Inertia Coupling Effects In The Motions Of Ship-Shaped Bodies

Basically, two different methods exist for motion prediction of floating bodies, model tests and numerical simulations. Combining the two methods; using model test results to determine hydrodynamic coefficients and to calibrate numerical models, and performing parameter variations by means of numerical simulations may give the most cost-effective analysis. The ultimate success of this approach depends on the effectiveness of the numerical (mathematical) modeling. Most numerical models predict first-order excitation and response with sufficient accuracy. However, with regard to second-order effect, there are variations both in excitation forces and the damping models. Normally, the second-order (low-frequency) motions are assumed to be uncoupled from the first-order motion this assumption is not generally valid, and that may be the reason why, for supply vessels moored in linear springs, large discrepancies have been observed between model test results and numerical simulations. This paper presents a numerical model where the equations of motion are simulated in the time domain in 6 degrees of freedom. Wave excitation forces and moments are modeled to second order, while the equations of motion are given in their genuine non-linear form. By numerical simulations, it is demonstrated that important contributions to the low-frequency yaw motion for both the supply vessel and a production tanker is the inertia coupling between roll and pitch motions. The instantaneous yawing moment is approximately proportional to the product of roll and pitch velocities. These observations agree well with model test results for a supply vessel, where these coupling effects are included in the measured wave drift moments. To the authors' knowledge, the magnitude of this coupling effect has not been demonstrated before. A consequence of this effect is that in order to reduce the low-frequency yaw motions, it may become necessary to reduce the roll motions.