Surf-riding and oscillations of a ship in quartering waves |
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Authors: | K J Spyrou |
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Affiliation: | (1) National Research Institute of Fisheries Engineering, Ebidai, Hasaki, Kashima, 314-04 Ibaraki, Japan |
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Abstract: | The behavior of a ship encountering large regular waves from astern at low frequency is the object of investigation, with a parallel study of surf-riding and periodic motion paterns. First, the theoretical analysis of surf-riding is extended from purely following to quartering seas. Steady-state continuation is used to identify all possible surf-riding states for one wavelength. Examination of stability indicates the existence of stable and unstable states and predicts a new type of oscillatory surf-riding. Global analysis is also applied to determine the areas of state space which lead to surf-riding for a given ship and wave conditions. In the case of overtaking waves, the large rudder-yaw-surge oscillations of the vessel are examined, showing the mechanism and conditions responsible for loss of controllability at certain vessel headings.List of symbols
c
wave celerity (m/s)
-
C(p)
roll damping moment (Ntm)
-
g
acceleration of gravity (m/s2)
-
GM
metacentric height (m)
-
H
wave height (m)
-
I
x
,I
z
roll and yaw ship moments of inertia (kg m2)
-
k
wave number (m–1)
-
K
H
,K
W
,K
R
hull reaction, wave, rudder, and propeller
-
K
p
forces in the roll direction (Ntm)
-
m
ship mass (kg)
-
n
propeller rate of rotation (rpm)
-
N
H
,N
W
,N
R
hull reaction, wave, rudder, and propeller
-
N
P
moments in the yaw direction (Ntm)
-
p
roll angular velocity (rad/s)
-
r
rate-of-turn (rad/s)
-
R(,x)
restoring moment (Ntm)
-
Res(u)
ship resistance (Nt)
-
t
time (s)
-
u
surge velocity (m/s)
-
U
vessel speed (m/s)
-
v
sway velocity (m/s)
-
W
ship weight (Nt)
-
x
longitudinal position of the ship measured from the wave system (m)
-
x
G
,z
G
longitudinal and vertical center of gravity (m)
-
x
S
longitudinal position of a ship section (S), in the ship-fixed system (m)
-
X
H
,X
W
,X
R
hull reaction, wave, rudder, and propeller
-
X
P
forces in the surge direction (Nt)
-
y
transverse position of the ship, measured from the wave system (m)
-
Y
H
,Y
W
,Y
R
hull reaction, wave, rudder, and propeller
-
Y
p
forces in the sway direction (Nt)
-
z
Y
vertical position of the point of action of the lateral reaction force during turn (m)
-
z
W
vertical position of the point of action of the lateral wave force (m)
Greek symbols
angle of drift (rad)
-
rudder angle (rad)
-
wavelength (m)
-
position of the ship in the earth-fixed system (m)
-
water density (kg/m3)
-
angle of heel (rad)
-
heading angle (rad)
-
e
frequency of encounter (rad/s)
Hydrodynamic coefficients
K
roll added mass
-
N
v
,N
r
yaw acceleration coefficients
-
N
v
N
r
N
rr
N
rrv
,N
vvr
yaw velocity coefficients K. Spyrou: Ship behavior in quartering waves
-
X
u
surge acceleration coefficient
-
X
u
X
vr
surge velocity coefficients
-
Y
v
,Y
r
sway acceleration coefficients
-
Y
v
,Y
r
,Y
vv
,Y
rr
,Y
vr
sway velocity coefficients
European Union-nominated Fellow of the Science and Technology Agency of Japan, Visiting Researcher, National Research Institute of Fisheries Engineering of Japan |
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Keywords: | surf-riding nonlinear wave ship motion stability chaos |
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