Returning again to the surge force spectrum ( Fig. 5 ), above 1.5 rad / s the complete second order solution spectral values are smaller than those of no free surface forcing and Newman’s approximations. Above 5 rad / s the no free surface forcing approximation results increase and become much larger than the complete solution results. Hooft’s based method gives similar results to the other approximations below 1 rad / s, but it over predicts the surge slow drift force for difference frequencies above 1.5 rad / s. In fact, Hooft’s based method largely overestimates surge QTF as the difference frequency increases above around 1.5 rad / s (see Figs. 6 and 8 ), which means the second order scattering potential cannot be neglected.