ARCHL
THE FACULTY OF ENGINEERING, KYUSHU UNIVERSITY FUKUOKA, JAPAN
COUPLED MOTIONS AND MIDSHIP BENDING MOMENTS OF A SHIP IN REGULAR HEAD SEAS
( ABSTRACT ) BY JUN-ICHI PUKUDA MARCH
1963
tab.
v.
ScheepsboiwkunJe
Technische Hogeschool____
Deift
ICoupled Motions and Midship Bending Moments of a Ship in Regular Head Seas (Abstract)
Jun-ichi Fukuda
1 Introduction
In the latest papers , the author has given the theory to
evaluate the motions and the bending moments of a ship in regular head seas, and shown the example of the numerical calculation for
T2-SE-Al tanker. In the process of calculation the equations of
motions
(I)
are solved first, and then the bending moments are calculated by using the solutions of the equations (1). If it is possible to assume that the ship form and weight distribution are approximatly symmetrical about the midship and that the effects of ship speed on the motions and the midship bending moments are not too much, the thidship bending moments are influenced much by heaving and little by pitching motions. Therefore, it is simplified to calculate the approximate midship
bending moments by the avobe assumptions. In this paper ,the author investigated the effects of the unsymmetry of ship form and the
forward speed of ship on the mot±ons and furthermore on the midship
2 Effects of the shipform's unsymmetry and ship speed on the motions and midship bending moments
The coefficients of miscellaneous terms of equ.ations (1) a,b,...; A,B...and G;the exciting forde F and the exciting moment M include the
following terms:
the terms based on the unsyrnmerty of the ship form arid the weight distribution
the terms based on the ship speed
With respect to (b), the terms including the ship speed V are con-sidered and the effects of the change of circular frequency of en-counter due to the change of speed are not considered.
Ignored the terms of (a), d, D and G vanish and the equations of motions are expreBsed in the form of
a
(S)+ b
(S),+
(V= F
CS)A+B+CP+E
=
Ignored the terms of (b) furthermore, e , g and E vanish and
the equations of motions are expressed in the form of
a+b°. +c'
=
(3)
+
+
=
The equations of motions (i) or (2) are the coupled equations of the heaving and pitching motions, but each of the equations
(3)
is theindependent equation of heaving or pitching motion. The author treated the following three cases:
2
}
strictly considered with (a) and (b) assumed the symmetrical ship ignoring (a)
assumed the symmetrical ship and neglecting the effects of ship speed - ignored (a) and (b)
and called the case (i), (ii) and (iii) respectively, "coupled
calcu-lation", "symmetrical calculation" arid. "uncoupled calcution". The ship
motions and the midship bending moments in the three cases were calcu-lated and the calcucalcu-lated results were compared with each other.
Differences between the coupled and the symmetrical calculation indi-cate the effects of unsymmetry of ship form and weight distribution, and those between the symmetrical and the uncoupled calculation indi-cate the effects of the ship speed.
3 Results of Calculations
The coupled, symmetrical and uncoupled calculation were performed for the full load condition of T2-SE-Al tanker. Her main particulars of fore and aft body are shown in Table 1, which correspond to (A)
condition of weight distribution in reference (1). The coupled calcu-lation was performed for (A) condition, and the symmetrical or the uncoupled calculation was parformefi for the assumed ship form having
the means of the geometrical values of fore and aft body about midship. Calculated results are expressed in the same non-dimniensional values as those in the reference (1).
(i) Coefficients of miscellaneous terms of eQuations of motions
In Fig. la ld, the coefficient" of miscellaneous terms of
equations of motions (1) are shown. Miscellaneous integrated values of
PS (
additional mass for section ) and N ( damping coefficient for section ) for the fore and aft body are shown in Fig 2a and 2b.Exciting forces and rnoments
Exciting forces and moments derived from the coupled, symmetrical and uncoupled calculation aje shown in Fig. 3a - 3d.
Ship motions
Heave and pitch derived from the three kinds of calculations are shown in Fig. 4a s- 4d and 5a "-' 5d.
Midship bending moments
Midship bending moments derived from the three kinds of calculations are shown in Fig. 6a
4 Conclusions
Compared with the derived results from the coupled, symmetrical and uncoupled calculations each other, the following conclusions were
conducted.
The effects of the unsymmetry of ship form and also the ship speed
on the coupling between the heaving and pitching motions can not be neglected. The coupling effects by e, g and E are important.
The effects of the unsymmetry of ship form and the ship speed on
the exciting forces are more than those on the exciting moment. So far as the coupling effects between the heaving and pitching motions are concerned, the effect on the heaving motions is more than that on the pitching motions.
The effects of the unsymmetry of the ship form and the ship speed,
and the effects of coupling of the heaving and pitching motions on the
midship bending moments cannot be ignored except the case of a ship
going with low speed. V
These conclusions were derived from the calculated results for T2-SE-Al tanker whose ship form is not too much unsymmetrical and speed
C
C
destroyers etc, whose ship form are more unsymmetrical, the effects of the unsymmetry of ship form and the ship speed on the motions and the midship bending moments will be more considerable.
References
J..Fukuda:"On the Midship Bending Moments of a Ship in Regular Waves" JSNA of Japan No.110 (1961)
J.Fukuda:"On the Bending Moments of a Ship n Regular Waves
-Longitudinal Distribution of the Bending Moments" JSNA of Japan
No.111 (1962)
J.Fukuda:"Coupled Motion8 and Midship Bending Moments of a Ship in Regular Head Seas" JSNA of Japan No.112 (1962)
03 0l 0 -- 02 - 03 Fig. ii 0.2 Fig. 1C Fig. 2 a 0.3 t7L. /L.. _05 S --Fig. lb Fig. 1 d Fig. 2b 6
Table I Main Particulars of Fore and Aft Body
Total Fore Body Aft Body
Weight W 0.504W 0. 446W
C. G. from midohip 0.0041. 0.188L. -0.183L
Mt. of inertia of wt. about midahip I 0. 513 II 0:48711
Buoyancy 0.506A 0.494k
C. B.from midahip 0.004L 0.199L -0.1961.
Water plane area A.. 0. 483A. 0. 517A..
Centre of w.p. area from nudahip -0.014 L 0.024 L -0.2181..
Fig. 3 a
Fig. 3 c
Fig. 3b
Fig. 3d
7
E XCI TING FORCE AND MOMENT o.4 I 0.2 0 COUPLEO ---SYMMETRIC ----UNCOUPLED - -I;-______________________ I
- -
. I,0 PH4SE ANGLEfl_ L.
-0 0.1 .- 0.2 0.3 EXCITING FORCE AND MOMENT 04 0,z 0 COUPLED ---SYMMETRIC ----UNCOUPLED ---.-__ I 90 PHASE ANGLE o 0,1 r. 0.2 0.3 EA'C/TING FORCE AND MOMENT 0.4 0.2 0 COUPLED -- - SYMMETRIC ----UNCOUPLED1 I -1R0 PHASE ANGLE 0 0.! F,.-- 0.2 0.3 EXCITING FORCE AND MOMENT 04 0.2 I, . . - . -COUPLED SYMMETRIC ----UNCOUPLED !80 PHASE ANGLE- .-0'.
0 0.1 Fr 0.2 0.3Fig. 4 a Fig. 4C Fig. 4b Fig.4 ci 1.50 f.00 HEAVING AMPLITUDE -- COUPLED SYMMETRJCj ----UNCOL/PLEOI . .- . ---=O.73 PHASE ANGLE 0.! F.. 0.2 0.3 1.50 1.00 HEAViNG AMPLITUDE
--
L /00 COUPLED -SYMMETRIC UNCOL/PLED PHASE ANGLE 1.50 I, HEAVING AMPLITUDE --= 1.25 COUPLED ---SYMMETRIC UNCOUPLED -180 PHASE ANGLE OOIF-.-02
03 l.0 0.50 1, HEAVING COUPLED AMPLITUDE -' =1.50 .YMMETPIC UNCOIPLEDl/Z/V
-1-!801o.
PHASE ANGLE O 0 I F-. Q.Z 03Fig. 5 a Fig. 5C Fig. 5 b Fig. 5d I.S.O I. 0 0 P1 rcH/NG -. COUPLED AMPLI T1/OE -- = 1.00 TRIC
1!
Sr*44E UNCOUPLED-lee-
PHASE ANGLE -o a! Pr. 02 1.0 a PITCHING AMPLITUDE -= 0.75 COUPLED SYM*4ETRIC UNCOUPLED 180'IA
PHASE ANGLE o 0.1 P-.-0.2 a3 Lie 0 nirH AMPLITUOE - 150 COUPLED r//
----Sral*fTRrC I 110 PHASE ANGLE o øt Pp. 0.2 1.10 PITCHING AMPLITUDE --L!25
COUPLED.srfMETR1c
- - - - UNCOUPLED o a 02 CSFig. 6 a Fig. 6C Fig. 6b Fig. 6d
