16 J4N. 1973
RCHIF
lab. y. Scheepsb
Technische Ho
Deift
."On the Heaving Motion of Two Circular Cylinders on the
Surface of a FluId.T'
"On the Motion of Multihull Ships in Waves (1)."
By Makoto OHKUSU ...-,
These papers are mainly
concerned with the most fundamentalEt
problems for the theoretical treatment of the motions in waves
of multihull ships such as catamaran ships or marine
struc-tures for the exploitation of ocean resources. That is to
cal-culate the hydrodynamic forces, the amplitude and the phase of the waves diverging at infinity, when two or more cylInders,
submerged or floating in afluid, are given a swaying, heaving
and rolling oscillation about their mean position.
In the first paper a theoretical procedure to calculate
exactly the hydrodynamic pressure and the wave amplitude caused
by the oscillation of two circular cylinders with their axes
on the surface of a fluid is developed and it is shown that
the theoretical wave amplitudes are in good agreement with the measured ones obtained on the forced heaving experiments.
This procedure for solving exactly the radiation problem of two circular cylinders, however, is not necessarily convenient
to
solve the more general problems for obtaining the
hydro-dynamic forces and the waves generated due to the oscillation
of two or more cylinders with arbitrary cross sections. Then
in the second paper is proposed an approximate method which
is very effective to solve the radiation problems of such
multi-cylinders. When the hydrodynamic coefficients
(added mass and
damping coefficients etc.) for a cylinder are known, the
num-ber of the cylinders by this approximate method. And their
accuracy are thought to be satisfactory because the solutions
for two circular cylinders by the approximate method almost
completely agree with the solutions calculated exactly by the
method described in the first paper.
According to Haskind relation extended by Bessho the phase
as well as the amplitude of wave forces and moments which act
upon a body when it is held fixed on incoming plane waves can
be derived from the solutions of the radiation problem of the
body. Using this relation and the solutions of the radiation
problem obtained with our approximate methOd, the equations of
the motions of a catamaran ( Fig.B-1 ) in beam seas are
formu-lated and their solutions are in good agreement with
experi-mental results ( Fig.B-2, 3 and ), where this ship has the
same Lewis form cross section over the length and the motions
in Fig.B-2 and 3 are not of the center of gravity G but of the
point M where the motions of the ship are measured as shown
in Fig.B-1 and the viscosity of a fluid is neglected.
It may be concluded from this result that we can treat easily
and accurately as well the motion of a catamaran in waves as those of an ordinary ship by solving the radiation problem of
each section with our method and applying the strip method.
Along this approach the author is now carrying out some
calcu-lations and experiments on the seakeeping qualities of catamaran
in head seas and beam seas. In addition our approximate method
can be powerful means for the theoretical investigations of the
motion of marine structures with more complicated forms because
the method gives the hydrodynarnic coefficients for submerged
or floating multi-cylinder composed of an arbitrary number of
cylinders with comparatively simple calculations. The author is now trying to apply the method for the researches of marine
structures? motion in the sea.
's-y
Fig.B-1 Madu Ship
T
T
u
Wave
P= 720
T=180
2o=
413
-QG34
Unit mm
J)
2.0
1.0
o
o
THEORE TI CAL
o
MEASURED
KT
(seT)
Fi.-2
Viaìn1itude,çf
catanïn in
g
O0.1
0.2
0.3
0.6
0.7
0.8
0.9
1.0
0.4
0.5
4f
N
2.0
¡.0
o
MEASURED
THEORETICAL
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
KT(-T)
Fig.B-3
4f
2.0
1.0
o
o
o
o
0
0.!
o
o
o
0.2
0.3
0.4
0.5
O
MEASURED
o
o
THEORE TI CA L
0.6
0.7
0.8
0.9
¡.0
-KT=weT)
Fig.B-4 Rolling amplitude
of a catamaran in beam
sea:
