Skip to main content
Log in

Slender bodies of revolution with minimum wave drag in nonequilibrium supersonic flow

  • Published:
Fluid Dynamics Aims and scope Submit manuscript


We examine the problem of finding the generatrix shape of a body of revolution which travels at supersonic speed and has minimum wave drag. We assume that any number of nonequilibrium processes can take place in the flow. The pressure distribution over the body surface is taken in the linear approximation [1, 2]. A survey of studies using linear theory to find bodies of revolution of optimal form in supersonic perfect gas flow can be found in [3]. The solution of the problem of finding the form of two-dimensional slender bodies of minimum wave drag in nonequilibrium supersonic flow was obtained in [4]. In the following we examine the optimization of only those bodies of revolution for which the leading point lies on the axis of symmetry.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  1. R. A. Tkalenko, “Supersonic nonequilibrium gas flow past slender bodies of revolution”, PMTF, no. 2, 1964.

  2. A. N. Kraiko, “Weakly disturbed supersonic flows with an arbitrary number of nonequilibrium processes”, PMM, vol. 30, no. 4, 1966.

  3. Theory of Optimum Aerodynamics Shapes, Extremal Problems in the Aerodynamics of Supersonic, Hypersonic, and Free Molecular Flows, Acad. Press, New York-London, 1965.

  4. A. N. Kraiko and R. A. Tkalenko, “Slender two-dimensional bodies of minimum wave drag in non-equilibrium supersonic flow”, Izv. AN SSSR, MZhG [Fluid Dynamics], vol. 2, no. 4, 1967.

  5. A. N. Kraiko, I. N. Naumova, and Yu. D. Shmyglevskii, “The construction of bodies of optimal form in supersonic flow”, PMM, vol. 28, no. 1, 1964.

  6. M. Parker, “Minimum drag ducted and pointed bodies of revolution based on linearized supersonic theory”, NACA. Rept. no. 1213, 1955.

  7. N. I. Muskhelishvili, Singular Integral Equations [in Russian], Gostekhizdat, Moscow, 1946.

    Google Scholar 

Download references

Author information

Authors and Affiliations


Additional information

The author wishes to thank A. N. Kraiko for his helpful comments.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tkalenko, R.A. Slender bodies of revolution with minimum wave drag in nonequilibrium supersonic flow. Fluid Dyn 4, 47–49 (1969).

Download citation

  • Issue Date:

  • DOI: