Effect of surge motion on the vertical responses of ships in waves

The paper investigates the effects of the surge hydrodynamic forces and surge mode of motion on the vertical responses of a container ship and a chemical tanker in waves. A partially body nonlinear time domain code based on strip theory is modified to include the surge mode. The Froude-Krylov and hydrostatic forces are calculated for the exact wetted surface area of the hull for each time instant. Certain practical engineering techniques are used to overcome the 2D limitations imposed by strip theory in order to include the surge. Surge hydrodynamic coefficients are calculated using conformal mapping technique and surge Froude-Krylov forces are calculated for instantaneous wetted surface. Surge radiation forces are calculated based on Cummins formulation. The analysis is done for the S175 container ship and a chemical tanker in head seas for a range of wave steepness and Froude numbers. The effect of surge on the transfer functions and the peaks values of the vertical motions and vertical bending moment are analyzed. The numerical results are compared with the experimental results. It is observed that longitudinal forces reduce the vertical bending moment about the transverse axis at deck level for the wave frequencies of interest.