Calculation of Differential-Turning Barrier Surfaces

Abstract

The computation of composite differential-turn trajectory pairs is studied for "fast-evader" and "neutralevader" idealizations introduced in earlier publications. Transversality and generalized corner conditions are examined and the joining of trajectory segments discussed. A criterion is given for the screening of "tandemmotion" trajectory segments. Main focus is upon the computation of barrier surfaces. Fortunately, from a computational viewpoint, the trajectory pairs defining these surfaces need not be calculated completely, the final subarc of multiple-subarc pairs not being required. Weapon effects are introduced in terms of generally forwardfiring but trainable weapons whose envelopes are described by radius limits and conic trainability limits. The pursuer may elect to fill a turn-angle gap with his weaponry, while meeting the usual energy-matching requirement, or he may choose instead to close angularly to tail-chase position, relying on the weapon's upward reach to compensate for an energy deficiency; most often the choice will be intermediate between these extremes. In some cases, dissimilarities in flight performance characteristics between the opposing aircraft tend to favor the pursuit tactic of closing angularly, then driving the evader aloft for an energy-attrition duel, and generally the upward reach of the weaponry increases the effectiveness of such a tactic, permitting its use with relatively low pursuer energy. Illustrative computations are presented for various pairs of example aircraft.

Guidance and control for own aircraft in the autonomous air combat: A historical review and future prospects

“…Similar to the barrier concept developed in formal approach and optimal theory-based method, the barrier surfaces were calculated in the DT-based approach, see Kelley and Lefton 145 for details. Also in Kelley and Lefton, 145 in contrast to the prior work in Kelley and Lefton 139,141 and Kelley, 142–144 which considers only the aircraft dynamics, the effect of the weaponry system was discussed. This effect was modeled via radius and conic limit of the weapon.…”

Planar pursuit-evasion with variable speeds, part 1, extremal trajectory maps

“…Differential turns (Refs. [5][6][7][8] is another three-dimensional game widely analyzed. The players' dynamics are quite realistic and complex.…”

A preference-ordered discrete-gaming approach to air-combat analysis

“…However, the literature focuses almost entirely on the case of an evader undefended save for evasive maneuvering, and has only limited applicability to air combat between aircraft of roughly equal capability. One approach to this situation which has received some attention is the calculation of outcomes with pursuit and evasion roles assigned, and again with them interchanged, then the use of these to define surfaces separating win, lose, and draw regions [l], [2]. This approach leads to ambiguous results with large-envelope weaponry which produces a large mutual-capture region when the assumption of pursuit, irrespective of the consequences, is maintained.…”