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NASA Contractor Report 201634

Sonic Boom Propagation Codes Validatedby Flight Test

Hugh W. Poling

Boeing Commercial Airplane Group, Seattle, Washington

Contract NAS 1-20220

October 1996

National Aeronautics and

Space AdministrationLangley Research Center

Hampton, Virginia 23681-0001

https://ntrs.nasa.gov/search.jsp?R=19970011188 2018-07-27T11:47:45+00:00Z

Foreword

The verification of sonic boom propagation codes has long been the desire of GeorgeT. Haglund. Working on supersonic transports virtually from their conception, hedeveloped many of the sonic boom analysis tools used at Boeing. He spearheadedinitial assessment of sonic boom characteristics of low-boom concepts at Boeing andoriginally proposed the idea of flying two aircraft in tandem to generate a shaped,long duration sonic boom source. Such a signature would require a very long

propagation distance to completely evolve into an N-wave and thus provide the idealsource to test propagation codes for their resolution of fine detail in the sonic boomwaveform. Recent near-field pressure signature measurement of a single supersonicaircraft using a novel probing technique lays a foundation for such propagation codeverification and ultimate demonstration of the viability of low-boom supersonic

transport design.

Contents

Foreword ...........................................................

Contents ............................................................

List of Figures in Text ..............................................

List of Figures in Appendices .......................................

S_ary oeoeooooeeooeooooeeeoeoeoeeooeooooooeoooeeoeeoe ee oeeoeeoooo

Propagation Codes

Comparison to Measurement ...........................................

Introduction ........................................................

Absorption ...........................................................

Code Development

SHOCKN Code ......................................................

Summary ............................................................

Atmosphere Model ....................................................

Sample Case .........................................................

Outputs .............................................................

ZEPHYRUS Code ...................................................

Summary ............................................................

Atmosphere Mode/ ....................................................

Sample Case .........................................................

Outputs .............................................................

Comparison of SHOCKN and ZEPHYRUS ..........................

Introduction .........................................................

Impact of Standard Atmosphere ........................................

Comparison Results ...................................................

Comparison to Experiment .........................................

SR71 Flight Test Summary ............................................

Weather Conditions ...................................................

Selected Flight Conditions .............................................

Derivation of Measured Waveforms for Extrapolation .....................

Analytic Propagation ..................................................

Comparison of Measured and Analytic Waveforms ........................

Noise Metrics ........................................................

Conclusions ........................................................

Propagation Codes ....................................................

Comparison to Measurement ...........................................

i

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1

1

1

2

2

2

4

4

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iii

Contents (Concluded)

pendix A-71 Measured Pressure Signatures and Flight Conditions ....... 37

Appendix BSignature Time Histories for Extrapolation ........................ 53

Appendix CWaveform Evolution ................................................ 63

Appendix DCalculation of Perceived Level ..................................... 67

References ......................................................... 68

iv

List of Figures in Text

Figure 1 Source Waveform for sample case .............................. 16

Figure 2Ground Signatures for sample case for three different atmospheres ........ 17

Figure 3Ground Signatures for sample case propagated with SHOCKN & ZEPHYRUS 18

Figure 4Noise Spectra for sample case propagated with SHOCKN and ZEPHYRUS .

Figure 5

Figure 6Selection

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19

Figure 20

Figure 21

Flight Conditions for SR-71 Flight Test .......................

19

22

of "Near" and "Far" Measurements for ZEPHYRUS propagation . 23

Measured Signature Durations ................................ 24

Propagation Parameters for ZEPHYRUS ....................... 25

Time History for Measurements #3 and #11 ................... 28

Time History for Measurements #15 and #19 .................. 28





Extrapolated Signature Characteristics ........................ 32

Spectra for Measurements #3 and #11 ......................... 33

Spectra for Measurements #15 and #19 ....................... 33


Spectra for Measurements #1 and #6 .......................... 34



V

Figure A.22

Figure A.23

Figure A.24

Figure A.25

Figure A.26

Figure A.27

Figure A.28

Figure A.29

Figure _4.30

Figure A.31

Figure A.32

Figure A.33

Figure A.34

Figure A.35

Figure A.36

Figure B.1

Figure B.2

Figure B.3

Figure B.4

Figure B.5

Figure B.6

Figure B.7

Figure B.8

Figure B.9

Figure C.1

Figure C.2

Figure C.3

Figure C.4

Figure C.5

Figure C.6

List of Figures in Appendices

Measurement

Measurement

Measurement

Measurement

Measurement

Measurement

Measurement

Measurement

Measurement

Measurement

Number i of SR-71 Flight 24 ....................

Number 2 of SR-71 Flight 24 ....................







Number 10 of SR-71 Flight 24 ..................


Measurement Number 14 of SR-71 Flight 24 ..................



Measurement

Measurement

Time History

Time History

Time History

Time History

Time History

Time History

Time History

Time History

Time History

Extrapolation

Extrapolation

Extrapolation

Extrapolation

Extrapolation

Extrapolation



for Measurement Number 1 of SR- 71 Flight 24 ....

for Measurement Number 3 of SR-71 Flight 24 ....

for Measurement Number 6 of SR-71 Flight 24 ....

for Measurement Number 10 of SR-71 Flight 24...



for Measurement Number 16 of SR-71 Flight 24 ...

for Measurement Number 17 of SR-71 Flight 24 ...


of Measurement Number 1 of SR-71 Flight 24 ....



of Measurement Number 15 of SR-71 Flight 24 ...



vi

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Summary

Propagation Codes

A major thrust of recent developments to sonic boom propagation codes has been tomore properly incorporate air absorption effects. This effort has been made practicalby the general availability of improved computing power since absorption effects arebased on inclusion of "higher order" terms in the basic thermodynamic equations.These terms were previously discarded in order to focus on the basic phenomena ofnon-Hnear wave steepening, formation of shocks, and shock propagation accordingto the equal-area rule. The higher order terms render a closed-form solutionimpossible and the equations are thus solved using an iterative technique over smallsteps along the wave propagation.

The sonic boom propagation codes reviewed in this study, SHOCKN and ZEPHYRUS,implement current theory on air absorption using different computational concepts.Review of the codes with a realistic atmosphere model confirm the agreement ofpropagation results reported by others for simplified propagation conditions.ZEPHYRUS offers greater flexibility in propagation conditions and is thus preferredfor practical aircraf_ analysis.

Comparison to Measurement

The ZEPHYRUS code was used to propagate sonic boom waveforms measured

approximately 1000 feet away from an SR-71 aircrai_ flying at Mach 1.25 to 5000feet away. These extrapolated signatures were compared to measurements at 5000feet. Pressure values of the significant shocks (bow, canopy, inlet and taft) in thewaveforms are consistent between extrapolation and measurement. Of particularinterest is that four (independent) measurements taken under the aircraf_ centerlineconverge to the same extrapolated result despite differences in measurementconditions. Extrapolated and measured signature durations disagree because themeasured duration of the 5000 foot signatures is either much longer or shorter thanwould be expected. The measured durations are 0.07 seconds, 0.21 seconds and 0.15seconds where a value of 0.1 might be expected.

These duration anomalies may have been introduced by the simplified method ofconverting the measured pressure at a position relative to the SR-71 to a timehistory at a fixed point in space. A more refined procedure has been suggested thataccounts for changes in SR-71 speed and position of the probe aircraft duringpressure measurement. Implementation of this procedure by others indicates a muchbetter resolution of near and far measurements.

Introduction

Absorption

Absorption of sound in air is primarily composed of five mechanisms: viscosity,thermal conduction, bulk viscosity and vibrational relaxation of oxygen and nitrogen.Viscosity and thermal conduction dissipate sound pressure into heat through vorticityand thermal conduction. Bulk viscosity summarizes the exchange of energy betweenrotational and translational modes of molecular motion (primarily of oxygen and

nitrogen molecules) as the air strives for thermal equilibrium after passage of thepressure signature. Vibrational relaxation is another process whereby soundpressure is converted to heat by increasing the vibrational energy of the (primarilyoxygen and nitrogen) molecules.

In addition to air absorption effects, shock discontinuities introduce pressure losses.Non-linear steepening of the waveform also redistributes energy from lowfrequencies to high frequencies, which are more effectively attenuated in air.

Reference 1 is recommended as excellent background information on sonic boom

propagation phenomenon, including absorption effects.

Code Development

During the last 25 years, the effects of molecular relaxation on sound propagationhave been developed in the acoustic community. More recently, this knowledge hasbeen applied to sonic boom propagation through NASA High Speed Research fundingof university studies at University of Mississippi, Pennsylvania State University andthe University of Texas. Methods are now available for predicting the importanteffect of molecular absorption on sonic boom propagation.

These methods trace their genesis to the 1973 doctoral dissertation by Pestorius 2.The Pestorius algorithm was developed for the case of plane waves propagating in atube, accounting for nonlinear distortion, dispersion and absorption. Nonlineardistortion as the wave propagates without losses leads to multivalueness in thewaveform, which is resolved using weak-shock theory. Weak-shock theory uses theassumption of simple wave flow on either side of a shock to allow calculation of shocklocation and strength. It allows dispersion of wave pressure to heat through thermalconduction, supplementing the tube boundary dispersion (and absorption) explicitlyincluded by the geometry of the Pestorius' problem. In his code, non-lineardistortion, shock strength and shock location are calculated in the time domain anddispersion and absorption in the frequency domain with Fast Fourier Transforms toswitch back and forth between the two domains.

The Pestorius code became the basis for two approaches to more fully account for

absorption effects as other researchers adapted the code to their (more general)problems. One approach was implemented by Anderson 3, who dropped the weak-

shock theory and modeled air as a thermoviscous fluid (that is, added the effect ofenergy dissipation due to thermal conduction and viscosity). This applicationdepends on a large number of points to properly model shocks in the waveform andsmall propagation step sizes to keep the waveform single-valued. The Anderson

codewas later extended to include molecular relaxation effects4and atmosphericstratification with the resulting computer codenamed SHOCKN 5. Since SHOCKNwasused to analyze stronger shocksand longer duration waveforms than Andersonwas concerned with, SHOCKN has a special absorption routine 6to ensure single-valueness of the waveform. If shock amplitude is sufficiently strong, the viscosity ofthe air is artificially increased such that at least ten points are always used todescribe the shock. This normally only occurs away from the ground so that normalabsorption smooths out any unrealism in the waveform.

The other significant approach was taken by Robinson 7 in his computer codeZEPHYRUS _. The air is modeled as a thermoviscus fluid with stratified

inhomogeneities, as in SHOCKN, but non-uniform, stratified winds are alsoallowed. Molecular relaxation effects are included. A three-dimensional ray theoryis used to generate ray paths associated with the sonic boom shock front.Propagation through reflections and weak (line-like) caustics is allowed. Waveformpropagation along these raypaths starts with the basic Pestorius marching algorithm,including weak-shock theory, with the updated absorption model for attenuation anddispersion effects. Shocks that are too strong to be modeled by the number of pointsin the waveform are handled by weak-shock theory and carried as discontinuities.

These methods have been authoritatively compared by Cleveland 5 on the basis of

theory using idealized propagation conditions to focus on absorption effects andshock modeling. The current work validates these propagation methods through amore realistic atmosphere.

Flight testing of NASA's SR-71 in 1995 provides data for evaluating the accuracy inpredicting detailed sonic boom characteristics. However, data available for this studyprovide only a short range (1000 feet to 5000 feet from the aircraft) of extrapolationso the absorption effects are minimal. Nevertheless, pressures are predicted

reasonably well. Inconsistencies with measured duration inhibit accuracy ofpredicted duration, but a proposed refined method of data reduction promises toresolve most of these effects.

SHOCKN Code

Sum.mary

SHOCKN calculates nonlinear distortion in the time domain and all other effects in

the frequency domain. The Fast Fourier Transform is used to transfer between thetime and frequency domains. For strong shocks, such as near the source, shocks areartificially thickened by extra viscous attenuation that is amplitude dependent.When the shock is weak enough, standard air absorption effects are modeled.

Since SHOCKN was basically written to verify certain absorption concepts, it islimited to propagation along the ray directly below the aircraft through theatmosphere coded into the program. The atmosphere does not include wind.Propagation halts at the ground so that ray reflection leading to secondary booms isnot allowed. The program allows signatures at intermediate altitudes to becalculated.

A copy of the SHOCKN code was obtained from Jim Chambers of the University ofMississippi and incorporated into the Boeing Sonic Boom Toolbox. To run the code,the user supplies the following parameters:

Aircraft (source) altitude - feet

Aircraft body length - feetDistance from aircraft to input waveform - feetAircraft Mach number

(any intermediate altitudes for output)(special value for number of points in signature)(special value for waveform sample rate)

In addition, the input waveform is supplied as a list of coordinates, time (seconds)

and pressure (psf).

Atmosphere Model

SHOCKN uses an atmosphere profile generated by a function within the code. The

code given to Boeing was set up with an isothermal atmosphere where, althoughtemperature is constant, gravity effects cause pressure and density to decreaseexponentially with altitude. The atmosphere function was rewritten to additionallyallow use of the standard atmosphereg. ' The relative humidity is constant at 20%. A

copy of the revised atmosphere function is presented as follows:

-4-

Subroutine Atmos (AI, t, p, r, hum)C

C Altitude (AI) in meters (input)

C Temperature (t) in K (output)

C Pressure (p) in atm. (output)

C Density (r) in kg/m**3 (output)

C relative humidity(hum) in %. (output)

C

INCLUDE "/acct/hwp2093/etc/boom/shockn/code/parameters"

c Standard atmosphere model included by Hugh Poling, March 6,

c Equations are from Anderson's book "Introduction to Flight"

c We start with given altitude in meters, AI.

c GRADIENT TROPOPAUSE

if ( A1 .it. ii000.0 ) then

c temperature in Kelvin

t=T0std-(0.0065*Al)

c pressure in arm

p=p0std*exp(ATM CONST*alog(t/T0std))

c density in kg/m_3

r=r0std*exp((ATM_CONST-l.0)*alog(t/T0std))c ISOTHERMAL STRATOSPHERE

elseif (AI .it. 25000.0 ) then

c establish parameters at base of layer

C (repeat of Tropopause equations)

hl=ll000.0

tl=T0std- (0. 0065"hi)

pl=p0std*exp (ATM_CONST*alog (tl/T0std))

rl=r0std*exp ( (ATM_CONST-I. 0) *alog (tl/T0std))

1996

(pp.56-61)

c next, calculate parameters at altitude, A1

t=tl

p=pl*exp ( GO* (hl-Al) / (GAS_CONST*tl) )

r=rl* (p/pl)else

stop ' ERROR - standard atmosphere not defined above 25000 m'

endif

hum=20.

write

return

end

(15,*) AI,' ',t,' ',p,' ',r,' ',hum

Sample Case

The sample case used to demonstrate operation of the SHOCKN and ZEPHYRUScodes is based on the numerical exercise reported by Cleveland 5, for reasons

explained in the section comparing the two codes. This section is only concernedwith setting up inputs to SHOCKN and running the program.

The input pressure signature is a "ramp" waveform at a distance of 183m (600 ft)directly below the source. The format used in SHOCKN is an uncommented file withtwo columns of data. The columns are the waveform time (seconds) and pressure

(psf). Note that the beginning and end of the waveform must be set to zero pressure,as shown following.

The flight altitude of the source is specified to be 14,630m (48,000 ft) and the Machnumber is 1.8.

-0 0045268

-0 0037723

-0 0023389

-0 0022634

0 0021843

0 0066321

0 0110798

0 0137691

0 0164584

0 0191477

0 0218370

0 0245263

0 0272155

0 0299048

0 0325941

0 0352834

0 0379727

0 0406620

0.0433513

0.0460406

0.0487299

0.0514192

0.0541085

0.0567977

0.0594870

0.0621763

0.0648656

0.0675549

0.0702442

0.0729335

0.0756228

0.0783121

0.0810014

0.0836907

0.0863799

0.0890692

0.0917585

0.0944478

0 00000000

0 77863348

1 55726409

2 33589768

1 99676502

1 65763271

1 31850016

1 35719407

1 39589095

1 43458498

1 47327888

1 51197278

1 55066967

1 58936357

1 62805748

1 66675138

1 70544529

1 74414217

1.78283620

1.82153010

1.86022413

1.89892077

1.93761492

1.97630870

2.01500273

2.05369973

2.09239340

2.13108754

2.16978145

2.20847821

2.24717236

2.28586602

2.32456017

2.36325717

2.40195084

2.44064474

2.47933888

2.51803565

0.0971371 2.55672956

0.0998264 2.59542346

0.1025157 2.63411736

0.1052050 2.67281437

0.1078943 2.71150827

0.1105835 2.75020218

0.1132729 2.78889608

0.1159621 2.82759309

0.1186514 2.86628699

0.1213407 2.90498090

0.1240300 2.94367480

0.1523103 -2.51619887

0.1549996 -2.47750497

0.1576889 -2.43881106

0.1603782 -2.40011406

0.1630675 -2.36142039

0.1657568 -2.32272625

0.1684461 -2.28403234

0.1711353 -2.24533558

0.1738246 -2.20664167

0.1765139 -2.16794753

0.1792032 -2.12925386

0.1818925 -2.09055686

0.1850000 -5.09709215

0.1887631 -1.71722066

0.1907429 -1.52609026

0.1929323 -1.37998676

0.1952548 -1.26247084

0.1976698 -1.16484416

0.2001530 -1.08188438

0.2026888 -1.01019764

0.2052661 -0.94744158

0.2078771 -0.89192647

0.2105160 -0.84239167

0.2131781 -0.79787028

0.2158601 -0.75760704

0.3000000 0.00000000

Outputs

SHOCKN provides files to plot up the signature at the specified distances from theaircraft. As the code runs, it supplies the following commentary:

SHOCKN run with inputs: -a 48000 -b 300 -d 600

ramp.wave

INPUT: Aircraft Altitude (m) 14630.40

(ft) 48000.00

INPUT: Aircraft Mach Number 1.800000

INPUT: Aircraft Body Length (m) 91.44000

(ft) 300.0000

INPUT: Input waveform distance (m) 182.8800

(ft) 600.0000

INPUT: sample rate 27600.00

INPUT: Points in spectra: 2 ^ 14 = 16384

-dx 4800 24000 -m 1.8

6

75 points read in with sample rate of 27600.0 Hz respaced toread in initial time = -0.004527 final time = 0.299953

respaced initial time= -0.004527 final time= 0.300000

8405 points

600.0 feet)from airplane

RiseTime=0.107807 seconds

4799.9 feet)from airplane

1 The wave form at 182.9 meters (

pmax= 2.9436 psf imx= 7538

pmin=-5.0886 psf imn= 92211 The wave form at 1463.0 meters (

pmax= 1.1261 psf imx= 6825

pmin=-l.1555 psf imn= 9836 RiseTime=0.091190 seconds

Switching from "FAIR" to "AIR" absorption at alt 13165.84 meters

1 The wave form at 7315.2 meters ( 23999.7 feet)from airplane

pmax= 0.7328 psf imx= 5906

pmin=-0.6061 psf imn= 9733 RiseTime=0.069129 seconds

1 The wave form at 14630.4 meters ( 47999.4 feet)from airplane

pmax= 0.7793 psf imx= 5690

pmin=-0.6432 psf imn= 10181 RiseTime=0.059572 seconds

Case description: DIST00183 SHOCKN wave with 2.944 psf max and 0.107807 sec

risetime

OVERALL LEVEL OASPL = 127.191 dB

A-WEIGHTED LEVEL SPLAW = 92.522 dB

C-WEIGHTED LEVEL SPLCW = 112.770 dB

PERCEIVED LEVEL SPLPL = 110.472 dB


risetime






risetime





Case description: DISTI4630 SHOCKN wave with 0.7793 psf max and 0.05957 sec

risetime





Case description: DISTI4630 SHOCKN wave with 0.7793 psf max and 0.05957 sec

risetime

Ground Reflection Factor 1.9





7

ZEPHYRUS Code

Summary

ZEPHYRUS propagates using weak shock theory in the time domain and appliesabsorption and dispersion effects in the frequency domain. Transfers between thetwo are done with the Fast Fourier Transform and occur when sufficient absorptionhas "accumulated" over the propagation distance. This happen over approximatelytwenty steps. The weak shock theory resolves shocks in the waveform betweenapplications of absorption.

A copy of ZEPHYRUS was obtained from Dr. Leick Robinson, now at SAIC. Thethree modules, "TSPLINE" to develop continuous curvefits of the atmosphere,"RAYTRACE" to calculate the ray paths, and "RAYPROP" to propagate a waveformalong a ray path were installed into the Boeing Sonic Boom Toolbox.

In addition to the atmosphere profile described following, parameters describing theray paths and waveform are needed. Examples of these files are included in thesample case.

Atmosphere Model

Zephyrus uses an atmosphere supplied by the user. The standard atmosphere profileused in this sample case looks like the following:

** ZEPHYRUS style air profile from ARAP .HAG output file *****************************************************************************

** This file constructed under the assumptions: **

** aircraft heading is 90 degrees compass, **

** North = ZEPHYRUS Y-direction per air navigation convention. **

** wind direction read from ARAP is based on **

** (0 degrees compass = ZEPHYRUS Y-direction) + 180 degrees, **

** but output ZEPHYRUS angle is measured from **

** X-dir per Conventional Cartesian geometry. ***W *W

** temperature and wind data are supplied at the same **** list of altitude values **WW *W

ATMOSPHERE FOR U.S. 1962 STANDARD ATMOSPHERE, NO WIND

Altitude Sound Speed wind Velocity Wind Velocity Air

along flight across flight Density

path path

(meters) (m/s) (m/s) (m/s) (kg/m3)

0

3O5

610

1219

1829

2438

3048

3658.

4267.

4877.

5487.

6096.

7011.

7925.

8839.

9754.

11019.

12192.

13411.

14326.

15240.

16764.

18288.

19812.

21336.

340.3052 0.00 0.00 1.22500883

339.1320 0.00 0.00 1.18957639

337.9581 0.00 0.00 1.15491395

335.5945 0.00 0.00 1.08793441

333.2142 0.00 0.00 1.02398986

330.8167 0.00 0.00 0.96296967

328.4051 0.00 0.00 0.90476391

325.9723 0.00 0.00 0.84932744

323.5247 0.00 0.00 0.79652170

321.0583 0.00 0.00 0.74627066

318.5694 0.00 0.00 0.69851661

316.0679 0.00 0.00 0.65312170

312.2728 0.00 0.00 0.58932064

308.4346 0.00 0.00 0.53041804

304.5444 0.00 0.00 0.47615435

300.6113 0.00 0.00 0.42624143

295.0788 0.00 0.00 0.36388839

295.0788 0.00 0.00 0.30267217

295.0788 0.00 0.00 0.24993006

295.0788 0.00 0.00 0.21649992

295.0788 0.00 0.00 0.18755608

295.0788 0.00 0.00 0.14766182

295.0788 0.00 0.00 0.11627384

295.0788 0.00 0.00 0.09157509

295.9402 0.00 0.00 0.07174076

Sample Case

The sample case used to demonstrate operation of the SHOCKN and ZEPHYRUScodes is based on the numerical exercise reported by Cleveland 5, for reasons

explained in the section comparing the two codes. This section is only concernedwith setting up inputs to ZEPHYRUS and running the program.

This is a NASA shaped wave obtained with the SHOCKN Code as a test case.

It is for a conceptual "low-boom" airplane at Mach 1.8, 48000 ft alt.

This waveform is 600 ft below the airplane, or 721.6 ft along the direction

of propagation. 721.6 ft is as long as 219.9 meters, by the way.

Time(sec)

-0.00452680

-0.00377230

-0.00233890

-0.00226340

0.00218430

0.00663210

0.0110798

0.0137691

0.0164584

0.0191477

0.0218370

0.0245263

0.0272155

0.0299048

0.0325941

0.0352834

0.0379727

0 0406620

0 0433513

0 0460406

0 0487299

0 0514192

0 0541085

0 0567977

0 0594870

0 0621763

0 0648656

0 0675549

0 0702442

0 0729335

0 0756228

0 0783121

0.0810014

0.0836907

0.0863799

0.0890692

0.0917585

0.0944478

0.0971371

0.0998264

0.102516

0.105205

0.107894

0.110583

0.113273

0.115962

0.118651

0.121341

0.124030

0.152310

0.155OOO

0.157689

Overpressure (Pascals)

@

0.00000

37.2812

74.5622

111.843

95.6056

79.3679

63.1301

64.9828

66.8356

68.6883

70.5410

72.3936

74.2465

76.0991

77.9518

79.8045

81.6572

83.5100

85.3627

87.2153

89.0680

90.9208

92.7735

94.6262

96.4789

98.3317

100.184

102.037

103.890

105.743

107.595

109.448

111.301

113.153

115.006

116.859

118.711

120.564

122.417

124.270

126.122

127.975

129 828

131 680

133 533

135 386

137 239

139 091

140 944

-120 476

-118 624

-116 771

-- 10 --

0.160378

0.163068

0.165757

0.168446

0.171135

0.173825

0.176514

0.179203

0.181893

0.185000

0.188763

0.190743

0.192932

0.195255

0.197670

0.200153

0.202689

0.205266

0.207877

0.210516

0.213178

0.215860

O.3OOOOO

-114.918

-113.065

-111.213

-109.360

-107.507

-105.655

-103.802

-101.949

-100.096

-244.050

-82.2210

-73.0696

-66.0741

-60.4474

-55.7730

-51.8009

-48.3685

-45.3637

-42.7057

-40.3339

-38.2022

-36.2744

0.00000

--II -

This is the file for parameters used to set up the ray path calculation in RAYTRACE.In this example, only the single ray directly under the aircraft is calculated. Thevalue of errortol sets the distance between points and usually needs to be optimized

for accuracy and running time for wave propagation. For the short extrapolations in

this report the value is not critical.

This is for a NASA shaped wave obtained with the SHOCKN Code as a test case.


sourcdir is the source direction in degrees ( zero = to East, not compass),

sourcez0 is the source altitude of 48000.0 feet cast in meters,

sourcedir sourcez0 sourcex0 sourcey0 sourcev

(degrees) (meters) (meters) (meters) (Mach)......

0.0 14630.0 0. 0. 1.800

rayt0 raytf rayti

(seconds) (seconds) (seconds)

@0 0 1

rayphi0 rayphif

(degrees) (degrees)

0.00 0.00

rayphii

(degrees)

......

1.0

Errortol stepstart

(seconds)

@0.0001 2.0

xcritical ycritical zcritical

(meters) (meters) (meters)@

-I.0 -i.0 -i.0

zreceiver

(meters)

@7315.

- 12-

The wave propagation along a ray is set by this set of parameters. Frequently, thepower of 2, resampratio and attensampm are adjusted for best performance for an

individual propagation.

This is the primary boom test case using a NASA shaped wave.


The airplane-waveform geometry is:

vertical distance from aircraft to waveform: 600.0 feet (182.9 meters)

with Mach number = 1.8, Co-Mach angle: 56.25 degrees

rest frame path length from airplane to signature: 721.6 feet (219.9

meters).

start distance (meters) characteristic time of waveform (sec)

219.9 0.401427

rel hum (%) power of 2 padding ratio attenuation threshold

@

20 14 0.50 9

nonlinear absorption dispersion@

1 1 1

resampratio stepratio

@30 5

ground impedance

6.0e06

ground flow resistivity@

270.0

reflectcoeff

@

attenerrorthresh attensampm

@0.00001 ii

- 13-

Outputs

The following is a typical commentary produced by the code when it is run. Other

files are constructed to plot the pressure wave, risetime and other wave parameters.

After the ZEPHYRUS propagation is concluded, the waveforms are automatically

processed through the Sonic Boom Toolbox module, LOUDBOOM, which performs

acoustic analysis of the waveforms. Frequency spectra are generated and metricswhich estimate loudness are calculated. The meaning of the acoustic analysis is

discussed in the following section discussing ZEPHYRUS propagation compared tomeasurement.

######################### getparams #########################

Enter name of input file containing propagation parameters: primary.propin

Enter name of input file containing ray data: primary.fan

Enter ray numbers (m [source time],n [ray angle]): 0 0

Total ray path length is 43904.0 meters with 77 points.

Enter name of input file containing the starting waveform: nasa/wave

######################### computeparams #########################

Enter name of output file for new ray parameters: primary.ray

######################### propagate #########################

Enter name of output file for waveforms along ray: primary_wave.ggp

Enter name of output file for rise-time function: primary.rip

Enter name of LoudBoom style file for pressure signatures: primary.lbin

Path Length= 220 Time= 0.75 S_00000219 *** Starting signature ***(76 points)

Path Length= 1277 Time= 4.33 S_00001276 Ordinary Pt, Alt=13568 m (120 points)

Path Length= 3333 Time= 11.30 S_00003333 Ordinary Pt, Alt=l1859 m (180 points)

Path Length= 7178 Time= 24.16 S_00007178 Ordinary Pt, Alt= 8680 m (181 points)

Path Length= 8854 Time= 29.60 S_00008854 Reciever at Alt= 7315 m (500 points)

Path Length=f5975 Time= 51.68 S_00015975 Ordinary Pt, Alt= 1660 m (300 points)

Path Length=18123 Time = 58.06 S_00018123 **At Ground Reflection **(333 points)

Reflection coefficient 'i' applied to 12618 wavepoints

Path Length=18123 Time= 58.06 S_00018123 Leaving Ground Reflection(333 points)

Path Length=27393 Time= 86.51 S_00027392 Reciever at Alt= 7315 m (370 points)

Path Length=30151 Time = 95.52 S 00030150 Ordinary Pt, Alt= 9568 m (368 points)

Path Length=38391 Time=123.38 S=00038391 Ordinary Pt, Alt=16413 m (281 points)

Path Length=43904 Time=142.06 S_00043904 End of ray, Alt=20996 m (255 points)

##### Start LoudBoom with inputs: primary.lbin

LoudBoom SampleRate for signature Sig53.00 is 53000 Hz

description *** S 00000219 *** Starting signature ** Time= 0.75 Dist=0

weightl: PERCEIVED LEVEL SPLPL = 110.673 dB


description *** S 00001276 Ordinary Pt, Alt= 13568 m Time= 4.33 Dist=0.501946



description *** S 00003333 Ordinary Pt, Alt= 11859 m Time=ll.30 Dist=0.981938



description *** S 00007178 Ordinary Pt, Aft = 8680 m Time=24.16 Dist=l.46394



description *** S 00008854 ****** At Reciever ****** Time=29.60 Dist=l.59792



description *** S 00015975 Ordinary Pt, Aft = 1660 m Time=51.68 Dist=l.94407

-- 14--

weightl: PERCEIVEDLEVELSPLPL= 92.240 dBLoudBoomSampleRatefor signature Sig53.06 is 52000Hz

description *** S 00018123 ** At GroundReflection **Time=58.06 Dist=2.00846weightl: PERCEIVEDLEVELSPLPL= 90.823 dB

Special Ground Reflection Calculation with Kr=l.9LoudBoomSampleRatefor signature Sig53.06 is 52000Hz

description *** S 00018123 ** At GroundReflection **Time=58.06 Dist=2.00846weightl: PERCEIVEDLEVELSPLPL= 96.780 dB

- 15-

Comparison of SHOCKN and ZEPHYRUS

Introduction

The sample case used to demonstrate operation of the SHOCKN and ZEPHYRUS

codes is based on the numerical exercise reported by Cleveland 5. Using the same

shaped (ramp) source waveform, the atmosphere was changed to the StandardAtmosphere with the motivation of comparing the codes under more realistic

conditions. Cleveland's study focused on the theoretical aspects of wave propagationand their practical implementation into propagation codes. The current effort is

concerned with extending these results to practical design analysis.

The input pressure signature is a "ramp" waveform at a distance of 183meters (600

feet) directly below the source, flying at 14,630m (48,000 feet) altitude with a Mach

number of 1.8. The waveform is not representative of a real aircraft configuration,but came from 10studies of shaping the source waveform for reduced annoyance . The

unusual shape with distinct shocks highlights nonlinear (wave steepening) andabsorption mechanisms during propagation.

3.0

2.0

1.0

0.0

_ -1.

_ -2.

0

TIME (seconds)

Figure i Source Waveform for sample case

- 16-

Impact of Standard Atmosphere

Cleveland's study used a uniform atmosphere and an isothermal atmosphere to

progressively introduce absorptive phenomena. The temperature of these twoatmospheres was set at -69.7 F (216.7K), a temperature representative of the

stratosphere. This study introduces the standard atmosphere to better quantify

absorption in practical analysis. The waveforms presented below are for waves at the

ground, with a ground reflection factor of 1.9 multiplying the propagated pressures to

simulate the signature as it would be heard by an observer.

¢,q

Standard Atmosphere

Isothermal(-69.7F)

Uniform

(-69. 7 F)

1.9 Ground reflection factor

TIME (0.1 seconds per tickmark)

Figure 2 Ground Signatures for sample case for three different atmospheres

The standard atmosphere gives results very close to the isothermal case, suggesting

that the initial propagation (where the atmosphere is similar for both cases)

dominates the waveform evolution. Overall, the standard atmosphere results in

slightly more attenuation (lower pressures) and the same wave steepening (sameduration) as the isothermal case.

- 17-

Comparison Results

Since the standard atmosphere gives results close the isothermal atmosphere results,the same good agreement noted by Cleveland applies here. ZEPHYRUS shows thesame wave shape, location of shocks and duration, as seen in Figure 3. Pressures forthe ZEPHYRUS propagation are slightly higher and are generally smoother. Theminor fluctuations in the SHOCKN case are similar to Cleveland's results and he

suggests them to be due to calculational inexactitudes introduced by the largenumber of Fast Fourier Transform operations.

Solid line: SHOCKN

Dash line: ZEPHYRUS


TIME (0.1 second per tickmark)

Figure 3 Ground Signatures for sample case propagated with SHOCKN andZEPHYRUS

As suggested by the shape and duration similarity of the two propagations, theoverall sound energy/pressure is essentially the same between SHOCKN andZEPHYRUS, being controlled by the high noise levels at low frequency (below 40 Hz).See Figure 4 on the following page. However, the implied increase in risetime by thepeak pressure reduction over the same duration of the SHOCKN propagation reducesthe high frequency content of the noise spectrum, with a corresponding reduction in

"ear weighted" noise metrics (five PLdB reduction, for example).

- 18 -

60.0

&

Solid line: SHOCKN

OASPL= 121 dB

SPL-A = 78 dB

SPL-C-- 99 dB

PL= 92 dB

Dash line: ZEPHYRUS

OASPL= 121 dB

SPL-A= 84 dB

SPL-C= 100 dB

PL= 97 dB

40.0


10 100 1000

1/3 Octave Band Center Frequency (Hz)

I

I0000

Figure 4 Noise Spectra for sample case propagated with SHOCKN and ZEPHYRUS

For propagation conditions of practical interest, SHOCKN and ZEPHYRUS give the

same results. Since they are different implementations of the same physics of thepropagation of sonic booms in air, they serve to verify that each implementation has

been constructed properly. In addition, ZEPHYRUS offers greater flexibility by

allowing winds, ray paths off of the centerline and easy changes to the atmosphere

profile. Because of this greater capability, ZEPHYRUS is preferred for solvinggeneral propagation problems.

- 19 -

Comparison to Experiment

SR71 Flight Test Summary

Data are becoming available from a 1995 flight test of the SR- 71 using a noveltechnique of probing the pressure field near the aircraft using a F-16XL chase planeflown through the shock waves 11. Measurements taken around 1000 feet and 5000feet from the SR-71 were used in an initial verification of the sonic boom

propagation codes. The data used were taken on March 16, 1995, with most of thedata obtained between 0930 and 1025 PST.

The data supplied by NASA include the weather conditions, flight conditioninformation for both SR-71 and F-16XL and the pressure signature located in space

relative to the SR-71. These pressure points were converted to a local pressure-time history based on a simplification to constant lateral and vertical separation andconstant probing speed. Appendix A presents the flight data, allowing evaluation of

the quality of these assumptions.

Nine of the twenty measurements taken at this range of distances are useful for thisexercise. The measurements naturally group into three sets of "near" and "far"

pairs, based on the angle from the vertical centerline of the SR-71.

Weather Conditions

Edwards sky condition reports were 22 Kfeet (AGL) scattered clouds at takeoff timeand 20Kfeet thin broken clouds the following two hours. Prevailing surface winds

were light, with less than five knots at Edwards AFB. Surface temperatures duringthe day are estimated at 56 to 63 F at Edwards, 62 to 66 F at Mojave, and 68 to 74 Fat China Lake, based on hourly measurements. At the ground boom-sensor (PATS)site they are roughly estimated to have been 65 +/- 6 E

The weather pattern was dominated by a surface high pressure in the IdahoMountain area with a weak offshore pressure gradient in the Nevada-California

area. The pressure dropped approximately 4 mb from the high to southern Nevadaand another 4 mb to the California coast. In the morning winds aloft were light at

low levles and westerly from 17 to 47 knots between 20 and 50 Kfeet MSL altitude.

By mid-afternoon winds increased approximately 20 knots between 20 and 35 Kfeet.IR and moisture satellite imagery showed that a high cloud region trailed acrosssouthern California from a core in central Nevada, in advance of a trough aloft. The

trough passed Edwards by sundown bringing clear skies from the northwest.

Analysis of upper air synoptic charts and interpolation to flight time indicated thatthe early morning air profile measurement would be more representative ofconditions at flight time than the afternoon observation. Temperature adjustments

of i degree C or less, and some wind increases reaching about 20 knots were made forthe reference air profile based at the Edward location. Larger temperaturemodifications were made in the surface layer on the basis of the hourly temperatureobservations.

Pressure heights nominally agree to better than 40 feet. At the surface the semi-diurnal pressure oscillation peak was 66 feet at 6:00 PM. Hence, an approximate

- 20 -

adjustment of 46 feet was used for the linearly interpolated synoptic heights derived

from noon on March 16 and midnight on March 17 charts. Temperatures at

mandatory levels agree to better than 1 deg C at altitudes above 10 Kfeet. Upperlevel humidities increased from near 25% in the early morning to near 60% in the

afternoon. The reference humidity profile values represent a subjectively smoothed

interpolation.

The following listing is the air profile configured for use by the sonic boom

propagation program, ZEPHYRUS. The entry for zero altitude (required forZEPHYRUS code) was created from extrapolated temperature and pressure data

(24.0 C and 1013.26 mB respectively).

ZEPHYRUS style air profile from SR71 Flight Data

***************************************************************************

Altitude Sound Speed Wind Velocity Wind Velocity Air

in X-Direction in Y-Direction Density

(Eastwardness) (Northwardness) (specific weight)

(meters) (m/s) (m/s) (m/s) (kg/m3)

0.0 345.580

2000.0 341.544

2302.3 340.307

2403.3 339.893

2605.9 339.301

2908.6 339.301

2915.3 339.301

3036.4 339.479

3536.1 339.834

4035.8 340.011

4153.8 340.247

4946.9 339.360

5035.4 339.242

5997.8 337.817

6034.6 337.817

7036.4 338.233

8035.0 337.401

10232.5 334.229

14033.6 328.529

16032.2 325.950

18887.8 321.167

20033.4 319.725

24272.3 313.505

28023.9 307.486

30813.8 302.279

34714.2 295.217

36002.3 293.099

36999.0 291.655

39321.3 295.285

-1.18

-1.18

-1.18

-1.18

-1.09

-0.99

-0.99

-0.99

-0.59

-0.51

-0.51

-0.51

-0.51

O.O7

0.91

2.67

2 22

3 60

6 25

8 O6

Ii 32

1400

1487

16.35

18.49

24.20

23.53

21.93

18.53

-0.99 1.1879087

-0.99 1.1347605

-0.99 1.1306385

-0.99 1.1292713

-1.09 1.1249437

-1.18 1.1126849

-1.18 1.1124173

-1.18 1.1063939

-0.84 1.0843346

-0.89 1.0638506

-0.89 1.0578623

-0.89 1.0333713

-0.89 1.0307840

-1.03 1.0036965

-0.16 1.0023469

1.54 0.9639376

2.64 0.9339329

2.92 0.8773427

2.92 0.7858023

2.16 0.7384183

0.20 0.6786824

0.00 0.6536466

1.30 0.5698102

2.01 0.5035302

1.29 0.4596891

0.00 0.4016229

0.00 0.3829193

0.00 0.3683661

0.00 0.3211502

- 21 -

Selected Flight Conditions

The "mid-field" data from Flight 24 were selected for this study, which includestwenty measurements. Within this set, fourteen signatures were examined for use inthe code verification exercise. Measurements 9 and 13 were rejected because the

lateral angle (PHI) was much greater than the other measurement conditions.Measurements 12, 18 and 20 were rejected because the flight direction of the probingaircraft was very non-parallel to the SR-71 during measurement. Measurement12, in particular, did not even traverse the length of the sonic boom waveform. Theacceptable measurements, with parameters of interest for the analytic projection arelisted in the following table.

Time

Measure Signature Signature dz0 dy0 Phiment Start End feet feet deg

SAM SAM

1 63001 63006 757.1 -17.1 -1.3

2 63035 63039 866.8 -90.3 -5.9

3 63392 63395 1372.1 107.2 +4.5

4 63438 63441 1991.8 26.8 +0.8

5 63492 63495 1871.6 48.0 +1.5

6 63949 63954

7 63994 63997

8 64078 64081

10

11

64310

64320

64317

64327

65732

Probing Conditions

845.3 -10.0 -0.7

762.6 -67.3 -5.0

567.8 -54.9 -5.5

5323.2

5215.5

1752.4

-198.6

395.3

34.2

-2.1

+4.3

+1.114 65729

15 65759 65761 956.9 -135.7 -8.1

16 65811 65815 714.3 -6.8 -0.5

17 65841 65845 1073.0 -53.9 -2.9

662266622319 -878.35127.1

SR71F_ght

Mach speedfps

1.24 1281.2

1.24 1285.9

1.26 1205.4

1.26 1197.8

1_5 1192.1

1.25 1297.1

1.25 1294.5

1.26 1306.8

1.25 1191.7

1.24 1184.8

1.26 1310.3

1.27 1313.4

1.25 1300.7

1.26 1306.5

-9.7 1.26

Alt GWfeet klb

31140 118.0

31082 116.7

30961 109.0

31007 107.8

31081 106.4

31163 103.2

31162 102.5

31097 101.7

30991 97.8

31012 97.3

31147 86.0

31128 85.8

31142 85.3

31181 84.6

31126 78.8 1195.2

Figure 5 Flight Conditions for SR-71 Flight Test

The signature start and end times in the above table, measured in Seconds AfterMidnight (SAM), are not the start and end times for data acquisition as listed inother test documentation but rather represent the duration of the actual boom

signature, taken to the nearest whole second outside the actual signature. Theseboundaries were established by inspection while preparing the data as described inthe following section.

With Mach number essentially constant at 1.25 and source altitude at 31,100 ft,examination of measurement distance and angle suggests comparison of "near"(around 1000 feet) and "far" (around 5000 feet) signatures at angles of -8.9, -1.6,

- 22 -

and 4.4 degrees from vertical downward. This is shown in the following graph. The"near" signature will be projected to the "far" distance for each set.

¢D

o

I

o

eD

6000- -

u B

4000- -

2000" -

m

0

-12

287

I, 1 1-8 -4

Cii|

0 4

.)

)

8

Angle from vertical downward, degrees

Figure 6 Selection of "Near" and "Far" Measurements for ZEPHYRUS Propagation

Derivation of Measured Waveforms for Extrapolation

The key measurement supplied from the SR71 flight test was pressure versus

longitudinal distance relative to the SR-71. However, to use the measurement in the

propagation code, it needs to be converted to pressure versus time at a fixed point in

space. If the fLxed point is chosen as the start of the signature (local longitudinaldistance, dx0=0) at position (local lateral distance, dy0), (local vertical distance, dz0)

relative to the the SR-71 nose (the origin of the coordinate system tied to the

SR-71) it will be appreciated that if dy0, dz0 and the SR-71 velocity are

independent of time, a longitudinal point at dx will arrive at the fixed point after thetime interval:

(incremental time of arrival, dt) = (longitudinal distance, dx)/[-(SR-71 speed)]

where the negative sign is required because of direction of flight of the SR- 71 in the

earth-based frame of reference. Because the real signature exists in three-

dimensional space and assumptions listed above were not strictly fulfilled, the ability

of a calculated value of dt based on a measured value of dx0 to correctly describe the

time sequence of the pressure signature is suspect. The degree of suspicion for

individual signatures may be assessed from examination of the distance by which dy0and dz0 deviate from their average value as well as how steady the SR-71 speed is.

This information is presented in Appendix A. The resolution was to add the

assumption that the relative speed of the SR-71 and the measurement probe in the

-23-

longitudinal direction is constant. The line comparing averagedx0/(measurementtime) to actual dx0 is also shown in Appendix A.

For the nine signatures used for propagation, Appendix B showsthe derivedsignature time histories. Of particular interest is the variation in signature duration,or length (since the speedis known). The far signatures are either extremely short(#10) or long (#11 and #19) and also have noticeable "fuzz" (short duration pressurefluctuations) in the data. The far measurements were also taken with the probeaircraft trajectory the most non-parallel to the SR-71 flight path. Extreme pressurespikes, which tend to be in adjacent pairs of values distinctly aboveand below thelocal averagevalue, were manually deleted in the three far waveforms in order toreduce the number of points that ZEPHYRUS would consider significant on output toan amount within the current capability of the code. Points were only deleted awayfrom shocks to preserve the character of the waveforms.

# Signature

feet

SignatureLength

Percent of

SR-71 length

RelativeDistanceDuration

sea

130 Near

Fuzz in data

Little1 0.1101 141.1

3 0.0983 118.5 110 Near Little

6 0.0988 127.5 119 Near Little

10 0.0659 78.5 73 Far Yes

11 0.2060 244.1 227 Far Yes

79

111

84.5

119.2

Near

Near

Near

Far

Little

Little

Little

Yes

15 0.0643

16 0.0916

17 0.1201

19 0.1509

156.9

180.3

146

168

Figure 7 Measured Signature Durations

- 24 -

Analytic Propagation

"Near" measurements 1, 3, 6, 15, 16, and 17 were extrapolated from theirmeasurement location to their corresponding "far" signature locations. The "far"

measurements were also processed through the extrapolation code without changingthe signature location in order to generate waveform fries in the same format as theextrapolated near measurements. Since the extrapolated signatures were comparedto measurements made "in the air", the ground reflection factor was set to 1.0 (no

reflection). The following table lists several parameters important to setting upinputs to the ZEPHYRUS code and the distances between the "source", "signature"and "receiver". The source is the SR-71 generating a pressure signal, the signatureis the pressure signal actually measured by the F-16XL and the receiver is aconceptual device detecting the pressure signal after it has propagated to a newlocation. The propagation distance in the table describes where the new location is.

# Propagation Parameters Propagation Distances

Mach

1

15 1.265

19 1.262

1 1.237

6 1.252

16 1.254

17 1.261

10 1.249

3 1.262

11 1.244

Headingdegrees Duration

62

242

61

61

62

62

242

242

243

Wave AveragePHI

sea angle

degrees

0.0643 -8.9

0.1509 -8.9

0.1101 -1.6

O.O988 -1.6

0.0916 -1.6

0.1201 -1.6

O.O659 -1.6

0.0983 4.4

0.2060 4.4

(SR-71)Source

Altitudefeet

31128

31127

31141

31165

VerticalDistance

(dz0)feet

957

5127

757

845

SignatureAltitude

feet

30171

26000

30384

30320

ReceiverAltitude

feet

26000

26000

25667

25667

PropagationDistance

feet

4171

0

4717

4653

31142 714 30428 25667 4761

31181 1073 30108 25667 4441

30993 5323

30961

25667

29589

25667

25796

2579631011 25796

1372

5215

0

3793

Figure 8 Propagation Parameters for ZEPHYRUS

-25-

Propagation parameters have to be "tuned" to each ZEPHYRUS propagation. Since

these data have many points in each signature and are propagated only a short

distance, the propagation parameters are different than those used in the exampleease:

rel hum (%)

45.0

nonlinear

l(yes)

resampratio

25

ground impedance

6.0e06

reflectcoeff

@l(hard ground)

attenerrorthresh

power of 2 padding ratio

14 0.25

absorption dispersion@

l(yes)

stepratio

@i0

ground

1 (yes)

flow resistivity

@

270.0

attensampm

@0.000001 12

attenuation threshold

@

Although the range of distance from "near" to "far" is not great, the expected trends

of increased duration, shock coalescence and peak pressure reduction are still seen.

Appendix C presents plots comparing "near" measured signatures to the extrapolated

signatures.

- 26 -

Comparison of Measured and Analytic Waveforms

First of all, it should be remembered that the range of extrapolation is not great forthis initial set of data. The "far" signature, approximately fifty body lengths awayfrom the source, shows some effects of non-linear steepening, with pressuresreduced by a factor of two to three and duration slightly increased, as shown by thesignatures in Appendix C. Most of the "fuzz" in the measurement has been smoothedout but significant shocks from bow, canopy, and inlets are still evident in thepropagated waves.

The following plots compare extrapolated waveforms to measured waveforms aswould be measured by the probe aircraft, that is, with no pressure increase due toground reflection (ground reflection factor equal to one). Considering pressureversus time, two of the comparisons (#15-#19 and #3-#11) show the extrapolatedsignature to be of much shorter duration than the signature measured at the farposition.

- 27 -

2

Dash Line:

Measured at 5215 feetfrom source

Solid Line:

Projected from 1372 feetto 5215 feetfrom source


Figure 9 Time History for Measurements #3 and #11

2

_o

I

1 Dash Line:I'II Measured at 5127feet, "_1 from source

r_ i _ Solid Line:: g J'_ _ Projected from 957 feet

ell _i, to 5127 feet.... From source

I I PI.- '_• .......

in" !



- 28 -

.L fl t Dash Line:i I\ ._ Measured at 5323 feet

2_ i\_ fromsourcei I _ • Solid Line:

_. 4- _a _ |i _ Projected from 757 feet| I_1\ I _tl'_, "_ t_o53_23 feet

_il_ [_r_ _ fromsource



I R J Dash Line:"_ I\ i Measured at 5323 feet

2 _ i \ ! from source| I _ • Solid Line:

1 __ I __ I Projected from 845 feet| _\ I • _ to 5323 feet

1 ._ "\1 _ It_ from source ]



- 29 -

Dash Line:Measured at 5323 feet

from sourceSolid Line:

Projected _][-rom714 feetto 5323 feetfrom source



2

Dash Line:Measured at 5323 feet

from sourceSolid Line:

Projected from 1073 feetto 5323 feetfrom source



- 30 -

In each of the comparisons, the measured far signature is at odds with expectation.

The signature generated at the aircraft is essentially the length of the aircraft, andwill only get longer with distance away from the source. Simple theoretical

considerations12-indicate the signature duration should grow at (ratio of distance) v',

which is somewhat faster than the duration growth rate seen in the detailed

propagations of Appendix C. Nevertheless, this indicates that it is primarily the

measured "far" signatures that are not consistent. Measurement 10 is too short andmeasurement 11 is too long. Measurement 19 is actually close to the expected

duration, but is paired with the shortest duration "near" signature.

During informal discussion of these results with Ed Haering 11 of Dryden Flight

Research Center, he suggested a refined data reduction method that appears toresolve these duration anomalies. Rather than setting the lateral (dy0) and vertical

(dz0) distances to the average value, the radial distance from the SR-71,

dr0 = _/(dyo 2 + dzo 2) (at each measurement point)

is calculated as the perpendicular component of the ray from the point of signal

generation at the SR-71 to the point of measurement, drar The longitudinal

component of dray is then found from the Mach angle, w,

_t= arcsine (1.0 / (Mach SR-71)

dxray - dray / tan

dxray is then added to the geometrical longitudinal distance, xo, resulting in a totaldistance back from the nose of the SR-71,

dback = dx0 + dxray = dx0 + (dray/tan _t)

The distance dback is then converted to time at a fixed point in space using the same

equation as the simplified procedure;

incremental time of arrival = dback / [-(SR-71 speed)]

where again the negative sign is needed to reconcile the coordinate system local to the

SR-71 to the ground based coordinate system. Note that the additional term, dxray 'has a constant value under the simplified procedure and would only shift the time

axis but has a variable value in the new procedure and decreases the relative time of

points measured closer to the SR-71.

Pressures of the shocks within the waveform match very well between the measured

and extrapolated waveforms, both the peak overpressures and intermediate peaks

from nose, canopy and other details of the aircraft geometry. Thus, by employing the

proposed new conversion for incremental time to resolve duration differences, the

prediction should match the measured signatures.

- 31 -

Noise Metrics

The frequency spectra and integrated noise metrics for each signature time history

were calculated using procedures outlined in Reference 13. Additionally, Reference14 describes the details of calculating the integrated metric, Perceived Level, which

has been found to give the best estimate of annoyance reaction to sonic boomsignatures. Because Perceived Level is calculated differently than the conventional

dB(A), dB(C) metrics, the procedure is outlined in Appendix D.

Reference 13 includes an instructive discussion of which aspects of a general

N-wave signature affect the sound spectrum. The salient aspects to the results of

this study are the similarity in low frequency (below 300 Hz) sound pressure levels

due to the similarity of peak pressures in the various signatures and the dissimilarity

of high frequency noise due to duration variation changing the time from beginning

of signature to peak pressure (an implied risetime). The duration/risetime also shifts

the specific frequencies that the low frequency maxima occur at, which changes the

overall energy of the spectra because the maxima fall along a six dB/octave slope fromthe peak SPL. The change is three to four decibels in sound pressure level for the

signatures in these comparisons.

MeasurementNumber

15 extrapolated

PeakPressure

psf

2.111

Signature Parameters

WaveDuration

sec

0.0603

OverallSound

PressureLevel

dB

120

PerceivedLevelPLdB

115

19measured 2.208 0.1509 123 112

I extrapolated 2.692 0.1006 121 116

6 extrapolated 2.752 0.0953 120 115

16extrapolated 2.367 0.0848 119 115

17extrapolated 2.475 0.1168 121 115

2.627 0.0659 118 11910 measured

3 extrapolated 1170.09352.559 114

llmeasured 2.339 0.2060 121 108

Figure 15 Extrapolated Signature Characteristics

Comments on specific comparisons of spectra are illustrated by plots following these

two paragraphs. The pairs, measurements #15-#19 and #3-#11, feature an

increase in OASPL (extrapolated to measured) but a decrease in PLdB. Additional

acoustic energy indicated by the increase in OASPL is at frequencies below 10 Hz (as

discussed above) which contributes very little to the annoyance response indicated by

PLdB. This energy appears to have partially come from frequencies above 1000 Hz,

thus encouraging reduction of PLdB. Measurements #3-#11, in particular, show

well defined peaks and valleys in their spectra, illustrating how duration shifts the

frequency of the acoustic energy distribution.

- 32 -

The four extrapolated signatures compared to measurement #10 are substantially the

same, with a spread in noise levels of only two decibels. Extrapolated durations are

all close to 0.1 second. They are compared to a far signature of 0.7 seconds duration,

so the ratio of durations (extrapolated to measured) is much closer to unity than the

previously discussed pairs. The high frequency spectra are also close, as would beexpected, but low frequency shifting of spectral peaks and valleys is still evident,

resulting in the three to four decibel differences between the extrapolated andmeasured noise metrics.

120|Solid Line

_----_Ii01 # _._,..,,,_ Measurementat957feet

| _ I i.._1 .__ extrapolated to 5127 feet• v 117. 4dB

100"1"-- " -__" "--" SPL-A= 98.67 dB

| V _,,_ SPL-C= 110 37 dB

I Dash Line "'_'_ _.PL= 113.93"dB

__ 90 I" Measurement at 5127 feet "__

! SPL-A= 92.61 dB __80+ :p "

PL= 108.02 dB _ •70

1 11,0 100 I000 I00001/3 Octave band Center Frequency (Hz)

Figure 16 Spectra for Measurements #3 and #11

Solid Line

120 It f_

Measurement at 1372 feet

_,__110 extrapolated to 5215 feet| OASPL= 120.11 dB

SPL-A= 99.47 dB

_-_ 100 L_ SPL-C= 111.58 dB

_v__.._PL= 114.81 dB

Dash Line _ _._


OASPL= 123.44 dS "_'_

SPL-A= 97.65 dB _ "_

SPL-C=110.35dB ___PL= 112.17 dB dB

, ,,,,,,, ,, ,,,,,,, , , ,,,,,,, , __,

9O

8O

7O I

I I I IIIIII I I lilllll I I I lJllll I I I I I Ill

0 I00 I000 I00001/3 _ctave band Center Frequency (Hz)


- 33 -

_-I i00 -L

90

80

70 ,1

Solid Line

Measurement at 757feet

extrapolated to 5323 feetOASPL= 120.66 dB

SPL-A= 100.08 dB

SPL-C= 111.99 dB

PL= 115.66 dB

Dash Line


OASPL= 118.40 dB

SPL-A= 99.20 dB

SPL-C= 110.73 dB

PL= 113.89 dB

| ! I | ||ta I ! ! | a |it| ! ! ! i |11|1 a' ' '"',6_c ' ' '"'_"oo ' ' ' '"'"_ooo '1/3 0cta b d Ce Freqve an nter uency (Hz)

! i II!11i0000


Solid Line

_-110(_

90,

80-Cb


__ extrapolated to 5323 feet. OASPL= 120.21 dB

__ SPL-A= 99.97 dB"W _ SPL-C: Ill. 75 dB

__ Dash_i.y_.... -_,_'__Measurement at5323 feet -_,_

OASPL= II8.40 dB

SPL-A= 99.20 dB _ _SPL-C= 110.73 dB

PL= 113.89 dB

70 ' ' '' ....... :''"" ' '' '":" ' '' '''"I I I i i illl I I I I lill i i I I i | II I I i i | ill

1 1(O IO0 I000 I00001/3 Octave band Center Frequency (Hz)


- 34 -

Solid Line


_olOO-

P.

_ 9o

_ 80

extrapolated to 5323 feetOASPL= 119.31 dB

SPL-A= 99.40 dB

SPL-C= 111.52 dB

PL= 114.81 dB

Dash Line


OASPL = 118.40 dB

SPL-A = 99.20dB

SPL-C= 110.73 dB

PL= 113.89 dB

I IIIIII ' ' ' ''''" ' ' ' ''''" ' ' ''....' ' '"01/3 Octave band Center Frequency (Hz)

70 ] I .....i ' "'/6ooo


121 f" Solid Line


_,_11 /" _% extrapolated to 5323 feet

I s,- _k% a_,_._.,_" SPL-A=OASPL=120.21 dB--. ,m _ 99.97 dB

100_ "q .A%_ SPL-C= 111.75 dB

_ l - -''V" _ PL=115"42dB¥ _

9°1 v_ Li_ _ _.--.__Measurement at 3523 feet -_OASPL= ll8.4O dB m_

_80J SPL-A=99.20dB __

SPL-C=110.73 dB

PL = 113.89 dB

70 _, I I[[ ..... ' .........................I IIII I l I I II_.il I I I I l IIII I I I I I III

0 b dCe °° Freq cy_z)lO0 100001/3 crave an nter uen

Figure 21 Spectra for Measurements #i and #17

- 35 -

Conclusions

Propagation Codes

The sonic boom propagation codes reviewed in this study, SHOCKN and ZEPHYRUS,implement current theory on air absorption using different computational concepts.Review of the codes with a realistic atmosphere model conf'nun the agreement of

propagation results reported by others for simplified propagation conditions.ZEPHYRUS offers greater flexibility in propagation conditions and is thus preferredfor practical aircraft analysis.

Comparison to Measurement

The ZEPHYRUS code was used to propagate sonic boom waveforms measured

approximately 1000 feet away from an SR-71 aircraft flying at Mach 1.25 to 5000feet away. These extrapolated signatures were compared to measurements at 5000feet. Pressure values of the significant shocks (bow, canopy, inlet and tail) in thewaveforms are consistent between extrapolation and measurement. Of particularinterest is that four (independent) measurements taken under the aircraft centerline

converge to the same extrapolated result despite differences in measurementconditions. Extrapolated and measured signature durations disagree because themeasured duration of the 5000 foot signatures either much longer or shorter than

would be expected. The measured durations are 0.07 seconds, 0.21 seconds and 0.15seconds where a value of 0.1 might be expected.

These duration anomalies may have been introduced by the simplified method of

converting the measured pressure at a position relative to the SR-71 to a timehistory at a fixed point in space. A more refined procedure has been suggested thataccounts for changes in SR-71 speed and position of the probe aircraft duringpressure measurement. Implementation of this procedure by others indicates a muchbetter resolution of near and far measurements.

- 35 -

Appendix ASR-71 Measured Pressure Signatures and Flight Conditions

Measurements of primary interest for sonic boom propagation study are the aircraft

(source) location and the signature pressures and location away from the aircraft.

Current propagation codes generally require non-accelerated flight, and ZEPHYRUS

in particular, requires steady level flight. The measured aircraft position and speedfor the 1995 SR-71 flight test (flight #24) are compared to the average values in this

appendix. The measurements taken around 5000 feet from the source are less steady

and less parallel the source than the measurements taken less than 1000 feet fromthe source, introducing more uncertainty to the propagation validation.

Time Probing Conditions SR71 Flight

Measure Signature Signature dz0 dy0 Phi Mach speedment Start End ft f_ deg fps

SAM SAM

1 63001 63006 757.1 -17.1 -1.3 1.24 1281.2

2 63035 63039 866.8 -90.3 -5.9 1.24 1285.9

63392

63438

63492

63395

63441

63495

1372.1

1991.8

1871.6

107.2

26.8

48.0

+4.5

+0.8

+1.5

1.26

1.26

1.25

1205.4

1197.8

1192.1

6 63949 63954 845.3 -10.0 -0.7 1.25 1297.1

7 63994 63997 762.6 -67.3 -5.0 1.25 1294.5

8 64078 64081 567.8 -54.9 -5.5 1306.8

Alt GWft klb

31140 118.0

31082 116.7

30961 109.0

31007 107.8

31081 106.4

31163 103.2

31162 102.5

31O97 101.7

3O991 97.8

31012 97.3

31147 86.0

31128 85.8

31142 85.3

31181 84.6

31126 78.85127.1

10 64310 64317 5323.2 -198.6 -2.1

11 64320 64327 5215.5 395.3 +4.3

14 65729 65732 1752.4 34.2 +1.1

15 65759 65761 956.9 -135.7 -8.1

16 65811 65815 71_3 -6.8 -0.5

17 65841 65845 1073.0 -53.9 -2.9

19 66223 66226 -878.3 -9.7

1.26

1.25

1.24

1.26

1.27

1.25

1.26

1.26

The following plots show the measured data for each of the above measurements.

1191.7

1184.8

1310.3

1313.4

1300.7

1306.5

1195.2

Line segments show the range defining "the signature", set to the nearest whole

second beyond the (non-zero) pressure signature. The lines mark the average value

(dy0, dz0, vtotsr) or speed (dx0 vs time) over that duration of (measurement) time.

The values beyond the line segment are not included in calculating the averages.The SR-71 source speed, vtotsr, is very steady over the signature duration. The

relative lateral (dy0) and vertical distance (dz0) tend to change steadily over time,

especially as distance between the SR-71 and the probe aircraft is increased. The

longitudinal position (dx0) has to change over time so the whole signature may be

measured. An average speed, dx0/dt, is plotted to show the unsteadiness in speed

during signature sampling.

- 37 -

Figure A.1 Measurement Number 1 of SR-71 Flight 24

-2oo

-4OO

-6OO

--80(

-1006 DO0

9XO - longitudinal distance from SR71 nose to F- 16XL shock pressure port, f_

xXX( X X X 36.3

_oo_ ,Joo__oo_ _oo_ _oo_ ,Joo,

__ dyO = -17.0670567

yYYYYYYYYYYYvY y yyyyyy y yyYyy

-2 YO - lateral distance from SR71 nose to F-16XL shock pressure port, feet

-360_'000 6:_001 6_002 631003 631004 6J005 631006 6,'-

900

85O

8OO

75O

7006_

10.

DZO- vertical distance from SR71 nose to F-16XL shock pressure port, feet

.... ._,_., 7.7 7 Z Z Z Z Z Z Z Z

Z Z Z Z Z Z Z E_/- z_ L z.. ,.- .... dzO = 757.124268

;et

63007

DO7

_oo ,Joo, ,_oo_,Joo_ ,Joo, Joo, ,Joo, I63007

5

0

-5

-10,6_

129(_

1285

128(

127

12763000

9PXL - overpressure

-I- ": =- I t I I

000 63001 63002 63003 63004 6Joo_6_oo6

VTOTSR- earth relative total velocity, sqrt(vdsr**2 + vesr**2 + vnsr**2), fps

vtotsr = 1281.15674

I63001

I I I I I63nn2 63003 . 63004 .63005 63006

TIME - seconas after mianlgm

- J i

63 007

63007

- 38 -

Figure A.2 Measurement Number 2 of SR- 71 Flight 24

--20_../

_404DXO -longitudinal distance from SR71 nose to F-16XL shock pressure port, f, :et

-8o '_""'"Y;'_ X X X10-

o y,.,,1DYO- lateral distance from SR71 nose to F-16XL shock pr_ssturYp_(_, Yeet 1

-lO_ y y ',rYY YY Y'f /

- 1 y y Y Y Y dy0=-90.2584991 I

-15t Y Y Y Y Y ' " I

-20_3 q:340

950

900

850

80(

9ZO - vertical distance from SR71 nose to F-16XL shock _esL_U _ I_rt_fe_t-., "7 7 Z ZZ..

Z Z Z Z Z Z Z Z Z A L "- dz0=866.773865B

75(:)34 63035 6,_

10

5

)40

-lq63034

130(;

129_

129(;

128,t

128(63034

VTOTSR - earth relative total velocity, sqrt(vdsr**2 + vesr**2 + vnsr**2), fps

I • m m

I63035

vtotsr = 1285.88892

II

I I I I

../._40_6_ 63037, G3P38. 63039seconas a_zermlanight

63040

63040

- 39 -


2XO- longitudinal distance from SR71 nose to F-16XL shock pressure port, h

X X X

X X XdxO = 74.4971205 x - 4723715.12

200

150

100

50.

0

63395 396

DYO - lateral distance from SR71 nose to F-16XL shock pressure port, feet

y y y v v v y y y v v v ',, ',, -, -,...... , , Y YydyO = 107.19471

t92

ii

160G DZO-vertical distance from SR71 nose to F-16XL shock pressure port, feet

)1_- - -' -" -7 Z 7 7 7 Z Z Z Z Z _

7_ Z Z Z Z_ £ z.. z.. - ,-- - dz0=1372.10938

136_914" 631392 631393/... 631394 631395 6;:

2" DPXL- overpressure in psf [ i/_1

y-2.

I /63391 6_392 q 63393 63394 63395 6_ t96

121.S u

.V-I'OTSR - earth relative total velocity, sqrt(vdsr**2 + vesr**2 + vnsr**2), fps

iii Iii

m

vtotsr = 1205.36768

121G

05 n ---

00-

1195 I ' v63393 63394

}3391 63392 TIME- seconds after midnight

I

63395 63396

- 40 -


DXO- longitudinal distance from SR71 nose to F-16XL shock pressure port,

CX X XX

dxO = -68.2836338 x + 4330296.48X X

50-

0

-5C

DYO - lateral distance from SR71 nose to F-16XL shock pressure port, feet

,., v v v V V Y Y Y Y Yy Y Y Y Y Y ITf " " dy0=26.8038826

2200

2109

2009

1909

180n6_

4

2

0

6,"

121(

120,_

120G

1195

119063437

2ZO - vertical distance from SR71 nose to F-16XL shock pressure port, feet

_' Z Z Z Z Z Z Z 7 Z E 2 z. z Z Z Z Z Z Z

dzO = 1991.80493

I

437 6_438 631439 631440 I63441 6_

_gPXL - overpressu

, , _1, ,

437 6_438 6_439 _440 6_441 6,_


vtotsr = 1197. 77148• n --

-- n

n I I I63438 63439 63440 63441

TIME - seconds after midnight

442

14.2

63442

- 41 -


9XO - longitudinal distance from SR71 nose to F-16XL shock pressure port, f_

X X X _7 x x x

-250(63494 63495

150 i

Ion_.DYO-lateral distance from SR71 nose to F-16XL shock pressure port, feet

Y Y Y Y Y Y Y Y Y Y V ','y y y y Y Y YdyO = 47.9715233

! 6 49a 6J49463491 63492

200£.

9ZO- vertical distance from SR71 nose to F-16XL shock pressure port, feet195(

190(

185G Z Z Z Z Z z L _' "-1 2 7 7 7 Z Z Z Z Z Z- dzO = 1871.62573

63494

- overpressure in psf

491 63494

1195

1194

1193

1192

119163491

/TOTSR - earth relative total velocity, sqrt(vdsr**2 + vesr**2 + vnsr**2), fps

vtotsr = 1192.11401

II • ._ .,

I I I63492 63495

163493 63494

TIME - seconds after midnight63496

- 42 -


XXX

X X X dxO = 35.7207609x- 2285083.56

9)(0 - longitudinal distance from SR71 nose to F-16XL shock pressure port,

K

=,et

distance from SR71 nose to F-16XL shock pressure port, feet

0

-50(

-100_

-150_

-200(6,- )48

100_.I

50-1DYO-lateral

['Y Y Y Y Y Y Y Y Y Y Y Y Y ¥ ','','

_ I

6_948 6_949 631950

900

850

8OO

750

7OO6,"

10

dyO = -10.0130672

Y Y YYYYYYYYYI

631951 631952 6J953 631954 63955

._777_, zZZZ zzzzzz

Z Z Z Z Z Z Z ZZ Z/- z..,..-- dz0=845.296448


948 6_949 631950 631951 631952 631953 631954 6C955

-1(

132e

131o

1300

129o

128o63948

955

ITOTSR - earth relative total velocity, sqrt(vdsr**2 + vesr**2 + vnsr**2), fps

q mm mm m

== II Ii

vtotsr = 1297.05737

I63949

I I I I I

6395"0"EHM63951 , 65.952 .,63953 63954- seconas aner mlamgm63955

- 43 -


5001

o tDXO-Iongitudinal distance from SR71nose to F-16XL shock pressure port, fletdxO = -84.0091678 x + 5375584.49 |

x x x x x x-100_ I

_ YO - lateral distance from SR71 nose to F-16XL shock pressure port, feet

dyO = -67.3150635

-6_-- Y Y Y y y y y V V _,' "," ","-i y y y' y y y

63993 63995 63996 63997 63998

9OO

800 Z Z Z 7 7 7 7 7 7 7 7 7 --, _ _

700.i dz0=762_4_58" z.. L Z Z Z

60 42Z0 - vertical distance from SR71 nose to F-16XL shock pressure port, feet

I5%93 631994 631995 631996 631997 63998

:tDPXL-°verpressureinps'__ I_._ l

-1(

130(

129_

129e

1285

128P63993 6_994

m

vtotsr= 1294.53564

/TOTSR - earth relative total velocity, sqrt(vdsr**2 + vesr**2 + vnsr**2), fps

6J995 1 63199763996TIME - seconds after midnight

63998

-44-


500_

0

-50(

-100

-150_6" 177

DXO- longitudinal distance from SR71 nose to F-16XL shock pressure port, flet< X X X

dxO = -85.2871942 x + 5464621.58 X X X

#o7 ,&o

-40

-60 y

lateral distance from SR71 nose to F-16XL shock pressure port, feet

.... ,, v v V Y Y Y Y Y Y

y y y y y y i . .dyO = -54.9129486

641078 641079 641080 6,_081 6,' 082

=_] ..., z y_ E -,' Z 7 7 Z z z Z Z z Z ']E_out- _ "-i Z /- L - /

%. _ dz0=567.832947 I

164077 64078 . 64079 64080 64081 64082

5 - _.

-5 DPXL - overpres

-106,' 177

131,5=

131(;

1305

1306

129564077

I J07964078 6_080 !64081 64082

• [] • .

vtotsr = 1306.79968


! I I I64078 64079 64080 64081 64082

TIME - seconds after midnight

- 45 -


-320E

-3406

-3606

-3806

-400[6,_

1000-

9)(0 - longitudinal distance from SR71 nose to F-16XL shock pressure port, f_:et

v ,,.. dxO = -14.9510993 x + 957647.009

^,,_X ........................ XXX:!K

500-

0

-50(

-100;6_

550G

540G

530G

520(

510(6z

4.

OYO- lateral distance from SR71 nose to F-16XL shock pressure port, feet

vvyyyyyyyyYYYYYY

_ ' ' dy0=-198.626434,yyyyyyyYYY Y Y Y 'y" ,_rV "'v


..... -.,--,==77777777ZZZZZZTZZZ

'.Z Z Z Z Z //_ _. z. z.._ ,- .- ...... dzO = 5323.21094

318

;18

1

0

,2, DPXL- overpressure in psf-'T

64309 64310 6,_311 64312

1200

I I I I I I

64313 64314 6,_315 64316 6,_317 6,_318

1195J

119(t,

1185,

118064309

vtotsr= 1191.74622 •

/-I'OTSR- earth relative total velocity, sqrt(vdsr**2 + vesr**2 + vnsr**2), fps

, I I I I I I I64310 6,_311 B4,'312 64313 64314 64_315. 64316 64317 64318

TIME-- seconds after mlanlght

- 45 -


-320E

-340E

-360_

-380E

--400f6_

80O

DXO-longitudinal distance from SR71 nose to F-16XL shock pressure port, fd

xXXXXX 82

319 J320 6,_321 6£22 641323 641324 6£25 6&26 641327 64

,et

328

600

400

200

06"

540(

53oq

5201

510(}

500e64

DYO- lateral distance from SR71 nose to F-16XL shock pressure port,.fe.e.ty

_,fvyyyyyyYY YYYYYYYYY

,yyyyyyyyyyyyY Y Y dyO= 395.286072

319 6&20 6&21 6&22 641323 641324 6£25 6&26 6&27 64 328

E Z Z Z Z Z ZZ Z Z ZZZ Z Z Z Z 7..7 .._,._._ dz0=5215.49268

-"-z"LZZZZZZZZzz

3ZO- vertical distance from SR71 nose to F-16XL shock pressure ponZfZE

319 64320

- overpressure in psf

122 64323 64325 64327

,20i11951-1,,.,.,., v, ** v r**- **^""119(_ -v jUTSR - earth relative total velocity, sqrt( dsr 2 + es z + vnsr z), rps I

• vtotsr= 1184.78857•1185 t • • • • • Tl

1180l l n I I I ! ! I64_319 64_320 64321 ..6.4-.322 64323,64324 6.4325 64326 64_327

//M_ - seconas after mzd-mght64328

- 47 -


1000

0

-1 O0

-200{;

-300(;6_

IO0-

)XO - longitudinal distance from SR71 nose to F-16XL shock pressure port, f,

X X X X ,, v v X " X v " v X " X X X Xj. a. al • a. al a_, a_ • a_ •

dxO = 72.9448023 x- 4796051.71

728 6J729 651730 657311 6J732 6{

_,et

733

v v V V Y Y Y Y

dyO = 34.1754913

3YO - lateral distance from SR71 nose to F-16XL shock pressure port, feet

65728

300£.

DZO - vertical distance from SR71 nose to F-16XL shock pressure port, feet250_

2oo 150 1

lOOm..65728 65729

--, --p "_ -p "7 ? 7 7 7 Z Z Z 7_Z Z Z _- = _ "-" "- .....

dzO = 1725.43506

I 6J730 I 6J73265731 65733

't I2 PXL - overpressure in psf

65 65730 65731 65732 65733

_I'OTSR- earth relative total velocity, sqrt(vdsr**2 + vesr**2 + vnsr**2), fps

-- n m

I u --

vtotsr = 1310.26807

I I I I65729 65730 65731 65732


132(3

1315

131G

1305

130C65728

- 48 -


500_/

tDXO - longitudinal distance from SR71 nose to F-16XL shock pressure port, t0

-5oo_ X X X y. v ,, y v v v Y _( X X-1004. .............. x

,_ dxO = -80.4780678 x + 5291409.51

0

'DYO- lateral distance from SR71 nose to F-16XL shock pressure port, feet

758

.FY y y ,, ,,, , ,,. ,., v v v y y y y

dyO = -135.7"0137

9ZO - vertical distance from SR71 nose to F-16XL shock pressure port, feet

1506 •dzO = 956.894653

_' Z Z Z 7 7 7 Z E 2 Z z.. zZ Z Z

758 65760

10-

6_ 762

5

0

-5

9PXL-overpressureinpsfN

-1065758

132_

1315

I I 65176165759 65760 65762

131G

1305

130_65758

vtotsr = 1313. 42383


I I I

6575__1M E 65760 a5761- secon-ds after midnighf65762

- 49 -


500_

0

-5O(

-100q

-150(

20-.

_XO -longitudinal distance from SR71 nose to F-16XL shock pressure port,

XXX

'_ X X X dxO = 57.2900867 x- 3771039.62

BIO }11 _12 3 916

0

-2

-40,

_,y y y v. vvv v v vvv v v vv ...., , y CYyy

dyO = -6. 7748 7183

3YO - lateral distance from SR71 nose to F-16XL shock pressure port, feet

810 311 2 }14 65815

900

316

80O.

700,

3ZO-vertical distance from SR71 nose to F-16XL shock pressure port, feet

_ .......z 7 7 Z Z Z Z Z Z Z /--

6001 Z Z Z Z Z Z Z Z /-- z. -... -.- dz0=714.27887

, , j j ,65816

10.

0

-5

-106,.

131C

1305

130G

129_

129(]65810

PXL-overpressure in psf.... _ -- - _ - -- - • - - -JI _-_ I " -

' ! • I _1 !810 65811 65812 65813 65814 65815

V-I'OTSR - earth relative total velocity, sqrt(vdsr**2 + vesr**2 + vnsr**2), fps

I I

E m II

vtotsr = 1300.76733

I65811

1 I I i

65813 G5,814. 65815seconcls after mlamght

65816

65816

- 50 -


500

0

-150_840

20O-

DXO- longitudinal distance from SR71 nose to F-16XL shock pressure port, f,

XX_xxx

6J841 6J842 6J843 I I65844 65845

_,et

65846

100.

0

-10q

-2On_6_

1200

1150

"DYO - lateral distance from SR71 nose to F-16XL shock pressure port, feet

.... ,, vv vyYY Y Y YY Y

y y y y y Y Y Y Y ' ' ' dyO=-53.8817825

i !

6,_846

"DZO- vertical distance from SR71 nose to F-16XL shock pressure port, feet

110G_ _ ...t -, ,-.7 _ --t -). 7 7 7 7 7 7 7 Z Z Z

1059_7 Z Z Z /--. z.. z. z... ,-.. --. - - - dzO= 1072.97266

lOOP 65!841 6J842 _ I I 65_845 l=

r''----"651841I 6J842 651843I 31.."-" _ I

132( '_INN

1314

131q

130_

130(65840

ii •


_otsr = 1306.45776

-- m m m

!65841

i I I I

65 43 G5 44 65845T_ 2- secon_4s after ml_zght

65846

-51 -


-100C

-200(

-300(

-4°° I X-500_,

66222

DXO - longitudinal distance from SR71 nose to F-16XL shock pressure port,

X X

dxO = -122.675854 x + 8120251.89

XXX

-400.I

__604DYO - lateral distance from SR71 nose to F-16XL shock pressure port, feet

-800_1 Y Y Y Y Y Y Y Y Y ,, __ ....

_et

<

227

i ' , , _ T y Y Y y y v-1 O0 dyO = -878.267151

5180

)ZO - vertical distance from SR71 nose to F-16XL shock pressure port, feet516G

514el .. _, 7 Z Z Z Z _7/ ='7Z7 z'-

512_ _ -. Z Z Z Z /-- L ""Z Z /- dzO = 5127.11914

........

2.[DPXL - overpressure in psf

6&23 ,&,, #=, #=, J66227

1205

120(}

1195

119G

118566222

/-I'OTSR - earth relative total velocity, sqrt(vdsr**2 + vesr**2 + vnsr**2), fps

vtotsr = 1195.17468

._. - • ..

I I I I66223 66224 66225 66226


- 52 -

Appendix BSignature Time Histories for Extrapolation

To prepare measurements of SR- 71 sonic boom pressure and location (relative to the

SR-71) for analytic propagation, they need to be converted to pressure versus time

at a fiLxed point in space. If the fixed point is chosen as the start of the signature(local longitudinal distance, dx0=0) at position (local lateral distance, dy0), (local

vertical distance, dz0) relative to the the SR-71 nose (the origin of the coordinate

system tied to the SR-71) it will be appreciated that if dy0, dz0 and the SR-71

velocity are independent of time, a longitudinal point at dx will arrive at the fixed

point after the time interval:

(incremental time of arrival, dt) = (longitudinal distance, dx) / [-(SR-71 speed)]

where the negative sign is required because of direction of flight of the SR- 71 in theearth-based frame of reference.

With the assumptions of dy0, dz0 and SR-71 velocity constant and dx0 a linearfunction of measurement time, the above equation was solved for the nine signatures

used for propagation. The plots in this appendix show these pressure signatures.

# Mach

1 1.237

3 1.262

6 1.252

10 1.249

11 1.244

15 1.265

16 1.254

17 1.261

19 1.262

Wave Average PHI (SR-71) Vertical SignatureDuration angle Source Distance Altitude

sec degrees Altitude (dz0) feetfeet feet

0.2 - 1.6 31141 757 30384

0.2 4.4 30961 1372 29589

0.2 - 1.6 31165 845 30320

0.1 -1.6 30993 5323 25667

0.3 4.4 31011 5215 25796

0.1 -8.9 31128 957 30171

0.1 -1.6 31142 714 30428

0.2 - 1.6 31181 1073 30108

0.3 -8.9 31127 5127 26000

- 53 -

I

{

IPressure (psf)

(1)

_°

CO

r_

0

m

(1)

_P

Z

0

Oo

{

I

t

Pressure (psf)o ro

I-.d o

o

O

q

0

I

t_ht_

I

I

"co"o

Pressure (psf)

o _0 ._ o_ oo o

_,,ao

rll

0

t_

0

I

I,-.4.

b_ht_

I

I

0

Pressure (psf)o

0

0

0

I

IL_

OO

I

Pressure (psf)o b_ 4_

r__r0

H-L

0

O3

I,'4

tO

Figure B.7 Time History for Measurement #16 of SR-71 Flight 24

-10 I I _ ' _ '0.38 0.40 0.42 044 0.46 0.48 0.50 0.52 0.54

" Time (seconds)

- 50 -

c'q

I

r_

o

o

° r,_l

° _1

oO

° _._

CO

(tsd)elnssaldI

I

I

Figure B.9 Time History for Measurement #19 of SR-71 Flight 24

4

2

-4 ! a ! ! I

' ' _o ' _,o3.12 3. 3.

I I I l I I

' 3._,4' 3._,s'3._2Time (seconds)

I

3.40

- 62 -

Appendix CWaveform Evolution

For the six examples of "near" waveforms propagated to "far" distances, the original

waveform is compared to the resulting far waveform after propagation. Pressures

have been reduced by a factor of two to three, duration has increased slightly andmost of the "fuzz" in the measurement has been smoothed out by non-linear

steepening effects. The significant shocks from bow, canopy, and inlets are still

evident in the propagated waves, however.

- 53 -

Figure C. 1 Extrapolation of Measurement Number i of SR-71 Flight 24

8\

6

Solid Line:

Measured at 757feet

from source

|

| Dot Line:

Projected to

5323 feetfrom source

TIME(O. 1 Seconds per Tickmark)

Figure C.2 Extrapolation of Measurement Number 3 ofSR-71 Flight 24

4

Solid Line:

Measured at 1372 feet

from source

Dot Line:

Projected to

5215 feet

from source

TIME(0.1 Seconds per Tickmark)

- 54 -

Figure C.3 Extrapolation of Measurement Number 6 of SR-71 Flight 24

8

6

O

Solid Line:

Measured at 845 feet

from source

|

S0

Dot Line:

Projected to

5323 feetfrom source


Figure C.4 Extrapolation of Measurement Number 15 ofSR-71 Flight24

6 _ _ Solid Line:

| _ Measured at 957 feet

4 _ from source

.i

-_" 'l N Projected to

_ i 5127feet


- 65 -

Figure C.5 Extrapolation of Measurement Number 16 ofSR-71 Flight24

8 Solid Line:

6 Measured at 714 feetfrom source

Dot Line:

Projected to

5323 feet

from source


Figure C.6 Extrapolation of Measurement Number 17 of SR- 71 Flight24

4

Solid Line:

Measured at 1073 feetfrom source

Dot Line:Projected to

5323 feet

from source


- 55 -

Appendix DCalculation of Percieved Level

CALCULATE 1t3OB SPECTRUM FROM GIVEN PRESSURE SIGNATURE

| ; .- I ". t >

, " , : ] I :.

m l--" i-J";"_v,i_l-"-!, .... ,--r'-_,_ O17....... .-._..:--.....,r--.._.--1

I " 1 ....

| t iI ] 1 __ ! I t t ="1

I ": i | ! |

TIME

j = ! ;|: :: ::;i i= |= =*:= :== i_h-, ; i il,":i I :i='l==" ' I:: _,}1 ,r i II%rq_ | = ' ;' [ = i • E I. _= "1_1 -

rJ-',.L;_;',_'_::_, _,--_.._.,.j=:,!,-..l., .:...l:,,.....I I I i::'.f I _ I IZ.'..'.'-_ _ I ". _ ! I I _)l=,

• : !:: ; .:: o : o_ll,=:= i= • ,_..',a,,_ • ,,o, . iq__.'.,...,Li.1, ......_.,_.,.,.,,._-..,

111_1"5",' I ,_iil!i_ t !""_il! '''=': i_,-.I-H.tl _I.=-_...-i--_.N-'N--. I.-;.,i.,_..R-':i--.-._.-H.:;._,!-:_.--.I

I I_>1 I ! ;iN'ill i i_i_i,' , i i'lll._ i

-l_'.!!---.i_,!l,_ , _ =,ll,_.%'.---,-.-' t..,:.,..-+-..i_,,_-

I_,ijll;." I i _,i!l.-'l ! ..' !ill_Jl

FREQUENCY"

CONVERT BAND PRESSURE LEVELS TO SONES (PERCEIVED MAGNITUDE}

:._.:-.. :" ...::-:-....'_- -_. _. - ....... - .... .___..=_,_._,,,.__ -- •. ..... .'.

I ", ""-?' ...':::_::.:'=::..":--::"-;:-.'::...... "........ - ............ _.,_._-..-.-_° .... L" .'::,"',",,_,,,.,>...-.. .....-..,.-...=-..:..........=....... ................__,,...... -... ....,. ",::,'._-__,.,..............o.......-...::..... -.......--:.......................... ...-, ......._. .... ..... ....• ...............,]

• _,_ .'_ "_.,._'_._'..,."..,. _. . --._ "--_ ...._.,t.,=... "-.. " ........... .."J _..._lllll//llll_ _ x_."_ ',...'_:_,_,_'._'.,.. ".. ...... - ......... - ..... • ......... ..-,..,.,',,,b,.",_"_,_.,, ""-_'.,.. "" ..... ".......... _"... ..... . .......... :.."

13,. $

f,,_,_,:=_-.:.-.._.=:::::.....:::-...........................: : ......

I I .,_ .;_ _ ..•,, --,,.'-...,.'--_ ...... • ......... :_-... •.... ..,./..

MAXIMUM $ONE LEVEL _._'--.:.......... _----..i'-"- ........ :2-"..,<._,-.',--_.............. ..... ...........

FREQUENCY

FLAG MAXIMUM SONE LEVEL AND READ SUMMATION FRACTION FUNCTION AT THIS VAf.TO ACCOUNT FOR MASKING OF SPECTRUM BY LOUDEST BAND

i:....... ...............................................-3

MAXIMUM SONE t I=VEL

CALCULATE 'TOTAL LOUDNESS IN SONES AND CONVERT TO PL IN DECII_ELS

- 67 -

References

H. S. Ribner, Atmospheric Propagation and Sonic Boom, AGARD Lecture Series No

77, (AGARD-LS-77) June, 1975.

2 F. M. Pestorius, Propagation of Plane Acoustic Noise of Finite Amplitude, Technical

Report ARL-TR-73-23, Applied Research Laboratories, The University of Texas

at Austin, August 1973.

3 M. O. Anderson, The Propagation of a Spherical N Wave in an Absorbing Medium

and its Diffaction by a Circular Aperture, Technical Report ARL-TR-74-25,

Applied Research Laboratories, The University of Texas at Austin, August 1974.

4 H.E. Bass, J. EzeU, and R. Raspet, Effect of Vibrational Relaxation on Rise Times of

Shock Waves in the Atmosphere, J. Acous. Soc. Am. "/4 (5) November 1983.

5 R. O. Cleveland, et. al., Comparison of Computer Codes for the Propagation of Sonic

Booms through the Atmosphere, Submitted to the JASA, July 1995. An oral version

was presented at the Spring 1995 Meeting ofASA (J. Acous. Soc. Am. 97 3259 (A)(1995).

6 J. Von Neumman and R. D. Ricktmyer, A Method for the Numerical Calculation of

Hydrodynamic Shocks, in '_lohn Von Neumann Collected Works", Vol IV (pp.380-385).

7 L.D. Robinson, Sonic Boom Propagation through an Inhom ogeneous, Windy

Atmosphere, Ph.D. Dissertation 9212620, The University of Texas at Austin, 1991.

8 L.D. Robinson, A Numerical Model for Sonic Boom Propagation through an

Inhomogeneous, Windy Atmosphere, presented at the 123 m Meeting of the Acoustical

Society of America, Salt Lake City, Utah, May 11-15, 1992.

9 J.D. Anderson, Jr., Introduction to Flight, 1978.

10 J. D. Leatherwood and B. M. Sullivan, Laboratory Study of Effects of Sonic Boom

Shaping on Subjective Loudness and Acceptability, NASA Technical Paper 3269,1992.

11 E. A. Haering, Jr., L. J. Ehernberger, and S. A. Whitmore, Preliminary Airborne

Measurements for the SR- 71 Sonic Boom Propagation Experiment, NASA TechnicalMemorandum 104307.

12 A. D. Pierce, Acoustics - An Introduction to its Physical Principles and Applications,

1989, page 613.

13 K.P. Shepard and B. M. Sullivan, A Loudness Calculation Procedure Applied to

Shaped Sonic Booms, NASA Technical Paper 3134, November 1991.

14 S. S. Stevens, Perceived Level of Noise by Mark VII and Decibels (E), J. Acous. Soc.Am 51 (2) (1972).

- 68 -

REPORT DOCUMENT PAGE Fom,pp v OMB No. 0704-0188

Pubtk reportln 8 for _ls c_llecflon of Informa:lon U est_nx_d _ tl_e.,xgt I bout _ nstm4u_ Letciudlng the time _ revlew_g In.gtzucllom, Jexrchlt_g exlstln8 data sources,

l,l._er trig and mxJatitalng U_ ¢Lsll _ and completing lind revlcwlag _ collecGon 43(' tnformntlon. 5eDd eomme_is reglrd_li Ulls burden cstl_Jt_ of" any other _Lspect Of t_tS

collection m" IEffo_tlon, tncludlng mggestlol_.8 foc rL, dXw.lng rials btwdr._ Io Wa_toa Hcl_qLutrlte_ Scrvlcm. DIr_tarat¢ for Information Ol_._tlons L_t Reports. t_d,5 J¢ffcrsoa

l_lt_ HJBhwlt 7. Suite 1_04. A,rJlnStoa, YA 2_02..430_ gild the _ d Mlzul_tn! add Budget, _r'work Redug_ Project (070_.01U), WsJhlnSma, DC 20_X

I.AGENCY USE ONLY (Leave blank) 2.REPORT DATE

October 1996

4 Tm.E _'_'Dsu_rrr_ 5. FUN_G r_'UMSERS

Sonic boom propagation codes validated by flight test

6. AUTHOR(S)

Hugh W. Poling

7. PERFORMINGORGANIZATIONNAME(S)ANDADDRESS(ES)

Boeing Commercial Airplane Group

Division of The Boeing Company

Seattle, Washington 98124-2207

).SPONSORING/MONrI_RINGAGENCYNAME(S)ANDADDRESS(ES)

National Aeronautics and Space Administration

Langley Research Center

Hampton, VA 23681-0001

3.REPORTTYPEANDDATESCOVERED

Contractor Report

NAS1-20220, Task 34

537-07-21

8. PER.FOR_MING ORGANIZATION

REPORT NUMBER

10. SPONSORING/MONI:I 1.)RINGAGENCY REPORT NUMBER

NASA CR-201634

I 1. SUPPLEMENTARY NOTES

Langley Technical Monitor: Daniel G. Baize

12a.DISTRIBUTION/AVAILABII/TYSTATEMFaNTUnclassified - Unlimited

Subject Category 02

I_.D_qKIBUTION CODE

13. ABSTRACT (Maximum 200 words)

The sonicboom propagationcodesreviewedinthisstudy,SHOCKN andZEPHYRUS, implementcurrenttheoryon airabsorption using different computational concepts. Review of the codes with a realistic atmosphere model confirm theagreement of propagation results reported by others for idealized propagationconditions. ZEPHYRUS offers greaterflexibility in propagation conditions and is thus preferred for practicalaircraft analysis.

The ZEPHYRUS code was used to propagate sonic boom waveforms measured approximately 1000 feet away from anSR-71 aircraft flying at Mach 1.25 to 5000 feet away. These extrapolated signatures were compared to measurements at5000 feet. Pressure values of the significant shocks (bow, canopy, inlet and tail) in the waveforms are consistent betweenextrapolation and measurement. Of particular interest is that four (independent) measurements taken under the aircraftcenterline converge to the same extrapolated result despite differences in measurement conditions. Agreement betweenextrapolated and measured signature duration is prevented by measured duration of the 5000 foot signatures either muchlonger or shorter than would be expected. The duration anomalies may be due to signature probing not sufficiently parallelto the aircraft flight direction.

14. SUBJECT TER.MS

I) Acoustics, 2) Sonic Boom, 3) Propagation, 4) Absorption,

5) Computer Code

17. SECUR/TY CLASSIFICATION

OF REPORT

Unclassified

18. SECURITYCLASSIFICATION119.SECURITYCLASSIFICATIONOFTHISPAGE OFABSTRACTUnclassified Unclassified

15.NUMBER OF PAGES

74

16. PRICE CODE A04

20. I..LMYI'ATIONOF ABSTRACT

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