Hydrodynamic analysis on optimal depth of water for streamlined glidins in swimming

Abstract

It is reported as an experimental study (Goya et al. 2002) that the optimal water depth for streamlined gliding motion in swimming is from 0.4 m to 0.8 m. It is considered that wave drag under streamlined gliding motion increases as a swimmer approaches the water surface, but that interference drag between a swimmer and the bottom of a swimming pool increases as he/she approaches the bottom of a swimming pool. Therefore, it is expected the optimal water depth must be somewhere from the water surface to the bottom of a swimming pool. The purpose of this study is to verify the optimal depth of water for streamlined gliding motion applying hydrodynamics to Rankine Body. There is a theoretical analysis (Wigley 1953) concerning wave drag decreasing as the depth of water increases. Therefore I use the result of this study. On the interference drag, the interference drag can be calculated applying Lagally theory to the method of images. Lagally theory (Landweber and Yih 1956) can calculate the forces which occur when fluid velocity, generated by hydrodynamic singularities around the body, flows into the hydrodynamic singularities in the body. The results are as follows : Wave drag is nearly zero under the condition 3.5 d = h as the beam of Rankine Body is "d" and the depth of water is "h" . Interference drag is nearly zero under the condition a = d as the length from the bottom of the swimming pool to Rankine Body is "a" .