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On parachutes of optimum shape in a subsonic gas flow

Published online by Cambridge University Press:  01 February 2007

D. V. MAKLAKOV ,
A. M. ELIZAROV  and
R. R. SHARIPOV
D. V. MAKLAKOV
Affiliation:
Chebotarev Institute of Mathematics and Mechanics, Kazan State University, Universitetskaya, 17, Kazan, 420008, Russia email: [email protected], [email protected]
A. M. ELIZAROV
Affiliation:
Chebotarev Institute of Mathematics and Mechanics, Kazan State University, Universitetskaya, 17, Kazan, 420008, Russia email: [email protected], [email protected]
R. R. SHARIPOV
Affiliation:
Kazan State Architectural–Building University, 1, Zelenaya str., 420043 Kazan, Russia
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Abstract

In this paper the problem of finding the impermeable parachute of optimum shape in a subsonic gas flow has been solved. The effects of compressibility have been taken into account out by making use of ideas of Chaplygin's approximate method. A formula for the drag coefficient has been deduced and by comparison with exact solutions it has been demonstrated that for bluff bodies its related error is no more than 0.5% for any Mach number at infinity less than unity. On the basis of the formula a functional for the drag force has been constructed and its global maximum has been found analytically. It has been shown that the optimum shape is slightly affected by compressibility.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 18 , Issue 1 , February 2007 , pp. 81 - 102
Copyright
Copyright © Cambridge University Press 2007

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