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
iii
V
vi
1
1
1
2
2
2
4
4
4
5
6
8
8
8
9
14
16
16
17
18
20
20
20
22
23
25
27
32
36
36
36
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
Time History for Measurements #1 and #10 ................... 29
Time History for Measurements #6 and #10 ................... 29
Time History for Measurements #16 and #10 .................. 30
Time History for Measurements #17 and #10 .................. 30
Extrapolated Signature Characteristics ........................ 32
Spectra for Measurements #3 and #11 ......................... 33
Spectra for Measurements #15 and #19 ....................... 33
Spectra for Measurements #1 and #10 ......................... 34
Spectra for Measurements #1 and #6 .......................... 34
Spectra for Measurements #1 and #16 ......................... 35
Spectra for Measurements #1 and #17 ......................... 35
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 3 of SR-71 Flight 24 ....................
Number 4 of SR-71 Flight 24 ....................
Number 5 of SR-71 Flight 24 ....................
Number 6 of SR-71 Flight 24 ....................
Number 7 of SR-71 Flight 24 ....................
Number 8 of SR-71 Flight 24 ....................
Number 10 of SR-71 Flight 24 ..................
Number 11 of SR-71 Flight 24 ..................
Measurement Number 14 of SR-71 Flight 24 ..................
Measurement Number 15 of SR-71 Flight 24 ..................
Measurement Number 16 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
Number 17 of SR-71 Flight 24 ..................
Number 19 of SR-71 Flight 24 ..................
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 11 of SR-71 Flight 24...
for Measurement Number 15 of SR-71 Flight 24...
for Measurement Number 16 of SR-71 Flight 24 ...
for Measurement Number 17 of SR-71 Flight 24 ...
for Measurement Number 19 of SR-71 Flight 24...
of Measurement Number 1 of SR-71 Flight 24 ....
of Measurement Number 3 of SR-71 Flight 24 ....
of Measurement Number 6 of SR-71 Flight 24 ....
of Measurement Number 15 of SR-71 Flight 24 ...
of Measurement Number 16 of SR-71 Flight 24 ...
of Measurement Number 17 of SR-71 Flight 24 ...
vi
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
54
55
56
56
58
59
60
61
62
63
64
65
65
66
66
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
Case description: DIST01463 SHOCKN wave with 1.126 psf max and 0.091190 sec
risetime
OVERALL LEVEL OASPL = 118.813 dB
A-WEIGHTED LEVEL SPLAW = 81.286 dB
C-WEIGHTED LEVEL SPLCW = 100.515 dB
PERCEIVED LEVEL SPLPL = 95.090 dB
Case description: DIST07315 SHOCKN wave with 0.7328 psf max and 0.06913 sec
risetime
OVERALL LEVEL OASPL = 114.814 dB
A-WEIGHTED LEVEL SPLAW = 81.657 dB
C-WEIGHTED LEVEL SPLCW = 94.088 dB
PERCEIVED LEVEL SPLPL = 95.070 dB
Case description: DISTI4630 SHOCKN wave with 0.7793 psf max and 0.05957 sec
risetime
OVERALL LEVEL OASPL = 115.405 dB
A-WEIGHTED LEVEL SPLAW = 72.527 dB
C-WEIGHTED LEVEL SPLCW = 93.691 dB
PERCEIVED LEVEL SPLPL = 86.281 dB
Case description: DISTI4630 SHOCKN wave with 0.7793 psf max and 0.05957 sec
risetime
Ground Reflection Factor 1.9
OVERALL LEVEL OASPL = 120.980 dB
A-WEIGHTED LEVEL SPLAW = 78.102 dB
C-WEIGHTED LEVEL SPLCW = 99.266 dB
PERCEIVED LEVEL SPLPL = 92.209 dB
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.
It is for a conceptual "low-boom" airplane at Mach 1.8, 48000 ft alt.
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.
It is for a conceptual "low-boom" airplane at Mach 1.8, 48000 ft alt.
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
LoudBoom SampleRate for signature Sig53.01 is 53000 Hz
description *** S 00001276 Ordinary Pt, Alt= 13568 m Time= 4.33 Dist=0.501946
weightl: PERCEIVED LEVEL SPLPL = 105.538 dB
LoudBoom SampleRate for signature Sig53.02 is 52000 Hz
description *** S 00003333 Ordinary Pt, Alt= 11859 m Time=ll.30 Dist=0.981938
weightl: PERCEIVED LEVEL SPLPL = 99.375 dB
LoudBoom SampleRate for signature Sig53.03 is 52000 Hz
description *** S 00007178 Ordinary Pt, Aft = 8680 m Time=24.16 Dist=l.46394
weightl: PERCEIVED LEVEL SPLPL = 97.597 dB
LoudBoom SampleRate for signature Sig53.04 is 52000 Hz
description *** S 00008854 ****** At Reciever ****** Time=29.60 Dist=l.59792
weightl: PERCEIVED LEVEL SPLPL = 93.453 dB
LoudBoom SampleRate for signature Sig53.05 is 52000 Hz
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
1.9 Ground reflection factor
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
1.9 Ground reflection factor
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
TIME (0.1 seconds per tickmark)
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" !
TIME (0.1 seconds per tickmark)
Figure 10 Time History for Measurements #15 and #19
- 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
TIME (0.1 seconds per tickmark)
Figure 11 Time History for Measurements #1 and #10
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 ]
TIME (0.1 seconds per tickmark)
Figure 12 Time History for Measurements #6 and #10
- 29 -
Dash Line:Measured at 5323 feet
from sourceSolid Line:
Projected _][-rom714 feetto 5323 feetfrom source
TIME (0.1 seconds per tickmark)
Figure 13 Time History for Measurements #16 and #10
2
Dash Line:Measured at 5323 feet
from sourceSolid Line:
Projected from 1073 feetto 5323 feetfrom source
TIME (0.1 seconds per tickmark)
Figure 14 Time History for Measurements #17 and #10
- 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 _ _._
Measurement at 5215 feet
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)
Figure 17 Spectra for Measurements #15 and #19
- 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
Measurement at 5323 feet
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
Figure 18 Spectra for Measurements #1 and #10
Solid Line
_-110(_
90,
80-Cb
Measurement at 845 feet
__ 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)
Figure 19 Spectra for Measurements #1 and #6
- 34 -
Solid Line
Measurement at 714 feet
_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
Measurement at 5323 feet
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
Figure 20 Spectra for Measurements #1 and #16
121 f" Solid Line
Measurement at 845 feet
_,_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 -
Figure A.3 Measurement Number 3 of SR-71 Flight 24
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 -
Figure A.4 Measurement Number 4 of SR- 71 Flight 24
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 - earth relative total velocity, sqrt(vdsr**2 + vesr**2 + vnsr**2), fps
vtotsr = 1197. 77148• n --
-- n
n I I I63438 63439 63440 63441
TIME - seconds after midnight
442
14.2
63442
- 41 -
Figure A.5 Measurement Number 5 of SR- 71 Flight 24
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 -
Figure A.6 Measurement Number 6 of SR- 71 Flight 24
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
DZO- vertical distance from SR71 nose to F-16XL shock pressure port, feet
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 -
Figure A.7 Measurement Number 7 of SR-71 Flight 24
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-
Figure A.8 Measurement Number 8 of SR- 71 Flight 24
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
VTOTSR - earth relative total velocity, sqrt(vdsr**2 + vesr**2 + vnsr**2), fps
! I I I64078 64079 64080 64081 64082
TIME - seconds after midnight
- 45 -
Figure A.9 Measurement Number 10 of SR- 71 Flight 24
-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
DZO- vertical distance from SR71 nose to F-16XL shock pressure port, feet
..... -.,--,==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 -
Figure A.10 Measurement Number 11 of SR-71 Flight 24
-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 -
Figure A.11 Measurement Number 14 of SR-71 Flight 24
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
TIME - seconds after midnight65733
132(3
1315
131G
1305
130C65728
- 48 -
Figure A.12 Measurement Number 15 of SR-71 Flight 24
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
VTOTSR - earth relative total velocity, sqrt(vdsr**2 + vesr**2 + vnsr**2), fps
I I I
6575__1M E 65760 a5761- secon-ds after midnighf65762
- 49 -
Figure A.13 Measurement Number 16 of SR-71 Flight 24
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 -
Figure A.14 Measurement Number 17 of SR-71 Flight 24
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 •
VTOTSR - earth relative total velocity, sqrt(vdsr**2 + vesr**2 + vnsr**2), fps
_otsr = 1306.45776
-- m m m
!65841
i I I I
65 43 G5 44 65845T_ 2- secon_4s after ml_zght
65846
-51 -
Figure A.15 Measurement Number 19 of SR-71 Flight 24
-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
TIME - seconds after midnight66227
- 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
I
I
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
TIME(0.1 Seconds per Tickmark)
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
TIME(0.1 Seconds per Tickmark)
- 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
TIME(0.1 Seconds per Tickmark)
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
TIME(0.1 Seconds per Tickmark)
- 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