Unsteady aerodynamic forces on parachute canopies
A research programme has been conducted, the objective of which has been the determination of unsteady force coefficients for a range of parachute canopy models. These coefficients are required for prediction of the aerodynamic stability of full scale parachutes under conditions of unsteady motion during descent. The method of obtaining these coefficients required the collection of force and acceleration data for parachute canopy models which were tested in unsteady conditions. This was achieved by imposing oscillatory motion on individual canopies during towing tests, which were conducted under water in a ship testing tank. Two modes of unsteady motion were imposed on a canopy under test; one in which it was oscillated along its axis, and one in which it was oscillated laterally. A mathematical model describing such modes of motion consists of a general equation for the unsteady force developed on a bluff body. In this model the force F(t) is expressed using two components; a velocity dependent force component, and an acceleration dependent force component. Each component of the aerodynamic force contains an unknown parameter denoted by the terms ‘a’ and ‘b’ in the equation, which is shown below; F( t ) = a( t ) • V²( t ) + b( t ) • V( t ). An identification technique is used to determine the mean values per cycle of each parameter by substitution of the data obtained from these tests as functional variables in the mathematical model. Mean values of the velocity dependent force and stability coefficients; CT and ∂CN/∂α, and the added mass coefficients k11 and k33 are then obtained from these parameters. The results of this programme indicate a strong dependence in oscillatory motion of the mean value per cycle for the axial added mass coefficient k11 on the unsteady force parameter called the Keulegan-Carpenter number KC; KC = Û • T/DO. Where; Û = the velocity amplitude of the oscillation, T = the period of an oscillation, and DO = a typical canopy dimension. The velocity dependent axial force coefficient CT exhibits a similar, although not as substantial dependency. Good agreement has been obtained between steady-state test results from this programme and results from other independent work. The effects of values obtained in this investigation are considered in the linearised dynamic stability model developed by Doherr and Saliaris (1), and their influence on the descent characteristics of full-scale parachutes is assesed.