Preliminary Numerical Study of a New Slender-Ship Theory of Wave Resistance

Abstract

Results of various numerical calculations of wave resistance designed to evaluate the new slender-ship approximations obtained in Noblesse [1]3 are presented. Specifically, three main wave-resistance approximations are evaluated and studied. These are the zeroth-order slender-ship approximation r(0), which is compared with the classical approximations of Hogner and Michell; the first-order slender-ship low Froude-number approximation rIF(1), which is shown to be practically equivalent: to the Guevel-Baba-MaruoKayo low-Froude-number approximation rIF; and the first-order slender-ship approximation r(1), which is evaluated for the Wigley hull and compared with existing experimental data, corrected for effects of sinkage and trim, and with numerical results obtained by using the theory of Guilloton, the low-speed theory, and Dawson's numerical method. The approximations r(1) and rIF(1) are obtained by taking the velocity potential in the Kochin free-wave amplitude function as the first-order slender-ship potential Φ(1) and its zero-Froudenumber limit Φ0(1) respectively. A major difference between the potentials Φ(1) and Φ0(1) resides in the wave potential ΦW(1) that is included in Φ(1), but is ignored in the zero-Froude-number potential Φ0(1). It is shown that the wave potential ΦW(1) may not be neglected in comparison with the potential Φ0(1) and in fact has a remarkable effect upon the wave resistance. In particular, the wave potential ΦW(1) causes a very large phase shift of the wave-resistance curve, which results in greatly improved agreement with experimental data.