Tools for Semi-planing / Semi-displacement Ship Design with Applications

A numerical re-formulation of Marou’s integral for slender body analysis of calm-water planing hydrodynamics with gravity wave-making is developed. Numerical computations are performed first for a flat triangular planing plate. The triangular planing plate has been the subject of previous work with the base Maruo theory. The comparisons are supportive of the formulation for performing wave lift and drag calculations for realistic planing craft configurations. An analysis is performed of the US Navy NSW 10 meter RHIB, for which some limited full scale measured data was available. Predicted boat trims versus speed are compared to measured values. The comparison is positive, even to the point of the prediction of lower speed, pre-planing “hump region” characteristics, which has never been within the reach of the traditional zero-gravity planing models. The code written also performs the zero gravity (infinite Froude number) computation as the limiting case. This allows relative evaluation of wave effects. The remarkable prediction, in the case of the Navy RHIB, is that while a wave resistance component does occur at finite Froude number, the overall resistance with wave making is reduced relative to the zero gravity prediction. This is because the lift of the boat generated wave system produces a favorable change in the boat running attitude. The effect is reduced transom draft and reduced trim. This combines to reduce the superposition of the other resistance components of spray, induced, and viscous drag more than that added by waves. This result is argued to be not too implausible in consideration of the different mind-set required in consideration of the hydrodynamics of planing craft, relative to that of displacement craft.