“The Effects of Ship Form on the Frictional Resistance” (Part I)

Abstract

The effects of ship form on the frictional resistance are calculated on the basis of the turbulent boundary layer theory.The stream is confined to be 2-dimensional, the effect of gravity is neglected. The boundary layer is assumed to be completely turbulent from the begining and the form effect is expressed as the ratio of the coefficient of frictional resistance of ship (Cf) to that of flat plate (Cf0)-the boundary layer of the flat plate is also assumed to be completely turbulent.The calculation of the turbulent boundary layer is worked out in accordance with Bun's method.At first, the ratio of length to breadth is maintained to be 7.00 (const.) and the water plane area coef. is varied, and then, the latter being maintained approximately constant, the ratio of length to breadth is varied.The forms of ship water plane in the Z1-plane are attained from the following equations1)Z1=Z+ma2/Z+na4/Z3 n=-1+4/3mthe ratio of lengh to breadth=7.002) Z1=Z+ma2/Z+na4/Z3 n=1-m/3where Z is put to be aeiθ, that is, these ship forms are the conformal representations in the Z1-plane of a circle in the Z-plane.If the frictional stress is assumed to be 0 at the rear portion of the separation point, the calculated results are as follows.1) m=.74 .76 .78 .80 k=1.203 1.174 1.145 1.1222) m=.70 .80 .85 k=1.158 1.122 1.087where k=Cf/Cf0 Cf=the coeft. of frictional resistance for ship form =Rf/ρLV2, L=length of the ship. Cf0=d0. for flat plate.These values are closely in accordance with the results of more elaborate calculation obtained by Okabe, the member of the Research Institute for Fluid Engineering, but in the range of small length-breadth ratio, the agreement is not so good, showing the fact that the form effect is not satisfactorily explained with the length to breadth ratio and the coeft. of fineness.The k values agree approximately with the results obtained from the experiments of usual ship form models.