Estimation of projected surface area of irregularly shaped fragments

Contribution to Compressibility Modelling in the Estimation of Forces Acting on Projectile Fragments

“…In the previous paper [5] of the authors, a generalized model for the estimation of aerodynamic forces and moments for irregularly shaped bodies (IE fragments of HE projectiles, secondary debris) was described, where irregularly shaped body was approximated with a triaxial ellipsoid. This model is a follow up on the previous work [6] of the authors where the exposed area of the irregularly shaped body is estimated. These models can be successfully used for the estimation of a trajectory parameters for a body with an irregular shape (i.e.…”

“…Here ρ is the density of the fragment material, Vul is the input velocity of the flow, Vizl is the output velocity of the flow, γvz is the angle between the velocity vector and the plane of the projected surface of the fragment (whereby these unit vectors are determined by the method explained in reference [6]), and a1, b1 are half-axes of the ellipse defining a curve in the plane separating the exposed part (to the flow) of the fragment from the rest of the fragment [6]. The integration of expression ( 1) is performed using the x and y coordinates in the plane of the projected fragment surface, where the integration boundary is defined by the ellipse half-axes a1 and b1.…”

New Method for Calculating the Windward Area of Irregular Fragments

“…When N approaches to infinity, the average value of the projection area will be approximately equal to the average windward area of the fragment. The expressions of each calculation step are shown in equations ( 5) to (12).…”

“…This method provides a new idea for the simulation calculation of the velocity attenuation, trajectory, and specific kinetic energy of irregular fragments, but the calculation accuracy of this method needs to be further improved. The equivalent ellipsoid model suffers from different degrees of errors with different projection angles, and the maximum error can reach 36% [12]. Therefore, a Monte Carlo subdivision projection simulation (MCSPS for short) algorithm is proposed in the current work, which can calculate the average windward areas of arbitrarily shaped fragments.…”

“…However, a certain error exists between the equivalent windward area and the real windward area. Elvedin [12,13] established an equivalent ellipsoid model on the basis of the maximum and minimum diameters of natural fragments and reported that the model can quickly estimate the windward areas of arbitrarily shaped fragments. This method provides a new idea for the simulation calculation of the velocity attenuation, trajectory, and specific kinetic energy of irregular fragments, but the calculation accuracy of this method needs to be further improved.…”