A fixed-point approach of a parachute problem

摘要

The object of this work is to determine the existence of that shape of a parachute, whichwould cause it to float indefinitely in an ascendant wind stream, even while subject to gravity. AHelmholtz type model is constructed for the unsteady, inviscid, incompressible and potential flowpast the parachute. The associated complex potential is determined by making certain reasonablesimplifying assumptions and the global action of the fluid (air) on the parachute is evaluated. Theexistence of a shape of the parachute that would result in its failure, i.e., floating indefinitely, is thendetermined using a fixed-point technique. A similar conclusion could be get for certain bucket shapeof a wind turbine, which leads to its immobility irrespective of the wind stream. This is a problemof practical interest for parachute (turbine) manufacturers, as such a shape should be avoided.