Pitching and heaving motions and hull bending moments of a T2-SE-A1 tanker model in regular waves

Technsche Hogesc:.'

Ddft

PITCHING AND HEAVING MOTIONS AND HULL BENDING MOMENTS

OF A T2-SE-A1 TANKER MODEL IN REGULAR WAVES by John F. Daizell and Naresh M. Maniar

INTRODUCTION

This note presents supplementary analysis of data obtained in tests of a T2-SE-A1 tanker model in regular waves of model length and moderate height*. _{Motions and phase data is given for the test labeled lA, Model}

1919. 1, CB = 0. 74, in the original report. This work was carried out by

the Davidson Laboratory. in order to participate more fully in international comparisons of data obtained in different laboratories.

The additional data analysis provides:

Double amplitudes of pitching and heaving motions, Phase relationships of pitching, heaving and bending

moments to waves,

The bending moment range data of the original report in non-dimensional form.

*t!Effect _{of Speed and Fullness on Hull Bending Moments in Waves'T,}

by Dalzell, J. F.; E. T. T. Report 707, 1959.

N-637

-1-NOMENC LATURE

B Maximum beam

h Wave height

L Length between perpendiculars

Weight density of water 2Z0 Double amplitude of heave

Double of amplitude of pitch ' Maximum wave slope

Moment Range = Sum of hogging and sagging bending moments Mom. range

C

(4

V _{Froude number based on length between perpendiculars (L)}

RESULTS

The results are presented as functions of Froude Number as follows:

Fig. 1, Nondimensionalized double amplitude of pitch, (2 O)

2 Z0

Nondimensionalized double amplitude of heave,

Fig. 2

Fig. 3, Phase lags of:

Maximum bow up pitch Maximum up heave Sagging moment (After wave crest at LCG)

A numerical summery of the experimental points and offsets of

the faired curvesare given in Table 1 and Table 2 respectively. Ship

arid model characteristics are reproduced in Table 3.

TABLE I

EXPERIMENTAL POINTS

TABLE 2

OFFSETS OF FAIRED CURVES

N-637

Phase Lag in Degrees With Reference to Wave Crest at LCG Number ZZ0/h 2./2U C Heave Pitch Bend. Mt.

0 .140 .414 .0178 324 306 200 .025 .165 .437 .0181 328 306 200 .05 .215 .478 .0187 335 306 200 .075 .300 .530 .0196 347 308 199 10 . 432 . 585 . 0207 0 313 198 125 .. 623 . 647 .0220 17 325 196 150 . 672 . 700 .0220 36 340 192 175 . 645 . 736 .0202 57 355 187 .200 .578 .745 .0196 81 12 180 .225 .480 .706 .0186 107 29 173 Froude Number Heave Double Ampi. Pitch Double Ampi.

2j2t

Phase Lag in Degrees With Reference to Wave Crest at LCG

Heave Pitch Bend. Mt.

0 .140 .414 .0178 324 306 200 .O966 .409 .573 .0206 6 308 204 .1288 .634 .678 .0222 14 328 186 .1392 .688 .696 .0228 26 337 193 .1609 .623 .639 .0211 50 356 187 .1714 .636 .676 .0203 50 352 188 .1923 .629 .773 .0199 78 9 185 .2245 .484 .668 .0186 103 27 173

503.0 513.0 68.0 30.0 21,770 T.

2.26 0. 7Li. 0.98 1.70 0i40 Ed.

22.8 LBP (ft.) INL. (Ft.) Beam (Pt.) Draft (Ft.) Even Keel

Displacement BAT Ch ./.(L/ioo)3 LCB,. °/o LBP

From Amidships Oyradius, o/ LEP Natural Pitching Period, Sec. Natural Heaving Period, Sec.

Natural frequency of Vertical

) .80 h .88 0. 648 0.286 Il..O2 LB. (F.w,) 2.26 0.7t. 0.98 170 0.140 Fwd, 22.8 0.721 0. 78Ii i. 80 L. 86 0. 61.8 0.286 3tLB. (F.w.) 2.26 0.8b 0.989 18L 2.D Fr.qd. 23.9 0.760 0.779

Two Noded Vibration

Model Freeboards:

Ftd. (in.) _{Aft. (in.)} 13.96 cps 3.15 2.37

13.63 cps 3. 19 2.30

Weights, Centers and (yradii of

Half Models:

Forward Part:

Weight., pou.nds LCO, inches fwd. Cyradius,,

O/

LBP/2

21.03 11.08 23, ) 23.95 12.19 25.0

After Part:

Weight, pounds LCG, inches aft. (yradius,

O/ LBP/2 19.99 11. ]J. 2)...6 20.39 U. 18 2). .5 TABLE 3 (From E. T. Report 707)

TABLE OF CHARACTERISTICS OF MODELS AND SHIP

Scale

(Based on T-2-SE-A1 Thnker)

.1/lOS

Ratios: Length, ].OS; Volume, 1,157,625;

Displacement, 1,188,809; Speed, 1O,21L'7

MJ

VALUES

Fufl Size T-2-SE-A1 Tanker Model Number Derived

from:

1919.1

T-2-SE-A].

1919.2

L0

0

0

NUMBER

)

FR0UD NJBER

FIG. 1

- 5

0.10

0.15

0.20

0.2c

0&N

0.10

0.20

0.2

000

o.oio

0.005

FP0U0 NUMBER

bEtDING

MOMENTS

0.0

0.20

40

u'o

_NUMBER

FG3

KEkVE

-Co

O.IS

0.20