B4THE EFFECTS OF TURNSU.K.
The remainder of this appendix explains how to calculate the required properties of the segments joining the profile points s,z that define the two-dimensional flight path in the vertical plane above the ground track. Segments are defined in sequence in the direction of motion. At the end of any one segment (or at the start of roll in the case of the first for a departure) where the operational parameters and the next procedural step are defined, the need is to calculate the climb angle and track distance to the point where the required height and/or speed are reached.
If the track is straight, this will be covered by a single profile segment, the geometry of which can then be determined directly (albeit sometimes with a degree of iteration). But if a turn starts or ends, or changes in radius or direction, before the required end-conditions are reached, a single segment would be insufficient because the aircraft lift and drag change with bank angle. To account for the effects of the turn on the climb, additional profile segments are required to implement the procedural step — as follows.
The construction of the ground track is described in Section 2.7.13 of the text. This is done independently of any aircraft flight profile (although with care not to define turns that could not be flown under normal operating constraints). But as the flight profile — height and speed as a function of track distance — is affected by turns so that the flight profile cannot be determined independently of the ground track.
To maintain speed in a turn the aerodynamic wing lift has to be increased, to balance centrifugal force as well as the aircraft weight. This in turn increases drag and, consequently the propulsive thrust required. The effects of the turn are expressed in the performance equations as functions of bank angle ε which, for an aircraft in level flight turning at constant speed on a circular path, is given by
All turns are assumed to have a constant radius and second-order effects associated with non-level flight paths are disregarded; bank angles are based on the turn radius r of the ground track only.
To implement a procedural step a provisional profile segment is first calculated using the bank angle ε at the start point — as defined by equation B-8 for the track segment radius r. If the calculated length of the provisional segment is such that it does not cross the start or end of a turn, the provisional segment is confirmed and attention turns to the next step.
But if the provisional segment crosses one or more starts or ends of turns (where ε changes)(1), the flight parameters at the first such point are estimated by interpolation (see Section 2.7.13), saved along with its coordinates as end-point values, and the segment truncated. The second part of the procedural step is then applied from that point — once more assuming provisionally that it can be completed in a single segment with the same end conditions but with the new start point and new bank angle. If this second segment then passes another change of turn radius/direction, a third segment will be required — and so on until the end-conditions are achieved.
Approximate method U.K.
It will be apparent that accounting fully for the effects of turns, as described above, involves considerable computational complexity because the climb profile of any aircraft has to be calculated separately for each ground track that it follows. But changes to the vertical profile caused by turns usually have a markedly smaller influence on the contours than the changes of bank angle, and some users may prefer to avoid the complexity — at the cost of some loss of precision — by disregarding the effects of turns on profiles while still accounting for the bank angle in the calculation of lateral sound emission (see Section 2.7.19). Under this approximation profile points for a particular aircraft operation are calculated once only, assuming a straight ground track (for which ε = 0).
To avoid contour discontinuities caused by instantaneous changes of bank angle at the junctions between straight and turning flight, sub-segments are introduced into the noise calculations to allow linear transitions of bank angle over the first and last 5° of the turn. These are not necessary in the performance calculations; the bank angle is always given by equation B-8.