Estimation of projected surface area of irregularly shaped fragments

Abstract

Abstract The essence and the main contribution of this paper are consisted of the suggested novel method for estimation of a projected surface area of an irregularly shaped fragment, which represents a significant step toward a new method of an aerodynamic force estimation of a fragment motion through a resistive medium. The suggested method is to use a tri-axial ellipsoid that has a continuous surface (given as a mathematical function) to approximate an irregularly shaped fragment so that the fragment trajectory can be estimated faster taking into consideration that the aerodynamic force is proportional to a projected surface area of the fragment. During their motion, fragments can take any orientation relative to the velocity vector and aerodynamic force is proportional to a projected surface area of fragment perpendicular to the velocity vector, so it is necessary to have a method for correct estimation of the projected area in an arbitrary direction relatively to the fragment. The model was validated with analytical and CAD techniques, and verified using 3D model of a real fragment. The comparison of the projected surface area values for the fragment, obtained using the CAD tools and using our model, are generally in good agreement. This method represents a step toward modeling that does not require a CFD result for estimation of the aerodynamic force of irregularly shaped bodies.