**
Appendix A to Part 36 - Aircraft Noise Measurement
and Evaluation Under §36.101**
Sec.

A36.1 *Introduction.*

A36.2 *Noise Certification Test and Measurement Conditions.*

A36.3 *Measurement of Airplane Noise Received on the Ground.*

A36.4 *Calculations of Effective Perceived Noise Level From
Measured Data.*

A36.5 *Reporting of Data to the FAA.*

A36.6 *Nomenclature: Symbols and Units.*

A36.7 *Sound Attenuation in Air.*

A36.8 *[Reserved]*

A36.9 *Adjustment of Airplane Flight Test Results.*

**Section A36.1 Introduction**

A36.1.1 This appendix prescribes the conditions under which
airplane noise certification tests must be conducted and states the
measurement procedures that must be used to measure airplane noise. The
procedures that must be used to determine the noise evaluation quantity
designated as effective perceived noise level, EPNL, under §§36.101 and
36.803 are also stated.

A36.1.2 The instructions and procedures given are intended to
ensure uniformity during compliance tests and to permit comparison between
tests of various types of airplanes conducted in various geographical
locations.

A36.1.3 A complete list of symbols and units, the mathematical
formulation of perceived noisiness, a procedure for determining
atmospheric attenuation of sound, and detailed procedures for correcting
noise levels from non-reference to reference conditions are included in
this appendix.

**Section A36.2 Noise Certification Test and Measurement
Conditions**

A36.2.1 *General.*

A36.2.1.1 This section prescribes the conditions under which noise
certification must be conducted and the measurement procedures that must
be used.

**Note:** Many noise certifications involve only minor changes to
the airplane type design. The resulting changes in noise can often be
established reliably without resorting to a complete test as outlined in
this appendix. For this reason, the FAA permits the use of approved
equivalent procedures. There are also equivalent procedures that may be
used in full certification tests, in the interest of reducing costs and
providing reliable results. Guidance material on the use of equivalent
procedures in the noise certification of subsonic jet and propeller-driven
large airplanes is provided in the current advisory circular for this
part.

A36.2.2 *Test environment.*

A36.2.2.1 Locations for measuring noise from an airplane in flight
must be surrounded by relatively flat terrain having no excessive sound
absorption characteristics such as might be caused by thick, matted, or
tall grass, shrubs, or wooded areas. No obstructions that significantly
influence the sound field from the airplane must exist within a conical
space above the point on the ground vertically below the microphone, the
cone being defined by an axis normal to the ground and by a half-angle 80°
from this axis.

**Note:** Those people carrying out the measurements could
themselves constitute such obstruction.

A36.2.2.2 The tests must be carried out under the following
atmospheric conditions.

(a) No precipitation;

(b) Ambient air temperature not above 95 °F (35 °C) and not below 14 °F
(−10 °C), and relative humidity not above 95% and not below 20% over the
whole noise path between a point 33 ft (10 m) above the ground and the
airplane;

**Note:** Care should be taken to ensure that the noise measuring,
airplane flight path tracking, and meteorological instrumentation are also
operated within their specific environmental limitations.

(c) Relative humidity and ambient temperature over the whole noise path
between a point 33 ft (10 m) above the ground and the airplane such that
the sound attenuation in the one-third octave band centered on 8 kHz will
not be more than 12 dB/100 m unless:

(1) The dew point and dry bulb temperatures are measured with a device
which is accurate to ±0.9 °F (±0.5 °C) and used to obtain relative
humidity; in addition layered sections of the atmosphere are used as
described in section A36.2.2.3 to compute equivalent weighted sound
attenuations in each one-third octave band; or

(2) The peak noy values at the time of PNLT, after adjustment to
reference conditions, occur at frequencies less than or equal to 400 Hz.;

(d) If the atmospheric absorption coefficients vary over the PNLTM
sound propagation path by more than ±1.6 dB/1000 ft (±0.5 dB/100m) in the
3150Hz one-third octave band from the value of the absorption coefficient
derived from the meteorological measurement obtained at 33 ft (10 m) above
the surface, "layered" sections of the atmosphere must be used as
described in section A36.2.2.3 to compute equivalent weighted sound
attenuations in each one-third octave band; the FAA will determine whether
a sufficient number of layered sections have been used. For each
measurement, where multiple layering is not required, equivalent sound
attenuations in each one-third octave band must be determined by averaging
the atmospheric absorption coefficients for each such band at 33 ft (10 m)
above ground level, and at the flight level of the airplane at the time of
PNLTM, for each measurement;

(e) Average wind velocity 33 ft (10 m) above ground may not exceed 12
knots and the crosswind velocity for the airplane may not exceed 7 knots.
The average wind velocity must be determined using a 30-second averaging
period spanning the 10 dB-down time interval. Maximum wind velocity 33 ft
(10 m) above ground is not to exceed 15 knots and the crosswind velocity
is not to exceed 10 knots during the 10 dB-down time interval;

(f) No anomalous meteorological or wind conditions that would
significantly affect the measured noise levels when the noise is recorded
at the measuring points specified by the FAA; and

(g) Meteorological measurements must be obtained within 30 minutes of
each noise test measurement; meteorological data must be interpolated to
actual times of each noise measurement.

A36.2.2.3 When a multiple layering calculation is required by
section A36.2.2.2(c) or A36.2.2.2(d) the atmosphere between the airplane
and 33 ft (10 m) above the ground must be divided into layers of equal
depth. The depth of the layers must be set to not more than the depth of
the narrowest layer across which the variation in the atmospheric
absorption coefficient of the 3150 Hz one-third octave band is not greater
than ±1.6 dB/1000 ft (±0.5 dB/100m), with a minimum layer depth of 100 ft
(30 m). This requirement must be met for the propagation path at PNLTM.
The mean of the values of the atmospheric absorption coefficients at the
top and bottom of each layer may be used to characterize the absorption
properties of each layer.

A36.2.2.4 The airport control tower or another facility must be
aproved by the FAA for use as the central location at which measurements
of atmospheric parameters are representative of those conditions existing
over the geographical area in which noise measurements are made.

A36.2.3 *Flight path measurement.*

A36.2.3.1 The airplane height and lateral position relative to the
flight track must be determined by a method independent of normal flight
instrumentation such as radar tracking, theodolite triangulation, or
photographic scaling techniques, to be approved by the FAA.

A36.2.3.2 The airplane position along the flight path must be
related to the noise recorded at the noise measurement locations by means
of synchronizing signals over a distance sufficient to assure adequate
data during the period that the noise is within 10 dB of the maximum value
of PNLT.

A36.2.3.3 Position and performance data required to make the
adjustments referred to in section A36.9 of this appendix must be
automatically recorded at an approved sampling rate. Measuring equipment
must be approved by the FAA.

**Section A36.3 Measurement of Airplane Noise Received on the
Ground**

A36.3.1 *Definitions.*

For the purposes of section A36.3 the following definitions apply:

A36.3.1.1 *Measurement system* means the combination of
instruments used for the measurement of sound pressure levels, including a
sound calibrator, windscreen, microphone system, signal recording and
conditioning devices, and one-third octave band analysis system.

**Note:** Practical installations may include a number of microphone
systems, the outputs from which are recorded simultaneously by a
multi-channel recording/analysis device via signal conditioners, as
appropriate. For the purpose of this section, each complete measurement
channel is considered to be a measurement system to which the requirements
apply accordingly.

A36.3.1.2 *Microphone system* means the components of the
measurement system which produce an electrical output signal in response
to a sound pressure input signal, and which generally include a
microphone, a preamplifier, extension cables, and other devices as
necessary.

A36.3.1.3 *Sound incidence angle* means in degrees, an angle
between the principal axis of the microphone, as defined in IEC 61094-3
and IEC 61094-4, as amended and a line from the sound source to the center
of the diaphragm of the microphone.

**Note:** When the sound incidence angle is 0°, the sound is said to
be received at the microphone at "normal (perpendicular) incidence;" when
the sound incidence angle is 90°, the sound is said to be received at
"grazing incidence."

A36.3.1.4 *Reference direction* means, in degrees, the
direction of sound incidence specified by the manufacturer of the
microphone, relative to a sound incidence angle of 0°, for which the
free-field sensitivity level of the microphone system is within specified
tolerance limits.

A36.3.1.5 *Free-field sensitivity of a microphone system*
means, in volts per Pascal, for a sinusoidal plane progressive sound wave
of specified frequency, at a specified sound incidence angle, the quotient
of the root mean square voltage at the output of a microphone system and
the root mean square sound pressure that would exist at the position of
the microphone in its absence.

A36.3.1.6 *Free-field sensitivity level of a microphone system*
means, in decibels, twenty times the logarithm to the base ten of the
ratio of the free-field sensitivity of a microphone system and the
reference sensitivity of one volt per Pascal.

**Note:** The free-field sensitivity level of a microphone system
may be determined by subtracting the sound pressure level (in decibels re
20 μPa) of the sound incident on the microphone from the voltage level (in
decibels re 1 V) at the output of the microphone system, and adding 93.98
dB to the result.

A36.3.1.7 *Time-average band sound pressure level* means in
decibels, ten times the logarithm to the base ten, of the ratio of the
time mean square of the instantaneous sound pressure during a stated time
interval and in a specified one-third octave band, to the square of the
reference sound pressure of 20 μPa.

A36.3.1.8 *Level range* means, in decibels, an operating
range determined by the setting of the controls that are provided in a
measurement system for the recording and one-third octave band analysis of
a sound pressure signal. The upper boundary associated with any particular
level range must be rounded to the nearest decibel.

A36.3.1.9 *Calibration sound pressure level* means, in
decibels, the sound pressure level produced, under reference environmental
conditions, in the cavity of the coupler of the sound calibrator that is
used to determine the overall acoustical sensitivity of a measurement
system.

A36.3.1.10 *Reference level range* means, in decibels, the
level range for determining the acoustical sensitivity of the measurement
system and containing the calibration sound pressure level.

A36.3.1.11 *Calibration check frequency* means, in hertz, the
nominal frequency of the sinusoidal sound pressure signal produced by the
sound calibrator.

A36.3.1.12 *Level difference* means, in decibels, for any
nominal one-third octave midband frequency, the output signal level
measured on any level range minus the level of the corresponding
electrical input signal.

A36.3.1.13 *Reference level difference* means, in decibels,
for a stated frequency, the level difference measured on a level range for
an electrical input signal corresponding to the calibration sound pressure
level, adjusted as appropriate, for the level range.

A36.3.1.14 *Level non-linearity* means, in decibels, the
level difference measured on any level range, at a stated one-third octave
nominal midband frequency, minus the corresponding reference level
difference, all input and output signals being relative to the same
reference quantity.

A36.3.1.15 *Linear operating range* means, in decibels, for a
stated level range and frequency, the range of levels of steady sinusoidal
electrical signals applied to the input of the entire measurement system,
exclusive of the microphone but including the microphone preamplifier and
any other signal-conditioning elements that are considered to be part of
the microphone system, extending from a lower to an upper boundary, over
which the level non-linearity is within specified tolerance limits.

**Note:** Microphone extension cables as configured in the field
need not be included for the linear operating range determination.

A36.3.1.16 *Windscreen insertion loss* means, in decibels, at
a stated nominal one-third octave midband frequency, and for a stated
sound incidence angle on the inserted microphone, the indicated sound
pressure level without the windscreen installed around the microphone
minus the sound pressure level with the windscreen installed.

A36.3.2 *Reference environmental conditions.*

A36.3.2.1 The reference environmental conditions for specifying
the performance of a measurement system are:

(a) Air temperature 73.4 °F (23 °C);

(b) Static air pressure 101.325 kPa; and

(c) Relative humidity 50%.

A36.3.3. *General.*

**Note:** Measurements of aircraft noise that are made using
instruments that conform to the specifications of this section will yield
one-third octave band sound pressure levels as a function of time. These
one-third octave band levels are to be used for the calculation of
effective perceived noise level as described in section A36.4.

A36.3.3.1 The measurement system must consist of equipment
approved by the FAA and equivalent to the following:

(a) A windscreen (See A36.3.4.);

(b) A microphone system (See A36.3.5):

(c) A recording and reproducing system to store the measured aircraft
noise signals for subsequent analysis (see A36.3.6);

(d) A one-third octave band analysis system (see A36.3.7); and

(e) Calibration systems to maintain the acoustical sensitivity of the
above systems within specified tolerance limits (see A36.3.8).

A36.3.3.2. For any component of the measurement system that
converts an analog signal to digital form, such conversion must be
performed so that the levels of any possible aliases or artifacts of the
digitization process will be less than the upper boundary of the linear
operating range by at least 50 dB at any frequency less than 12.5 kHz. The
sampling rate must be at least 28 kHz. An anti-aliasing filter must be
included before the digitization process.

A36.3.4 *Windscreen.*

A36.3.4.1 In the absence of wind and for sinusoidal sounds at
grazing incidence, the insertion loss caused by the windscreen of a stated
type installed around the microphone must not exceed ±1.5 dB at nominal
one-third octave midband frequencies from 50 Hz to 10 kHz inclusive.

A36.3.5 *Microphone system.*

A36.3.5.1 The microphone system must meet the specifications in
sections A36.3.5.2 to A36.3.5.4. Various microphone systems may be
approved by the FAA on the basis of demonstrated equivalent overall
electroacoustical performance. Where two or more microphone systems of the
same type are used, demonstration that at least one system conforms to the
specifications in full is sufficient to demonstrate conformance.

**Note:** An applicant must still calibrate and check each system as
required in section A36.3.9.

A36.3.5.2 The microphone must be mounted with the sensing element
4 ft (1.2 m) above the local ground surface and must be oriented for
grazing incidence, i.e., with the sensing element substantially in the
plane defined by the predicted reference flight path of the aircraft and
the measuring station. The microphone mounting arrangement must minimize
the interference of the supports with the sound to be measured. Figure
A36-1 illustrates sound incidence angles on a microphone.

A36.3.5.3 The free-field sensitivity level of the microphone and
preamplifier in the reference direction, at frequencies over at least the
range of one-third-octave nominal midband frequencies from 50 Hz to 5 kHz
inclusive, must be within ±1.0 dB of that at the calibration check
frequency, and within ±2.0 dB for nominal midband frequencies of 6.3 kHz,
8 kHz and 10 kHz.

A36.3.5.4 For sinusoidal sound waves at each one-third octave
nominal midband frequency over the range from 50 Hz to 10 kHz inclusive,
the free-field sensitivity levels of the microphone system at sound
incidence angles of 30°, 60°, 90°, 120° and 150°, must not differ from the
free-field sensitivity level at a sound incidence angle of 0° ("normal
incidence") by more than the values shown in Table A36-1. The free-field
sensitivity level differences at sound incidence angles between any two
adjacent sound incidence angles in Table A36-1 must not exceed the
tolerance limit for the greater angle.

A36.3.6 *Recording and reproducing systems.*

A36.3.6.1 A recording and reproducing system, such as a digital or
analog magnetic tape recorder, a computer-based system or other permanent
data storage device, must be used to store sound pressure signals for
subsequent analysis. The sound produced by the aircraft must be recorded
in such a way that a record of the complete acoustical signal is retained.
The recording and reproducing systems must meet the specifications in
sections A36.3.6.2 to A36.3.6.9 at the recording speeds and/or data
sampling rates used for the noise certification tests. Conformance must be
demonstrated for the frequency bandwidths and recording channels selected
for the tests.

A36.3.6.2 The recording and reproducing systems must be calibrated
as described in section A36.3.9.

(a) For aircraft noise signals for which the high frequency spectral
levels decrease rapidly with increasing frequency, appropriate
pre-emphasis and complementary de-emphasis networks may be included in the
measurement system. If pre-emphasis is included, over the range of nominal
one-third octave midband frequencies from 800 Hz to 10 kHz inclusive, the
electrical gain provided by the pre-emphasis network must not exceed 20 dB
relative to the gain at 800 Hz.

A36.3.6.3 For steady sinusoidal electrical signals applied to the
input of the entire measurement system including all parts of the
microphone system except the microphone at a selected signal level within
5 dB of that corresponding to the calibration sound pressure level on the
reference level range, the time-average signal level indicated by the
readout device at any one-third octave nominal midband frequency from 50
Hz to 10 kHz inclusive must be within ±1.5 dB of that at the calibration
check frequency. The Frequency response of a measurement system, which
includes components that convert analog signals to digital form, must be
within ±0.3 dB of the response at 10 kHz over the frequency range from 10
kHz to 11.2 kHz.

**Note:** Microphone extension cables as configured in the field
need not be included for the frequency response determination. This
allowance does not eliminate the requirement of including microphone
extension cables when performing the pink noise recording in section
A36.3.9.5.

A36.3.6.4 For analog tape recordings, the amplitude fluctuations
of a 1 kHz sinusoidal signal recorded within 5 dB of the level
corresponding to the calibration sound pressure level must not vary by
more than ±0.5 dB throughout any reel of the type of magnetic tape used.
Conformance to this requirement must be demonstrated using a device that
has time-averaging properties equivalent to those of the spectrum
analyzer.

A36.3.6.5 For all appropriate level ranges and for steady
sinusoidal electrical signals applied to the input of the measurement
system, including all parts of the microphone system except the
microphone, at one-third-octave nominal midband frequencies of 50 Hz, 1
kHz and 10 kHz, and the calibration check frequency, if it is not one of
these frequencies, the level non-linearity must not exceed ±0.5 dB for a
linear operating range of at least 50 dB below the upper boundary of the
level range.

**Note 1:** Level linearity of measurement system components may be
tested according to the methods described in IEC 61265 as amended.

**Note 2:** Microphone extension cables configured in the field need
not be included for the level linearity determination.

A36.3.6.6 On the reference level range, the level corresonding to
the calibration sound pressure level must be at least 5 dB, but no more
than 30 dB less than the upper boundary of the level range.

A36.3.6.7 The linear operating ranges on adjacent level ranges
must overlap by at least 50 dB minus the change in attenuation introduced
by a change in the level range controls.

**Note:** It is possible for a measurement system to have level
range controls that permit attenuation changes of either 10 dB or 1 dB,
for example. With 10 dB steps, the minimum overlap required would be 40
dB, and with 1 dB steps the minimum overlap would be 49 dB.

A36.3.6.8 An overload indicator must be included in the recording
and reproducing systems so that an overload indication will occur during
an overload condition on any relevant level range.

A36.3.6.9 Attenuators included in the measurement system to permit
range changes must operate in known intervals of decibel steps.

A36.3.7 *Analysis systems.*

A36.3.7.1 The analysis system must conform to the specifications
in sections A36.3.7.2 to A36.3.7.7 for the frequency bandwidths, channel
configurations and gain settings used for analysis.

A36.3.7.2 The output of the analysis system must consist of one-third
octave band sound pressure levels as a function of time, obtained by
processing the noise signals (preferably recorded) through an analysis
system with the following characteristics:

(a) A set of 24 one-third octave band filters, or their equivalent,
having nominal midband frequencies from 50 Hz to 10 kHz inclusive;

(b) Response and averaging properties in which, in principle, the
output from any one-third octave filter band is squared, averaged and
displayed or stored as time-averaged sound pressure levels;

(c) The interval between successive sound pressure level samples must
be 500 ms ±5 milliseconds(ms) for spectral analysis with or without slow
time-weighting, as defined in section A36.3.7.4;

(d) For those analysis systems that do not process the sound pressure
signals during the period of time required for readout and/or resetting of
the analyzer, the loss of data must not exceed a duration of 5 ms; and

(e) The analysis system must operate in real time from 50 Hz through at
least 12 kHz inclusive. This requirement applies to all operating channels
of a multi-channel spectral analysis system.

A36.3.7.3 The minimum standard for the one-third octave band
analysis system is the class 2 electrical performance requirements of IEC
61260 as amended, over the range of one-third octave nominal midband
frequencies from 50 Hz through 10 kHz inclusive.

**Note:** IEC 61260 specifies procedures for testing of one-third
octave band analysis systems for relative attenuation, anti-aliasing
filters, real time operation, level linearity, and filter integrated
response (effective bandwidth).

A36.3.7.4 When slow time averaging is performed in the analyzer,
the response of the one-third octave band analysis system to a sudden
onset or interruption of a constant sinusoidal signal at the respective
one-third octave nominal midband frequency, must be measured at sampling
instants 0.5, 1, 1.5 and 2 seconds(s) after the onset and 0.5 and 1s after
interruption. The rising response must be −4 ±1 dB at 0.5s, −1.75 ±0.75 dB
at 1s, −1 ±0.5 dB at 1.5s and −0.5 ±0.5 dB at 2s relative to the
steady-state level. The falling response must be such that the sum of the
output signal levels, relative to the initial steady-state level, and the
corresponding rising response reading is −6.5 ±1 dB, at both 0.5 and 1s.
At subsequent times the sum of the rising and falling responses must be
−7.5 dB or less. This equates to an exponential averaging process (slow
time-weighting) with a nominal 1s time constant (*i.e.,* 2s averaging
time).

A36.3.7.5 When the one-third octave band sound pressure levels are
determined from the output of the analyzer without slow time-weighting,
slow time-weighting must be simulated in the subsequent processing.
Simulated slow time-weighted sound pressure levels can be obtained using a
continuous exponential averaging process by the following equation:

Ls (i,k)=10 log [(0.60653) 10^{0.1 Ls[i, (k−1)]} +
(0.39347) 10^{0.1 L (i, k)}]

where Ls(i,k) is the simulated slow time-weighted sound
pressure level and L(i,k) is the as-measured 0.5s time average sound
pressure level determined from the output of the analyzer for the k-th
instant of time and i-th one-third octave band. For k=1, the slow
time-weighted sound pressure Ls[i, (k−1=0)] on the right hand
side should be set to 0 dB. An approximation of the continuous exponential
averaging is represented by the following equation for a four sample
averaging process for k ≥ 4:

Ls (i,k)=10 log [(0.13) 10^{0.1 L[i,(k−3)]} +
(0.21) 10^{0.1 L[i, (k−2)]} + (0.27) 10^{0.1 L[i, (k−1)]}
+ (0.39) 10^{0.1 L[i, k]}]

where Ls (i, k) is the simulated slow time-weighted sound
pressure level and L (i, k) is the as measured 0.5s time average sound
pressure level determined from the output of the analyzer for the k-th
instant of time and the i-th one-third octave band.

The sum of the weighting factors is 1.0 in the two equations. Sound
pressure levels calculated by means of either equation are valid for the
sixth and subsequent 0.5s data samples, or for times greater than 2.5s
after initiation of data analysis.

**Note:** The coefficients in the two equations were calculated for
use in determining equivalent slow time-weighted sound pressure levels
from samples of 0.5s time average sound pressure levels. The equations do
not work with data samples where the averaging time differs from 0.5s.

A36.3.7.6 The instant in time by which a slow time-weighted sound
pressure level is characterized must be 0.75s earlier than the actual
readout time.

**Note:** The definition of this instant in time is needed to
correlate the recorded noise with the aircraft position when the noise was
emitted and takes into account the averaging period of the slow
time-weighting. For each 0.5 second data record this instant in time may
also be identified as 1.25 seconds after the start of the associated 2
second averaging period.

A36.3.7.7 The resolution of the sound pressure levels, both
displayed and stored, must be 0.1 dB or finer.

A36.3.8 *Calibration systems.*

A36.3.8.1 The acoustical sensitivity of the measurement system
must be determined using a sound calibrator generating a known sound
pressure level at a known frequency. The minimum standard for the sound
calibrator is the class 1L requirements of IEC 60942 as amended.

A36.3.9 *Calibration and checking of system.*

A36.3.9.1 Calibration and checking of the measurement system and
its constituent components must be carried out to the satisfaction of the
FAA by the methods specified in sections A36.3.9.2 through A36.3.9.10. The
calibration adjustments, including those for environmental effects on
sound calibrator output level, must be reported to the FAA and applied to
the measured one-third-octave sound pressure levels determined from the
output of the analyzer. Data collected during an overload indication are
invalid and may not be used. If the overload condition occurred during
recording, the associated test data are invalid, whereas if the overload
occurred during analysis, the analysis must be repeated with reduced
sensitivity to eliminate the overload.

A36.3.9.2 The free-field frequency response of the microphone
system may be determined by use of an electrostatic actuator in
combination with manufacturer's data or by tests in an anechoic free-field
facility. The correction for frequency response must be determined within
90 days of each test series. The correction for non-uniform frequency
response of the microphone system must be reported to the FAA and applied
to the measured one-third octave band sound pressure levels determined
from the output of the analyzer.

A36.3.9.3 When the angles of incidence of sound emitted from the
aircraft are within ±30° of grazing incidence at the microphone (see
Figure A36-1), a single set of free-field corrections based on grazing
incidence is considered sufficient for correction of directional response
effects. For other cases, the angle of incidence for each 0.5 second
sample must be determined and applied for the correction of incidence
effects.

A36.3.9.4 For analog magnetic tape recorders, each reel of
magnetic tape must carry at least 30 seconds of pink random or
pseudo-random noise at its beginning and end. Data obtained from analog
tape-recorded signals will be accepted as reliable only if level
differences in the 10 kHz one-third-octave-band are not more than 0.75 dB
for the signals recorded at the beginning and end.

A36.3.9.5 The frequency response of the entire measurement system
while deployed in the field during the test series, exclusive of the
microphone, must be determined at a level within 5 dB of the level
corresponding to the calibration sound pressure level on the level range
used during the tests for each one-third octave nominal midband frequency
from 50 Hz to 10 kHz inclusive, utilizing pink random or pseudo-random
noise. Within six months of each test series the output of the noise
generator must be determined by a method traceable to the U.S. National
Institute of Standards and Technology or to an equivalent national
standards laboratory as determined by the FAA. Changes in the relative
output from the previous calibration at each one-third octave band may not
exceed 0.2 dB. The correction for frequency response must be reported to
the FAA and applied to the measured one-third octave sound pressure levels
determined from the output of the analyzer.

A36.3.9.6 The performance of switched attenuators in the equipment
used during noise certification measurements and calibration must be
checked within six months of each test series to ensure that the maximum
error does not exceed 0.1 dB.

A36.3.9.7 The sound pressure level produced in the cavity of the
coupler of the sound calibrator must be calculated for the test
environmental conditions using the manufacturer's supplied information on
the influence of atmospheric air pressure and temperature. This sound
pressure level is used to establish the acoustical sensitivity of the
measurement system. Within six months of each test series the output of
the sound calibrator must be determined by a method traceable to the U.S.
National Institute of Standards and Technology or to an equivalent
national standards laboratory as determined by the FAA. Changes in output
from the previous calibration must not exceed 0.2 dB.

A36.3.9.8 Sufficient sound pressure level calibrations must be
made during each test day to ensure that the acoustical sensitivity of the
measurement system is known at the prevailing environmental conditions
corresponding with each test series. The difference between the acoustical
sensitivity levels recorded immediately before and immediately after each
test series on each day may not exceed 0.5 dB. The 0.5 dB limit applies
after any atmospheric pressure corrections have been determined for the
calibrator output level. The arithmetic mean of the before and after
measurements must be used to represent the acoustical sensitivity level of
the measurement system for that test series. The calibration corrections
must be reported to the FAA and applied to the measured one-third octave
band sound pressure levels determined from the output of the analyzer.

A36.3.9.9 Each recording medium, such as a reel, cartridge,
cassette, or diskette, must carry a sound pressure level calibration of at
least 10 seconds duration at its beginning and end.

A36.3.9.10 The free-field insertion loss of the windscreen for
each one-third octave nominal midband frequency from 50 Hz to 10 kHz
inclusive must be determined with sinusoidal sound signals at the
incidence angles determined to be applicable for correction of directional
response effects per section A36.3.9.3. The interval between angles tested
must not exceed 30 degrees. For a windscreen that is undamaged and
uncontaminated, the insertion loss may be taken from manufacturer's data.
Alternatively, within six months of each test series the insertion loss of
the windscreen may be determined by a method traceable to the U.S.
National Institute of Standards and Technology or an equivalent national
standards laboratory as determined by the FAA. Changes in the insertion
loss from the previous calibration at each one-third-octave frequency band
must not exceed 0.4 dB. The correction for the free-field insertion loss
of the windscreen must be reported to the FAA and applied to the measured
one-third octave sound pressure levels determined from the output of the
analyzer.

*A36.3.10 Adjustments for ambient noise.*

A36.3.10.1 Ambient noise, including both a acoustical background
and electrical noise of the measurement system, must be recorded for at
least 10 seconds at the measurement points with the system gain set at the
levels used for the aircraft noise measurements. Ambient noise must be
representative of the acoustical background that exists during the flyover
test run. The recorded aircraft noise data is acceptable only if the
ambient noise levels, when analyzed in the same way, and quoted in PNL
(see A36.4.1.3 (a)), are at least 20 dB below the maximum PNL of the
aircraft.

A36.3.10.2 Aircraft sound pressure levels within the 10 dB-down
points (see A36.4.5.1) must exceed the mean ambient noise levels
determined in section A36.3.10.1 by at least 3 dB in each one-third octave
band, or must be adjusted using a method approved by the FAA; one method
is described in the current advisory circular for this part.

**Section A36.4 Calculation of Effective Perceived Noise Level
From Measured Data**

A36.4.1 *General.*

A36.4.1.1 The basic element for noise certification criteria is
the noise evaluation measure known as effective perceived noise level,
EPNL, in units of EPNdB, which is a single number evaluator of the
subjective effects of airplane noise on human beings. EPNL consists of
instantaneous perceived noise level, PNL, corrected for spectral
irregularities, and for duration. The spectral irregularity correction,
called "tone correction factor", is made at each time increment for only
the maximum tone.

A36.4.1.2 Three basic physical properties of sound pressure must
be measured: level, frequency distribution, and time variation. To
determine EPNL, the instantaneous sound pressure level in each of the 24
one-third octave bands is required for each 0.5 second increment of time
during the airplane noise measurement.

A36.4.1.3 The calculation procedure that uses physical
measurements of noise to derive the EPNL evaluation measure of subjective
response consists of the following five steps:

(a) The 24 one-third octave bands of sound pressure level are converted
to perceived noisiness (noy) using the method described in section
A36.4.2.1 (a). The noy values are combined and then converted to
instantaneous perceived noise levels, PNL(k).

(b) A tone correction factor C(k) is calculated for each spectrum to
account for the subjective response to the presence of spectral
irregularities.

(c) The tone correction factor is added to the perceived noise level to
obtain tone-corrected perceived noise levels PNLT(k), at each one-half
second increment:

PNLT(k)=PNL(k) + C(k)

The instantaneous values of tone-corrected perceived noise level are
derived and the maximum value, PNLTM, is determined.

(d) A duration correction factor, D, is computed by integration under
the curve of tone-corrected perceived noise level versus time.

(e) Effective perceived noise level, EPNL, is determined by the
algebraic sum of the maximum tone-corrected perceived noise level and the
duration correction factor:

EPNL=PNLTM + D

A36.4.2 *Perceived noise level.*

A36.4.2.1 Instantaneous perceived noise levels, PNL(k), must be
calculated from instantaneous one-third octave band sound pressure levels,
SPL(i, k) as follows:

(a) Step 1: For each one-third octave band from 50 through 10,000 Hz,
convert SPL(i, k) to perceived noisiness n(i, k), by using the
mathematical formulation of the noy table given in section A36.4.7.

(b) Step 2: Combine the perceived noisiness values, n(i, k), determined
in step 1 by using the following formula:
$$

where n(k) is the largest of the 24 values of n(i, k) and N(k) is the
total perceived noisiness.

(c) Step 3: Convert the total perceived noisiness, N(k), determined in
Step 2 into perceived noise level, PNL(k), using the following formula:
$$

**Note:** PNL(k) is plotted in the current advisory circular for
this part.

A36.4.3 *Correction for spectral irregularities.*

A36.4.3.1 Noise having pronounced spectral irregularities (for
example, the maximum discrete frequency components or tones) must be
adjusted by the correction factor C(k) calculated as follows:

(a) Step 1: After applying the corrections specified under section
A36.3.9, start with the sound pressure level in the 80 Hz one-third octave
band (band number 3), calculate the changes in sound pressure level (or
"slopes") in the remainder of the one-third octave bands as follows:

*s*(3,*k*)=no value

s(4,*k*)=SPL(4,*k*)−SPL(3,*k*)

•

•

s(*i,k*)=SPL(*i,k*)−SPL(*i*−1,*k*)

•

•

s(24,*k*)=SPL(24,*k*)−SPL(23,*k*)

(b) Step 2: Encircle the value of the slope, s(i, k), where the
absolute value of the change in slope is greater than five; that is where:

&bond;Δ*s*(*i,k*)&bond;=&bond;*s*(*i,k*)−*s*(*i*−1,*k*)&bond;>5

(c) Step 3:

(1) If the encircled value of the slope s(i, k) is positive and
algebraically greater than the slope s(i−1, k) encircle SPL(i, k).

(2) If the encircled value of the slope s(i, k) is zero or negative and
the slope s(i−1, k) is positive, encircle SPL(i−1, k).

(3) For all other cases, no sound pressure level value is to be
encircled.

(d) Step 4: Compute new adjusted sound pressure levels SPL'(i, k) as
follows:

(1) For non-encircled sound pressure levels, set the new sound pressure
levels equal to the original sound pressure levels, SPL'(i, k)=SPL(i, k).

(2) For encircled sound pressure levels in bands 1 through 23
inclusive, set the new sound pressure level equal to the arithmetic
average of the preceding and following sound pressure levels as shown
below:

SPL'(*i,k*)=
1/2[SPL(*i*−1,*k*)+SPL(*i*+1,*k*)]

(3) If the sound pressure level in the highest frequency band (i=24) is
encircled, set the new sound pressure level in that band equal to:

SPL'(24,*k*)=SPL(23,*k*)+*s*(23,*k*)

(e) Step 5: Recompute new slope s'(i, k), including one for an
imaginary 25th band, as follows:

*s*'(3,*k*)=*s*'(4,*k*)

*s*'(4,*k*)=SPL'(4,*k*)−SPL'(3,*k*)

•

•

*s*'(*i,k*)=SPL'(*i,k*)−SPL'(*i*−1,*k*)

•

•

*s*'(24,*k*)=SPL'(24,*k*)−SPL'(23,*k*)

*s*'(25,*k*)=*s*'(24,*k*)

(f) Step 6: For i, from 3 through 23, compute the arithmetic average of
the three adjacent slopes as follows:

*s
*(*i,k*)=
1/3[*s*'(*i,k*)+*s*'(*i*+1,*k*)+*s*'(*i*+2,*k*)]

(g) Step 7: Compute final one-third octave-band sound pressure levels,
SPL' (i,k), by beginning with band number 3 and proceeding to band number
24 as follows:

SPL'(3,*k*)=SPL(3,k)

SPL'(4,*k*)=SPL'(3,k)+*s
*(3,*k*)

•

•

SPL'*(i,k*)=SPL'(i−1,k)+*s
*(i−1,k)

•

•

SPL'(24,*k*)=SPL'(23,k)+*s
*(23,k)

(h) Setp 8: Calculate the differences, F (i,k), between the original
sound pressure level and the final background sound pressure level as
follows:

*F*(*i,k*)=SPL(*i,k)*-SPL'(*i,k*)

and note only values equal to or greater than 1.5.

(i) Step 9: For each of the relevant one-third octave bands (3 through
24), determine tone correction factors from the sound pressure level
differences F (i, k) and Table A36-2.

(j) Step 10: Designate the largest of the tone correction factors,
determined in Step 9, as C(k). (An example of the tone correction
procedure is given in the current advisory circular for this part).
Tone-corrected perceived noise levels PNLT(k) must be determined by adding
the C(k) values to corresponding PNL(k) values, that is:

PNLT(*k*)=PNL(*k*)+*C*(*k*)

For any i-th one-third octave band, at any k-th increment of time, for
which the tone correction factor is suspected to result from something
other than (or in addition to) an actual tone (or any spectral
irregularity other than airplane noise), an additional analysis may be
made using a filter with a bandwidth narrower than one-third of an octave.
If the narrow band analysis corroborates these suspicions, then a revised
value for the background sound pressure level SPL'(i,k), may be determined
from the narrow band analysis and used to compute a revised tone
correction factor for that particular one-third octave band. Other methods
of rejecting spurious tone corrections may be approved.

A36.4.3.2 The tone correction procedure will underestimate EPNL if
an important tone is of a frequency such that it is recorded in two
adjacent one-third octave bands. An applicant must demonstrate that
either:

(a) No important tones are recorded in two adjacent one-third octave
bands; or

(b) That if an important tone has occurred, the tone correction has
been adjusted to the value it would have had if the tone had been recorded
fully in a single one-third octave band.

A36.4.4 Maximum tone-corrected perceived noise level

A36.4.4.1 The maximum tone-corrected perceived noise level, PNLTM,
must be the maximum calculated value of the tone-corrected perceived noise
level PNLT(k). It must be calculated using the procedure of section
A36.4.3. To obtain a satisfactory noise time history, measurements must be
made at 0.5 second time intervals.

**Note 1: **Figure A36-2 is an example of a flyover noise time
history where the maximum value is clearly indicated.

**Note 2: **In the absence of a tone correction factor, PNLTM would
equal PNLM.

A36.4.4.2 After the value of PNLTM is obtained, the frequency band
for the largest tone correction factor is identified for the two preceding
and two succeeding 500 ms data samples. This is performed in order to
identity the possibility of tone suppression at PNLTM by one-third octave
band sharing of that tone. If the value of the tone correction factor C(k)
for PNLTM is less than the average value of C(k) for the five consecutive
time intervals, the average value of C(k) must be used to compute a new
value for PNLTM.

A36.4.5 *Duration correction.*

A36.4.5.1 The duration correction factor D determined by the
integration technique is defined by the expression:

where T is a normalizing time constant, PNLTM is the maximum value of
PNLT, t(1) is the first point of time after which PNLT becomes greater
than PNLTM-10, and t(2) is the point of time after which PNLT remains
constantly less than PNLTM-10.

A36.4.5.2 Since PNLT is calculated from measured values of sound
pressure level (SPL), there is no obvious equation for PNLT as a function
of time. Consequently, the equation is to be rewritten with a summation
sign instead of an integral sign as follows:

where Δt is the length of the equal increments of time for which PNLT(k)
is calculated and d is the time interval to the nearest 0.5s during which
PNLT(k) remains greater or equal to PNLTM-10.

A36.4.5.3 To obtain a satisfactory history of the perceived noise
level use one of the following:

(a) Half-Second time intervals for Δt; or

(b) A shorter time interval with approved limits and constants.

A36.4.5.4 The following values for T and Δt must be used in
calculating D in the equation given in section A36.4.5.2:

T=10 s, and

Δt=0.5s (or the approved sampling time interval).

Using these values, the equation for D becomes:
$$

where d is the duration time defined by the points corresponding to the
values PNLTM-10.

A36.4.5.5 If in using the procedures given in section A36.4.5.2,
the limits of PNLTM-10 fall between the calculated PNLT(k) values (the
usual case), the PNLT(k) values defining the limits of the duration
interval must be chosen from the PNLT(k) values closest to PNLTM-10. For
those cases with more than one peak value of PNLT(k), the applicable
limits must be chosen to yield the largest possible value for the duration
time.

A36.4.6 *Effective perceived noise level.*

The total subjective effect of an airplane noise event, designated
effective perceived noise level, EPNL, is equal to the algebraic sum of
the maximum value of the tone-corrected perceived noise level, PNLTM, and
the duration correction D. That is:

EPNL=PNLTM+D

where PNLTM and D are calculated using the procedures given in sections
A36.4.2, A36.4.3, A36.4.4. and A36.4.5.

A36.4.7 *Mathematical formulation of noy tables.*

A36.4.7.1 The relationship between sound pressure level (SPL) and
the logarithm of perceived noisiness is illustrated in Figure A36-3 and
Table A36-3.

A36.4.7.2 The bases of the mathematical formulation are:

(a) The slopes (M(b), M(c), M(d) and M(e)) of the straight lines;

(b) The intercepts (SPL(b) and SPL(c)) of the lines on the SPL axis;
and

(c) The coordinates of the discontinuities, SPL(a) and log n(a); SPL(d)
and log n=−1.0; and SPL(e) and log n=log (0.3).

A36.4.7.3 Calculate noy values using the following equations:

(a)

SPL ≥ SPL (a)

n=antilog {(c)[SPL−SPL(c)]}

(b)

SPL(b) ≤ SPL < SPL(a)

n=antilog {M(b)[SPL−SPL(b)]}

(c)

SPL(e) ≤ SPL < SPL(b)

n=0.3 antilog {M(e)[SPL−SPL(e)]}

(d)

SPL(d) ≤ SPL < SPL(e)

n=0.1 antilog {M(d)[SPL−SPL(d)]}

A36.4.7.4 Table A36-3 lists the values of the constants necessary
to calculate perceived noisiness as a function of sound pressure level.

**Section A36.5 Reporting of Data to the FAA**

A36.5.1 *General.*

A36.5.1.1 Data representing physical measurements and data used to
make corrections to physical measurements must be recorded in an approved
permanent form and appended to the record.

A36.5.1.2 All corrections must be reported to and approved by the
FAA, including corrections to measurements for equipment response
deviations.

A36.5.1.3 Applicants may be required to submit estimates of the
individual errors inherent in each of the operations employed in obtaining
the final data.

A36.5.2 *Data reporting.*

An applicant is required to submit a noise certification compliance
report that includes the following.

A36.5.2.1 The applicant must present measured and corrected sound
pressure levels in one-third octave band levels that are obtained with
equipment conforming to the standards described in section A36.3 of this
appendix.

A36.5.2.2 The applicant must report the make and model of
equipment used for measurement and analysis of all acoustic performance
and meteorological data.

A36.5.2.3 The applicant must report the following atmospheric
environmental data, as measured immediately before, after, or during each
test at the observation points prescribed in section A36.2 of this
appendix.

(a) Air temperature and relative humidity;

(b) Maximum, minimum and average wind velocities; and

(c) Atmospheric pressure.

A36.5.2.4 The applicant must report conditions of local
topography, ground cover, and events that might interfere with sound
recordings.

A36.5.2.5 The applicant must report the following:

(a) Type, model and serial numbers (if any) of airplane, engine(s), or
propeller(s) (as applicable);

(b) Gross dimensions of airplane and location of engines;

(c) Airplane gross weight for each test run and center of gravity range
for each series of test runs;

(d) Airplane configuration such as flap, airbrakes and landing gear
positions for each test run;

(e) Whether auxiliary power units (APU), when fitted, are operating for
each test run;

(f) Status of pneumatic engine bleeds and engine power take-offs for
each test run;

(g) Indicated airspeed in knots or kilometers per hour for each test
run;

(h) Engine performance data:

(1) For jet airplanes: engine performance in terms of net thrust,
engine pressure ratios, jet exhaust temperatures and fan or compressor
shaft rotational speeds as determined from airplane instruments and
manufacturer's data for each test run;

(2) For propeller-driven airplanes: engine performance in terms of
brake horsepower and residual thrust; or equivalent shaft horsepower; or
engine torque and propeller rotational speed; as determined from airplane
instruments and manufacturer's data for each test run;

(i) Airplane flight path and ground speed during each test run; and

(j) The applicant must report whether the airplane has any
modifications or non-standard equipment likely to affect the noise
characteristics of the airplane. The FAA must approve any such
modifications or non-standard equipment.

A36.5.3 *Reporting of noise certification reference conditions.*

A36.5.3.1 Airplane position and performance data and the noise
measurements must be corrected to the noise certification reference
conditions specified in the relevant sections of appendix B of this part.
The applicant must report these conditions, including reference
parameters, procedures and configurations.

A36.5.4 *Validity of results.*

A36.5.4.1 Three average reference EPNL values and their 90 percent
confidence limits must be produced from the test results and reported,
each such value being the arithmetical average of the adjusted acoustical
measurements for all valid test runs at each measurement point (flyover,
lateral, or approach). If more than one acoustic measurement system is
used at any single measurement location, the resulting data for each test
run must be averaged as a single measurement. The calculation must be
performed by:

(a) Computing the arithmetic average for each flight phase using the
values from each microphone point; and

(b) Computing the overall arithmetic average for each reference
condition (flyover, lateral or approach) using the values in paragraph (a)
of this section and the related 90 percent confidence limits.

A36.5.4.2 For each of the three certification measuring points,
the minimum sample size is six. The sample size must be large enough to
establish statistically for each of the three average noise certification
levels a 90 percent confidence limit not exceeding ±1.5 EPNdB. No test
result may be omitted from the averaging process unless approved by the
FAA.

**Note:** Permitted methods for calculating the 90 percent
confidence interval are shown in the current advisory circular for this
part.

A36.5.4.3 The average EPNL figures obtained by the process
described in section A36.5.4.1 must be those by which the noise
performance of the airplane is assessed against the noise certification
criteria.

**Section A36.6 Nomenclature: Symbols and Units**

------------------------------------------------------------------------
Symbol Unit Meaning
------------------------------------------------------------------------
antilog............... ...................... Antilogarithm to the
base 10.
C(k).................. dB.................... Tone correction factor.
The factor to be added
to PNL(k) to account
for the presence of
spectral irregularities
such as tones at the k-
th increment of time.
d..................... s..................... Duration time. The time
interval between the
limits of t(1) and t(2)
to the nearest 0.5
second.
D..................... dB.................... Duration correction. The
factor to be added to
PNLTM to account for
the duration of the
noise.
EPNL.................. EPNdB................. Effective perceived
noise level. The value
of PNL adjusted for
both spectral
irregularities and
duration of the noise.
(The unit EPNdB is used
instead of the unit
dB).
EPNL[INF]r[/INF]...... EPNdB................. Effective perceived
noise level adjusted
for reference
conditions.
f(i).................. Hz.................... Frequency. The
geometrical mean
frequency for the i-th
one-third octave band.
F (i, k).............. dB.................... Delta-dB. The difference
between the original
sound pressure level
and the final
background sound
pressure level in the i-
th one-third octave
band at the k-th
interval of time. In
this case, background
sound pressure level
means the broadband
noise level that would
be present in the one-
third octave band in
the absence of the
tone.
h..................... dB.................... dB-down. The value to be
subtracted from PNLTM
that defines the
duration of the noise.
H..................... Percent............... Relative humidity. The
ambient atmospheric
relative humidity.
i..................... ...................... Frequency band index.
The numerical indicator
that denotes any one of
the 24 one-third octave
bands with geometrical
mean frequencies from
50 to 10,000 Hz.
k..................... ...................... Time increment index.
The numerical indicator
that denotes the number
of equal time
increments that have
elapsed from a
reference zero.
Log................... ...................... Logarithm to the base
10.
log n(a).............. ...................... Noy discontinuity
coordinate. The log n
value of the
intersection point of
the straight lines
representing the
variation of SPL with
log n.
M(b), M(c), etc....... ...................... Noy inverse slope. The
reciprocals of the
slopes of straight
lines representing the
variation of SPL with
log n.
n..................... noy................... The perceived noisiness
at any instant of time
that occurs in a
specified frequency.
n(i,k)................ noy................... The percieved noisiness
at the k-th instant of
time that occurs in the
i-th one-third octave
band.
n(k).................. noy................... Maximum perceived
noisiness. The maximum
value of all of the 24
values of n(i) that
occurs at the k-th
instant of time.
N(k).................. noy................... Total perceived
noisiness. The total
perceived noisiness at
the k-th instant of
time calculated from
the 24-instantaneous
values of n (i, k).
p(b), p(c), etc....... ...................... Noy slope. The slopes of
straight lines
representing the
variation of SPL with
log n.
PNL................... PNdB.................. The perceived noise
level at any instant of
time. (The unit PNdB is
used instead of the
unit dB).
PNL(k)................ PNdB.................. The perceived noise
level calculated from
the 24 values of SPL
(i, k), at the k-th
increment of time. (The
unit PNdB is used
instead of the unit
dB).
PNLM.................. PNdB.................. Maximum perceived noise
level. The maximum
value of PNL(k). (The
unit PNdB is used
instead of the unit
dB).
PNLT.................. TPNdB................. Tone-corrected perceived
noise level. The value
of PNL adjusted for the
spectral irregularities
that occur at any
instant of time. (The
unit TPNdB is used
instead of the unit
dB).
PNLT(k)............... TPNdB................. The tone-corrected
perceived noise level
that occurs at the k-th
increment of time.
PNLT(k) is obtained by
adjusting the value of
PNL(k) for the spectral
irregularities that
occur at the k-th
increment of time. (The
unit TPNdB is used
instead of the unit
dB).
PNLTM................. TPNdB................. Maximum tone-corrected
perceived noise level.
The maximum value of
PNLT(k). (The unit
TPNdB is used instead
of the unit dB).
PNLT[INF]r[/INF]...... TPNdB................. Tone-corrected perceived
noise level adjusted
for reference
conditions.
s (i, k).............. dB.................... Slope of sound pressure
level. The change in
level between adjacent
one-third octave band
sound pressure levels
at the i-th band for
the k-th instant of
time.
[Delta]s (i, k)....... dB.................... Change in slope of sound
pressure level.
s[prime] (i, k)....... dB.................... Adjusted slope of sound
pressure level. The
change in level between
adjacent adjusted one-
third octave band sound
pressure levels at the
i-th band for the k-th
instant of time.
s (i, k).............. dB.................... Average slope of sound
pressure level.
SPL................... dB re................. Sound pressure level.
20 μPa............. The sound pressure
level that occurs in a
specified frequency
range at any instant of
time.
SPL(a)................ dB re................. Noy discontinuity
20 μPa............. coordinate. The SPL
value of the
intersection point of
the straight lines
representing the
variation of SPL with
log n.
SPL(b)................ dB re................. Noy intercept. The
SPL (c)............... 20 μPa............. intercepts on the SPL-
axis of the straight
lines representing the
variation of SPL with
log n.
SPL (i, k)............ dB re................. The sound pressure level
20 μPa............. at the k-th instant of
time that occurs in the
i-th one-third octave
band.
SPL[prime] (i, k)..... dB re................. Adjusted sound pressure
20 μPa............. level. The first
approximation to
background sound
pressure level in the i-
th one-third octave
band for the k-th
instant of time.
SPL(i)................ dB re................. Maximum sound pressure
20 μPa............. level. The sound
pressure level that
occurs in the i-th one-
third octave band of
the spectrum for PNLTM.
SPL(i)[INF]r[/INF].... dB re................. Corrected maximum sound
20 μPa............. pressure level. The
sound pressure level
that occurs in the i-th
one-third octave band
of the spectrum for
PNLTM corrected for
atmospheric sound
absorption.
SPL[prime] (i, k)..... dB re................. Final background sound
20 μPa............. pressure level. The
second and final
approximation to
background sound
pressure level in the i-
th one-third octave
band for the k-th
instant of time.
t..................... s..................... Elapsed time. The length
of time measured from a
reference zero.
t(1), t(2)............ s..................... Time limit. The
beginning and end,
respectively, of the
noise time history
defined by h.
[Delta]t.............. s..................... Time increment. The
equal increments of
time for which PNL(k)
and PNLT(k) are
calculated.
T..................... s..................... Normalizing time
constant. The length of
time used as a
reference in the
integration method for
computing duration
corrections, where
T=10s.
t( °F) ( °C) °F, °C..... Temperature. The ambient
air temperature.
[alpha](i)............ dB/1000ft db/100m..... Test atmospheric
absorption. The
atmospheric attenuation
of sound that occurs in
the i-th one-third
octave band at the
measured air
temperature and
relative humidity.
[alpha](i)[INF]o[/INF] dB/1000ft db/100m..... Reference atmospheric
absorption. The
atmospheric attenuation
of sound that occurs in
the i-th one-third
octave band at a
reference air
temperature and
relative humidity.
A[INF]1[/INF]......... Degrees............... First constant climb
angle (Gear up, speed
of at least V[INF]2[/
INF]+10 kt (V[INF]2[/
INF]+19 km/h), takeoff
thrust).
A[INF]2[/INF]......... Degrees............... Second constant climb
angle (Gear up, speed
of at least V[INF]2[/
INF]+10 kt (V[INF]2[/
INF]+19 km/h), after
cut-back).
[delta]............... Degrees............... Thrust cutback angles.
[egr]................. The angles defining the
points on the takeoff
flight path at which
thrust reduction is
started and ended
respectively.
[eta]................. Degrees............... Approach angle.
[eta][INF]r[/INF]..... Degrees............... Reference approach
angle.
[thetas].............. Degrees............... Noise angle (relative to
flight path). The angle
between the flight path
and noise path. It is
identical for both
measured and corrected
flight paths.
[psi]................. Degrees............... Noise angle (relative to
ground). The angle
between the noise path
and the ground. It is
identical for both
measured and corrected
flight paths.
μ.................. ...................... Engine noise emission
parameter.
μ[INF]r[/INF]...... ...................... Reference engine noise
emission parameter.
[Delta][INF]1[/INF]... EPNdB................. PNLT correction. The
correction to be added
to the EPNL calculated
from measured data to
account for noise level
changes due to
differences in
atmospheric absorption
and noise path length
between reference and
test conditions.
[Delta][INF]2[/INF]... EPNdB................. Adjustment to duration
correction. The
adjustment to be made
to the EPNL calculated
from measured data to
account for noise level
changes due to the
noise duration between
reference and test
conditions.
[Delta][INF]3[/INF]... EPNdB................. Source noise adjustment.
The adjustment to be
made to the EPNL
calculated from
measured data to
account for noise level
changes due to
differences between
reference and test
engine operating
conditions.
------------------------------------------------------------------------

**Section A36.7 Sound Attenuation in Air**

A36.7.1 The atmospheric attenuation of sound must be determined in
accordance with the procedure presented in section A36.7.2.

A36.7.2 The relationship between sound attenuation, frequency,
temperature, and humidity is expressed by the following equations.

A36.7.2(a) For calculations using the English System of Units:
$$

and
$$

where

η(δ) is listed in Table A36-4 and f0 in Table A36-5;

α(i) is the attenuation coefficient in dB/1000 ft;

&thetas; is the temperature in °F; and

H is the relative humidity, expressed as a percentage.

A36.7.2(b) For calculations using the International System of Units (SI):
$$

and
$$

where

η(δ) is listed in Table A36-4 and f0 in Table A36-5;

α(i) is the attenuation coefficient in dB/100 m;

&thetas; is the temperature in °C; and

H is the relative humidity, expressed as a percentage.

A36.7.3 The values listed in table A36-4 are to be used when
calculating the equations listed in section A36.7.2. A term of quadratic
interpolation is to be used where necessary.

**Section A36.8 [RESERVED]**

**Section A36.9 ***Adjustment of Airplane Flight Test Results.*

A36.9.1 When certification test conditions are not identical to
reference conditions, appropriate adjustments must be made to the measured
noise data using the methods described in this section.

A36.9.1.1 Adjustments to the measured noise values must be made
using one of the methods described in sections A36.9.3 and A36.9.4 for
differences in the following:

(a) Attenuation of the noise along its path as affected by "inverse
square" and atmospheric attenuation

(b) Duration of the noise as affected by the distance and the speed of
the airplane relative to the measuring point

(c) Source noise emitted by the engine as affected by the differences
between test and reference engine operating conditions

(d) Airplane/engine source noise as affected by differences between
test and reference airspeeds. In addition to the effect on duration, the
effects of airspeed on component noise sources must be accounted for as
follows: for conventional airplane configurations, when differences
between test and reference airspeeds exceed 15 knots (28 km/h) true
airspeed, test data and/or analysis approved by the FAA must be used to
quantify the effects of the airspeed adjustment on resulting certification
noise levels.

A36.9.1.2 The "integrated" method of adjustment, described in
section A36.9.4, must be used on takeoff or approach under the following
conditions:

(a) When the amount of the adjustment (using the "simplified" method)
is greater than 8 dB on flyover, or 4 dB on approach; or

(b) When the resulting final EPNL value on flyover or approach (using
the simplified method) is within 1 dB of the limiting noise levels as
prescribed in section B36.5 of this part.

A36.9.2 *Flight profiles.*

As described below, flight profiles for both test and reference
conditions are defined by their geometry relative to the ground, together
with the associated airplane speed relative to the ground, and the
associated engine control parameter(s) used for determining the noise
emission of the airplane.

A36.9.2.1 *Takeoff Profile.*

**Note:** Figure A36-4 illustrates a typical takeoff profile.

(a) The airplane begins the takeoff roll at point A, lifts off at point
B and begins its first climb at a constant angle at point C. Where thrust
or power (as appropriate) cut-back is used, it is started at point D and
completed at point E. From here, the airplane begins a second climb at a
constant angle up to point F, the end of the noise certification takeoff
flight path.

(b) Position K1 is the takeoff noise measuring station and
AK1 is the distance from start of roll to the flyover
measuring point. Position K2 is the lateral noise measuring
station, which is located on a line parallel to, and the specified
distance from, the runway center line where the noise level during takeoff
is greatest.

(c) The distance AF is the distance over which the airplane position is
measured and synchronized with the noise measurements, as required by
section A36.2.3.2 of this part.

A36.9.2.2 *Approach Profile.*

**Note:** Figure A36-5 illustrates a typical approach profile.

(a) The airplane begins its noise certification approach flight path at
point G and touches down on the runway at point J, at a distance OJ from
the runway threshold.

(b) Position K3 is the approach noise measuring station and
K3O is the distance from the approach noise measurement point
to the runway threshold.

(c) The distance GI is the distance over which the airplane position is
measured and synchronized with the noise measurements, as required by
section A36.2.3.2 of this part.
$$

The airplane reference point for approach measurements is the
instrument landing system (ILS) antenna. If no ILS antenna is installed an
alternative reference point must be approved by the FAA.

A36.9.3 *Simplified method of adjustment.*

A36.9.3.1 *General.* As described below, the simplified
adjustment method consists of applying adjustments (to the EPNL, which is
calculated from the measured data) for the differences between measured
and reference conditions at the moment of PNLTM.

A36.9.3.2 *Adjustments to PNL and PNLT.*

(a) The portions of the test flight path and the reference flight path
described below, and illustrated in Figure A36-6, include the noise time
history that is relevant to the calculation of flyover and approach EPNL.
In figure A36-6:

(1) XY represents the portion of the measured flight path that includes
the noise time history relevant to the calculation of flyover and approach
EPNL; XrYr represents the corresponding portion of
the reference flight path.

(2) Q represents the airplane's position on the measured flight path at
which the noise was emitted and observed as PNLTM at the noise measuring
station K. Qr is the corresponding position on the reference
flight path, and Kr the reference measuring station. QK and QrKr
are, respectively, the measured
$$

and reference noise propagation paths, Qr being determined
from the assumption that QK and QrKr form the same
angle &thetas; with their respective flight paths.

(b) The portions of the test flight path and the reference flight path
described in paragraph (b)(1) and (2), and illustrated in Figure A36-7(a)
and (b), include the noise time history that is relevant to the
calculation of lateral EPNL.

(1) In figure A36-7(a), XY represents the portion of the measured
flight path that includes the noise time history that is relevant to the
calculation of lateral EPNL; in figure A36-7(b), XrYr
represents the corresponding portion of the reference flight path.

(2) Q represents the airplane position on the measured flight path at
which the noise was emitted and observed as PNLTM at the noise measuring
station K. Qr is the corresponding position on the reference
flight path, and Kr the reference measuring station. QK and QrKr
are, respectively, the measured and reference noise propagation paths. In
this case Kr is only specified as being on a particular
Lateral line; Kr and Qr are therefore determined
from the assumptions that QK and QrKr:

(i) Form the same angle &thetas; with their respective flight paths;
and

(ii) Form the same angle ψ with the ground.

**Note:** For the lateral noise measurement, sound propagation is
affected not only by inverse square and atmospheric attenuation, but also
by ground absorption and reflection effects which depend mainly on the
angle ψ.

$$

A36.9.3.2.1 The one-third octave band levels SPL(i) comprising PNL
(the PNL at the moment of PNLTM observed at K) must be adjusted to
reference levels SPL(i)r as follows:

A36.9.3.2.1(a) For calculations using the English System of Units:

SPL(*i*)r=SPL(*i*)+0.001[α(*i*)−α(*i*)0]QK

+0.001α(*i*)0(QK−QrKr)

+20log(QK/QrKr)

In this expression,

(1) The term 0.001[α(*i*)−α(*i*)0]QK is the
adjustment for the effect of the change in sound attenuation coefficient,
and α(i) and α(i)0 are the coefficients for the test and
reference atmospheric conditions respectively, determined under section
A36.7 of this appendix;

(2) The term 0.001α(i)0(QK − QrKr)
is the adjustment for the effect of the change in the noise path length on
the sound attenuation;

(3) The term 20 log(QK/QrKr) is the adjustment
for the effect of the change in the noise path length due to the "inverse
square" law;

(4) QK and QrKr are measured in feet and α(i)
and α(i)0 are expressed in dB/1000 ft.

A36.9.3.2.1(b) For calculations using the International System of
Units:

SPL(i)r=SPL(i)+0.01[α(i)−α(i)0]QK

+0.01α(i)0 (QK − QrKr)

+20 log(QK/QrKr)

In this expression,

(1) The term 0.01[α(i) − α(i)0]QK is the adjustment for the
effect of the change in sound attenuation coefficient, and α(i) and α(i)0
are the coefficients for the test and reference atmospheric conditions
respectively, determined under section A36.7 of this appendix;

(2) The term 0.01α(i)0(QK − QrKr)
is the adjustment for the effect of the change in the noise path length on
the sound attenuation;

(3) The term 20 log(QK/QrKr) is the adjustment
for the effect of the change in the noise path length due to the inverse
square law;

(4) QK and QrKr are measured in meters and α(i)
and α(i)0 are expressed in dB/100 m.

A36.9.3.2.1.1 *PNLT Correction.*

(a) Convert the corrected values, SPL(i)r, to PNLTr;

(b) Calculate the correction term Δ1 using the following
equation:

Δ1=PNLTr − PNLTM

A36.9.3.2.1.2 Add Δ1 arithmetically to the EPNL
calculated from the measured data.

A36.9.3.2.2 If, during a test flight, several peak values of PNLT
that are within 2 dB of PNLTM are observed, the procedure defined in
section A36.9.3.2.1 must be applied at each peak, and the adjustment term,
calculated according to section A36.9.3.2.1, must be added to each peak to
give corresponding adjusted peak values of PNLT. If these peak values
exceed the value at the moment of PNLTM, the maximum value of such
exceedance must be added as a further adjustment to the EPNL calculated
from the measured data.

A36.9.3.3 *Adjustments to duration correction.*

A36.9.3.3.1 Whenever the measured flight paths and/or the ground
velocities of the test conditions differ from the reference flight paths
and/or the ground velocities of the reference conditions, duration
adjustments must be applied to the EPNL values calculated from the
measured data. The adjustments must be calculated as described below.

A36.9.3.3.2 For the flight path shown in Figure A36-6, the
adjustment term is calculated as follows:

Δ2=−7.5 log(QK/QrKr)+10 log(V/Vr)

(a) Add Δ2 arithmetically to the EPNL calculated from the
measured data.

A36.9.3.4 *Source noise adjustments.*

A36.9.3.4.1 To account for differences between the parameters
affecting engine noise as measured in the certification flight tests, and
those calculated or specified in the reference conditions, the source
noise adjustment must be calculated and applied. The adjustment is
determined from the manufacturer's data approved by the FAA. Typical data
used for this adjustment are illustrated in Figure A36-8 that shows a
curve of EPNL versus the engine control parameter μ, with the EPNL data
being corrected to all the other relevant reference conditions (airplane
mass, speed and altitude, air temperature) and for the difference in noise
between the test engine and the average engine (as defined in section
B36.7(b)(7)). A sufficient number of data points over a range of values of
μr is required to calculate the source noise adjustments for
lateral, flyover and approach noise measurements.

A36.9.3.4.2 Calculate adjustment term Δ3 by
subtracting the EPNL value corresponding to the parameter μ from the EPNL
value corresponding to the parameter μr. Add Δ3
arithmetically to the EPNL value calculated from the measured data.

A36.9.3.5 *Symmetry adjustments.*

A36.9.3.5.1 A symmetry adjustment to each lateral noise value
(determined at the section B36.4(b) measurement points), is to be made as
follows:

(a) If the symmetrical measurement point is opposite the point where
the highest noise level is obtained on the main lateral measurement line,
the certification noise level is the arithmetic mean of the noise levels
measured at these two points (see Figure A36-9(a));

(b) If the condition described in paragraph (a) of this section is not
met, then it is assumed that the variation of noise with the altitude of
the airplane is the same on both sides; there is a constant difference
between the lines of noise versus altitude on both sides (see figure
A36-9(b)). The certification noise level is the maximum value of the mean
between these lines.

A36.9.4 *Integrated method of adjustment*

A36.9.4.1 *General.* As described in this section, the
integrated adjustment method consists of recomputing under reference
conditions points on the PNLT time history corresponding to measured
points obtained during the tests, and computing EPNL directly for the new
time history obtained in this way. The main principles are described in
sections A36.9.4.2 through A36.9.4.4.1.

A36.9.4.2 *PNLT computations.*

(a) The portions of the test flight path and the reference flight path
described in paragraph (a)(1) and (2), and illustrated in Figure A36-10,
include the noise time history that is relevant to the calculation of
flyover and approach EPNL. In figure A36-10:

(1) XY represents the portion of the measured flight path that includes
the noise time history relevant to the calculation of flyover and approach
EPNL; XrYr represents the corresponding reference
flight path.

(2) The points Q0, Q1, Qn represent
airplane positions on the measured flight path at time t0, t1
and tn respectively. Point Q1 is the point at
which the noise was emitted and observed as one-third octave values SPL(i)1
at the noise measuring station K at time t1. Point Qr1
represents the corresponding position on the reference flight path for
noise observed as SPL(i)r1 at the reference measuring station
Kr at time tr1. Q1K and Qr1Kr
are respectively the measured and reference noise propagation paths, which
in each case form the angle &thetas;1 with their respective
flight paths. Qr0 and Qrn are similarly the points
on the reference flight path corresponding to Q0 and Qn
on the measured flight path. Q0 and Qn are chosen
so that between Qr0 and Qrn all values of PNLTr
(computed as described in paragraphs A36.9.4.2.2 and A36.9.4.2.3) within
10 dB of the peak value are included.

(b) The portions of the test flight path and the reference flight path
described in paragraph (b)(1) and (2), and illustrated *in Figure
A36-11(a) and (b),* include the noise time history that is relevant to
the calculation of lateral EPNL.

(1) In figure A36-11(a) XY represents the portion of the measured
flight path that includes the noise time history that is relevant to the
calculation of lateral EPNL; in figure A36-11(b), XrYr
represents the corresponding portion of the reference flight path.

(2) The points Q0, Q1 and Qn
represent airplane positions on the measured flight path at time t0,
t1 and tn respectively. Point Q1 is
the point at which the noise was emitted and observed as one-third octave
values SPL(i)1 at the noise measuring station K at time t1.
The point Qr1 represents the corresponding position on the
reference flight path for noise observed as SPL(i)r1 at the
measuring station Kr at time tr1. Q1K
and Qr1Kr are respectively the measured and
reference noise propagation paths. Qr0 and Qrn are
similarly the points on the reference flight path corresponding to Q0
and Qn on the measured flight path.

Q0 and Qn are chosen to that between Qro
and Qrn all values of PNLTr (computed as described
in paragraphs A36.9.4.2.2 and A36.9.4.2.3) within 10 dB of the peak value
are included. In this case Kr is only specified as being on a
particular lateral line. The position of Kr and Qr1
are determined from the following requirements.

(i) Q1K and Qr1Kr form the same
angle &thetas;1 with their respective flight paths; and

(ii) The differences between the angles
1 and
r1 must be minimized using a method, approved by the FAA. The
differences between the angles are minimized since, for geometrical
reasons, it is generally not possible to choose Kr so that the
condition described in paragraph A36.9.4.2(b)(2)(i) is met while at the
same time keeping
1 and
r1 equal.

**Note:** For the lateral noise measurement, sound propagation is
affected not only by "inverse square" and atmospheric attenuation, but
also by ground absorption and reflection effects which depend mainly on
the angle.

A36.9.4.2.1 In paragraphs A36.9.4.2(a)(2) and (b)(2) the time tr1
is later (for Qr1Kr > Q1K) than t1
by two separate amounts:

(1) The time taken for the airplane to travel the distance Qr1Qr0
at a speed Vr less the time taken for it to travel Q1Q0
at V;

(2) The time taken for sound to travel the distance Qr1Kr-Q1K.

**Note:** For the flight paths described in paragraphs A36.9.4.2(a)
and (b), the use of thrust or power cut-back will result in test and
reference flight paths at full thrust or power and at cut-back thrust or
power. Where the transient region between these thrust or power levels
affects the final result, an interpolation must be made between them by an
approved method such as that given in the current advisory circular for
this part.

A36.9.4.2.2 The measured values of SPL(i)1 must be
adjusted to the reference values SPL(i)r1 to account for the
differences between measured and reference noise path lengths and between
measured and reference atmospheric conditions, using the methods of
section A36.9.3.2.1 of this appendix. A corresponding value of PNLr1
must be computed according to the method in section A36.4.2. Values of PNLr
must be computed for times t0 through tn.

A36.9.4.2.3 For each value of PNLr1, a tone correction
factor C1 must be determined by analyzing the reference values
SPL(i)r using the methods of section A36.4.3 of this appendix,
and added to PNLr1 to yield PNLTr1. Using the
process described in this paragraph, values of PNLTr must be
computed for times t0 through tn.

A36.9.4.3 *Duration correction.*

A36.9.4.3.1 The values of PNLTr corresponding to those
of PNLT at each one-half second interval must be plotted against time (PNLTr1
at time tr1). The duration correction must then be determined
using the method of section A36.4.5.1 of this appendix, to yield EPNLr.

A36.9.4.4 *Source Noise Adjustment.*

A36.9.4.4.1 A source noise adjustment, Δ3, must be
determined using the methods of section A36.9.3.4 of this appendix.

A36.9.5 Flight Path Identification Positions
------------------------------------------------------------------------
Position Description
------------------------------------------------------------------------
A................................. Start of Takeoff roll.
B................................. Lift-off.
C................................. Start of first constant climb.
D................................. Start of thrust reduction.
E................................. Start of second constant climb.
F................................. End of noise certification Takeoff
flight path.
G................................. Start of noise certification
Approach flight path.
H................................. Position on Approach path directly
above noise measuring station.
I................................. Start of level-off.
J................................. Touchdown.
K................................. Noise measurement point.
K[INF]r[/INF]..................... Reference measurement point.
K[INF]1[/INF]..................... Flyover noise measurement point.
K[INF]2[/INF]..................... Lateral noise measurement point.
K[INF]3[/INF]..................... Approach noise measurement point.
M................................. End of noise certification Takeoff
flight track.
O................................. Threshold of Approach end of runway.
P................................. Start of noise certification
Approach flight track.
Q................................. Position on measured Takeoff flight
path corresponding to apparent
PNLTM at station K See section
A36.9.3.2.
Q[INF]r[/INF]..................... Position on corrected Takeoff flight
path corresponding to PNLTM at
station K. See section A36.9.3.2.
V................................. Airplane test speed.
V[INF]r[/INF]..................... Airplane reference speed.
------------------------------------------------------------------------

A36.9.6 Flight Path Distances
------------------------------------------------------------------------
Distance Unit Meaning
------------------------------------------------------------------------
AB..................... Feet (meters)....... Length of takeoff roll.
The distance along the
runway between the start
of takeoff roll and lift
off.
AK..................... Feet (meters)....... Takeoff measurement
distance. The distance
from the start of roll
to the takeoff noise
measurement station
along the extended
center line of the
runway.
AM..................... Feet (meters)....... Takeoff flight track
distance. The distance
from the start of roll
to the takeoff flight
track position along the
extended center line of
the runway after which
the position of the
airplane need no longer
be recorded.
QK..................... Feet (meters)....... Measured noise path. The
distance from the
measured airplane
position Q to station K.
Q[INF]r[/INF]K[INF]r[/ Feet (meters)....... Reference noise path. The
INF]. distance from the
reference airplane
position Q[INF]r[/INF]
to station K[INF]r[/
INF].
K[INF]3[/INF]H......... Feet (meters)....... Airplane approach height.
The height of the
airplane above the
approach measuring
station.
OK[INF]3[/INF]......... Feet (meters)....... Approach measurement
distance. The distance
from the runway
threshold to the
approach measurement
station along the
extended center line of
the runway.
OP..................... Feet (meters)....... Approach flight track
distance. The distance
from the runway
threshold to the
approach flight track
position along the
extended center line of
the runway after which
the position of the
airplane need no longer
be recorded.
------------------------------------------------------------------------

[Amdt. 36-54, 67 FR 45212, July 8, 2002; Amdt. 36-24, 67 FR
63195, 63196, Oct. 10, 2002]