Planing in Shallow Water at Critical Speed

This article summarizes experiments to determine the effect of shallow water on flat-bottomed prismatic hulls towed fixed in heave and trim over a wide range of speed regimes. The experimental design allowed for the separate measurement of pressure forces normal to the bottom and viscous forces tangential to the bottom. The experiments showed that below a depth Froude number of unity (subcritical speeds), shallow water resulted in a reduction in pressure forces on the bottom of the hull. Around a depth Froude number of unity (critical speed), a solitary wave formed at the model, increasing the wetted length and also increasing the bottom pressure forces, which became unsteady. Above a depth Froude number of unity (supercritical speeds), the pressure forces on the bottom of the hull were greater in shallow water than in deep water. Observations of the inception of transom ventilation showed that full ventilation occurred at lower Froude numbers in shallow water and that trim has a strong effect on transom ventilation at all water depths. To assist in explaining these effects, each of the forces acting on a flat-bottomed hull are discussed and it is shown how they vary with speed and water depth. The observed trends from these fixed model tests are in qualitative agreement with experiments with free to trim and heave models as well as two-dimensional theories of planing in shallow water.