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.
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Abbreviations
- 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(φ,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)
- β :
-
angle of drift (rad)
- δ :
-
rudder angle (rad)
- λ :
-
wavelength (m)
- ξ :
-
position of the ship in the earth-fixed system (m)
- ρ :
-
water density (kg/m3)
- φ :
-
angle of heel (rad)
- ψ :
-
heading angle (rad)
- ω e :
-
frequency of encounter (rad/s)
- 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
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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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Spyrou, K.J. Surf-riding and oscillations of a ship in quartering waves. J Mar Sci Technol 1, 24–36 (1995). https://doi.org/10.1007/BF01240010
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DOI: https://doi.org/10.1007/BF01240010