Maximum Range Of Ballistic Missiles

Global conflicts in 2020 have highlighted the unexpected employment of advanced ballistic missiles and unmanned aerial vehicles by developing military powers. The development of ballistic missiles by Iran, or the export of advanced drones by Turkey, are ultimately the result of the American-led revolution in military affairs that, during the Gulf War, established the potential of precision guided weapons and reconnaissance systems. In response, America’s competitors have adapted their military doctrines and developed weapons designed to both counter and copy the West’s technological advantages. As the Government of Canada implements its defence policy—Strong, Secure, and Engaged—it has promised to procure a ground-based air defence system for the Canadian Armed Forces. Careful consideration and analysis are required, however, to ensure that Canada procures the best possible solution given limited funding and a wide array of potential threats.

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The Determination of Maximum Range for an Unpowered Atmospheric Vehicle

Journal of the Royal Aeronautical Society ◽

10.1017/s0001924000061364 ◽

1964 ◽

Vol 68 (638) ◽

pp. 111-116 ◽

Cited By ~ 2

Author(s):

D. J. Bell

Keyword(s):

Calculus Of Variations ◽

Lagrange Multipliers ◽

Digital Computer ◽

Necessary Conditions ◽

Lagrange Equations ◽

Initial Portion ◽

End Conditions ◽

Maximum Range ◽

Isothermal Atmosphere

SummaryThe 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.

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