(13)

Section 2.7.13, ‘Construction of flight path segments’, is replaced by the following: ‘2.7.13 Construction of flight path segments Each flight path has to be defined by a set of segment coordinates (nodes) and flight parameters. The starting point is to determine the co-ordinates of the ground track segments. The flight profile is then calculated, remembering that for a given set of procedural steps, the profile depends on the ground track; e.g. at the same thrust and speed the aircraft climb rate is less in turns than in straight flight. Sub-segmentation is then undertaken for the aircraft on the runway (takeoff or landing ground roll), and for the aircraft near to the runway (initial climb or final approach). Airborne segments with significantly different speeds at their start and end points should then be sub-segmented. The two-dimensional co-ordinates of the ground track (*) segments are determined and merged with the two-dimensional flight profile to construct the three-dimensional flight path segments. Finally, any flight path points that are too close together are removed. Flight profile The parameters describing each flight profile segment at the start (suffix 1) and end (suffix 2) of the segment are: s1, s2 distance along the ground track, z1, z2 aeroplane height, V1 , V2 groundspeed, P1 , P2 noise-related power parameter (matching that for which the NPD-curves are defined), and ε1, ε 2 bank angle. To build a flight profile from a set of procedural steps (flight path synthesis), segments are constructed in sequence to achieve required conditions at the end points. The end-point parameters for each segment become the start-point parameters for the next segment. In any segment calculation the parameters are known at the start; required conditions at the end are specified by the procedural step. The steps themselves are defined either by the ANP defaults or by the user (e.g. from aircraft flight manuals). The end conditions are usually height and speed; the profile building task is to determine the track distance covered in reaching those conditions. The undefined parameters are determined via flight performance calculations described in Appendix B. If the ground track is straight, the profile points and associated flight parameters can be determined independently of the ground track (bank angle is always zero). However ground tracks are rarely straight; they usually incorporate turns and, to achieve best results, these have to be accounted for when determining the 2-dimensional flight profile, where necessary splitting profile segments at ground track nodes to inject changes of bank angle. As a rule the length of the next segment is unknown at the outset and it is calculated provisionally assuming no change of bank angle. If the provisional segment is then found to span one or more ground track nodes, the first being at s, namely s1 < s < s2 , the segment is truncated at s, calculating the parameters there by interpolation (see below). These become the end-point parameters of the current segment and the start-point parameters of a new segment – which still has the same target end conditions. If there is no intervening ground track node the provisional segment is confirmed. If the effects of turns on the flight profile are to be disregarded, the straight flight, single segment solution is adopted although the bank angle information is retained for subsequent use. Whether or not turn effects are fully modelled, each 3-dimensional flight path is generated by merging its 2-dimensional flight profile with its 2-dimensional ground track. The result is a sequence of co-ordinate sets (x,y,z), each being either a node of the segmented ground track, a node of the flight profile or both, the profile points being accompanied by the corresponding values of height z, ground speed V, bank angle ε and engine power P. For a track point (x,y) which lies between the end points of a flight profile segment, the flight parameters are interpolated as follows: z = z1 + f ·(z2 – z1) (2.7.3) (2.7.4) ε = ε1 + f · (ε2 - ε1) (2.7.5) (2.7.6) where f = (s - s 1)/(s 2 - s 1) (2.7.7) Note that whilst z and ε are assumed to vary linearly with distance, V and P are assumed to vary linearly with time (namely constant acceleration (**)). When matching flight profile segments to radar data (flight path analysis) all end-point distances, heights, speeds and bank angles are determined directly from the data; only the power settings have to be calculated using the performance equations. As the ground track and flight profile coordinates can also be matched appropriately, this is usually quite straightforward. Takeoff ground roll When taking off, as an aircraft accelerates between the point of brake release (alternatively termed Start-of-Roll SOR) and the point of lift-off, speed changes dramatically over a distance of 1 500 to 2 500 m, from zero to between around 80 and 100 m/s. The takeoff roll is thus divided into segments with variable lengths over each of which the aircraft speed changes by specific increment ΔV of no more than 10 m/s (about 20 kt). Although it actually varies during the takeoff roll, an assumption of constant acceleration is adequate for this purpose. In this case, for the takeoff phase, V1 is initial speed, V2 is the takeoff speed, nTO is the number of takeoff segment and sTO is the equivalent takeoff distance. For equivalent takeoff distance sTO (see Appendix B) and takeoff speed V1 and takeoff speed VTO the number nTO of segments for the ground roll is nTO = int (1 + (VTO - V 1) /10) (2.7.8) and hence the change of velocity along a segment is ΔV = VTO/nTO (2.7.9) and the time Δt on each segment is (constant acceleration assumed) (2.7.10) The length sTO,k of segment k (1 ≤ k ≤ nTO) of the takeoff roll is then: (2.7.11) Example: For a takeoff distance sTO = 1 600 m, V1 = 0m/s and V2 = 75 m/s, this yields nTO = 8 segments with lengths ranging from 25 to 375 metres (see Figure 2.7.g): Similarly to the speed changes, the aircraft thrust changes over each segment by a constant increment ΔP, calculated as ΔP = (PTO - Pinit ) / nTO (2.7.12) where PTO and P init respectively designate the aircraft thrust at the point of lift-off and the aircraft thrust at the start of takeoff roll. The use of this constant thrust increment (instead of using the quadratic form equation 2.7.6) aims at being consistent with the linear relationship between thrust and speed in the case of jet-engine aircraft. Important note: The above equations and example implicitly assume that the initial speed of the aircraft at the start of the takeoff phase is zero. This corresponds to the common situation where the aircraft starts to roll and accelerate from the brake release point. However, there are also situations where the aircraft may start to accelerate from its taxiing speed, without stopping at the runway threshold. In that case of non-zero initial speed Vinit the following “generalised” equations should be used in replacement of equations 2.7.8, 2.7.9. 2.7.10 and 2.7.11. (2.7.13) In this case, for the takeoff phase, V1 is initial speed Vinit , V2 is the takeoff speed VTO , n is the number of takeoff segment nTO , s is the equivalent takeoff distance sTO and sk is the length sTO,k of segment k (1[Symbol]k[Symbol]n). The landing ground roll Although the landing ground roll is essentially a reversal of the takeoff ground roll, special account has to be taken of — reverse thrust which is sometimes applied to decelerate the aircraft, and — aeroplanes leaving the runway after deceleration (aircraft that leave the runway no longer contribute to air noise as noise from taxiing is disregarded). In contrast to the takeoff roll distance, which is derived from aircraft performance parameters, the stop distance sstop (namely the distance from touchdown to the point where the aircraft leaves the runway) is not purely aircraft specific. Although a minimum stop distance can be estimated from aircraft mass and performance (and available reverse thrust), the actual stop distance depends also on the location of the taxiways, on the traffic situation, and on airport-specific regulations on the use of reverse thrust. The use of reverse thrust is not a standard procedure – it is only applied if the needed deceleration cannot be achieved by the use of the wheel brakes. (Reverse thrust can be exceptionally disturbing as a rapid change of engine power from idle to reverse settings produces a sudden burst of noise.) However, most runways are used for departures as well as for landings so that reverse thrust has a very small effect on the noise contours since the total sound energy in the vicinity of the runway is dominated by the noise produced from takeoff operations. Reverse thrust contributions to contours may only be significant when runway use is limited to landing operations. Physically, reverse thrust noise is a very complex process but because of its relatively minor significance to air noise contours it can be modelled simplistically – the rapid change in engine power being taken into account by suitable segmentation. It is clear that modelling the landing ground roll is less straightforward than for takeoff roll noise. The following simplified modelling assumptions are recommended for general use, when no detailed information is available (see Figure 2.7.h.1). The aircraft crosses the landing threshold (which has the co-ordinate s = 0 along the approach ground track) at an altitude of 50 feet, and then continues to descend on its glideslope until it touches down on the runway. For a 3° glideslope, the touch-down point is 291 m beyond the landing threshold (as illustrated in Figure 2.7.h.1). The aircraft is then decelerated over a stop-distance sstop – aircraft specific values of which are given in the ANP database – from final approach speed Vfinal to 15 m/s. Because of the rapid changes in speed during this segment it should be sub-segmented in the same manner as for the takeoff ground roll (or airborne segments with rapid speed changes), using the generalised equations 2.7.13 (as taxi-in speed is not equal to zero). The engine power changes from final approach power at touchdown to a reverse thrust power setting Prev over a distance 0,1•sstop , then decreases to 10 % of the maximum available power over the remaining 90 percent of the stop distance. Up to the end of the runway (at s = -s RWY) aircraft speed remains constant. NPD curves for reverse thrust are not at present included in the ANP database, and it is therefore necessary to rely on the conventional curves for modelling this effect. Typically the reverse thrust power Prev is around 20 % of the full power setting and this is recommended when no operational information is available. However, at a given power setting, reverse thrust tends to generate significantly more noise than forward thrust and an increment ΔL shall be applied to the NPD-derived event level, increasing from zero to a value ΔLrev (5 dB is recommended provisionally (***)) along 0,1•sstop and then falling linearly to zero along the remainder of the stop distance. Segmentation of the initial climb and final approach segments The segment-to-receiver geometry changes rapidly along the initial climb and final approach airborne segments, particularly with respect to observer locations to the side of the flight track, where the elevation angle (beta angle) also changes rapidly as the aircraft climbs or descends through these initial/final segments. Comparisons with very small segment calculations show that using a single (or a limited number of) climb or approach airborne segment(s) below a certain height (relative to the runway) results in a poor approximation of noise to the side of the flight track for integrated metrics. This is due to the application of a single lateral attenuation adjustment on each segment, corresponding to a single segment-specific value of the elevation angle, whereas the rapid change of this parameter results in significant variations of the lateral attenuation effect along each segment. Calculation accuracy is improved by sub-segmenting the initial climb and last approach airborne segments. The number of sub-segments and the length of each determine the lateral attenuation change “granularity” which will be accounted for. Noting the expression of total lateral attenuation for aircraft with fuselage-mounted engines, it can be shown that for a limiting change in lateral attenuation of 1,5 dB per sub-segment, the climb and approach airborne segments located below a height of 1 289,6 m (4 231 ft) above the runway should be sub-segmented based on the following set of height values: z = {18,9, 41,5, 68,3, 102,1, 147,5, 214,9, 334,9, 609,6, 1 289,6} metres, or z = {62, 136, 224, 335, 484, 705, 1 099, 2 000, 4 231} feet For each original segment below 1 289,6 m (4 231 ft), the above heights are implemented by identifying which height in the set above is closest to the original endpoint height (for a climb segment) or start-point height (for an approach segment). The actual sub-segment heights, zi, would then be calculated using: zi = ze [z’i / z’N] (i = k..N) where: ze is the original segment endpoint height (climb) or start-point height (approach) z’i is the ith member of the set of height values listed above z’N is the closest height from the set of height values listed above to height ze k denotes the index of the first member of the set of height values for which the calculated zk is strictly greater than the endpoint height of the previous original climb segment or the start-point height of the next original approach segment to be sub-segmented. In the specific case of an initial climb segment or last approach segment, k = 1, but in the more general case of airborne segments not connected to the runway, k will be greater than 1. Example for an initial climb segment: If the original segment endpoint height is ze = 304,8 m, then from the set of height values, 214,9 m < ze < 334,9 m and the closest height from the set to ze is z’7 = 334,9 m. The sub-segment endpoint heights are then computed by: zi = 304,8 [z’i / 334,9] for i = 1 to 7 (noting that k =1 in that case, as this is an initial climb segment) Thus z1 would be 17,2 m and z2 would be 37,8 m, etc. Segmentation of airborne segments For airborne segments where there is a significant speed change along a segment, this shall be subdivided as for the ground roll, namely nseg = int (1 + |V 2 - V 1|/10) (2.7.14) where V1 and V2 are the segment start and end speeds respectively. The corresponding sub-segment parameters are calculated in a similar manner as for the takeoff ground roll, using equations 2.7.9 to 2.7.11. Ground track A ground track, whether a backbone track or a dispersed sub-track, is defined by a series of (x,y) co-ordinates 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 Δξtrans in any turn are dictated by bank angle change requirements. The remainder of the arc with change of heading Δξ - 2·Δξtrans degrees is divided into nsub sub-arcs according to the equation: nsub = int (1 + (Δξ – 2•Δξ trans ) / 10 (2.7.15) 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 Δξ = (ξ-2•Δξ trans ) / nsub (2.7.16) where nsub needs to be large enough to ensure that Δξ sub ≤ 10 degrees. The segmentation of an arc (excluding the terminating transition sub-segments) is illustrated in Figure 2.7.h.2 (****). Once the ground track segments have been established in the x-y plane, the flight profile segments (in the s-z plane) are overlaid to produce the three-dimensional (x, y, z) track segments. The ground track should always extend from the runway to beyond the extent of the calculation grid. This can be achieved, if necessary, by adding a straight segment of suitable length to the last segment of the ground track. The total length of the flight profile, once merged with the ground track, must also extend from the runway to beyond the extent of the calculation grid. This can be achieved, if necessary, by adding an extra profile point: — to the end of a departure profile with speed and thrust values equal to those of the last departure profile point, and height extrapolated linearly from the last and penultimate profile points, or — to the beginning of an arrival profile with speed and thrust value equal to those of the first arrival profile point, and height extrapolated linearly back from the first and second profile points. Segmentation adjustments of airborne segments After the 3-D flight path segments have been derived according to the procedure described in Section 2.7.13, further segmentation adjustments may be necessary to remove flight path points which are too close together. When adjacent points are within 10 metres of each other, and when the associated speeds and thrusts are the same, one of the points should be eliminated. (*) For this purpose the total length of the ground track should always exceed that of the flight profile. This can be achieved, if necessary, by adding straight segments of suitable length to the last segment of the ground track." (**) Even if engine power settings remain constant along a segment, propulsive force and acceleration can change due to variation of air density with height. However, for the purposes of noise modelling these changes are normally negligible." (***) This was recommended in the previous edition of ECAC Doc 29 but is still considered provisional pending the acquisition of further corroborative experimental data." (****) Defined in this simple way, the total length of the segmented path is slightly less than that of the circular path. However the consequent contour error is negligible if the angular increments are below 30°.’."