for the test data, including sound emission coordinates (t, X, Y, Z) for each measured acoustic spectrum (k) in the acoustic spectral time-history data set. Once the sound emission coordinates have been identified, sound propagation distances and acoustic emission angles are calculated, which are used to determine the position of the aircraft on the reference flight path. For the integrated method of adjustment only, the series of positions on the reference flight path are then used to obtain the effective duration for each spectrum k for the reference condition acoustic data set.
403(a)(2)(A) Assumptions [ETM 4.3.1.2.1]
a) The test aircraft position during noise measurements can be represented by a straight-line flight path;
b) the ground reference system used in the figures, a right-handed coordinate system, is assumed to be fixed to the surface of a flat earth with th e X axis pointing along the reference ground track, the Y axis pointing to the left of the reference ground track, and the Z axis pointing up;
Note.— For airplanes the term “reference ground track” refers to the “extended centerline of the runway” or the “extended runway centerline” referred to in B36.3 of part 36.
c) the point on the ground directly beneath the centerlin e microphone is the origin of the XYZ coordinate system (X=0, Y=0, Z=0);
d) the X-coordinate value increases with time as the aircraft moves through the noise measurement test site;
e) the single-point flight path descriptors represent average values over the noise duration as defined in §36.9.4.2(b) of part 36; and
f) angular quantities are expressed in radians except where otherwise noted.
403(a)(2)(B) Steps involved [ETM 4.3.1.2.2]
a) Characterization of a straight-line average test flight path based on descriptors for a single point (see 403(a)(2)(C));
b) determination of test ai rcraft position at time of sound emission of each acoustic spectrum (see 403(a)(2)(D));
c) calculation of the geometric minimum distance between the test flight path and the microphone (see 403(a)(2)(E));
d) determination of test aircraft noise geometry (sound propagation distance, acoustic emission angle) for each acoustic spectrum (see 403(a)(2)(F));
e) determination of reference flight path (see 403(a)(2)(G));
f) determination of reference sound propagation dist ance for each acoustic spectrum (see 403(a)(2)(H)); and
g) determination of effective duration for each acoustic spectrum for the integrated procedure (see 403(a)(2)(I)).
403(a)(2)(C) Characterization of a straight-line average flight path based on descriptors for a single point [ETM 4.3.1.2.3] A straight-line flight path can be defined knowing the aircraft position, speed, and three-dimensional direction (vector) at a single point in time (see Figure 37). For the method described in this section the “single-point” descriptors are:
— tOH is the time at overhead (the time when the aircraft X coordinate = 0.0);
— XOH is the X coordinate of the centre line microphone, X = 0.0;
— YOH is the lateral offset of the aircraft from the reference ground track at tOH ;
— ZOH is the aircraft height above the reference X-Y ground plane at tOH;
— VG is the average groundspeed over the noise duration;
— γ is the average climb/descent angle; and — χ is the average lateral cross-track angle.
Note.— The average ground speed, VG, used in calculations for aircraft noise geometry is independent from any cockpit instrumentation, and is to be determined from the aircraft position measurements. For reference conditions, the reference groundspeed, VGR, is to be determined from the reference climb/descent angle and its relationship to the reference true airspeed value, VR.
Generate the straight-line average aircraft flight path t, X, Y, Z position time history from the single-point flight path descriptors at an appropriate sample rate (typically two times per second):
For any relative time, t(p):
X(p) = (t(p) – tOH) (VG cos (χ)) + XOH Y(p) = (t(p) – tOH) (VG sin (χ)) + YOH Z(p) = (t(p) – tOH) (VG tan (γ)) + ZOH Page 194
Figure 37. Single-point flight path descriptors 403(a)(2)(D) Determination of test aircraft position at time of sound emission of each acoustic spectrum [ETM 4.3.1.2.4] Sound emitted from the aircraft takes a finite time to propagate prior to being received at the measurement microphone.
During this time, the aircraft has travelled a finite distance along the flight path. Therefore, it is necessary to determine the time and position coordinates of the aircraft for the point of sound emission for each acoustic record k (see Figure
38).
The spectral time history of measured aircraft noise data includes a series of slow sample times as specified in A36.3.7.5 of part 36. For each of these measurement times, tm(k), the associated time of sound emission, tE(k), as well as the sound emission coordinates, X E(k), YE(k), ZE(k), can be determined using information about the microphone, the measured aircraft position and time, and the test speed of sound (c).
The microphone position descriptors are:
— XMIC is the longitudinal distance along the reference ground track, between microphone location and coordinate system origin (typically 0.0);
— YMIC is the lateral distance between microphone location and the reference ground track (typically 0.0 for centerline microphone, and ±492 ft (±150 m) or ±1476 ft (±450 m) for lateral microphones);
— ZMIC is the height of ground at microphone location relative to the reference ground plane (typically 0.0);
and — HMIC is the height of microphone above local ground (4 ft (1.2 m));
Figure 38. Aircraft position at time of sound emission Using the average straight-line flight path position time history from 403(a)(2)(C) and the microphone position descriptors listed above, develop an emission/reception arra y for eventual determination of aircraft sound emission coordinates for each measured acoustic spectral data record, k, as follows:
a) Calculate sound speed (c) for test-day conditions (see 308);
b) For each pth aircraft position sample in the position time history, t( p), X(p), Y(p) and Z(p ), calculate the following:
1) Slant range between the aircraft and the microphone:
SR(p) = [(X(p) – XMIC)2 + (Y(p) – YMIC)2 + (Z(p) – (ZMIC + HMIC))2]0.5
2) Sound propagation time:
δtprop(p) = SR(p) / c
3) Reception time:
trec(p) = t(p) + δtprop(p)
c) The emission/reception array should now include the following for each aircraft position:
t(p), X(p), Y(p), Z(p) and trec(p) Using linear interpolation, determine the time of sound emission, t E(k), for each kth measured acoustic spectral data record in the spectral time history:
tE(k) = t(p2) + ([ t(p1) - t(p2)] ([tm(k) - trec(p2)] / [trec(p1) - trec(p2)])) where:
— tE(k) is the relative time when spectrum k was emitted;
— tm(k) is the acoustic measurement time for spectral record k (as per Section 3.7.6 of Appendix 2 of the Annex) — p1 is the aircraft position record where trec(p) is > tm(k); and — p2 is the aircraft position record where trec(p) is < tm(k).
Once the time of sound emission has been determined generate the sound emission coordinates XE(k), YE(k) and ZE(k) for each kth measured acoustic spectral data record as follows:
XE(k) = (tE(k) – tOH) (VG cos(χ)) + XOH YE(k) = (tE(k) – tOH) (VG sin(χ)) + YOH ZE(k) = (tE(k) – tOH) (VG tan(γ))+ ZOH 403(a)(2)(E) Calculation of the geometric mi nimum distance between the test flight path and the microphone [ETM 4.3.1.2.5] Using the single-point flight path descriptors identified in 403(a)(2)(C) and the coordinates of the microphone identified in 403(a)(2)(D), calculate the geometrical minimum distance (closest point of approach or “CPA”), the line from the microphone of interest which intersects the straight line flight path at right angles:
CPA = (Gnorm2 + GCPA2)0.5 Intermediate calculations for determination of CPA (see Figures 4-31 and 4-32) include:
a) Lateral distance from micropho ne to average ground track at tOH:
Ydis = YMIC – YOH
b) Line on the ground from the microphone location which intersects the average ground track at right angles:
Gnorm = (Ydis) cos (χ
c) Vertical distance of flig ht path above microphone:
Malt = ZOH – (ZMIC + HMIC)
d) Distance along average ground track between X=0.0 and intersection with Gnorm:
Ginc = (Ydis) sin (χ
e) Vertical difference between G alt and ZOH:
Zinc = (Ginc) tan (γ
f) Vertical height of flight path above microphone at intersection of Gnorm and average ground track Galt = Malt + Zinc Page 197
g) Line from the point at the microphone height (H MIC) vertically above the point where Gnorm intersects the average ground track, which intersects the average straight line flight path at right angles GCPA = (Galt) cos (γ Figure 39. Basic CPA geometry Note.— In contrast to the previous figure, the horizontal X-Y plane illustrated in this figure is now at the height of the microphone, not the reference ground plane where Z=0.0.
Figure 40. Detailed CPA geometry Note.— This figure illustrates the CPA geometry for a lateral microphone, but also includes intermediate elements used in the calculation of Gnorm and G CPA applicable to a centerline microphone. Also, the X-Y plane in this figure is at the height of the lateral microphone.
Figure 41. Sound propagation distance, SR( k) Page 199
403(a)(2)(F) Determi nation of test aircraft noise geometry (sound propagation distance and acoustic emission angle for each acoustic s p e c t r u m ) [ETM 4.3.1.2.6] Using the sound emission coordinates from 403(a)(2)(D) calculate slant range SR(k), the sound propagation distance between the aircraft and the microphone, for each spectrum k in the spectral time history (see Figure 41):
SR(k) = [(XE(k) – XMIC)2 + (YE(k) – YMIC)2 + (ZE(k) – [ ZMIC + HMIC])2]0.5 Using the sound propagation distance, SR(k), and the geometric minimum distance between the flight path and microphone, CPA, from 403(a)(2)(E), calculate the three-dimensional acoustic emission angle, θ, for each spectrum k (see Figure 42):
θ(k) = arcsin (CPA / SR(k)) when aircraft is positioned prior to CPA θ(k) = π/2 (i.e. 90 degrees) when aircraft is positioned at CPA θ(k) = π – arcsin (CPA / SR(k)) when aircraft is positioned subsequent to CPA The resulting noise geometry time history for each acoustic spectral data record k now includes:
— tm(k) is the acoustic measurement time for spectrum k;
— tE(k) is the sound emission time for spectrum k, received at the microphone at tm(k);
— XE(k) is the X-coordinate at time of sound emission for spectrum k;
— YE(k) is the Y-coordinate at time of sound emission for spectrum k;
— ZE(k) is the Z-coordinate at time of sound emission for spectrum k;
— SR(k) is the sound propagation distance (slant range) for spectrum k; and — θ(k) is the three-dimensional acoustic emission angle for spectrum k.
Note.— SR(k) is used for calculations of sound attenuation due to spherical spreading, as well as for sound attenuation due to atmospheric absorption, and for the distance-dependent portion of the Δ2 duration adjustment term used in the simplified method; θ(k) is used for determining the aircraft position on the reference flight path when adjusting noise data to reference conditions.
Figure 42. Acoustic emission angle, θ 403(a)(2)(G) Determination of ref erence flight path [ETM 4.3.1.2.7] By definition, the reference flight path is a straight line with no lateral displacement. This makes the associated noise geometry relatively simple.
The reference flight path geometry has the following characteristics:
— ZOHR is the vertical height of the reference flight path above the reference ground plane at tOH;
— VGR is the reference groundspeed;
— cR is the reference sound speed, 1135.5 ft/s (346.1 m/s) as per 308 of this AC;
— γR is the reference climb/descent angle;
— YMICR is the lateral distance between the reference microphone location and the reference ground track; and — HMICR is the height of the reference microphone (4 ft (1.2 m)) above the reference ground plane.
Calculate CPAR, the reference flight path geometrical minimum distance, or closest point of approach to microphone (see Figure 43a & b):
CPAR = (CPAOHR2 + YMICR2)0.5 where:
CPAOHR = (ZOHR – HMICR) cos (γR) Page 201
Note.— CPAOHR is the minimum distance directly under the reference flight path between the reference flight path and the reference microphone height at the intersection of the reference ground track and the lateral microphone line.
For centerline microphones, CPAR = CPAOHR.
Figure 43. CPA R for centre line and lateral microphones 403(a)(2)(H) Determin ation of reference sound propagation distance for each acoustic spectrum [ETM 4.3.1.2.8] The reference sound propagation distance, SR R(k), can be determined from the geometric relationship between the acoustic emission angle, (k), which is kept constant between the test and reference cases, and the geometric minimum distance between the reference microphone and the reference flight path, CPAR (see Figure 44):
SRR(k) = CPAR / sin (θ(k)) Page 202
Figure 44. Determination of ref erence sound propagation distance, SRR(k) 403(a)(2)(I) Determination of effect ive duration for each acoustic spectrum for the integrated procedure [ETM 4.3.1.2.9] When using the integrated method of adjustment described in A36.9.4 of part 36, an effective duration ( δtR(k)) for each reference condition PNLT value must be determined for use in the ca lculation of EPNL. The uniform, one-half second time intervals between the samples of the measured test aircraft noise data become non-uniform when projected to the reference case, due to adjustments for differences between test and reference conditions. The effective duration represents the time interval between successive acoustic data samples that would have been measured at the reference microphone under reference conditions.
Two elements are involved in determining the “measurement” time for each reference condition acoustic data sample, k:
a) the time of sound emission, tER(k); and
b) the sound propagation time, δtpropR(k).
Determining the time of sound emission, tER(k), for reference conditions requires calculation of three distances along the reference flight path, FPDist(CPAR), FPIncR(k), and FPDistR(k) (see Figure 45).
Figure 45. FPDist concept for centerline and lateral microphones FPDist(CPAR) is the distance along the reference flight path from CPA R to t OH (taking its sign from the reference climb/descent angle, R), such that:
FPDist(CPAR) = (CPAOHR) tan (γR) Note.— FPDist(CPAR) is positive when γR is positive.
FPIncR(k) is the distance along the reference flight path from sound emission point k to CPAR, such that:
FPIncR(k) = CPAR / tan(θ(k)), taking its sign from acoustic emission angle θ(k) as follows:
a) FPInc R(k) is positive when θ(k) < π/2 (i.e. < 90 degrees);
b) FPInc R(k) = 0 when θ(k) = π/2 (i.e. 90 degrees); and
c) FPInc R(k) is negative when θ(k) > π/2 (i.e. > 90 degrees).
FPDistR(k) is the distance along the flight path from point k to the overhead point, such that:
FPDistR(k) = FPDist(CPAR) + FPIncR(k) Note.— FPDistR(k) is positive when k is before overhead.
tER(k) is the time of sound emission for point k (found in this case by backing the aircraft along the flight path from tOH), such that:
tER(k) = tOH – (FPDistR(k) / VR) Note.— VR is the true airspeed for reference conditions.