Numerical calculation of the optimum shape of a body of revolution moving at steady speed in the soil environment

The problem of determining the optimum shape of a body of revolution with minimum drag penetrating into the soil is solved numerically by using a modified version of the method of local variations and a quadratic trinomial local interaction model. Good agreement has been reached between the results for the generatrix of a body of revolution in the form of a parametric Bezier polynomial and a piecewise linear curve. Convergence of successive approximation methods for the solution of a parametric optimization problem is studied. An error made in determining the drag force as a function of variations in the generatrix parameters is considered. The difference in drag forces between the bodies of absolutely optimal shapes and the bodies of calculated optimal shapes is analyzed for different body length and various strength characteristics of the medium. It is shown that the approximation of the body generatrix by the Bezier polynomial previously used only in the problems of aerodynamics can be successfully applied to parameterization of the generatrix of a body penetrating into the soil. The proposed algorithm can be generalized to calculate the drag force in the framework of continuum mechanics.