Moriya's 1st approximate formulae to caluculate velocity distributions on blade surfaces and the lifting force of 2-dimensional blade sections in ideal flow, are popularly used in Japan. The Fourier series in the formulae, however, diverges in the calculation of blade sections with non-zero trailing edge thickness, and converges slowly in the case of non-zero trailing edge angle.
In this paper, the formulae are progressed and re-examined in some points. The main results are as follows ;
(1) Adding a logarithmic term to the mapping function, the 1st approximate formulae to caluclate the velocity on sufaces of blade sections with non-zero thickness at the trailing edge, are obtained. In the case of such blade sections, assuming that the pressure at the trailing edge surface is to be same as one at infinite distance, the thrust force is disappeared.
(2) Calculating the terms concerning to trailing edge angle separately, the Fourier series converges rapidly. The logarithmic singularity, however, appears in the terms.
(3) Formulae presented here are equivalent to the Hanaoka's formulae.
(4) The effect of blade thickness on the lifting force is disappeared, due to the approximation of the formulae shown in this paper.