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TOApproved for public release, distributionunlimited
FROMDistribution authorized to U.S. Gov't.agencies only; Test and Evaluation; 15 Feb1972. Other requests shall be referred toAir Force Flight Dynamics Lab./FY,Wright-Patterson AFB, OH 45433.
AUTHORITY
Air Force Flight Dynamics Lab ltr dtd 27Aug 1979
THIS PAGE IS UNCLASSIFIED
K(
"AFFDL-TR-71-22
A GUIDE FOR PREDICTINGTHE AURAL DETECTABILITY OF AIRCRAFT
ERIC E. UNGAR, El AL
BOLT BERANEK AND NEWMAN, INC.
TECHNICAL REPORT AFFDL-TR-71-22
0- L
MARCH 1972
, -- Distribution limited t,- U.S. Government agencies only; test and evaluation; state-merit applied 15 February 1 72.. Other requests for this document must be referredio AF Flight Dynamics Laboratory/FY, Wright-Patterson AF8, Ohio 45433.
AIR FORCE FIAGHT DYNAMI-- LABORATORYAIR FORCE SYSTEMS COMMAND
WRIGHT-PATTERSON AIR FORCE BASE, OHIO
NOTICE
When Government drawings, specifications, or other data areused for any purpose other than in connectiou with a definitelyrelated Government procurement operation, the United StatesGovernment thereby incurs no responsibility nor any obligationwhatsoever; and the fact that the Government may have formulated,furnished, or in any way supplied the said drawings, specifica-tions, or other data, is not to be regarded by implication orotherwise as in any manner licensing the holder or any other per-son or corporation, or conveying any rights o- permission to man-ufacture, use, or sell any patented invention that may in any waybe related thereto.
Pi'C Fvzf SE:LC30"q',R. •O.i [.2
" * . . . . . . . . . . . . i
-LCIAL,
Copies of this report should not be returned unless returnis required ;,y security considerations, contractual obligations,or notice on a specific document.
AIR FORCE: 10-4-72/150
A GUIDE FOR PREDICTINGTHE AURAL DETECTABILITY OF AIRCRA T
RI!C E. UN'GARU, Fl AL
Distribution limited to U.S. (6 vcrrmcnt agencies onlyý test and evaluation; state-
ment applicd 15 Fcbruart 1972) Other rcqucsts for this dtocument must be referredto Al: Flight Dyniamics Laboratort//FY, Wright-Patterson AFB, Ohio 45433.
!
"l~
FOREWORD
The work presented in this report was performed by Bnlt Beranri< andN•,.'ran Inc., Cambridge, Massachusetts, under USAF Contract No. t33615-70- tC-1276. This contract was initiated under Project 1471, "Aero-AcousticProblems in Air Force Flight Vehicles", Task 147102, "Prediction andControl of Noise Associated withi USAF Flight Vehicles", arid administered bythe Aero-Acoustics Branch, Vehicle Dynamics Division, Air Force FlightDynamics Laboratory, Wright-Pattcrson Air Force Base, Ohio. Mr. i)avey L.Smith served as Project Engineoer; his assistance and cooperation are grate-fully acknow-ledged. The reported work was carried out between January 1970and January 1971. Tl'his report lhas beeC assigned Bolt Beranek and NewmanInc. Report No. 2104.
'I
Severa.l meembers of tie staff of Bolt Beranek and Newman Inc. made majorcontributioris to tie work reported here. Mr. raniel L.. Nelson is responsiblefe[ tire appendix - on "Rotational Noise of Propellers , and :Mr. .ioseph Siriullinfor i rat on "Vortex Noise of Prupellers". Jr. Istvani Ver prov-I&-d mucli of theinformation that appears in the appendixes dealing with "Noise of Gas Jets","Gear Noise", and "Aural Detectability" and also authored tie appendix on
I-c auia Lu tiU.:, ibyL0Z\et~rtL'LCu llcite A d iby 'oinL For es", as,well as that port ion of the appendix on "Sound Radiated from Flow over RigidSurfaces" which deals with turbulent Iounliary layers. Mr. Richard E. Hayden
contribluted thie section of tire' last-mentioned appundix concernin-g soundfrom flo.: past finite bodies. Mr. Robert Abilock prepared most of tieal-pendix onr "AtmospirLric Propagation Effects" arid an;soserlbled that part of Lite"Aural Detectalbility" appendix which dea~l with background noise lvL-els.
Dr. Ulricih J. Kurze atithored the appendix on "Sourd Atterruation in CircularDucts", and :1r. Sankaran ilariharan participated in the literature rtview anddata analysis for tie appendixes dealing with the noise of piston, roLatinigCotulerstion, and turboshaft engines. Mr. Davey L. Sr;riti and Capt. Rodney 1'.
Paxsen ef AFFDL contributed tie appendix describing an "Alternate Method forDeterrmining Uncorrected Detection Range". Dr. E-ri: E. Ungar was resporisiblefor the coordination and integration of all efforts into this report, as wellas for tire rest of the technical work presented mciue.
lhe report was submitted by tire authors oil 1 February 1971.
This report has bheui reviewed and approved.'II
. ;/ ( 7
ý-.AJJA'!I ./j. M'YKYT)W
Ass ' for Research and TecrlnologyVehicle Dynamics D ivision
• '' "_ *._ - 't - . *.," .S
ABSTRACT
The concepts which underlie the detection of aircraft bythe human ear are described. A scheme is delineated for predic-ting the range at which a given aircraft will first be heard byan "average" listener; this scheme is also applicable to compar-ing the aural detectabilities of alternate aircraf't configura-tions and to identifying those components of the noise of a givenconfiguration which bear prime responsibility for the aircraft'sdetectability. Means are presented for predicting the noise dueto all sources likely to be significant for light aircraft, theattenuation of acoustic slgnal,) propagating from an aircraft toa listener on the ground, and the ability of a listener to de-tect an acoustic signal in the presence of background noise.
ii
!ii
TABLE OF CONTENTS
page
LIST OF FIGURES .... ............................... ........
LIST OF SYMBOLS .............. .. ....... . ....... .........INTRODUCTION .. .... .... ..... .... . .. .......... . .....
PURPOSE AND SCOPE ........... 6 ................. ............. 1ORGANIZATION Or REPORT .................................... 2
SOME BASIC CONCEPTS .................. o ............ 3
AURAL DETECTABILITY .... ............................... 3ACOUSTIC QUANTITIES ............................ 4
Sound Power Level and Sound Pressure Level ................ 4Denendence of Sound Pressure on Sound Power Level 5Dependence of Levels on Bandwidth .................. 6Multiple Sources ........................... .... .... 6
DETECTION RANE CALCULATION ................................. 8GENERAL APPROACH ......................................... 8ACOUSTIC POWER EMITTED BY AIRCRAFT ............................ 8DETECTION LEVEL SPECTRUM .................................. 10DETECTION RANGE SPECTRUM .................................. 10
APPENDIX A: ROTATIONAL NOISE OF PROPELLERS.................... 16DIPOLE SOUND .......... . ..................................... 16MONOPOLE SOUND ............................................ 21
Effects of Disturbed Inflow and Forward Motion .......... 23Comparison of Theoretical Predictions with Measured
Data ................. .................. 23ESTIMATION OF TOTAL PCOUSTIC POWER.........................26ESTIMATION SCHEME ......................................... 27
Illustrative Calculation ................................ 29REFERENCES FOR APPENDIX A ................................. 32
APPENDIX B: VORTEX NOISE OF PROPELLERS .................... 40VORTEX NOISE LEVEL ..................................... .. 40SPECTRUM SHAPE ............................................ 42DIRECTIVITY.. ............................................... 43COMPARISON OF PREDICTIONS WITH EXPERIMENTAL DATA .......... 45ESTIMATION SCHEME .......................................... 48
Illustrative Calculation ........................ 49REFERENCES FOR APPENDIX B ................................. 50
PRMEDIMG PAGE LA1IK--!•T FIIL4D
-a'
page
APPENDIX C: NOISE OF PISTON ENGINES ........................ 56NOISE SOURCES ............................................. 56DATA ...................................................... 57
Availability of Data on Spark-Ignition and DieselEngines ............ .. ............................. ... 57
Similarity of Spark-Ignition and Diesel Engine Noise... 57A vai lab le D ata . ............................. .... . . ... .. 5 8
DATA ANALYSIS: ESTIMATION SCHEME ........................ 59Exhaust Noise ....................... #..o.. . ...... .... 59Intake Noise ............................................ 60
Casing Noise ......................................... .. 60ESTIMATION SCHEME ............................................ 61
Illustrative Calculatton................................. 61REFERENCES FOR APPENDIX C.................................. 63
APPENDIX D: NOISE OF ROTATING COMBUSTION ENGINES ........... 72DATAC..D......... .... 72
DISCUSSION .................................................... 73ESTIMATION SCHEME ......................................... 73
Illustrative Calculation ................................ 73REFERENCES FOR APPENDIX D ................................. 74
APPENDIX E: NOISE FROM TURBOSHAFT ENGINES .................. .. 79AVAILABLE DATA ............................................ 79NOISE SOURCES.................................................. 79COLLAPSE OF DATA ........... .............................. 80ESTIMATION CURVES ................. .......... 81ESTIMATION SCHEME ................. 6 ..... . ..... 82
Illustrative Calculation .............................. 83REFERENCES FOR APPENDIX E .. .......................... 84
APPENDIX F: DISCRETE-TONE NOISE PRODUCED BY TURBOJET FANS.. 97INTRODUCTION ........................................... 97SOURCE MECHANISMS . . . . . ............................ 97PREDICTION. ............... .......... .... ...... .... . 98ESTIMATION SCHEME, .................. ..................... . . 98
Illustrative Calculation ............................... . 99REFERENCES FOR APPENDIX w .............. ................. 101
APPENDIX G: NOISE OF GAS JETS .............................. 102ACOUSTIC EFFICIENCY AND MECHANICAL POWER ................... 102SPECTRUM SHAPE AND DIRECTIVITY- .......................... 103ESTIMATION SCHEME ................ 6 ...... ............... . 104
Illustrative Calculation....... ............... 105REFERENCES FOR APPENDIX G1................................107
vi
S" ....... • - • < . .' .. .. *• -.'• i:;;L M ',t:• • ;• v• -•% • "' ... ...
page
APPENDIX H: SOUND ATTENUATION IN CIRCULAR DUCTS ............ 111INTRODUCTION .............................................. 111HIGH FREQUENCY ATTENUATION ................................ 112
Directly Emitted Rays ................................... 113Reflected Rays; Attenuation of Short Ducts................. ll4Attenuation of Long Ducts ............................... 114
LOW-FREQUENCY ATTENUATION ................................. 116Source Distribution ..................................... 116Duct Terminations and Lining Discontinuities ............ 116Source Connected to Absorbing Duct via Unlined Duct ..... 117Sound Source Located Directly at the Inlet of the
Absorbing Duct ........................................ 119PROPAGATION CONSTANTS FOR CIRCULAR DUCTS..................... 120ESTIMATION SCHEME ......................................... 123
Sample Results .......................................... 125REFERENCES FOR APPENDIX H ................................. 129
APPENDIX J: GEAR NOISE ........... .... ................... 137MECHAN{ISM OF NOISE GENERATION ............................. 137
Tooth Contact Forces .................................... 137Characteristics of Noise ................................ 137
DATA ......... .......................................... 138Available Data ....................................... 138Denendence of Overall Noise on Transmitted Power and
Tooth Force ........................................... 138Noise Snectra ........................................... 139
PREDICTION CURVES ....................................... 139ESTIMATION SCHEME .......................................... 139
Illustrative Calculation ............................. 140REFERENCES FOR APPENDIX I ................................. 141
APPENDIX K: SOUND RADIATED FROM PLOW OVER RIGID SURFACES... 148SOUND FROM TURBULENT BOUNDARY LAYER ......................... 148
Infinite Surface .................................... 148Mathematical Model of Boundary Layer................... 148
Sound Radiation ......................................... 149Frequency Distribution ................................. 151Effects of Surface Edges ................................ 152
SOUND FROM FLOW PAST FINITE BODIES ........................ 152Airfoil In Large-Scale Turbulent Flow ................... 152Small-Scale Turbulent Flow over Airfoil .............. 153
ESTIMATION SCHEME ......................................... 154Flow over vuselage ...................................... 154Flow over Airfoils ...................................... 155
REFERENCES FOR APPE4DIX K .................. ..... ........ 157
vii
page
APPENDIX L: SOUND RADIATION FROM BEAM-REINFORCED PLATESEXCITED BY POINT FORCES .......................... 162
INTRODUCTION ........................... . ...... * . 162PO1ER INPUT FROM POINT FORCE .............................. 162
Admittance of Beam-Plate System............................ 163Admittance of Plat e ...................................* 163Power Input ............ *.*............. .... .... 163
EXCITATTON ACTING ON BEAM OF BEAM-PLATE SYSTEM ............ 164Components ................................. ... ... ... 164Near-wield Radiation .................................... 164Radiation from Waves Propagating along Beam ............. 164Radiation from Plate; Estimation Scheme ................. 165
EXCITATION ACTING ON PLATE ................................ 166ESTIMATION OF LOSS FACTOR AND RADIATION EFFICIENCY ........ 166
Loss Factor ............. .......................... .... 166Radiation Efficiency .................................... 166
ESTIMATION SCHEME .................................... .... 166REFERENCES FOR APPENDIX L ................................. 168
APPENDIX M: ATMOSPHERIC PROPAGATION E'FFCT.................INTRODUCTION ....................................... ...... 170"P .FT CTABL " PpECTS........... I . ........................... 171
SpreadinE Loss .......................................... 171Atmospheric Absorption ...................................... 171
"VARIABLE" EFFECTS ........................................ 173wocusing ................................................ 173Terrain Attenuation ..................................... 174Attenuation Due to Turbulent Scattering ................. 1714Shadow Zones ........ ................................... 175Attenuation Due to Fo. and ?ain ........................... 176
E.PECTS OF PROPAGATION OW PR!ESSURE IGNATURES ............. 176ATTENUATION CALCULATIONS .................................. 177
Sound Pressure at a riven Range... ......................... 177Range for Civen Sound Preure...........,..........177
REFERENCES FOR APPENDIX M ..... ....................... ... 17')
AP'PENDTX N: AURAL DETECTABILITV ............................ 188INTRODUCTION ........................ ..................... 188DETECTABILITY OR PURE TONES.. ............................... 189
Hearing Threihold ....................................... 189Masking by Noise ........................................ 189Detectability ......... . ................................... 190
DETECTABILITY OF BROADBAND NOISE .......................... 190Hearing Threshold ....................................... 190Masking by Noise ........................................ 190Detectahility .. ......................... . .... ....... ... 191
Comnlications .......... ....................... 192BACKGROUND NOISE LEVELS. .............................. 192REFERENCE,"S FOR APPENDIX N .. 1...,....4..... ............ 4
viii
page
APPENDIX P: ALTERNATE METHOD FOR DETERMINING UNCORRECTEDDETECTION RANGE . .. . ............................ 200
INTRODUCTION .................... .............. s ......... 200RESULTS OF SAILPLANE AURAL DETECTION STUDY ................ 200ESTIMATION OF? UNCORRECTED DETECTION RANGE FROM RECORDED
FLYBY SOUND. ............................................. 201ESTIMATION OF UNCORRECTED DETECTION RANGE FROM PREDICTE'D
NOISE SOURCE CHARACTERISTICS ............................ 203REFERENCES FOR APPENDIX?......................................... 205
II
lx
47.
LIST OF FIGURES
Figure page
1 Chart for Combining Two Uncorrelated AcousticLevels, L1 and L2 . Levels May Be Power Levelsor Sound-Pressure Levels 13
2 Illustration of Detection Rangle CalculationApproach 14
3 Detection Range Spectra Corresnonding to Figure 2 15
Al Force Variation at Typical Location in PropellerPlane. h -- Propeller Width In Plane, at Radius r 33
A2 Coordinates 33
A3 Thickness Function S(rl,€ 1 ) in Non-Rotatlnr-Coordinates 311
A4 Narrow-Band Sound Pressure in Piane of OV-1Propeller for Conditions of Reference 9, Table iII 35
A5 Narrow-Band Sound Pressure in Plane of OV-1Propeller for Conditions of Reference 9, 36
A6 Narrow-Band Sound Pressure in Plane of U-10Propeller for Conditions of Reference 10, TablE II 37
A? Narrow-Band Sound Pressure out of Plane of OV-lPropeller for Conditions- of Figure A5
A 8 Narrow-Hand Sound 1'ressure out of' !lane of U-10Propeller for Conditions of Figure A6 39
B1 Definitions of Ang:les for Directivitv Analysis 51
B2 Vortex Noise as a Function of Lift Coefficient andAngle of Attack, for Helicopter Rotor of Reference5, (at 7.5' Behind Rotation Plane) 52
B3 Lift-DraE- Characteristic:s of NACA 001? AirfoilSection 53
B4 Comparison of Mea. ured and Predicted Vorrtex Noisefor Lockheed Q-Star 50
B5 Comparison of Measured and Predtcted Vortex Noisefor H.D. 1 }Hovercraft at 15' Out of ProrellerPlane, 100 ft from Hub 3
S. .' , •-,• ".. . < .. .... .• ,,, --..•; "• •77, -" ... . .. '" ,..
Fi gure page
Cl Exhaust Noise of Nine Unmuffled Diesel Engines(160 to 7000 Hp 240 to 1800 rpm, 2 & 4 StrokeCycles, 30 to 4A0/see Firing Frequency) 65
C2 Exhaust Noise of Unmuffled Diesel Engines, asFunction of Frequency/Firing Frequency 66
C3 Intake Noise of Six Unmuffled Diesel Engines(300 to 4000 Hp, 260 to 1200 rpm, 2 and 4 StrokeCycles, 22 to 60/sec Firing Frequency) 67
C4 Intake Noise of Diesel Engines as Function of9requency/'Firing Frequency 68
C5 Casing Noise of 27 Diesel Engines L12.5 to 2900 kw(9 to 2200 HO) 2 to 4 Stroke Cycles, 240 to 1800rrm, 30 to 480 sec Firing Rates Turbocharged andNatura]ll Aspirated 4,5,8,10 Cylinders, In-Lineand V] 69
C6 Casing Noise of 27 Diesel Engines as Function ofFrequency/Firing Frequency 70 ,
C7 Estimation of Noise of Piston Engines 71
Dl Intake Noise of Hotating Combustion Engines 75
D2 Exhaust Noise of Rotating Combustion Engines 76
D3 Casing Noise of Rotating Cormibu.;tion Engines 77
D4 Average Sound Power of Rotary Combustion Engines 78
El Inlet Noise of 26 Cas Turbines (Rated Between240 and 1.350 Hp) 85
E2 Gas Turbine Inlet Noise as Function of BladePassage Frequency fB 86
E3 Gas Turbine Inlet Noise as a Function of ShaftRotation Frequency f. 87
E4 E~xhaust Noise of 30 Gas Turbines (Rated Between240 and 1350 Hr,) 88
E5 Gas Turbine Exhaust Noise as Function of BladePassage Frequency fB 89
xi
S.... • .,.-.. .. .- --.I... * ,. . ,. ,, . •: - - .. ... . . .. .
Figure page
E6 Gas Tuibine Exhaust Noise as Function of ShaftRotation Freagrincy fs 90
E7 Casing Noise c 1.8 Gas Turbines (Rated at 240to 1500 Hp) 91
E8 Casing Noise ci 18 Gas Turbines as Function ofBlade Passage Frequency fB 92
E9 Casing Noise of 18 Gas Turbines as Function of
Compressor-Shaft Rotation Frequency f s 93
El0 Estimation of Turbine Inlet Noise 94
Ell Estimation of Turbine Exhaust Noise 95
E12 Estimation of Turbine Casing Noise 95
E13 Estimated Noise from 90 Hp Turboshaft Engine with22 Blades in First Stage, Operating at 27,000 rpm 96
311 Acoustic Efficiency of Air Jets at Zero Altitudeand Room Temperature 108
G2 Nlormalized Octave-Band Spectrum of Jet Noise 109
33 Directivity of Jet Noise 110
H9 Rays Emitted from Circular Duct without Reflectionfrom Walls 130
112 Rays Emitted from Duct after One Reflection(Constructed from Image Sources) 131
H3 Lined Duct with Rigid Tailpipe 132
H14 Duct Lining Geometry 133
115 Calculated Attenuation of the Lined Duct andReflection Loss of Tailnine 134
H16 Excess Attenuation due to Reflections at Transitionfrom L.ned Duct to the Rigid Tailpipe, arid Reflec-tion Loss at the Onen E-d of Unflanged Tailpipe,for Various Ratios of Length LR of the Tailpipe tothe Duct Diameter D. (Same Duct Lining as in FigureH5) 135
xii
Figure page
H7 Points Along Cross-Section of Lined Duct UsedFor Finite-Difference Approximation of Differen-tial Equation (28) 136
Jl Schematic Time-Variation of Gear Interaction Force 142
J2 Overall Sound Power Level of Gears as a Functionof the Transmitted Mechanical Power 143
J3 Octave-Band Sound Power Spectra for PlanetaryGears, rpm > 1500 144
J4 Octave Band Sound Power Spectra for Spur Gears,rpm > 3000 145
J5 Octave Band Sound Power Spectra for Spur, Bevel,
and Bevelspur Gears, rpm < 1500 146
J6 Estimation of Gear Noise 147
K1 Normalized Fixed-Transducer Spectrum of PressureField under Turbulent Boundary Layer 158
K2 Normalized Octave and Third-Octave Band Spectrumof Boundary Layer Pressure Fluctuations 159
K3 Edge Noise Spectrum for Turbulent Boundary LayersFlowing Over a Trailing Edge 160
K4 Wake Noise Spectrum for Airfoils at Small Anglesof Attack 161
Li Estimation of Acoustic Radiation Efficiency ofPanels 169
MIla Values of Air Absorntion Coefficients at 590 Fand Various Relative Humidities (from Reference 1) 180
Mlb Values of Air Absorption Coefficients at 20°Fand Various Relative Humidities (from Reference 1) 181
MIc Values of Air Absorption Coefficients at 100OFand Various Relative Humidities (from Reference 1) 182
M2a Terrain Loss Coefficients for Urass Areas (fromReference 3) 183
xiii
S. . .... , -" , •" .•-. ; - • , ,j17 ,-A 4 . - ; . • • .
fI
Figure page
M2b Terrain Loss for Tropical Forest Areas (fromReference 3) 184
M2c A Chart from Which to Estimate Terrain LossCoefficients for Tropical Jungles. Zones I through5 (from Reference 3) 185
M3 Effect of Terrain and Elevation Angle on theTerrain Loss Coefficient in the 150-300 Hz OctaveBand (from Reference 5) 186
N! 4 Effect of Absorption on Range from Given Source
at Which Pres-cribed Sound Pressures are Observed 187
Ni Threshold of Hearing 195
? laNaRing of Pure Tone:.; by Noise (Reference 2), andCorrection fo)r Obtaining Octave-Band Detection 4Levels Ld,OCT from Pure-Tone Detection Levels Ld 196
'3a Davtime Variation of Detection Levels in PanamaForesnt and Jungle (from Reference 6) 197
"':31 !,ightimp Variation of Detection Levels in PanamaPorrst and Jungle (from Reference 6) 198
":.'4 !-erresentative Detection Levels in Jungles andForests 199
.I Samole Aural Detection Evaluation (from heference i) 206
xiv
3 7-
LIST OF SYMBOLS
A area
A total propeller blade areab
A area of jet
A• Fourier coefficient of blade section profileA Rourier coefficient
s
B bending stiffness of beam, or number of plates
CD drag coefficient
CL lift coefficient
D flexural rigidity of plate, or jet diameter, or ductdiameter
D (r ) maximum blade thickness at radius r,
E- Young's rncduluz
F force, or force component
F• d drag force at effective radiu3
F total thrust
I. Green's function
H duct width
acoustic intenitv.', or moment of inertia
j 1Bessel function of order mM
L duct length
Ld detection level, or eddy decay distance
Il • noise s5rectrurn level
L 1'f noise level in freguency1 hand Af
LN noise level in critical bandsF
LOA overall level
I.-,CBP level in octave hand
xv
1 , 1 -
L sound pressure levelP
L unlined duct length
LS lined duct length
LSl spectrum level of signal
LSAf signal level in frequency band Af s
LSPO signal level in critical bandL sound power levelw
AL attenuation
AL spreading lossS
Mach number
M rotational Mach number at effective radius1N number of cvlinderro
Nt number of teeth
Pj nressure in jet
F 0 ambient pressure
I rate of mass disnlncement
R distance from sound ,ource
.R corrected detection rangec
P reference distance
rain minimum range
. uncorrected detection range
duct cross-sectional area
"blade thickne;s function
I total drag torque
TP effective contact durationC ff
U free-stream velocity, or flow sneed
xvi
T&
U absorptive duct perimetera
U convection velocity
U jet velocity
UO velocity of entering air
Utip tip speed of nropeller or fan blade
U0.7 blade speed at 0.7 radius
VD oropeller disc volume
W acoustic power
Wd dissipated power
W power input
W mechanical power
W reference nower = 10-12 wattsref
X distance from leading edge
XS distance at beginning of shadow zoneYb point input admittance of beam
Y point input admittance of beam-plate system
Yd point input admittance of plate
Z duct wall impedance
Zn impedance of nth mode
a nropeller radius
ad effective rroneller radius
am propeller mean radius
a effective nrooeller radius for thrustz
a¢ effective oropeller radius for torque
b chord length
xvii
bL lining thickness
c speed off sound in air
cb speed of bending waves in beam
CL longitudinal wave velocity
c speed of bending waves in plate
d blade thickness
d projected bl.de thicknessp
e base of natural logarithms
f frequency
fB blade passage frequency
f frequency at which X D
fp firing frecjuenc.y
f center frequency of octave band
f neak frequency
fs shaft rotation frequency
f tooth contact frequency
Af frequency hand
h plate thickness
h mean heicrht of sound source and receiver
i :
k wavenumber
k wavenumber of nressure disturbancep
k radial wavenumberr
1( axial wavenumberZ
z index number, or mean free path
M mass flow rate of air
"•b mass per unit length of beam
xviii
... . - ~-- ---. - .-- ,•.- -- -- - '. "... - "". - --.. . .... .. .. -.. .S~ ~ ~ ~ ~~ ~.. ...-... , ..- ,•-% ,°'. ;
M
mf mass flow rate of fuel
mD mass per unit area of plate
p pressure or (rms) sound pressure
PbZ root-mean-square pressure in boundary layer
reference pressure = 2 x 10- dyn/cm2 = 2 x 10-5 Newton/m 2Pr, .
q source density
r radial coordinate, or distance, or Cp/Cb
s harmonic number index
t time
U1 rms root-mean-square fluctuating velocity
v velocity amolitvude
w span-wise dimension of airfoil Pdge, or width of beam
x Cartesian coordinate
z axial coordinate
du/dz vertical -radient of effective sound velocity
- flow resistance of lining per unit thickness
ac spectrum of radiated acoustic pressureac
4)d eddy-decay spectrum function
¢Pf fixed-location spectrum of' pressuref
D ý normalized ýf(see Eq. 14 of Appendix K)
pressure spectrump
D 3 cross-stream nnectrum function
P angular velociLv
Q 0,Q soherical angle:;
aX angle of attack, or absorption coefficient
aT radius of gyration
xix
* -- **
a classical absorption coefficient
amo1 molecular absorption coefficient
a s normalized Fourier coefficient of thrust force
ascat attenuation coefficient for atmospheric scattering
atot total attenuation coefficient, or total absorptioncoefficient
a absorption coefficient for- axial waves
pitch angle
B/D
Fourier coefficient for blade thickness function
6 boundary layer thickness, or diameter/wavelength ratio6te trailing edge thickness
6 wake thicknessw6* boundary layer displacement thickness
0 angle between propeller plane and line from propellercenter to observer
6e angle of elevatione
0 (f) critical band correctionc
0. angle from jet axis3
00 angle at sound source, subtended by duct end (see Fig.Hl)
E small angle
n acoustic convertion efficiency, or structural. c..ssfactor
X acoustic ,javelenptth
bendinF wavelenrth
Ac wavelength at critical frequency
v angle (see Pig. A2), or kinematic viscosity of air
xx
p density of air
Ps density of structural material
T real part of duct propagation constant
T n real part of propagation constant of nth duct modeC acoustic radiation efficiency, or imaginary part of
duct propagation constant0ac acoustic efficiency
a porosity of liningp
a imaginary part of propagation constant of nth duct mode
angular coordinate
prc-ssuirc correlation function
x structure factcr of lining
angle between propeller blade and plane through huband observation noint (see Fig. Bl)
w radian frequency
wB blade oassage radian-frequency 2B
xxi
INTRODUCTION
PURPOSE AND SCOPE
It is desirable for all military aircraft to be impossibleto detect by the enemy until it is too late for him to employcountermeasures or take evasive action. Modern high-speed strikeor reconnaissance aircraft approach this ideal by flying at tree-top level, but their high speeds limit their utility for certainmissions. Consequently, there exists a continuing interest inslow-flying aircraft of minimum detectability.
Much is known about designing aircraft and countermeasuresto reduce detectability by radar, optical and infrared means;also, all of these means tend to be useful only for very limitedranges against aircraft flying at treetop level. In contrast,the acoustic noise emanating from aircraft may be detected - andlocalized - at very considerable ranges, even by the unaidedhuman ear. Thus, low-speed aircraft tend to be extremely vulner-able to aural detection by personnel on the ground.
Although there exists much information relevant to the de-sign of "quiet" aircraft, this information is widely scattermdthroughout the literature and is generally inaccessible to thenonspecialist in acoustics. It is the purpose of the presentreport to provide a collection of information pertinent to the
design of aircraft from the standpoint of minimum aural detection,and to present this information in a form in which it may be read-ily used without reference to a multitude of other documents.
A "quiet" aircraft must satisfy aural detectability specifi-cations, in addition to the usual performance specifications (e.g.,payload, range, speed). Generally, many different alternativeconfigurations will sat]i-fy the various requirements to variousderpeps, and the ni roroft desi goer sl nl y 1? ; fac ed with selectingthe best compromises. The designer of an aircraft that must meetstringent aural detectability requirements will generally need tobegin with a first-cut configuration designed on the basis of bothperformance and acoustic requirements; he must then evaluate theaural detectabillty of his initial design, identify what acousticchanges are required, modify or, redesign the aircraft accordingly- and repeat the evaluation-modification cycle until he reachesan acceptable result.
. ...... V_- 4*
Ii
The information provided in the present report may be used:(1) to compare the aural detectabilities of alternate components(in order to enable one to make favorable initial choices), (2)to evaluate and compare the aural detectabilities of aircraftdesigns, (3) to estimate the ranges at which aircraft may be de-tected by ear, and (4) to identify what components of noise con-tribut.e most to the aural detectability of a given design (andthus what components of noise must be reduced in order to reducedetectability). Although some hints are provided concerning tac-tics (e.g., selection of favorable terrain and meteorological con-ditions) for reducing the probability of aural detection and con-cerning how one might obtain more precise detection-range predic-tions for given situations, these topics are considered generallybeyond the scope of this report.
ORGANIZATION OF REPORT
The first of the following sections summarizes the basicconcepts involved in aural detectability analysis, presents com-monly used acoustical quantities and notation, and indicates themost important characteristics of these quantities. The secondsection delineates a scheme for determining the range at whichan aircraft can first be heard, provides guidelines for obtainingthe information needed to apply this scheme, and illustrates itsuse.
In the f'ourteen appendixes of this report are provided thetools for implementing the suggested detection range estimationsclheme. These appendixes deal with the various noise sourceslikely to be significant for light "quiet" aircraft, with theability of human listeners to detect an acoustic signal in thepresence of background noise, and with the attenuation acoustic6igna! experience as they propagate through the atmosphere.Each appendix attempts to provide the reader with some insightinto the basic processes; some appendixes - in particular thosewhich present newly developed information - even contain completederivations. Each appendix also includes, usually at its end,specific directions for application of the given information.
.1~. :
SOME BASIC CONCEPTS
AURAL DETECTABILITY
Aural detectability involves three major considerations•
1. Characteristics of acoustic noise generated at the source,
2. Modifications experienced by acoustic signals as they propa-gate from the aircraft to listener locations on the ground,
3. Ability of human listeners to detect aircraft noise in theirbackground noise environment.
A noise source may be described most conveniently in termsof its acoustic power spectrum (i.e., the frequency distributionof the acoustic power emitted by the source), its directivity(i.e., the variation of the acoustic power with direction as mea-sured from reference axes attached to the source), and any time -variations of the spectrum and directivity. Because the noisesources associated with aircraft in steady flight are not likelyto change with time, time-variations need not be considered here;rather slow variations, such as may result from maneuvers orchanges in engine or propeller settings may be analyzed simply interms of sequences of quasi-steady conditions.
In most military situations in which one is concerned withaural detection, enemy personnel may be located in any directionfrom the aircraft. One therefore would prefer to design suchan aircraft so that there exist no directions in which the radi-ated sound is more intense than in others - except that one maywish to direct much of the noise upward, where there are no lis-teners, or possibly backward, where the noise heard at a fixedlocation on the ground after the aircraft has passed is likely tobe less intense than when the aircraft is more nearly overhead.However, for most noise sources of interest here one can do littleto change their directivity significantly. Although the variousnoise sources discussed later do have some inherent directivitycharacteristics, the directivity effects are generally not verypronounced. For this reason, and because consideration of direc-tivity effects complicates the analysis and greatly increasesthe computational burden, directivity considerations are not em-phasized here. (But directivity information has been includedin the appendixes, as far as it is readily at hand, so that itmay be available for more detailed analyses than those generallyadvocated here.)
3
111M- rr ,• •,' - M ,,I
As an acoustic signal travels away from a source, its energyis spread out over a larger area, so that less energy reaches asensor (ear or microphone) of a given size. In addition, theatmosphere through which a signal propagates absorbs energy fromit, again reducing the signal that reaches a given sensor. Atmos-pheric gradients also refract (deflect) signals, and may eitherreduce or increase the amount of energy reaching a sensor; thesame is true of terrain and vegetation, which may reflect and/orabsorb acoustic energy. An acoustic signal generally is describedby its spectrum (frequency-distribution) of acoustic pressure;only spreading attenuates all frequency-components equally, theother attenuation effects generally are frequency-dependent.
A human listener can detect an acoustic signal only if itis strong enough to be above the threshold of sensitivity of hishearing system and if it is sufficiently intense so that he candistinguish it from the background noise that always reaches hisear (e.g., due to wind, rustling leaves, machinery, human activ-ity). The hearing sensitivities of different individuals differwidely and are also affected by exposure to noise. Of course,any ear covering tends to reduce this sensitivity, whereas lis-tening aids (even cupped hands) may enhance it. An individual'sability to detect an acoustic signal also depends on many psycho-aogical factors, such as fear and fatigue, whose effects cannotbe readily predicted. The "masking" effect of background noisedepends on the spectral (and time-dependent) character of boththe noise and the signal. Prediction of whether a given signalwill be detected (or better, of the probability that a given sig-nal will, be detected) under given conditions clearly is a verycomplex problem. Fortunately, this problem and most of its com-N exities may he by-passed here, since for purposes of evaluatingaternate aircraft components and designs it suffices to consideran average listener under representative conditions.
ACOUSTICAL QUANTITIES
Sound Power Level and Sound Pressure Level
Because the values of sound power and sound pressure encoun-tered in most acoustics problems extend over several orders ofmagnitude, it has become customary to represent these quantitiesin logaribhmic terms. Thus, the sound power level Lw of a sourcewhich radiates acoustic power W is defined as*
Lw= 10 log (W/We) (1)ref
*IPl logiarithms in this report refer to base 10.
II
-T-~ -.- -%PA --
where Wref is a reference power. The internationally acceptedstandard value Wref = in-'- watt z 7.38 x 10-13 ft lb/sec is usedthroughout this report. The power level Lw is a dimensionlessquanti'-y, but to indicate its logarithmic character and the factthat it is defined with a factor of 10, it is given the "units"of decibels (dB). Because different reference values have beenused, it is also customary to indicate the reference value oneuses. For example, the power level corresponding to an acousticpower of 2.0 watt would be written as Lw = 123 dB, re 10-12 watts.
The sound pressure level Lp corresponding to a mean-squareacoustic pressure p2 is defined in a manner similar to Eq. (1) as
Lp = 10 log (pZ/p 2 ) 20 log (p/pe) (2)pref ref
2
where Pref represents a refererce mean-square pressure, and wherep and Pref represent the root-mean-square values that correspondto p 2 and P2ef. The internationally accepted standard referencevalue Pref = 0.0002 microbar = 0.0002 dyne/cm2 = 2 > 10- 5 newton/m2
1 2 x 10- 1 0 atm : 2.86 x 10- 9 psi is used throughout this report.Again, it is customary to append the "dB" designation to thesound pressure level and to indicate the reference quantity; forexample, the pressure level corresponding to an acoustic pressureof p = 10 microbar would be written as Lp = 94 dB, re 0.0002microbar.
In the forepoing definitions W and p may represent eitherthe total power and mean-square pressure measured at all frequen-cies, or those same quantities measured in specified frequencybands. If these quantities are measured in bands and the result-ing Lw and Lp values are plotted as a function of frequency (usu-ally, the center frequency of the bands used), one obtains soundpower and sound pressure spectra. Spectra are most often givenin octave bands (which span a factor of 2 in frequency) and 1/3octave bands (which span a factor of 21/3 in frequency).
Dependence of Sound Pressure on Sound Power Level
The mean-square acoustic pressure(measured at a given fre-quency or in a given frequency band) at a given location withrespect to a sound sou-oce is proportional to the acoustic powerproduced by that source (at the same frequency or in the samefrequency band). In a free field, where no reflections occur,the ac.ustic pressure decreases with increasing distance fromthe source; at several wavelengths' distance from the source, themean-square pressure varies inversely as the square of the dis-tance from the source (because in c63ence the acoustic poweremanating from the source is spread over a larger surface area
and a sensor of a given area intercepts less of the power).
.. . . .. S ..1 **'~'.
NNW4
The aforementioned variation, when expressed logarithmicallyand with the appropriate constants, results in a simple expression
for the sound pressure level Lp measured at a distance R from anondirective source (i.e., a source that radiates uniformly inall directions) emitting sound with a sound power level LwL (dB~re 0.0002 microbar) - L w(dB,re 10"1 2 watt) - 20 log R - 0.5 (3)
where R denotes the distance in feet.
Dependence of Levels on Bandwidth
It is often necessary to express levels given in bands ofone width in terms of levels in bands of other widths. For sig-nals whose narrow-band spectra are relatively flat within thebroader (overlapping) bands Af, and Af 2 , one may assume the powe rto be approximately uniformly distributed over freauency in thevicinity of' the bands of concern. If W, represents the power inthe band Afi and W2 that in Af 2 , then
wII/afl W2/Lf2 ,(4)"[
The power level Lw 1 in the band Af then is related to the levelL' 2 as
LW = I _ • + 10 loF (Afl/Af 2 ) (5)
If Af] is an octave band and Af 2 a 1/3-octave band of the samecenter frequency, then Af 1 /Af 2 = 3.0 and Lwj - Lw 2 z 5 dB.
Multiple Sources
The total acoustic power radiated by several sources Iseoual to the sum of the i.ndividual contributions. This is trueof the overall power (including all frequencies), as well as inan: frequency band.
The mean-square prezsure observed at a given location as theresult of several sources similarly is equal to the sum of theindividual mean-square contributions (overall, or in specifiedhands), provided that the various Individual contributions areuncorrelated (i.e., not substantially in phase with each other)*
*''or correlated zsignals, the total root-mean-square pressure isequal to the sum of' the root-mean-square components.
Since it is unlikely that the noise components produced by dif-ferent sources on an aircraft will be correlated, one may consid-er them generally uncorrelated for all practical purposes.
It is usually convenient to work only in terms of the levels,and to avoid converting from levels back to the basic quantities,combining these quantities as outlined above, and then convertingthe results again into levels. One may obtain the (power, or pres-sure) level Lcomb which corresponds to the combination of twocomponents, one at level L, and one at L 2 , by using the chart ofFig. 1. For example, by use of this chart one may determine veryeasily that a signal of 90 dB and one of 96 dB combine to producea signal of 97 dB (not 186 dB!).
One may obtain the level corresponding to a combination ofseveral signals by using the chart repetitively for two componentsat a time; the sequence of forming the two-at-a-time combinationsis immaterial. For example, consider four levels: L, = 60 dB,L 2 = 65 dB, L 3 = 66 dB, L4 = 68 db. Then one finds L1+ 2 = 66.2 dcB,L 3 +4 = 70.1 dB, and L(1+ 2 )+( 3 +4 ) = 71.6 dB; or
L(1+2)+3= 69.0 dB, L[(I+a)+S]+4 = 71.6 dB.
---
DETECTION RANGE CALCULATION
GENERAL APPROACH
The "aural detection range" of a given aircraft operating atspecified conditions may be defined as the greatest distance atwhich an "average" listener on the ground can distinguish the air-craft sound from his ambient background noise environment. Inorder to estimate this detection range, one may proceed as follows:
1. Determine the frequency distribution of the acoustic poweremitted by the aircraft, due to all sources;
2. Determine the "detection level spectrum"t , i.e., the soundpressure level spectrum of signals that the average listen-er can just detect in the presence of the ambient noise;
3. Calculate the distance within which the aircraft sound (ateach frequency) reaches the level at which it can be de-tected by the listener. This process results in a frequencydistribution of ranges, or a "detection range spectrum". Themaximum of this spectrum then is the detection range.
This approach is illustrated graphically in FiE:. 2, to which fur-ther reference will be made below.
ACOUSTIC POWER EMITTED BY AIRCRAFT
In order to determine the spectrum of the acoustic roowergenerated by a given aircraft under specified operating condi-tions, one generally may proceed best by considering each noisesource separately, and then combininF the effects -f all .;uchsources. Where acoustic data directly pertinent to ";pecificcomponents (e.g., enFines, propellers, or engine-zroneller combi-nations) are available, this data snould be used. If .:uch dataare not in hand, one may use the estImation techninues nresentedin the appendixes to this report.
vor propelZer-d4rive aircraft, ,ne -.hould consider the fcl- tlowing sources (listed in the rrohable order of imrortance)*:
*Note: The capital letters preceding each noise component listedindicate the anpendix which may be used to estimate the noisefrom that component.
8 i
1. PronellerA Rotational (pure-tone) noiseB Vortex (broad-band) noise
2. Engine exhaust, intake, ana casingC Piston enginesD Rotating combustion enginesE Turboshaft engines
3. Power transmission systemsJ Gears
4. Aerodynamic noiseK Boundary layer turbulenceK Movement through atmospheric turbulenceK Turbulent wakes
5. Vibrating internal. componentsL Radiation from point-excited surface structures
For jet-engine drive airoraft, one should consider the fol-lowing sources (again listed in the probable order of importance)*:
1. Pronulsion systemE Turbine exhaust, inlet, casingP Pan and comnressor (nure-tone) noiseG Jet exhaust flowH Effects of inlet and exhaust ducts
2. Aerodynamic noiseK Boundary layer turbulenceK Movement through atmospheric turbulenceK Turbulent wakes
3. Vibrating internal componentsL Radiation from point-excited surface structures
The uoper part of rig. 2 illus-trates the acoustic powerspectra for an hynothetical Propeller-driven aircraft. For thesake of clarity, only two broad-band source-spectra (propellervortex noise and engine casing noise**) and pure tones from onlyone source (propellcr rotational noise) are shown. The figurealso shows the totPl broad-band noise snectrur,, obtained by com-bin'.ng the two contr-ibutions according to Fig. 1.
:;Note: The capital letters preceding each noise component listedind.cate the appendix which may he used to estimate the noisefrom that component.
**"or thl.s hynothetical aircraft, the exhaust was assumed to be well
muffled, so that exhaust noise i.; effectively abs.ent.
W;A#- L-. AW _.W
DETECTION LEVEL SPECTRUM
As discussed in Appendix N, the sound pressure level of anacoustic signal that a listener can just detect depends on thelistener's threshold of hearing and on the ambient noise thatsurrounds him. The threshold of hearing for pure tones isslightly different from that for bands of noise, and a given(broad-band) background noise generally can mask a broad-bandsignal better than it can a pure tone. Therefore, one must treatpure-tone and broad-band signals separately.
Appendix N presents standard hearing threshold curves andindicates how one may determine the detection levels which corre-spond to given ambient noise spectra. (The detection level repre-sents the sound pressure level of a signal which is just detect-able against the background noise.) A signal is detectable ifit exceeds at any frequency both the hearing threshold level andthe detection level - thus, if it exceeds the higher of these twolevels. A curve which at any frequency follows either the hear-Ing threshold level curve or the detection level curve, whicheveris higher, thus constitutes a "detection level spectrum", whicha signal must exceed to be detectable.
Information on the ambient noise in some environmentslikely to be of interest in relation to quiet aircraft designis also presented in Appendix N, in terms of detection levels forpure-tone signals.
Figure 2 illustrates how one may derive pure-tone and octave-band detection level spectra from the hearing threshold curvesand detection levels. The hearing threshold curves in Fig. 2have been taken from Fig. Ni. The pure tone detection level cor-responds to nighttime data for a dense Panama jungle kj'rom Fig.N4); the octave-band detection data has been derived from the pure-tone data with the aid of Fig. N2. The heavy solid and dashedcurves then correspond to the detection level spectra, for pure-tones and octave-band noise, respectively.
DETECTION RANGE SPECTRUM
If one knows the spectrum of acoustic power levels Lw ofthe noise of an aircraft and also the spectrum of detection levelsLd applicable to given conditions, one may easily determine the Vdistance over which each frequency-component of the aircraftnoise must travel (in an ideal non-absorbing and non-scatteringatmosphere) so that the sound pressure level of the signal iseaual to the detection level. In view of Eq. (3), this distanceRu (ft) may be found from
10
TM7=
20 log Ru - Lw Ld 0.5 .Lw Ld (6)
Lw and Ld are expressed in decibels, referred to the standardreference power and pressure, respectively. Because of the un-certainties usually involved in estimating Lw and Ld, one mayusually neglect the 0.5 dB correction.
By applying Eq. (6) to each frequency component, one mayarrive at a spectrum of "uncorrected detection ranges" R.. Thedesignation "uncorrected" implies that corrections for atmospher-ic and terrain attenuation effects have not yet been included.
If Lw and Ld are plotted to the same scale, as in Fig. 2,one may determine 20 log Ru graphically, as shown in the figure.Again, one must carry out separate calculations for the pure-toneand for the broad-band noise components. The uncorrected detec-tion range spectrum one obtains from Fig. 2 is shown as the dot-ted curve of Fig. 3 for broad-band noise and as the open circlesfor pure-tone noise. *
From the information presented in Figs. Ml though M3 (ofAppendix M) one may estimate the total absorption coefficientatot(dB/ft) due to atmospheric and terrain effects at each fre-quency. From Fig. M4 or the corresponding relation (see lastfootnote of Appendix M) one may then correct the previously found"uncorrected detection range" spectrum, to obtain a spectrum ofactual (corrected) detection range. The maximum of this spectrumdetermines the range at which the aircraft will first be heardunder the specified conditions; by noting the frequency at whichthis maximum is found and referi.ng back to the noise sourcespectra, one may then determine which noise component is primarilyresponsible for earliest aural detection of the aircraft - i.e.,which noise component must be reduced to reduce the detectionrange significantly.
The solid curve and filled-in circles of Fig. 3 representthe corrected detection range spectrum for the octave-band andpure-tone noise components, respectively, as obtained from theuncorrected spectrum for certain conditions (atot : 0.02 dB/ft).One finds that the maximum of the corrected range spectrum cor-responds to 20 log Rc, 70 indicating that the aircraft will firstbe detected aurally at a range of about 3000 ft. One finds thatthe 160 Hz pure tone component of propeller rotational noise willbe heard first. If this component can be reduced by a littlemore than 3 dB, then the 80 Hz tone becomes predominant, and thedetection range is reduced to about 2000 ft, If all the propeller,pure-tones could be eliminated (or reduced by 10 dB or more), thedetection range would be about 1000 ft; with the noise comporient•.
•Afpendix P presents an alternate method for determining R1u. ThL.-
alternate method is preferable if recorded flyby noise data are
available, or if there exists considerable uncertainty about whethera noise component should be considered as a pure-tone or broadband.
!]
between 125 and 160 liz being heard first. One notes from Fig. 2that at these frequencies the noise is primarily engine casingnoise; therefore, one would need to reduce the noise from thissource in order to achieve any further reduction In detectionrange.
ii
I
Lcomb-L1 ,dB
3.0 2.0 1.0 0.5I i l , ,,, i , , , , I ,, I' II ' I' 'I ' I
0 2 4 6 8 10LI -L 2 ,dB
/I
/
Lcomb -L I dB
0.4 0.3 0.2 0.1 0.05II I I IIIII I I I I I I
10 12 14 16 18 20L I -L 2 ,dB
FIGURE 1 CHART FOR COMBINING TWO UNCORRELATED ACOUSTIC LEVELS,L1 and L2. LEVELS MAY BE POWER LEVELS OR SOUND-
PRESSURE LEVELS
w '2w
U) ) =gd Pw jO p)z
0 .0 a
U)
O4 I-I0 w %
4 0 C0
V)) g o
w cr OR~ I 0I- ) 0 0 IA
CD-u zZ LZJ
UJ Z u
0 f 0'4 /0 w
00
0 0LLAJO ~ j (~3u
.4 -. In e.~~CI
U) 4 bi
0 00 0 0
w 0 UM1(J.IVM~~~~~~ 0O. 3C P 1 3Y 3~danSj
Wv7wOO WW 'g)d 3A1rlS~LUf
(L W 9L V. . .. . . .. . . .. . . .. . .
00 000cc____ 00_________No
0~
000D
0
/ 0-0
/ LL
______________0 u.
/z 0~
2w IdJ w C
U2~UJ0 Of
0 0 o:zo0
w CL
I LU
CY)
Vo NO LU
00~ ~ ~ N 9VJN1133 L
APPENDIX A
ROTATIONAL NOISE OF PROPELLERS
DIPOLE SOUND
Early investigations of propeller noise (Ref. i) showed thatthe lift and drag forces acting on the propeller blades give riseto equal and opposite inertia forces on the fluid medium, andthese force. constitute arrays of acoustic dipole sources distri-buted over the propeller disk and rotating in the propeller planeat the propeller's angular velocity.
In order to analyze the acoustic effects of thes,;e dipolesources, it is convenient to treat first the case of a propellerhaving B blades, rotating at angular velocity S, (but not advanc-ing axially) with uniform inflow to the propeller. An elementof the fluid medium at polar coordinate position r ,0 1 in theplane of the propeller is subjected to forces FZ and Fg as theproneller passes the element's location, which corresp nd toinfinitesimal increments of the thrust and the drag on the pro-peller blade. When there is no propeller blade present at theposition r1 ,01 , there is no force exerted on the fluid.
The duration of each force pulse is determined by the local f
width of the propeller blade, projected onto the propeller diskplane, and by the propeller',% rotational speed. The force onthe fluid at a typical location then varies with time as shownin Pig. Al. If one expands such a periodic function in a Fourierseries, one obtains a sum of harmonic functions whose frequenciesare multiples of the blade passage frequency (B = QB.
()ne may express (see Ref. 2) the axial force distribution as
Fz(t;r 1 ,#,) = SAsexp[-isw B(t-¢t/•)1s
co
= P••asexp(isB 1 )expý-isBt) (1)
whhere A. and ao are Fourier coefficients; s is the harmonic num-ber index; F' is the thrust force amplitude.
l77'1 fl
- .- -, •..2,.1'.aht,.- : , .- A. .ar.'-,, , ... V, . IY,, •
Similarly, the drag force distribution may be expressed as
FF(t;rOrex F seXp(isBp1 )exp(_isB~t) (2)
As shown in Ref. 3, application of a concentrated force at apoint in a fluid is equilralent to locatine an acoustic dipolesource at that point, with the dipole axis In the direction ofthe force. Thus, the double array of forces over the propellerdisk due to thrust and drag gives rise to acoustic radiation froma double array of dipole sources, the thrust-related array havingall sources aligned parallel to the propeller shaft and the drag-induced sources aligned parallel to the propeller plane.
To find the sound field produced by the previously givenforce distributions, one may use the Green's function for a di-pole source of unit strength in the z-direction and of sinusoidalfrequency w, (Ref. 2)
e ikr +- m¢¢ ) -i~tGlz -ikcosv -E I J mJ(krlsinv)e e (3)
where the distances r and r, and angles Nv,O and 01 are definedin Pig. A2, and where J. reoresents the m'th order Be:ssel function,Also, k = w/c is the wavenumber and c represents the wave propa-gation speed, i.e. the speed of sound. The Green's function fora unit dipole in the 0 1-direction is similarly given by
O, - r eikr m'iJ (kr sinv)e e1 'i (4)I0 I-- _r ITT
The foregoing forms of the Green's functions involve approxi-mations which are valid only if the point of observation is in thegeometric, as well as In the acoustic far-field of the source,... e., if the observation distance is much greater than both the
physical dimensions of propeller disk and the acoustic wavelengthin the fluid medium.
The sound pressure due to the thrust force then may be de-termined from
pz~r@•t ýffF z(t;rl,¢•)Glz(rl,¢l;r,O,v)rldr~doI (5)
17
and that due to the drag force from
p,(r,•,V,t) =ffF•(t;r 1 ,•,)G 1l(r, , 1 ;r,•,v)rldrld$ 1 (6)
By substituting Eqs. (1) and (3) into (5) and noting that thefrequency in the Green's function must be the ;ame as that of the
"source component (w = sBS1, k skj) one obtainsCI
Pz(r,'v't) sf" -Ero J ( r sin\v)eIsklr
0im((0-0I) e-isBilt eisB~j la I17r r
Because of the factor,; e and e , the integrationover ý, repsults in zero terms, except for m = sB, and where theintefration introduces a factor of 27r. (Since the radiation func-tion G0 z i- built up of components periodic in 4), as measuredfrom some reference angle, and since the source distribution is"also compoý;ed of terms period c _In ( , only those radiation furic-ti on hnrmonios which are spatially in prhase with the source dis-thrulut.on terms contribute to the sound pressure disturbancea;r'rIvinp- ft the point (,f observation.) rTjhje summation with re-sheet to n and the intepration over the anr..le . can thus behiandled quite simnoly, and Eq. (7) may be r.'duceh to
- 11k 1c M1V [ B lsk r I .;1 s1.2.. .P z ~ r ¢ v t 4 T i r " s 1 e E e
fF rxJ i(sk r :;inv)21Tridrij (8)
Si mlthrly, the sound pressure due to the torque-related forces2o u oijd to he
!•(r, ,'),,t) 4 • !; • i B e jsS• ] ;
T r -s
S. ....... • -k -- • - - r- .; , n v ) .Tr d . ; { -. . • • , • i .. . , .. • . .
This elementary theory based on the rotating forces exerted
on the fluid medium by the propeller blades predicts two seriesof discrete-frequency pressure disturbances; each series is com-
posed of multiples of the blade passage frequency, and each pres-sure term varies inversely with the first power of the distancefrom the propeller hub to the observation point. Each se'ries
term J .volves a directivity factor, and the source level of eachterm is related to the aerodynamic harmonic forcing functionwhich produces the dipole source. From the exponential factors
in each series representation, one may note that at a fixed valueof r, the angular position 4 of constant phase rotates with theshaft velocity fý
Since the factors FP, FO, and a. in general are functionsof radial position r1 , eJaluation of the integrals in Eqs. (8)and (9) presents some difficulties. Some approximations are pos-
sible. a3 presented below. By use of the mean-value theorem, onemay write
Oa FzcsJsB(sklrlsinv)2rrldrl =
arrjsJsB(Sklrlsinv)Irl=azf o~az2nrrdr= [asJsB(Sklr sinv)]r..-az
where a denotes the propeller radius, az is an "effective radius"at which asJsB is to be evaluated in order to produce the correctvalue of the integral, and Ft represents the total thrust forceexerted on the propeller. Equation (8) then may be reduced to
Pik 1 cosv sisBn/2 isk r is34 e-isBiQtPz(r,•'v't) = - •' •rbee
cITJs 3 (. klrslnv)1r _a1z (10)
and, similarly, Eq. (9) may he rewritten as
(rivt) T() •sB isBr/2 isk r isBýe-isB~t-- l~ sB
a s iB (Skirlsinv)] rl=a*
'9
StA
where a, is the effective radius for drag, analogous to az fortliruot, and T represents the total drag torque. The values ofa7 and ao depend up on both the radial variation in loading repre-soented by FO and FA and the angular variation of blade forcesrepresented by theofactor as; since the value of a is differentfor each frequency contribution, the effective radii a. and aýgenerally also depend on the harmonic index s.
Morse and Ingard (Ref. 2) introduce the approximation thataz Z a = ad so that the total sound pressure due to the two di-pole s6urce mechanisms is given by the sum
p p+ p 1 1:skiFt cosv + aTB (sk r sinv) "(ad) 2 s B I I rl=a
isB($ + 2 -is(B2t-k r)e e- (12)
•rom this. r sult one find.s that the amplitude of the Sth harmonicfrequency mponent is given by
(a ) rBQs co' + J (sB(' sinv) (13)s 4rc td) SB d
wi•ore Mdrepi esents the rotational Mach number at the effectivera•ilus ad,
adS
d c
L nd where Fd = T/ad represents the drag force.
Equation (13) give:, the amplitude of propeller noise due todipole sourae meclhanisms associated with the aerodynamic forceloadings on the propeller blades which give rise to thrust androtational drag. By virtue of the cosv term, the thrust contri-Lution vanishes 4.n the plane of the propeller; the sum of thetwo contributiorrs vanishes on the propeller axis, in view of theBeosel function directivity factor. (Equation (13) may be seento be a generalization of Gutin's formulation.]
- -4ý - I&- ~ -
MONOPOLE SOUND
In addition to providing net lift and drag, a propeller bladeelement displaces some fluid by virtue of its thickness, and thusacts as a monopole sound source. In order to analyze this soundcontribution, one may describe the propeller in terms of a bladethickness function Sj(r.,4•), which defines the blade thicknessdistribution in polar coordinates r1,41 rotating with the propellerFor a fixed radial distance r. in the propeller plane, the thick-ness function may be expresseA as
Si (r'¢) = D (r'1)S ( = D(r') .0 (14)
where D,(rl) gives the maximum blade thickness as a function ofradial distance, and S1 (¢') and its Fourier expansion describesthe blade cross-section profile. In terms of the nonrotating co-ordinates r = r' and € ' + 2t, the thickness function becomesS(r 1 ,¢ 1 - t)'and Aas the form"Vketched In Fig. A3.
The monopole source term in the general wave equation is thetime derivative of the rate Q at which mass is displaced per unitarea of the propeller plane. Here one finds that Q is given by
, 4
Q(r = PROt= -OS' P -, (15)
where p denotes the densit:y of air, 3o thit the acoustic sourceterm is
2a-Q (r • (16)
a2
Using Eq. (14), one may rewrite this term as
a i•B¢'
aQ (r ,0 = -p02) (r X2B2 a (
To obtain the acoustic pressure at the observation point(r,¢,v), one may form the product of the source function and
. • ... ~ ~ ~~~~~~.. . ..... .-.•.• . .•. .,-,-,- --. ,,'.:,.; . ,••- -
Green's function for a monopole source, and integrate this pro-duct over the source plane. After some mani.pulation, one arrivesat
B_2 _t ( r/ + e- it(.t r)p(r,¢,v,t) -T- ) e
fDA(rj)8gJtB(£kr, sinv)2nrdrj (18)
As before, one is faced with evaluating an integral containingthe product of a Bessel function and of two possibly complicatedfunctions of the variable of integration. One may again applythe mean-value theorem and express the integral as
f D1(r,)BkJLB(9,klrl sinv)2!rdr1
= s LinBv)Y fa D(r)2wr dr=[8ZJZB(£k r si ]r, " m 0 1,r 1 1 ,
= iJ B ((1kr, sinv)]r =a "VD ' (19)I m
where VD denotes the volume of a solid disk having the radius; aof the propeller and the same radially-varying thickness as apropeller blade, and am represents an appropriate mean radius.
Thus, the sound pressure amplitude of the sth harmonic com-ponenit due to the blade thickness (monopole source effect) isgiven by
Ps '" p S D2 V sJ2 B(Sk iri sinv)]r =a (20)
One may observe that here the directivity (the dependence on v)i.; the same as for combined dipole ,;ources, -ee Eq. (13). Also,the monopole term of Eq. (20) var.es inversel.," with distance, Justlike the dipole term of Eq. (13). Comparing the monopole and di-pI(]( :;ource term3 further, one find.; that the monopole term variesa;.- the square of sBIQ, whereas the thrust-dipole term involves thefJrst power of sBQ and the drag-dipole term involves the first
SI- 'ne
-- ,. -- , •,w • - • • •- - -, ....... ... -. . . . ..... .. • •...... ......--- • " ,, X -
power of abe, modified by the rotational Mach number Md. Also,one may observe that the dipole and monopole terms are 900 outof phase.
Effects of Disturbed Inflow and Forward Motion
The previous analysis has dealt only with the simple case ofa rotating propeller with no forward motion and no nonuniformitiesin the inflow.
The effects of nonuniform flow are considered, for example,in the theoretical analysis of Morse and Ingard (Ref. 2) and havebeen given extensive attention in studies of compressor noise,(e.g., Refs. 4,5,6) where the presence of struts, stators, etc.ahead of the rotating blades serves to disturb inflow and thusproduces perturbations of the aerodynamic loadings on the propel-ler blades. For small propeller-driven aircraft designed forquiet operation, this source of noise is likely to be unimportantand is not discussed here.
The effects of motion of the acoustic.,ource(s) - that is,of forward motion of the aircraft - have also been studied (Refs.2,7, 8 ).Primarily, there result the well-known Doppler shift ofobserved frequencies and changes in the directivity. Both ofthese phenomena are amenable to straightforward analysis, but areof little interest here, and therefore are not treated further.
Comparison of Theoretical Predictions withMeasured Data
Comparison of theory with experiment is made difficult bythe complexity of the calculations (particularly for the higherharmonics), by the approximations lnvolved in the derivations, byuncertainties in the experimental conditions, and by lack of suf-ficiently detailed data. Since the concern here is with discretefrequency noise, one needs narrow-band data for comparison, or atleast an assessment that the data in specific bands are due pre-dominantly to pure-ten- )ropeller contributions. Because of thesignificant directivit., effects, one also needs to know thesource-receiver orientation rather precisely. Nearly all of theuseful data presently available is from stationary operation(gnound run-up), with mnea:nurements taken at several azimuthalpositions around the airplane. (Comparison between theory andmeasurements usually is most convenient for positions in theplane of the propeller; however, the thrust-related dipole termvan'ishes here, and itj contribution can then not be determined.)
Figures A4 and A5 compare the results of calculations withexperimental measurements for the three-bladed OV-1 propeller.
'~3
Both figures pertain to the same observation position given from thepropeller axis, in the plane of the propeller, but the formerfigure corresponds to a lower rotational speed and shaft horse-power than the latter. Dipole sound prediction calculations werecarried out on the basis of Eq. (13), taking 2as = 1, which corre-sponds to a uniform distribution of aerodynamic forces over theblade width. Results are shown for two values of ad: 70% and80% of the propeller radius a; one notes that these two resultsagree well for the fundamental, but diverge increasingly for thehigher harmonics - indicating that the choice of ad affects thehigher harmonics more strongly.
Also indicated in Figs. A4 andA5 are the sound pressure levelspredicted for this same propeller due to monopole radiation. Forthe prediction calculations corresponding to Fig. A4 the diskvolume VD was approximated from a graph of blade thickness versusradius. For the lowest two harmonics, the calculation was car-ried out on the basis of Eq. (18), and by accomplishing the inte-gration by means of a series expansion, with only the largestterms retained. For these harmonics, the effective radius a wasfound to be 0.57a and 0.64a, respectively. The third harmonTccontribution was estimated by use of Eq. (20), with an effectiveradius am = 0.75a. The values plotted in the figure are basedon the assumption of a rectangular blade cross-section profile(which assumption affects the Fourier coefficients 8s).* Sincethe effective radius and the Fourier coefficients to be used inthe approximate Eq. (20) are related to the propeller geometry,and not the operating conditions, it seems valid to use values ofthese parameters which yield acceptable results at one set ofoperating conditions to predict noise levels at other operatingconditions of the same propeller by use of the simpler Eq. (20).Figure 5 shows the monopole sound pressure levels calculated inthat manner, assuming a rectangular blade profile and am = 0.55afor s = 1,2, and 0.75a for s = 3.
*Levels for the first two harmonics were also calculated on thebasis of a triangular variation of blade thickness with angle ¢•.At the fundamental, the triangular thickness gave nearly thesame result as the rectangular thickness, but at twice that fre-quency, the triangular distribution gave a level which was lowerby nearly 10 dB. By the nature of the Fourier series represen-tations, one would expect the difference between levels to in-crease rapidly with higher harmonics. As another example of thesensitivity of the theoretical model to small variations in theassumptions necessary for numerical evaluation, the level of thethird harmonic was calculated using a rectangular thickness pro-file, but at an effective radius of 0.60a. This result wasfound to be about 13 dB lower than the value obtained witham = 0.75a.
4 A 7! P
Combination of sound levels due to monopole and diple sourcesis accomplished by the usual method of adding uncorrelated soundlevels, since the pressures due to the two sources are 900 out ofphase. Results of combination of the monopole terms with the di-pole terms for ad - 0.8a are shown in Figs. A4 and A5 as well ascorresponding measured data.* (It should be noted that themeasured levels of Fig. A5 are obtained from octave-band, notnarrow-band data; however, narrow-band data suggest that theoctave-band levels are predominantly due to the discrete frequencycontributions.] The agreement between predicted and measuredlevels is quite good. One notes that although the dipole termalone predicts the first harmonic quite accurately and approximatesthe second harmonic reasonably, inclusion of the monopole con-tribution greatly improves the prediction for the third harmonic.
Figure A6 presents a comparison between predictions and datafor another propeller, and also indicates predictions computed bymethods from Hubbard (Ref. 9) and Dodd (Ref. 10) for the dipoleand dipole-plus monopole sources. Insufficient information re-garding the propeller geometry is available to allow predictionof the bldde thickness pressure term by the method of Eq. (20).The measured data shown in Fig. A6 are seen to agree reasonablywell with the levels predicted here by use of only the dipoleterm based on. ad = 0.8a. Estimates of the monopole sourcecontribution shown in Fig. A6 have been prepared on the basis ofthe assumption that the propeller of Fig. A6 is geometricallysimilar to that of Figs. A4 and A5.
In order to assess how well one may predict the thrust di-pole contribution, calculations have been carried out for observerpositions out of the planes of the two previously discussed pro-pellers. Calculated levels and measured data are compared inFigs. A7 and A8. For the U-10 propeller (Fig 8) agreement betweenestimated and measured values is seen to be quite acceptable forpositions 300 ahead and behind the propeller plane, but very poorfor 600 behind the plane of the propeller, particularly in thesecond and third harmonics. The agreement for the OV-l propeller(Fig. A7 is generally poor. Brief further study shows that thehigh-frequency predictions are even worse for angles closer tothe axis of rotation; in particular, the data suggests thepresence of strong tonal contributions in the axial direction,which the theory predicts to vanish.
*In order to make the "free-field" predictions correspond to themeasurements made near the ground, 6 dB has been added to allpredicted values, in order to account for ground reflection.
25 -
What physical arguments can one advance regarding the dif-ference between the predicted and actual behaviors? (1) Non-uniform flow: It seems unlikely that parts of the aircraft up-stream from the propeller could disturb the inflow seriously. Itis of interest, however, that the aircraft for which best agree-ment was obtained at 300 out of the propeller plane has a singleengine, whereas the other craft has two wing-mounted engines.Conceivably, the forebody of the airplane might disturb the inflowin the latter case, but it seems doubtful that the effect wouldbe as strong as observed. (2) Reflection and radiation from theground, and from wings, fuselage, etc.: Again, these effectsappear incapable of producing the large observed difference be-tween calculated and measured levels;* radiation of sound fromairplane surfaces (e.g., due to structureborne vibration) cannotbe evaluated from the available data. (3) Approximations inanalytical evaluation: The thrust and drag forces on the propel-ler blades have been approximated by uniform loading distribu-tions, and in the evaluation of the resulting Fourier coefficientsthe propeller solidity was taken to be sufficiently small so that
essentially point loadings result. These approximations assurerelatively large high-frequency content in the excitation due todipole-related forces. Similarly, expansion of the blade thick-nes.s distribution on the basis of a uniform cross-section nrob-ably overemphasizes the actual high-frequency spectral content.Since the disagreement between theory and measurements becomesgreater with increasing frequency at positions out of the pro-peller plane, it appears that the above approximations are notthe source of any discrepancies.
None of the above possibilities presents themselves as ob-vious sources of discrepancies between theory and data; deeperinvestigation of these and other conceivable mechanisms is re-quired, but is beyond the scope of the present work.
ESTIMATION OF TOTAL ACOUSTIC POWER
One may determine the acoustic power radiated by the dipoleand monopole sources by integrating acoustic intensities obtainedfrnm Eqs. (13) and (20) over a sphere of' radius r (i.e., over all-inv1e, v) and adding the results. However, this computation may1,e -.omewhat complicated, and one may do just as well for general
*Iiowever, ground reflection may cause the directivities measuredwith the aircraft on the ground to differ from those produced bythe aircraft in flight.
''I,ý
* .V
estimation purposes by evaluating the pressures at an "average"angle v = 450 and multiplying the resulting average intensityby the area of the sphere.
Thus, one may estimate the acoustic power W• of the sth har-monic due to both dipole and monopole uources from
W 27r 2 + 21 ] \. (21)
where Psz represents the value of the dipole-related pressure, asfound from Eq. (13) for v = 450 and psi represents the monopole-related pressure, as obtained from Eq. (20) with v = 450.
ESTIMATION SCHEME
The acoustic rower W for each harmonic component must becalculated separately. Generally only the lowest few components(s = 1,2,3) are of interest.
1. Calculate rps• from the modified* Eq. (13),sz4
rn ~sBf2 T -'tM/17 (13a)S2 -i c adMd sB(SBMd//2)
where Md ad /c
ad 0 0.8a
The propeller thrust Ft and drag torque T usually are avail-able from propulsion system characteristics. Otherwise, fora nropeller with radius a, constant section lift and dragcoefficients CL and CD, and with a small pitch angle, onemay use
*Obtained by taking v = 459 and 2as 1. This approximation fora. apolies for uniform distribution of the aerodynamic forcesover the blade width.Note that values of Jm(x) are available in standard tables ofBessel functions andj that (see Ref. 2)
2 Wcs 2m+lCms X 7T) for x >> 1
.3 r
Ft 0.17CLPU2ipA
T Z 0.13CDPU•- A a"D t ip b
where Utip is the blade tip speed and Ab the total bladearea (for B blades, projected onto plane of rotation).
2. Find rps, from the modified Eq. (20),
rps1 , VDs JsB a (20a)
where one may find the propeller disc volume VD by integrat-ing the radial thickness distribution, or approximately from
VD = 7ra 2 d
where d is the average blade thickness. The Fourier coef-ficient ýs of the circumferential blade thickness distribu-tion may be calculated from a known thickness function S(O)for the promeller, from
as= 2- S(W) cos(mB¢)dO
or may be aoproximated for a low solidity-ratio propeller by
"" Ts r (a avg
where (b/a)avg rerresents the average propeller chord toradius/ratio. Unless better information is available, onemay take am = 0.55a for s = 2, am = 0.65a for s = 2,am = 0.75a for s = 3.
3. Calculate the total acoustic power Ws produced at frequencyw sBQ from
Ws = 2ZT [(rp )2 + (rps)Z] (21a)PC 52
SIIand then find the corresponding power level from
LW = 10 log(Ws/Wref)
4. Determine the frequency w. at which the sth component occursfrom
W (radians/sec) = sBQ
or
fs (Hz) = w s/27 = sBQ/21
Illustrative Calculation
Consider a three-bladed propeller of 4 ft radius, rotatingat 2100 rpm and producing a thrust of 340 lb at a torque of 350ft/lb, at 1000 ft altitude (where the air density is 0.070 lb/ft 3
and the speed of sound is 1100 ft/sec).To use Eq. (13a), find
Q= 2100 rev/min = 2100(2n/60)rad/sec = 220 rad/sec
ad = 0.8a = 0.8(4 ft) = 3.2 ft
Md ad 2/c = (3.2 ft)(220 rad/sec)/(ll00 ft/sec) = 0.64
BMd/4! = 3(0.64)//I = 1.35
BS I T Ft 3(220 rad/sec) 350 ft-lb 340 lbr adMd _- 4i 1 (I00 ft/sec) (3.2 ft)(0.6 4) 1
= 0.0525 1 170 - 240 1 = 3.7 lb/ft.Then,
for* s = 1.5 rDs = 3.7 J 3 (1.35) = 3.7(4.5xi0-2 ) = 0.17 lb/ft
for s = 2, rp., = 2(3.7) J6 (2.70) = 7.4(6.5X10- 3 ) = 0.048 lb/ft
for s = 3, rps, = 3(3.7) J 9 (4.05) =11.1(1.05x10-3)= 0.011 lb/ft
*Values of Bessel functions J 3 ,Jfi ,J 9 found from Handbook ofMathematical Functions., Ed. by M. Abramowitz and I.A. Stegun,National Bureau of Standards, Washington, D. C. 1964, p. 398.
JI
To use Eq. (20a), one needs to know also the average bladethickness d and the average ratio of the blade chord to the bladeradius. These values, which may be obtained from a drawing ofthe propeller, here are taken as d = 0.2 ft, (b/a)avg = 0.25.
Then find
VD •T a 2 d = Tr(4 ft) 2 (0.2 ft) 1 10.1 ft,
"b!- = (0.25) z 0.24s T alvg T
0.07 lbm/ft-- Vbm [(3)(220 rad/sec)] 2 3V as = -• (10.1 ft ) (0.24)
32.2 lbm ft/sec 2 lb
= 180 lb/ft
Ba = 3(220 rad/sec)(4 ft) 1.70
c 2- V2(IOl00 ft/sec)
and
for s = 1, rps5 = 180 J 3 [1.70(0.55)] = 180 J 3 (0.93)
= 180(.015) = 2.7 lb/ft
for s = 2, rps = 4(180) J6 [2(1.70)(0.65)] 720 J 6 (2.2)
= 720(2.lX10- 3 ) = 1.5 lb/ft
for s = 3, rnsn = 9(180) J 9 [3(1.70)(0.75)] = 1620 J9(3.8)
= 1620(6.1x0-') = 1.0 lb/ft
Since Pc .\3"•,2 (1100) = 2.4 lb sec/ft 3 . so that2TT/pc = 2.8 ft3/lb sec, one finds from Eq. (21a) that
for s = 1, Vs- = 2.8[(0.17)2 + (2.7)2] = 20.4 ft lb/sec
for s 2, Ws = 2.8[(0.048)2 + (1.5)21 = 6.3 ft lb/sec
i'or s = 3, Ws = 2.8[(0.011)2 + (1.0)2] 2.8 ft lb/sec
3, r
. ... .. -...."- "- -: v- Y ... - ' J "- -- ' " - •': '• • . • --'- .--..--,----
'4P1
ta i I I I I
Then since Wref = 0.74 x i0- ft lh/sec,
for s - 1, Lw - 10 log [20.4/(0.74x10- 1 2 )] - 135 dBre 10-12 watt
for s = 2, Lw - 10 log [ 6.3/(0.74x10- 1 2 )] - 129 dB,re 10-12 watt
for s = 3, LW 1 10 log C 2.8/(0.74x×10- 2 )] - 126 dB,re 10-12 watt
Since BQ = 3(220 rad/sec) = 660 rad/sec, the frequenciesassociated with the foregoing "pure tone" sound levels areW, = 660, W 2 = 2(660), w = 3(660) rad/sec or f, - 105, fa 210,f3 = 315 Hz.
f
I.
, . . .. .. ... .... .... 4
, , i iI I I
SiI
REFERENCES FOR APPENDIX A
1. Gutin, L., "On the Sound Field of a Rotating Propeller",Translation, NACA TM 1195, October 1948.
2. Morse, P.M. and K.U. Ingard, Theoretical Acou8tice, McGrawHill Book Co;, New York, 1968.
3. Lamb, Sir H., Hydrodynamica, Dover Press, 1945.
4. Lowson, M.V., "Theoretical Studies of Compressor Noise",NASA CR 1287, 1969.
5. Morfey, C.C., "Sound Generation in Subsonic Turbomachinery",ASME Paper No. 69-WA/FE-4, 1969.
6. Sharland, I., "Sources of Noise in Axial Flow Fans", J. Sound& Vib., I (3), 1964.
7. Garrick, I.E., and C.E. Watkins, "A Theoretical Study of theEffect of Forward Speed on the Free-Space Sound-PressureField Around Propellers", NACA TN 3081, 1953.
8. Lowson, M.V., "The Sound Field for Singularities in Motion",Proc. Roy. Soc. (London) Vol. 286, Series A, 1965, pp. 559-572.
9. Hubbard, H. H., "Propeller Noise Charts for TransportAirplanes", NACA TN 2968, 1953.
10. Dodd, K. N. and Roper, G. M., "A Deuce Programme forPropeller Noise Calculations", Royal Aircraft EstablishmentTechnical Note No. M.S. 45, January 1958.
I.
TIM, tm
b /r,0Le FO -4
U.
TIME,t
FIGURE Al FORCE VARIATION AT TYPICAL LOCATION IN PROPELLERPLANE. b = PROPELLER WIDTH IN PLANE, AT RADIUS r
y
TYPICAL POINT ON PROPELLER DISK
x
TYPICAL OBSERVATION POINT
FIGURE A2 COORDINATES
33
. ... ....... .. Y.... .. .. ***--- Y_ *-- , .. . ... : _ .• ..... .. --_ .... . -- •• - •? - • • , .' ', . . .. . i l
THICKNESS b/r,
FUNCTIONS(r1,j61)
i,__2 W./ B_-
TIME, t
FIGURE A3 THICKNESS FUNCTION S(r],¢ 1 ) IN NON-ROTATINGCOORDINATES
LLI.0 CL
qF'4 / -- -'o.
o o
WWZ 4 IL.
o u 0 -C 0
:)I~ ILwGo -
0 z~
Q -i - 0 j
IL w il-J J 0 _j x c
w~oo.loo
010
o 00 0 0 0
(MVS9tO~IP4MO 3000 U9P) '13AT1 3uflsS3Hd ONlos W
06 0
0-la_ __ 13 OD00
00 .c'ClWW zu~ If -11
* -0
z ~w
J -J
M =
0
_j J3 OO -
IL C-
w- - 0
/ I
CL
0 0 08 40
HVSoHDwe 3000*0 3U OP) '13A3-1 3uflsS38d aNflos
0
2F0
- - -
-j-
woo Z i~ww- I
Z - w w U-_ _ _ _ _I
0 w
L) L)0 -
w L) 0 C.) 0.ff ---
or www 00 1- _
4000zzo - 4 C
a -J
- -0 C0
/l VI~ I'
0:
0 0::
(NVO0I01Y ZOOO'O 38 SP) '13A31 38nSS38d ONflos U-
-AJ
z w 1
AI > _ _ _ _ _:I.00 0
W 4 LLJ
I0 .. J U.
00W A
IV oJ 0I j 0 0 )4d 0La Z 0 CA i L
wa~o 4z 7)- Ma 0 iol
a o4~ W4tow~ C 0C. (0-
0 -
'I,
LLI
- U-(HMNOM- ZOO 3b S) 1331Mnbda.o
zw
9L -
u .0p
%rCLU
*a..
0 _j
z: :3-, 1,.0 -j
40 Cc__ -j z C
/1 4 U.
0 bw 2 VI
w .L Z-f C j z.j0
mt~i 4 U.2L____ O 0
cr CDV4
LL a. -13 _- o
-i ~ LL0-/d BA
/4 UJC
- .0
00 0 CC.
(M9ONDW ?0000 3H) 8P '13A31 38flSS38d ONflos
APPENDIX B
VORTEX NOISE OF PROPELLERS
VORTEX NOISE LEVEL
For low-speed quiet propellers, the broadband noise associ-ated with vortex shedding becomes an important contributor to theacoustic power generated (Ref. 1). E.Y. Yudin (Ref. 2) originallydeveloped a theory for the noise generated by rotating rods.H.H. Hubbard (Ref. 1) extended Yudin's work to the case r rotat-ing airfoils, postulating that propeller-generated vortex noiseis proportional to the first power of the blade area and the sixthpower of the flow speed. Schlegel et al. (Ref. 3) have developedan empirical prediction scheme for the vortex noise obtained atfifteen degrees behind the propeller plane.
Schlegel's prediction for the overall vortex-noise soundpressure level L may be expressed asp .
Lp(8=150 ) = -62 - 10 log Ab + 60 log U0.7
- 20 log (R/3) + 20 log (CL/0.4) (1)
where Ab is the area of the propeller blade (in ft 2 ) projectedonto the propeller plane; U0.7 is the air velocity relative tothe airfoil at the seven tenths radius (in ft/sec), R is the dis-tance to the propeller hub (in ft), and C Is the blade lift co-efficient. This prediction was based on data obtained atC =0.4, and implies that there is not vortex noise for CL = 0;tkis is clearly not the case - rotating rods provide zero liftbut do make vortex noise.
D. Ross (Ref. 4) developed a scheme for dealing with vortexnoise involving an "acoustic conversion efficiency" q, which re-lates the acoustic power, W to the mechanical drag power (i.e., tothe blade section drag power) Wm. For cylindrical bodies of allshapes, Ross gives the conversion efficiency as
= 1W/Wm = 9.0 x 10- 3 M , (2)
mi
where M is the Mach number. For a two-dimensional airfoil, themechanical power ner unit length is given by
)io
~7 ... . .17...-
W 1 PbU3CD (3)
where b is the foil's chord length, U the local flow speed andCD the drag coefficient. The acoustic power radiated by a pro-peller blade of radius a thus may be written as
w - 9 P a0 U6 (r)b(r)CD(r)dr (4)0c 0
where c sound speed
U(r) = flow speed at radius r
b(r) = chord length at radius r
CD(r) = drag coefficient at radius r.
For a propeller with B blades and a constant section dragcoefficient CD = 0.01, operating in air at sea level, one findsthe acoustic power to be given by
aW(ft lb/sec) = 8 X 10-1 7 B f U'(r)9(r)dr (5)
for U in ft/sec and b, r, a in ft. If the chord length is con-stant, the blade area Ab = Bab may be introduced, and the pre-vious expression may be rewritten as
1.0
W = 8 x 10-1 7 Ab f U6 (r/a)d(r/a) . (6)0
For a propeller with a small pitch angle, U(r) is very nearlyproportional to r, and
0 ~ 1.0u6 (L)d =U6 d (11) a(7)oip ( )f a0 0
where U0. 7 is the blade speed at the seven tenths radius.
1
I
By substituting Eq. (7) into (6) and taking the logarithms, oneobtains
10 log W = -160 + 10 log Ab + 60 log U0. , (8)
which, when converted to watts and referred to 10-2 watts, yieldsthe acoustic power level as
Lw(dB, re l0-2 watts) = -40 + 10 log Ab + 60 log U 0.7 (9)
where Ab is in units of ft 2 and U0. 7 in ft/sec.
If the vortex noise were generated by a family of dipoles,all aligned in the plane of the propeller, then the sound pres-sure would vary as sin20, where 0 is the angle which a line fromthe observation point to the propeller hub makes with the propel-ler plane. One would then write the overall sound pressure levelat the observation point as
L (dB, re 0.0002 microbar) = Lw(re 10-12 watts) - 8p w
+ 20 log sine - 20 log3
-48 + 10 log Ab + 60 log U0.7
R+ 20 log sinO - 20 log . (10)
The value CD 0.01, for which the foregoing expressions havebeen derived, is estimated to be typical for a standard propeller.Aection at CL = 0.4. A comparison on this basis between Eq.(10) for 6 = 150 and Schlegel's prediction at CL = 0.4 [Eq. (1)].rIjtw, that Eq. (10) predicts a level that Is 2 dB greater than that
1 v(r i by Eq. (1); thus, the agreement between the theoretically:iiid (.xperlmentally derived prediction schemes is seen to be good.
SPECTRUM SHAPE
Schlegel (Ref. 3) gives an empirical spectrum shape for thevrt(.x noise. The peak frequency fokof this spectrum depend,; on
V .... .......- - -- r1
Fa
the Strouhal number at the seven tenths radigs,'based on the pro-jected blade thickness
dp = d cosa + b sina (11)
and is given by
f = 0.28 L' ./d , (12)PkC 0.7 p
where d Is the actual blade thickness, b Is the chord and a theblade's angle of attack. The shape of the spectrum about thispeak frequency is given in the Table below.
OCTAVE BAND SPECTRUM OF PROPELLER VORTEX NOISE
1
fOB/fIk 1 2 4 8 16
LoA-LOB 8 4 8 9 13 14
fOB center frequency of octave band
f )k =peak frequency of vortex noise spectrum
LOA overall level
LOB level in octave band
DIRECTIVITY
If all of the dipole sources on the propeller blades werealigned parallel to the shaft axis, the vortex noise field wouldbe that of a dipole along the propeller axis. However, in factthe dipoles on the propeller blades are not aligned from blade toblade, due to the pitch; this causes a smearing of the directivitypattern. An aligned dipole field would radiate nothing in theplane of the propeller, but a highly pitched propeller can gen-erate considerable noise in its plane of rotation.
At an angle 0 out of the plane of rotation, the angle be-tween the line from the observer to the propeller hub and thenormal to the axis of a dipole on a blade with pitch angle 8 Is
a 8 cos*-e , (13)
where ' is the angle the propeller blade makes with a planepassing through the shaft axis and the observation point (seeFig. Bl). The sound pressure level at the observation point (Inthe farfield) varies as sin 2a; the average level for a rotatiiigpitched propeller blade may be written as
L (e,$) = L (Tr/2,0) - sin2 ( cosi-e)di , (14)pp 27r o
in terms of the on-axis sound pressure level L (R/2,0) of an un-pitched propeller (at the same distance from the hub).
By expanding the integrand, one may rewrite the integral ofEq. (14 ) as
271 21Tsin2(-O + 8 cosi)dp =(sin2e)f cos 2 [O cosip] diP
0
+ (cos 2 0) sinz[$ cosip]d*0
- 1 (sin 20) f sin[28 cos,] dip (15)
0
The first integral on the right-hand side then can be expressedin terms of the zero order Bessel function, J 0 :
2rr f 2 7rf cos 2 [6 cosi] di = [1 + cos(2a costp)]dtP0 0
= n [1 + J 0 (28)] (16)
from which it follows that the second integral obeys
f sin2 [n cosildi = 7 [l-J0(2B)] . (17)0
['Pe l.ast integral vanishes because sin[2a cosi] is an odd function) F.
By use of the foregoing results one may now rewrite Eq. (14)as
L(6,) L [LJ((2/) cos 2e] (18)
The modification of the directivity pattern due to pitch isparticularly significant for propellers designed to operate atvery low rotation speeds, because propellers with low tangentialto axial velocity ratios must have high pitch. The flattened di-rectivity pattern associated with high pitch results in a lessen-Ing of the rise and fall of the vortex noise recorded on theground as a propeller driven craft flies over at constant alti-tude. For the zero pitch case, the vortex noise level is great-est when the angle with the propeller plane is 450 (peaking onceas the aircraft approaches and once as it flies away). For aslow speed propeller with a 45' pitch angle, the sound level at450 out of the propeller plane is about the same as for the un-pitched propeller, but continues to increase slowly as the aircraftapproaches until a peak is reached (only a few dB higher than thatat 450) at 260 out of the propeller plane; the sound level thenremains constant, within 0.5 dB, until the 260 peak is passed asthe aircraft leaves.
COMPARISON OF PREDICTIONS WITH EXPERIMENTAL DATA
By combining Eq. (10) with (18) and including a drag coeffi-cient proportionality relation, one obtains
=-48 + 10 log Ab + 60 log U + 10 log (CDLp b .7 \.01)
+ 10 log 11 [l-J,(2$) cos 2]3 -20 log (.) (19)
In order to test this nrediction relation, a search of theliterature was made for well-documented propeller noise data.Enough must be given so that one can evaluate all of the param-eters which appear in the foregoing relation. In addition, inorder to check a vortex noise prediction against measured data,one needs a narrow-band spectrum, so that one can separate thebroad-band vortex noise from rotational and engine harmonic noise(unless the vortex noise center frequency is in a region wherevortex noise clearly dominates the one-third or octave band levels).Of noise measurements made on subsonic propellers and helicopterrotors, few have been made with an eye toward determining the
:. -.-7777777
vortex noise. Consequently, most reported measurements do notgive sufficient data; only three have been found which give de-tail to permit checking the vortex noise prediction scheme: oneset of measurements is for a helicopter rotor (Ref. 5), one fora hovercraft pusher propeller (Ref. 6), and one for the low-speed>propeller of a "quiet" aircraft.
In an investigation of helicopter rotor noise by Stuckey andGoddard (Ref. 5), a 3-bladed NACA 0012 section helicopter rotorwas spun on a whirl tower at various speeds and pitch settings.The rotor' thrust and sound pressure levels were i-_--orded. Testswere conducted at rotational speeds between 180 and 450 revolu-tions per minute. The vortex noise levels were obtained by tak-ing overall levels of the noise between 100 and 2500 Hz, whichhad been corrected for ground reflection. This procedure isjustified, because this frequency range extends over the regionof major vortex noise and is above the range of frequencies whereblade rate harmonics contribute significantly to the noise level.FigureB2 shows the sound level measured at 7.50 behind the rota-tion plane and 151 ft away from the rotor h-ub (and corrected byStuckey and Goddard for ground reflection) as a function of themean lift coefficient CL,
aa)Cm = L/[Ab f U2 (r)dr] A Ab U2 (0.58 a), (20)
0
which relations are based on the assumption of a constant liftcoefficient over the constant chord blade. The rotor pitch angleis also noted in the figure. The dotted curve of the figurerepresents the data, modified by use of Eq. (18) to correspond toa zero pitch propeller. For the rotor blade area Ab = 114.8 ft 2
and for U0.7 = 451 ft/sec at 220 rpm, the zero-pitch sound pres--;ure level at the measurement location is
Lp(7.50, 151 ft) = 80 + 10 log ( (21)
Figure]B3 shows the reported drag characteristics of the NACA0012 section (Ref. 7), together with the section drag coefficientwhi•h is required to make the Lo calculated from Eq. (21) matchtit zero-pitch level of Fig. B2. Since the mean Reynolds numberfor drag calculations (at 0.58 a) is 3.6 x 106, and since the rotor]; likely to have a standard roughness finish, this calculateddrag curve seems to be not an unreasonable one.
. ----
-- , "~..-- f, -•. .
In a series of noise measurements on a low performance liqrhtaircraft, vortex noise data was obtained for two propeller condi-tions and at two different angles to the propeller rotation plane.The tests included noise measurements in the propeller plane andon the rotation axis during ground run-up tests, and an additionalmeasurement as the aircraft flew past a microphone. (Microphoneswere mounted over woodchip-filled boxes, which should have elimi-nated ground reflections when the aircraft was at a relativelyhigh angle, as during the flyby. The woodchip boxes were toosmall to affect the ground reflection path from the aircraft whentied down.)
For a highly pitched nropeller, the axial component of U0 7is appreciable and cannot be neglected. The axial velocity forthe 'ground run-un test was estimated from the given shaft horse-power and the reasonable efficiency of 55%; the induced axialvelocitv was comouted from energv considerations. In ground run-up, the blades of this propeller arc- under-nitched at the tips,leadinv to an Increase in the mem.n ]ift coefficient by an esti-mated 15%. Figure B4 shows a comnarlson of the measured vortexnoise with that Prodl ct d 'v use of En. (19) and Schlegel t s spec-trum share. (The measured noise frer the tie-down test has beencorrected for 3 dB cround reflection.) The prediction for theground run-up i:, nruablV t,,O low because the proreller bladesection drag• wa: undere;:tirntcd for this heavily loaded condit-ion.
!l:irr(,w-Larnd ","uno p,'. :uc level data have heen reported for
t:le :)u.'. 'r pr,,e 11.- p f !i i o y prcraft. i ewvolopmtýnt Itd . JTDl hover-o •i't (srI'. 6). 'i',,. m,;i:"r- .nt: ,.•,ere conducted with the craftt-,-i down on a Mm.rt ', ..uy. Measurements were made at anangle of 15° betiind prop,'ill' plane, at a distance of 100 ft fromthle hub, with the micropnone 3.5 ft above the )ýround surface. The
pi.opeller is a two-hladed one, with a 7 ft diameter, a total blade
area of 2.9 ft 2 , a blade pitch angle at 0.75a of 80 ] 0 t, and a
t>.' ,knec;s at 9.7a cf 0.445 in. Hun., were made at 1500 rpm (23and 24O lb thru.t) a•,d at r-5'0J rpm (112 SHP and 670 lb thrust).
The blade section lift coefficient, based on the foregoing
infurmation and on the a::umtlon of' constant lift coeffici ,nt-)ver the length of the 1~llo i.; C 0.61 at both rotath ispoeds..ij.ce the propeller' p itch1 an ile = I0 lot is small compared ,:ithtic, out-of-plane an-lý ! = 150, the directivity function can be
-valuated as
- - . - ~ ~ * ~ - ~ . -
w
l0{log 1 [1-J 0 (20) cos2O]} z 20 log (sine) = -11.8 (22)
Because of the hard surface over which the microphone waslocated, the predicted sound pressure level should be increasedby 3 dB, to account for ground reflection. With this correctionand an estimate of CD = 0.016 for the drag coefficient at CL0.61, the predicted sound pressure levels are,
L (dB, re 0.002 microbar) 95, at 1500 rpm
82, at 2500 rpm
For an assumed 4' blade angle of attack of a 7% camberedsection operating at CL = 0.61 (Ref. 7), the projected bladethickness is found from Eq. (11) to be 0.073 ft. With this valueEq. (11) gives the center frequencies for the vortex noise to be1420 and 2360 Hz for 1500 and 2500 rpm, respectively. Figure B5shows a comparison of the prediction with the measured data; theagreement is seen to be acceptable.
ESTIMATION SCHEME
To determine the snectrum of the (broad-band) noise powergenerated by a given proneller, one may proceed a: follows:
1. Find the overall acoustic power level from
Lw(dB,re 10-12 watts) = - 10 + 10 log Ab(ft 2 ) + 60 log U0 .7 (ft/sec). (9a)
Here A. is the total blade area and U0.7 % 0.7as.
2. Yind the nrojected blade thickness dD from
d = d cosa + b sina (I1)
where d is the blade thickness and b the blade's chordlenCth (at the 0.7a radial location), and a its angle ofattack. Then calculate the spectrum peak frequency from
f =k 0.28 U 0 7 /dP (12)
1i 77
3. Use the table below to develop the. octave band spectrum ofpower.
OCTAVE BAND SPECTRUM OF PROPELLER VORTEX NOISE
1 1 2 4 8 16foB/fok
LoA-LOB 18 4 1 9n 1 14
fOB = center frequency of octave band
fk 1= peak frequency of vortex noise spectrum
LOA overall level
LOB = level in octave band
Illustrative Calculation
Consider the three-bladed propeller described at the end ofAonendix A, again rotating at 2100 rpm. The total blade area isAb = 4 ft 2, the blade thickness is d = 0.2 ft, the blade chordlength is 0.8 ft, and the propeller's angle of attack is 150.Then
UO.7 = 0.7a2- 0.7(14ft)(220 rad/sec) = 615 ft/sec
= - 40 + 10 log Ab + 60 log U 0.7
= - 40 +10 log( 4 .0) + 60 log(615) o - 140+ 0(0.6) +60(2.8)
1- 134 dB,re 10- 1 2wattt;
d = d cosa + h vina = 0.2 cos 150 + 0.8 .;in 15' = 0.40 ftp
"fke = 0.28 U 0./dT) = 0.28(615)/0.40 1430 Hz;
and from the table,
foB (Hz) 215 430 860 1720 3440) 6900
[,w(OB)(dBre 10- 1 2.,,:atts) 126 130 126 125 121 120
S~~~~~~~~~~~~~~~........................"'• ,,. • *"""-,..i.. " ';;'' "• -.......... ,
REFERENCES FOR APPENDIX B
1. Hubbard, H.H., "Propeller-Noise Charts for Transport Air-planes", NACA TN 2968, Washington, D.C., June 1953.
2. Yudin, E.Y., "On the Vortex Sound from Rotating Rods", NACATM No. 1136, Washington, D.C., March 1947.
3. Schlegel, R., R. King, H. Mull, "Helicopter Rotor Noise Gen-eration and Propagation", USAVLABS T.R. 66-4, Ft. Eustis,Virginia, October 1966.
4. Ross, D., "Vortex Shedding Sounds of Propellers", BBN ReportNo. 1115, Cambridge, Massachusetts, March 1964.
5. Stuckey, T.J. and J.O. Goddard, "Investigation and Predictionoff Helicopter Rotor Noise", J. Sound Vib., 5 (1), pp. 50-80(1967).
6. Trillo, R.L., "An Empirical Study of Hovercraft PropellerNoise", J. Sound Vib., 3 (3), pp. 476-509 (1966).
7. Abbott, I.H. and A.E. VonDoenhoff, Theory of Wing Sections,Dover Press, New York, 1949.
Widnall, S.E., "A Correlation of Vortex Noise Data from8. Helicopter Main Rotors", Engineering Notes, 6, No. 3 (May
1969).
t fJ
0 *
I-
Lii
LLJ
ww L)Li>
-V) - 4cr. 0- :
0 C0
0 LL0
/n0LU Icr=
94 --
-d MEASURED LEVEL (REF 5)
92 f- LEVEL MODIFIED FOR-ZERO PITCH
-J 90
ww 86
0 00
co
II
-07 il 11 13. 15 .17
0 ~PITCH ANGLE -. DEGREES
0 .2 .3 .4 .5 . ,7 .8 ,9 1.0LIFT COEFFICIENT, CL
FIGURE B2 VORTEX NOISE AS A FUNCTION OF LIFT COEFFICIENT ANDANGLE OF ATTACK, FOR HELICOPTER ROTOR OF REFERENCE5, (AT 7.50 BEHIND ROTATION PLANE)
9'i
.032
.028____ _
CD REQUIRED FOR
_ MATCHING PREDICTION
WITH DATA (REF 5)R =3.6 x 106 /
.024o- 1 .REYNOLDS NO. R
S9x 106
03 6 x 106
w__5.020 0 3 x 10U.t STANDARDIL ROUGHNESS0
S.016 po
.012
.008 _
.004 ,.. .
0 0.4 0.8 1.2 1.6 2.0LIFT COEFFICIENT, CL
FIGURE B3 LIFT-DRAG CHARACTERISTICS OF NACA 0012 AIRFOIL SECTION
00
do
00
0
C0z I--
ow W.
-0 w
a LL, wL
wO w!a F-z 0- ___ ow
-0z 0a.
Ow 0Ii ''
~Z 04zi 03
21 IXI W0 U/
w on U V)zz U. 0---
000
zzx W6 0
iz cw0w 0
MDCII Im 0
00~0
000 0 * L.
(8V8eO3iN 00OOOO B)133 38nfsS38d ONnos
U- ~
0 q
0
0
90~
9~000
A 00
I 0I~0~
0 CD
011 LLJH- 0 t..-)LJ.
In
0 t-j.
N0
ON ~0,Z
0n L iX0>- I-L_
afl() LL C
0 0 LL
0 w0
0 i-0 Z LLJ~0 ULJ w C4r L.) =,
V S 0 V) 0
0<
I- o LL.
a. 4' 0.a:uIno
U 0 O
I0 Cn
0 f
00 0 0 0 0em Go f0 DU
(8VGOH~IbN ZOOO'O 38U2P)'-13A31 3dnsS38ddGNflos
S. ... I
APPENDIX C
NOISE OF PISTON ENGINES
NOISE SOURCES
The noise of piston engines, like that of any air-breathinginternal combustion engine,may be considered in terms of threecomponents: (1) intake, (2) exhaust, and (3) casing noise. Inun-muffled engines, exhaust noise typically predominates. Casingnoise - defined as the noise of an engine with "completely"muffled* exhaust and intake - is important only if the exhaust(and possibly the intake) indeed is well muffled.
The exhaust systems of internal combustion engines essen-tially release puffs of gas (possibly at considerable pressure)to the atmosphere as the exhaust valves open - and these pres-sure pulses constitute the primary components of exhaust noise.Clearly, exhaust ducting (such as manifolds, pipes, by-passvalves) can have very significant effects on the intensity andshape of these pressure pulses - and thus on the exhaust noise -
in addition to adding noise (e.g., of a rushing or whistlingnature) due to the flow in this ducting. (Ref. 1)
The foregoing remarks concerning exhaust noise also applyto intake noise, except that the intake ingests puffs of air,rather than emitt!ng them. Acoustically, ingested puffs havethe same effect as emitted ones; however, the exhaust pressurepulses have greater pressure differences associated with themthan do intake pressure pulses. For this reason, and also be-cause high-nressure pulses tend to change into shock-waves asthey propagate along a duct, unmuffled exhausts usually are muchmore noisy than unmuffled intakes.
Casing noise may be ascribed to (1) the nearly explosion-like pressure pulses obtained from ignition of the fuel, (2)internal mechanisms, such as "piston slap" (lateral impacts ofpistons against the cylinder walls) and impacts associated withvalves and valve-l.fters, (3) accessories, such as fuel pumpsand fuel injectors, and (N) power transmission components, suchas gears and bearings. (Ref. 2)
*'Phe exhaust and intake of' an engine may be considered as com-pletely muffled if the addition of further attenuation for theserources does not reduce the observed noise of the engines.
._T
DATA
Availability of Data on Spark-Ignition and Diesel Engines
The available data on the noise of spark-ignition (SI) en-gines is extremely limited and so inadequately documented thatit is inadequate to serve as the basis for development of a noiseprediction scheme. On the other hand, there does exist a usefulbody of information on the noise of diesel engines (Pefs. 3, 4).Therefore, it appears sensible to use this diesel engine data asa basis for estimation, although aircraft are more likely to useSI engines than diesel engines.
Similarity of Spark-Ignition and Diesel Engine Noise
One may indeed argue that the noise of SI engines 3hould bevery much like that of a similar diesel engine. Clearly, theintake process does not depend on whether the fuel-air mixtureis ignited by a spark or by compression later' In the cycle, sothat one would expect the intake noise of a given engine to bethe same, whether that engine uses spark or diesel ignition.However, the intakes of SI engines may be designed somewhat dif-ferently than those of diesels (because SI engines may have car-burators, for example), and thus may sound somewhat different.
The same sort of remarks as were made above concerningintake noise also apply to exhaust noise. Again, the exhaustpuff does not depend on the ignition process - but rather onthe exhaust valve timing, on the cylinder pressure at the in-stant the valve opens, and on the cylinder pressure-time charac-teristics during the time the valve is open. Although "indicatordiagrams" (plots of cylinder pressure versus piston displacementor crank angle) for diesels differ considerably from those ofSI engines for the compression and combustion narts of the cyele,the portions of these diagrams corresponding to the exhaust pro-cess tend to be very similar. (Ref. 1)
On the other hand, one might expect the casing noise of SIand diesel engines to differ more significantly. Diesel enginestypically are designed for higher compression ratios than SI en-p;ines, and the (internal) combustion pressure pulses in diese1.;tend to be more sharply explosive than thosE in ST engines. Thiecylinder pressure spectra of diesels thus generally are htghFrthan those of SI engines, and tend to have much more high-freqýri,,ycontent (Refs. 5-8). However, diesels usually are built much mc-r(
I.
massively (to contain the higher pressures), so that less combus-tion noise tends to get through the structure (Refs. 9,10). Theseverity of piston-slap impacts depends on the cylinder pressureto some extent, so that these impacts are more severe in diesels(Refs. 4,11). Again, the more massive structures of dieselstend to reduce the noise radiated as a result of these impacts.Piston-slap is likely to make no significant contribution to thecasing noise of any relatively small high-speed engines withtight-cylinder/piston clearances, which one might use in aircraft(Refs. 4,11).
Comparatively little is known about the accessory noise ofthe various types of engines (Ref. 12). There appears to be noreason that would lead one to believe that the noise of a powertransmission component should be much different from that of asimilar component in a different engine. (Also, these compo-nents usually do not contribute very significantly to the totalcasing noise.) Because of these considerations, and in the lightof the foregoing discussion, it appears logical to base a noiseprediction scheme for SI engines on diesel engine data. Such ascheme will at least provide a first approximation, which shouldprove useful until adequate SI engine data become available.
Available Data
An extensive field measurement and literature review program(Ref. 3) has yielded noise data on a large variety of diesel andnatural-gas engines in electrical power plants and similar sta-tionary installations. More than 50 engines (about half with14-stroke and half with 2-stroke cycles), with power ratings be-tween 12.5 and 5150 kw (9.5 to 3850 Hp), were studied at actualpower outputs between 0 and 5150 kw and at speeds between 225and 1800 rpm.
The "casing noise" of these engines was deduced from mea-s;urements in engine rooms, with the engine intakes and exhaustseither outside the rooms or well-muffled. Measured acousticcharacteristics of the rooms were used to interpret the enginenolse data in terms of acoustic power spectra of the sources.
For some of these engines, the air intake or engine exhaustrioiso was measured out of doors, at some convenient distancefrom tlie intake or exhaust opening. Where no muffler was present,the:-c measurements were directly interpreted in terms of acousticpnwer; where exhaust mufflers were present, the measured datawofer corrected b% means of estimated attenuation characteristicsn'f th• muffler and exhaust piping to yield the approximate acousticpower of the unmuffled exhaust.
The data of Ref. 3 were re-analyzed in order to provide animproved method for predicting the engine noise spectra of inter-est here. This re-analysis involved discarding all data on gasengines (because these are inherently quieter than diesels), alldata on engines with nonstandard structures (e.g., with thermalinsulation), and all data on engines with Roots blowers (becausethese blowers add to the noise and are not likely to be used inaircraft); in addition, it involved re-examining the data interms of a reduced frequency based on the "firing frequency".The results of this analysis are shown in the attached figures.
DATA ANALYSIS; ESTIMATION SCHEME
Exhaust Noise
Figure Cl summarizes octave-band exhaust noise data obtainedfrom measurements on nine diesel engines with widely differingoperating characteristics. In addition to points correspondingto individual measurements, this figure(as well as all the otherfigures of this section) also shows "average" and "average plusstandard deviation" spectra, which were obtained by carryingout the appropriate arithmetic operations on the data correspond-ing to the points indicated at each frequency.* Because theacoustic power of engine noise sources has been found to be pro-portional to the engine power, the sound power levels in Fig. 1arid in the rest of the figures of this section have been reducedwith respect to the engine power.
Because the exhaust valve of an engine cylinder opens onceper cycle (i.e., once per power stroke or once per firing), theexhaust of an engine emits one puff per firing per cylinder.One would thus expect the exhaust noise spectrum to have a majorpeak at the firing frequency fF, which for an N-cylinder enginemay be found from
fF(Hz) = engine speed (rev/sec) - n • N,
*The averaging, etc., computations were carried out not on thedecibel values which correspond to the data points, but on themean-square pressures they represent. The "energy" averages ob-tained in this way are likely to be most meaningful for e.-tima-tion purposes. (Ref. 13)
L A jj , , ,j• ",...jjj,...M••i •< • ", '• • WW i ,
where n is the number of power strokes per revolution. For afour-stroke cycle engine, n = 1/2; for a two-stroke cyple engine,n = 1.
The data of Fig. Cl are shown in Fig. C2, replotted againstthe ratio of octave band center frequency to firing frequency.Better collapse of the data is evident. Also shown in Fig. C2is a curve which was suggested by Franken and Beranek (Ref. 14)for estimating the average exhaust noise levels one may expectfrom unmuffled piston engines; this curve may be seen to encom-pass most of the peaks of the average data curve, but to over-estimate the high-frequency noise considerably, An improved es-timation curve, which follows all of the data peaks of Fig. C2,is presented in Fig. C7.
Intake Noise
Intake noise data obtained from measurements on six engineswith unmuffled intakes are summarized in Fig. C3. The same dataare shown in Fig. C4 as a function of firing frequency. Unlike!for exhaust noise, this replotting does not improve the collapseof the data materially. However, since it does bring out theexistance of a physically meaningful spectrum peak near thefiring frequency, it appears advantageous to base an estimationscheme on Fig. C4, rather than on Fig. C3. The correspondingcurve of Fig. C7 represents a smoothed envelope of the peaksof the "average" spectrum of Fig. C4.
Casing Noise
Figure C5 shows octave-band data on casing noise for 27diesel engines with widely varying engine parameters, as indi-cated in the figure heading. The sound power levels indicatedagain are normalized with respect to engine output horsepower(lip) and include A and C correction terms, which were found
useful in Ref. 3 for Improving the estimates of the overalllevels. An "average curve", which is expected to be useful forgeneral prediction purposes, (calculated on the basis of energyaveraging, after discaraing the most extreme points) is alsogiven in the figure.
Pigure c6 differs from Fig. C5 only in that the data are
plotted against the ratio of octave band center frequency toengine firing frequency. A somewhat better collapse of the datais evident, so that use of' Fig. C6 for estimation purposes appearsproferable. The casing noise estimation curve given in Fig.C7is a smoothed envelope of the peaks of the "average" curve ofFir. C6.
it,
ESTIMATION SCHEME
Fig. C7 summarizes an estimation scheme for all threenoise components; how the various estimation curves were de-veloped was indicated above. As evident from Pig. C7, thenoise of unmuffled exhausts always predominates. With a well-muffled exhaust, casing noise becomes most important. Silencingof the intake cannot reduce the total noise of an engine unlessthe exhaust and casing noise components have been reduced dras-tically.
In order to predict the noise of a given engine, cae mayproceed as follows:
1. First calculate the firing fr(.uency from
fF(.z) = engine speed (rev/sec) • n • N
where N is the number of cylinders and
Sfor four-stroke cycle enginesn 2
1 for two-stroke cycle engines.
Then determine what actual frequencies f correspond to thereduced frequencies fifF of Fig. C7.
2. Find 10 log(Hp), A, C, using the relations given in Fig. C7.For each of the three noise components represented in thefigure, use the values of Lw - 10 loj(Hp) + A + C read fromthe figure to determine the corresponding octave band spect.'a.
Note that one may obtain these spectra simply by relabelingthe frequency and Lw scales, and by shifting the casingno'ise curve downward by the amount A + C with respect to
other two curves.
Illustrative Calculation
Consider an unmuffled "V-6" 6-cylinder four-stroke-cycleengine producing 90 Hn at 2100 rpm. Here
f = rps • n • N - •(2- 0)(l- (6) = 101 Hz.
Thus f/f= -- 1 corresponds to f 105 Hz, f/fF 1 to f 52 Hz,
f/fr = 4 to 420 Hz, etc. 2
:I • .... L-
Since 2100 rpm > 1500 rpm, one finds A - 0, and .*r a "V"
engine, C = 1; and
10 log(Hp) 1 10 log(90) = 1.9.5 dB
Therefore one obtains the engine noise spectra by relac.eling thevertical coordinate scale of Fig. 07 as simply IV(dB,r.- 10- 2watts),increasing all numbers indicated along this scale by 19.5 dB, andshifting the casing noise curve downward by 1 dB.
One thus finds, for example, that the peak exhaust noisepower level is 131.5 dB (at 52 and 105 Hz), that the peak intakenoise power level is 91.5 dB(re 10- 2watts) at 105 Hz, and thatthe highest casing noise level of 108.5 dB occurs between 840and 1680 Hz.
I
F;)
A- ft , 7 ,-.:
REFERENCES FOR APPENDIX C
1. Kern, F. R., Jr., "Simulation of Exhaust Pressures of Air-craft Piston Engines," BBN Report No. 2072, prepared forNASA Langley Research Center under Contract NAS1-9559-4(November 1970). To appear as a NASA Contractor Report.
2. A.isten, A. E. W. and T. Priede, "Noise of Automotive DieselEngines; Its Causes and Reduction," SAE International Auto-motive Engineering Congress Paper 1000A (Jan. 1965).
3. Miller, L. N., "Acquisitlon and Study of the Noise Data ofDiesel and Gas Engines," BBN Report No. 1476, prepared forthe Dept. of the Army, Office of the Chief of Engineersunder Contract DA-49-129-ENG-565 (April 1967).
4. Poss, D. and E. F. Ungar, "On Piston-2lap 9s a Source ofEngine Noise," ASME Parer 65-OGP-10 (1965).
5. Priede, T., "Noise due to C•nnhustlnn in Penlprocating ' C. C.Engines," pp. 93-128 in Advances in Automobile Engineering,Part III, Ed. L):, G. 1. Tidhury, Cranfield internationalSymposium Series Vol. 7, Pergamon Press (1965).
6. Priede, T., E. L. Crover and D. Anderton, "Comhustion In-duced Noise In Diesel F'ngines," Preorlni. 317, pre.-ented at.the General Meeting of Inst.ltute of Mnrirn? E.nflneers,(16 Nov. 1967).
7.Andrtn, P., N. Lalor, F. C. Grover, and ?. PrIede,ment and Control of Combustion Induced 'oi.-r in T. C. Engine.;,Combustion Engine Progress, pD. 48-53 (1969).
8. Priede, T., "Pelatlon Between Form of Cylinder Pres:;urf,D)I.fram In Diesel Engines," Proceedings of the Institute ofM'echanical Engineers, (AD) No. i (]96,0-961).
9. Priede, T., F. C. Grover and 11. I,alor, "Relation BetweenNoise and Basic Structural Vibrations of D)isel Eng'ine.-,".'AE Paper No. 690450 (14ay 1969).
10. nriede, 9%, A. E . W. Austen and F. C. Grover, "iEffct1 ofEnrine Structure on Noise ofr Structural Enigines ," Pro-ceedingo of tho institute o! "echanical, Enginýeres, ri.'.113-136 (19614-1965).
11. UnFar, F. F. and D. Ross, "Vibrations and Noise due toPiston-Slap in Reciprocating Machinery," Journal of Soundand Vibration., 2(2), pp. 132-146 (1965).
12. Priede., T., "Noise of Diesel Fngine Injection Equipment,"Journal of Sound and Vibration, 6, pp. 443 (1967).
13. Kerwin, R. M., Jr., "Decibels and Levels," Chapter 3 ofNoise Reduction, Ed. by L. L. Beranek, McGraw-Hill BookCo., Inc., New York, 1960.
14. Pranken, P. A., p. 693 In Noise Reduction, Ed. by L. L.Beranek, Mck-zraw-Hill Book Co., Inc., New York, 1960.
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APPENDIX D
NOISE OF ROTATING COMBUSTION ENGINES
DATA
Data on the noise of Curtiss-Wright Corp. rotating combustion(Wankel) engines are presented in Ref. 1. These data, adjustedfor engine speed and horsepower output (so as to make the datacollapse into a form best suited for prediction purposes), aresumma,'ized in the figures which follow this text.
As in virtually all engines, intake and exhaust noise tendsto dominate over noise from all other sources. This noise from"all other sources", which one observes if the intake and exhaustare effectively muffled, is called casing noise and is labeled assuch in the figures. (Also see corresponding discussion underthe heading of "Noise of Piston Engines".)
AIR-COOLED AND WATER-COOLED ENGINES
The data points indicated in the figures correspond to
measurements carried out on two RC-2-60 water-cooled engines*,onerating at between 2500 and 5000 rpm while producing between30 and 103 Hp. The two engines to which these data points applydiffer only in their intake port configurptions; one has side-ports, the other, pertpheral ports. The peripheral port con-firruration tends to result in noise levels which are slightlyhitfrhpe (by at most 0.5 dh for casing noise, 1.5 db for exhaustnoise, and 2.5 db for intake noise) than those for side-ports.
Although detailed data on the noise of air-cooled enginesare not given in Ref. 1, that document does present comparisonsbetween the noise levels of an air-cooled RC-2-90 engine andthose of water-cooled PC-2-60 engines. The curves for a.r,-cooled engi.nes in the attached figures were obtained from thedIfferences between tynlcal air-cooled and water-cooled engrinedata.
*Uu-tir ss-Wrtght use-s the first number after the HC to designatethe number of rotors, and the second to give the displacement(in cubic inches) per rotor.
'1;'
DISCUSSION
The data available were measured on only three differenttypes of engines, all having two rotors, with about the samedisplacement. The effects of adding more rotors are not known,but one might expect the noise spectrum to shift with the firingfrequency.
No data on the effects of engine size (rotor displacement)are available at all. The number of Wankel engine types in opera-tion is very limited; some small engines of lawyi-mower size arein production, as are some engines for small automobiles, but noengines rated significantly above 100 Hp appear to be availableas yet.
ESTIMATION SCHEME
Clearly, an average of the measured spectra should servefor prediction purposes. Probably the most meaningful averageis that which corresponds to the mean-square value computed forall of the data points at each frequency. Correspondingly, the"average" and "average plus standard deviation" curves indicatedin the figure have been obtained, not by performing the appropriatearithmetic operations on the decibel numbers represented by thevarious data points, but by performing those operations on thecorresponding mean-square values. (See Ref. 2.) Because of therelatively large standard deviations calculated for most of thedata, "average minus standard deviation" values generally turnout to be too low to fit on the plots and therefore do not appearin the figures.
Average curves for all three types of noise from rotatingcombustion engines are summarized in Fig. D4.
In order to estimate the acoustic power produced by a givenrotary combustion engine, calculate 15 log(rpm/1000) + 10 log(Hp),add this value to the numbers given on the vertical scale of Fig.D4, and relabel that scale simply Lw(dB,re 10-1 2 watts).
Illustrative Calculation
For an air-cooled rotating combustion engine producing 90 Hpat 2100 rpm,
15 log(rnm/1000) + 10 log(Hp) = 15 log(2.1) + 10 log(90) s 24.5 dB.
Thus, for example, the 110 dB value of Fig. D4, at which the exhaust.noise peak occurs (at 1000 Hz), corresponds to 134.5 dB.
7I
REFERENCES FOR APPENDIX D
1. Berkowitz, M., W. Hermes and 11. Lamping, "Rotating Combustion.nfine Evaluation for Low Noise Level Aircraft Applications,"Curtlss-Wright Corp. Report CW-WR-69-078.F; prepared forNaval Air Systems Command under Contract N000019-69-C-0460,January 1970.
2. Kerwin, E. M., Jr., "Decibels and Levels," Chapter 3 ofNoise Reduction, Ed. by L. L. Beranek, McGraw-Hill Book Co.,Inc., New York, 1960.
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O INDICATES ESSENTIALLY PURE-TONECOMPONENT, LEVEL NOT SO MARKEDCORRESPOND TO BROAD-BAND COMPONENTSFOR PREDICTION PURPOSES,
31o.5"; 63 125 250 500 1000 2000 3150 8000
OCTAVE BAND CENTER FREQUENCY (Hz) ;
FIGURE D4 AVERAGE SOUND POWER OF ROTARY COMBUSTION ENGINES
78
-. - , -.
S_ -- _
APPENDIX E
NOISE FROM TURBOSHAFT ENGINES
AVAILABLE DATA
Although no broadly useful collection of data pertaining tothe noise of aircraft turboshaft (turbo-prop) engines appears tobe available, such a collection of data has been assembled forstationary gas turbine installations (Ref. 1). Accordingly, itappears useful to develop a noise prediction method on the basisof this collected stationary engine data, until more directlyrelevant data become available. The data reported In Ref. 1were obtained largely from measurements carried out on operatinginstallations rated between 240 and 1500 Hp and rotating at be-tween 1,200 and 43,000 rpm.
NOISE SOURCES
The noise from turbine inlets and exhaust tends to be mostprominent. if these sources are well-muffled, one is left withthe "casing noise" of the turbine.
As air flows through the turbine inlet into the compressor,the compressor blades "chop" the flow; the compressor acts likea siren and produces a rather pure-tone noise component. Thiscomponent typically results in a peak in the noise at the "blade-passage frequency" of the rotating, blades in the first compressorstape. The blade-passage frequency fB(Hz) is given by the pro-duct of the numher of blades in that stage and the compressorspeed in revolutions/sec. Another pure-tone component, whichoften results in a minor spectrum peak, usually occurs at theshaft rotation frequency. This frequency fs(Hz) is equal to theshaft rotation speed in revolutions/sec.
The flow within a turbine also produces noise by siren-actionto some extent. But there the corresponding pure-tone componentstend to be masked by broader-band noise components associated withturbulence and turbulence-related fluctuations in lift and dragof the turbine blades. Accordingly, casing noise and exhaust noisetends to be more nearly of a broad-band character, although spec-trum peaks at the blade-passage and shaft-rotation frequenciestend to be present.
79
4-41
COLLAPSE OF DATA
Figure El summarizes all of the intake noise data availablefrom Ref. 1, in terms of octave-band power level, reduced withrespect to rated power, plotted against actual frequency. (Anattempt at referring the noise to the actual power produced bythe turbines resulted in much greater scattering of the data;turbines make considerable noise even when operating at zeropower output, and the noise of a turbine often increases rela-tively little as its power output increases. Although otherparameters, such as intake flow rate, possibly may affect thenoise, insufficient data is available for the assessment oftheir importance.)
In addition to all of the data points, Fig. El also showsthree sample spectra which illustrate the typical double-peakedcharacter of inlet noise, with peaks at the blade-passage andshaft-rotation frequencies.
Figures E2 andE3 show the same data as Pip. El, but plottedaryainst the ratio of frequency to blade-passage and to shaft-rotation frequencyi, respectively. In the construction of Fiig.E2,only data near the high-frequency peak of spectra like thoseshown in P'ig. El were retained; low-frequency data were omitted.Tn cases where not enough information was available to permitdetermination of the blade-passafe frequency, it was assumed forpurposes of constructing Fir,. E2 that this frequency correserndsto the aforementioned high-frequency peak.
PigureE3 similarly shows only data near the low-frequ- icpeak of the original un-reduced spectra. Here, however, theshaft rotation frequency was known in all cases.
wigureE•4 presents exhaust noise data in terms of actualfrequency, and Figs. E5 andE6 present the same data, but interms of ratios of frequency to blade-passare and shaft-rotationfrequencies. FiguresE7,E8, andE9 are similar plots for casingnoise.
The spread of the inlet noise data is seen to be consider-ably less in the reduced frequency plots of Firs. E2 andE3 thanin the actual frequency plot of Fig. El. Similarly, the exhaustnoise data cluster somewhat better in Fi-s. E5 andE6 than in Pig.E4,and the casing roise data collapse better in Rigs. E8 and E9than in Fig. E7.
80
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ESTIMATION CURVES
The "average" and "average plus standard deviation" spectrashown in the figures have been calculated by performing the ap-propriate arithmetic operations on the mean-square values whichcorrespond to the data points at each frequency. Such energyaverages (Ref. 2) are expected to be most meaningful for estima-tion purposes. (Note that no "average minus standard deviation"spectra are given in the figures. Because of the relativelylarge standard deviations found here, such spectra would falloff the bottom of the graphs.)
The various "average" spectra are most applicable for gener-al estimation purposes, whereas the "average plus standard devia-tion" spectra are useful for estimatinp the highest noise levelsone is likely to obtain.
Because the average inlet noise spectrum has pronouncedpeaks at the blade-passage and shaft-rotation frequencies, onemay base an estimation scheme on Figures E2 and E3. Such a schemeis presented in Fig. El0, which suggests estimating the inletnoise spectrum of any turbine engine in two parts - a low-frequencypart centered at the shaft-rotation frequency, and a high-frequencypart centered at the blade-passage frequency* - and interpolatingbetween these two parts as needed. Comparison of Fig. El0 ,thPig. El shows that the scheme of Fig. El0 preserves the essentialcharacter of the unreduced-frequency spectra.
If one attempts to construct a prediction scheme for exhaustnoise like that which was developed for inlet noise, than onefinds that either the two partial spectra must coalesce, or onecannot reproduce the essertal character of the average spectrumof Fig. E4 . Because the shaft-rotatIon frequency is physicallymore meaningful for exhaust noise than is the blade-passage fre-quency, a prediction scheme based on the shaft-rotation frequencyis suggested. This scheme is presented !n Fig. Ell , which isbased on averaging and smoothing of the spectra of Figs. E5 and E6(aligned so that the peak-frequencies coincide). Again, Fig.Ell may be seen to be very similar to the average spectrum of Fig.E4,which is plotted in terms of actual (non-rtduced) frequency.
*The partial spectra of Fir. El0 were obtained by smoothing theaverage spectra of Figs. E2 and E3 and by omitting those portionsof these spectra which are so far from the peak-frequenciesthat the estimation is likely to be unreliable.
i 81
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Finally, one finds that the two reduced casing noise spectraof Figs. E8 and E9 cannot be made to coalesce in any meaningfulway to produce an estimation which resembles the average spectrumof Fig. E7. Also, it is likely that casing noise may be dom..natedby the effects of auxiliary components and casing structural para-meters, rather than by the siren-like blade-passage effects. Thus,the average spectrum of Fig. E7, which spectrum is reproduced insomewhat smoothed form in Fig. E12, is likely to be best for es-timation purposes.
ESTIMATION SCHEME
In order to Predict the noise produced by a given turboshaftenpine, one should deal with each of the three major noise compo-nents (inlet, exhaust, casing) separately.
1. Use Fig. El0 to estimate the inlet noise power. Calculatethe shaft rotation frequency f from
S
fs(Hz) = compressor rotation speed (rev/sec).
and the blade-passage frequency fB from
fB(Hz) = fs number of blades in firstcompressor rotor stage
Determine the actual frequencies that correspond to thefrequency ratios indicated in Fig. El0 and the power levelsL that correspond to the reduced levels shown.
Plot the levels corresponding to each octave-band centerfrequency.
Re-plot the two partial snectra obtained b}i thfs process,and connect the point corresponding to f/f i = 4 with thatfor f/fB = 1/4 by a straight line (corresponding to thedotted line of Fir. Elr). If the two partial spectraoverlan, use a smoothed (upper bound' envelope for the totalsDect rum.
2. Use Pig. Ell to estimate the exhaust noise, by replacingthe frequency ratios in that figure with the correspondingfrecuencies and the reduced power level by the actual powerlevel.
3. Use Fig. E12 to estimate the casing noise, by replacing thereduced power levels indicated by the corresnonding actualpower level.
- -
S3N!?
Illustrative Calculation
Consider a turboshaft engine rated at 90 Hp, with a com-pressor which has 22 blades in its first (rotating) stage, andwhich rotates at 27,000 rpm.
Since here 10 log(Hp) = 19.5 dB and fs - 27,000/60 - 450 Hz,fB = (450)(22) = 9,900 Hz, one finds the following power levelscorresponding to Fig. FlO:
f/fs 1/4 112 1 2 4
f/fB 1/4 112 1 2 4
f(Hz) 112 225 450 900 1,800 2,500 5,000 10,000 20,000 40,000Lw(dB) 95 103 105 102.5 101 10-3 ill 118 116 113
By shifting the computed values to the nearest standard octave-band frequency and connecting those two partial spectra, oneobtains the curve shown in Fig. El3.
Using the same values of fs and 10 log(Hp) in conjunctionwith Figs. Ell and E12, one similarly obtains the exhaust andcasing noise ctuves also shown in Fig. E13.
83
REFERENfES FOR APPENDIX E
1. Miller, L. N., "Acquisition and Study of the Noise Data ofGas Turbine Engines". BBN Report No. 1477, prepared forDept. of the Army, Office of the Chief of Engineers, underContract DP-49-129-ENG-656 (August 1967),
2. Kerwin, E. M., Jr., "Decibels and Levels", Chapter 3 ofNoise Reduet.on, Ed. by L. L. Beranek, McGraw-Hill Book Co.,Inc., New York, 1960.
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APPENDIX F
DISCRETE-TONE NOISE PRODUCED BY TURBOJET FANS
INTRODUCTION
Fans and compressors of turbojet engines typically producehigh-pitched whining sounds, which consist primarily of one ormore pure-tone components. Axial-flow fans resemble multi-bladedpropellers, and the basic mechanisms responsible for fan noiseare in part the same as those which cause propeller noise. Also,in both cases, the pure-tone components are associated with pres-sure fields that spin about the axis of rotation.
However, propeller noise theory is inapplicable to fans (andits use can lead to gross underestimates of fan noise). The ductsin which fans are housed affect the aerodynamics, as well as thepropagation of sound, and the dominant sources of fan noise areassociated with the interactions of successive rows of (rotor andstator) blades.
SOURCE MECHANISMS (Ref. 1 - 3)
Two sources of pure-tone noise are of primary importance forsubsonic rotors - i.e., for rotors which move subsonically rela-tive to the air flow: (1) The fluctuating lift generated on adownstream blade row as it interacts with the wakes formed by teupstream blade row produces an effective acoustic force field inthe plane of the blades. (2) A siren-like volume source effectis produced as successive blade rows present a periodic obstruc-tion to the flow; the obstruction is minimum when the wakes arein line, and maximum when they are alternately spaced.
The mechanisms present in subsonic fans also are present insupersonic fans, but in supersonic fans there occur also othermechanism, which may be of greater importance. These mechanismare associated with the rotor shock-wave field, which radiatesdirectly, and which also produces lift fluctuations on the statorblades. Because of the greater noise from supersonic rotors,such rotors should be avoided in "quiet aircraft" applications,and will not be discussed further here.
97
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PREDICTION
Much theoretical work has been done on the various noisemechanisms (e.g., Refs. 2 - 4 ). However, most of the relationsthat have been developed are not very useful for prediction ofnoise because they require information on various aerodynamicdetails which is generally not available until a prototype hasbeen built. And by then, of course, one may obtain much betterdata on the noise simply by measuring it.
Perhaps the best means for predicting the level of the fun-damental pure-tone component generated by a fan consists of arelation derived in Ref. 3, which gives the sound pressure levelL.( 2 0 0 1 ) produced at 200 ft to the side of fan engines, at theblade-passage frequency, as
L2 (dB,re 0.0002pbar) =50 log Utip(ft/sec) + 20 log D(in) -75(1)
in terms of the tip speed Utip of the fan blade and the fan dia-meter D.
If one assumes the directivity to be uniform - an assumptionthat is not strictly valid, but that is Justified for the simpli-fled scheme for estimation of aural detection suggested in thisreport - then one may easily determine the sound nower level thatcorres:-onds to Ec. (1). Noting that Utin = RD = DTRr/30, whereQ renrrsents the fan rotational speed in radians/sec and Q. thatsame speed in rom, and by changing the dimensions of D to ft,one may obtain
Lw(d9,re 10-12 watts) = 50 log r(rpm) + 70 log D(ft) - 56 (2)
In Ref. 3 there is also presented a comparison of Eq. (1)with experimenta2 data obtained on 6 different fans. For tip. neods up to about 700 ft/sec, Eq. (1) is very nearly an upnerbound to the data; the data in this region fall largely within+ 1 dB and - 7 dB of the values giv,:n by Eq. (1). For transonictin speeds, i.e. between 700 and 1500 ft/sec, the data are morewidely scattered and fall essentially between + 5 dB and - 10 dBof Eq. (1).
Although it is well known that fan noise in general alsocontains several significant harmonics of the fundamental blade-nassage frequency, no adequate means are available for predictingthe sound levels associated with these harmonics. Experimental
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data (Ref. 2) also indicate wide fluctuations in the relativelevels of the first few harmonics, even in successive runs of thesame engine. On the basis of the very limited amount of dataavailable, it may suffice for aural detectability estimation pur-poses to consider only the first three harmonics of the fundamen-tal, and to take the levels of successive harmonics to decreaseby 3 dB.
ESTIMATION SCHEME
To estimate the discrete-tone sound levels produced by aturboject fan, proceed as follows:
1. Calculate the blade-passage frequency
f = BQB
where B represents the number of rotor blades in the fan'slast stage, and Q the fan's rotational speed (in radians/sec).Then use Eq. (2) to determine the acoustic power Lw producedat that frequency.
2. Then take Lw - 3 dB at 2 f
Lw - 6 dB at 3 fB
and Lw - 9 dB at 4 fB
as the remaining significant pure-tone components for de-tectability estimation purposes.
3. Repeat steps 1 and 2 for the fan's next-to-last stage, but
reduce all levels by 3 dB (Ref. 1).
Illustrative Calculation
Consider a 1.65 ft diameter fan with 22 blades in its firstand 29 blades in its second (and last) stage rotor, operating at5,800 rpm ( - 610 rad/sec).
For the last stage, then, fB = BO = 29(610) = 17,500 Hz and
L = 50 log Qr + 70 log D - 56
= 50 iog(23,300) + 70 log(l.65) - 56 = 171 dB,re 10-1 watts.
Thus one obtains 171 dB at 17.5 kHz, 168 dB at 35 kHz, 165 dB at52.5 kHz, and 162 dB at 70 kHz.
9£)
* -• .,-, . .. , . •• .• - ;•* -, .%•.. •-
Then for the first stage, one finds that at fB * 22(610) ~13.5 kHz, Lw 171 - 3 = 168 dB, and at 27 kllz one obtains 165 dB,etc.
Note, however, that frequencies above 30 kHz are of no con-cern in relation to aural detection. Also see illustrative calcu-lation at end of Appendix H.
iI
L -
-. ,, ...
REFERENCES FOR APPENDIX F
1. H.S. Ribner, "The Noise of Aircraft", Trans. Fourth Congresson Aeronautical Sciences, pp. 13-71.
2. Anon., "Investigation of Discrete-Frequency Noise Generationby Aero-Engine Compressors and Fans", Bolt Beranek and NewmanInc., Report No. 1617 (Feb. 1968). Submitted to Genera].Electric Co., Aircraft Engine Group, Evansdale, Ohio.
3. M.V. Lowson, "Theoretical Studies of Compressor Noise", WyleLaboratories Research Staff Report WR68-15 (Aug. 1968). Pre-pared under Contract NAS1-6885.
4. "Fan Noise Research". Sec. II of Basic Aerodyamic NoiseReeearah, ed. I.A. Schwartz, NASA SP-207 (1969). (A collec-tion of papers by several contributors.)
5. S.L. Bragg and R. Bridge, "Noie From Turbojet Compressors",J. Royj. Aero. Soc. 68, pp. 1-10 (Jan. 1964).
KN7 _
-r r
APPENDIX G
NOISE OF GAS JETS
The primary source of noise from any well-muffled and acous-tically enclosed aircraft propulsion system (e.g., from a turbo-fan engine "buried" in the fuselage of an aircraft and providedwith appropriate inlet and exhaust ducts) Is due to the thrust-producing jet efflux from the system.
Much work has been done on the noise of jets, and well-validated prediction methods are available, particul-rly for.Jets with relatively small velocities (Refs. 1-3), which arelikely to be of greatest interest in relation to small quietaircraft.
ACOUSTIC EFFICIENCY AND MECHANICAL POWER
Perhaps the best and simplest estimation method may be ob-tained on the basis of the summary study undertaken by Heckl(Ref. I). It has often been observed that similar rockets orjets have very nearly the same "acoustic efficiency" aac whichis defined as
Cac m (i)
where W represents the total (overall) acoustic power radiatedand Wm the mechanical power of the flow. This mechanical poweris given by
Wm =FtU (2)
where Ft denotes the thrust and Uj the jet velocity. The thrust Ftof air-breathing propulsion systems obeys* (Ref. 5)
0t = ma (UJ - U0 ) + infU. + A (PJ - P) (3)
*Note that this relation applies for any type of system thatoroduces thrust by accelerating air; it thus applies equallywell for propeller and jet-engine systerm.
]0?
I- OP| I i i iV
'1 "
where ma represents the mass-flow rate of air through the propul-sion system, which flow enters the system with a relative velocityUo (typically the vehicle air-speed) and leaves with velocity U.Similarly, mf represents the mass-flow rate of fuel, which entersthe propulsion system with essentially zero velocity and exitswith velocity Uj. In addition, Aj represents the area of the jet,Pj the pressure in the jet, and P0 the ambient (intake air) pres-sure. In most propulsion systems, ma/mf > 50, and Po w Pj, sothat
Ft ma(Uj - U0 ) t maUJ - U•A , (4)
where p represents the density of air in the Jet and the usualcondition U >> U has been assumed. Thus, the mechanical powermay be apprgxima~ed by
pA U (5)Wm
Figure Gl summarizes the observed dependences of the acoustic
efficiency on Jet velocity, taken from Ref. 4. The band indi-cated for low velocities represents the scatter of data in thisregion; higher-turbulence Jet flows here have significantlyhigher acoustic efficiencies. Also indicated in the figure areexpressions which give the dependences of cac on Mach numbercorresponding to the various straight lines shown in the figure.The dotted line within the low-frequency band represents an ap-proximate energy average between the upper and lower bounds ofthat band, and may be used for general estimation purposes.
SPECTRUM SHAPE AND DIRECTIVITY
The jet noise spectrum may be estimated by use of Fig. 02,which shows how the octave-band levels differ from the overalllevel. The spectrum has the typical haystack shape, with itspeak at the dimensionless frequency (Strouhal number)fUg/D= 0.2, where f represents the actual frequency and D theJe• (nozzle) diameter.
A curve for the estimation of directivity effects is givenin Fig. G3. It shows that the highest sound levels occur at about30' from the jet efflux axis, and that the sound levels ahead of
the Jet (at 1800 from the efflux axis) are nearly 10 dB lowerthan the spatial average value.
103
ESTIMATION SCHEME
In *rder to estimate the noise produced by a given jet at agiven location, one may proceed as follows:
1. Use the mechanical power Wm ana the diameter D of the jetto calculate the jet velocity U~, of an equivalent jet atroom temperature and zero altitrde from
Uje [Wm/pAj I/ (5a)
taking p 0.07 lb/ft3 .
2. Use Fig. G1 to find pac, and from cac find the overall acous.-tic power of the equivalent jet from
W = GacWm (la)
Then calculate the corresponding power level from
L (dB,re 10- 1 2 watts) = 10 log(W/10- 1 2watts)wI3. Add to this overall power level the correction AL for
atmospheric pressure and temperature
ALw= 10 log (P /P ) + 40 log (Tn/r-) - 35(T /T)w at at,,o 0j ao0
where P = actual atmospheric pressureat
P = standard atmospheric pressureato
T = absolute temiperature of jet
T = absolute temperature of ambient air
T = absolute reference (room) temperature
4. Apply the directivity correction from Fig. G3, if directivityinformation is of interest.)*
5. Calculate the jet diameter from
D2 = 4Ft/mIPUJ (4a)
orD2 = 4Wm /r0U (5b)
m j
and use Fig. G2 to obtain the octave band noise spectrum.
*Directivity effects are not used in the estimation method for auraldetection suggested in this renort. Directivity estimation is in-cluded here only for the sake of completeness.
o014
'V7.17 '7 7C 7%1
Illustrative Calculation
Consider a propulsion system whi-h generates a thrust of155 lb by producing an air jet that e anates from a 1.65 ft dia-meter duct at 300 ft/sec and 250 0 F. The mechanical power of thisjet is
Wm = FtUj = (155 lb)(300 ft/sec) = 46,500 ft lb/sec
and its area is A = wD2//4 = 2.44 ft 2 . Hencej
U Wm (4.65Xi04ft lbf/sec) (32.21bmft t 83= p•j ... --8.80 x 106 -L
J (0.071bm/ftS)(2.44ft) bfse
Uje 206 ft/sec.
From Fig. GI, Oac z 2 x
W = m (2 i0- 7 )(4.65xl0 4 ft lb/sec)(1.36 watt sec/ft Ib)
= 1.26 x 10-2 watts
Lw 10 log(l.26X10- 2 /10-1 2 ) = 10 log(l.26xi01 0) = 10ldB,rel0- 1 2 watts
If the ambient air is at T = 40OF = 500OR and Pat,o = 0.9atm,whereas the reference air tempehature isTo = 70OF = 5301R, the correction required isP TTa
=Lw 10 log(kP ) + 40 log ( - 35 log(o"at ,o 0 0
10.atm+ 11 250+460°R• .[500°R•
= 10 logfO ) 40 log ( 530oR +-35 o (530 -6R)-0.4 +5.0+0.8
5.5 dB
Therefore the overall sound power level is Lw + ALw106.5 dB,re 10-1 2 watts.
105 F Z...
Since UJ /D = (300 ft/sec)/(l. 6 5 ft) " 180/sec, fD/Uj = 1corresponds to f = 180 Hz. One may thus assign frequencies tothe Strouhal numbers shown in Fig. G2. Some octave-band powerlevels found from the previously determined overall level of106.5 dB, as obtained from Fig. G2,then are as follows:
COB (Hz) 18 36 72 180 360 720
LOB(dB,re 10- watts) 96 100 90 94 91 87
jI
I I I I I I I I I I I IjI I I
REFERENCES FOR APPENDIX G
1. "Sonic and Vibration Environments for Ground Facilities -
A Design ManuaV". Ed. by L. C. Sutherland, Wyle Labora-tories, Research Staff Report No. WR68-2, prepared underContract NAS8-11217 (March 1968).
2. Eldred, K., W. Roberts, and R. White, "Structural Vibrationsin Space Vehicles," WADD Technical Report 61-62 (Dec. 1961).
3. Franken, P.A., "Jet Noise," Chapter 24 of Noise Reduction,Ed. by L.L. Beranek, McGraw-Hill Book Co., Inc., New York,1960.
4. Heckl, M., "StrSmungsgergusche," VDI-Zeitachrift, FortschrittBerichte, Reihe 7, No. 20, (Oct. 1969).
5. Boden, R.H., "Propulsion," Chapter 20 of System EngineeringHandbook, Ed. by R.E. Machol, McGraw-Hill Book Co., Inc.,New York, 1965.
] q] '[
C
.. . . -- -"
%co2xlO---
oac'l 104 M5.
oac, 8x10.5 MS
(HIGH TURBULENCE)u\z
•- ••,••,•-O'cc= 8 x 10"5 M 3.-S0~
10-
________ ____(LOW TURBULENCE) _____ __
0.1 1.2 1.5 2 3 4 a 6s 7 a 9 1 1.2 1.5 2' 3
JET MACH NUMBER, MI I I i t I I t i L l
50 10o 1.5 2 3 4 5 6 7 6 91ooo
EXPANDED JET VELOCITY, Uje(m/sec)I I _ , I I , I i t ,Il I II
150 2 3 4 5 6 7 a 961000 1.5 2 3000
EXPANDED JET VELOCITY, Ujo(ft/sec)
FISURE G1 ACOUSTIC EFFICIENCY OF AIR JETS AT ZERO ALTITUDE ANDROOM TEMPERATURE
106J
* tv
w~ -10
w -200
-j
> -30
too OCTAVE BAND CENTERFREQUENCY
S-40 D JET (NOZZLE) DIAMETER'J UJ JET EFFLUX VELOCITYI--_
o -50 - - -
0.02 0.1 2 D 10
STROUHAL NUMBER, fjD (DIMENSIONLESS)
FE.
FIGURE G2 NORMALIZED OCTAVE-BAND SPECTRUM OF JET NOISE
1 (-
* . . .*-
IL C-i
IJJJ
w
LJ
-, 0
wY CIj
'77
APPENDIX H
SOUND ATTENUATION IN CIRCULAR DUCTS
INTRODUCTION
The attenuation of sound propagating in ducts is a functionof the sound source and of the geometrical and acoustical para-meters of the duct.
The source may be described in terms of the spatial distri-bution of the sound-producing elements, and is usually expressedin terms of wave number parameters or modes. This source descrip-tion also involves frequency-dependent impedance terms, which canbe related to the various individual modes. Although flow canaffect the source characteristics, it is convenient to considerthis effect separately.
The geometry of a duct can be described in terms of the ra-tios of length to diameter of the lined duct, the ratio of liningthickness to duct width (or diameter), and the ratio of the lengthof the lined section to that of the unlined section of the duct.One then needs only one absolute length to describe the geometry,and one may compare this length to the acoustic wavelength.
The acoustical properties of a duct are commonly describedin terms of the propagation constants Tn and Gn of modes, whichconstants are defined by the axial pressure function
-ikz(tn-in) ikz(Tn-iAn)p(z) =•I•Pn+e + - pn-e (1)
n n
where k denotes the acoustic wavenumber (in free space). Thepropagation constants are related to characteristic modal impe-dances Zn by
Z = Pc/(t - io ). (2)n n n
In designing a duct, the one variable over which one hascontrol, in addition to the geometry, is the wall impedance Z.For a rectangular duct. without flow, the impedance of a homo-geneous, locally reacting wall is related to the propagation con-stants as (Refs. 1-4)
ill
= 1 (n~ia~n ) tan (kHV~1 (- rni)2 (3)
where H denotes the width of the rectangular duct (assumed linedon one side). For a circular duct of diameter D, one may deter-mine that
ipc -IS V,-i )2- an )'n~2]
where J 0 , J, denote the Bessel functions of order 0 and 1. (Thisresult is derived in the last part of this section.)
Air flow through the duct and/or high-intensity sound, leadsto changes in the effective wall impedance and in the relationbetween the wall impedances and the axial sound propagation (Ref.5). The changes are small, however, for centerline flow speedsthat correspond to Mach numbers below 0.1 and for sound pressurelevels below 140 dB (re 0.0002 microbar). Because high flowspeeds and sound pressure levels are of limited interest here,their effects are neglected in the subsequent discussion.
Sound absorption at the duct walls and turbulent air flowcause the modes to interact. Therefore, the concept of modes,which is a mathematical device introduced to describe soundfields in rigid enclosures in terms of orthogonal functions, isnot a useful one here. In particular, it makes no sense to con-sider modal distributions in a duct which are not compatible withany source configuration. Because of these problems with modesconcept, and also because of the mathematical difficulties aris-ing from the complex transcendental equations which describe therelation between wall impedances and modal parameters [Eqs. (3)and (4)], the analysis of sound attenuation presented here isbased on approximations, which approach the idea of modes onlyinsofar as a stabilized cross-distribution of sound pressure F(with minimum attenuation along the duct) can be identified witha fundamental mode.
HIGH FREQUENCY ATTENUATION
It is convenient to consider two limiting frequency regions;a hIL-rh-frequency region in which the acoustic wavelength X issimai compared to the duct diameter D, and a low-frequency regionin which A > D.
S.. ... . v- -- •I" -,-..-D -••"•. -' • ,, • .- *• •%•@,' Trrv• •-•• p--n < .o , •
For high frequencies, the sound propagation in ducts may beanalyzed in terms of rays. Figure Hlshows a cylindrical duct oflength L and diameter D with incoherent point sources assumed lo-cated at one end, in the z m 0 plane. The source density is takento be a function q(r) of the radius r, but not of the angular po-sition *.
Directly Emitted Rays
If the duct is lined with an absorbing material, most of thesound radiated out of the duct is due to rays which propagatethrough the duct without being reflected from the walls. Suchunreflected rays which emanate from an element rdrd¢ of the sourceregion are confined to a spherical angle Q0. If no duct were pre-sent, the same source element would radiate into the sphericalangle 27T. Therefore, the acoustic intensity due to rays emittedfrom the element rdrdo and propagating without reflections is
dI dI 0 - = dI° sin -2- , (5)
where dI denotes the intensity obtained with a very short orcompletely rigid duct. The intensity emitted from tne entiresource region is a function of the source distribution q(r) andobeys
D/2
J q(r)dr
I = JO (6)D/2 q [(r)i/,3ir.4] dr
The duct geometry affects the angle e0 ;
0r2L r 2r 1)]2(/ (7)sin-•" = 1l + -- +[ •(•- 'ii7
Considerable reduction of the sound intensity can be obtainedonly if 0 is small; then
00 eo ~ Dsin -(8)
I
-~ -- 7. P
and
1=0D0.
for any source distribution.
Reflected Rays; Attenuation of Short Ducts
In order to take account of the imperfect absorptivity ofthe duct lining, one must consider the rays that are reflectedfrom the walls before they leave the duct. The rays which sufferone reflection are confined to the spherical angle f - 00, whereQ = 2r sine /2 corresponds to rays that are emitted from a ductwith a diameter of 3D, as shown in Fig. H2. If one again limitsoneself to a relatively long duct for which Eq. (8) holds, thenone finds chat the contribution from rays which are reflected be-fore they leave the duct is given by
I = 1 (l-a)D (10)
where a represents the absorption coefficient of the duct wall.From Eqs. (9) and (10), one may then determine the attenuation(in decibels) to obey
AL = -10 log (11)
this relation provides one with an estimate of the performance ofshort ducts lined with an absorbing material. Because the absorp-tion coefficient a usually increases with increasing angle of in-cidence or, equivalently, because rays which suffer more reflec-tions are attenuated more highly, one usually may neglect thecontributions from multiply reflected rays.
Attenuation of Long Ducts
One may analyze the multiple reflections of rays in longducts by considering the mean free path Z of a ray between suc-cess3ive reflections at the walls. The intensity in the duct thendecays according to
I = e-az/Z (12)
S. .. ..- . -....... - . .. -:•.- • ••.• • _'.. W U ,. "' ,. . - ,,';.ýVAV- V -*
7_ý '53
R I
For weakly attenuated rays 8 which propagate almost axially,the mean free path length X is found to vary directly as the ductdiameter D and inversely as the (small) angle c between the walland the initial direction of propagation
(13)
The set of rays which results in a pressure minimum at the wallsuffers the least attenuation. For this set of rays, the anglec is determined by the ratio of the radial to the axial wavenum-bers,
k kc & tan c r -Z r E X (14)
For circular ducts, the pressure minimum at the wall is de-termined by the first zero ot the Bessel function JO(krr); thiszero occurs for krr = 2.4, corresponding to which
kr z 4.8/D (15)
Accounting only for rays which emanate from the source nearlyaxially (e << s), one obtains the attenuation AL (in decibels),as
43 cL X 4.8.. LX
AL =4.35 D -L D = 3.3a L X (16)
The absorption coefficient c for such rays usually is small, andcan be approximated by
z4c Rle PC (17)t Z
where Re{Z/Pc} is the real part of the wall impedance for nor-mally incident sound, divided by the characteristic impedance pcof the gas. in the duct.
Since the attenuation in a longer duct turns out to be pro-portional to the square of X/D - which is small in the region ofhigh frequencies - no great improvement can be obtained by ex-tending a short duct. The initial section, for which the attenu-ation is approximately given by Eq. (11), contributes almost all
1 1•
.'A
of the attenuation. If one desires to increase the attenuationsubstantially, one needs to curve the duct or add obstructionsto interact with the axial rays.
LOW-FREQUENCY ATTENUATION
Analysis of the performance of lined ducts at frequencies atwhich the ducts are not very long compared to the wavelength in-volves three problems. They are associated with the source re-gion, with transitions from a rigid duct to a lined duct (andvice versa), and with the duct termination.
Source Distribution
As previously mentioned, the spatial distribution of sourcescan be described (only inadequately by modes. At low frequencies,at which the acou :tic wavelength is greater than the duct diam-eter, the spatial distribution becomes stable in a very shortdistance along the duct. The stabilized radial distribution suf-fers the least att.nuation with distance; one may therefore ob-tain a conservativw estimate of the attenuation performance oflined ducts by con.;Ldering only the stabilized distribution.This approach, wh: .i does not account for the actual sourcecharacteristics, i1 employed below.
Duct Terminations and Lining Discontinuities
The exact calculation of reflection and transmission coeffi-cients at the transLtion from a rigid duct to a lined duct is ex-tremely difficult. Heins and Feshbach (Ref. 6) applied a Wiener-Hopf technique to dwvelop series approximations. The first termof their series agrees witn results obtained from the simplestconsiderations, using the basic modal impedances ZR = Oc for rilg']ducts and ZS = pc/(T-ia) for lined ducts. Such approximationsare appropriate in the case of moderate attenuation, and will beemployed in the present analysis. Effects of duct terminationshave been studied by Levine and Schwinger (Ref. 7), who have cal-culated the radiation from an unflanged pipe. One finds that onemay obtain an adequate approximation by considering only the massreactance in parallel with the plane wave impedance at the openend of a rigid duct (Ref. 8). Results fox' the radiation fromlined ducts generally show somewhat higher values than obtainedfrom this approximation; this difference can be ascribed in partto the curvature of the wavefront in the duct.
The geometry of discontinuities in the duct lining and ofunflanged open tailpipes to be studied is shown in Fig. H3, whichindicates a lined duct of length Ls, connected to a tailpipe oflength LR with rigid walls; the duct and tailpipe are taken tohave the same diameter D.
i 7117
The transmission of sound through individual homogeneousparts of the duct may conveniently be described by means of'transfer matrices, which involve the propagation constant andthe characteristic impedance of the stabilized radial distribu-tion (or fundamental mode). The effects of' series-arrangementsof different parts may then be determined by multiplication of Ithese transfer matrices. Thus, the sound pressure and velocityat the inlet of the absorbing duct are related to those quanti-ties at the open end of the rigid tailpipe, to the first orderof approximation, by
sin[kLs (r-io)]
v, pc i(T-iCo) sin[kLs(T-10)] cos[kLs(0-ic)] '
1B
(cos kL R i sin kL R)(P7
i sin kLR cos kLR pcv 2 (18)
At the open end of an unflanged pipe of diameter D, thepressure and velocity are related by
v 2 0c 1 4my 1 + i••.(19)P2 k
One may then calculate the attenuation of the duct in terms ofthe ratio of the pressure at the inlet of the absorbing duct tothat at the open end of the tailpipe, as
AL = 20 log dB . (20)SP2
The inlet pressure p(,) depends on the source conditions, as dis-cussed below.
Source Connected to Absorbing Duct via Unlined Duct
Here the pressure p, results from the complex amplitudes p1 +and p of an incident wave and of the wave reflected at the
wave-impedance discontinuity at the inlet of the absorbing duct;
117
Iý - '7 7. ITW I4UII
• :..•.,_ •_• ..... ""'-:o, ~~~ ~ ~~~. :" " •...... - •". .......... ............. '."" """°:-
P1 =P+ + p- (21)
For the plane wave in the rigid inlet duct, there applies therelation
vPc = Pl÷ - p- • (22)
If the source is not specified otherwise, one may assume that itsinternal impedance is equal to the characteristic impedance PC.Then the pressure p(i) is equal to the pressure pj+ of the inci-dent wave, and from Eqs. (18) to (22) one obtains the attenuation(in decibels) as
AL = 8.7kaLs + 10 log (I + 2) (23)
-2ikLs(T-i0)+ 20 log 1 + 1-e _(l-T+ia) l-T+i + (l+T-iC)
4T(T-ihe) i +ikD/2
The first term represents the attenuation of a homogeneous linedduct. The second term gives the reflection loss at the end ofan unflanged pipe. The part of the third term which involves
l-e- 21kLs(t-iC) accounts for waves propagating back and forth inthe lined duct, which result from reflections at the discontinui-ties in the duct. lining; the part of the third term with the co-efficient e-21kLR accounts for waves reflected between the end ofthe lined duct and the open end. (Note that the latter reflectedwaves disappear for kD• +-, which corresponds to an anechoic termi-nation of the rigid tailpipe).
For strong reflections from the open end of the tailpipe(kD -0), and weak interaction between the two ends of the absorb-Ing duct, the third term of Eq. (23) reduces to
20 log 1 1+ [ -r t+ia + e-2 1kL R(l+T-io )J
which for T > 1 >> a becomes
1 18
2 kL
20 log 1 - e-'1 e1. 2T
Thus, quarter wavelength resonances in the tailpipe (kLR = w/2)result in positive values and half wavelength resonances (kLR = n)in negative values of the third term of Eq. (23), as long as T >1,which is the case below the first resonance in the duct lining.
For very short absorbing ducts (kLs ÷0), the third term of
Eq. (23) becomes
20 log 1 + ikLs(l-T+ia) 1 - T + io + e (1+ -io)2 l+iIkD/2
Sound Source Located Directly at the Inlet of theAbsorbing Duct
For a low-impedance source (pressure source), the pressureP(i) which characterizes the attenuation performance of the ductis qual to the pressure pl. Equations (18) and (19) here yield
AL = 8.7kLs + 10 log 1 +
1, (kD)z1
- 2 ikLR -2ikL (',r-io)
+ 20 log e + l-e s + (24)I+ikD/2 2(T-ia)
11 -21kLR
1 - T + e (+ + T - ic (24a)i+ •kD/2
Within the approximation valid for T 1, the third term hereaccounts for reflections from the discontinuity of the duct lin-ing and from the end of the tailpipe, in agreement with Eq. (23).
For a high-impedance source (velocity source) at the inletof the absorbing duct, the reference pressure P() results fromthe velocity v, multiplied by the characteristic impedancepc/(T-ia), ano one obtains
lii()
•, ,/ .•,•.,, ". - +~ • .•, .D,•,- '•..ti , .... .,.. -
AL = 8.7kaLs+ 10 log i+ +(kD) 21
?21ikL -2ikL (T-IO)
20 log 1 + + l-e(25)l+ikD/2 2(T-iC )
F e-21kLR
8, 1l - T + ia + (e + T - ia) (25a)l+ikD/2
This result differs from Eq. (24) only in the algebraic sign re-lating to the phases of reflected waves in the lined duct.
The source fmpedance does not affect the attenuation perfor-mance of the duct, if the reflected wave from the discontinuity
of the duct lining can be neglected (e- 2 kLs<< 1 ).
PROPAGATION CONSTANTS FOR CIRCULAR DUCTS
The linearized wave equation in cylindrical coordinates r,zis
+ (r + p = 0 (26)az
2
With the axial dependence
p(z) - e"ikz(T-iC) (27)
one obtains Bessel's differential equation for the radial depen-dence,
2 + r •P + k27[ _ (T-_iC) 2 ]p = 0.3r 2 r ar (28)
The solution compatible with a finite axial pressure is
p(r) ~ J 0 [kril - (r-io)2], (29)
] P0
where J. is the zero order Bessel function. Boundary conditionsat a homogeneous, locally reacting wall at r - D/2
- V - = V1 - (T-1-)Z J1[krV1 (Tl) (30)1 ie p 30
J Ekr/i-T ('T-15T]0
can be described by the wall impedance
= rr../ (31)rr=D/2
Thus, the propagation constants r,a may be calculated from
J [kD Y/1 (T-iCOT]iPc = (t-i) 2 1 1 (32)Z J 0 [kD /I - (T--177]
The various solutions of this transcendental equation are common-ly attributed to various mode3.
A reasonable approximation for the fundamental mode (whichhas the smallest attenuation constant 0) can be ob~tained by afinite-difference approximation:
(rI MI(r +~2 (33)2i~ar n D n 2m)I P (rn-2!m/
S(rn) - [,p(r 2p(r ) + p (34)8 (rn 2 n T-R n ( n 2mi'
ar 2 '
where m denotes the number of elements considered in 0 .< r 5. D/2.The subscript n refers to a particular location.
Figure H7 shows the system considered for m - 2. The finite-difference approximations of Eq. (28) at the points 1 and 2 maybe written
121
L6 (-p1 +p2) + 26(2P + O (-ia2 p, 0 (35)
16 16 (p 3_p ) + k 2 [l _ ( T -ia)'] P 2
D 2 D2 2 =0(36)
D-1 (p,_2p,+p1p ) + -._ (p 3 _p,) + k2[1] - (U-ia)2 ] p2 = 0 (36)DD
The boundary conditions Eqs. (30) and (31) can be approxi-mated by
2P3 1- 2 P 2 (37)
8Z1+ ikDPc
The coefficients of the homogeneous system of Eqs. (35) to (37)vanish for
1O C+ 11 2(8-T - ics =of1 - (5)+'\_�" l +2 (38ikDpo i c ik
For 18Z/kDocl >> 1, the result
T - i -Z -Z (39)
:irrees with the general approximation for propagation constantsIn ducts of arbitrary shape, with weak effects of the absorbingwall (Ref. 3)
S- i P C i U (40)
,.'here Ua denotes the absorptive part of the duct perimeter, S the:jrea of the duct cross section.
-];,-,
- ~ -. t~fw..w w...~ n V '- -
I.
For 18Z/kDpcI << 1, Eq. (38) yields
There is no wave propagation in a duct with soft walls belowthe cut-off frequency at which
V,
kD 4 (142)
This value closely approximates the first zero of the zero-orderBessel function.
As evident for the extreme cases of rigid and soft duct lin-
ings, Eq. (38) gives a good approximation for the propagationconstant of the fundamental mode. In the vicinity of
-D c 1 (6 .i (43)k Dp c
a vanishing square-root in Eq. (38) indicates the highest attenu-
ation.
ESTIMATION SCHEME
In order to estimate the attenuation provided by a givenduct, one may proceed as described below.
1. Determine the frequency
f = c(T)/D
above which the duct may be considered as large compared toa wavelength (that is, D>),). Here c(T) denotes the speed of'sound in the gas in the duct (which speed is proportional tothe square-root of the absolute temperature).
2. Calculate the duct diameter/length ratio D/L.
1 ? .•
3. For frequencies f > fD (where X <D),
(a) If D/L< 1, find the attenuation AL from
AL = 10 log . -) ("a)
(b) If D/L>l, find the attenuation from
AL = 3.3 a D Re (16a)z D D D ~ PCf
4. For frequencies f <fD (where A >D), the lengths LS and LRof the lined and unlined duct portions (if any), must beconsidered, in addition to the type of sound source.
Consider a duct geometry as shown in Fig. H3, with a ductlining configuration as shown in Fig. H4. Radial partitionsare used in order to obstruct axial sound propagation insidethe lining. The absorptive material is assumed to have arigid, oren-pore structure; the acoustical properties re-quired for its specification are the flow resistance Eb/pc,the structure factor X and the porosity c. For a layer ofabsorptive material that is thin compared to the wavelength,X~ T'l.
(a) Calculate the wall impedance Z of the lined duct from
1I- -1- cot(kwbL)cot kd 1 -Z _K i w 1(44)
O k aok ( 1) 4
cot(kwbL) + cot kd d
where
7c = c R ' (451
and k denotes the wavenumber in free space.
(b) Find the approximate propagation constants O,T of theduct by use of Eq. (38),(39), or (41), whichever isapolicable, depending on the value of 8Z/kDpc.
. -.III I. .. . . I . . . a I . . ..IIII
* .,. , . -.-.
(c) Calculate the attenuation that results over the lengthLS of a lined duct from
ALL(dB) = 8.7 koLS
(d) Calculate the attenuation that results due to reflec-
tions at the end of the duct from
ALE(dB) = 10 log [1 + (2/kD) 2 ]
(e) Determine the attenuation due to interaction betweena lined section and an unlined tailpipe from
(0, if entire duct is lined
AL I (dB) =1Athird term* of Eq. (23), otherwise
(f) Determine the attenuation due to source effects from
AL S(dB) = third term of Eq.(24), for low-impedance source
Ithird term of Eq.(25), for high-impedance source
(g) Find the total attenuation from
AL = ALL + ALE + ALI + ALS
Sample Pesults
The results of some sample calculations are plotted in Figs.H5 andH6.Figure H5pertains to a duct which is lined over a lengthLe= 3D and which has an unlined tailpipe of the same length;t[e lining thickness is (d = D/2) and the absorbing material isa thin layer of thickness b , d/10 with a flow resistance that istwice the characteristic impedance pc of the gas. The attenuation
8.7 kaLs over a length Ls of a homogeneous lined duct and thereflection loss 10 log El + (kD/2) 2 ] of the tailpipe are plottedin Fig. H5. Figur'e H6shows the excess attenuation AL - 8.7 kaL s ,which accounts for interactions in the case of a pc-source imped-ance. The excess attenuation can be approximated by the reflec-tion loss of the tailpnpe in the frequency region where the totallength Ls + LR exceeds a quarter wavelength,
*or apnroximations, see text
125
.,"
Illustrative Calculations
High-Freguency Effect
Evaluate the effect of placing a 13 ft long duct of 1.65 ftexit diameter at the outlet of a small turbofan engine, if theflow leaving the duct is at 250'. (This duct obviously willaffect only the noise emanating from the engine outlet; a ductat the inlet will be required to reduce the noise emanating fromthat end of the engine.)
The speed of sound at 70OF is 1100 ft/sec; thus at 250 0 F,
c =1100 0+250 = 1270 ft/sec. Then460+70
f = c(t)/D (1270 ft/sec)/(l.6 ft) = 770 HzDj
At all frequencies above 770 Hz, the duct is large compared tothe acoustic wavelength.
Since D/L = 1.65/13 = 0.127, Eq. (1la) applies. If the ductis unlined, a = 0 and the attenuation provided by the duct is
AL = 10 log 10 log 13/1.65 = 7 dB1.5-a 1.5-0
at all frequencies above about 800 Hz. (If the duct contains alining with an absorptive coefficient a = 0.4, one obtainsAL = 8.5 dB. The value of a generally depends on frequency, how-ever, so that one would need to carry out the foregoing calcula-tion at several frequencies in the range of interest.)
Ducts Muffling only One of Two Like Sources
If an unmuffled (and unducted) fan produces 171 dB,re 10-12
watts at 17.5 kHz, one may assume 168 dB from the outlet and 168dB from the inlet.* Adding a duct with AL = 7 dB to the outletwould reduce the noise from that source to 161 dB, but would notaffect the inlet noise - and thus would result in a level of 169dB,re 10-12 watts (which corresponds to a decrease of only 2 dB).H1owever, adding a duct with AL = 7 dB to both inlet and outletwould reduce the 171 dB by 7 dB, i.e. to 164 dB.
*S;ee Fig. 1 for combined acoustic levels.
i;7
U. ..':.- ,,.. . ,. .,5...v 2.:• ••:..:J -•.') ", •••,•.".
Low-Frequency Effect V
Consider now what effect the previously describe!! duct wouldhave on sound at 150 Hz, if half of the duct is lined with anacoustically absorptive system having a wall impedance Z = 2.5pc(at 150 Hz), and half is unlined (see Fig. H5 for general con-figuration).
Since fD = 770 Hz, one must use item 4 of the preceding es-timation scheme. If Z is given (as obtained from experimentaldata, for example) one need not calculate it. Since
k = w1/c 2f/c - 27(150/sec)/(1270 ft/sec) 0.743/ft,
one finds !j
8Z/pc 8(2.5) 20.0 16.3kD (0.7T43/ft)(1.65 ft) = 1.3=
This value is much greater than unity; therefore Eq. (39) applies.With (4/kD)(0c/Z) = (4/1.23)(1/2.5) = 1.30 that equation becomes
S- Io = [I-i(1.30)]"• [J+(1.30) e-i arc tan 1.30 1/2
1.64e-i524 /=1.2e-i26. 20= " = 1.28e "
- 1.28(cos 26.2'-i sin 26.20) = 1.15 - i0.565
Then, since the lined length is LS = 6.5 ft,
ALL = 8 .7koLS = 8.7(0.743/ft)(0.565)(6.5 ft) = 23.5 dB
ALE = 10 log[l+(2/kD) 2 ] = 10 log[l+(2/1.23) 21 5.5 dB
/and from Eq. (23), letting = T - i,
aE ) n- e2ikLS
ALI 20 log 1+1 +I•(I•
i 2•"
e-2 ik LR
where + = 1 - + (1 +)l+ikD/2
one finds after much arithmetic that 6, -1.08 + i(2.18) andAL, 4 0 dB.
For a high-impedance source (which produces es'entially thesame acoustic pressure with and without the added duct - probablya reasonable approximation for engine noise sources) one findsfrom Eq. (25) that
AL 201log 1 - + e 2 kLS& 4 dBl+ikD/2 2ý
The total attenuation at 150 Hz therefore is 23.5 + 5.5 - 0 + 4= 33 dB.
A- - -ILI& r ~
5-...- mom
REFERENCES FOR APPENDIX H
1. Morse, P.M., "The Transmission of Sound Inside Pipes,"J. Acouet. Soc. Am. 11, p. 205 (1939).
2. Cremer, L., "Nachhallzeit und Dampfungsmass bel streifen-dem Einfall," Akust. Z. 5, p. 57 (1940).
3. Cremer, L., "Theorie der Luftschall-Dgmpfung im Rechteck-kanal mit schluckender Wand und das sich dabei ergebendeh~5chste Ddmpfungsmass," Acustica 3, p. 249 0953).
4. Kurze, U., "Untersuchungen an Kammerdgmpfern," Acustica15, p. 139 (1965).
5. Kurze, U., "Influence of Flow and High Sound Levels onthe Attenuation in a Lined Duct,' (Abstr.), J. Acoust.Soc. Am. 47, p. 122 (1970).(To be published by U. Kurzeand C. H. Allen).
6. Heins, E. and H. Feshbach, "The Coupling of Two AcousticalDucts," J. Math. and Physice XXVI, p. 143 (1947).
7. Levine, H. and J. Schwinger, "On the Radiation of Soundfrom an Unflanged Circular Pipe," Phyo. Rev. 73, p. 383(1948).
8. Kurze, U., "Schallabstrahlung an der Austritts-3ffnungvon Kanalen," Acustica 20, p. 253 (1968).
129
roj 4
ABSORPTIVE DUCTLIN IN G
FIGURE HI RAYS EMITTED FROM CIRCULAR DUCT WITHOUT REFLECTIONFROM WALLS
ro~l,-
FIGUE H RAY EMTTEDFRO DUT AFER NE RFLETIO(CONTRUCED ROM MAG SOUCES
T r
Pl P2
EI
FIGUE H LIND DCT WTH IGIDTAIPIP
PA RT ITION
d
-SOUND ABSORPTIVE MATERIAL
FIGURE H4 DUCT LINING GEOMETRY
.1'---
~. -- -. - -- 1~X-
10 +-
-jZ II-0 C0
9L 0
-LJU-
LUI
UiLA
Lii
LU -
LLU
040
LI-
C'-A
LiiIt
C N 0 it £0 0 OD 40 U 00
(S P) No iJifN31LV
49.I... ýe
* ~LLIZ
I-T I-
m LI-
caD*L M C3
1- -J
w 4 b4 Op
.7 w I-.~LLJLI
'ILL..JM
~Lo *- I o~0 = ex
410_
LU I
(nL 0. -1 Li
o<0 LL C
0 LL0
CD 00 W W- LL 0 D 0LL.~~ W 3 L
W (LD== 1(
--
TI
FIGURE H7 POINTS ALONG CROSS-SECTION OF LINED DUCTUSED FOR FINITE-DIFFERENCE APPROXIMATIONOF DIFFERENTIAL EQUATION (28)
1 36
! ! I F
APPENDIX J
GEAR NOISE
MECHANISM OF NOISE GENERATION
Tooth Contact Forces
Gear sets transmit torque and power by virtue of forcestransmitted via mating gear teeth. When a given tooth does notmake contact with a mating tooth, it is subject to zero force;when contact is made, the inter-tooth force increases, reachesa maximum, decreases, and again returns to zero when tne toothdisengages. These dynamic tooth forces, which are inherent inthe operation of gears (and which may be modified or aggravatedby inaccuracies in gear tooth profiles and gear alignment),cause the gear to vibrate. These gear vibrations may radiatesound directly, or they may cause vibrational energy to travelvia the shaft and bearings to the gearbox, which may then radiatesound into the surrounding air.
Characteristics of Noise
One may deduce some qualitative properties of the gear noisespectrum by considering the dynamic tooth interaction forces.The force acting on a gear, and thus the gear noise, may be ex-pected to have a periodic component associated with the toothcontact frequency ft. In addition, one would expect periodiccomponents at the sheft-rotation frequencies of the various inter-acting gears, due to any asymmetries and other geometric inaccura-cies of the gears.
For a geometrically perfect gear set, the force spectrum(and therefore also the sound spectrum) would have components atonly the tooth contact frequency and its harmonics, with the am-plitude of these spectral components depending on the shape ofthe force-time curve corresponding to a single tooth contact.The amplitudes of these components may be expected to be approxi-mately constant up to the frequency which corresponds to the re-ciprocal of the effective duration Teff of a contact force pulse(see Fig.Jl); beyond this frequency, the amplitudes are expectedto decrease rapidly.
i •i '.'-. .D~..
I1
For an imperfect gear, or with unsteady driving moment, theshapes - as well as the amplitudes - of the tooth-force pulsesmay vary with a period that corresponds to the shaft-rotationfrequency fs, as sketched in Fig. Jl. Because of this "amplitudemodulation" of the tooth force pulses, the spectra here may beexpected also to contain components at the shaft rotation fre-quency and at harmonics of that frequency. Measured spectra ofgear noise (e.g., see Fig. 10 of Ref. 1) are in agreement withthe foregoing qualitative considerations.
DATA
Available Data
Although much work has been done on gear noise, only quali-tative understanding of it rests on a relatively firm basis.The present state of the technology does not permit one to predictthe noise of a gear set from the basic physical parameters of thatset (except from correlations of empirical data), and generallyalso does not permit one to predict with much confidence the ef-fects of design changes on noise. A number of relevant recentpublications are indicated in the appended reference list.
The only available collection of data on the noise of manydifferent gears, measured under well-known conditions, appears tobe that of Refs. 1 and 2. These references summarize the resultsof noise measurements on 76 sets of power gears (including spurand bevel gears and planetary sets) transmitting between 10 and25,000 kw (7.5 and 18,500 Hp) at peripheral speeds between 3.6and 160 m/sec (12 and 525 ft/sec) with gearing ratios up to 256.
nependence of Overall Noise on Transmitted Power andTooth Force
A careful statistical analysis of the measured rear noisedata revealed a strong correlation (0.87 correlation coefficient)between the total acoustic power produced by a gear set and themechanical power transmitted by that set. A similar correlationwa• found between noise and the average tooth force.
Figure J2 (taken from Ref. 2) shows how the measured overall:•c,und power levels of gear sets vary with the transmitted power(which for these measurements was between 75% and 100% of the
d(-,e n power f'or the sets tested). Also indicated in that figure!:; n line which corresponds to the mean of the measured points,a.- well as dashed lines which correspond to one standard devia-1. •cn from the mean. An equation for the mean line is also givenin the fifure.
el1
Noise Spectra
Octave-band noise spectra, derived from Refs. 1 and 2,are presented in Figs.J3,J4 andJ5 for the three classes ofgears and speeds treated in the original references. Fipures J3and J4, which may be seen to be very similar, pertain to plane-tary and spur gear. sets operating at relatively high speeds;Fig.J5 pertains to gears of various types operating at lowerspeeds.
The spectra in Figs.J3-5 are presented in terms of differ-ences between overall levels and octave band levels. In addi-tion to spectra corresponding to the means of the data, curvesare given which correspond to the mean + standard deviationi.
PREDICTION CURVES
By combining the average dependence of overall acousticpower on transmitted mechanical power, as given in Fig.J2, withthe spectra of Figs. J3-5 one may arrive at octave-band spectraof sound power referred to mechanical power.
Figure J6 shows mean spectra obtained in this manner, andis readily applicable for general. noise estimation purposes.Because of the similarity of the mean-curves of Yips.J3 and J4,these two have been combined (averaged and smoothed) into asingle "high-speed" gear noise curve; the "low-speed" curve isobtained directly from Fig. J5.
ESTIMATION SCHEME
In order to estimate the noise produced by a gear set (twomating gears), one may proceed as follows:
1. Select the curve of Fig. J6 that corresponds to the rota-tional sneed (rtm) of the smaller (. _,er-sneed) gear.
2. Calculate 10 log((Hp), where Hp is the mechanical horse-power transmitted by the gear set, and add this value tothe numbers shown along the vertical scale of Fig. J6.The resulting numbers then represent the octave-handsound power levels for the gear set.
3. Calculate the tooth contact frequency from
ft(Hz) = Nt(rpm)/60
where Nt is the number of teeth on either gear and rpm i.:the rotational speed (in revolutions/mmn) of that ;aTe gear.
-- =: . . .. .. : - , " :' ••= . • .'} . ? ' .- " * . : ,, . : .- .
Then, for aural detection estimation, take the levels (ob-tained from the foregoing steps) at frequencies ft, 2ft,
3ft to correspond to pure tones, and the levels for octavebands above 3ft to correspond to broad-band noise. Deleteall parts of the spectrum of Fig. J6 below ft. (No appre-ciable noise is produced at these low frequencies.)
Illustrative Calculation
Consider a gear set transmitting 100 Hp, with the smallergear (which has 18 teeth) rotating at 3000 rpm. Here
A•..
10 log(Hp) = 20
ft = Nt (rPm)/60= 18(3000)/60 = 900 Hz
This is a "high-speed" gear set (rpm > 1500); the dashed curveof Fig. J6 applies. For aural detection estimation, one thusobtains the following pure tone noise levels:
f(Hz) 200 1800 2700 f
Lw(dBre 10-12 watts) 91 89 86
olus the following octave-band levels:
f(Hz) W40o 8000
L (dn,re 10-12 watts) 85 78
with no significant noise below 900 Hz.
J 5
77.-" .... . . .. . . . .
II
REFERENCES FOR APPENDIX J
1. Zumbroich, J., "Untersuchungen des GerauschverhaltensModerner Hochlastgetriebe," PhD Thesis, TechnischeHochschule Aachen, June 1964.
2. Opitz, H., J. Zumbroich and J. Timmers, "Serienunter-suchungen des Gerauschverhaltens Moderner Hochlastgetriebe,"Indu8strie-Anzeiger, Essen, 87, No. 96, pp. 445-455 (1965).
3. Schlegel, R. C., R. J. King and H. R. Mull, "How to ReduceGear Noise," Machine Design, 6, pp. 134-142 (27 Feb. 1964).
4. Michalec, G. W., "Vibration in Geared Systems," MachineDesign, 37, pp. 164-173 (16 Sept. 1965).
5. Niemann, G. and M. Unterberger, "Reduction of Gear Noise," FVDI Zeitschrift 101(6), pp. 201-212 (1959) German.
6. Klykin, I. V., "Controlling the Noise of Reduction Gearingand Marine Internal Combustion Engines," in "Control ofNoise and Vibration in Ships," U. S. Dept. of Commerce,Office of Technical Services, Report No. DTS 63-21340,Chapt. 17, pp. 346-353 (1963).
7. Nakamura, K., "Experimental Studies about the Effects ofDynamic Tooth Loads upon Gear Noise," Bull. Japan Soc. Mech.Eng. 10(37), rp. 180-188 (1967).
8. Nakamura, K., "Tooth Separations and Abnormal Noise onPower Transmission Systems," BuZZ. Japan Soc. Mech. Eng.,10(41), pp. 846-854 (1967).
9. Thomson, D. C., "Investigation of the Relationship betweenGear Design and Tooth Noise," Marine Engg. Lab., Annapolis,Maryland, Report No. 1.78164 (Sept. 1964).
10. Ehrenreich, M. and M. Rubin, "Noise Analysis of a VehicleTransfer Gearbox," Proc. Inst. Mech. Engra. AD, 175, pp.337-350 (1960-1961).
11. Rosen, M. W., "Acoustic Studies on Power Transmission,"in Underwater Missile PropuZsion, Ed. by L. Greiner, CompassPublications, Arlington, 'Ia. (1967).
12. Rabek, E. E., "Airborne and Structure-Borne Noise of Smallnlear Motors," J. Sound and Vibration 9., pp. 8-14 (June 1967).
14 1
S/.
fs a SHAFT ROTATION FREQUENCY
ft a TOOTH CONTACT FREQUENCY
Teff - EFFECTIVE CONTACT FORCEPULSE DURATION
W Tt l/f T$s"1/f= -.u tINDIVIDUALn- ,•,' FORCE PULSE
u.Teff
TIME
FIGURE J1 SCHEMATIC TIME-VARIATION OF GEAR INTERACTION FORCE
-~0
0
______ _ ___ ____
00 d
0
tLL.
+ zr___0____
0. LA-
0-
0 Of t ~
a_ _ _ _ _ _ C CD
-- LN
it___ -o N z '
__ -cr
00 C~
LU
o 0
n (I - 0
I--
MEAN + e ,
MEAN
-10
MEAN -o"c r
-20I I
%
Lw =SOUND POWER LEVEL INOCTAVE BAND(dB, RE 10"2 WATTS)
-30 L.(oWOVERALL SOUND POWERLEVEL(dB, RE 10-'? WATTS)
o =STANDARD DEVIATION j
-4063 125 250 500 1000 2000 4000 8000 16000
OCTAVE BAND CENTER FREQUENCY (Hz)
FIGURE J3 OCTAVE-BAND SOUND P014ER SPECTRA FOR PLANETARY GEARS,RPM > 1500
0
II
-30 ~ ~ ~ ~ ~ .- Nk~OEAL ON OE
.- #,
( RWA
-20
63 15 20 0 00 200 40 "80 60
" "Lw =SOUND POWER LEVEL IN
OCTAVE BAND(dB, RE 1O-'PWATTS)
-F0 LE(oA CTOVERALL SOUND POWERLEVEL(dB, RE ]0-'2wATTS)
ar STANDARD DEVIATION
-40163 125 250 500 1000 2000 4000 8000 16000
OCTAVE BAND CENTER FREQUENCY (Hz)
FIGURE J4 O)CTAVE BAND SOUND POW•ER SPECTRA FOR SPUR GEARS, !RPM > 3000
I ~4 I
0....- -. tA
44
-10 %
0
"J -20
-J Lw =SOUND POWER LEVEL INOCTAVE BAND(dB, RE IO-'? WATTS)
-30 Lw(oATOVERALL SOUND POWERLEVEL '
(dB, RE 10-12WATTS)cT=STANDARD DEVIATION
-40
63 125 250 500 1000 2000 4000 8000 16000
OCTAVE BAND CENTER FREQUENCY (Hz)
FIGURE J5 OCTAVE BAND SOUND POWER SPECTRA FOR SPUR, BEVEL, ANDBEVELSPUR GEARS, RPM < 1500
'111
SO
HIGH-SPEED GEARSRPM 1 500•
70
C.x LOW-SPEED GEARScp RPM < 1500•
soN7 600
Lw a SOUND POWER LEVELIN OCTAVE BAND
50 (dB, RE 10-' WATTS)Hp - MECHANICAL POWER
TRANSMITTED BY GEAR (Hp)
40, I I L63 125 250 500 1000 2000 4000 8000
OCTAVE-BAND CENTER FREQUENCY (Hz)
FIGURE J6 ESTIMATION OF GEAR NOISE
4. 4., ~ ~ 4 ...~- .4-.- .4% *-I
Ft
APPENDIX K
SOUND RADIATED FROM FLOW OVER RIGID SURFACES
SOUND FROM TURBULENT BOUNDARY LAYER
Infinite Surface
The sound power radiated to the atmosphere (per unit area)from an infinite turbulent boundary layer supported by a rigidflat surface provides a lower bound for the sound power radiatedby a finite system. Because of this fact, and because analysisof the inflnite case is relatively simple and exhibits the im-portant parameters, presentation of a summary of the analysis isJustified here.
Mathematical Model of Boundary Layer
Extensive experimental and theoretical work has been done toobtain descriptions of the pressures on surfaces under turbulentboundary layers (Refs. 1-6). These pressures usually are des-cribed in terms of space-time correlation functions
ScP(x ,x3,t) =- p(XX 0,X30,t0)P(XIo+xIX30+x3,to+t)> (i2
where xl0 and X3. rep resent coordinates on the surface, x, Inthe direction of the flow and x30 perpendicular to the flo di-
r -i1on; x, and x 3 represent the separation between two observa-cion noints, the brackets <...> indicate averaging over xxand time t,. One may calculate the wavenumber-f•.oquency spectrumof the pressure as:
,Pp (k ,w) =- f/f-p ,t)e-(L--n*1wt) dx dt (2)(27r)
where k is the wavenumber vector, with the components k, and k3,and x is the separation vector, with components x1 and x 3 , and wrepresents the radian frequency.
It has been shown (Ref. 1) that the observed behavior of thewavenumber-frec)uency spectrum may be represented by
Pp- (k' W) f(w) *dlk,(w) - ,-1 31k,(w)1 (3)
l48.- ~**... .*I~V.3
.4
where Yf(w) represents the frequency spectrum one measures with atransducer that is fixed at one location on the surface$ Pd(ki)describes the decay of eddies in the flow direction, and t3(k3)
is the wavenumber spectrum in the cross-stream direction.
The two wavenumber spectra typically obey
4)d(kl) = (L /n)(l + k L2) (4)
i 3 (k 3 ) (L3/n)(l + k2L2) (5)
where Ld represents the eddy decay length, which may be approxi-mated by
L 9U /W (6)d c
and L 3 is the transverse correlation length, which may be approxi-mated as
L 3 f Uc/0.7w (7)
in terms of the convection velocity Uc, which is approximately0.7 times the free-stream velocity U.
The "fixed transducer" spectrum Cf(w) may be determined fromthe corresponding normalized spectrum, which is given in Fig. K1and further discussed below.
Sound Radiation
Only those fluctuating pressure components for which thewavenumbers kp are smaller than the acoustic wavenumber k = w/c
(where c represents the speed of sound) contribute to the soundradiation. Accordingly, the spectrum of the radiated acousticpressure at the wall is given by
4P(W) = f(W) fd k "- 3 ) 3 •dkdk, (
(I +Z3 <k)
1 3
If one substitutes Eqs. (4), (5), (6) and (7) into Eq. (8)9 andlimits oneself to the usual case of interest here where the con-vection velocity Uc is much smaller than the speed of sound(Uc << c), one obtains
(1 +7 3<k)
(9)
4f(w) [6.3t2]z "rk2
With Uc C 0.7U, this result reduces to
Oac(w) 2.5 x< 20- 2 M2 P f(W) (10)
where M= U/c represents the pac. number of the free-stream flow.
Equation (10) gives 1he accuscic pressure spectrum in termsof the boundary layer pressure spectrum. From this result onemay readily obtain the relation
p2/Pz v 2.5 x 10-2 M2 (1)
which holds between the mean-square acoustic pressure p2 in agiven frequency band Aw and the mean-square pressure P~l in theboundary layer in the same band; these pressures are related tothe siectra as
=2 fOac(w)dw pbI f Pb f (w)dw . (12)
The acoustic power W radiated from a surface of area A maybe estimated from
W = Ap 2 /4pc (13)
where p repiresents the density of the air, as usual.
-. '. . IqlA .i.*:..%
Frequency Distribution
The fixed-transducer spectrum of boundary layer pressurefluctuations, which also determines the spectrum of radiatedsound in view of Eq. (10), may be determined from the normalizedfixed-transducer spectrum t'(w)U/6* shown in Fig. Klas a functionof the dimensionless frequency (Strouhal number) S = w6*/U, where6* represents the displacement thickness of the boundary layer.
The spectrum values are adjusted so that Pl(w) satisfies therelation
f $'Ui)dw = 1 ; (14)
then the actual spectrum Df(w) is related to the normalized spec-trum 0'(w) as
(P ) = P0A If(W) (15)
in terms of the overall mean-square fluctuating pressure pOA in
the boundary layer. From Fig. K1 and Eq. (15) one may deduce howthe fluctuating pressure 0 2 in third-octave bands varies with-blfrequency; the result is indicated in Fig. K2.
The boundary layer displacement thickness 6* is a functionof the Reynolds number and Mach number. For low Mach numbers,and for Reynolds numbers in thL range between 106 and 107, whichis of primary interest for small aircraft, one may estimate 6*from
6* z 0.0025 X (16)
where X is the distance from the front (leading edge) of the bodyof concern (Ref. 7).
ln order to estimate the actual levels, one still requiresthe mean-square overall boundary layer, pressure D2 There
exists much evidence (Ref. 8) that the correspondinf, root-mean-square pressure is proportionai to the free-stream dynamic pres-sure q. The constant of proportionality denends on Reynolds num-ber, Mach number, and surface roughness, but for most smooth air-craft surfaces one may take
POA 0.006 q (P')
Effects of Surface Edges
Whereas pressures acting on a rigid surface can pive rise tono appreciable acoustic particle velocities, pressures near anedge do not encounter the high impedance of the surface and thuscause greater velocities, and therefore more noise radiation.Thus, the noise associated with edges is likely to dominate overthe noise from boundary layers on relatively rigid surfaces. Thenoise associated with edges is discussed in the following section.
SOUND FROM FLOW PAST FINITE BODIES
Airfoil in Large-Scale Turbulent Flow
A body moving through a turbulent fluid experiences unsteadylift and drag forces; the related reaction forces on the fluidare responsible for sound radiation. In most practical cases ofinterest, e.g., of an aircraft flying through atmospheric turbu-lence, the spatial scale of the pressure fluctuations is consid-erably larger than the airfoil dimensions. There then occur liftand drag fluctuations, which act essentially like acoustic pointdipole sources. (The point source approximation is valid becausethe associated acoustic wavelengths are much greater than thecharacteristic surface dimensions.)
The acoustic nower W radiated by a point dipole at frequencyf is given by
W = vF 2 f 2/3Pc 3 (18)
where F2 represents the mean-souare fluctuating force, 0 the den-sity of the ambient air, and c the speed of sound in air.
One may express the root-mean-square fluctuating lift ordrag force in terms of the corresponding lift or drag coefficientGL(or D) as
1 lu 2lC (u /U) (9L(or D) 2 pAL(or D) rms (19)
where U reoresents the free-stream (mean) velocity , A a reference;ýirea, and urms the root-mean-square fluctuating velocity. If onebnowzt the turbulence spectrum urms(f)/U, one may then calculatethJ( corresponding force spectra, and from these, the associatedacoustic power.
1',:j
Measurements by Clark and Ribner (Rpf. 9) have verified theproportionality of sound radiated from an airfoil in large-scaleturbulent flow to the mean-square fluctuating force on the air-foil, and Sharland (Ref. 10) has observed that the directivitypattern of the sound radiation from such an airfoil is like thatof a classical dipole..
Smal 1-Scale Turbulent Flow over Airfoil
If the disturbances on the airfoil and the associated acous- -
tic wavelengths X are small compared to the airfoil dimensions(e.g. the chord b), one no longer has the effect of point dipolesInstead, for A < b, one has essentially arrays of unsteady forcesacting at the various edges (Refs. 11, 12).
Chanaud and Hayden (Refs. 11-13) have considered two separattrailing-edge noise sources*: (1) interaction of turbulent bound-ary layer with the edge, and (2) forces due to wake vortices act-ing on the edge. By analysis of the problem in terms of dimen-sionless groups of parameters and application of empirical data.they have derived the following prediction expression for theoverall acoustic power level:
L X + 10 log (6wU 6 ) - 5 (20)w(OA)
where Lw(A) = overall acoustic power' level (dB, re 10-12 watts)
w = spanwise dimension of edge (ft)
U = free-stream velocity (ft/sec)
6 = boundary layer thickness or wake thickness (ft)
X -27 dB for boundary layer/edge interactionX = -23 dB for wake vortex effect.
The corresponding octave band spectra (Ref. 13) may be obtainedfrom Figs. K3 and K4.
The turbulent boundary layer thickness 6 at the trailin7edge of an airfoil depends on the angle of attack, the surfacecondition of the airfoil, and the smoothness of the inflow.
*No corresponding leading edge studies have been undertaken, butbecause the pressure fluctuations at the trailing edee 'enerallvexceed those at the leading edge when the inflow is undisturbed,trailing edge noise tends to dominate.
1"•
Unless one has better information, one may estimate 6 from thecorresponding value for a smooth flat plate, for which
6 :0.4 bA (v/U)(21)
where 6 and the chord b are in units of ft, v represents thekinematic viscosity of the air (ft 2 /sec) and U is the free-streamvelocity (ft/sec).
The wake thickness 6W also depends strongly on the condition
of the airfoil. For thin tapered-edge airfoils at small anglesof attack one may estimate 6 as the sum of the airfoil edgewthickness and 26. For airfoils at considerable angles of attack(say, lal > 50), one may estimate 6W from
6 z b sina (22)
where b is the chord length. Note that narrow-band wake noise.ioldom occurs for Jlj > 5', and only boundary layer/edre inter-action noise is significant for such cases.
ESTIMATION SCHEME
Flow Over Fuselage
In order to estimate the broad-band noise Produced by turbu--lernt flow over a fuselage (or similar body), one may proceed asfollows:
1. Divide the fuselage into a number of convenient re7.ions over
which the boundary layer is relatively uniform.
2. V,'or each region,
(a) Determine the boundary layer displacement thickness 6*by using available aerodynamic data or estimatinr onthe basis of
6* = 0.0025 X
where X represents the distance from the aircraft noseto the middle of the region. Then calculate the actualfreciuencies f that correspond to the reduced freauen-c.; f6*/UI shown along the horizontal axis of Fig. K2.
S... . -•" """''A A I
(b) Determine the corresponding octave band sound power
level Lw(OB) by adding*
51 + 20 log q (lb/fpt 2 ) + 10 log A (ft 2 )
to the numbers shown along the vertical coordinate of'Fig. K2.
4. Combine the octave-band levels for all regions (band by band),by the method discussed in the main text and Fig. 1 of themain text.
Flow Over Airfoils
In order to estimate the noise produced by flow over airfoils,proceed as follows:
1. Find the (broad-band) noise due to turbulent flow by
(a) Estimating the boundary layer thickness 6 at the trail-ing edge, either from aerodynamic data or by use ofEq. (21)
(b) Calculating the overall acoustic power level from Eq.(20), with X = -27 dB
(c) Determining the octave-band spectrum by use of Fig. K3.
2. Find the (essentially pure-tone) noise associated with vor-tex shedding by
(a) Estimating the wake thickness, either from aerodynamicdata or from
= 6te + 26 for Icl < 508W
b sina for jal > 50
*By combining Eqs. (11), (13) and (17), taking p = 0.07 lb/ft 3
and c = 1100 ft/sec, and using the standard definitions and re-ference value for power level, one finds that
Lw = 10 log [1.3 x l05 q 2 (lb/ft 2 ) A (ft 2 )] + 20 10c [PO3/DOA]
7?
where 6 represents the airfoil's trailinv edge thick-
ness. (Note that vortpx noise occurs only very rarelyfor jai > 5o.)
(b) Calculating the overall acoustic power level from Eq.(20), with X = -23 dB.
(c) Determining the octave-band spectrum by use of Fig. K4.(For aural detection estimation, use the value atfSw/U z 0.2 as a pure tone, and consider remainder of
spectrum as broad-band noise.)
3. If the (predominantly low-frequency) noise due to fli'~htthrough large-scale turbulence is of concern, estimate thisnoise for a specified turbulence spectrum u (f)/U by
rms(a) calculating the fluctuating lift and drafr forces from
Eq. (19)
(b) using Eq. (18) and Lw = 10 log (W/Wre ) to determine
the sound power level at each frequency.
f1
ZIA-
REFERENCES FOR APPENDIX K
1. Chandiramani, K.L., "Fundamentals Regarding SpectralRepresentation of Random Fields--Application to Wall-Pressure Field Beneath a Turbulent Boundary Layer,"BBN Report No. 1728, (15 September 1968).
2. Ffowcs-Williams, J.H. and R.H. Lyon, "The Sound Radiatedfrom Turbulent Flows near Flexible Boundaries," BBN ReportNo. 1C54, Contract Nonr 2321(00) (August 1963).
3. Corcos, G.M., "The Structure of the Turbulent PressureField in Boundary-Layer Flows," J. Fluid Mech., 18, pp. 353-353-378 (March 1964).
4. Corcos, G.M., "Resolution of Pressure in Turbulence,"JASA, 35, pp. 192-199 (1963).
5. Willmarth, W.W. and C.E. Wooldridge, "Measurement of theFluctuating Pressure at the Wall beneath a Thick TurbulentBoundary Layer," J. Fluid Mech., 14, pp. 187-210 (1962).
6. Bull, M.K., et at., "Wall Pressure Fluctuations in BoundaryLayer Flow and Response of Simple Structures to RandomPressure Fields," University of Southampton AASU Report 243,(July 1963).
7. Bies, D.A., "A Review of Flight and Wind Tunnel Measurementsof Boundary Layer Pressure Fluctuating and Induced Struc-
tural Response," NASA CR-626 (1966).
3. Chandiramani, K.L., S.E. Widnall, R.H. Lyon and P.A. Franken,"Structural Response to Inflight Acoustic and AerodynamicEnvironments," BBN Report No. 1417 (July 1966). Preparedfor NASA Marshall Space Flight Center.
9. Clark, I-.J.F. and H.S. Ribner, "Direct Correlation ofFiucLuating Lift and Radiated Sound for an Airfoil in Tur-bulent Flow," J. Acoust. Soc. Am., 46, 3 (Part 2), (1969).
10. Sharland, I.J., "Sources of Noise in Axial Flow Fans,"J. Sound and Vibration, 1(3), (1964).
11, Hayden, R.E., "Sound Generation by Turbulent Wall Jet Flowover a Trailing Edge," M.S. Thesis, Purdue University (1969).
12. Hayden, R.E., Paper FF-10 with R.C. Chanaud, 1910 SpringMeeting of the Acoustical Society of America, Atlantic City,New Jersey.
13. Chanaud, R.C. and R.E. Haydan, "Edge Sound Produced by TwoTurbuient Wall Jets," Paper FF-II, 1970 Spring Meeting ofthe Acoustical Society of America, Atlantic CliCy, Ne,', Jerscy.
1 ' 7I
54-
2-
0.1 -F
eGO 4
2 -
• 4
U FREE-STREAM VELOCITY
0.01 8' BOUNDARY LAYER
DISPLACEMENT THICKNESS
5- O -NORMALIZED SPECTRUM4 - OF PRESSURE
S- wm 2ff, RADIAN FREQUENCY
2-
0.001 t lI i I | I i J
0.03 8o.1 2 3 5 1,8 1 2 3 5 8 0 20
o811/u
FIGUIRE K1 NORMALIZED FIXED-TRANSDUCER SPECTRUM OF PRESSUREFIELD LINDER TURBULENT IOUNDARY LAYER
I Co
U.40
0t
w~cozl
__ w zi~f~~
__ ILI-. ~ L J ~ ~ 6 QL
>- 41 w
8I I i Ir 400
w >U
cr U .1 ''.1
I • • • ;,•, - • . '. • .• . .. ': .. • ;
vr I
20 I III'" ' I 1 jI I I I I I
LW(O10 r ACOUSTIC POWER LEVELIN OCTAVE BAND
10 LW(OA) = OVERALL ACOUSTICPOWER LEVEL
f OCTAVE BANDCENTER FREQUENCY
S0 x WAKE THICKNESS
- U FREE- STREAM VELOCITY
0
-_ - 1 0
-20
-30
0.063 0.0125 0.025 0.05 0.1 0.2 0.4 0.8
WAKE STROUHAL NUMBER Ss faw (DIMENSIONLESS)U
FIGURE K3 EDGE NOISE SPECTRUM FOR TURBULENT BOUNDARY LAYERSFLOWING OVER A TRAILING EDGE
20 "1 Ii yr I I ' 'I |
Lw (o0) ACOUSTIC POWER LEVELIN OCTAVE BAND
10 Lw (OA) -OVERALL ACOUSTICPOWER LEVEL
f = OCTAVE BANDCENTER FREQUENCY
0 8w = WAKE THICKNESSU a FREE-STREAM VELOCITY
"-20
-30
-40 III
0.0063 0.0125 0.025 0.05 0.1 0.2 0.4 0.8WAKE STROUHAL NUMBER S- (DIMENSIONLESS)U
FIGIIRE K4 WAKE NOISE SPECTRUM FOR AIRFOILS AT SMALL ANGLES OFATTACK
10
APPENDIX L
SOUND RADIATION FROM BEAM-REINFORCED
PLATES EXCITED BY POINT FORCES
INTRODUCTION
An unsteady. force applied to an aircraft structure (e.g.,to a stringer or directly to the skin), sets this' structure intomotion, and such motions lead to the radiation of sound. Thissection oresents an approach toward estimatin'g thle sound radi-ated from typical aircraft structures ex~cited by a normal pointforce.
Aircraft surface structures typically consist of a thinskin, reinforced at intervals by stringers, rings, frames, etc.For the present approximate prediction purposes it :;uffices toconsider all such structures as thin flat plates with straightreinforcing beams, and to address the two simplest and most sig-nificant corresponding sound radiation problems. Accordingly,the following paragraphs deal with sound radiation from beam-reinforced plates: excited by oscillating localized (point)forces, which act normal to the plane of the plate, either onthe skin or on a reinforcing beam.
POWEP INPUT FROM POINT FORCE
Admittance of Beam-Plate System
'Tlie point innut admittance Yc of a system which consistz; ofLn infinitely long, uniform reinforcing, beam connectu;d continu-ously all along its length to a uniform plate of infinite extentj:; given (Ref. 1) by
v y [ + (3-r2)cos-'r + (3+r2)sin:I r1b U IMb 2r'( -r)l/2 .-r'
Thil: expression applies for the simplest case in which the ex-c-Iting force Is so located and the beam section is of such a *
.hapci that the beam does not twist a. it flexe- The first tern,
YV = [2rcb (l+i) ]- 1 (2)
represents the point input admittance of the beam in absence ofthe plate, whereas the rest represents the contribution due tothe plate. The symbols employed in the foregoing relations havethe following definitions:
w - 2nf = radian frequency
mb = mass per unit length of beam
I = B/D 121/h3
r= cp/Cb
B - EI = bending stiffness of beam
"D Eh 3 /12 = flexural rigidity of plate
E - Young's modulus
I = centroidal moment of inertia of beam cross-section
h = plate thicknessCp [whCL/1/T]
S= [speed of bending waves in plate
c b = I-a-IcL = speed of bendin- waves in beam
CL = V s7 = longitudinal wave velocity
P = density of material of beam and plate
0I = radius of gyration of beam cross-section
Admittance of Plate
The point input admittance of an infinite plate is given(Ref. 2) by
Y = 8 r 4h2 _ h2pc (3)
where m is the mass per unit area of the plate. This expressionalso represents the frequency-average of the admittance of afinite plate, provided that the averaging interval encompassesseveral resonances (Ref. 3).
Power Input
The power Win supplied to a system by an oscillating forceof amplitude F depends only on the real part of the input admit-tance Y,
Win -- IFI 2Re(Y) ; (4)
ini
hence one obtains
for excitation on beams ofSI12 / 8 mbcb beam-plate systems
SI F I 2 /16/5m p for excitation plates
EXCITATION ACTING ON BEAM OF BEAM-PLATE SYSTEM
Components
The sound radiation here may be considered as composed ofthree parts:
(1) radiation from the vicinity of the excitation point (near-field radiation),
(2) radiation from waves propagating along the beam, arid
(3) radiation from reverberant vibration field on the plate.
Near-Field Radiation
The acoustic power radiated by the near-field in the vicin-ity of the excitation point may be approximated (Def. 7) bv
" "V4: 0.34(A +W)pcxbV 2 (6)
where X T hhCL / '3 c = fLexural wavelength of plate at criticalfrequency
X11= c /f = bending wavelength of beam
w = width of' beam
p = dens;ity of ambient air
c = speed of sound in ambient air
v = veflocity amplitude at excitation point.
V'.,-I, v I'Yjcl nd Yc as given by La. (.),one may then readilyde(ii~ne the power W,
Radiation froyi Waves Propagating along Beam
'Niea:(? reinf'oreing beams typically are strongly coupled totIh, plate, eiiergy in waves travelling along the beam tend, to be
,. ;njgn i .te-d int~o the plate within a relatively short distance.(,. ''' 'i, I, tinn from these propat-.tinr, ,r.wave.ý tends to be neg-
<1 !")1('
•-I Iw P I I
Radiation from Plate; Estimation Scheme
The plate flexural wavenumber in the direction parallel tothe beam is equal to the wavenumber kb = w/cb for waves on thebeam. This wavenumber component is small compared to the (total)wavenumber k W/c for free bending waves on the plate. There-fore, free plate flFxural waves propagate in directions nearlyperpendicular to the beam (Ref. 4).
If the plate is infinite and if c < c, the free flexuralwaves radiate no sound at all; if cp > c, they radiate well.However, the plates in actual aircraft structures cannot be con-sidered infinite, so that infinite-plate results here are rela-tively meaningless.
As plate waves propagate along a finite structure, they soonencounter beams, where they are partly reflected and partlytransmitted. In any bay between reinforcing beams the initialand multiply-reflected waves build up a reverberant wave field,in which amplifications can occur as the result of resonance ef-
fects, and where sound is radiated because of interaction of theplate waves with the boundaries. In order to analyze this casemost simply, one may make the very reasonable assumptions thatall of the power supplied to the structure is transmitted to theplate, and that in the steady state the power input to the platemust equal the power lost by the plate.
The loss of power from a finite panel may be considered asconsisting of two parts: acoustic radiation (W) and mechanicaldissipation (Wd). Hence one may write an energy balance
Win ' 2W + Wd = A<v 2 >(mpwn + 2pco) (7)
where A = area of plate (one side)
n = loss factor of plate
<v 2 > - mean-square velocity of platea = acoustic radiation efficiency.
The factor 2 appears in the above equation, because acoustic en-ergy generally is radiated from both sides of a plate. The acou,;-tic power radiated from one side may then be written as
Win
W = A<v 2 >pccr Wi n+
pca
where the second form was obtained by use of Eq. (7). Win may 1,tcalculated from Eq. (5).
EXCITATION ACTING ON PLATE
If a force acts on a finite plate, there again results areverberant flexural wave field on the plate, as previously dis-cussed. Whereas the plate wave field due to excitation on a beamtndus to consist primarily of wave components propagating perpen-dicular to the beam, tnat due to point excitation directly on theplate tends to be more homogeneous in direction.
However, the same energy balance considerations apply hereai: before, so that Eq. (8) applies for the present case as well;tihe only difference is that Win and 0 rad are different for thetwe excitation conditions. Win here is given by Eq. (5), and
0 rac here is computed on the basis of the entire plate perimeter(ue iPig. LI).
ESTIMATION OF LOSS FACTOR AND RADIATION EFFICIENCY
Loss Factor
In srhito of considerable effort that has been expended onthe problem, th(.rv -till exists no reliable general means forn!ed) etictno- the clcs factor n of realistic aircraft structural
,I'-nI(-.. -ome .oues' rediction means are suglieted in Ref. 5, but_..r 'truotur- <. Iow are as complex as those ýn actual aircraft,I.- pr.-nr ict1,,w! f..a:e..; are not much more reliable than simply
Radiation Efficiency
T aoist3 e -adiation cIf cienc; oa ' 'eam-reinforced
I.I' i,:: :,.,, a•iclyzed in .rf; . 3 and , am] 5.. a 1iscusse(11, ,, :.i I,.k" ( ''' , 7). Yi-ureb]:uml ~ z:• the dependence
" " , ;firl t,: uanol on i'm. 3201e: amid time various pane)
". , 1..li." r'. U-s(-(i to e•t,-t .e a
ESTIMATION SCHEME
i, idci' to e:ntimate the si(,urd radiated from a panel excitedvn ,soCLlator'v point force of' amrlitude 171 acting either di-
:,C'ctjy5 is tite panel or on a reinif'orcinv. beam (or rib) at theu 1' 'de-,, one may proceed as-, follows:
i. i.-. m.--. ,Ii to esti 'ite tliw -iidiation efficiency, as a func--' ,,,'* Ie'i•u eney. 'Tils 1 e:at don': by calculatinr the
values u!, tihe various pararetc-Ž's lmiluated in the fiture, ti-i ]C aI iyr'aniD like that in Wir-. bl, based on those
I I
' .. . - =: ;.1. '..;2..tC i g.• • : i &u.. .,•:
* * r ,. la ' --
2. Find the power input Win from the appropriate form of Eq. (5).
3. Calculate the radiated power W (at each frequency) from Eq.(8) (using the structural loss factor value n z 0.01 unlessbetter information is available) and determine the soundpower level from Lw 10 log (W/Wref).
i
1 ~'
REFERENCES FOR APPENDIX L
1. Lamb, G.I., Jr., "Input Impedance of a Beam Coupled to aPlate, J. Acoust. Soc. Am. 33, 5, pp. 628-633 (1961).
2. Ungar, E.E., "Mechanical Vibrations," Chapt. 6 of MechanicalDesign and Syste:ns Handbook, Ed. by H.A. Rothbart, McGraw-Hill Book Co., Inc., New York (1964).
3. Smith, P.W., Jr., and R.H. Lyon, "Sound and Structural Vi-bration," NASA CR-160 (March 1965).
4. Cremer, L. and M. Heckl, K5rperschall, Springer Verlag (1967).
5. Ungar, E.E., "Damping of Panels," Chapt. 14 of Noise andVibration Control, Ed. by L.L. Beranek, McGraw-Hill BookCo., Inc., New York (1971).
6. MaJdanik, G., "Response of Ribbed Panels to Reverberant
Acoustic Fields, J. Acoust. Soc. Am. 34, 6, pp. 809-826(1962).
7. Ver, I.L. and C.H. Holmer, "Interaction of Sound Waves withSolid Structures," Chapt. 11 of Noise and Vibration Control,Ed. by L.L. Beranek, McGraw-Hill Book Co., Inc., New York(1971).
-~ l
I-I
wcTJ
higi freq
O'hioh ,reqISo'plateau XC /A
b ,!.b
>-
a•
w plateauU.
w f, C r--1]-PANEL FUNDAMENTAL
RESONANCE FREQ.
f2 100 p2
< f3 w fC/4
fc seVco/'rhcL ,CRITICAL FREQ.
flf2 f3 fc
FREQUENCY f (LOGARITHMIC SCALE)
P s EFFECTIVE PERIMETER OF PANEL*
x c = c0 /c a PANEL FLEXURAL WAVELENGTH AT CRITICAL FREQUENCYA x PANEL AREA (ONE SIDE)
uL LONGITUDINAL WAVE VELOCITY IN PANEL MATERIALcc s SPEED OF SOUND IN AMBIENT AIR
h z PANEL THICKNESS
* FOR EXCITATION ON PANEL, P s ACTUAL PANEL PERIMETER
FOR EXCITATION Olt BEAM P x 2* (LENGTH OF EXCITED EDGE BEAM)
FIGURE LI ESTIMATION OF ACOUSTIC RADIATION EFFICIENCY OF PANELS
n i
APPENDIX M
ATMOSPHERIC PROPAGATION EFFECTS
INTRODUCTION
The aural detectability of an aircraft is determined notonly by the acoustic characteristics of the source and by theacoustic environment and sensitivity of the receiver, but alsoby the propagation characteristics of the intervening atmosphere.This section summarizes the propagation effects which may affectthe detectability of a small "quiet" aircraft approaching aground observer at an altitude of a few hundred feet. The slantranges of interest here are of the order of a few thousand feet,and the angles of elevation 0e typically are small (usually lessthan 20I"). .
Most of the available literature on sound propagation isconcerned with either overhead flight (Oe > 200) of air-craft or $with ground-to-ground propagation (8e = 00). For the case ofoverhead flight, only the effects of spreading and atmosphericabforption are significant. For ground-to-ground propagation,the effects of ground absorption and atmospheric refraction mustaloo Le considered and may, in fact, make the principal contri-butiori to attentuation.
()ne may consider, two types of propagation factors: (1)"pre)I otable" factors, which occur ar all times and at all loca-tions, and (2) "variable" factors, which vary with time and lo-,2atlon. ThPe predictable factors include spreading and atmospher-Jc a•L,;oiptlon; spreading is independent of all meteorologicalvarlatih!•:, and absorption can be predicted from given temperatureýJii humiudity profiles. The variable factors include terrainatti-tiuallon, attenuation due to turbulent scattering, attenuationiy fug aiiu rain, focu,;ing and formation of shadow zone,,s b,, re-'v tctl'nu; all of' these depend on the local te~rrain and/or pre-
vallinii n..teorological conditions.
i, addition to attenuating an acoustic signal, propagation,-i'Ft. may alter the acoustic "signature" (i.e. the waveform,. V1,11'!tru, or time-variation of the -;pectrum) of a source. A)-
bLw1 this consideratior, is" of greater importance for helicop-tu.' au~iIlit.y than for quiet aircraft, it will also be con-
, I�'�'d�hcVr'v briefly.
771 I:
~**~'~ -. . . . - - .-.
S. .. .. " ' -•" .. . --- . ....... •" • ... ~ .... ,••- " T "• • •:T ' • ' -- *. .. , .. "-. " . ".....i "' ", r
J /
"PREDICTABLE" EFFECTS
Spreading Loss
The energy from an acoustic source spreads over an increas-ing area as it propagates away from the source. This spreadingresults in a decrease in the acoustic intensity with increasingdistance from the source, or in "spreading loss" AL. which obeys
ALs(dB) - 20 log (R/R 0 ) (1)
where R represents the range from the source to the observationpoint and R. represents the range to a reference point (usuallyat unit distance from the source). AL. thus indicates how muchreduction in the acoustic pressure one measures as the resultof moving the observation point from to R.
Atmospheric Absorption
Atmospheric absorption is usually described in terms of anabsorption coefficient a, which generally is measured in unitslike dB/1000 ft and accounts for "excess attenuation" beyondthat due to spreading. The classical absorption coefficieata,& accounts for losses due to viscosity, heat conduction, heatra iation and diffusion; it is negligible at frequencies belowseveral kHz. The molecular absorption coefficient amol accountsfor absorption of energy from the sound field by internal modesof the gas molecules, and is negligible at frequencies up toseveral hundred hz.
The vast literature on this subject has been discussed iia recent review (Ref. 1) and empirically aerived correctionshave been added to the theoretical results, resulting in formu-lae which match the available data almost perfectly. The re-sults are outlined below and are illustrated in Fig. Ml.
The classical absorption coefficient at a temperature of59 0 F obeys
acl(dB/1000 ft) = 5.3 x 10-2(f/1000) 2 (2)
where f represents the frequency in Hz. This absorption coeffi-cient is independent of humidity and increases by about 1% foreach 20'F increase in temperature.
171
- _ -3 - - - -C - - -.
4nM - -pp.¾
The molecular absorption coefficient is given by
S2 f/fM)2 ]
ft .(d13/1000 ft) arax .18 f + (3)m mal+(f/f )4
m
where a = 0.0078 f m(T*)-2"5e7"77(I-1/T*)
fm = (10 + 6600 h + 4,4400 h2)P*/(T*)3"8h I T*11o = 7.57 Tv = Percent Mole Ratio
III = humldity(Gm/m3)
r* = P /P00
,* -= T/T= - atmoL.pheric pressu:re (psl)
o0i00 = reference atmospheric pressure 14l.7 p:;1
T = absolute temperature ('R)
9, = reference temprature = 519PR
C = frequency (Oiz)
!'S rcelation Is nlotted In Pi,. M1 for the particular, te]mperatures-,poO, 59' and 10 0°. W. Fxamination of the curves reveal! thait for a'.r'-nieal (- mate (temperature approaching 100°'., hurTrmt-; treaterItian 4D)" the coeffi.o~ent may be approximated rather pre-isely by
a mo1 (dlB!'90 ft) = 2(f/1000) (l)
". f' aPair, represent., the frequency in Hlz.
1 7T
"VARIABLE" EFFECTS
Focusinq
The possibility of anomalously high intensities over dis-tant regions has been a subject of great interest in the studyof ground-to-ground propagation of rocket launch noise. Whenwind and temperature profiles are favorable, prop-gation gainsof around 15 dB at all frequencies may be observe., relative tonormally observed levels. Such gains occur when the effectivesound velocity decreases with height up to a certain altitudeand then increases with height above that.
In general, the probability that focusing will decrease theP-,,Al detection range of small low-flying aircraft is small, forti. following reasons:
1. Even for rround-to-ground propagation, the conditions forfocusing occur rarely. (For example, in static firingsof a rocket at NASA's Marshall Space Plight Center, fo-cusing occurred only in about 13% of the caies. Ref. 2)As the source is raised, the probability of focus forma-tion is decreased.
2. For ground-to-ground propagation, the distance to a focalregion is rarely less than two or three miles- (Ref. 2).Any air-to-ground focal regions would occur at even greaterdistances. If an aircraft is detected under non-focusingconditions at a distance of the order of a mile or less,then some signal enhancement at a distance of several mileswill be of little concern, because it will largely be can-celled by the increased spreading and absorption losses.
If low-altitude flights are envisioned in areas where themeteoroloical conditions may present an appreciable probabilityof focusing, then it may be worthwhtle to obtain meteorologicaldata in order to minimize this probability. Often appropriatechoices of aircraft approach azimuth nay be available to mini zethe probability of focusing in the target area. (See Ref. 2.)
173
------------------
S- -
Terrain Attenuation
For low angles of elevation, additional attenuation may beprovided by ground cover. Reference 3, which reports measure-ments of ground-to-ground propagation through a jungle in Panamais the classical paper on this subject. The principal resultsare shown in Fig. M2.
The important question for aircraft detectability considera-tions is how these results are affected as the source elevationis increased. A number of studies indicate that terrain attenua-tion decreases monotonically with source height and becomes neg-lirible at an elevation angle of around 60. For example, Parkinand Scholes (Ref. 4) found that the attenuation of a helicopterat a range of 3000 ft began to increase rapidly as it descendedbelow 300 ft height. Hubbard and Maglieri (Ref. 5) found thatthe detectability of a single-propeller aircraft decreased gub-stantially with decreasing elevation angle and attributed thisto the increased terrain attenuation; they also conducted anumber of measurements to determine the functional dependenceof the terrain loss coefficient on elevation angle (Fig. M3).Loe'wy (Ref. 6) has attempted to develop a general procedure toaccount for the effect of elevation angle, but his procedureappears to be based on insufficient information and has not beenvalidated.
Although a great deal of work remains to be done beforere~lal le quantitative predictions can be made, it is clearqualitatively that the aural detectabilit. of an aircraft canbe reduced by flying along a path along which the ground atten-uation Is high (e.g., where there is heavy foliage), and/orby flying at as low an altitude as possible. If a choice isavilable, detectability can be decreased by approaching thereceiver on an azimuth along which the foliage is heaviest. Forlow-altitude flight over a forest or Jungle, terrain attenuationmay far outweigh the combined effects of spreading and atmospher-Ic absorption.
Attenuation Due to Turbulent Scattering
At low frenuencies, additional attenuation may be causedby scattering from turbulent fluctuations in the wind and tem-perature field. For isotropic turbulence, the scattering at-tenuatlon coefficient is proportional to frequency and to thevustiness (i.e., the root-mean-square wind speed fluctuation,divided by the mean wind speed).
17)1
-. k..
For an rms wind fluctuation of one m/see, Horluchi (Ref. 7)has estimated the attenuation coefficient to be on the order of'.002 f dB/1000 ft. Based on experiments conducted at the MarshalSpace Flight Center, the following suggested minimum values wereobtained for the average meteorological conditions prevailingthere (Ref. 1):
ascat (dB/1000 ft) = 0.03 for f < 7 Hz
= 0.0042f for 7 < f < 60 Hz
= 0.25 for 60 < f < 200 11z
At these low frequencies, the attenuation due to turbulentscattering may be greater than that due to absorption; at higherfrequencies, absorption effects tend to predominate.
Shadow Zones
Refraction by wind and temperature gradients can sometimeslead to "shadow zone" regions in which the sound levels aregreatly reduced. The distance X to the beginning of the shadowzone is given approximately by
r2hCl 1/2
xs z 6rj.
where hs is the mean height of source and receiver-, c is thesound velocity and du/dz is3 the gradient of effective -ound ve-locity (Ref. 8). For purpos-es of minimizing detectab~lIty, onewishes to decrease X as much as possible. Thli; can be accom-plished by flying at low altitude into the wind. riowever, evenfor a reasonably large gradient of 0.01 ft/sec per ft, one (h-talns a shadow zone at a distance as large as about two miles,for a source height of 4400 ft.
An ideal shadow zone occurs only in the Unmiting case of'Feornetric acoustics (h~m erci,,rcie.). In oractice, appre-ciable energy is diffracted and :,cattered into a s;hadow zone.l.:.ave acoustics predicts an attenuation coeffici.ent inside t;ueshadow which is proportional to f'/' (Ref. 9) .-o that high fre-quenlefie are attenuated most.
175
r
Attenuation Due to Fog and Rain
The presence of suspended water droplets may cause addi-
tional attenuation through the mechanisms of viscous dissipationand heat conduction. The theoretical and experimental facts
have been reviewed in Ref. 10. Attenuations on the order' of0.5 dB/1000 ft (increasing with frequency) may be obtained for
prnpap.ation through heavy natural fogs. Analysis of measurements
reported in Ref. 10 indicates that the effect of light rain onsound propagation is very small.
EFFECTS OF PROPAGATION ON PRESSURE SIGNATURES
Aircraft detectability may be increased by the existence
of easily recognizable regularitles in the acoustic (pressure
vs. time) "signature" of the source. These regularities are of
primary importance for helicopter detection (Ref. 6), but may
also play a significant role for other types; of aircraft. There-fore, a brief description of the effect of the propagation chan-
nel on acoustic signatures is also included here.
Random inhomogeneities in the refractive index cause
frequency-dependent fluctuations in the amplitude and phase1 racoustic wave,. Fxpressions for these fluctuations have
been derived by Tatarski (Ref. 11). The effect on the signal"•orm can be determined by introducinp, these expressions into
the spectral representation of the sirnal and then calculatingo' itatistical average. This procedure has bec'n carried out by
Th~rkova (Pef. 12). For simple wave' forms, -.uch as a rectangularr.ulse, he obtained analytical formulas for the distortion. Thedistortion of an arbitrary waveform can be calculated by numeri-cal methods.
.A major criticism of Shlrokova's work is that lie assunmes anormal distribution for the correlation coefficient (-f the re-
.f'ractive index fluctuatton.s. flowever, Tatarski ha.-- shown thAat
a correlatlrn proportional to the 2/3 power of di:;tance provides
M nrre accurate description (,f the fluctuations. Therefore,Thi.rokova'.- formulae should be revised to account for this.
Tn general, one may expect larger distortion of signal
.=hape( when the conditions near the vround are unstable. Insta-
W i ity is us-uall:. characterized by gusty, winds and superadiabati"
]anse rate:-, which result in turbulence near the ground. Experi-
mental evldeP.ce of this effect lian been obtained by observing
thfl .ýtortion of pressure wave form,; from s•onic booms (Ref. 13).
]rl'" in th, morning when conditions near the ground are general-
1- -table, the wave forms closely resemhled the theoretical "N"J~a);:~c on _tion,. prevail,V-!:-a?:e, In the afternoon when superadiabatic cond.1I
ii7
wide variations ranging from spiked to rounded signatures werenoted. In fact, the magnitude of the correlation coefficientto be used in the formula discussed above can be expressed di-rectly in terms of the gradients of wind and temperature nearthe ground (Ref. 11).
ATTENUATION CALCULATIONS
Sound Pressure at a (iiven Range
The reference quantities for sound power level Lw and soundpressure level L. are such that the sound pressure levelLP(Ho=l ft) at 1 ft from a point source is related to the powerlevel of that source as (e.g., Ref. 14)
Lp (Ro) = Lw - 0.5 dB (6)
The sound pressure level at any range R from the source may thenbe calculated from
Lp(R) = Lp(Ro) - AL (7)
where the total attenuation AL is given by
AL = AL + aot ' R. (8)Ap As o
Here, ALS represents the loss due to spreading and atot the ab-sorption coefficient (in dB/unit distance) resulting from allother effects.
By combining Eqs. (1) and (6)-(,) and expressing R in feet,one obtains the sound pressure level L (W) at a range of R ftfrom a source with acoustic power leveý Lw as
L (R) Lw - 20 log R - atot (dB/ft) B R - 0.5 (9)
Range for Given Sound Pressure
By substitution into the foregoing equation one may readilydetermine the sound pressure that results at a given distancefrom a given source. However, det._Lmining the range at which aprescribed sound pressure is obtained from a given source is
177
-. .. . .. .. ,- - | I I I I
more difficult, because Eq. (9) cannot be solved algebraicallyfor R. Figure M4has been prepared to facilitate the numericalsolution of this inverse problem; It permits one to ottain a"corrected" value*R which corresponds to a given value of atotfrom the easily calsulated "uncorrected" value R that oneobtains from Eq. (9) for atot - 0.
toti
*Thie corrected and uncorrected ranges are related b,/
20 log Ru 20 logR 0 +a totR c
and, of' course,
20 log Ru = Lw lp 0.5
where both Lw and Lp are piven.
178
REFERENCES FOR APPENDIX M
1. Wyle Labs., Sonic and Vibration Environments for GroundFacilitiee - A Design ManuaZ, Chapter 7, 1968.
2. Essenwanger, 0., "Profile Types of Sound Speed in theLower Atmosphere and their Relationships to AcousticFocusing", U.S. Army Missile Command, Redstone Arsenal,Alabama, Report RR-TR-66-6, 1966.
3. Eyring, C.F., "Jungle Acoustics", J. Acoust. Soc. Amer. 18,257 (1946).
4. Parkin, P.H. and W.E. Scholes, "Oblique Air-to-GroundSound Propagation Over Buildings", Acustioa, 8, 99 (1958). i
5. Hubbard, H.H. and D.J. Maglierl, "An Investigation of'Some Phenomena Relating to Aural Detection of Airplanes",NACA TN-4337 (1958).
6. Loewy, R.G., "Aural Detection of Helicopters in TacticalSituations", Am. HeZicopter So. J. 8, 36 (1963).
7. Horiuchi, I., "Effects of Atmospheric Turbulence on thePropagation of Sound", ONR Technical Report (1953).
8. Ingard, U., "The Physics of Outdoor Sound", Proc. of the
Fourth Annual National Noise Abatement Symposium (1953).
9. Pridmore-Brown, D.C. and U. Ingard, "Sound Propagationinto the Shadow Zone in a Temperature-Stratified Mediumabove a Plane Boundary", J. Acoust. Soc. Amer. 27, 36 (1955).
10. Bolt Beranek and Newman Inc., "Investigation of Acoustic
Signalling Over Water in Fog", BBN Report No. 674 (1960).
11. Tatarski, V.I., Wave Propagation in a Turbulent Medium,Dnver Publications (1961).
12. Shirkova, T.A., "The Variation in the Form of a Pulse Caused
by the Effect of Random Inhomogenieties in a Medium", Soviet-
Physics-Acoustics 9, 78 (1963).
13. Maglieri, D.J. and T.L. Parrott, "Atmospheric Effects on
Sonic-Boom Pressure Signature", Sound 2, 11 (1963).
14. Peterson, P.G. and E.E. Gross, Jr., Handbook of NoiseMeasurement, General Radio Co., West Concord, Mass., 6thEdition, Sec. 2.8, 1967.
179
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FIGUR Mlc VALUES OF AIR ABSORPTION COEFFICIENTS AT 100 0FFIGUR Mic AND VARIOUS RELATIVE HUMIDITIES (FROM REFERENCE 1)
192*
'a--'. 15
zw
u 10w
(0<_ / . . D0-j
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100 500 1000 5000 10,000
FREQUENCY (Hz)
FIGURE M2a TERRAIN LOSS COEFFICIENTS FOR GRASS AREA. (A) OVER TERRAINTHINLY COVERED WITH SHORT (6-121N.) GRASS; (B) OVER TERRAINTHICKLY COVERED WITH SHORT (181N.) GRASS; (C) THROUGH ATHICK S;AND OF SHORT GRASS; (D) THROUGH SHRUBBERY AND OVERSHORT GRASS; (E) THROUGH THICK TALL (6FT.) GRASS (FROMREFERENCE 3)
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FIGURE M2b TERRAIN LOSS FOR TROPICAL FOREST AREAS (FROMREFERENCE 3)
84 P,.L,
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FIGURE M2c A CHART FROM WHICH TO ESTIMATE TERRAIN LOSS COEFFICIENTSFOR TROPICAL JUNGLES. ZONE 1, VERY LEAFY, ONE SEES ADISTANCE OF APPROXIMATELY 20 FT., PENETRATION BY CUTTING;ZONE 2, VERY LEAFY, ONE SEES APPROXIMATELY 50 FT.,PENETRATED WITH DIFFICULTY BUT WITHOUT CUTTING; ZONE 3,LEAFY, n.NE .FES A D!STANCE nF APPRnXIMATELY 100 FT., FREEWALKING IF CARE IS TAKEN; ZONE 4, LEAFY, ONE SEES A DIS-TANCE OF APPROXIMATELY 200 FT., PENETRATION IS RATHEREASY; ZONE 5, LITTLE LEAFY UNDERGROWTH, LARGE BRACKETEDTRUNKS, ONE SEES A DISTANCE OF APPROXIMATELY 300 FT.,PENE-RATION IS EASY (FROM REFERENCE 3).
L--
0 0 ol .1
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FIGURE M4 EFFECT OF ABSORPTION ON RANGE FROM GIVEN SOURCE AT
WHICH PRESCRIBED SOUND PRESSURES ARE OBSERVED
187
.T , , .
APPENDIX N
AURAL DETECTABILITY
INTRODUCTION
In the absence of any ambient noise, an aircraft may beheard if the level of its noise at the location of the listenerexceeds the threshold of hearing of the listener in any frequencyrange. The presence of the ambient noise tends to raise thethreshold of detectability to a higher level, which may be calledthe "detection threshold". Increased intensity of the ambient noisein a given frequency band causes the detection threshold to exceedthe threshold of hearing by increasing amounts.
Generally speaking, an aircraft is aurally detectable if itsacoustical signal at the location of the listener exceeds boththe threshold of hearing and the masking threshold. Consequently,a necessary condition for aural detection is that the signal ex-ceeds the threshold of hearing of the observer in at least onefrequency band; a sufficient condition is that the acousticalsignal exceeds also the detection threshold corresponding to theambient noise level present at the time of observation at thelocation of the listener.
Since the ambient noise varies from place to place - andalso varies with the time of day at any given location - theaural detectability of a given aircraft differs for differentsituations.
In addition, aural detection is affected by such psvcholo-gical factors as the observer's familiarity with the aircraft'sacoustic signature (i.e., whether he knows what he is supposedto listen for), his other duties (which may interfere with hislistening concentration), and the penalties associated withfailure to hear an approaching aircraft as early as possible.
Because of the many variables involved in determination ofdetectability criteria for a complex signal in the presence offluctuating ambient noise, the problem is a very complex one.In order to arrive at an engineering approximation of detecta-bility described in this report, it was necessary to rely onlaborat~ry data of the threshold of hearing for pure tones andbands of noise, and on the concept of critical bandwidth toevaluate the masking effect of the ambient noise. The approachsuggested here is likely to lead to significant errors in pre-dicting detectability in actual field situations, but Is expectedto be adequate for the purpose of comparing the detectabilitiesof alternate aircraft designs.
188
The acoustical signature of an aircraft generally consistsof pure tones and broadband noise. Since either type of compon-ent can be responsible for aural detectability, both must beconsidered. They are discussed separately in the followingparagraphs.
DETECTABILITY OF PURE TONES
Hearing Threshold
As has been mentioned, the level at which a signal becomesdetectable depends on the threshold of hearing and on the maskinglevel provided by the ambient noise. The threshold of hearingfor pure tones has been investigated extensively in the labora-tory. Figure N1 shors the threshold of hearing for pure tones, asa function of frequency, as recommended by the InternationalStandard Organization (Ref. 1). This figure pertains to an"average" young listener, and indicates that the ear is mostsensitive to frequencies between about 3000 Hz and 5000 Hz.
Masking By Noise
Hawkins and Stevens (Ref. 2) measured the masking effect ofwhite noise on a pure tone signal by exposing test subjects simul-taneously to the pure-tone signal and the masking noise and notingat which noise levels the subjects could just recognize the toneas having a definite pitch. Figure N2 shows the observed differ-ence between the pure tone level and the masking white noiselevel (in 1 Hz bands).
There exists some evidence that the human auditory system
senses separately the energies in certain "critical bands" (whosebandwidths are such that the energy in the masking noise in thesebands matjhes the energy in the just audible pure tone at theband's center frequency). Accordingly, one may treat variouspure-tone components separately and use Fig. N2 as the basis foran acceptable detectability prediction scheme.
One may calculate the detection level Ld(f), which is thelevel of a pure tone which is just detectable in the presence ofnoise with a spectrum level LN,l(f), simply from
Ld(f) = LN,l(f) + ec () (1)
where 8 (f) is a correction factor which is plotted in Fig. N2
and which gives one the noise in critical bands. The spectrum(1 Hz bandwidth) level LN 1 is related to the noise level LNAfmeasured in a frequency band Af (with center frequency) as
189
• " ... .. . ." .' • ' • "' •• ,, •.•-•. - • •'•,• • "4 . ... . ... .
LN,1 LN,Af -10 log Af
- LNoct - 10 log f + 1.5 for octave bands
L N,1/3 oct 10 log f + 6.5 for 1/3-octave bands. (2)
Detectability
A pure-tone signal thus may be considered detectable in thepresence of noise, if the ,;ignal exceeds both the detection levelLd(f) given by Eq. (1) and the hearing threshold of Fig. Ni.
DETECTABILITY OF BROADBAND NOISE
Hearing Threshold
The threshold of audibility of octave bands of white noise(constant spectral level within the pass band) was determined byRobinson and Whittle (Ref. 3). Their result is shown as thedotted curve of Fig. Nl. Comparing the threshold curves for puretones with that for octave bands, one finds that the two curvesare almost identical. The difference between the two thresholdsis les6 than the errors in estimation procedures, and also ismuch smaller than the variation Ln the threshold of hearing forindividual listeners.* (It should be noted, however, that theoctave band threshold curve was obtained for constant spectrallevel within the pass band of the octave filter. Accordingly,these results are strictly applicable only for similar conditions.)
Masking By Noise
Like a pure-tone signal, a broad-band signal also may bemasked by noise. Unfortunately, there appears to be availableno experimental data directly applicable to predicting the mask-ing of a broad-band signal by broad-band noise. The addition ofa broad-band signal in a given band to a similar noise in thatband would be sensed by a listener merely as an increase in loud-ness, unless the signal has a spectrum which differs from that of
the noise - in which case the listener would eventually notice achange in the frequency content of what he hears.
One may perhaps obtain the best estimate of masking effectsby comparing the levels of the signal and noise in critical bands.
*"wicker and Heinz (Ref. 11) give threshold variances of 5.5 dB at50 Hz, 3.8 dB at 1 kHz, and 10 dB at 12 kHz.
]90
- .. . ......-LA
In other words, if one has a signal spectrum Ls,6fs(f) given in
frequency bands 6f, with center frequencies f, and a noise signalLNAfn(f) in bands Afn, one may compute the corresponding sound
pressure levels in critical bands from
Lsje(f) = LsAf s(f) - 10 log Afs + e P(,)(3)
LNOe(f) = LNbAf n (f) - 10 log Afn + e8(f)
Detectabi I ity
The signal LS Afs (f) may be considered as audible if itsoctave band levpl '
LS oct L (f) + 10 log (f/Afs) (4)
exceeds the threshold of hearing for octave bands, and if in ad-dition the sound pressure level LS e(f) of the signal in anycritical band exceeds the level LN:e(f) in the same critical band.
Note that if the signal and noise are given in the samebands, so that Afs = Afn = Af, then
Lse(f) - LN,e(f) = LS (f) - LN,Af(f). (5)
Therefore, if signal and noise are given in the same bands, thesignal may be considered detectable if it exceeds in any bandboth the hearing threshold and the noise. In other words, herethe band detection level is equal to the noise level in the same
band;
Ld,Af(f) = L M,Af(f) (6)
i0l- f .,.i,* A f
A-k 2.t'
Complications
Superposition on ambient noise of a broadband signal whichis not of completely random character, but which exhibits an am-plitude modulation, results not only in an increase in intensitybut also in a change of the character of the composite signal.This change in character may enable a listener to detect thesignal at a lower level than for a completely random signal.
Feldkeller and Zwicker (Ref. 5) have measured the effect ofmodulation on the detection of amplitude-rmodulated pure tones andbands of random noise. For bands of random noise with soundpressure levels above 20 dB and center frequencies above 1 kHz,one can notice amplitude modulations with modulation indexes ex-ceeding 0.06.
Since in these experiments only a single band of amplitude-modulated noise was presented to the listener, the results arenot immediately applicable to the aural detection of aircraft,where ambient noise is present in all bands and may compete forthe attention of the listener. However, the extreme sensitivityof the ear to amplitude-modulation should be taken into accountin designing aircraft for minimum aural detectability.
BACKGROUND NOISE LEVELS
Data on the ambient noise levels in Jungles and forestedareas are presented in the papers of Eyring (Ref. 6), McLaughlinand Hand (Ref. 7)and Saby and Thorpe (Ref. 8). The data given inthese papers excludes transitory sounds, such as wind, rain andanimal calls and may thus be used to obtain conservative esti-mates of aural detectability.
Eyring presents detection levels (Pig. N3) at various timesof day for a dense, leafy jungle and for a forested area inPanama. The frequency range covered is from 100 to 6000 Hz. Hisdetection levels were calculated essentially according to Eas. (1)and (2), and thus apply to the detection of pure tones. In viewof Eqs. (1), (2), and (6), the corresponding detection levels forbands of width f are higher than those shown in Fig. N3 by anamount Ld ^f - Ld = 10 log Af - ec(f). [Values of the correction(Ld oc 'd) from pure-tone to octave-band masking levels aresho~n cin Fg. N2.]
rlcLaughlin and Hand present one-third octave band backgroundlevels at various locations and times in a Thailand jungle, for afrequency range from 100 to 1000 Hz. Although this paper is notreadily available, some representative data for average day andnight conditions have been reproduced in Ref. 9. Saby and Thorpepresent spectrum levels of background noise in a Panama jungle,frnr hiph frequencies, from 8,000 to 25,000 Hz.
]02
....... ....... ~
In Fig. N4 are shown the combined results derived from theaforementioned sources, all in terms of detection levels for puretones. The two figures apply to average daytime and nighttimeconditions, respectively. (For purposes of comparison, Fig. N4also includes a curve for the minimum nighttime detection levelsfor a residential area, as derived from the background noise dataof Ref. 10.)
The various sets of data are quite consistent and indicatethat (a) detection levels increase with increasing density ofvegatation, at all frequencies; (b) nighttime detection levels arelower than daytime levels at low frequencies, but are much higherat high frequencies. The latter effect is attributable to thenearly continuous presence of high-pitched inset sounds duringthe night. Over most of the frequency range, the detection levelsare highest during early evening hours and lowest around midday.The variation of detection level with time of year was not investi-gated, but would be expected to be small relative to the diurnalvariations.
An interesting question concerns the effect of the humanlistener on these detection levels, since the reported measure-ments were all made with a microphone placed a large distance fromhuman observers, whereas the aural detection problem involves thedetection level in the immediate vicinity of an observer. Ac-cording to Ref. 8, however, the quieting of nearby insects in thepresence of an observer does not measurably alter the detectionlevels.
193
REFEPENCES FOR APPENDIX N
1. International Standards Organization, Document ISO, R226,(1961).
2. Hawkins, J.E., Jr. and S.S. Stevens, "The Masking of PureTones and Speech by White Noise," J. Acoust. Soc. Amer. 22,pp. 6-13 (1950).
3. Robinson, D.W. and L.S. Whittle, "The Loudness of Octave-Bands of Noise," Acustica 14, p. 33 (1964).
4. Zwicker, E. and W. Heinz, "Hgufigkeitsverteilung derH5rschwelle,' Acustica, 5, Beiheft 1, p. 75 (1955).
5. Feldkeller, R. and E. Zwicker, Das Ohr als Nachrichtenemp-fanger, S. Hirzel Verlag, Stuttgart, 1956.
6. Eyring, C.F., "Jungle Acoustics," J. Acoust. Soc. Amer. 18,p. 257 (1946).
7. McLaughlin and Hand, "Analysis of Background Sound fromData Recorded in Thailand," Report No. 8743-1-F, preparedfor the Advanced Research Projects Agency, (1967).
8. Saby, J.S. and H.A. Thorpe, "Ultrasonic Ambient Noise inTropical Jungles," J. Acoust. Soc. Amer. 18, p. 271 (1946).
9. Smith, D.L. and R.P. Paxson, "The Aural Detection of Air-craft," Air Force Flight Dynamics Laboratory Report No.TM-69-1-PDDA (1969).
10. Bonvallet, G.L., "Levels and Spectra of Traffic, Industrial,and Residential Area Noise," J. Acoust. Soc. Amer. 23,p. 435 (1951).
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APPENDIX P
ALTERNATE METHOD FOR DETERMINING UNCORRECTEDDETECTION RANGE
i
INTRODUCTION
The "Detection Level Spectrum" discussion in the main bodyof this report, as well as the corresponding aural detectabilityestimation approach presented in Appendix N, are based on the re-sults of psychoacoustic studies of the detectability of stationary(i.e., time-independent) pure-tone and broadband signals. Sincedifferent detectability criteria apply to pure-tone and to broad-band signals, one must approximate the noise from any givensource in terms of stationary pure-tone and broadband components,in order to apply the suggested approach.
H1owever, the noise that reaches a listener on the ground dueto an aircraft flyover Is nonstationary and ty/lcally consists ofmany broadband and "pure-tone" components that chance both inanparent frequency and amplitude. Thus, one faces the often verydifficult problem of estimating enuivalent stationary pure-toneand broadband levels. The various noise nrediction schemes pre-sented in the previous appendices sugfest how these levels maybe estimated for the various noise sources considered, and may beadequate for many purposes - particularly in the light of theoften considerable uncertainties associated with the noise sourcepredictions -; however, an alternate method, which does not re-,uire the user to differentiate a priori between nure-tone andbroadband siqnal components, has been found useful for determin-inr detectability, esnecially, from recorded data (Ref. 1). Thisalternate method is described in the nresent aorendix.
RESULTS OF SAILPLANE AURAL DETECTION STUDY
7eference 1 reports the results of a study of the flybynoise (as perceived on the rround) riroduced by three differentsailplanes at various altitudes and sneeds. This studY served tocharacterize the noise, but also included some subjective deter-minations of when the sailplanes could just be heard.
It was found that the observed detection ranges agreed wellwith predictions obtained by comparfnin the spectrum levels ofthe received sound to an aural detection spectrum for oure tones,where the rpectrum levels were determined (by means of an anoro-priate "ourier analyzer) with an effective averaging time of
... .,
50 milliseconds,* and were obtained by reducing the bandwidth ofthe signal analysis until the level remained constant. Since thisanalysis procedure resulted in signal levels that were 9 to 12 dBgreater than the spectrum livels calculated from the third-octavelevels using the usual bandwidth conversion relation,** which isbased on the assumption that the energy is uniformly distributedin each band, it appears that for audibility estimation purposesone should increase the "constant energy" spectrum levels LS, 1
obtained from broadband spectra by about 10 dB in order to accountfor the ability of a listener to detect rapid changes in frequencyand amplitude.
ESTIMATION OF UNCORRECTED DETECTION RANGE FROM RECORDEDFLYBY SOUND
In order to determine the uncorrected detection range of anaircraft from tape-recorded flyover noise data, one may proceedas described below. (An example, taken from Ref. 1, is shown inFig. Pl.)
1. Determine the pure-tone detection level spectrum Ld(f) from
the Dure-tone hearinp threshold and the background noisespectrum, as indicated in Appendix N and Fig. 2 of the bodyof this report.
2. Determine the maximum sound pressure level in each one-thirdoctave band during the flyover, using an averaging time nogreater than 0.3 sec. Listen to the signal durinr the datareduction, and/or carry out preliminary narrow-band analyses,judge whether pure tones are dominant.
*This averaging time is within the 20 to 250 millisecond range
of integration times of the ear, as reported in Ref. 2.N* i.e.,
LS,1 = LS,Af - 10 log Af (1)
where LS Af represents the level measured in a band of width Af
(e.g., a third-octave band), and L1 denotes the correspondin
"constant-energy" spectrum level.
201
3. Find the one-third octave band in which the difference be-tween the detection level (Step 1) and the measured third-octave band signal level (Step 2) is greatest. (In the ex-ample of Fig. P1, this greatest difference occurs in theband centered at 315 Hz and amounts to 30.5 dB.)
4. Conduct a narrow-band analysis of the signal over a fre-quency range that includes the band selected in Step 3,using an averaging time for the analysis that does not ex-ceed 0.1 sec.
Repeat this analysis with narrower and narrower analysisbandwidths, until the peak level remains essentially un-changed. Note this peak level and the frequency at whichit occurs. (In the example of Fig. P1, this spectrum levelis 37 dB, at 285 Hz.)
5. Determine the difference between this peak level and thedetection level spectrum Ld(f) at the peak frequency. (InFig. P1, this difference is 20.5 dB.)
6. If the received signal is not dominated by pure tones, anda narrow band analysis cannot be conducted.
(a) Determine the effective signal spectrum levels LS,1
from the one-third octave band spectrum levels LS
oct found in Step 2, by use of
LS,1 = LS, 1 / 3 oct - 10 log f + 16.5 (2)
where f represents the center frequency of the third-octave bands (in Hz).
(b) Consider the levels Ls,l to occur at the center fre-
quencies of the corresponding third-octave bands, anddetermine the greatest difference between these signallevels and the pure-tone detection level Ld. (In theexample of Fig. P1 the greatest difference, 22 dB isobtained at 3].1. T-zi.
7. Find the uncorrected detection range Ru from
20 log (Ru/Rmin) = LS,l - Ld (3)
202
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where Rin is the minimum distance between the aircraft and
the microphone during the flyby (and is equal to the alti-tude in the case where the aircraft passes directly over themicrophone), and LSI-Ld is the greatest difference between
the signal spectrum and the detection spectrum levels, asobtained from Steps 3 and 4. (In the example of Fig. P1,uncorrected detection ranges of 1340 and 1580 ft were ob-tained.)
Note that this calculation of Ru does not take account of
atmospheric and terrain attenuation effects. Corrections forthese effects may be made by means of the data given in AppendixM. If Rmin is large, one must also consider that these attenua-
tion effects can affect the recorded signals.
ESTIMATION OF UNCORRECTED DETECTION RANGE FROMPREDICTED NOISE SOURCE CHARACTERISTICS
In order to determine the uncorrected detection range fromthe predictions of aircraft noise, as given in the various fore-going appendices, one may proceed as follows:
1. Determine the pure-tone detection level spectrum Ld(f) from
the pure-tone hearing threshold and the applicable back-ground noise spectrum, as described in Appendix N and Fig. 2of the body of this report.
2. Determine the power level and frequency for each pure-tonenoise component from each source.
3. Determine the octave-band power level spectrum for each noisesource, and combine the levels from all of the sources asdescribed in the body of this report.
4. Find the corresponding effective signal spectrum level LS 1from
LS,1 = Lsoct - 10 log f + 11.5 (4)
where Lsoct represents the combined octave-band level (as
found in Step 3) at the center frequency f.
5. Compare the power levels Lw of all pure tones (from Step 2)
and the combined effective signal spectrum level LSI (from
203)
Step 4) with the pure-tone detection level spectrum gd (from
Step 1). Find the greatest differences L w-L d and L SI-L d
and the corresponding frequencies.
6.Calculate the uncorrected detection range Ru from
20 log R u(ft) = (L-L d)max
where (L-1.d max represents the greater of the two maximum
differences, Lw-Ld and LS,-d
0 111
REFERENCES FOR APPENDIX P
1. Smith, D.L. and R.P. Paxson, "Measurements of the RadiatedNoise from Sailplanes", Air Force Flight Dynamics LaboratoryTM-70-3-FDDA (1970).
2. Zwislocki, J., "Theory of Temporal Auditory Summation",J. Acoust. Soc. Amer. 32, p. 1046 (1960).
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UNCLAS SIFIEDSecurity Classification
.4 = LINHKA LINK a LIN ICKIEV WORDS
AO t r w* r MOLf I wt SOL E WT
Aural detection
Aircraft noise
Empire noise
Propeller noise
Aerodynamic noise
Jet noiseDucts
Sound propagation and attenuation
DD .Mo° .. 1473 (BCK) UNCLASSIFIEDSecurity Classification
61U.S.Govornment Prlntlnq Officee 1972 - 759.084/475
