A model test was performed on a 67,000 dwt tanker. The tanker was moored in head seas fore and aft with linear springs in combinations of regular waves and current. At the initiation of each test run, the vessel was displaced and released from its equilibrium position and the resulting motions and 1ine loads were recorded. The data was analyzed to determine the effect of the wave amp1itude and frequency as well as the current on the damping factor and the added mass coefficient. The first order responses and steady drift loads resulting from the regular waves are also presented.
Moored tankers in the open ocean respond to waves at two distinct frequencies. The first frequency corresponds to the wave frequency and is caused by an applied wave load that is a linear function of the wave amplitude. The second frequency corresponds to the system's natural frequency which is typically quite different than the wave frequency (e.g., in surge) and is caused by an applied load which is proportiona1 to the square of the wave amplitude. Although this load is second order in nature and therefore quite small, the response of the system is amplified, because the load occurs near the natural period of the system. While damping plays an insignificant role in the motion at the wave frequency, it is a key deterrent to the motion at the natural frequency.
A moored system experiences damping from two natural sources, namely, material and hydrodynamic. In a single point mooring system, the material damping is, generally, small and is usually neglected in the analysis of the system. Therefore, the resonant response of the moored floating vessel is limited only by the amount of hydrodynamic damping present in the system. Thus, the magnitude of damping in waves as well as in waves and current is an important design consideration. The hydrodynamic damping appears in the form of the 1i near radiation damping, 1i near viscous damping and nonlinear viscous damping.
The loads created by the linear damping contributions are proportional to the vessel's velocity. The loads created by the nonlinear damping term are proportional to the square of the vessel's velocity. Radiation damping is linear in nature and arises as the vessel creates surface waves during motion in still water. Linear viscous damping is created by the vessel's resistance to motion in still water, current and waves. When the damping at low frequency motions associated with second order drift loads is investigated, the contribution to the viscous damping from waves is referred to as wave drift damping.
The determination of low frequency damping has been the subject of several studies. In general, experimental studies have taken precedence over theoretical analyses in determining hydrodynamic damping coefficients. The added mass coefficients may also be determined from these experiments. Generally, the added mass related to surge is extremely small compared to the vessel displacement mass and is of little consequence in the design of such systems.