Linearized numerical methods are extensively used to design marine propellers since blade thickness ratios are generally small. These methods mainly consist of distributing normal dipoles and sources on the mean blade surface to represent lifting and thickness effects. They are particularly adapted to the design process since they do not require the exact knowledge of the actual surface; furthermore, they give satisfactory results for very low panel numbers, enabling fast and accurate iterations of the design process. These are the advantages they have against more sophisticated methods like panel methods, for which singularity panels are distributed on the actual surface.
However, linear singularity methods have inherent problems, among them is the fact that the kernel associated with the dipole distribution has a Cauchy type singularity. They have also to deal with square root singularities at the leading-edge and the blade tip. To cope with these problems, collocation methods: like the Vortex Lattice Method (VLM), have been devised. Although these methods are well founded in two dimensions, their application in three dimensions is still somewhat empirical and sometimes inaccurate. Actually, they are not reliable in predicting the force and pressure distribution in the vicinity of the blade tip if the blades are highly skewed, or if the blade aspect ratio is very small.
In the present paper, the origins of these inaccuracies are thoroughly discussed, and after a simple mathematical analysis, a new scheme is proposed to overcome them. It is mainly a matter of adapting the panel arrangement to the blade boundaries: leading-edge, tip and trailing edge. The force calculation is reviewed in the second part of this paper. It is shown that the pressure induced force along with leading-edge suction can be accurately determined everywhere on the blades.
