Division Ground track

A ground track, whether a backbone track or a dispersed sub-track, is defined by a series of (x,y) coordinates in the ground plane (e.g. from radar information) or by a sequence of vectoring commands describing straight segments and circular arcs (turns of defined radius r and change of heading Δξ).

For segmentation modelling, an arc is represented by a sequence of straight segments fitted to sub-arcs. Although they do not appear explicitly in the ground-track segments, the banking of aircraft during turns influences their definition. Appendix B4 explains how to calculate bank angles during a steady turn but of course these are not actually applied or removed instantaneously. How to handle the transitions between straight and turning flight, or between one turn and an immediately sequential one, is not prescribed. As a rule, the details, which are left to the user (see Section 2.7.11), are likely to have a negligible effect on the final contours; the requirement is mainly to avoid sharp discontinuities at the ends of the turn and this can be achieved simply, for example, by inserting short transition segments over which the bank angle changes linearly with distance. Only in the special case that a particular turn is likely to have a dominating effect on the final contours would it be necessary to model the dynamics of the transition more realistically, to relate bank angle to particular aircraft types and to adopt appropriate roll rates. Here it is sufficient to state that the end sub-arcs Δξ_trans in any turn are dictated by bank angle change requirements. The remainder of the arc with change of heading Δξ – 2 · Δξ_trans degrees is divided into n_sub sub-arcs according to the equation:

where int(x) is a function that returns the integer part of x. Then the change of heading Δξ_sub of each sub-arc is computed as

where n_sub needs to be large enough to ensure that Δξ_sub ≤ 30 degrees. The segmentation of an arc (excluding the terminating transition sub-segments) is illustrated in Figure 2.7.f ^f1.