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The Determination of Maximum Range for an Unpowered Atmospheric Vehicle

Published online by Cambridge University Press:  04 July 2016

D. J. Bell
D. J. Bell*
Affiliation:
Department of Mathematics, Bristol College of Science and Technology
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Summary

The problem of maximising the range of a given unpowered, air-launched vehicle is formed as one of Mayer type in the calculus of variations. Eulers’ necessary conditions for the existence of an extremal are stated together with the natural end conditions. The problem reduces to finding the incidence programme which will give the greatest range.

The vehicle is assumed to be an air-to-ground, winged unpowered vehicle flying in an isothermal atmosphere above a flat earth. It is also assumed to be a point mass acted upon by the forces of lift, drag and weight. The acceleration due to gravity is assumed constant.

The fundamental constraints of the problem and the Euler-Lagrange equations are programmed for an automatic digital computer. By considering the Lagrange multipliers involved in the problem a method of search is devised based on finding flight paths with maximum range for specified final velocities. It is shown that this method leads to trajectories which are sufficiently close to the “best” trajectory for most practical purposes.

It is concluded that such a method is practical and is particularly useful in obtaining the optimum incidence programme during the initial portion of the flight path.

Type
Research Article
Information
The Aeronautical Journal , Volume 68 , Issue 638 , February 1964 , pp. 111 - 116
Copyright
Copyright © Royal Aeronautical Society 1964

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References

1.Bell, D. J.A Review of Flight Optimisation Along Synergic Paths in the Period 1945-1960. Journal of the Royal Aeronautical Society, Vol. 67, pp. 119–123, February 1963.Google Scholar
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3.Bliss, G. A.Lectures on the Calculus of Variations. The University of Chicago Press, Chicago, 1946.Google Scholar
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5.Raybould, B.Approximate Trajectories for Maximum Range. Journal of the Royal Aeronautical Society, Vol. 67, pp. 385–386, June 1963.Google Scholar