 12 the rate _{of slamming (Variable 1) increases}

as the

rela-tive heading (Variable 5) decreases _{(numerically, toward 000°,}

or head seas).

This is confirmed by the "t" _{value of -2.257.}

For the other voyages, however, inspection of the figures indicates

that there are little data concerning this

relationship, and the regression _{analysis confirms this with}

very small "t" values.

The three-voyage analysis (Table _{VI-B) includes Draft as a sixth variable,}

resulting in a somewhat different _{set of correlations.}

With slamming rate as the dependent variable (Selection 1),

the correlations with maximum pressure, relative heading, and draft have the _{highest "t" values, higher than}

those for any single

voyage. However, taking all three _{voyages together and using maximum HP2}

pressure

as the dependent variable (Table VI-B,

Selection 2) the correlations _{with all}

(26)

A0.SLYSIS 0F 969165CC roo THE REGRESSION 5399ES 5F 040247105 DESECES 0400 OF MB AM F VALUE OF FACE008S SIOJARES S OU AR ES AT7RIO4TU0LF TO ACL0055ION 1427.SR204 356.77305 21.6463'

00618TI5.'. F606 REGRESS IO'.

63 6 39.75 110 02 .90 386 TOTAL. '9 2060,94326

6MULYSIS OF VAIllANCE POU OHO REGRESSION

53404CC 0F VARIATIOM

DES530S _{0F FREEDOM}

RNRLYSIS OF 968045CC FOP TVE REGRESSION

SOUSE! 0F VAQ!ATION 09G RE E D 5/9 SF MEAN F VALUE OF FREES.DM SCA AR E S SQUARES

ANALYSIS DF 949195CC F04 TVE AESRESSION

SCORER OF PAMIATION DEGREES SUP QV 65E AN F VALUE OF FREEDOM 50 jA O E $ SCUIVES S jo'ioi 68.63413 62.38609 0.60306 0.13374 0.03399 3,93*83 3 SEi, SIATE 6,92916 6.576363 -0.603*3 -0.03025 0.47746 -3.13702 4 RPM 87.74333 10.3801) 0.39300 0,08698 0.04704 1.78766

S REt HEAD R.3IISS

5,07218 -0.22036 0.09201 0.05)66 -1.03030 REP EN2E 637 1 100. OLAMS4.7708) 3. 86603 ¡77093607 6.2 54 0* MULTIPLE CSRRELAT103 0.77701 STD, C8ROR O' ESTIMATE 1, 64093 027142 TAULE 10-0(0, 5E LCS IO 4 VARIABLE MEAN $7452990 CORRELATION REGRESSION STD. 04009 CORUT0 DEVIATION A VS Y. COErE ¡CIENO OF RES.COEF. T VALAE 1 NO. SLAMS 4.17083 3,66603 0.61806 0.97943 0.30308 3,93-AS 3 SEA STASe 3,22916 1.07662 -0.30880 '5.50021 1.92747 3.529A4 4 RPM 57.745N3 ¡0.3801, 0.29445 S.S3978 3.16947 .2.00962 O RELVE/ID 3.3125V 9.07218 -0,0671* 0.22062 0,20926 1.03492 SOPE 73E N T 2 HOi PSI 18.85413 10.5 ¡608 UTIRIPJTASLE TO VETUCSSISN A 2024.04102 73 1.01016 7.085 83 900141300 FR099 6035055155 *3 4*38.62013 103 .22 870 TOTAL 67 7,62.66016 SELECT lOO. 0 VUS IA3LE MEAN '.0. STANOARD DEVIATION CORRELATION X VS Y 0050E5010S COEFFICIENT STD. CR906 0F RES.COEF. COPSOU000 T VALUE 300. SiJM5 3.271*2 -5.73047 0.392MO 0.50*48 0,37*79 2.41307 3 SEA STATE 0.8*255 0.694*0 0.40280 0.43523 3.23723 -3.1)444 4 RPM 46.21429 7.86809 .0.53774 .0.34346 0,31224 .1.09997 S 7CL VEAU 1 3.00071 9.60000 .0.56036 -0.25962 0.2080. .8.02603 807 003E 5 0 2 922 PSI 14.22(54 14.22984

STTÇIVJT..ÇLE TO AECRESSIOG SCAIABIO'. PROV REGRESSIO9

701 AL 4 ₀₅ 69 5627.S29C6 6344.59377 13976.71467 1406,18076 328.37835 16.55006 VARIA900 MEAN '.0. 50608490 DEVIATION COSRELATION VS Y RECR050IOP COOFFICIEN? STO. ERROR OF REQ.COEF.

CPRPATOO T VALUE 2 HP2 PSI SV,2265'. 04.22984 0.06290 0.09591 0.0)767 2,46323 3 SEA STOlE 5,84215 0.69448 0.70836 3.96691 0.00238 4.37740 4 0.801 66.21429 7,0A826 -0.606,7 0.04306 0.04958 0.55332 5 REL HEAD 13,98571 9.66315 .0.67459 -0.17931 0.07943 -2.28736 0E 9E DENT FITEVCEPT 2G.80463 MULTIPLE CORRELATIOM 0.79361 $00. ERRAS OF E5TIFATE 3.59209 INTERCEPT 66.77935 MULTIPLE CORRALATIOOI 2.63019 STD. 09903 SF ESTIMATE 10.150RO ISTESCEPT 38.37670 'OULTIPLE COARSL09105 0.43*02 STD. 06909 3F ESTIMATE 16.330*1 MULTIPLE 9ES0:s'.:V' V267A2 TABLE V-A(0 SELSCTIO'I I 5. 7 0047 0...TI0LE OCESESSION 026340 SEELE HI-82( OJI710..0 1005ESSISM...H27143 TAULE V0-U)) E.LECT 106 1 VARIABLE HORN STANDARD CORRELATION REO9EOSION 513. ERROR COYFUICO 00, DEVIATION X VS Y COEFFICIENT OF RES.COEF. T VALUE TOTAL 17 702 ''074 ATNIRATU9LT TO REGRESSION 6 'SFRIATIS', FROM P059050100 '5 SAM OF PEON p VALUE SQUARES SQUARES *00.53970 600,0*367 64,6 30 20 200,90404 4,07451

(27)

SOUP-CE OF VAUTIOM

V20891

TAlLE VI-A(S)

SELFET ¡04

t _{ANALYSIS OP VAA!A9CE pSA THE REG9055ION}

000REES 559 00 OF F00000'1 5504905 40 ST_ ...24845 24011 VI-A(0) 1E.ECTI3N 2

ANAL9OIS 0F VARIANCE POR TVE R05060S!S9

ZIO 1. II 608 DEC-lUI SUO 00 OF PRCEOOM S011ARES 4 974.9938 20 IAIN.1Nt,,9 84 E A N S 34 AR OS 195.16879 12.461/4 'ULTIRLE 9CC900SIO'8 3 VOl'S SOL001ION...j IA8LE AI-O(i) 969188LP --- OEAN STANDARS CORREL6IION 90690S5109 '40. DEVIATION 8 05 Y 000FF ICIEMT 2 8422 PS! lt.09459 94.04629 0.64765 0.18784 3 024 STATE 7.20000 ¡.91053 0.35615 0.10282 4 DOM 58.75720 80.52740 -2.41438 0.07901 O TEL HOOD 10.09333 8.32869 -0,32535 -0,18470 6 EV.AFT 17.60657 0,72855 0.44029 3,14j79

--

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

--.---.

I 000. SLAMS 6.7933...6,C'.823 TMI090007 63.18712 -MELTIPL! 00900LATION 5.76173 513. ERROR CF ESTIVAlE -3.99603 ...

-ANALYSIS OF VARIANCE POR THE 000RES3IOPI

SOURCE 0 9*92*1 ICI 00260(3 AUN 07 FRAN -0E FREEDOM 50069ES 52060ES

671919i.T47,.E TO R0500SSION 2/EV bOTTOM PROV RE61CSSIO3

244 ₁₄₉ 3100.64793 672.32978 2287.94482 10.88450 5400.59776 STO. ESOSI C0900'E1 0F 900.COEP. T VAL-4E 0.12709 5.97349 0.31073 2.19819 0.05493 1,43023 0.08423 3.83149 0.55973 -9,68491 F VALUE 33.0 105 7

-O MEAN 51At5U95 000IATISII CORRELATIOS U VU Y R0090VIIOM COEFICIENT OTO. 09908 OF 600,COEF. COMPUTUO T VALUE 3.16080 0.47632 0.00017 0.27507 3.22904 8.62500 0.49166 0.2S565 5.31300 2012.65920 0.00256 48,44995 1,93773 0.31174 0.16447 198.58857 ..0.00545 2,25000 00.14942 0.02264 9,31614 63.17311 0.00593 30.56872 5.80734 77.70901 0.54471 7.24236 MEAN STANOASS 006IATION COMÑELAOION O VS Y 800VESSIO# COFICIEST STD, 09909 0F RES.COE. COMPUTED T VALUO 8,40734 0.47631 0.30830 0.09973 3.02044 0.89199 0.19873 -1 .7666 ¡215.58394 0.00045 45.64995 1.95773 0.11481 0.55931 255.76660 0.00025 io. -s.o,os 0.26711 37.S0355 -0.00716 NAR!ASLE 90. 9044 -STAS2AVO DEVIATION 00990IATION R VS Y REGRESSION COEFFICIENT 5TO. 00909 OP REU,CSEP, CO NP U T / T VALUS I ¡(O. SLAMS 6.73333 6.04623 0.64763 8.33240 0.19216 8, 95 049 3 OEA 52416 7.00020 1.52058 0.32997 0.51088 O.86',39 0.06043 4 RPM 59.15720 10.32740 -0.39510 0.00532 0.14714 -0, 6475 3 REL lACAD 03.29333 9.32665 -0.33659 -0.13395 0.23430 -O, 99733 L D?ATO 17.61657 0.72488 -5,23069 0.17207 1.305)8 0,10037 9.26902 8.7312 0.64175 4.26753

£TTVIVJFARLE 73 070NESSION ---- OPVIATIC/4 FOSO 906400510/4

TOTAL ,. 1 -144 - 13065,85549 -16224.62893 5633. 77100 122.49500 23.3U989 149 29397,45442 A 27 807,52231 I'ULTIFLE 900985510i 3 YOYO OELECT ION 2 TOSLE 42-0(2) 2 tIPO PSI 29,

1349914.08629

-I0.09245 --- MULTIPLE 009RRLATION -- 0.U6929 --ST0-,R9O9 OP ESTIMATE 10.61997

-

--ANALYSIS OF *8414300 F09 TVE REGRESSION

SOURCE 0F VARIATION 50000Es SAM CF MEAN F VALUA - --...- OP FREEDOM SOUARES -SCU6909 MEAN F VALUE 50./69ES 08.27209 4.72692 04.24158 TOTAL 826.20726 F VOLAD _3.69384

(28)

IV. PRESSURE-VELOCITY RELATIONSHIP

Detailed measurements were made on a number of slams which occurred during

Interval 57 of Voyage 288W3. These measurements are described and illustrated in the Appendix.

The relationship between relative impact velocity and slamming pressure was

studied, with emphasis on the "threshold" velocity for slamming. This

relation-ship is of particular interest to naval architects because it brings together two

facets of design which are capable of some control: seakeeping qualities having

to do with pitching motion, and the hull form forward.

There is a considerable literature on slamming which considers the

pressure-velocity relationship. Model tests have shown that the pressures associated with

slamming are proportional to the square of the impact velocity, and that the

rela-tionship depends on a coefficient "k" which is a function only of the shape of the

hull section:l

where p = kv

p = peak pressure, psi

Vr= relative impact velocity, feet/second

n = exponent, experimentally determined as very close to 2

Ochi1 showed that, in both regular and irregular waves, a MARINER model had a

k = 0.086 at Station 2. He also summarized3 from a number of sources data

in-dicating that there is a threshold velocity of about 12 feet/second for all hull

forms below which slamming impact does not occur. Recent studies on a barge model

indicated a "k" of 0.11 at Station 3 on the particular model instrumented.

Reference 2 considered data from 5 slams on the WOLVERINE STATE, and reported

a k value of 0.077. In that investigation relative velocity was determined by the

slope of the pressure-time record of the pressure transducer (LP21) at the forepeak

during reentry following a slam. As derived in the reference: p = ogh

P =

P5Vy,dt

or,

where

Ap = pgVAt

p = impact pressure, psi p = sea water mass density

g = acceleration of gravity

h = depth of immersion of pressure transducer

Vr = impact velocity, feet/second

(29)

-18-Solving for _vr:

r t pg

This same relationship has been used in _{the present work, with values}

ob-tained from the basic data in the Appendix (derived _{parameter No. 18, VREL).}

How-ever, the approach has been modified and improved.

One obvious source of error in the earlier work was the fact that relative

velocities determined by measurements _{at the forepeak were being used in conjunction}

with pressure data from transducer HP2,

located just forward of Station 2, 28 feet

further aft. Dr. Ochi provided additional information _{bearing on this problem by} examining the distribution of relative velocity along the length of a V-MARINER

model. _{These experimental data indicated that}

the amplitudes of relative motion

velocity in waves reduce significantly _{with increase of distance from the}

forward

perpendicular, and it appears that the reduction

is linear with increase in

dis-tance. _{Significant relative velocity amplitudes}

along the ship length were also computed for the MARINER, and were also found to be linear.

To review some past history of this slaming investigation on the WOLVERINE

STATE, the original decisions concerning _{the dynamic range of the}

pressure

trans-ducers were based on the premises that a)

slamming pressures were likely to be as

high as 300 psi, and b) transducers having _{a range of O-50 psi would be useful for}

1) detecting bow emergence, and 2) providing the reentry slope for determining

relative velocity. Thus, of the 20 pressure transducers _{installed, 16 were}

"high-pressure' (HP), and 4 were "low-pressure" (LP). _{The locations of these transducers}

are shown in Figure 1. _{Only 7 of the 20 could be recorded}

at one time.

Review of the data for the preparation _{of Reference 2 was accomplished}

by

re-producing the signals on the oscillograph in _{the normal manner.}

Both the

calibra-tion signals and the transient data were of relatively low amplitude on these

records.

In the course of doing the detailed measurements on the HP transducers reported

here, the HP signals were reproduced _{at significantly higher amplitudes,}

as described in the Appendix. _{Examination of the resulting records}

indicated that the HP

trans-ducers, despite their range of 0-350 psi, were quite capable of responding to the

emergence and reentry pressures with adequate

resolution, in exactly the same manner

as the LP transducers. _{Therefore, it was possible to derive relative}

velocity

in-formation directly from HP2 itself by _{measuring the DEL} _{* and DEL 1* values in}

the

same manner as reported in the Appendix for LP21. _{The results are shown in Table}

VII, which summarizes transient

pressure data for all of the HP transducers, plus

VREL* data for LP21 and HP2.

Having now measured VREL at _{a different station from LP2}

, the question of the

linear distribution along the ship was investigated. _{The VREL data for LP21 and}

HP2 were plotted for each slam _{as shown in Fìgure 15.}

It is obvious that there is no consistent linear decrease in relative velocity

with distance along the ship

at the instant of slam impact. _{A possible explanation for the}

result is the fact

that the relative velocity is a function of both the downward vertical

velocity of the ship, and the upward (or downward)

vertical velocity of the wave surface at

the instant of impact. _{Over the 28 feet which separate}

the two locations,

(30)

TABLE VII

I'RE6SUI&E ANIS RELATIVK VI1LOCITY DATA

Slain Nonher (See Appewils) 60 50

Q

40 10 20 1.921

liistance from Forward Perpendicular, Pert

Figure 15

RclatiVc Velocity vs. Distance

lo

I)

- 'lo

30 10

Slain

Treinnient Pressure l'IUIITA, poi

(Trausditror, distance aft of 99)

VAIL, f/a 11I'1 112 816 1119 11912 1,121 41 5' 52' 8" 82' 5" 98 (' 132' 5" 26' 8" 5?' 8" 1 16.69 26.53 0 0 0 20.35 25.8 2 15.9 12.86 0 0 0 21.41 18.6 3 10.33 1/.68 0 0 0 19.99 13.4 4 16.69 32.62 0 0 0 20.37 27.5 5 22.25 17.95 0 0 0 20.0? 21.4 6 15,10 16.34 0 0 0 17.87 17.3 8 19.87 20.90 0 0 0 17.31 20.1 9 31.80 29.47 4.50 0 0 21.46 27.0 10 10.33 13.66 0 0 0 18.56 15.5 12 15.10 36. ?1 11.00 6.23 0 27,71 29.9 13 25.43 35.64 48.00 7.01 0 35.03 35.1 14 15,90 24.38 9.00 0 0 22.20 24.8 15 15.10 26.26 0 0 0 19.98 16.9 16 12.71 25.19 0 0 0 16.69 17.8 17 30.20 60.73 39.50 8.19 0 35.17 33.6 18 31.00 37.25 8.50 0 0 24.61 24.0 19 23.05 0 0 0 0 19.75 23.4 20 11.12 23.04 0 0 0 16.95 18.8 21 10.33 26.7? 0 0 0 24.16 20.8 22 11.92 32.69 0 0 0 15.27 17.0 23 11.12 35.64 37.00 9.75 0 28.92 23.4 24 23.85 56.54 0 0 0 18.80 19.4 25 19.81 30.28 8,50 0 0 23.57 22.1 26 14.30 27.33 0 0 0 17.38 22.2 27 23.85 20.63 '0 0 0 19.90 30.9 28 15.1,0 27.33 0 0 0 28.02 26.6

(31)

The derivation of the relative velocity relationship with pressure turned, therefore, to direct use of pressure and velocity data derived entirely from HP2.

The results are based on data from Table VII, and are plotted in Figure 16.

Al-though there is some scatter in the data, a straight line with a slope of 2 fits

quite reasonably, and the intercept produces a 'k" value of 0.053. Dr. Ochi

provided also a plot of calculated "k" value vs. station for the WOLVERINE STATE,

based on the changing hull form. This plot is reproduced here as Figure 17, and

the experimental value of 0.053 has been added at the location of HP2. Although

the experimentally-determined "k' is low in comparison with the theoretical value, the method is inherently subject to quite variable results because of the

dif-ficulty of estimating the slope of the tangent (see Figure A-1). This rather

crude approximation method was used only because there was no direct measurement

of relative velocity. It should be noted that no bottom damage was reported as a result of the slamming experienced on this voyage.

The threshold velocity again appears to be approximately 12 feet/second. The

total of 52 new values of VREL from Table VII range from 13.4 to 35.17 feet/second. These slams, of course, were selected to be the largest, so the general average

is expected to be considerably above the threshold. The distribution of the 52

VREL values is shown as a histogram in Figure 18. The average of the LP21 VREL

values is 22.17, and that of the HP2 values is 22.89, for an overall average of

22.53 feet/second. The overall results from the two transducers are almost identical, even though, as shown by Table VII, the individual values vary widely

for each specific slam.

V. CORRELATION WITH MIDSHIP TRANSIENT STRESS

Several investigations were undertaken to determine how midship transient stress (SSuBTR), or "whipping", is related to bow acceleration.

SSUBTR vs. Acceleration Phase

"Acceleration phase" is defined as the portion of an acceleration period by which the slam lags behind the peak of the static acceleration (ASUBST), as

illustrated in Figure 19. Figure 19 also shows the relationship of acceleration

phase to transient stress for the 26 detailed

slams, from

data summarized in Table

VIII. This table also includes the stress phase data (PHASE). Inspection of the

figure indicates that the slam occurs between 50° and 80° after the acceleration peak, but there does not appear to be a consistent trend relating the magnitude of transient stress to acceleration phase.

SSUBTR vs. Transient Acceleration

To gain insight into the relationship between the magnitudes of midship whipping stress (SSUBTR) and transient bow acceleration (ASUBTR), the two were

plotted from the data given in the Appendix. As shown in Figure 20, for low values

there is a definite position correlation between the two. At higher values the

data are scattered and sparse. With only 3 data points over 3 kpsi whipping stress

and over 0.5q transient acceleration, no firm conclusions can be stated.

HP2 Transient Pressure vs. Transient Acceleration

Figure 21 plots this relationship, and, as expected, there is a good

(32)

61 Sc..

tu

q

Niir

Ilelott'ev votoulty cam mtlntcd by rs Icy a rri:cIt nyprox 4m,

t lori method

from the mea..::rod pressure.

0.20 0.11 O. 10 0.05 14 (.015 OPt OPI (iS F(gure 17 Computed "k vs. Statics SS POLVOROSO SISTC Kot.:

Relativo valority was ootlr.ated by usinO a

cruda

approxtraEIoo ceibO tren

tug measured pro asure. Experimental Voles u Fu4ura IS

llitcram of 9000. OPSS end 11P2

L1'21 1101 SPi

I

16 22 24 24 35 34

Eirleslic VlooC,y (tOiL). isot/svcosd

dl IS 25 25 50 4(1 so udiI (vo V.. I r: y (ett/anmorr,l hii,ari, 10

frs.00r:ro so. lirlatlo,, Viert t?, lIPS

(33)

0

Ilirio,

KOSI

Figare 20

M1dhip transient Stress s,. iranslret Aectieratton

Accoler at I . r.

Acceleration Phase, degrees

Figura 19

AcceleratIon Phase va. transient Strass

Voynpa 38143 60 50 30 20 10 o

/

F4uro 21 HF, trafl,Jr Pressure vs. trsr.nient Actalvestlon

k

PHASE 0° 90° o o o o o 0 o

0000

0

0000

0 0 o .fo +2b '-'33 .20 -c-60 *70 *iO 0.20 0.40 0.65 0.80 1.00 5.00 1.10 450916. 8" 1.0 2.0 3.2 4.0 5.0 1.0

(34)

TABLE VIII

ACCELERATION PHASE DATA

-24-SLM1

NO. PHASE SSUBTR ACC. PHASE

1 39.6 1.08 57.4 2 24.0 1.02 64.9 3 20.7 0.55 56.5 4 23.0 1.10 60,8 5 27.6 1.27 60.0 6 19.0 0.83 73.0 7 23.8 0.66 62.3 8 - - 61.6 9 32.9 1.10 60.5 10 25.4 0.44 61.1 11 - - 56.8 12 33.7 2.76 80.2 13 21.0 3.98 65.6 14 21.2 2.18 72.5 15 67.8 1.44 67.5 16 50.4 1.24 52.0 17 33.0 5.34 54.5 18 25.0 1.49 74.1 19 -52.0 0.69 80.6 20 20.1 0.80 58.1 21 22.7 1.46 72.6 22 25.8 1.69 69.6 23 25.1 3.60 62.8 24 32.6 1.49 82.4 25 35.0 2.54 74.3 26 72.0 0.94 60.5 27 32.9 1.10 65.5 28 51.1 1.93 78.3

(35)

occasional large acceleration will not be accompanied by a corresponding high

pres-sure at HP2, and vice versa.

PRESSURE-LOCATION-TIME DISTRIBUTION

Two slams were selected from the 26 for a detailed study of the passage of the

pressure wave along the keel; for each, two figures are presented: the first

show-ing an amplitude-time distribution with emphasis on the duration of the pressure, and the second showing amplitude, time, and location.

Figure 22 shows the amplitude-time distribution for Slam 12. The first three

pressure impulses are approximately lOO milliseconds in duration, rising to 150 and

300 milliseconds at HP6 and HP9. Slam 23 (Figure 23) is somewhat different, with

all of the HP transducers showing pressure durations of approximately lOO

milli-seconds. The time base zero was arbitrarily established at the time of the peak

pressure at LP21. Positive times are earlier; negative times are later.

In order to show the entire passage of the pressure wave in amplitude, time, and location for the same 2 slams, the basic data were displayed as shown in Figures

24 (Slam 12) and 25 (Slam 23). Pressure amplitudes are shown by vertical lines,

time progresses from bottom to top, and location from right to left. _Comparing

these two figures, it is evident that Slam 12 progressed forward hitting HP9 first,

then HP6, HP2, HP1, and LP21. Slam 23, however, hit HP1, HP2, HP6, and HP9 almost

simultaneously, and finally, LP21. Using Midship transient stress (SSUBTR) as a

criterion of slamming intensity. Slam 23 was 30 percent more intense than Slam 12.

The pressure at HP2, however, was about the same in both cases.

Figures 24 and 25 are informative in terms of the propagation characteristics

of the pressure wave along the hull. In Figure 24, Slam 12 appears to have a

uni-form rate of propagation from HP6 through HP2 to LP21 of 232 feet/second. Slam 23

(Figure 25), however, may have actually been two separate impacts, one concentrated

in the region from HP1 aft, and the other only at the forepeak. The apparent

simultaneous impact over a fairly large region is probably the reason why Slam 23 caused a more severe structural response in the hull.

RESULTS AND CONCLUSIONS

A. Additional analysis of frequency-of-occurrence data showed considerable

variation in goodness-of-fit to the Poisson distribution. The general applicability

of the Poisson distribution to these severe slamming data is somewhat

questionable. _{The distribution of elapsed-time-between-slams appears to}

be overly heavy in the first group, probably due to the repeated slams

separated by one pitching period. _{Chi-squared tests of the}

goodness-of-fit of the experimental data to the truncated Rayleigh probability density function indicated a fit at the 5 per cent level for the data from 277W2.

3. A detailed correlation of slamming incidence with environrr.ntal conditions

showed the relative effects of sea state, RPM, and relative heading. _{A regression}

analysis providing the same information in the form of regression coefficients and

't" values showed that for Voyage 263W2 the correlation between slamming _{rate and}

relative heading was significant. Analyzing all three voyages together, relative

heading and draft appeared to have the most probable correlation with _{a slamming}

(36)

40 30 2 Ftgora 22 Amp13tudeTimt D1ttributOfl Slto 12 +0.1 40- 30 0.150 0.100 0.050 Figure 2J AmpliCuJe-Isscn Dlstributtoo Slats 23

Dintance from PP. feet

0.150 0.100 0.050 0 000 _-0.050 'e . -0.100 -0.150 -0.200 -0.250 -0. t00 -0.350 -0.400 / I / 36.7 P1?J/

Ii

i

/

I-I/

150 I SPI 2 11(0 '.1, I I

II

H9 11Ff. 1102 lIP!

Distance from II',

feet 2 I I ('21 lP

j

0.000 ,, -0.050 et -0.100 -5 -0.150 E. -0.200 -0.2 50 -0. 300

j-LJ

I1.5 (('12 l'ho DI'S hII'6 (50 ¡((2 31 2 1.P,1 fIgure 24 Fiperts 25 Pre.sore-1,ocdLto,t-'IIfl,c' DIstrIbution. Slsm 12

Prennssre-Lncatiot,-11r-,n DIstributIon, Sloe 23

-0.3

-0.2

-0.1

Tines, seconds

(37)

Since the relative velocity between waves and ship bow was not measured

in the trials, the velocity was estimated by using _{a crude approximation method}

from the measured pressure. _{The k-value, which gives the pressure-velocity}

rela-tionship, thus estimated was 0.053 near Station _{2 as compared with the calculated}

value 0.092.

Comparison of relative velocity values associated _{with slam impact at}

the two locations LP2Ì and HP2 showed that there _{was no consistent relationship}

between them. The relative velocity values indicated, _{as before, a threshold at}

12 feet/second. _{The average relative impact velocity}

at the two locations for a

group of 26 slams was practically identical at 22.53 _{feet/seconds.}

Midship transient ("whipping') stress was examined in conjunction with

transient acceleration and acceleration phase, _{and it was found that slamming}

occurs within the acceleration phase range 50-80 degrees, _{but that there was no}

evident correlation with midship transient stress. There was, however, a definitive

positive correlation with transient acceleration.

Two slams were examined in detail to determine if pressure-time

informa-tion would be useful. _{The results showed that in the}

case where the impact

oc-curred at all locations more-or-less

simultaneously, the midship transient stress was 30 percent more severe than in a case of progression of the impact from aft to

forward.

VIII. REFERENCES

Ochi, M. K. _{"Prediction of Occurrence and Severity of Ship Slamming} _at Sea." _{Office of Naval Research, Fifth Symposium of Naval}

Hydrodynamics, 1964.

TELEDYNE MATERIALS RESEARCH

WALTHAM, MASS.

23 AUG 72

PROjECT 1434

ANALYSIS OF SLAMMING DATA FROM SS WOLVERINE STATE

CONTRACT NSSC-N00024-72-C-5047

DETAILED MEASUREMENTS FROM TAPE 288W3, INTERVAL 57

AVG WAVE PERIOD 5 SEC

AVG WAVE LENGTH 100 FT

AVG SWELL HT 20 FT

AVG SWELL LENGTH 100 FT

SWELL

DIRECTION SW TRUE

BAROMETER 29.84

SEA TEMP 59F

AIR TEMP 58

WEATHER OVERCAST

FWD DRAFT 16,5 FT

HOVE TO IN SW GALE

-28-MARCH 3. 1969

LOGBOOK DATA

0100 GMT

POSITION APPROX 41.6 DEG

NORTH,

RPM 46.8

61 DEG

WIND

WEST, COURSE

215 DEG

AVG SPEED 2 Kl

SPEED 43 Kl WIND DIRECTION SW TRUE

(39)

DEcINITIONSOF PARAMETERSMEASURED FROM OSCILLOGRAPH RECORD

NO. --- ABßREVIAT!ON DESCRIPTION --UNIT

-DURATiON OF EMERGENCC INCH

2 PSU3ST STATIC PRESSURE DIVISIONS

---3--

-PSUBTR

_{TRANSIENT PRESSURE} _DIVI5I0NS

4 PSUBSM STAGNATION PRESEURE DIVISIONS

P ---- RE-ENTRY PRESSURE CHANGE DIVISIONS

6 DEL T RE-ENTRY TiME CHANGE INCH

-7- ----TSUUREL

SLAM TIME REF LP21 SLAM - INCH

8 TSUBDT TRANSIENT PRESSURE DURATION INCH

---9--- ---ASUBST _{STATIC ROW ACCELERATION} _DIVISIONS

lo

._-

ASURTR TRANSIENT 130W ACCELERATION DIVISIONS

SSURWB -- - STATIC WAVE BENDING STRESS _DIVISIONS

12 SGURTR TRANSIENT WAVE BENDING STRESS DIVISIONS

13---...SSUQT - - TOTAL WAVE BENDING STRESS _DIVISIONS

14 PHASE SLA PHISE FROM HOG PEAK DEGREES

15 --- DEL ST ---'--- ADDITIVE PART OF SLAM STRESS DIVISIONS

16 SSURWH P-T WHIPPING STRESS DIVISIONS

VSURA ...INTEGRATED ACCELERATION....- DIV X TIME

---DEFINITIONS OF DERIVED PARAMETERS

18 V R E L -PSUBOC

CONSTANTS ...

O"E INCH-HORIZONTALLY ON OSCILLOGAPH RECORD EQUALS 2.5 SECONDS

RHO FOE SEA WATER EQUALS 200 POUNDS-SEC-SQ

or<

FEET 4TH

ACCELERATION OF GRAVITY EQUALS 32.2 FT/SEC/SEC .

XUCR ---L-P2

---CALiBRATION DERIVATION

HP2

5

HP9 HP12 BOW ACC STRESS

HP1

TRACK 1 10 5 6 9 13 3 11

CL DIV

19.4 23.4 35.0 34.3 34.2 33.8 27.9 36.1

CAL SLAM 15.7 3.4 7.3 9.3 1.6 3.5 15.0 37.0

RUN SLAM 16.7 3.2 13.6 9.5 2.1

58

8.7 37GO

UN CAL 19.9 22.0 65.2 35.0 44.9 56.0 13.5 36,1

CAL AMP

25O

175.0 175.0 175.0 175.0 175.0 1.0 10.0

CAL UNiT PSI PSI PSI PSI PSI PSI G KPSI

UNITS/DIV l26 7.95 2.68 5.00 3.90 3.12 0,07

027

-VELOCiTY FROM -DEL P, DEL T. ...

RHO. AND G FT/SEC

STAGNATION PRESSURE FROM

(40)

LP 21 (or HP2) vs. Time i' 2. PSUBST Static Pressure 1. TSUBE Duration of Emergence Stagnation Pressure (Measured)

j

4. PSUj

/

!___________ _I

6. DEL

Re-entry Time Change

DE FIN ITIONS OF OSCI LLOGRPPHI C MEASUREMENTS Figure A-1 -30-LP 21 Pressure vs. Time -Ic-5. DEL P Re-entry Pressure I Change

(41)

HP i HP 2

Ressure

3. PSUBTR

f

Transient PressureU 3. PSUBTR

4

i ¡

-

8 TSUBDT

-

i....TSUBREL

u

8. TSUBDT Transient Pressure

Duration

TSUBREL Slam Time

Referred to LP21 3. PSIJBTR

L

i 8. TSU[3DT I

7

TS[JDREL IP 6, 9, 12 _{3. PSUBTR} ?'3

DEFIITrONS CF OSCILLOCflPH

_MEASUCETS

Figure 14-2

(42)

13. SSUBT

11. SSUBWB

Static Wave Bendinq Stress

Midship Bending Stress

vs. Time

SSUBT = Total Wave Bending Stress

1/2

Midship Bending Stress

vs. Time

15. DEL ST Additive Part of Slam Stress

12. SSUBTR

Transient Wave Bending Stress

DEFINIT ONS OF OSCJLLOGRAPH MEASUREMENTS

Fioure A-3

-32-Slam Phase from Hog Peak

(43)

9 ASUBST lO. ASUBTR

Static Bow Transient Bow

Acceleration Acceleration

1r

17. VSUBA

Integrated Acceleration

DEFINITIONS OF OSCILLOGRAPH MEASUREMENTS

Figure A-4

(44)

00 VOlL

FRON OIL P OVES DEL T

TINES 09E OVER RHO 0 G VRIL (GUAU

25.41 FT/SEC

---'---00 PSU---'---000

FROH SSO

ORTI. 1126910 OVER ToD,

CALCULATES STAGNATION PRTOSUQE IGUALO 7.1V PST. COMPARE 91114 P00059, HONOURED STAGNATION P9055300 (.0 01.69 51.614 90. 1 TASLE O DATO TASLI I

DATA CONVERTED TO (96191(9196 UNITS

RAW

31J002 PROM COCILL069APV RICORDO

OP N NP 12 STISS NO. #00 UNII LP 21 VP 0 HP 2 VP 6 HP 9 HP 12 0066CC 51510$ NO. NOR UNIT LP 20 VP 1 VP 2 OP 6 0066CC O TSUNE SEC 0.60 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1 T5U0E IN 1.07 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2 P51)051 PSI 04.74 0.00 0.00 0.00 0.05 0.00 0.00 0.00 O P1005? DIV 11.70 0.00 0.00 0.00 0.00 0.00 0.00 PSURIR P01 0.01 16.69 26.07 0.00 0.00 0.00 0.00 0.02 O P5UVTR DIV 6.62 2.10 6.90 0.00 0.00 0.00 0.00 4 P53509 PST 3.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 8 #56009 01V 2.00 0.00 0.00 0.00 0.90 0.00 0.00 0.00 SEI. P P01 22.30 0.00 0.00 0.00 0.00 0.00 0.00 0.02 DEL P 01V 17.70 0.00 5.00 0.00 0.00 0.30 0.00 0.00 6 OIL 7 SEC 2.44 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6 DEL T IO 0.90 0.00 0.00 0.00 0.00 0.00 0.00 0.00 7 TS0900L SEC 0.00 -0.10 -0.10 0.30 0.00 0.00 0.30 0.00 7 ISUOREL 15 0.00 -0.04 -0.04 0.00 0.00 0.00 0.00 0.00 150601 SEC 0.15 0.00 0.07 0.00 0.00 0.00 0.00 0.00 TSJRDT IN 0.06 0.04 0.00 0.10 0.00 0.00 0.00 0.00 9 650651 5 0.00 0.00 0.00 0.00 0.00 0.50 0.13 0.00 O ASUSST DIV 0.00 0.00 0.00 0.00 0.00 0.00 10.00 0.00 10 #50019 5 0.00 0.OU 0.00 0.00 0.00 0.00 0.29 0.00 10 6506TO 01V 0.00 0.00 0.00 0.00 0.00 0.00 4.00 0.00 10 SSUMOR (PII 0.00 0.00 0.00 0.05 0.00 0,00 0.00 0.49 11 553569 DIV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 15.70 12 5505TO (P50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 12 053009 DIV 0.00 0.00 0.00 3.00 0.00 0.00 0.00 2.90 13 5SUST (PSI 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6.01 10 SOuRI DIV 0.00 0.03 0.03 3.00 0.00 0.00 0.00 21.70 14 PHASE 0ES 0.00 0.00 0.00 0.05 0,00 0.00 0.00 39.60 14 OSASE 305 0.00 0.00 0.00 0.00 0.00 0.00 0.00 39.80 10 DEL ST (PSI 0.00 0.00 0.00 0.00 0,20 0.00 5.00 0.00 00 DEL 51 DIV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 16 15996V (P50 0.00 0.00 0.02 0.00 0.00 0,00 0.00 0.6 16 552969 DIV 0.00 0.00 0.00 3.00 0.00 0.00 0.00 2.90 07 USURA F510 0.00 0.00 0.00 0.00 0.00 0.02 7.00 0.00 17 SOUSA DXI 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 -96.69--NO. PARAMETERS I TASLE 3 31915(0 55. VRIL

PRO' DOL P 03(9 20.30 FT/SEC FR09 OVO 9 0000.

DEL T

715ES ONE OVER RAD 0 5, V#EL £SIJALS

-- ----

TWO.

CALCULATED STAGNATION

ROTS P5u059, MEASURED

19 P1UOSC

SQUARED OVER --2.01 -PSI.-COMPARE

TARLI 0

SLAP 90.

P61503RE E051ALO STAGNATION P015SURE

2

SLOP ND.

Z

1601.1

0

DAlA CONVERTED TO (961010919G UNITS

RAW DATA 6(6005(0 FRON 0001LLOGRVPN RICORDO

VP 6 HP NP 12 NO. ARO UNIT LP 20 VP I VP 0 VP 6 9F 9 VP 12 0096CC STRESS NO. ARR UNIT LP Dl HP i NP S 5096CC 1700(1 0.00 0.00 0.00 1 1559E SEC 2.97 0.00 0.00 0.00 0.00 0.00 0.00 0.00 O TSUOE IN 0.19 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.00 2 PDAOST P01 14.61 0.00 0.00 0.00 0.00 0.00 0.00 0.00 O FlUSSI 00V 11.60 2.00 0.00 0.00 0.00 0.00 3 PSURT9 P51 9.90 ¡0.90 12.06 0.00 0.00 0.00 0.30 0.00 O P50800 DIV 7.50 2.00 4.00 0.00 4 P150534 P51 4.66 0.00 0.00 0.50 0.00 0.00 0.00 0.00 4 P50959 DIV 1.70 0.00 0.00 0.00 0.00 0.00 0.00 0.00 DEL P PSI 03.94 0.00 0.00 0.05 0.00 0.00 0.00 0.00 0 OIL P DIV 19.00 0.00 0.20 0.00 0.00 0.30 0.00 0.00 0.00 0.00 0.09 6 DEL T SEC 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0,00 6 OIL T IV 1.00 0.00 0.00 0.00 0.00 7 T208REL SEC 0.00 -0.22 -0.39 0.00 0.00 0.00 0.00 0.00 7 TOUO30L IV 0.00 -0.09 -0.18 0.00 0.00 0.00 0.00 0.00 0 TNIJVDT SEC 0.00 0.10 0.17 0.00 5.00 0.05 0.00 0.00 R TSUOOT 16 0.06 0.04 0.07 0.00 0.00 0.00 0.00 0.00 W AlUNiT G 0.00 0.00 0.00 0.00 0.00 0.00 0.72 0.00 9 653951 DIV 0.00 0.00 0.00 0.00 0.00 0.00 ¡0.00 0.00 10 ASURIR 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 10 ASUOTR DIV 0.00 0.00 0.00 0.00 0.00 0.00 0.12 0.00 11 5508VO (PSI 0.00 5.00 0.00 0.00 0.00 0.00 0.00 8.10 11 OSUNAS 01V 0.00 0.00 0.00 0.00 0.00 0.00 0.00 lt.00 12 SSUOTR (P51 0.00 0.00 0.00 0.00 0,00 2.00 0.00 1.00 52 550019 DIV 0.00 0.03 0.00 0.00 0.00 0.00 0.00 0.70 13 55301 IPSO 0.00 0.00 0.00 0.00 0.20 0.00 0.00 0.33 19 55391 DIV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 20.20 14 PAASE 3ES 0.00 0.00 0.00 0.00 0.00 0.00 0.00 24.00 14 PUASE DEi 0.30 0.00 0.00 0.00 0.00 0.00 0.00 28.00 0.00 10 DEL OT (251 0.00 0.00 0.00 0.00 0.00 O.00 0.00 0.00 19 DEL 01 DIV 0.00 5.00 0.00 0.00 0.00 0.00 0.00 IA 5559A9 (PST 0,00 0.03 0,00 0.00 0.00 0.00 0.00 0.56 16 550960 DIV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.20 17 VSUO4 F510 0.00 0.00 0.00 0.00 0.00 0.00 6.20 0,00 17 VUUOA DXI 0.00 0.00 0.00 0.00 0.00 0.00 9.00 0.00 --ALAM90,---2---IAOI.E-0 -Ù00lv(9 PARAMETERS