A generalisation of the Breguet range equation for multiple payload drops

Abstract

This paper has arisen from a more general investigation aimed at identifying appropriate manned aircraft that would make suitable stand-off cruise missile platforms. One primary measure of an aircraft's ability to fulfil such a role is found in its payload-range envelope for flight profiles involving one or more payload drop. To this end, a generalisation of the Breguet Range equation is developed initially for a radius-of-action scenario in which the entire payload is ejected at altitude at the designated drop point and the aircraft returns home. The more general problem is then addressed, namely that of establishing the payload-range envelope for an aircraft flying a predefined mission profile comprising a maximum of four consecutive legs each separated by a single payload release point. The ability to include a partial payload release at any drop point is built into the model to permit planners to investigate typical ‘what if?’ effects on the overall mission. Six numerical examples are included, all based upon the Boeing C-17 as the parent aircraft. These examples describe in detail missions of increasing complexity in order to demonstrate the versatility and efficacy of the current method. Attention is confined to turbojet-powered aircraft cruising in the stratosphere, although the analogous case of a turboprop-powered aircraft can be simulated simply by amending a single group of constants that appears in all the formulae. Neither air-to-air refuelling policies, nor complicating atmospheric effects such as headwinds, are considered in this paper.