Apparent mass - Its history and its engineering legacy for parachuteaerodynamics

Abstract

The paper describes the physical meaning of apparent mass and the relevance which it appears to have to both parachute canopy inflation models and the equations of motion for the descent of fully-deployed steady-state parachute systems. It considers the essential differences between the unsteady motion of parachutes through ideal fluids, when potential flow solutions are possible, and through real fluids, when recourse must be made to experimental studies. It explains contemporary understanding of its significance, setting it in its historical context and outlining the manner in which further experimental work needs to be done. Because of its complexity, its probable lack of relevance to the parachute problems to which it has been applied in the past and the dearth ot good experimental data, it concludes that the apparent mass concept has little more to offer to contemporary parachute design. Since the earliest days of parachute technology, a feature of the equations of motion for the oscillations of the system comprising the fully-inflated parachute canopy and its payload, as well as the characteristics of the parachutepayload system during the canopy inflation stage is an indeterminate number of dimensionless apparent mass coefficients. As experiments in real fluids have yielded numerical values for only a few of these coefficients and even these have been determined for an unrepresentative number of canopy shapes, angles of attack and Reynolds numbers, for the most part these equations are satisfied by extrapolation of what experimental data there are to the required canopy shapes and Reynolds numbers; by appeal to ideal fluid theory or (more usually) by disregarding the apparent mass coefficients altogether. Recourse to the latter expedient offers at least an excuse for the characteristic behaviour of a parachute system in flight differing from that predicted by the system equations. Examination of equations of motion for symmetrical immersed bodies reveals that there are twenty-one apparent mass components and that for systems in which the momentum of the fluid displaced by the immersed body is not negligible compared with that of the body, all of these components would appear to be of significance. Further, because of the body wake in a real fluid, their experimental