This paper treats the rolling of a ship of a moderate size relative to the wave by a similar method as Prof. Kriloff did, but it is endeavoured to get a more accuracy for approximation, and several new results are obtained. At first, the general equations of motion are deduced retaining the terms of order γ
0/
R compared to unit, but as these are too complicated for practical use, gentle waves are taken as a first approximation for analysis. Moreover, a simple ship form is taken instead of real one for the convenience of the deduction of practical formulae,
i. e., the cylindrical form with the section of the load water plane, but the draft being modified so as to give the probable results.
Important results are those :
1. Equations of motion of centre of gravity of a ship are written;
V0/
gd2Xg/
dt2=_??_
wAwh'
A sin ω
t-_??_
wAwMθ cos ωt.
V0/
g d2yg/
dt2+
Awyg'=γ
0Aw [
B-
h'/
RA] cos ω
t-_??_
wAwMθ sin ω
t …… (1)
where
A_??_
e3γ [1-αβ/2-β
2/6
A3/
A1]
B_??_1-β
2/6
A3/
A1M=
bβ [
A3/3
A1-α
2/2],
A1=1-1/
n+1,
A3=1-3/
n+1+3/2
n+1-1/3
n+1.
If θ is small, the 2nd terms of the right-hand sides can be neglected, and
xg and
yq are obtained as
xg=-γ
0A sin ω
t.
yg=
a+γ
0 [σ
d2B-ω
2A] /σ
d2-ω
2cos ω
t=
a+
r0B-
h'/
RA/1-
h'/
Rcos ω
t.
these show that the path of
C. G. of the ship is elliptic, major axis being vertical, and the motion is less as the
C. G. lies higher. The draft is much more influential than breadth for this motion.
2. When the rolling is considerable such as in a synchronous one, 2nd terms of thé right-hand sides of (1) are not negligible, and, by inserting θ=θ
o sin (
tω-δ), approximate solutions can be got. By these substitutions, a constant term _??_
wAw/2γ
0θ
0 sin δ appears in both equations, positive in the first and negative in the second.
The positive constant term in the first means a drifting force in the direction of wave propagation, though, in the second, the constant term only changes the origin of the vertical oscillation. This drifting force was shown by Dr. Suyehiro's experiment, though owed to the quite different cause. By inspecting
M, it will be seen that the drifting force is positive for a broad and shallow ship, and is negative for a narrow and deep one, which phenomena can be simply tested in the experimental tank.
3. By rejecting the terms of order γ
0/
R, the equation for rolling is;
Id2θ/
dl2+
Wmθ=_??_
wρ
gKsin ω
t+_??_
wρ
gθ·
Q cos ω
t…… (2)
where
K=2
R∫
l0dε∫
ξ0-ξ
0ξsin ξ/
Rdξ-∫∫∫
v0e-η/R (ξsinξ/
R+ηcosξ/
R)
dv
抄録全体を表示