Fluid Mass Associated with an Axisymmetric Parachute Canopy

Abstract

An analytical technique for calculating the fluid mass associated with parachute canopies of arbitrary axisymmetric cross section operating in an in viscid, incompressible fluid is presented. The effects of porosity, both nominal and geometric, are included. The procedure replaces the physical parachute canopy with a mathematical vortex sheet of a strength which is determined through application of velocity boundary conditions. The strength then is used to find the fluid kinetic energy. Equating this energy to the system translational kinetic energy gives the mass in question. Final and intermediate results compare favorably with those of previous analysis and experiment. I. Introduction K NOWLEDGE of the air mass associated with the trajectory of a parachute canopy is required to describe that trajectory analytically. Because of the complexities associated with typical canopy geometries and the porous nature of their surfaces, computations in the past have relied very heavily upon experimental determination of this mass. This paper details a procedure for calculating the sum of included and additional mass inherent in the axial motion of parachutes with arbitrary axisymmetric cross sections. II. Analysis Lambl gives the kinetic energy of a stream of vortex rings immersed in an incompressible, inviscid fluid which is at rest at infinity as