Drag Force Analysis of Spheres Penetrating Gelatin Based on Surface Integral

Abstract

A new method based on surface integral is presented in the research of mechanical mechanism of spheres penetrating gelatin. On the assumption that each wetted area element is applied with dynamic force perpendicular to the surface, frictional force parallel to the surface and material resistance which is a constant, the resultant force applied on spheres was integrated containing three unknown coefficients. Transparent gelatin was used in the experiments and steel spheres were fired at speed around 800m/s. High speed cameras got the position data of the penetrating spheres. The uncertain coefficients in the movement equations were determined with these data. The equations were solved in analytical forms. Experiments show that the coefficients are constant for spheres with different radiuses. Calculation results demonstrate that the mechanical model is good to predict the movement of spheres in gelatin.