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technical information Flight Research N
technical information Flight Research NOISE PROPAGATION Pwforming Organization and f’eriod This paper reviews the the propa- aircraft noise. understood propaga- cnergy due spherical spreading, cowr are ground-induczd absorption scattering due aircraft noise. Unclassified Uncla

ssified the National Service, Sprinyfiel
ssified the National Service, Sprinyfield, TABLEOFCONTENTS Page INTRODUCTION . Over Hard Source Over Source Size at Grazing Incidence AIR-TO-GROUND ATMOSPHERIC ATMOSPHERIC ABSORPTION a Homogeneous, Quiescent Atmosphere a Homogeneous, Quiescent Atmosphere Molecular Attenuation Reco

mmended Rlolecular Theoretical Considera
mmended Rlolecular Theoretical Considerations Temperature Inversions .2 .5 .5 .6 -6 .7 .9 . 10 . 11 . 12 . 14 . 15 . 16 . 16 . 18 . 19 . 19 . 19 . 20 . 22 . 23 . 23 . 24 . 25 . 25 . 26 . 26 * . 26 . 27 . 27 . 28 . 30 technological society increased, the account for noise into the

factors governing the earth's surface. n
factors governing the earth's surface. noise propagation the atmosphere and the ground include the absorption and ground or losses due the scattering precipitation also necessary before in the the levels sound propagated the atmosphere near the sound propagation. This report the pro

pagation noise. The report factor that i
pagation noise. The report factor that influences noise which each factor affects sound propagation the understanding the atmosphere attenuation function coefficient (eq numerical constant defined nozzle diameter separation distance ith one-third octave at which vertical temperatu

re gradient propagation constant change
re gradient propagation constant change in reflection factor wave reflection wave reflection radial distance reflected path reflected path length path length reflected path plane surface between nozzle nepers per sound wave the noise a sound the atmosphere the analysis presented p

ropagates through atmosphere above sound
ropagates through atmosphere above sound propagation in the field; sound be stationary. of motion the source UNIFORhl SPREADING sound level the receiver and the field can represented by Using equation inverse square losses in the far a noise a sound propagates nearly parallel earth

's surface, sound waves earth's surface.
's surface, sound waves earth's surface. perfect reflector sound and an one that face with a spectrum measured destructive interference pattern in the spectrum measured field) sound section, the including the source size and directivity. The available experimental and an sound propa

gating geometric configuration sound pro
gating geometric configuration sound propagation the sound sound propagated along the reflected sound The reflected sound in reference plane (where the finite bandwidth source spectrum. spectrum slope noise spectrum was that for actual spectrum the assumption the equations octave ba

nd the difference data meas- a reflectin
nd the difference data meas- a reflecting plane center frequency, important limiting length difference emits only a single frequency, classic patterns constructive and destructive interference interference + (+) 22 + 2 cos (2xAr/hi The general ‘. elidity of these equations was

established by experiments geometries l
established by experiments geometries like the the vali source over specular reflecting ground plane the reflection was assumed reflective plane given incidence the plane modification, equation equation t l:.l + - Ill ( 2) where 6i octave band defined by the incidence The inclusio

n wave reflection the analysis significa
n wave reflection the analysis significant effects. in equation by the interference. a perfectly the absorptive the phase made to determine the normal impedance reported in obtained for moisture conditions and the normal impedance through the hertz and practical appiications. normal

impedance and phase phase cos2 (cp) - 1
impedance and phase phase cos2 (cp) - 132 + 4(x/pco)i cos2 cp Qi = \ll? (Zi/pco)2 cos2 (cp) + 1 + B(R/pco)cos cp Using the values shown in tude and calculated and used calculate the reflection effects a sound spectrum for a given involving the equations to measured noise the propc

sed draft correcting spectra ground plan
sed draft correcting spectra ground plane particular ground plane to account grazing angles. this type on Weyl's solution to was expanded compared with characteristics, such and fiber analyses, the propagation constant a function was developed in Again, the comparison between experi

ment and for sound propagation fibrous a
ment and for sound propagation fibrous absorbent for the to tlle The ratio the incident given by reflection coefficient for a propagation constant propcgation constant (13) to then used includes the the filter be used. Again, the ance and propagation constant the plane wave reflect

ion coefficient the strength source give
ion coefficient the strength source gives data was reported in impedance for dry grass function of incidence sound propagation constant apply the propagating over asphalt and incidence with the predictions in and spectral however, the establishing the characteristics. Figvre shows t

hat also have different amplitude and ph
hat also have different amplitude and phase in the phase angles Source Size The discussion the distance the source source itself, different points apparently generated exhaust plane the interference vertical plane. the jet nozzle diameter)', the peaks the spectra the reflected the

jet jet can other by in figilre an eleme
jet jet can other by in figilre an elementary the difference the path length difference source at the nozzle by an aircraft engine, that the ground absorption and and then determine the the ground an understanding the ground surface preceding analysis propagating sound wave; howeve

r data limits usefiil determiuation soun
r data limits usefiil determiuation sound propagating data must experiments have more important The ground attenuation data presented in a wide theoretically calculated that the least loss and atmospheric the differences especially for band frequencies (ref. 18). in the was signific

ant and including the 4800-hertz octaire
ant and including the 4800-hertz octaire that the linearly proportional that included center frequency distance. These sound attenuation that octave determine whether this loudspeaker was a noise propagated and measured downwind propagation with data obtained and figure data taken

was measured fact, an was evident. other
was measured fact, an was evident. other end distance. This hertz and showed no attenuation to sound absorption hertz and peak absorption occurred near absorption was Theoretical investigations that the greatly dependent shift in difference in the ground-to-ground propagation acquir

ed in radial line that extended into dis
ed in radial line that extended into distant measurements other obstructions the aircraft and the downwind attenuation distance and no attenuation problems in frequencies above cient data the variability this type engineering procedure was developed the extra ground propagation was

based primarily with both The pro- absor
based primarily with both The pro- absorption effects 20, 21, all the upon which the ground recommended that ground absorption. shows the distance. These at distances these data, downwind attenuation flying into temperature lapse and additional attenuation occurs due give the Furth

ermore, reference calculates the the gro
ermore, reference calculates the the ground a grass-covered agreement between those and the when both the source in this area confidence can be achieved in estimates acoustic impedance incidence and a number grass-covered soil. the effects surface roughness Large-scale expcrii broad

band and verify the usefulness statistic
band and verify the usefulness statistical significance. Experimentation to ATMOSPHERIC PROPAGATION the ground-to-ground near the the earth's been proposed the transition propagation. The widely known noise, and in refer- The transition in figure the angle and the line the ground w

hereas at the ground attenuation must un
hereas at the ground attenuation must units, such Two models attenuation that situ ttions which the and the ltipiicative transition factor for each shown in for elevation the lincar that the believed that that they pro-. ldure The transition attenuation for a multiplier The transiti

on to elevation The ground attenuation
on to elevation The ground attenuation recommended and landing opera- transition factor. The data in reference sound attenuation at elevation the ground found to the British in figure unfortunately, the and perceived noise level angles greater and the to account for the transition

recommended that evident that theoretica
recommended that evident that theoretical and experimental the proper to account for attenuation with imperative that octave-band sound frequency should and the level The propagation by the assumed that values were the any horizontal the atmosphere. a Homogeneous, Quiescent propagat

ed in the absorption losses be classifie
ed in the absorption losses be classified in categories: classical the change into heat; the change and atmospheric nepers per the change in level at the absorption distance and the classical Classical absorption for normal molecules among lumped together range (refs. and 30). to 3

0. available, reference developed the ex
0. available, reference developed the expression for losses in in 0.7972(T)3/2] - f T + 107 P a A= .T = 5.42 X lo-" C The reference speed Absorption in the classical absorption was established theory established the relaxation frequency oxygen molecules, and for a number techniques

and apparatus were determine the The th
and apparatus were determine the The theory a constant these measurements, and experimental absorption based flyover noise temperature and and the subsequent attenuation determined was in However, it the flight measurements that lacked sufficient careful experiments temperature and

the atmospheric predicted by well with
the atmospheric predicted by well with the measured attenuation attenuation measured the recording noise measurements given in compared with values using the actual predictions were and that given by Sutherland overestimates the laboratory measurements The theoretical transfer rat

es data for method of atmospheric acoust
es data for method of atmospheric acoustic absorption sound physical for a temperature cnd Molecular Attenuation measure the in reference absorption shifted pointed out elevations between sea level, the reduced by must be absorption coefficients. the variation in temperature the ent

ire noise propagation taken into propaga
ire noise propagation taken into propagation path calculated attenuation data measured meters above those calculated The measured the values atmospheric absorption practical ;ipplicntions, computed for in reference frcquencies can actual absorption the shape the sound atmospheric ab

sorption ith band propagating a distanc
sorption ith band propagating a distance distance (:(f)df] - 10 expression for the attenuation of sound r. -A (f )r d f ] The upper and ith band respectively, and atmospheric attenuation The existence density and attenuation function the integral sign The propagation the integral s

hows that in absorption can occur freque
hows that in absorption can occur frequencies and absorption function, verified over for computing atmospheric absorption sound indicated and one-third the original with mathematical for machine The equations and equations and cubic meter, and temperature b T and the per deg to com

pute in grams frequency by the frequency
pute in grams frequency by the frequency air temperature, temperature, (f) + 8.42994 X 10e3T - 2.7556243 a = 10 molmax The ratio of the molecular absorption coefficient to the maximum molecular absorption coefficient is then related to the ratio be expressed arnolmax hmolrnax by us

ing corresponding value the table. by us
ing corresponding value the table. by using desired frequency Then the equations, the long propagation involved, careful source spectrum, actual propagation the actual atmospheric conditions along a homogeneous, quiescent atmospheric conditions result in serious the atmospheric been

a subject where further the absorption
a subject where further the absorption ture, pressure, experimental data computing atmospheric acoustic wave can be significantly arrplitude and fluctvstions in passing through sound waves can substantial fluctuations the direct and their relative phases quiescent atmosphere, leve

l nonzero. sound away the source The pri
l nonzero. sound away the source The primary effect to the turbulence. valid only The acoustic Early theoretical the scatter consideration. Refer- using thc scattering due comparison with attenuation sound propagation its experimmtal plane reflecting boundary and The primary the tu

rbulence in the the interference previou
rbulence in the the interference previously disclissed no attenuation incressing tur quantiktive relationship flyover noise data reportcd in reference show no consistent attenua- atmospheric absorption was left, the sc;ittcr more than in gcnei.;il atrnospherc was sound attenuation n

eglected in calculating thc determine t
eglected in calculating thc determine the in comparison attenuation mechanisms. characteristics correlate Obviously, a sound wave propagating through the atmosphere the absolute velocity, depending whether the atmosphere, temperature height above decreasing vertical causes the heig

ht above sound speed For down- height ab
ht above sound speed For down- height above the direction sound path the relative sound velocity passing through have different the sound at a particular receiving sound. Figure the possible sound sound velocity Shadow Zones the ground ture or limiting sound ray is ground at a dista

nce to the equat!on from vertical temper
nce to the equat!on from vertical temperature theory predicts zone, sound scattering and calculating the sound in the quite useful. however, in the relative cosines, and results, the and temperature averaged over the high-speed Then acoustic developed that noise intensity noise lev

el predicted to approximately predicted
el predicted to approximately predicted and measured noise make it predict the levels accurately. aircraft has no detailed measured aircraft short, there justify a in sound that which would normally expected. Such noise spectrum since higher by the way to the sound level neither the

frequency The propagation also affected
frequency The propagation also affected temperature inversions. was investigated an aircraft over in angles greater the temperature inversion the noise. level because shadow zones increase in acoustic path that neglects include the required in the meaairement parameters to the pre

dicted consider refraction these questio
dicted consider refraction these questions predicted refraction other factors that influence These factors further research that fog, indicate the small amount fog, in little wind and the at a shadow zones sound attenuation attenuating mechanisms. factor that affects noise propagat

ion and other levels in the Such detaile
ion and other levels in the Such detailed noise contours; however, attenuation coefficients for sound propagation through an environment. Reference that the source can attenuation over through an substantiating data should be devel- noise was conducted. The and can predicting the gr

ound-to-ground propagation whenever the
ound-to-ground propagation whenever the and the distributioil absorption should be based experimental data recommended that angles greater that the homogeneous segment atmosphere was account for humidity along consistent data sound attenuation no attenuation lence and show small thi

s reason, and temperature understood qua
s reason, and temperature understood qualitatively; however, the quantitative acoustic resu,ts is and temperature other factors experimental data upon which accurate predictive do not Research Center Space Administration R-35, 1959. Reflection Application TT F-14,185, 246, 1969. N

ormal Acoustic 6. Pao, Sound Propagation
ormal Acoustic 6. Pao, Sound Propagation Sound Attenuation for Natural Ground 9. Rudnick, Acoust. SOC. Note on Ground Absorption Noise Near Absorbing Plane. Vibration, vol. and Olson, Practical Measurements. America, Boston, 1b-13, 1973. Ottawa, Canada Rng., Feb. Sound Field Source

in the Presence Engineering Practices E
in the Presence Engineering Practices Expeiimental Study Field Measurements Inst. Tech. and Scholes, the Ground, and Landing. Operations: Technical Review. van Niekerk, Earth's Surface Wright Air Martin: Rotational Relaxation Oxygen, and Air. Atmospheric Absorption Sound-Absorptio

n in in Terms Temperature and Humidity f
n in in Terms Temperature and Humidity for Evaluating Aircraft Flyover Germany, Sept. Atmospheric Attenuation Measured in Acoustic Flight Atmospheric Absorption Aircraft Flyover Atmospheric Attenuation and Tempera- Atmospheric Absorption Considerations Airplane Flyover 85th Meetin

g America, Boston, 10-13, 1973. Temperat
g America, Boston, 10-13, 1973. Temperature and 515, Nat. 1957, 1956, the Excess CR-95138, 1968. Tech Rep. SOC. America, Acoustical Society University College, London, Eng Acoustic, Atmospheric, Prop- Applications Meeting, University College, London, Res. Center, Boeing Commercial

The Physics Source Over Into Shadow Soun
The Physics Source Over Into Shadow Sound Propagation Smith, Orvel Atmospheric Refraction on of NASA Large Sub- SP-189, 1968, Thompson, Robert Meteorological Effects on Temperature Inversions 5 SO(JYLS (.s RgWACm WINO 4ND mM?~flAm@E: lrpq0~VTS Figure 1. Schematic description of pri

mary factors affecting noise propagation
mary factors affecting noise propagation. 35 /’ / I 1 I I Y Figure 2. Coordinate s. stem. 36 free field with spectrum '/h, I I AT= r'-r I ' /' 1 J* '/' 1 I I Figure 4. Geometry of noise field in the presence of a plane surface. 38 Grass covered Specific acoustic 0 -2 -4 -6

$ I -1 0 -I 2 4 -1.; -I 6 I I 1 1 I I 1
$ I -1 0 -I 2 4 -1.; -I 6 I I 1 1 I I 1 2 00 (b) Mineral covered areas. Figure 5. Concluded. 40 Figure 6. Jet exhaust nozzle with respect to the ground plane. 41 a function c - .- . , t I . -. .. - -. _.. ---I -f . --- , - -. 1- I ? 4- . ..- - ..I- .&- -, r- i- -. - .. t t ! ! 4

3 44 1 I 1 I 0 0 \ I 0 \ 0 N 45 I Fig
3 44 1 I 1 I 0 0 \ I 0 \ 0 N 45 I Figure 11. Downwind attenuation a8 a function of distance (adapted from ref. 23). 46 . .- I I 1 I I f I ___ . ,. .- I I I ! I-- ! , .---- Figure 12. Downwind attenuation as a function of distance and frequency. 47 ,c L ,2 \ \ \ \ \ \ \ \ . i N

\ \ \ -\ - *\ .\ CIVIL NEF 1 SAE DRAFT \
\ \ \ -\ - *\ .\ CIVIL NEF 1 SAE DRAFT \ \ \ \ ANGLE ABOVE HORIZON, DEG Figure 13. Transition from ground-to-ground to air-to-ground attenuation (from ref. 24). 48 49 I I , I , I -t ! I I I - -t I I I I I I -1- I i I i -! ! ! \ ,a 1 I 0- 50 Aircraft Corporation between airplane

52 72 0 0 P -0 L -2 -L) -6 a c - Ill Il
52 72 0 0 P -0 L -2 -L) -6 a c - Ill Ill I1 111111111111 1111 50 200 So0 2000 5.910 /qOGO FREQVENCy (flZ) Figure 17. Difference between atmospheric absorption Figure 18. with meteorological above ground along the Frequency dependence scattering due Figure 20. Effects of atmosphe