De Bortoli, Álvaro Luiz

Sandrini, Vanessa S.

English

Lume 5.8

Parachutes Optimization by Numerical SimulationVanessa S. Sandrini, Álvaro L. De BortoliPrograma de Pós-Graduação em Matemática Aplicada, IM-UFRGS,91509-900, Porto Alegre, RSE-mail: nessa@mat.ufrgs.br, dbortoli@mat.ufrgs.brABSTRACTParachutes were in the past developed mainlyto military use; actually, however, they are beingemployed in many areas, such as to sports, spatialprojects, car-race, etc.A paraglider is a special kind of parachute, of ba-nana form. A difference between the conventionalparachute and the paraglider is the jump’s altitude.In a jump with parachute, an airplane is employedand the jump must happen between 3000-4000 me-ters; the parachute is opened around 900 metersfrom the soil. Before opening the parachute theparachutist can accelerate to 190 km/h in around40 seconds, which is its maximum velocity. For ajump with paraglider 1200 meters of altitude aresufficient and the jump can be realized from thetop of a mountain or other geographic unlevelling.Another style of parachute is that of automaticopening, where the equipment opens without inter-vention of the parachutist. The jump is done from aplane at about 1200 meters. Other important appli-cation of parachute appears in spatial expeditions,where robots are cast from a rocket or a spatialbus in places not yet explored by the men. Theparachute is then designed to avoid a strong crashof sensible equipment with the soil.The present work develops a numerical method toanalyze a jump with a parachute. The set of bidi-mensional incompressible unsteady N-Stokes equa-tions is solved together with a Poisson’s equationsfor pressure, which comes from N-Stokes and themass conservation equation. The numerical modelis based on the finite difference explicit Runge-Kutta three-stages scheme for second order timeand space approximations.Preliminary results showed to compose well withand analytical simplified model, whose results areshown in Fig. 1, that comes from the followingequationmdvdt = P − P v2awhere a = 2400 when the parachute is closed anda = 30 when it is opened.We strong the fact that there are few informationabout parachutes and paragliders in the availableliterature, specially for sport activities; the contri-bution of our work goes in this direction.Figure 1: Displacements a),velocity b) and acceler-ation c) for a conventional parachute jumpReferences[1] V. Kalro and T. Tezduyar, A parallel 3D com-putational method for fluid-structure interac-tions in parachute systems, Comput. MethodsAppl. Mech. and Engrg., 190 (2000) 321-332.[2] K. Stein, R. Benney, T. Tezduyar and J.Potvin, Fluid-structure interactions of a crossparachute: numerical simulation, Comput.Methods Appl. Mech. Engrg., 191 (2001) 673-687.[3] T. Tezduyar and Y. Osawa, Fluid-structure in-teractions of a parachute crossing the far wakeof an aircraft, Comput. Methods Appl. Mech.and Engrg., 191 (2001) 717-726.[4] T. Tezduyar, K. Stein, R. Benney, V. Kumarand J. McCune, Numerical Methods for Com-puter Assisted Analysis of Parachute Mechan-ics, em ”Proceedings of the 8th Int. Conf. onNum. Meth. in Continuum Mech.”, LiptovskyJan, Slovakia, 2000.

Parachutes optimization by numerical simulation

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Parachutes optimization by numerical simulation

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Lume 5.8