The Effect of Bottom Warp on the Performance of Planing Hulls

Abstract

The hydrodynamic lift, wetted area and center of pressure of a constant beam, warped bottom planing surface were obtained experimentally for a model having a 3 deg./beam increase of deadrise from 10 deg. at the transom to 30 deg at the stem (typical for the planing area of a warped hull). Towing tank tests of this warped bottom hull were conducted over a wide range of speeds, trim angles and wetted lengths. An analysis of the data indicated that established planing equations for prismatic hulls are also suitable for this warped hull if the effective deadrise of the warped hull is taken to be that at the mean wetted length of the bottom area. Also, the effective trim angle is not the keel angle relative to the level water surface but is the angle of the ¼ buttock line (at the mean wetted length position) relative to the level water surface. Published equations for prismatic planing hulls have shown that the longitudinal position of the mean wetted length (relative to the transom) is a known function of the longitudinal position of the center of bottom pressure and the speed coefficient. It is independent of trim angle or deadrise angle. Hence, assuming that the LCG of the craft is located at the longitudinal center of pressure and the thrust moment is small, the mean wetted length is easily determined. Locating this distance on the lines plan of a warped hull identifies the effective deadrise and trim angle of an equivalent prismatic hull to be used with published planing equations. Using these observations, a procedure is provided for estimating the smooth water performance of warped planing hulls. Two examples are provided and show that the analytical results agree with model data obtained at the Davidson Laboratory. Also a comparison in made with model data obtained at MARIN on tests of a 70 ft. long warped planing hull and show equally good correlation. If the reference deadrise angle is taken to be that at the transom, it is shown that the use of warp in the planing area deteriorates the planing efficiency of the hull.