— 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.
δtpropR(k) is the sound propagation time for sound emission point k, such that:
δtpropR(k) = SRR(k) / cR tR(k) is the time of sound reception at the microphone for sound emitted at point k, such that:
tR(k) = tER(k) + δtpropR(k) Finally calculate δtR(k), the effective time duration for the sound received at the microphone at time tR(k), as specified in A36.9.4.2.1 of part 36 where:
tR(k) = [(tR(k) – tR(k-1)) + (tR(k+1) – tR(k))]/2 403(a)(3) Computation of EPNL by the simplified method of adjustment [ETM 4.3.1.3] Section A36.9.3 of the part 36 provides specifications for the simplified adjustment method. The following procedure illustrates one method for meeting the requirements of this section.
403(a)(3)(A) Inputs required for performing the simplified method [ETM 4.3.1.3.1] The following inputs are required for the simplified method:
a) The one-third octave band spectrum representing the measured test-day aircraft noise at the time of PNLTM, SPL(i, kM), plus the spectra representing the measured test-day aircraft noise for any PNLT(k) values within 2 dB of the level of PNLTM (secondary peaks), SPL(i,k), determined in accordance with A36.9.3.2.2 of part
36. Additional guidance is provided in 401(c);
b) The average atmospheri c absorption coefficients, α(i) for each one-third octave band, i, determined for testday conditions, in dB per 100 metres, as determined from measured test-day meteorological data in accordance with A36.2.2.3 of part 36. Additional gui dance is provided in 401(b)(2) (Calculation of sound attenuation coefficients for the effects of atmospheric absorption);
c) The atmospheric ab sorption coefficients, α(i)0 for each one-third octave band, i, determined for reference conditions in dB per 100 meters, as determined in accordance with A36.2.2.3 of part 36. Note that reference conditions for atmospheric absorption are specified in B36.7 of part 36 for airplanes being certified under Stage 3 or Stage 4 or Stage 5 requirements, and in H36.3(a) of part 36 for helicopters, as a homogenous atmosphere with temperature of 77°F (25°C) and relative humidity of 70%;
d) The sound propagation distance (in meters) between the aircraft and the microphone at the time of emission of the PNLTM noise data record, SR( kM), and for each secondary peak record, SR(k ), as determined in 403(a)(2);
e) The reference sound propagation distance (in meters) between the aircraft and the reference microphone at the time of emission of the PNLTMR noise data record, SRR(kM), and of each secondary peak record, SRR(k), as determined in 403(a)(2);
f) The test-day bandsharing adjustment, ΔB, as determined in A36.4.4.2 of part 36;
g) The test-day aircraft groundspeed, V G, as determined from th e measured aircraft tr acking TSPI data from 403(a)(2);
h) The reference aircraft groundspeed, V GR, as determined from 403(a)(2);
i) The test-day value for EPNL, as specified in A36.4 of part 36;
j) The test-day value fo r PNLTM, as specified in A36.4 of part 36; and
k) A source noise adjustment, Δ3, as determined in A36.9.3.4.2 of part 36.
403(a)(3)(B) Adjustmen t of sound pressure levels to reference conditions [ETM 4.3.1.3.2] Adjust each measured test-day one-third octave band SPL in the spectrum associated with PNLTM, and in the spectra associated with any secondary peaks, for spherical spreading (also known as “inverse square law”) and the effect of the change in sound attenuation due to atmospheric absorp tion for differences between th e test and reference flight paths, using the equation provided in A36.9.3.2.1 of part 36:
For the measured test-day acoustic data spectrum associated with PNLTM, kM:
For all one-third octave bands, i:
SPLR(i,kM) = SPL(i,kM) + 0.01 [α(i) – α(i)0] SR(kM) + 0.01 α(i)0 (SR(kM) – SRR(kM)) + 20 log (SR(kM)/ SRR(kM)) For each measured test-day acoustic data spectrum associated with a secondary peak, k:
For all one-third octave bands, i:
SPLR(i,k) = SPL(i,k) + 0.01 [α(i) – α(i)0] SR(k) + 0.01 α(i)0 (SR(k) – SRR(k)) + 20 log (SR(k)/ SRR(k)) 403(a)(3)(C) De termination of reference-condition tone-corrected perceived noise levels [ETM 4.3.1.3.3] Calculate the reference-condition tone-corrected perceived noise level, PNLT R(kM) for the adjusted spectrum associated with PNLTM, kM, and for each spectrum associated with a secondary peak, k, using the procedures specified in A36.4.6 of part 36, including calculation of perceived noise level, PNLR(k) and tone-correction factor, CR(k).
403(a)(3)(D) Application of test-day ba ndsharing adjustment to reference-condition maximum tone-corrected perceived noise level and determination o f t h e 1 simplified adjustment term [ETM 4.3.1.3.4] In order to account for the presence of bandsharing in the measured te st-day PNLTM and EPNL, the test-day bandsharing adjustment, Δ B, as determined in A36.4.4.2 of part 36, is applied to the adjusted reference-condition PNLTR(kM) value prior to determination of other adjustment factors, and subsequent calculation of the simplified reference-condition effective perceived noise level, EPNLR as specified in A36.9.3 of part 36:
PNLTMR = PNLTR(kM) + ΔB Page 206
The simplified adjustment term Δ1 is then calculated per A36.9.3.2.1 of part 36, by subtracting the test-day (bandsharing-adjusted) value for PNLTM (as determined in accordance with A36.4.4.2 of part 36) from the referencecondition (bandsharing-adjusted) value for PNLTMR obtained from the equation above:
Δ1 = PNLTMR – PNLTM 403(a)(3)(E) Det ermination of the ΔPeak simplified adjustment term to account for the effects of secondary peaks [ETM 4.3.1.3.5] Using the bandsharing-adjusted reference-condition PNLTM R value as determined in 4.3.1.3.4, and the referencecondition values of PNLTR for each of the secondary peaks, as determined in 4.3.1.3.3, calculate the secondary peak adjustment term, ΔPeak, specified in A36.9.3.3.2 of part 36 as follows:
a) Compare the PNLT R values for all of the secondary peaks to determine which has the maximum value of PNLTR, and identify this secondary peak value as PNLTR(MaxPeak).
b) If the value of PNLT R(MaxPeak) exceeds that of PNLTMR, then calculate the secondary peak adjustment term, ΔPeak, by subtracting PNLTMR from PNLTR(MaxPeak) such that:
ΔPeak = PNLTR(MaxPeak) – PNLTMR 403(a)(3)(F) Det ermination of the Δ2 simplified adjustment term to account for change in noise level [ETM 4.3.1.3.6] Section A36.9.3.3.1 of part 36 specifies that whenever the flight path and/or ground velocity of aircraft differ between test-day and reference conditions, then a duration adjustment should be determined and applied.
This duration adjustment term, Δ2, comprising two components, accounts for the effects on the EPNL noise duration of differences between the test and reference distance and speed. These components are determined as follows:
Δ2 [distance component] = -7.5 log (SR(kM) / SRR(kM)) where:
kM is the noise data point at which PNLTM occurred; and Δ2 [speed component] = +10 log (VG / VGR) where:
VG and VGR are the test and reference ground speeds of the aircra ft, determined from aircraft tracking TSPI data, as determined in 403(a)(2).
The complete equation for the simplified duration adjustment is:
Δ2 = -7.5 log (SR(kM) / SRR(kM)) + 10 log (VG / VGR) 403(a)(3)(G) Determination of the Δ3 simplified adjustment term to account for differences in source noise [ETM 4.3.1.3.7] Section A36.9.3.4.2 of part 36 defines and describes various means of determining a Δ3 adjustment term to be used in the calculation of reference-condition effective perceived noise level.
Determine the appropriate process, and calculate the value for Δ3 per A36.9.3.4.2 of part 36, to account for the effects of differences in source noise between test-day and reference conditions.
Application of this adjustment term, Δ3, is illustrated in 403(a)(3)(H).
403(a)(3)(H) Determinati on of the simplified reference-condition effective perceived noise level [ETM 4.3.1.3.8] Compute the simplified reference-condition effective perceived noise level, EPNLR, as specified in A36.9.3.1 of part 36 as follows:
EPNL R = EPNL + Δ1 + ΔPeak + Δ2 + Δ3 where:
— EPNL is the test-day value for effective perceive d noise level, determined in accordance with A36.4.6 of part 36;
— Δ1 is the simplified adjustment term for the eff ects of adjusting the PNLTM spectrum to reference conditions as determined in 403(a)(3)(D);
— ΔPeak is the secondary peak adjustment term as determined in 403(a)(3)(E);
— Δ2 is the simplified adjustment term for duration effects as determined in 403(a)(3)(F); and — Δ3 is the adjustment term for source noise effects as described in 403(a)(3)(G).
403(a)(3)(I) Worked example calculat ions illustrating the simplified method [ETM 4.3.1.3.9]
4.3.1.3.9 Worked example calculations illustrating the simplified method [Reserved] 403(a)(4) Computation of EPNL by the integrated method of adjustment [ETM 4.3.1.4] Section A36.9.4 of part 36 provides specifications for the integrated method. The following procedure illustrates one method for meeting the requirements of A36.9.4.
403(a)(4)(A) Inputs required for performing the integrated method [ETM 4.3.1.4.1] The following inputs are required for the integrated method:
a) the one-third octave band spectral time-history repr esenting the measured test-day aircraft noise, SPL( i,k), encompassing at least the test-day EPNL noise duration as defined in A36.4.6 of part 36; additional guidance is provided in 401(c);
b) the average atmospheric absorption coefficients, α(i), for each one-third octave band, i, determined for testday conditions, in dB per 100 meters, as determined from measured test-day meteorological data in accordance with A36.7 of part 36; a dditional guidance is pr ovided in 401( b)(2) (Calculation of sound attenuation coefficients for the effects of atmospheric absorption);
c) the reference atmospheri c absorption coefficients, α (i)0 for each one-third octave band, i, in dB per 100 metres, as determined in accordance with A36.7 of part 36; note that reference conditions for atmospheric absorption are specified in B36.7 of part 36 for airplanes being certified under Stage 3, Stage 4 or 5 Page 208