4.2. KVLCC2 pitching and heaving in head waves
The seakeeping simulations of KVLCC2 was carried out as described in Table 2. Three different conditions C1, C2 and C3 with three different wave lengths were studied. The ship is set free to pitch and heave motions. Time histories of the total resistance Fx, heave motion z and pitch angle q are obtained
from simulations. Conditions C1, C2 and C3 have frequencies of encounter of 0.761, 0.654 and 0.538, respectively. For those
computations, the similar time step value of 125 time steps per wave encounter period is used. Time histories of z and q for conditions C1, C2 and C3 are depicted in Figs. 7e9.
During the first six periods, the amplitudes of the heave and pitch motions are progressively reached its maximum values. The solutions experience a permanent response. Fig. 10 shows the computed free surface elevations for the four-quarter periods. The heave and pitch functions are approximated with Fourier Series (FS) expansions given as (Irvine et al., 2008):