The wave making resistance prediction of a mini-submarine by using tent function method

This paper describes the wave making resistance solution of a mini submarine operating in under water surface with different level depth. The Thin ship theory was adopted to solve the problem for a case of the slenderness body. The source distribution along the centre plane of the body was expressed in Green’s function of Havelock source potential under water surface. The Tent function method was proposed to illustrate the hull form based on offsets data, and to solve the Michell integral problem numerically. Four operational conditions were performed i.e. floating, snorkelling, and diving with 0.5m and 1m under water surface. The computational results for the mini submarine with length of 2m and diameter of 0.25m explained a more deeply operated under water surface cause to decrease a value of wave making resistance for all cases of Froude numbers. While in the diving conditions of 0.5m and 0.1m under the water surface, the wave making resistance were resulted about 64% and 74% less than the case of floating condition respectively. Furthermore, the effect of vertical fin on the body was investigated, where the wave making resistance could increase average 7.2% in snorkelling, 11.4% in 0.5m diving, and in the 1m diving about 9.07% for all Froude numbers. Over all the results of this approach shown a good agreement with the results come from Mitchell code.

The Fundamental Solution in the Theory of Steady Motion of a Ship

The paper presents a simplified new expression for the fundamental solution (the Green function) in the theory of steady motion of a ship, that is, the linearized disturbance velocity potential of the steady, inviscid free-surface gravity flow due to a unit source in an oncoming uniform stream, sometimes also referred to as the "Havelock source potential."

Sinkage and Trim in First-Order Thin-Ship Theory

In first-order thin-ship theory, the sinkage and trim of a ship moving with constant speed into still water can be obtained from a pair of linear equations associated with force and moment. The right-hand sides of these equations are triple integrals of the Havelock source function over the undisturbed underwater profile. By approximating the hull form by a piecewise linear one, these terms may be taken to be composed of two distinct types of integrals whose values are calculated. Sinkage and trim for two mathematical and five Series 60 models have been calculated using these integrals. The results are compared with the corresponding experimental values. The agreement between theoretical and experimental values is considered satisfactory, especially for sinkage and for sufficiently small beam/length ratio.