Domenic J. Maglieri

Percy J. Bobbitt

Kenneth J. Plotkin

Kevin P. Shepherd

Peter G. Coen

David M. Richwine

BOOM

SONIC

Six Decades of Research

https://ntrs.nasa.gov/search.jsp?R=20150006843 2017-09-14T14:13:23+00:00Z

Six Decades 

of Research

NASA/SP-2014-622

Langley Research Center

Hampton, Va. 23681-2199

SONIC 

BOOM
1RWLFH7UDGHQDPHVDQGWUDGHPDUNVDUHXVHGLQWKLVUHSRUWIRULGHQWL¿FDWLRQRQO\

7KHLUXVDJHGRHVQRWFRQVWLWXWHDQRI¿FLDOHQGRUVHPHQWHLWKHUH[SUHVVHGRULPSOLHG

E\WKH1DWLRQDO$HURQDXWLFVDQG6SDFH$GPLQLVWUDWLRQ
 About the Authors/Acknowledgements

iii

ABOUT THE AUTHORS

Domenic J. MaglieriJUDGXDWHGIURPWKH8QLYHUVLW\RI3LWWVEXUJKLQZLWKD%DFKHORURI6FLHQFH%6GHJUHH

LQ0HFKDQLFDO(QJLQHHULQJ$HURQDXWLFDO(QJLQHHULQJ0($(DQGEHJDQKLVSURIHVVLRQDOFDUHHUDWWKH1DWLRQDO

$GYLVRU\&RPPLWWHH IRU$HURQDXWLFV 1$&$/DQJOH\$HURQDXWLFDO/DERUDWRU\ /$/ QRZ1$6$/DQJOH\

5HVHDUFK&HQWHU>/D5&@+HKDVRYHU\HDUVRIH[SHULHQFHLQQRLVHFRQWURODQGPHDVXUHPHQWVRQVXEVRQLF

DQGVXSHUVRQLFDLUFUDIWURWRUFUDIWDQGYHUWLFDOVKRUWWDNHRIIDQGODQGLQJYHKLFOHV+HUHWLUHGIURPWKH1DWLRQDO

$HURQDXWLFVDQG6SDFH$GPLQLVWUDWLRQ1$6$LQDQGMRLQHG(DJOH$HURQDXWLFVDV'LUHFWRUIRU3URMHFWV

+HLVFRQVLGHUHGRQHRIWKHOHDGLQJQDWLRQDODQGLQWHUQDWLRQDOH[SHUWVRQVRQLFERRPV+LVVRQLFERRPÀLJKWWHVW

LQYROYHPHQWEHJDQLQDQGKDVFRQWLQXHGIRURYHUDKDOIFHQWXU\'XULQJKLV\HDUFDUHHUZLWK1$&$

1$6$DQG\HDUVZLWK(DJOH$HURQDXWLFVKHKDVSDUWLFLSDWHGLQHYHU\PDMRUVRQLFERRPÀLJKWWHVWSURJUDP

DQGKDVDXWKRUHGRUFRDXWKRUHGRYHUSXEOLFDWLRQVRIZKLFKDUHRQVRQLFERRP+HLVD)HOORZRIWKH

$FRXVWLFDO6RFLHW\RI$PHULFDDERDUGFHUWL¿HGPHPEHURIWKH,QVWLWXWHRI1RLVH&RQWURO(QJLQHHULQJDQGDQ

$VVRFLDWH)HOORZRIWKH$PHULFDQ,QVWLWXWHRI$HURQDXWLFVDQG$VWURQDXWLFV$,$$

Percy J. BobbittJUDGXDWHGIURP&DWKROLF8QLYHUVLW\LQZLWKD%6GHJUHHLQ$(DQGEHJDQKLVFDUHHUDW

WKH1$&$/$/LQ'XULQJKLV\HDU1$&$1$6$FDUHHUKHVSHFLDOL]HGLQVXSHUVRQLFDQGWUDQVRQLF

ÀRZ WKHRU\ DLUFUDIW DHURG\QDPLFV DHURHODVWLF ORDGV DHURWKHUPRG\QDPLFV RUELWDO HQWU\ YHKLFOHV VXSHUVRQLF

SDUDFKXWHVVKXWWOHWKHUPDOSURWHFWLRQZLQGWXQQHOÀRZTXDOLW\DQGODPLQDUÀRZFRQWURO+HUHWLUHGLQDV

&KLHIRIWKH$SSOLHG$HURG\QDPLFV'LYLVLRQZKHUHKHZDVUHVSRQVLEOHIRUWKHFRQGXFWRIDHURQDXWLFDOUHVHDUFK

LQIXQGDPHQWDOÀXLGÀRZVFRQ¿JXUDWLRQDHURG\QDPLFVWHVWWHFKQLTXHVDQGSURSXOVLRQV\VWHPLQWHJUDWLRQ+H

ZDVD NH\PHPEHU RIWKH6KXWWOH&HUWL¿FDWLRQ&RPPLWWHH IRU¿UVWÀLJKWDQG KHDQG KLV GLYLVLRQZHUHPDMRU

FRQWULEXWRUVLQEULQJLQJWKH1DWLRQDO7UDQVRQLF)DFLOLW\WRRSHUDWLRQDOVWDWXV+HMRLQHG(DJOH$HURQDXWLFV,QF

LQDV&KLHI6FLHQWLVWDQGIRUWKHSDVW\HDUVKDVEHHQDFWLYHLQDSSOLHG&)'FRGHUHVHDUFKSDUWLFXODUO\LQ

WKHDUHDRIVRQLFERRPJHQHUDWLRQSURSDJDWLRQSUHGLFWLRQDQGLQWKHGHVLJQRIORZERRPFRQ¿JXUDWLRQV+HKDV

ZULWWHQRYHUSXEOLVKHGWHFKQLFDOUHSRUWVUHFHLYHGQXPHURXVDZDUGVIURP1$6$WKH$,$$DQGWKH6RFLHW\

of$XWoPoWLYH(QJLQHHUV6$(QoZ6$(,QWHUQDWLoQDODQGLVDQ$,$$)HOOoZ

Kenneth J. PlotkinUHFHLYHGKLV%6GHJUHHfUoPWKH3oO\WHFKQLF,QVWLWXWHof%UooNO\QLQDQGKLV0DVWHU

of(QJLQHHULQJ0(DQG'oFWoUDWHof3KLOoVoSK\3K'fUoP&oUQHOO8QLYHUVLW\ZKHUHKH¿UVW

EHFDPHDFTXDLQWHGZLWKVoQLFEooP+HKDVZoUNHGDW:\OH/DEoUDWoULHVfoUoYHU\HDUVULVLQJto the position 

of &hief 6Fientist +is inteUests oYeU thDt tiPe peUioG hDYe inFOXGeG DnDO\tiFDO DnG e[peUiPentDO DspeFts of 

DiUFUDft DnG hiJhZD\ noise PoGeOinJ DtPospheUiF soXnG pUopDJDtion FoPPXnit\ noise UoFNet noise hiJhspeeG

ÀXFtXDtinJ ÀoZ tUXFN tiUe noise ps\FhoDFoXstiFs FoPPXnit\ noise noise FontUoO DnG soniF EooP +e hDs Eeen 

inYoOYeG Zith soniF EooP foU neDUO\ hDOf D FentXU\ DnG is inteUnDtionDOO\ UeFoJni]eG foU his FontUiEXtions to 

XnGeUstDnGinJ DnG DOOeYiDtion of soniF EooPs +e is D )eOOoZ of the $FoXstiFDO 6oFiet\ of $PeUiFD DnG hDs Eeen 

D PePEeU of the $,$$ foU oYeU  \eDUs

Kevin P. Shepherd UeFeiYeG 06  DnG 3h'  GeJUees fUoP the ,nstitXte of 6oXnG DnG 9iEUDtion 

5eseDUFh 8niYeUsit\ of 6oXthDPpton 8. +e hDs Eeen enJDJeG in DFoXstiFs UeseDUFh Dt 1$6$ /D5& foU oYeU

 \eDUs +is UeseDUFh inteUests hDYe UDnJeG fUoP ZinG tXUEine noise DnG soXnG pUopDJDtion of DiUFUDft noise

inFOXGinJ heOiFopteUs DiUpoUt noise DnG soniF EooP +is soniF EooP UeseDUFh inteUests hDYe FenteUeG on theiU

effeFts on peopOe DnG stUXFtXUes DnG hDYe spDnneG the pDst  \eDUs +e FXUUentO\ heDGs the 6tUXFtXUDO $FoXstiFs 

%UDnFh Dt 1$6$ /D5& 7he pUiPDU\ DUeDs of UeseDUFh DUe pUeGiFtion DnG UeGXFtion of DiUFUDft inteUioU noise

enJine DFoXstiF OineU teFhnoOoJ\ À\oYeU noise s\nthesis DnG siPXODtion DnG DiUpoUt FoPPXnit\ noise DnG soniF

EooP +e hDs pXEOisheG e[tensiYeO\ DnG is D )eOOoZ of the $FoXstiFDO 6oFiet\ of $PeUiFD

Continued next page 
About the Authors/Acknowledgements

iv

Peter G. Coen UeFeiYeG his %6 GeJUee in $eUospDFe (nJineeUinJ fUoP 3oO\teFhniF ,nstitXte of 1eZ <oUN in 

DnG his 06 in $eUonDXtiFDO (nJineeUinJ fUoP 7he *eoUJe :DshinJton 8niYeUsit\ in  +e EeJDn his FDUeeU Dt 

1$6$¶s /DnJOe\ 5eseDUFh &enteU in  DnG hDs ZoUNeG in the DUeDs of s\stePs DnDO\sis teFhnoOoJ\ inteJUDtion 

DnG PXOtiGisFipOinDU\ GesiJn DnDO\sis DnG optiPi]Dtion 0'$2 0ost of his FDUeeU hDs Eeen foFXseG on 

sXpeUsoniF FUXise ÀiJht 'XUinJ the 1$6$ +iJh 6peeG 5eseDUFh +65 3UoMeFt he seUYeG on the 3UopXOsion DnG

$iUfUDPe 7eFhnoOoJ\ ,nteJUDtion 7eDPs DnG OeG the /onJitXGinDO &ontUoO $OteUnDtiYe 3UoMeFt /&$3 Dn eDUO\

0'$2 effoUt 3ost +65 he FontinXeG to ZoUN in the DUeD of sXpeUsoniF DiUFUDft GesiJn Zith inFUeDsinJ ePphDsis 

on soniF EooP UeGXFtion +e ZDs the 1$6$ teFhniFDO PonitoU foU the '$53$ 4Xiet 6XpeUsoniF 3ODtfoUP 463

3UoJUDP DnG 6hDpeG 6oniF %ooP 'ePonstUDtion 6inFe  he hDs Eeen the 1$6$ foFDO point foU sXpeUsoniF

teFhnoOoJ\ GeYeOopPent DnG FXUUentO\ seUYes Ds 3UoMeFt 0DnDJeU foU the +iJh 6peeG 3UoMeFt +e hDs Eeen D

PePEeU of $,$$ sinFe eDUO\ in his FDUeeU

David M. Richwine UeFeiYeG his %DFheOoU of 6FienFe0eFhDniFDO (nJineeUinJ %60( GeJUee fUoP the 

8niYeUsit\ of 9iUJiniD in  DnG 0($ fUoP 7he *eoUJe :DshinJton 8niYeUsit\ in  +e hDs ZoUNeG in 

aeronautics research for over  \ears at 1$6$ /a5& anG 1$6$ 'r\Gen )OiJht 5esearch &enter ')5&

'urinJ his  \ears at 1$6$ ')5& initiaO Guties incOuGeG aeroG\naPics structures ÀoZ visuaOi]ation anG

ÀiJht s\stePs for the ) +iJh $Opha 5esearch 3roJraP anG other research e[periPents on the ; %

65 anG various ) research aircraft /ater Guties incOuGeG technicaO anG proMect PanaJePent of the )%

)OiJht 5esearch 7estEeG anG various ÀiJhttest ¿[tures for supersonic anG suEsonic ÀiJht research e[periPents

+e aOso serveG as the 'r\Gen 3roMect 0anaJer for '$53$¶s 463 3roJraP anG )( ÀiJht test $t 1$6$ /a5&

he has priPariO\ perforPeG proMect PanaJePent Guties in support of 1$6$¶s 6upersonics 3roMect anG is currentO\

assiJneG as a 'eput\ 3roMect 0anaJer for 1$6$¶s +iJh 6peeG 3roMect +e has Eeen a PePEer of the $,$$ for 

over  \ears

ACKNOWLEDGEMENTS

7he authors Zish to e[press their appreciation to the Pan\ contriEutors for their assistance in the preparation 

of this coPprehensive puEOication 7hanNs to %ett\ 3 -o\ner of (aJOe $eronautics ,nc for her untirinJ efforts 

in the preparation coPpiOinJ anG eGitinJ of the Pan\ Graft versions of the te[t eTuations taEOes anG ¿Jures

6peciaO appreciation is aOso e[tenGeG to 6usan + 6teZart of the 1$6$ /anJOe\ ,nforPation 0anaJePent %ranch 

for her eGitoriaO efforts in JuiGinJ this GocuPent throuJh puEOication as ZeOO as 6usan . 0iOOer of the 7echnicaO

/iErar\ in searchinJ for anG proviGinJ copies of the Pan\ references containeG in this report

7hanNs anG appreciation to .enna . 0acauOe\ of $naO\ticaO 0echanics $ssociates ,nc for the preparation of 

the ¿naO ¿Jures anG Jraphics 0arN $ &haPEers of 1&, ,nforPation 6\stePs ,nc for his untirinJ efforts as 

technicaO eGitor anG 0ichaeO 6ean :aOsh aOso of 1&, for cover GesiJn anG print preparation

7he authors ZouOG aOso OiNe to thanN the 3eer 5evieZ &oPPittee coPpriseG of -aPes 0 /ucNrinJ of 1$6$

/a5& as the &oPPittee &hairPan anG three forPer 1$6$ /a5& ePpOo\ees Zith over  \ears of e[perience in 

the ¿eOG of aeronautics research for sharinJ their e[pertise invaOuaEOe insiJht anG coPPents 7hese &oPPittee 

PePEers Zere -oseph 5 &haPEers &hristine 0 'arGen anG :iOOiaP / :iOOshire
Contents

v

CONTENTS

ABOUT THE AUTHORS .............................................................................................................................. iii

ACKNOWLEDGEMENTS ........................................................................................................................... iv

CONTENTS ................................................................................................................................................... v

INTRODUCTION .......................................................................................................................................... 1

CHAPTER 1

THE SONIC BOOM PHENOMENON

 Description of Shock Flow Field and Development of the Sonic Boom Footprint ............................ 5

 Ray Paths .................................................................................................................................. 7

 Sonic Boom Ground Footprint ................................................................................................. 8

 Review of the U.S. Sonic Boom Flight Database ................................................................................. 10

 The Decade of the 1950s ........................................................................................................... 10

 The Decade of the 1960s ........................................................................................................... 10

 The Decades of the 1970s, 1980s, and 1990s ........................................................................... 11

 The First Decade of the 21st Century ....................................................................................... 11

 Sonic Boom Flight Database – Aircraft Types .......................................................................... 12

 Range of Boom Overpressures Experienced ............................................................................ 18

 Chapter 1 Summary Remarks .............................................................................................................. 19

 Chapter 1 References ........................................................................................................................... 19

CHAPTER 2

INFLUENCE OF THE ATMOSPHERE

 Primary Booms .................................................................................................................................... 23

 Macro Atmospheric Effects ..................................................................................................... 24

 Temperature and Wind Gradients ................................................................................ 24

 Effects on Boom Amplitudes ........................................................................................ 26

 Effect on Lateral Spread .............................................................................................. 27

 Lateral Spread Footprint ............................................................................................. 28

 Focusing at Lateral Cutoff ........................................................................................... 30

   5HÀHFWLRQ)DFWRU .......................................................................................................... 33

 Micro Atmospheric Effects ....................................................................................................... 35

 Signature Distortions .................................................................................................... 35

 Effect of Aircraft Pitching Motion .............................................................................. 41

 Effect of Time of Day .................................................................................................. 43
Contents

vi

CHAPTER 2 continued

 Turbulence and Gust Structure .................................................................................... 44

 Effect of Microphone Orientation ................................................................................. 47

 Signature Deturbing ................................................................................................... 51

 Off-Track Variability ..................................................................................................... 52

 Statistical Variations ................................................................................................................ 53

 Effect of Mach Number ............................................................................................... 54

 Effect of Lateral Distance ............................................................................................. 55

 Rise Time Variability ..................................................................................................... 56

 Joint Acoustic Propagation Experiment (JAPE) Sonic Boom Experiments ................. 57

 Atmospheric Absorption ......................................................................................................... 59

 Secondary Booms ................................................................................................................................. 62

 Chapter 2 Summary Remarks .............................................................................................................. 65

 Chapter 2 References ........................................................................................................................... 65

CHAPTER 3

INFLUENCE OF MANEUVERS

 Nature of Focus Patterns ....................................................................................................................... 71

 Military Operations ............................................................................................................................... 72

 Dives ..................................................................................................................................... 73

 Climbout/Pushover ................................................................................................................... 74

 Turns ..................................................................................................................................... 76

 Transition Flight .................................................................................................................................... 78

 On-Track ................................................................................................................................... 79

 Lateral Locations ...................................................................................................................... 84

 Modeling Focus Boom Footprint .............................................................................................. 84

 InÀuence of Signature Shape ................................................................................................................ 85

 Design Cruise and Incoming Transition Signatures .................................................................. 88

 Dedicated Flight Transition Experiments .................................................................................. 91

 Launch Vehicle Transition Focus Boom ............................................................................................... 92

 Focus Boom Avoidance Charts ............................................................................................................. 95

 Sonic Booms at High Subsonic Mach Numbers ................................................................................... 98

 Booms from Low-Altitude Level Flight ................................................................................... 98

 Booms from Dive Pull-Up Maneuver .................................................................................. 100

 Chapter 3 Summary Remarks ......................................................................................................... 101

 Chapter 3 References ....................................................................................................................... 102
Contents

vii

CHAPTER 4

IN-FLIGHT FLOW-FIELD SIGNATURE MEASUREMENTS

 Review of Available Methods ........................................................................................................... 105

 Brief Review of Existing Database ................................................................................................... 107

 Early Flight Tests .............................................................................................................................. 108

 Insight into Nature of Flow Field .......................................................................................... 108

 Measurements of Near-Field Shocks from Passing Aircraft ................................................. 110

 Insight into Effects of Aircraft Lift ....................................................................................... 111

 Validation of CFD Codes .................................................................................................................. 115

 SR-71 Aircraft ....................................................................................................................... 115

 F-5E Inlet Spillage Shock Measurements (ISSM) ................................................................ 119

 Shaped Sonic Boom Demonstrator (SSBD) Aircraft ............................................................ 120

 F-15B Quiet SpikeTM Aircraft ............................................................................................... 124

 Flow-Field Database Utilization ....................................................................................................... 127

 Chapter 4 Summary Remarks .......................................................................................................... 129

 Chapter 4 References ....................................................................................................................... 129

CHAPTER 5

APPROACHES TO SONIC BOOM MINIMIZATION

 Boomless Flight ................................................................................................................................ 133

 Schematic of Flight Situation ................................................................................................ 133

 Boom Responses ................................................................................................................... 134

 Boom Minimization through Aircraft Operations ............................................................................. 135

 InÀuence of Altitude and Mach Number .............................................................................. 135

 Flight Path Angle .................................................................................................................. 136

 Mach Cut-Off Operations ..................................................................................................... 138

 Tailoring Flight Path ............................................................................................................. 143

 Active Control-Unsteady Flight Path .................................................................................... 144

 Boom Minimization through Aircraft Shaping ................................................................................. 146

 Con¿guration/Planform ........................................................................................................ 146

 Volume and Lift Distribution ................................................................................................ 148

 Vehicle Shaping – Wind-Tunnel Results .................................................................... 149

 Vehicle Shaping – Flight Test Results ....................................................................... 150

 Exhaust/Aft Shock Interaction – Flight Test Results ................................................. 152

 Wing Planform ...................................................................................................................... 154
Contents

viii

CHAPTER 5 continued

 Wing Dihedral ....................................................................................................................... 155

 Low-Boom Concepts ............................................................................................................ 159

 Supersonic Transports .............................................................................................. 159

 Supersonic Business Jets .......................................................................................... 163

 Boom Minimization through Exotic Concepts ................................................................................. 165

 Heat or Mass Addition .......................................................................................................... 166

 Airstream Alteration ................................................................................................. 166

 Thermal Fins ............................................................................................................. 168

 Forward Swept Keel ................................................................................................. 171

 Focused Microwave Energy ..................................................................................... 172

 Shock Refraction ................................................................................................................... 173

 Exhaust -et Sheet DeÀection ................................................................................................. 174

 Other Unique Exotic Minimization Schemes ....................................................................... 175

 Overview of Exotic Concepts ............................................................................................... 177

 Chapter 5 Summary Remarks .......................................................................................................... 178

 Chapter 5 References ....................................................................................................................... 179

CHAPTER 6

THEORETICAL CONSIDERATIONS AND APPLICATIONS

 Fundamental Boom Theory .............................................................................................................. 185

 Signature Evolution .......................................................................................................................... 190

 Signature Aging and Shock Coalescence .......................................................................................... 196

 Pressure Signature Propagation in a Real Atmosphere ..................................................................... 197

 Ray Tracing ........................................................................................................................... 197

 Pressure Signature Propagation Codes ................................................................................. 201

 The Near-Field/Mid-Field Dilemma ................................................................................................. 204

 Shock Smearing and Fitting .................................................................................................. 204

 Mid-Field Pressure Propagation Methods ............................................................................ 206

 Lateral Variation and Extent of Sonic Boom Signatures .................................................................. 208

 Hypersonic Sonic Boom Methodology ............................................................................................. 214

 Boom Predictions and Correlations with Experiment ...................................................................... 227

 Correlation of Boom Predictions for Aircraft ....................................................................... 228

 Bodies of Revolution ............................................................................................................ 229

 Diamond Cross-Section, Body and Wing Body ................................................................... 232

 Apollo Capsule ...................................................................................................................... 233
Contents

ix

CHAPTER 6 continued

 Saturn V Launch Vehicle ...................................................................................................... 236

 Space Shuttle ......................................................................................................................... 239

 Peak Overpressure Predictions ............................................................................................. 250

 Chapter 6 Summary Remarks .......................................................................................................... 250

 Chapter 6 References ....................................................................................................................... 251

CHAPTER 7 

SONIC BOOM MINIMIZATION FOR VARIOUS AERODYNAMIC CONFIGURATIONS

 F-Function Boom Minimization ........................................................................................................ 261

 The Rapid Pressure Recovery/Expansion ......................................................................................... 268

 Minimization of Sonic Boom Using Various Optimization Schemes ............................................... 269

 The Effect of Engine Nacelles on Sonic Booms ............................................................................... 286

 F-Function Methodology ...................................................................................................... 286

 The Effect of Engine Exhausts on Sonic Booms ............................................................................... 304

 Calculated Results for Initial Slope and Contours of Jet Plumes ......................................... 308

 Calculation of Exact Ș(0) ....................................................................................................... 312

 Con¿guration Design/Analyses Concepts ......................................................................................... 314

 Large Supersonic Commercial Transport Jet Studies ............................................................ 314

 Supersonic Commercial Jets .................................................................................................. 316

 Supersonic Business Jet Studies ............................................................................................ 331

 Recent Supersonic Business Jet Studies ................................................................................ 332

 Chapter 7 Summary Remarks ........................................................................................................... 339

 Chapter 7 References ........................................................................................................................ 339

CHAPTER 8

RESPONSE TO SONIC BOOMS

 Factors Involved in Sonic Boom Exposures ...................................................................................... 345

 Loading on Buildings ............................................................................................................. 345

 Sonic Boom Stimuli ............................................................................................................... 347

 Structural Response ........................................................................................................................... 350

 Damage Complaints ............................................................................................................... 350

 Induced Damage .................................................................................................................... 350

 Damage Studies ..................................................................................................................... 351

 Plaster Cracking ....................................................................................................... 351
Contents

x

CHAPTER 8 continued

 Window Breakage ...................................................................................................... 354

 Wall Damage ............................................................................................................ 358

 Damage to Historical Structures ............................................................................... 360

 Building Response to Low Amplitude and Shaped Booms .................................................. 361

 Human Response ............................................................................................................................... 366

 Loudness and Annoyance ...................................................................................................... 367

 Startle ......................................................................................................................... 369

 Rattle .......................................................................................................................... 371

 Sleep Interference .................................................................................................................. 372

 Acceptability .......................................................................................................................... 372

 Effects on Human Health ....................................................................................................... 375

 Animal Responses .............................................................................................................................. 376

 Other Responses ................................................................................................................................. 378

 Seismic ................................................................................................................................... 378

 Marine Life ............................................................................................................................ 380

 Effect on Other Aircraft ......................................................................................................... 383

 Observations from Intense Boom Levels ............................................................................... 385

 Chapter 8 Summary Remarks ........................................................................................................... 386

 Chapter 8 References ........................................................................................................................ 387

CHAPTER 9

SONIC BOOM SIMULATION DEVICES AND TEST TECHNIQUES

 Validation of Sonic Boom Design and Predictive Codes ................................................................... 393

 Wind Tunnels ......................................................................................................................... 394

 Test Section Flow Quality .......................................................................................... 395

 Models ....................................................................................................................... 396

 Pressure Measurement Plate ........................................................................................ 399

 Pressure Measurement Probes ..................................................................................... 401

 Pressure Measurement Rails ..................................................................................... 407

 Model Support .............................................................................................................. 409

 Ballistic Range – Free Flight Models .................................................................................... 412

 Signature Distortions by Turbulence ................................................................................................. 415

 Ballistic Range – Projectiles and Duct Flow Turbulence ...................................................... 416

 Spark Discharge and Gas-Filled Bubble ................................................................................ 421

 Shock Tube Horn and Air Jet ................................................................................................. 423

 Shock Tube and Grid Turbulence .......................................................................................... 425
Contents

xi

CHAPTER 9 continued

 Projectiles into Atmospheric Turbulence ............................................................................... 427

 Spark Discharge and Fan Duct Turbulence ............................................................................ 429

 Quantifying Focus Boom Intensities ................................................................................................. 434

 Mach Cutoff Focus Using Ballistic Range-Mixed Gases ...................................................... 434

 Transition Focus Utilizing a Rocket Sled Track .................................................................... 435

 Maneuver Focus ..................................................................................................................... 437

 6SDUN0LUURU5HÀHFWRU ................................................................................................. 437

 6KRFN7XEH5HÀHFWRU .................................................................................................... 439

 Ballistic Range-Mixed Gases ..................................................................................... 439

 Underwater Studies ............................................................................................................................ 440

 Blasting Caps/Flooded Quarry ............................................................................................... 441

 Ballistic Range Water Tank ..................................................................................................... 444

 Diffraction and Refraction of Sonic Boom Due to Buildings and Topography ................................. 450

 Spark Discharge – Parabolic Mirror ...................................................................................... 451

 Ballistic Range – Projectiles .................................................................................................. 455

 Indoor-Outdoor Subjective Response ................................................................................................ 460

 Headphones ............................................................................................................................ 461

 Loudspeaker Chambers .......................................................................................................... 463

 BBN Chamber ............................................................................................................ 463

 Lockheed Chamber .................................................................................................... 464

 University of Toronto Institute for Aerospace Studies (UTIAS) Chamber ................ 465

 NASA Langley Chamber ........................................................................................... 468

 Lockheed Martin Chamber ........................................................................................ 470

 Gulfstream Portable Chamber .................................................................................. 470

 Sound Restitution Cabin ............................................................................................ 472

 In-Home Sonic Boom Simulation ............................................................................. 474

 Georgia Tech Simulator ............................................................................................. 476

 NASA LaRC Indoor Sonic Boom Simulator .............................................................. 477

 Piston Systems ....................................................................................................................... 479

 Explosive Charges .................................................................................................................. 480

 Exercise Crackerjack ................................................................................................. 480

 Exercise Westminster ................................................................................................. 483

 U.S. Army/Construction Engineering Research

 Laboratories (USA/CERL)Tests ................................................................................. 486

 Building Response Simulations ......................................................................................................... 488

 Linear Charges ....................................................................................................................... 488

 Air Modulation Devices ......................................................................................................... 496

 Royal Aircraft Establishment (RAE) Blunderbuss ........................................................ 496
Contents

xii

CHAPTER 9 continued

 LTV Twin Shock Tube ................................................................................................ 497

 General Applied Science Laboratories (GASL) ........................................................ 497

 Wyle Laboratories ...................................................................................................... 499

 Piston-Driven Devices ........................................................................................................... 499

 Loudspeakers ......................................................................................................................... 500

 Wyle Laboratories Acoustic Drivers .......................................................................... 500

 Acta Simulator Experiment ........................................................................................ 503

 Chapter 9 Summary Remarks ........................................................................................................... 505

 Chapter 9 References ........................................................................................................................ 505

CHAPTER 10

OUTLOOK FOR CIVILIAN SUPERSONIC OVERLAND FLIGHT

 Predicted Annoyance to Cruise Boom Levels ................................................................................... 515

 Transition Focus Boom ...................................................................................................................... 516

 Atmospheric Distortion of Sonic Boom Signatures ........................................................................... 517

 Sonic Boom Induced Structural Damage, Vibration, and Rattle ....................................................... 518

 Research Needs .................................................................................................................................. 519

 Low-Boom Flight Demonstration ...................................................................................................... 520

 Chapter 10 Summary Remarks .......................................................................................................... 520

 Chapter 10 References ....................................................................................................................... 521
Introduction

1

INTRODUCTION

When Chuck <eager piloted the Bell ;-1, an experimental aircraft designed speci¿cally to penetrate the sound 

barrier, to a speed of Mach 1.07 in level Àight at 42,000 ft. on October 14, 1947, it ushered in the era of manned 

supersonic Àight. The introduction of the Century Series ¿ghter aircraft in the 1950s, with their ability to Ày at 

supersonic speeds in level Àight due largely in part to the incorporation of Richard Whitcomb¶s area rule as an 

aircraft design feature, brought into prominence the sonic boom phenomenon. Since then, sonic booms from 

military aircraft are widely observed around the world and studies aimed at understanding and controlling sonic 

booms continue to play a role in the formation of environmental impact statements regarding the establishment of 

military operational training areas.

Shock waves are inherent to supersonic Àight in the atmosphere, and the passage of these shock waves over 

people, animals, and structures on the ground cannot be completely eliminated. However, the real concern is 

for civil supersonic overland Àight operations that will cause repeated sonic booms over very large areas. The 

feasibility of routine civil supersonic Àight operations and particularly their acceptance by the general public for 

overland routes may be largely a function of the severity of the sonic boom but also encompasses a plethora of 

sociological as well as technological considerations.

Practical methods for shaping the boom signature and reducing the intensity to an acceptable level are possible. 

There was a concerted research effort beginning in the 1960s that produced a multitude of sonic boom Àight 

tests, wind-tunnel experiments, and laboratory tests to establish a credible database, along with hundreds of 

theoretical investigations in conjunction with the proposed United States Supersonic Transport (SST) Program 

and the eventual entry of the British-French Concorde into commercial service in 1976. As a result of some of the 

earlier sonic boom studies, the Federal Aviation Administration (FAA) prohibited civil aircraft from exceeding 

Mach 1 (or the sonic boom from reaching the ground) over the United States in 1973 (ref. I.1). To comply with the 

above restriction, British and French commercial aviation regulatory authorities con¿ned Concorde supersonic 

operations to overwater routes until its ¿nal Àight in 2003. 

Countless papers, journals, and conference proceedings have been published as a result of the SST, Concorde, 

and various military Àight programs. The ¿rst Sonic Boom Symposium sponsored by the Acoustical Society 

of America (ASA) summed up the state of the art as of 1965 (ref. I.2) and recognized the complexity of sonic 

booms in that so many disciplines were involved in sonic boom research. Engineers and scientists from diverse 

disciplines including mathematics, aerodynamics, atmospheric physics, meteorology, physical acoustics, structural 

dynamics, architectural acoustics, geophysics, electronics, and physiological and psychological acoustics were 

represented. Each discipline had made contributions toward the understanding and minimization of sonic booms 

and their impact. The 1965 ASA Symposium was followed by ASA symposiums in 1970 (ref. I.3) and 2002 (ref. 

I.4). NASA also sponsored Sonic Boom Research conferences in 1967, 1968, and 1970 (refs. I.5, I.6, and I.7) 

dealing with boom generation, propagation, prediction, and minimization. 

In 1988 (ref. I.8), 60 of the world¶s experts in sonic boom attended a 2-day NASA Sonic Boom Workshop to 

review the status of sonic boom methodology and understanding and to establish the research needs in theory, 

minimization, atmospheric effects during propagation, and human response. Three primary challenges were 

identi¿ed – (1) establish criteria for acceptable shaped sonic boom signatures, (2) design a viable aircraft with 

acceptable boom signatures, and (3) quantify atmospheric effects on shaped boom signatures. Soon after the 

1988 gathering, signi¿cant efforts went into conducting further research on sonic boom and were then reported 

at annual NASA Sonic Boom Workshops that were held in 1992 (ref. I.9, Vol. 1, and ref. I.10), 1993 (ref. I.11 

and ref. I.12), 1994 (ref. I.13 and ref. I.14), and in 1995 (ref. I.15 and ref. I.16). The First Annual High-Speed 

Research Workshop, held in 1992, also addressed sonic boom issues (ref. I.17, Part 3). Since then, additional 

Àight, experimental and theoretical studies have been conducted resulting in a multitude of publications on the 

subject of sonic boom. 
Introduction

2

The numerous publications over the past six decades address the physics, measurement, and minimization of sonic 

booms and have been included in the reference materials of this publication. In 2010, NASA published Benson¶s 

historical review entitled 3Softening the Sonic Boom 50 <ears of NASA Research ́ (ref. I.18), followed by the 

publication 3Quieting the Boom The Shaped Sonic Boom Demonstrator and the Quest for Quiet Supersonic 

Flight ́ (ref. I.19). The authors recommend these publications as additional historical resources for those interested 

in sonic boom research.

The goal of the authors is for this publication to serve as a comprehensive reference document. The chapters of 

this document have been structured so that the reader can obtain an overall understanding of sonic boom research 

conducted over the past six decades and so that a researcher can acquire details on a speci¿c area of interest. 

The authors have attempted to present the most original data and terminology from the reference materials, 

but have adapted many of the ¿gures in this document from these reference materials for improved clarity and 

standardization of nomenclature.

With a publication of such wide scope, some important information and references may be left out. Representative 

papers have been chosen for some subjects and in other cases there simply may have been an oversight or they 

may have been published after this report was completed.

Introduction References

I.1 Code of Federal Regulations, Title 14, Vol. 2, Part 9 – General Operating and Flight Rules,

 Subpart 1 – Operating Noise Limits, Sec. 91.817, Civil Aircraft Sonic Boom, 1973.

I.2 Proceedings of the Sonic Boom Symposium. J. Acoust. Soc. Am., Vol. 39, Issue 5B, May 1966.

I.3 Proceedings of the Second Sonic Boom Symposium. J. Acoust. Soc. Am., Vol. 51, Issue 2C, Feb. 1972.

I.4 Sonic Boom Symposium. Journal of Acoustical Society of America, Vol. 111, No. 1,

 Part 2 of 2, Jan. 2002.

I.5 Sonic Boom Research. NASA SP-147, April 1967.

I.6 Second Conference on Sonic Boom Research. NASA SP-180, May 1968.

I.7 Third Conference on Sonic Boom Research. NASA SP-255, Oct. 1970.

I.8 Status of Sonic Boom Methodology and Understanding. NASA CP-3027.

I.9 High Speed Research Sonic Boom, Vol. I. NASA CP-3172, Feb. 1992.

I.10 High Speed Research Sonic Boom, Vol. II. NASA CP-3173, Feb. 1992.

I.11 High Speed Research Sonic Boom, Vol. I. NASA CP-10132, May 1993.

I.12 High Speed Research Sonic Boom, Vol. II. NASA CP-10133, May 1993.

I.13 High Speed Research 1994 Sonic Boom Workshop, Atmospheric Propagation and Acceptability

 Studies. NASA CP-3279, June 1994.

I.14 High Speed Research 1994 Sonic Boom Workshop, Vol. II – Con¿guration Design, Analysis,

 and Testing. NASA CP-1999-209699, Dec. 1999.

I.15 1995 NASA High Speed Research Program Sonic Boom Workshop, Vol. I. NASA CP-3335, Sept. 1995.

I.16 1995 NASA High Speed Research Program Sonic Boom Workshop, Vol. II – Con¿guration Design, 

 Analysis, and Testing. NASA CP-1999-209520, Dec. 1999.
Introduction

3

I.17 First Annual High-Speed Research Workshop. NASA CP-10087, Part 3, April 1992.

I.18 Benson, Lawrence R. Case 4, Softening the Sonic Boom 50 <ears of NASA Research. NASA¶s 

 Contributions to Aeronautics, Vol. 1, edited by Richard P. Hallion, NASA/SP-2010-570-Vol 1, 2010, 

 pp. 180–274.

I.19 Benson, Lawrence R. Quieting the Boom The Shaped Sonic Boom Demonstrator and the Quest for

 Quiet Supersonic Flight. NASA SP-2013-601, 2013.

Chapter 1 The Sonic Boom Phenomenon

5

CHAPTER 1 THE SONIC BOOM PHENOMENON

This chapter is intended to provide a brief overview of the general nature of sonic booms beginning with a description 

of the Àow ¿eld and shocks surrounding vehicles in supersonic Àight together with the acoustic ray paths, along 

which the shocks propagate to the ground, and the role the atmosphere plays in establishing the sonic boom footprint 

on the ground. Both primary and secondary carpet booms are produced by supersonic aircraft and the differences 

in their character are described. Discussions are provided relative to the character of the boom signature measured 

under both stable and unstable atmospheric conditions within the primary carpet, during steady cruise Àight, along 

the aircraft ground track, and laterally out to the cutoff where the ray paths become tangent to the ground and booms 

are no longer observed. In addition, the focus boom region that is produced during transition Àight of the aircraft as 

it accelerates from subsonic to supersonic speed is also discussed.

Complaints from members of communities exposed to sonic booms within the ground footprint have ranged from 

those members complaining about being startled and annoyed to those raising their concerns of interrupted sleep 

and worries of detrimental effects on their long-term health. In addition, concerns about structural damage and the 

effect of booms on wildlife and marine life, and the potential for triggering earthquakes and avalanches are also 

mentioned. Answers to, and alleviation of, all these concerns required a better understanding of the sonic boom 

in regard to its generation, propagation, and prediction. The research paths included analytical and experimental 

efforts involving wind-tunnel tests of supersonic vehicle models, laboratory simulation devices, and test techniques 

such as boom simulation chambers, ballistic ranges, and explosive charges as well as Àight-test programs. For over 

6 decades, the development and use of experimental simulation techniques have ful¿lled a wide variety of boom 

research needs. Use of these devices has complemented and, in some cases, taken the place of complex, lengthy, 

and costly supersonic Àight tests. All three of these research paths – analytical, experimental laboratory, and Àight 

tests – contributed equally to providing the understanding of and solutions to the sonic boom problem. However, 

sonic boom Àight tests are always the ¿nal requirement.

The chapter concludes with a review of the United States sonic boom Àight-test programs that have been conducted 

over the past 6 decades. Each of these Àight activities contributed to the understanding of sonic booms that in turn 

stimulated and guided analytical and laboratory efforts. Discussion of the thrust of these sonic boom Àight-test 

programs along with an indication of concurrent analytical and laboratory efforts will be presented.

Description of Shock Flow Field and Development of the Sonic Boom Footprint

Any body that moves through the air at speeds exceeding the local speed of sound has an associated system of nearconical shock waves attached to the body, as shown in ¿gure 1.1. A simple body of revolution (i.e., a projectile) 

generally has two shocks – one attached to the front called the bow shock and the other emanating from the rear 

called the tail shock (¿g. 1.1(a)). More complicated con¿gurations, such as the small aircraft model and the fullscale aircraft on the right (ref. 1.1) shown in ¿gure 1.1(b), produce whole systems of shock waves. At very large 

distances from the body, the wave system tends to coalesce into bow and tail waves as in the case of the simple 

projectile.

Figure 1.1(c) shows a schematic diagram representing the shock Àow ¿eld surrounding an aircraft in Àight. In the 

near ¿eld, close to the aircraft, the pressure signature exhibits several shocks that emanate from the nose of the 

aircraft, the canopy, inlet, wing, and tail. As these shocks propagate away from the aircraft to the mid ¿eld, some 

of them have coalesced such that the pressure signature now consists of only three shocks. In the far ¿eld, only the 

bow and tail shocks remain to form the N-wave signature at the ground.
Chapter 1 The Sonic Boom Phenomenon

6

At the ground, compression occurs at the bow shock in which the local pressure rises to a value above atmospheric 

pressure. Increments in pressure (both positive and negative) relative to the atmosphere are typically denoted by 

the symbol ǻp. Following the bow shock, a slow expansion then occurs until a value below atmospheric pressure 

is reached, after which there is a sudden recompression at the tail shock. Generally, as the bow and tail shocks 

reach their maximum value they have a slight slope associated with these shocks known as rise time (o), after 

which, in the case of the bow shock, the pressure decreases in a linear fashion to the tail shock. This nominal sonic 

boom N-wave signature moves with the aircraft and is associated with continuous supersonic Àight, not just with 

breaking the sound barrier. 

A full-range microphone placed on the ground would detect the N-wave pressure time history, as indicated in 

¿gure 1.1(c). Since the human ear is sensitive to higher frequencies, it responds to the rapidly changing part 

of the waveform and not to the portion that is changing slowly. If the time interval ǻt between those two rapid 

compressions is small, as for a bullet, the ear is not able to distinguish between them and they seem to be as one 

explosive sound, or crack. If the time interval is on the order of 0.10 sec or greater, as is the case for an aircraft at 

high altitude, the ear detects two booms (or bangs) corresponding to the rapid pressure changes at the front and 

rear of the N-wave signature. It is of interest to note that the sonic boom overpressures normally observed from 

supersonic aircraft at nominal Àight altitudes are on the order of only 1.0 lb/ft2

 to 3.0 lbs/ft2 more than the uniform 

atmospheric pressure of a2116 lbs/ft2 experienced by the body at sea level.

(c) Near-, mid- and far-¿eld boom signatures.

Figure 1.1. 6KRFNÀRZ¿HOGSUHVVXUH

(a) Flow ¿eld from a projectile. (b) Typical Àow ¿eld for aircraft con¿gurations.
Chapter 1 The Sonic Boom Phenomenon

7

Ray Paths

The atmosphere above and below the aircraft plays a signi¿cant role in establishing the character of the sonic 

boom signature as it propagates away from the aircraft to the ground and de¿nes the extent of the boom footprint 

on the ground. Two types of effects are present. The ¿rst type is classi¿ed as macro effects that are comprised 

of atmospheric pressure, temperature, and wind pro¿les and gradients. These result in the bending or refraction 

of the ray paths along which the shocks propagate and thus de¿ne the intensity, location, and lateral extent of the 

sonic boom footprints. In contrast, turbulence, especially in the lower layers of the atmosphere near the ground, 

plus atmospheric absorption and molecular relaxation are classi¿ed as micro effects, yet can have a signi¿cant 

effect on altering the boom signature causing large variations in the shock strength and rise times.

The inÀuence of macro effects of the atmosphere, temperature, and wind above and below an aircraft on the sonic 

boom ground footprint is presented in the ray diagram of ¿gure 1.2. Rays describe the paths that the shocks travel 

along as they propagate away from the aircraft. On the right-hand side of ¿gure 1.2 are examples of temperature 

and wind pro¿les for a representative atmosphere. Note that there is a portion of the higher atmosphere above 

the aircraft Àight altitude, the thermosphere, in which the temperature increases with altitude as compared to 

the lower portions of the atmosphere below the aircraft. The rays that propagate above the aircraft are turned 

downward towards the ground as they reach the thermosphere. Below the aircraft (the tropopause), the downward 

propagating rays that are refracted continue until they reach the thermosphere and are then bent downward back 

towards the ground. The wind-speed gradient will also inÀuence refraction and may reinforce or counteract the 

effects due to temperature gradient. 

On the left-hand side of ¿gure 1.2 is a ray diagram showing a variety of ray paths that the shock waves travel 

for an aircraft in supersonic Àight at an altitude of 60,000 feet, traveling toward the viewer. The downward 

propagating rays, shown by the solid lines, impact the ground to form the primary boom carpet, as indicated in 

the ¿gure. At a lateral distance of about 25 nmi in the example shown, the rays refract away from the ground and 

thus de¿ne the lateral extent of the primary boom carpet.

Also indicated is a secondary carpet, at about 65 to 85 nmi from the Àight track, in which the dashed-line rays 

impact. These dashed-line rays arrive in two different ways – they either travel directly to the secondary carpet as a 

result of bending in the upper atmosphere or they may ¿rst impinge in the primary carpet, reÀect upward from the 

surface, and then bend downward after traveling through a portion of the upper atmosphere. The representation of 

the secondary carpet in this illustration is somewhat oversimpli¿ed, because there is reason to believe that it could 

consist of several well-de¿ned impact areas (ref. 1.2). Variations in atmospheric wind and temperature pro¿les, 

Figure 1.2. 5D\SDWKGLDJUDPLQSODQHQRUPDOWRWKDWRIÀLJKW
Chapter 1 The Sonic Boom Phenomenon

8

however, could cause these impact areas to be ill de¿ned. Some of the steep-angle rays above the aircraft may 

travel in such a way that they are dissipated without ever approaching the ground.

Sonic Boom Ground Footprint 

The nature of the sonic boom carpets for a representative civil supersonic transport during which the aircraft 

Àies a large portion of the distance supersonically is shown in ¿gure 1.3. Two ground exposure patterns in which 

booms can be experienced are shown. The primary boom carpet contains the normally observed sonic boom 

shortly after the passage of the aircraft and results from shocks that have propagated through the atmosphere 

below the aircraft. Secondary boom carpets involve the portion of the atmosphere above the aircraft as well as 

that below the aircraft. Between the primary and secondary carpets exists a region in which no sonic booms are 

observed. The secondary booms, which can arrive as much as 10 to 15 min after the passage of the aircraft, are 

more remote from the ground track with overpressure levels much smaller than those within the primary carpet.

The waveform characteristics of the boom signatures in the boom carpet can vary widely at different observation 

points as indicated in the ¿gure. A focus boom having a signature as shown in the left side of ¿gure 1.3 is the 

¿rst boom to impact the ground. Focus booms will always result when any aircraft accelerates from subsonic to 

supersonic speeds. In addition, any rapid deviation of a vehicle from steady-level supersonic Àight such as turns, 

dives, and pushover usually associated with military operations can also result in considerable modi¿cations in 

the location, number, and intensity of the ground shock wave patterns, resulting in multiple booms and focused 

booms. For civil supersonic operations, all maneuvers that could result in a focus boom on the ground can be 

avoided except for the unavoidable transition focus boom. The transition focus booms, which occur along the 

crescent shaped black region shown in the lower left of ¿gure 1.3, are followed by a region on the ground (shaded 

area) in which multiple booms are observed. Transition focus booms can be placed to within a few thousand feet 

of a designated location and can be minimized by proper scheduling of acceleration and altitude, and by favorable 

shaping of the aircraft and thus the boom signature. The focus booms associated with aircraft of the past 6 

decades are similar in overall shape to the N-wave signatures generated in steady-level Àight operations but with 

leading and trailing shocks that have been ampli¿ed. Focus booms are a one-time occurrence and are not dragged 

along with the aircraft as are the primary and secondary carpet booms.

Figure 1.3. 6FKHPDWLFRIVRQLFERRPJURXQGH[SRVXUHV
Chapter 1 The Sonic Boom Phenomenon

9

In the region of the primary boom carpet, on or near the ground track, N-wave signatures are usually observed. 

For military aircraft at typical high-altitude cruise conditions, these booms have usually been on the order of 1 

lb/ft2

 to 3 lbs/ft2 in intensity and from 0.10 to 0.30 sec in duration. In addition to the macro atmospheric effects 

previously discussed, micro atmospheric effects can alter the boom signatures causing large variations in the 

shock strength and increased shock rise times as shown in ¿gure 1.4 (ref. 1.3). The measured boom signatures 

shown in ¿gure 1.4 were recorded by ¿ve microphones (100 feet apart) arranged in a cruciform array. The aircraft 

was Àown at a slightly different Mach number and altitude on two different days, one day having low-wind 

conditions and the other with high winds and gusts.

Referring back to ¿gure 1.3, at the fringes of the primary boom carpet near the lateral cutoff, the signatures 

degenerate into weak sound waves and they lose their N-wave characteristics. In the region of the secondary 

boom carpet, the disturbances tend to be very weak in intensity (on the order of 0.02 to 0.20 lb/ft2

) and persist 

over longer periods of time (on the order of 5 to 10 sec). 

Higher overpressure N-wave booms within the primary boom carpet have resulted in complaints from those 

within the communities overÀown that include being startled and annoyed, loss of sleep, and concern about the 

long-term effects on their health in general. Worries of booms causing structural damage, their effects on wildlife 

and marine life, and the potential for causing avalanches and even earthquakes have also been cited. On the other 

hand, the lateral cutoff booms and the secondary booms, which do not have an N-wave character and are much 

lower in intensity, tend to be more of a curiosity and are not apt to be the source of serious community response 

problems. Near the lateral cutoff, booms usually resemble low rumbles or rolling thunder. Secondary booms are 

generally not audible (0.1 to 1.0 Hz), but can cause building vibrations that can be detected.

(a) Low-wind conditions (Mach 1.65 at 47,000 ft). (b) High-wind and gust conditions (Mach 1.35 at 43,000 ft).

Figure 1.4. 9DULDELOLW\LQERRPVLJQDWXUHVUHVXOWLQJIURPWKHDWPRVSKHUHDGDSWHGIURPUHI
Chapter 1 The Sonic Boom Phenomenon

10

Review of the U. S. Sonic Boom Flight Database

Table 1.1 provides a listing of the major sonic boom Àight-test studies carried out in the United States and 

highlights the numerous studies conducted over the past 6 decades. Each of these efforts was aimed at acquiring 

information relative to a speci¿c sonic boom issue. A brief discussion of the major objectives of these Àight-test 

programs is presented along with some discussion of the ongoing analytical and laboratory efforts during this 

period.

Table 1.1. Summary of U.S. Sonic Boom Flight-Test Programs

The Decade of the 1950s

Beginning in the 1950s, sonic boom Àight tests by the U.S. Air Force (USAF) focused on gaining a better 

understanding of the mysterious sonic boom phenomenon. In particular, these studies investigated where on the 

aircraft shocks emanate, their intensities, how far they propagate, as well as their predictability. There were also 

concerns that the shocks from an aircraft in supersonic Àight on another aircraft Àying in close formation could 

pose Àight safety issues. This concern led to in-Àight measurements of the shock Àow ¿eld surrounding the aircraft 

using an instrumented probing aircraft. In the ensuing years, in-Àight probing took on even more signi¿cance 

in establishing the role that aircraft volume and lift play in de¿ning the aircraft¶s sonic boom characteristics and 

the manner in which the shocks coalesce as they propagate away from the aircraft. This Àight data also provided 

a comparison with wind-tunnel measurements and the validation of boom prediction codes. Additional material 

relating to this topic can be found in Chapter 4. Towards the end of the decade, analytical studies and wind-tunnel 

testing of supersonic cruise con¿gurations was underway at NASA. The need for Àight tests designed to initiate a 

sonic boom database on boom generation and propagation, along with acquiring some measurements of building 

responses, was realized and performed.

The Decade of the 1960s

During the 1960s, a Àurry of boom Àight tests occurred that were conducted in conjunction with the increased 

operation of high-performance supersonic military aircraft. Research was conducted in support of the proposed 

U.S. Supersonic Transport (SST) and the anticipated entry of the supersonic Concorde into routine commercial 

service. Three major community response studies were conducted over St. Louis, Oklahoma, and Edwards Air 

Force Base (EAFB). Studies of the sonic boom impact (ref. 1.4) from these tests showed that the anticipated 1.5 
Chapter 1 The Sonic Boom Phenomenon

11

lbs/ft2 to 2.0 lbs/ft2 SST booms would not be acceptable. Research on methods to reduce sonic booms became 

all important and provoked research in the areas of improvement of sonic boom prediction methods, methods to 

minimize booms by means of aircraft operations, and the shaping of the aircraft¶s volume and lift distribution. 

This research also included studies and wind-tunnel tests on several exotic schemes such as altering the Àow ¿eld 

surrounding the aircraft to create a phantom body. These studies, along with several major efforts conducted in 

England and France, provided considerable insight as to the generation, propagation, prediction, and minimization 

of sonic booms and their effects on people, animals, and structures. A major portion of the ¿ndings from these 

Àight tests are presented and discussed in Chapters 5–9.

The Decades of the 1970s, 1980s, and 1990s

Following the decision to terminate the U.S. SST effort and the shift by England and France to limit the supersonic 

segment of Concorde operations to overwater sonic boom studies continued at a much slower pace during the 

1970s, 1980s, and early 1990s and focused primarily on developing a database for the formation of environmental 

impact statements regarding the establishment of military operations areas (MOAs) (ref. 1.5) and the Apollo 

and Space Shuttle programs (ref. 1.6). Substantial progress was made toward the understanding of atmospheric 

propagation. Molecular absorption was found to make a signi¿cant contribution in establishing the boom signature 

rise time and was identi¿ed as becoming more inÀuential and bene¿cial as boom overpressure decreased. It was 

also validated that turbulence is the primary cause of boom signature distortions, as demonstrated in the early 

Àight tests of the 1960s (discussed in Chapter 2). Psychoacoustic studies showed that boom signatures having 

large rise times were indeed quieter than conventional N-wave signatures. Limiting civil supersonic operations to 

overwater routes as an option to overland routes also posed a concern for marine life. This concern was addressed 

by the development of models for penetration of the sonic boom into the ocean, along with laboratory and Àight 

experiments as discussed in Chapter 9.

NASA¶s High Speed Civil Transport (HSCT) and High Speed Research (HSR) Programs in the early and mid1990s caused a major resurgence of sonic boom studies. The era of aircraft design by linear supersonic area 

rule was coming to a close and the era of Computational Fluid Dynamics (CFD) analysis began to transform 

modern aircraft design and analysis as discussed in Chapter 6. The activities of the 1960s directed towards sonic 

boom minimization approaches that focused on aircraft operations and exotic approaches, such as altering the 

airstream surrounding the aircraft, continued at a slower pace. The use of aircraft shaping to achieve sonic boom 

minimization continued at an accelerated pace (Chapters 5 and 7).

The First Decade of the 21st Century

In the early 2000s, the Defense Advanced Research Projects Agency (DARPA) funded the Quiet Supersonic 

Platform (QSP) (ref. 1.7) that was to be a long-range highly ef¿cient low-boom supersonic airplane having an 

initial boom of 0.3 lb/ft2

. Included in the QSP effort was the Shaped Sonic Boom Demonstrator (SSBD) Àighttest program (ref. 1.8) and its follow-on effort, the Shaped Sonic Boom Experiment (SSBE). Prior to the SSBD, 

all supersonic aircraft were classed as N-wave designs with minimal concern for sonic boom minimization. As 

a result, all of the sonic boom signatures from sonic boom Àight tests prior to this program were saw-toothed or 

N-wave. Theory and wind-tunnel tests indicated that proper shaping of the aircraft¶s volume and lift distributions 

would alter and soften the boom signature. The SSBD Àight test became the ¿rst Àight demonstration in which 

a full-scale aircraft Àying in a real atmosphere was designed to produce more desirable shaped signature at the 

ground. A picture of the F-5E baseline aircraft and its modi¿ed version, the SSBD, is shown in ¿gure 1.5 (ref. 

1.8). Also shown are the original and modi¿ed equivalent area distribution plots and resulting boom signatures 

measured at the ground.
Chapter 1 The Sonic Boom Phenomenon

12

This ¿nding stimulated a renewed interest in designing low-boom aircraft capable of ¿nding community acceptance 

to civil supersonic Àight operations. The NASA Low-Boom tests conducted at EAFB in 2007–2008 (refs. 1.9, 

1.10, and 1.11) along with the NASA Waveforms and Sonic boom Perception and Response (WSPR) (ref. 1.12) 

low-boom community response pilot program conducted at EAFB in 2011 – 2012 are expected to provide further 

information that could be used to de¿ne community acceptance metrics and levels discussed in Chapter 10.

Even as these efforts were proceeding, the requirement to ¿nd solutions that will minimize the transition focus 

boom did not go unchallenged. Several U.S. sonic boom Àight-test programs that included transition Àight 

maneuvers were conducted in 1961, 1965, 1970, and 1994. In 2011, NASA completed a series of transition 

focus boom Àight tests identi¿ed as Superboom Caustic and Analysis Measured Program (SCAMP) that were 

speci¿cally aimed at quantifying the focus boom footprint (see refs. 1.13, 1.14, and Chapter 3 of this publication).

Sonic Boom Flight Database – Aircraft Types

Some interesting points must be made regarding the large database for sonic booms from aircraft. Most of the 

database is from aircraft operating within the Mach number range 1.0 to 3.0 and altitudes from about 50 feet 

to 80,000 feet. In addition, Space Shuttle measurements have been made on Àights spanning supersonic and 

hypersonic conditions from Mach 1.3 at an altitude of 58,000 feet to Mach 23 at an altitude of 250,000 feet 

during reentry Àight. About half the database is essentially steady-level Àight since the Àights were aimed at 

the operational range of the proposed U.S. SST. The other half of the sonic boom database includes combat 

Figure 1.5. 0RGL¿FDWLRQRIWKH)(LQWRWKH66%'DGDSWHGIURPUHI

1$6$SKRWR 1$6$SKRWR
Chapter 1 The Sonic Boom Phenomenon

13

maneuvering training operations that occur in Military Operating Areas that include various types of maneuvers 

and low and high Mach-altitude operations.

The sonic boom signatures, which were for the most part saw-tooth type or N-waves, had overpressures for 

steady-level Àight that ranged from about 0.75 lb/ft2

 to 3.0 lbs/ft2 (excluding Àights at very low altitudes and focus 

booms due to maneuvering). Since the military inventory of supersonic aircraft was devoid of any vehicles that 

would generate very low overpressure levels along the ground track or signatures that are non-N-wave in shape, 

little information is available for low-boom shaped signatures. The previously mentioned NASA Low Boom Àight 

test recorded booms down to a few tenths of a lb/ft2

 through the use of a special dive maneuver using an F-18 

(ref. 1.9) and booms of less than 0.1 lb/ft2

 have been measured from a small reentry vehicle (refs. 1.15 and 1.16).

Table 1.2 lists the 19 supersonic aircraft for which sonic boom ground measurements have been obtained and 

also includes the Space Shuttle Orbiter on reentry. The vehicles ranged in size from about 46 feet in length for the 

F-5/T-38 to 185 feet for the ;B-70. Wing spans of the vehicles ranged from 25 feet for the F-5/T-38 to 105 feet for 

the ;B-70. Gross weights varied from 10,000 lbs for the ;-15 to 450,000 pounds for the ;B-70. Measurements 

have also been obtained on the Shuttle and Apollo ascent and reentry. Although not part of the U. S. sonic boom 

Àight database, sonic boom ground measurements were obtained on the Concorde and TU-144 civil supersonic 

transports. Pictures of aircraft included in the U.S. sonic boom Àight database, as well as the Concorde and the 

TU-144 civil supersonic transports are shown on the next few pages.

Table 1.2. Aircraft Types for which Data is Available in the United States Sonic Boom Flight Database
Chapter 1 The Sonic Boom Phenomenon

14

Aircraft Types for which Data is Available in the United States Sonic Boom Flight Database

0F'RQQHOO'RXJODV)&3KDQWRP,, 1RUWKURS)(7LJHU,,

1RUWKURS77DORQ

*UXPPDQ)7RPFDW

1$6$SKRWR(& 1$6$SKRWR(&)U

1$6$SKRWR('

1$6$SKRWR(&

3KRWRFRXUWHV\RI'RQ0DOOLFN

1$6$SKRWR(&

&KDQFH9RXJKW)8&UXVDGHU

0F'RQQHOO'RXJODV)%(DJOH
Chapter 1 The Sonic Boom Phenomenon

15

1$6$SKRWR(/

86$LU)RUFHSKRWR

1$6$SKRWR(& 86$LU)RUFHSKRWR

86$LU)RUFHSKRWR

*HQHUDO'\QDPLFV))LJKWLQJ)DOFRQ

/RFNKHHG)6WDU¿JKWHU 5HSXEOLF)'7KXQGHUFKLHI

1RUWK$PHULFDQ)'6XSHU6DEUH 0F'RQQHOO)$9RRGRR
Chapter 1 The Sonic Boom Phenomenon

16

&RQYDLU)% 'HOWD'DUW

&RQYDLU%+XVWOHU

*HQHUDO'\QDPLFV)$$DUGYDUN

/RFNKHHG65%ODFNELUG

1$6$SKRWR

86$LU)RUFHSKRWR

1$6$SKRWR(&

1$6$SKRWR(&

1$6$SKRWR(&

1RUWK$PHULFDQ;%$9DON\ULH

QRWHWKHDLUFUDIWLVLQVXSHUVRQLFFUXLVHFRQ¿JXUDWLRQ
Chapter 1 The Sonic Boom Phenomenon

17

1RUWK$PHULFDQ;

3DQDYLD7RUQDGR

6SDFH7UDQVSRUWDWLRQ6\VWHP6762UELWHU

6SDFH6KXWWOH

1RUWKURS*UXPPDQ)(6KDSHG

6RQLF%RRP'HPRQVWUDWRU66%'

1$6$SKRWR(&

86$LU)RUFHSKRWRE\$LUPDQVW&ODVV&KULVWRSKHU*ULI¿Q

1$6$SKRWR(& 1$6$SKRWR(&
Chapter 1 The Sonic Boom Phenomenon

18

Examples of Once Operational Supersonic Transports for which Sonic Boom Data Have Also Been Obtained

Range of Boom Overpressures Experienced

The ranges of overpressures involved in community response, structural, and special studies under various Àighttest programs are listed chronologically shown in table 1.3. B-58 training represents military operational booms to 

which various U.S. cities have been exposed to supersonic training Àights of the USAF, with no relation to a sonic 

boom research purpose. Sonic boom levels were less than 5 lbs/ft2 (refs. 1.3 and 1.17). Little Boom (ref. 1.18) 

refers to studies at Nellis AFB to evaluate the potential of using sonic booms from Àying aircraft supersonically 

at very low altitudes as a combat weapon. Overpressures as high as 120 lbs/ft2

 were experienced. St. Louis was 

one of the B-58 training Àight programs, with the community response observations (ref. 1.17) being conducted 

as a piggyback operation. Project Little Man (ref. 1.19) refers to a study to establish the inÀuence of booms of 

up to about 14 lbs/ft2

 on light aircraft during takeoff, landing, and cruise Àight. The Oklahoma City community 

response tests (refs. 1.20, 1.21, and 1.22) were conducted over a period of 6 months with about eight booms/day 

of overpressures from about 1.3 lbs/ft2

 to 1.7 lbs/ft2. The White Sands (ref. 1.23) test was conducted to investigate 

building response and damage due to sonic booms of up to about 25 lbs/ft2

. Chicago, like St. Louis, was another 

of the B-58 training Àight programs with the emphasis on examining the variability of sonic boom signatures due 

to the atmosphere, which differed from the desert area (ref. 1.3). A summary of boom complaints and damage 

were also documented. Joint Task Force II (ref. 1.24) was an effort similar to project Little Boom wherein boom 

levels of 144 lbs/ft2

 were measured.

Table 1.3. Range of Sonic Boom Overpressures Experienced in Various Studies

$HURVSDWLDOH%ULWLVK$HURVSDFH&RQFRUGH

6XSHUVRQLF7UDQVSRUW667

7XSROHY786XSHUVRQLF7UDQVSRUW667

1$6$SKRWR(& 1$6$SKRWR(&
Chapter 1 The Sonic Boom Phenomenon

19

During the 1966 – 1967 time period, the U.S. National Sonic Boom Program conducted an extensive sonic boom 

study at EAFB and involved the USAF, Federal Aviation Administration (FAA), National Oceanic and Atmospheric 

Administration (NOAA), and National Aeronautics and Space Administration (NASA) (ref. 1.25). In 1987, the 

USAF conducted an extensive Àight-test program to measure the sonic boom signatures from all existing military 

supersonic aircraft. This activity involved eight aircraft performing 43 steady-supersonic Àights over a 6-day 

period. This measured database (called BOOMFILE) is presented in reference 1.26. It is not included in the table 

since it does not relate to response studies. Instead, the database is useful for veri¿cation of analytical codes for 

further studies of boom propagation through the atmosphere. From 1992 through 1995, the Western USA Sonic 

Boom survey (ref. 1.27) was conducted to acquire residents¶ reactions to long-term exposures to sonic booms 

in the Nellis AFB, Nevada and EAFB, California regions. In order to acquire a database regarding the response 

of humans outdoors and indoors to low-level sonic booms, along with building responses, NASA conducted 

the 2006 – 2007 Low Boom (refs. 1.9, 1.10, and 1.11) and 2011 – 2012 WSPR Àight-test programs (ref. 1.12) at 

EAFB.

Chapter 1 Summary Remarks

Any body that moves through the air at speeds exceeding the local speed of sound has an associated system 

of shock waves that, when propagated to the ground, are observed as a sonic boom. The sonic boom ground 

signature is characterized by a bow shock with a local pressure rise followed by an expansion, other shocks and 

the tail shock which all typically coalesce into an N-wave.

The sonic boom ground footprint from the aircraft shock waves propagates through the atmosphere above and 

below the aircraft and is comprised of primary carpet booms that result from shock waves propagating through 

the atmosphere below the aircraft. The secondary carpet booms result from shock waves that propagate through 

the atmosphere above and below the aircraft. Atmospheric effects can play an important role in the character and 

magnitude of these primary and secondary carpet booms.

Primary booms have been intensely researched resulting in an extensive database on 19 aircraft. Apollo and 

Shuttle vehicles and boom signatures have been measured from Àights at Mach numbers of 1.12 at a test altitude 

of 50 feet up to Mach 23 at an altitude of 250,000 feet. The normally observed sonic booms from military aircraft 

at Àight altitudes are in the 1.0 lb/ft2 to 3.0 lbs/ft2 range. However, sonic boom overpressures from less than 0.1 

lb/ft2 to 144 lbs/ft2 have been measured during specially designed Àight tests. With the exception of the Shaped 

Sonic Boom Demonstrator (SSBD) signature, all 6 decades of measured primary boom carpet signatures have 

been sawtooth or N-wave in character.

Secondary boom signatures are shockless and an order of magnitude lower in overpressure and frequency than 

those of primary booms. As a result, they are dif¿cult to sense outdoors but can be noticeable indoors as vibrations.

Chapter 1 References

1.1 Weinstein, Leonard An Optical Technique for Examining Aircraft Shock Wave Structures in Flight. 

 NASA CP-3279, June 1994, pp. 1–17. 

1.2 Plotkin, K. J. Page, J. A. and Haering, E. A Extension of PCBoom to Over-The-Top Booms, Ellipsoidal 

Earth, and Full 3-D Ray Tracing, AIAA 2007-3677, May 2007.

1.3 Hilton, David A. Huckel, Vera and Maglieri, Domenic J. Sonic Boom Measurements during Bomber 

Training Operations in the Chicago Area. NASA TN D-3655, Oct. 1966.

1.4 Von Gierke, Henning E. and Nixon, Charles W. Human Response to Sonic Boom in the Laboratory and 

the Community. J. Acoust. Soc. Am., 51, 1972, pp. 766–782.
Chapter 1 The Sonic Boom Phenomenon

20

1.5 Draft Environmental Assessment Reserve Military Operations Area New Mexico. USAF Tactical Air 

Command. Dec. 1989.

1.6 Environmental Impact Statement Space Shuttle Program. April, 1978.

1.7 Wlezien, R. and Veitch, L. Quiet Supersonic Platform. AIAA Paper 2002-0143, Jan. 2002.

1.8 Pawlowski, Joseph W. Graham, David H. Boccadoro, Charles H. Coen, Peter G. and Maglieri, Domenic 

J. Origins and Overview of a Shaped Sonic Boom Demonstration Program. AIAA Paper 2005-0005, Jan. 

2005.

1.9 Sullivan, Brenda M. Klos, Jacob Buehrie, Ralph D. McCurdy, David A. and Haering, Edward A., Jr.

Human Response to Low-Intensity Sonic Booms Heard Indoors and Outdoors. NASA TM 2010-216685, 

June 2010.

1.10 Klos, Jacob and Buerie, Ralph D. Vibro-Acoustic Response of Buildings Due to Sonic Boom Exposure, 

June 2006, Field Test, NASA TM-2007-214900, Sept. 2007.

1.11 Klos, J. Vibro-Acoustic Response of Buildings Due to Sonic Boom Exposure July 2007 Field Test, 

NASA TM-2008-215349, Sept. 2008.

1.12 Page, J. Hodgdon, K. Hobbs, C. Wilmer, C. Kreker, P. Koeing, C. Holmes, T. Cowart, R. Gaugler, 

T. Shumway, D. Rosenberger, J. and Phillips, D. Waveforms and Sonic Boom Perception and Response 

(WRSP) Low Boom Community Response Program Pilot Test Design, Execution, and Analysis. Wyle 

Report WR 12-15, Dec. 2012.

1.13 Page, Juliet Plotkin, Ken Piacsek, Andrew Sparrow, Vic Salamone, Joe Cowart, Robbie Elmer, Kevin

Ladd, John and Maglieri, Domenic Superboom Caustic Analysis and Measurement Program (SCAMP) 

Comparison Report, Wyle Report WR 11-23, October 2011.

1.14 Plotkin, Ken Page, Juliet Salamone, Joe Sparrow, Vic Cowart, Robbie Elmer, Kevin Welge, Bob and 

Piacsek, Andrew Analysis of Acceleration Focus Booms from Four Low-Boom Con¿guration Designs. 

Wyle Report WR 11-26, Dec. 2011.

1.15 Plotkin, K. J. Franz, R. J. and Haering, E. A., Jr. Prediction and Measurement of a Weak Sonic Boom 

From an Entry Vehicle. Paper 2aPA3, Fourth Joint Meeting of the Acoustical Society of America and the 

Acoustical Society of Japan, Nov. 2006.

1.16 Plotkin, K. J. Haering, E. A., Jr. and Murray, J. E. Low-Amplitude Sonic Boom From a Descending 

Sounding Rocket. Proceedings of the 17th International Symposium on Nonlinear Acoustics, American 

Institute of Physics, Melville, New <ork, July 2005, pp. 615–618.

1.17 Nixon, Charles W. and Hubbard, H. Results of the USAF-NASA-FAA Flight Program to Study Community 

Response to Sonic Booms in the Greater St. Louis Area. NASA TN-D 2705, 1965.

1.18 Maglieri, Domenic J. Huckel, Vera and Parrott, Tony L. Ground Measurements of Shock Wave Pressure 

for Fighter Airplanes Flying at Very Low Altitudes and Comments on Associated Response Phenomena. 

NASA TN D-3443, 1966.

1.19 Maglieri, D. J. and Morris, Garland J. Measurements of the Response of Two Light Aircraft to Sonic 

Booms, NASA TN D-1941, 1963.

1.20 Hilton, D. A. Huckel, V. Steiner, R. and Maglieri, D. J. Sonic Boom Exposures During FAA Community 

Response Studies Over a 6-Month Period in the Oklahoma City Area. NASA TN D-2539, Dec. 1964.
Chapter 1 The Sonic Boom Phenomenon

21

1.21 Maglieri, Domenic J. and Sothcott, Victor E. Summary of Sonic Boom Rise Times Observed During 

FAA Community Response Studies Over a 6-Month Period in the Oklahoma City Area. NASA CR 

4277, 1990.

1.22 Borsky, P. N. Community Reactions to Sonic Booms in the Oklahoma City Area. National Opinion 

Research Center, AMRL Rept. TR 65-67, Repts. I and II, 1965.

1.23 Blume, John A. and Associates Structural Reaction Program. National Sonic Boom Study Project. FAA 

Rept. SST-65-15, Vol. I, Apr. 1965.

1.24 Nixon, C. W. Hille, H. K, Sommer, H. D. and Guild, Elizabeth Sonic Booms Resulting From 

Extremely Low Altitude Supersonic Flight Measurements and Observations on Houses, Livestock and 

People. AMRL-TR-68-52, USAF, Oct. 1968.

1.25 National Sonic Boom Evaluation Of¿ce Sonic Boom Experiments at Edwards Air Force Base. NSBEO 

1-67 (Contract AF 49(638)-1758) Stanford Research Institute, July 28, 1967.

1.26 Lee, R. A. and Downing, J. M. Sonic Booms Produced by the United States Air Force and United 

States Navy Aircraft Measured Data. AL-TR-1991-0099, 1991.

1.27 Fields, James M. Reactions of Residents to Long-Term Sonic Boom Noise Environments. NASA CR 

201704, June 1997. 

Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

23

CHAPTER 2 INFLUENCE OF THE ATMOSPHERE

In this chapter, the inÀuence of the atmosphere on primary carpet sonic booms is examined in terms of the macro 

and micro effects macro being associated with the so-called gross effects of pressure, temperature, and wind 

pro¿les and the micro being associated with turbulence, especially in the ¿rst few thousand feet of the earth¶s 

atmosphere. The role of atmospheric absorption on boom signatures is also addressed. The chapter concludes with 

a discussion of the inÀuence of the atmosphere on the secondary over-the-top booms.

For more than half a century, it has been observed that when the atmosphere between the aircraft and the ground 

was quiescent, the sonic boom signatures acquired from supersonic overÀights have always been undistorted 

N-wave shapes. This is illustrated in ¿gure 2.1, which presents a set of measured sonic boom signatures from four 

different vehicles operating at a range of Mach numbers and altitudes. All of the signatures represent on-track 

measurements for steady level Àight. Included are the Space Shuttle Orbiter, Concorde, SR-71, and F-104.

However, it has also been observed that the atmosphere, in particular the lower few thousand feet of the earth¶s 

boundary layer, exerts a signi¿cant inÀuence on the ¿nal character of the ground-measured signature.

Primary Booms

Figure 2.2 is intended to indicate the atmospheric parameters that signi¿cantly inÀuence the sonic boom signature 

as it propagates from the vehicle to the ground. These atmospheric inÀuences are classi¿ed as macro and micro 

effects. Current sonic boom prediction capabilities can account for Àights in non-standard atmospheres with winds 

and for the inÀuence of atmospheric absorption. However, the prediction codes cannot account for the inÀuence of 

local atmospheric instabilities (such as turbulence), especially those that occur within the earth¶s boundary layer. 

Figure 2.1. Measured sonic boom signatures in a quiescent atmosphere.
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

24

Referring to ¿gure 2.2, a few pertinent features should be noted. First, viscous losses, heat, conduction, and 

turbulence effects are known to be inÀuential in the lower few thousand feet of the earth¶s surface. Atmospheric 

absorption or relaxation plays its role from the ground to tropopause. At greater altitudes, humidity is nearly nonexistent. The effects of absorption and molecular relaxation and clouds on sonic boom signatures, especially in 

increasing shock rise times, will be discussed in later sections.

Macro Atmospheric Effects

The next few ¿gures relate to the macro inÀuences of the atmosphere on sonic booms (i.e., the effects of temperature 

and winds on the on-track and lateral boom propagation). One of the most detailed studies of meteorological 

effects on sonic boom, based on analysis of NASA data prior to the summer of 1964, was given by Kane and 

Palmer (ref. 2.1). In general, subsequent investigations have con¿rmed many of their conclusions.

Temperature and Wind Gradients

It is known that atmospheric temperature variations between the airplane and the ground will cause the ray path, 

which describes the path of the shock wave through the atmosphere, to refract. In general, a negative temperature 

gradient (temperature decreases with increasing height above the ground) will cause the ray to bend upwards, 

while a positive temperature gradient will cause it to bend downwards. This distortion of the ray path leads to 

the formation of shadow zones beyond the edge of the primary boom carpet (negative temperature gradient) 

and secondary booms (positive temperature gradient). The effect of temperature variations on boom strength 

under the airplane has been studied for several model atmospheres. These models characterize meteorological 

conditions including tropopause heights and associated temperature gradients, temperature inversions near the 

ground caused by nocturnal radiation, snow cover, coastal clouds, multiple temperature inversions due to mixing 

and advection, frontal temperature inversions, and combinations of the above. As such, these temperature pro¿les 

contain many variations of lapse rate and inversions that cause the ray paths of sonic booms to curve. The models 

are summarized in ¿gure 2.3 (ref. 2.1), which shows the standard atmosphere with no winds for reference.

Figure 2.2. $WPRVSKHULFSDUDPHWHUVLQÀXHQFLQJVRQLFERRPVLJQDWXUHFKDUDFWHULVWLFV
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

25

Variation in wind speed, wind shear, and direction between the airplane and the ground will tend to alter the ray 

path in much the same manner as variations in temperature. In general, headwinds cause the rays to bend up away 

from the ground, while tailwinds cause them to bend downwards. Distortion of the ray paths will cause some 

variation in sonic boom strength. This variation was investigated by constructing a set of model wind pro¿les and 

calculating the resulting ground overpressures. The wind models were selected to be characteristic of gradients in 

zonal and meridonal wind components, high-speed jet streams near the tropopause, and low-level jet streams over 

the Great Plains. Each model was assumed to be omnidirectional (i.e., no lateral shear). The wind models were 

summarized in ¿gure 2.4 (ref. 2.1) for each of the above categories.

Figure 2.3. Summary of atmospheric models (ref. 2.1).

Figure 2.4. 6XPPDU\RIPRGHOZLQGSUR¿OHVUHI
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

26

The effect of winds on the overpressures received at the ground was studied by assuming that the wind velocities 

were aligned parallel and perpendicular to the airplane Àight path. In this manner, the inÀuence of headwinds, 

tailwinds, and sidewinds was studied.

Effects on Boom Amplitudes

A summary of the macro inÀuences of the atmosphere on sonic boom overpressures is given in ¿gure 2.5 (ref. 2.1) 

for several horizontally strati¿ed atmospheres. The effect of temperatures is shown at the top of the ¿gure, while 

the lower portion shows the effects of winds. Calculations of on-track overpressure for steady level Àights above 

the troposphere through various models of atmospheric temperature pro¿les (¿g. 2.3) and wind pro¿les (¿g. 2.4) 

were divided by the overpressures in a standard atmosphere with no winds for Mach numbers from Mach cutoff 

(Mach 1.16 for Àight above the tropopause 36,000 ft, in a standard atmosphere) to Mach 3.0.

The results indicate that for Àight at Mach ! 1.5, the largest inÀuence of temperature and wind pro¿les on the 

sonic boom overpressure along the aircraft ground track is generally no more than about 5 percent from that 

generated in the still (no wind) standard atmosphere. One can observe that for Mach ! 1.5, temperatures lower 

than standard on the ground and tailwinds at altitude increase the boom levels. On the other hand, temperatures 

higher than standard on the ground and headwinds at altitude decrease the boom levels. This is a result of the 

decrease in the length of the ray paths for the former case and an increase in ray path lengths in the latter case.

Signature shapes were assumed to be unaltered from the initially propagated N-wave. It is of interest to note that 

even with the extreme high-speed jet wind pro¿le (270 ft/sec at 30,000 ft altitude) at Mach ! 1.5, the increase or 

decrease in overpressure (depending upon whether applied as a headwind or tailwind) is quite small, the order of 

1 percent or 5 percent, respectively. A similar ¿nding for essentially the same jet stream conditions was reported 

using the =EPH<RUS computer program (ref. 2.2), which is capable of modeling signature propagation in a 

windy atmosphere. Reported results from analysis of Concorde Àight experience (ref. 2.3) note that while boom 

variability turned out to be low for cruising-Àight booms on the ground track, the variability is higher at distant 

lateral locations. 

Figure 2.5. Effect of temperature and winds on sonic boom overpressures (ref. 2.1).
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

27

For Àight at Mach numbers between 1.0 and 1.5 the meteorological conditions in the tropopause between the 

airplane and the ground result in more signi¿cant variations in the overpressure. For Mach  1.5, temperatures 

lower than standard at the ground generally reduce the overpressure, while higher temperatures generally result in 

focusing and increase in the boom level. For physically realistic conditions, this variation may be as much as 15 

percent at Mach 1.2. For Mach  1.5, headwinds generally increase (focus) the boom while tailwinds decrease 

the boom. Winds may cause variation in the overpressure from that in a still atmosphere (no wind) of as much as 

20 percent at Mach 1.3. However, later Àight experiments relating to continuous Àight at Mach cutoff (ref. 2.4), 

to be discussed in Chapter 5 of this publication, show that overpressure increases (focusing) of up to a factor of 

3.0 are possible.

Effect on Lateral Spread

Variations in the temperature and wind pro¿les will cause variations in the location of the lateral cutoff as 

compared to a standard atmosphere without winds. The lateral cutoff is the point on the ground where the sonic 

boom ray path is refracted upward. As such, the shock pattern is not observed at ground level and only acoustic 

rumbles are observed beyond this point. Lateral cutoff is independent of the aircraft type and depends only upon 

the aircraft altitude, Mach number, and atmosphere. The extent of the lateral distribution of sonic boom strength 

was computed for each of the atmospheric models shown previously in ¿gures 2.3 and 2.4.

The variation in lateral extent is shown in ¿gure 2.6 (ref. 2.1) for the two models of temperature pro¿les that 

produced the widest deviations from the values in the standard atmosphere and for the mean zonal wind. The lateral 

extent in the standard atmosphere is shown for reference. Figure 2.6(a) shows that, in the extreme temperature 

pro¿le cases, variations in the boom total lateral spread of from 5 to 10 miles may occur. In general, temperatures 

lower than standard on the ground will increase the lateral extent, <max, while ground temperatures higher than 

standard will decrease <max. 

Figure 2.6. ,QÀXHQFHRIWHPSHUDWXUHDQGZLQGRQODWHUDOFXWRIIDGDSWHGIURPUHI

(a) Temperature variations.

(b) Wind variations.
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

28

Wind shears will also affect the location of lateral cutoff as shown in ¿gure 2.6(b). The magnitude of the variation 

caused by moderate winds was studied in the standard atmosphere with the mean zonal wind pro¿le. The value of 

<max was computed for a headwind, tailwind, and sidewind. For purposes of comparison, these three <max values 

were divided by the value of <max with no wind for the same Mach number and altitude, and are shown plotted 

against airplane Mach number. Figure 2.6(b) shows that for moderate winds the maximum variation occurs at 

Mach numbers near 1.2. For Mach numbers greater than 1.5, the variation is of the order of 5 percent. In general, 

tailwinds and side winds (on the downwind side) increase the value of <max, while headwinds and sidewinds (on 

the upwind side) decrease <max. Strong winds, on the other hand, may substantially increase the magnitude of <max. 

Lateral Spread Footprint

A relatively large amount of sonic boom information has been acquired at EAFB. In 1992, Lundberg (ref. 2.5) 

assessed the state-of-the-art methodologies for long-term sonic boom prediction in seasonally varying atmospheres 

in the EAFB supersonic Àight corridor. Predictions of the sonic boom footprints for steady Àight at altitudes of 

10,000 feet and 30,000 feet were made for Àights east- and west-bound for average atmospheres observed at 

EAFB during the four seasons of the year. Results for the average summer and winter atmosphere are given in 

¿gures 2.7 and 2.8, respectively.

(b) Average summer atmosphere

at EAFB.

Figure 2.7. 6XPPHUDWPRVSKHULFFRQGLWLRQVDQGUHVXOWLQJVRQLFERRPJURXQGIRRWSULQWIRUHDVWERXQGÀLJKWDGDSWHGIURPUHI

(a) F-111, Mach 1.34 steady at 30,000 feet

MSL east-bound.
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

29

The predicted sonic boom ground footprint for an east-bound Àight of an F-111 aircraft Àying steady-level at a 

Mach number of 1.34 and at an altitude of 30,000 feet MSL is shown on the left side of each ¿gure. The summer 

and winter average temperature pro¿les and winds are presented on the right-hand side of the ¿gures.

Note that there is about a 10°

C increase in the temperature between winter and summer and almost a halving of 

the wind speed. Although these differences have a small inÀuence of the sonic boom overpressure levels along the 

footprint ground track, a signi¿cant difference is quite evident regarding the lateral extent of the boom footprint to 

each side of the aircraft ground track – to more than a doubling of the cutoff distance to the south from 14.2 miles 

to 33 miles between summer and winter due to the wind speed gradient. Table 2.1 (from ref. 2.5) presents lateral 

cutoff distances associated with all four seasons¶ annual atmospheric conditions and also includes the lateral 

cutoff for Àight in a standard atmosphere with no wind.

Figure 2.8. Winter atmospheric conditions and resulting sonic boom ground footprint 

IRUHDVWERXQGÀLJKWDGDSWHGIURPUHI

(b) Average winter atmosphere

at EAFB.

(a) F-111, Mach 1.34 steady at 30,000 feet

MSL east-bound.
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

30

Focusing at Lateral Cutoff

In addition to examining the inÀuence of temperature and winds on the extent of the sonic boom lateral cutoff, 

Palmer and Kane (ref. 2.1) showed that, as in the case of focusing under the Àight track (see ¿g. 2.5), intensi¿cation 

of the boom to the side of the Àight track may occur simultaneously with the lateral cutoff. Results of their studies 

are given in ¿gure 2.9 (ref. 2.1) for Àights above the tropopause for assumed wind conditions on standard cold 

and hot days. The ¿gure indicates the wind components required to cause off-track focusing for a range of Mach 

numbers from 1.10 to 1.40.

)LJXUH:LQGVSHHGVUHTXLUHGWRSURGXFHIRFXVLQJRIIWKHÀLJKWWUDFNDGDSWHGIURPUHI

Table 2.1. Predicted Lateral Spread of Sonic Boom for the EAFB Range Average Seasonal Atmospheres and Standard 

Atmosphere for an Eastbound Aircraft in Steady Level Flight at an Altitude of 30,000 Feet MSL (from ref. 2.5)
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

31

As stated in reference 2.1, it is evident that this off-track focusing situation is restricted to the very low Mach 

numbers because of the large magnitude of the wind speeds required at the higher Mach numbers.

Dressler and Fredholm (ref. 2.6) and Lundberg, Dressler, and Lagman (ref. 2.7) argued that the combination of 

sidewinds and turbulent scattering would cause a large increase in the sonic boom level near lateral cutoff and, as 

such, a continuous line of focused overpressure would exist on each side of the Àight track throughout the cruise 

phase of Àight of an SST. There was also a concern that even without large sidewinds there could be focusing at 

lateral cutoff during steady-level Àight due to atmospheric refraction in that the linear theory shows that as the 

ray tube area goes to zero at grazing, the boom levels go to in¿nity (see ¿g. 69 of ref. 2.8). However, Haglund 

and Kane (ref. 2.8) point out that the linear theory incorrectly predicts an in¿nite intensity at cutoff due to ray 

focusing.

Flight test measurements during this time period did not indicate that sidewinds and turbulence scattering would 

cause large increases in the boom level near lateral cutoff or that boom levels would be in¿nite. Two cases are 

shown in ¿gures 2.10 and 2.11 that illustrate the character of the sonic boom signatures for various distances from 

the ground track out to and beyond the lateral cutoff for an aircraft in steady-level Àight. Figure 2.10 (ref. 2.9) 

displays signatures measured to each side of the ground track (station 5) at three lateral locations of 5, 17, and 26 

miles. The predicted lateral cutoff in a standard atmosphere with no winds for Àight at Mach 2 and an altitude of 

52,200 feet is shown to be about 21 miles from the aircraft ground track.

Figure 2.10. Measured sonic boom ground pressure signatures at several measuring stations at different distances 

to each side of WKHDLUFUDIWJURXQGWUDFN$LUSODQHLQVWHDG\OHYHOÀLJKWDWDQDOWLWXGHRIIHHWP

DQG0DFKÀLJKWDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

32

These data were obtained at mid-morning and under fairly quiescent atmospheric conditions. The 

signatures measured to each side of the track are similar in shape and display a progressive rounding 

and decay with increasing lateral distance. A similar set of measurements from steady-level flight 

obtained in France and cited by Onyeowu (ref. 2.10), describing the character of the boom signatures 

to one side of the aircraft ground track to beyond the lateral cutoff is shown in figure 2.11. The lateral 

cutoff for a standard atmosphere with no winds is estimated to occur between transducers 17 and 18. 

Once again, the signatures display a progressive rounding and decay with increasing lateral distance.

Dressler and Fredholm (ref. 2.6) stated that focusing at lateral cutoff was not being observed in the ¿eld 

measurements because of the extreme dif¿culty in positioning the recording instruments at or near where the peak 

magni¿cation would occur. In 1970, during the 1500-foot high BREN tower tests (refs. 2.11 and 2.8), a concerted 

effort was made, through a special series of Àight tests, to more quantitatively de¿ne the situation at lateral cutoff 

(speci¿cally to observe if focusing does occur due to atmospheric refraction). A view of the test arrangement and 

resulting data are shown in ¿gure 2.12 (ref. 2.11). Figure 2.12(a) schematically illustrates the lateral cutoff focus 

concern. The experimental Àight-test setup is indicated schematically in ¿gure 2.12(b). A 3200-foot horizontalcrosswise ground array near the lateral cutoff location with a 200-foot microphone spacing and a 1500-foot 

vertical microphone array with 100-foot spacing are indicated. The Àights were accomplished so that the edge 

of the exposure pattern was placed in or near this array. The data shown in ¿gure 2.12(c) are representative of 

those obtained from the 3200-foot array during one aircraft Àight. A de¿nite trend in signature shape variation is 

evident.

Figure 2.11. Measured signatures in French tests. Distance between transducers is 1000 m. Closest 

WUDQVGXFHUWRÀLJKWWUDFNLVQXPEHUDGDSWHGIURPUHI
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

33

By means of repeated Àights offset in lateral distance from the tower, numerous overpressure signatures were 

measured at the edge of the pattern. Some of these signatures, and the associated peak overpressure data, are 

presented in ¿gure 2.12(d). It can be seen that there is a general decrease in overpressure as distance increases. 

There is also a corresponding trend away from N-shape signatures, which are observed as booms, to a U-shape 

signature and ¿nally to signatures with no de¿nite shape characteristics, which are observed as acoustic rumbles. 

There is no indication of large overpressure enhancement at the edge of the carpet. Other work of signi¿cance 

regarding sonic booms beyond the lateral cutoff (in the shadow zone) can be found in references 2.12 and 2.13.

5HÀHFWLRQ)DFWRU

Signature rounding and decay is inÀuenced by increasing distance, ground impedance, shock incidence angle, 

shock reÀection coef¿cient KR (de¿ned as the total pressure jump divided by the pressure jump in free air) and 

turbulence scattering. It should be noted that most of the Àight-test measurements used in determining ground 

reÀection coef¿cient have been acquired on hard clay desert, dry lake beds or outlying sandy areas, paved surfaces, 

or Àat rooftops. Scant data exist on measurements over snow cover, grassy areas, gravel surfaces, and ocean 

waves.

Walker and Doak (ref. 2.14) looked at the effect of changes in ground impedance and shock incidence angle 

on an N-wave signature for on-track and lateral locations out to cutoff. Kane and Palmer (ref. 2.1) discuss the 

variation of the ground reÀection factor and how it varies theoretically from a value of 2.0 for an oblique shock for 

locations near the ground track to 1.0 for a normal shock as would occur at lateral cutoff. Haglund and Kane (ref. 

2.8) present measured values that varied from 2.18 to 0.86. Onyeowu (ref. 2.10) used the Haglund-Kane results 

to derive an empirical relation for a variable reÀection factor. Figure 2.13, excerpted from his paper, shows the 

variation of the reÀection factor near cutoff using his empirical formula.

Figure 2.12. Characteristics of sonic boom near lateral cutoff (adapted from ref. 2.11).

(b) Sketch of experiment test setup.

(d) Variation of overpressure near lateral cutoff.

(a) Schematic of lateral cutoff focus concern.

(c) Signatures observed near lateral cutoff.
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

34

Onyeowu went on to show the effect of the variable reÀection factor on the overpressure distribution with 

lateral distance from the aircraft ground track using the measured data of reference 2.9 and assuming a standard 

atmosphere. These results are given in ¿gure 2.14 (ref. 2.10).

The three experimental points represent the Àight data. The nominal curve with KR 1.9 is designated ABFG 

and the simple theory of Whitham using a variable KR is designated ABFH. Curves ABCD and ABCE are from 

the Hayes ray-tube area theory with a constant and variable KR, respectively. It can be seen that the simple theory 

of Whitham using a variable KR is in better agreement with the measured data than the ray-tube area approach. 

Onyeowu also notes that the effects of variations in KR only become noticeable beyond the last 40 percent of the 

distance to lateral cutoff.

Figure 2.13. 9DULDWLRQRIUHÀHFWLRQIDFWRUQHDUFXWRIIUHI

Figure 2.14. /DWHUDOGLVWULEXWLRQRIRYHUSUHVVXUHVKRZLQJHIIHFWVRIUHÀHFWLRQIDFWRUYDU\LQJZLWK

angle of incidence and diffraction into shadow zone (ref. 2.10).
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

35

Micro Atmospheric Effects

The previous discussion was limited to the study of the effect of a horizontally strati¿ed atmosphere on the 

propagation of the sonic boom (so called macro effects). As noted by Kane and Palmer (ref. 2.1), the turbulent 

process in the atmosphere (micro effects) is the result of some form of instability. This may be either a result 

of mechanical instability, such as produced by wind shear, or Àow over obstacles, or thermal instability such as 

produced by solar heating of the ground. These forms of instability produce random, turbulent Àuctuations in 

wind and temperature that can only be studied and described in statistical terms. 

Signature Distortions

One of the ¿rst Àight experiments that pointed to the fact that disturbances in the lowest few thousand feet of the 

atmosphere may be most signi¿cant in affecting the shapes of the sonic boom signatures measured at the ground 

was obtained during a sonic boom Àight test program at EAFB in 1961 (ref. 2.15). The results are illustrated by 

the data of ¿gure 2.15 (ref. 2.15).

Temperature is plotted against altitude as determined from wiresonde and rawinsonde soundings taken during 

the Àight times. The ¿lled symbols represent the temperature pro¿le existing for the morning Àights whereas 

the open symbols apply to the afternoon Àight. It may be seen that the temperature conditions of the upper 

atmosphere do not vary appreciably from the morning to the afternoon. On the other hand, in the ¿rst thousand 

or so feet of the lower atmosphere (within the earth¶s boundary layer), the temperature pro¿le varies markedly. In 

the morning, a temperature inversion exists during which time the surface layer of the atmosphere is quiescent. 

Later in the day, as the surface temperature increases, the temperature pro¿le may change to the extent that a 

super-adiabatic (i.e., temperature decreases with height at the rate greater than 10° C per kilometer and is referred 

to as absolute instability) lapse rate condition can exist as indicated. For such a temperature pro¿le, the surface 

layer of the atmosphere is inherently unstable and severe thermal-induced turbulence may be generated. There is 

a strong correlation between the type of signature measured and the temperature pro¿le in the lower atmosphere. 

Figure 2.15. (IIHFWRIHDUWK¶VERXQGDU\OD\HURQWHPSHUDWXUHSUR¿OHDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

36

Consistent N-wave types of signatures were measured when the lower atmosphere was quiescent, whereas large 

variations in the shape of the signatures from peaked to rounded were measured when the lower atmosphere was 

considered to be unstable.

Past experience in the measurement of sonic booms during Àight tests has indicated a substantial amount of 

variability in the signatures (see reference 2.16) compared to the expected N-wave signature. In order to establish 

that the signature variability that was being observed was not due to instrumentation, a special Àight test was 

conducted (ref. 2.17). The objective of this test was to obtain comparable data from several channels of measuring 

instrumentation of the same type under conditions where weather effects would be essentially eliminated. In order 

to do this, seven of the microphones having a frequency response of 0.10 to 10,000 Hz were shock-mounted in a 

3 by 3-foot reÀection board within an area of less than 1 square foot. Data obtained from this instrument setup for 

a special Àight test, are shown in ¿gure 2.16 (from ref. 2.17).

Data were obtained from an F-104 in steady Àight at an altitude of 41,200 feet and at a Mach number of 1.52. 

The test was accomplished at about 1400 hours when there was considerable atmospheric turbulence and thermal 

activity in the test area.

The most obvious result of ¿gure 2.16 is that the measured boom signatures, which are peaked in character, show 

remarkable similarity. Peak amplitudes of the signatures presented in the ¿gure are somewhat different because of 

variations in the sensitivity of the various channels of equipment. However, the measured peak values indicated in 

the ¿gure are noted to be within a range of 15 percent or the equivalent of about 1 dB. It is concluded that the 

signature distortions are a result of atmospheric inÀuences and that any variability resulting from instrumentation 

and measurement procedures are minimal.

The signature variability observed during Àight experiments at EAFB, which appears to be associated with the 

changes in the lower layers of the atmosphere, was also noted to occur during the 6-month sonic boom over-Àight 

program in Oklahoma City where the atmosphere, especially the lower layers, is not typical of the desert regions 

of EAFB, California. Some results are presented in ¿gure 2.17 (ref. 2.18). The data shown were derived from an 

accurately calibrated and oriented array of matched microphones along the aircraft ground track. The variations 

in the wave shapes measured during one steady Àight of an F-104 at a speed of Mach 1.7 and at an altitude of 

Figure 2.16. F-104 Sonic boom signatures from seven microphones grouped within a one-square foot 

DUHDRQJURXQG0DFKDQGDOWLWXGHRIIHHW ǻpo LVLQOEVIW࣠2

 (adapted from ref. 2.17).
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

37

28,000 feet are sketched for the appropriate measurement locations. A wide variation in wave shape occurs even 

over a distance on the ground of a few hundred feet. This variation in boom signature shape, which is associated 

with changes in atmospheric conditions, resulted in substantial variations in the peak ground overpressure (about 

a factor of 3.0), the larger values being associated with the sharply peaked waves and the lower values with the 

rounded-off waves.

Variations in sonic boom signature shape similar to those observed at EAFB and Oklahoma City were also 

measured during the USAF B-58 training mission over the Chicago area. The data are shown in ¿gure 2.18 (ref. 

2.19) and are measured signatures from the ¿ve microphones in a cruciform array spaced 100 feet apart under 

the aircraft Àight track. The signatures on the left hand side of the ¿gure were obtained for a different Àight on a 

different date and for markedly different weather conditions than those on the right hand side of the ¿gure. The 

surface weather conditions differed mainly in wind velocity and wind direction. The signatures on the right-hand 

side of the ¿gure were obtained for wind velocities on the order of 28 knots with gusts, whereas the signatures on 

the left hand side were obtained for lower wind velocities. A much wider variation in the signature shapes exists 

for the condition of high winds. The main distortions of the signatures in each case are once again associated with 

the rapidly rising portions of the boom signatures, and these distortions are of the same general nature as has been 

previously observed for other airplanes and other atmospheric conditions in other geographical areas.

Figure 2.18. 6RQLFERRPIURPWZR%ÀLJKWVRYHUWKHFLW\RI&KLFDJRXQGHUGLIIHUHQWDWPRVSKHULF

conditions (adapted from ref. 2.19).

Figure 2.17. 9DULDWLRQVLQVRQLFERRPVLJQDWXUHVDORQJJURXQGWUDFNIRUVWHDG\OHYHOÀLJKWDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

38

As a follow up to the EAFB, Oklahoma City, and Chicago experiments shown in the previous ¿gures, another 

experiment at Wallops Island, Virginia was performed to investigate the effects of time with regard to atmospheric 

distortion effects. This experiment was performed using two airplanes of the same type that were Àown at the 

same altitude of 40,000 feet and Mach number 1.5, on the same nominal Àight track, and about 5 seconds apart, 

as illustrated in the upper portion of ¿gure 2.19 (ref. 2.15). By means of the 1500-foot ground microphone array it 

was possible to measure sonic boom signatures that traveled along essentially the same ray path from high altitude 

to the ground for a distance of approximately 15 miles along the ray path, but at slightly different times.

The signature tracings at the bottom of ¿gure 2.19 illustrate one of the results of the experiment. It can be seen 

that quite different shapes are associated with measurements at times a few seconds apart. Such a result suggests 

that the integrated effects of changes in the atmospheric conditions along a given ray path may be signi¿cant even 

for such a small difference in time.

Another demonstration that the boom signature may vary widely over short distances and time is illustrated in 

¿gure 2.20 (ref. 2.15). These results were obtained at Wallops Island, Virginia where the ¿rst few thousand feet 

of the atmosphere are not typical of the desert region of EAFB. 

Figure 2.19. Measured sonic boom pressure signatures for two F-106 DLUFUDIWÀ\LQJDW0DFKDQDOWLWXGHRI

IHHWDQGVHFRQGWLPHLQWHUYDOVRYHU:DOORSV,VODQG9LUJLQLDDGDSWHGIURPUHI

Figure 2.20. (IIHFWRIDWPRVSKHUHRQERRPVLJQDWXUHVPHDVXUHGRQWRZHUDQGJURXQGIRUWZR)ÀLJKWVRYHU

Wallops Island9LUJLQLD0DFKIWDOWLWXGHDQGDWVHFRQGWLPHLQWHUYDOVDGDSWHGIURPUHI
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

39

Flights were made over an instrumented range consisting of a linear microphone array of 100-foot spacing on 

the ground and extending over about 1500 feet, in combination with a vertical array on an instrumented tower 

extending to about 250 feet at 50-foot intervals above the ground. An F-106 was Àown at an altitude of 40,000 

feet and at a Mach number of 1.5 for a variety of weather conditions. The objective of the studies was to correlate 

the sonic boom measurements with the extensive meteorological data obtained on the instrumented tower.

In situations where waveform distortion was noted to exist, it was found that similar wave shapes were measured 

both at the ground surface and on the instrumented tower. A particularly interesting and signi¿cant result of these 

studies is illustrated by the waveform tracings, which suggest that similar types of distortions exist at points along 

any given ray path and that waveforms on nearby paths may differ markedly. 

Results indicate that, for these particular tests, the 250-foot layer of the atmosphere near the surface of the ground 

did not appreciably affect the signature shapes. It follows then that the portion of the atmosphere above 250 feet 

was important for the conditions of this experiment with regard to wave shape distortions.

In an attempt to gain more insight into the inÀuence of the ¿rst few thousand feet of the atmosphere on boom 

signatures, a unique Àight experiment was performed. The Goodyear blimp, 0D\ÀRZHU, was used to carry 

microphones to an altitude of 2000 feet above Rogers Dry Lake at EAFB, well above the level of the active lower 

layer and at a height where both the incident and reÀected boom signatures would be captured. An F-106 aircraft 

was Àown over the test site in steady level Àight numerous times at Mach 1.5 and at an altitude of 40,000 ft MSL. 

The results are presented in ¿gure 2.21 (ref. 2.15). 

It can be seen that the incident boom signature, which has not yet entered the active lower layer of the atmosphere, 

is a fairly clean undistorted N-wave. On the other hand, the reÀected signature, which has traveled twice through 

the active lower layer, is distorted, with a bow and tail shocks showing peaked character. It is to be noted that the 

lakebed surface upon which the incident shocks reÀected from is Àat, smooth, and hard and expansive without 

any nearby structures, trees, bushes, or underbrush. Since the two waveforms were measured at different times, 

the experiment does not give direct information concerning the effects of the lowest 2000 feet. However, a larger 

proportion of incident waveforms (as contrasted to reÀected waveform) was relatively undistorted. This would 

suggest that the 2000-foot surface layer was responsible for a major portion of the distortion, even though the 

distortion could not be proven to be solely attributed to the lowest 2000 feet.

A similar Àight experiment to that shown in ¿gure 2.21 was conducted during the 2004 NASA Shaped Sonic Boom 

Experiment (SSBE). The SSBE was a follow-up Àight test program to the 2003 Shaped Sonic Boom Demonstration 

(SSBD) Àight tests, which were aimed at proving the persistence of a shaped sonic boom signature to the ground. 

During SSBE, a sailplane with a wing-tip mounted microphone was used as the airborne measurement platform. 

The test setup and results of this particular Àight test are shown in ¿gure 2.22 (developed from refs. 2.20 and 

Figure 2.21. ,QÀXHQFHRIORZHUOD\HUDWPRVSKHUHRQVRQLFERRPVLJQDWXUHVIRUDQ)DLUFUDIWÀ\LQJRYHU($)% at Mach 

DQGDWDQDOWLWXGHRIIHHWDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

40

2.21). An F-5E was Àown at a steady Mach number of 1.4 and altitude of 32,000 feet and the glider was at about 

6000 feet above the desert Àoor, well above any active lower layer of the atmosphere. At this height, both the 

incident and reÀected boom signatures were captured.

Once again, it can be seen that the incident boom signature, which has not yet entered the lower layer of the 

atmosphere, is a fairly clean undistorted N-wave. The signature at ground level shows little distortion resulting 

from its travel through the 6000 feet from the glider to the ground. On the other hand, the reÀected signature that 

has traveled twice through the lower layer has experienced some distortion in the form of peaking of the bow and 

tail shocks. Here again, as was the case in ¿gure 2.21, the experiment gives direct information concerning the 

effects of the lowest 6000 feet and suggests that for the EAFB desert environment below 6000 feet, surface layer 

is responsible for a major portion of the signature distortion. 

The data presented in the last few charts produced evidence that suggests that there is a strong correlation 

between signature distortion and identi¿able local disturbances in the atmosphere. A special Àight experiment was 

performed in an attempt to produce evidence of direct correlation between signature distortion and identi¿able 

local atmospheric disturbances. Figure 2.23 (ref. 2.22) illustrates the test setup and resulting boom measurements. 

Use was made of a large subsonic KC-135 aircraft to generate wing tip vortices (ref. 2.23) in the test area, which 

consisted of a 7000-foot array of microphones, in such a manner that the shock waves produced by an F-106 in 

steady level Àight at Mach 1.5 and an altitude of 35,000 feet would pass through these vortex disturbances. 

Figure 2.22. ,QÀXHQFHRIORZHUOD\HUDWPRVSKHUHRQVRQLFERRPVLJQDWXUHVIRUDQ)(DLUFUDIWÀ\LQJRYHU($)% in 2004 at 

0DFKDQGDWDQDOWLWXGHRIIHHWUHIDQG
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

41

The resulting measurements of peak overpressure values (two Àights) from the microphones in the linear ground 

array are shown at the bottom of ¿gure 2.23. Of particular interest are the six data points at distances from 5200 

to 5600 feet along the ground track where markedly larger overpressure values were recorded. Although the peak 

overpressures increased a signi¿cant amount over those locations beyond the inÀuence of the wing-tip vortex 

generated by the KC-135 aircraft, no signi¿cant changes were noted in the overall character of the signature 

shapes from those not affected by the KC-135 vortices. Such an observation suggests that the turbulence structure 

within the wing-tip vortices are different than that of the lower layer of the atmosphere.

Effect of Aircraft Pitching Motion

It was recognized that measurements of sonic boom signatures on the ground may be affected by variations in the 

aircraft pitching motion (lift variations) as well as by the atmosphere. An experiment was performed in an attempt 

to evaluate the effects on measured signatures of altitude perturbations of the aircraft about its nominal Àight path. 

In order to accomplish this study, the same test setup, shown in ¿gure 2.23, was employed. A schematic of the 

test setup and results are presented in ¿gure 2.24 (ref. 2.15). The aircraft was Àown at a ¿xed altitude and Mach 

number and on a given heading directly over and along a 6200-foot-long array of 40 microphones, as shown in 

¿gure 2.24(a). The aircraft, which was specially instrumented to record its motions, was Àown both in steady 

level and pitching motion Àight. All Àights were made at a nominal altitude of 35,000 feet and a Mach number 

of 1.5 with an F-106 aircraft. For the pitching motion Àight, the pilot caused the airplane to deviate from steady 

level Àight conditions by cycling the controls to produce a 0.5g normal acceleration at the center of gravity of 

the aircraft. These induced motions have a period of about 1 second and thus, the wavelengths of the motion were 

about 1500 feet for the particular Àight conditions.

Figure 2.23. 7HVWDUUDQJHPHQWVDQGUHVXOWVIURPDLUFUDIWVKRFNZDYHYRUWH[LQWHUDFWLRQH[SHULPHQWDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

42

Ground overpressure measurements for the two types of Àights are shown in ¿gure 2.24(b). The data points for 

three steady Àights and for four pitching motion Àights were obtained from individual microphones located at 

various stations along the ground track as indicated in the schematic sketch of ¿gure 2.24(a). Note that the same 

ranges of overpressure were measured for each of the Àight conditions. Furthermore, an inspection of the data 

suggests the occurrence of cyclic variations of the overpressures for both the steady and pitching motion Àight 

conditions. Since it is believed that the pitching motion Àight condition might produce a cyclic variation of 

overpressure at a preferred wavelength on the ground, the data of several such Àights were analyzed in such a 

manner as to accentuate this effect, if it existed. These results are shown by the individual histograms shown in 

¿gure 2.24(c) that indicate variations in the absolute values of the differences in the overpressures measured at 

pairs of points and are separated by the distances indicated. If the effects of the airplane motion were faithfully 

transmitted to the ground, it is reasonable to expect that smaller differences in overpressure values would be 

obtained at some separation distances than at others. The sample data from these histograms (¿g. 2.24(c) represent 

separation distances varying from 100 feet to 1600 feet for comparison. In order to better de¿ne the trend of the 

variations, the data are presented in a more convenient form in ¿gure 2.24(d). 

The quantity ǻp, which is the root mean square overpressure difference, is plotted as a function of separation 

distance for the distances for which data are available. A single curve seems to represent the variation of ǻp as 

a function of distance for both the steady and pitching motion Àight cases. Both sets of data are seen to increase 

monotonically as a function of separation distance. Such a result strongly suggests that perturbations about the 

Àight track of the order resulting from the 0.5 g pitching motion Àight do not propagate faithfully to the ground 

from high altitude. It is therefore believed that the observed variations in boom level along the ground track 

are due mainly to atmospheric effects rather than to effects of the aircraft¶s pitching motion. For lift dominated 

vehicles, such as the ;B-70 or an SST, these ¿ndings may not be applicable.

Figure 2.24. ,QÀXHQFHRIDQ)DLUFUDIW¶VPRWLRQRQVRQLFERRPVLJQDWXUHVDWJURXQG7KHDLUFUDIWZDVÀ\LQJRYHU

($)%DW0DFKDQGDQDOWLWXGHRIIHHWDGDSWHGIURPUHI

(a) Schematic of test arrangement.

(c) Histograms of overpressure differences.

(b) Measured peak overpressures.

(d) Root-mean-square differences.
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

43

Effect of Time of Day

During the 1966 time period, systematic measurement studies designed to minimize all effects other than those of 

the local atmosphere were conducted at EAFB to document the variability of sonic boom signatures at the ground. 

A total of 34 F-104 supersonic Àights were made at constant Mach and altitude over an 8000-foot linear array 

of microphones at different times of the day for 8 days over a period covering 2 months. Figure 2.25 (ref. 2.24)

presents the results of two such Àights made about 1 month apart and at different times of the day.

In the upper left of the ¿gure, the peak overpressures obtained from the microphone systems of the array with 

separation distances ranging from 50 feet to 200 feet for each Àight are plotted as a function of distance along the 

8000-foot array. Each data point represents the maximum positive peak overpressure reading from a particular 

microphone of the array. Also shown in each of the two cases is a horizontal dashed line representing the calculated 

nominal overpressure for the average Àight conditions of the test and for standard atmospheric conditions. 

It can be seen that a rather small variability in the overpressure values was present for the early morning Àight 

(Àight 8K-1) when the lower layer of the atmosphere was fairly stable. In the case of the early afternoon Àight 

(Àight 8K-20), when the lower atmosphere was becoming more unstable, considerable variability in boom levels 

was observed and the data plot has a cyclic or wavelike appearance where measured overpressure values included 

those markedly higher than, and lower than, the calculated nominal value. 

In order to de¿ne better the nature of the overpressure variations just noted for Àight 8K-20, some signature data 

are included. The signatures correspond to the overpressure data points shown by the solid symbols. These solid 

symbol data points are associated with a group of microphones for which the separation distance was generally 

200 feet. Note that the highest overpressure values are associated with the peaked waveforms, whereas the lower 

overpressure values are associated with the rounded waveforms. In the case of Àight 8K-20, there is an orderly 

progression of the wave shape between the lower overpressure and higher overpressure signatures. During the 

January 2004 SSBE Àight tests (ref. 2.20) a supersonic run was performed over a 12,500-foot linear array of 26 

ground microphones, spaced 500 feet apart, in the afternoon time period when the lower layer of the atmosphere 

is normally unstable. Figure 2.26 presents the measured boom signatures along the linear array for Àight 19-2 on 

January 14, 2004 at 1347 hours local time.

Figure 2.25. 9DULDELOLW\LQVRQLFERRPRYHUSUHVVXUHVDQGVLJQDWXUHVKDSHVRIDQ)DLUFUDIWÀ\LQJDERYH($)%DW0DFK

DQGDQDOWLWXGHRIIHHW7KLVYDULDELOLW\ZDVPHDVXUHGDORQJDQIRRWDUUD\DGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

44

The F-5E aircraft Àew steady level at Mach 1.4 and an altitude of about 32,000 feet. Although the boom signatures 

show some evidence of turbulence inÀuences, they are all generally N-wave in character and the variation in 

boom levels and bow-shock rise time are not as great as those observed on the 8K-20 Àight shown in ¿gure 2.25. 

The above results suggest the possible existence of a characteristic structure of the atmosphere that is changing as 

a function of time, but has characteristic dimensions of a few hundred to a few thousand feet.

Turbulence and Gust Structure

Garrick and Maglieri (ref. 2.25) pointed out that the characteristic length of turbulence in the lower atmosphere 

below 1000 to 2000 feet depends on the height above terrain. An interesting detailed view of the vortex structure 

near the ground is afforded by ¿gure 2.27 (from ref. 2.26), which shows equal velocity contours, or isotachs, 

obtained from measurements taken during 25 seconds of gusty winds. The horizontal section shows the isotachs 

obtained from measurements taken at eight stations along an array of 50-foot poles equally spaced over a linear 

distance of 420 feet. The vertical section shows the isotachs obtained from measurements taken at ¿ve equally 

spaced stations up a 250-foot high tower. In each section, the ordinate represents distance along the array or up 

the tower and the abscissa is time. During the sampling period, the average wind traversed a distance of over 1000 

feet. The vortex structure depicted in ¿gure 2.27 was acquired in an open unobstructed area. One can imagine 

a completely different vortex structure associated with areas in which cluster homes are located between and 

among high-rise structures and in valleys and on hilly terrain. It is obvious that the inÀuence of such wide-ranging 

atmospheric situations on the boom signatures that propagate through them will be different. 

Turbulence in the upper atmosphere has been probed by instrumented airplanes (ref. 2.27). Typical results of 

measurement for moderate turbulence are shown in ¿gure 2.28 as the variation of power spectral density of 

vertical velocity with wave number (1/wavelength).

Figure 2.26. 0HDVXUHGVRQLFERRPVLJQDWXUHVIURPWKH)(DORQJDIRRWDUUD\RIJURXQGPLFURSKRQHVVSDFHGIHHW

DSDUW)OLJKWRQ-DQXDU\DWKRXUVORFDOWLPHDGDSWHGIURPUHI
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

45

The dashed extension to the measurements follows the theoretically expected 5/3 power of the wave number. The 

shape of this curve tends to be relatively invariant while the amplitude is a function of the severity of the turbulence. 

The curve shows the distribution of power in the various wavelengths and the area under the curve yields the 

total power. This same type of ¿gure can also apply approximately near the ground with relatively less power 

in the longer wavelengths. It may be noted that a sonic boom pressure signature of 0.3 to 0.4 seconds duration 

covers acoustic wavelengths that range from about 1000 meters to fractions of a foot. Thus, the interaction of the 

pressure signature and the turbulence occurs over the entire spectrum shown and includes acoustic wavelengths 

less than and greater than the characteristic vortex sizes.

As previously noted, the atmosphere, particularly the ¿rst few thousand feet of the earth¶s boundary layer, plays 

a signi¿cant role relative to the sonic boom signature waveforms for a given aircraft. It has also been found that 

these atmospheric inÀuences appear to have similar effects on aircraft signatures independent of aircraft size (i.e., 

signature duration). Figure 2.29 (ref. 2.25) presents examples of sonic boom waveforms that were measured at 

different times and on different Àights in the primary carpet for three different types of aircraft. The measured 

Figure 2.28. A spectrum of atmospheric turbulence (adapted from ref. 2.27).

Figure 2.27 Gust structure near the ground as revealed by isovelocity contours (adapted from ref. 2.26).
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

46

waveforms for the 55-foot long F-104 aircraft are for a time duration (ǻt) of about 0.10 second and are seen to 

differ from the nominal N-wave shape, varying from a sharply peaked to a gently rounded shape. Similar tracings 

are shown for the B-58 (about 98 feet long) and ;B-70 (about 185 feet long) aircraft. The B-58 signatures are 

roughly 0.2 second in duration and the ;B-70 signatures are approximately 0.30 second in duration. The main 

differences between the boom signatures for a given aircraft occur at the time of the rapid compressions (i.e., the 

bow and tail shocks of the N-wave signature). The largest overpressures (ǻp) are generally associated with the 

sharply peaked waves, whereas the lower pressures are associated with the rounded waveforms, which display 

longer rise times (IJ).

Initially, rise time was de¿ned as the time from the onset of the shock from ambient pressure to the maximum 

overpressure. Further de¿nitions included the rise time to the 1/2 and 3/4 overpressure amplitude. Today, the 

preferred description of a boom signature rise time is the time from the 10 percent of the overpressure amplitude 

from ambient pressure to the 90 percent value of the overpressure. As will be discussed in later chapters of this 

report, rise time (IJ) plays a signi¿cant role in human response both outdoors and indoors to sonic booms and also 

to the response of building structures to booms.

Also of signi¿cance is the fact that distortions displayed on the bow shocks are duplicated at the tail shock and are 

independent of the signature length or duration for the three cases shown of about 0.10 to 0.30 second.

The fact that virtually all N-wave signatures of 300 msec or less exhibit the same turbulence distortion patterns 

of the bow and tail shocks suggests certain features of the turbulence structure can be considered frozen within 

this time-space regime. It has also been found that as the N-wave signature durations grow larger, as for the case 

of measurements from the Shuttle Orbiter on reentry at high Mach-altitude conditions, that this bow-tail shock 

duplication is not evident.

Measured results from 10 sonic boom sites in the California area that were located along and laterally from the 

ground track on STS-26 reentry, are illustrated in ¿gure 2.30 (ref. 2.28). Also shown on the ¿gure are the Mach 

number and altitude at which the boom was generated. Note that the ten signatures cover the range of Mach 

numbers from 4.57 to 3.18 and altitudes from about 115,000 feet to 95,000 feet, respectively.

Figure 2.29. ,QÀXHQFHRIDWPRVSKHUHRQERRPVLJQDWXUHVIURPGLIIHUHQWVL]HDLUFUDIWDGDSWHGIURPUHI
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

47

It can be seen that all signatures are similar, being N-wave in shape with fairly rapid rise times on most of the 

signatures. Durations vary from about 0.45 second to 0.68 second and overpressures from 0.61 to 1.28 lbs/ft2

. 

There are indications of atmospheric effects on the signatures, in particular, sites 4, 6, 7, and 12, but all 10 

signatures remain N-wave in character.

It should be noted, however, that at the high Mach-altitude conditions, where the signature durations are large, the 

nature of the bow and tail shocks may differ and that whatever peaking or rounding of the bow shock resulting 

from atmospheric turbulence in the lower layers of the atmosphere is not exactly repeated at the tail shock (for 

example, site 2 vs site 12). A similar observation is evident for the ¿rst two high Mach-altitude on-track measured 

signatures on STS-1 reentry (ref. 2.29). This fact suggests that the previously mentioned assumption of a frozen 

atmosphere does not apply in all cases when the signature lengths are larger than the scale of the atmospheric 

disturbances. 

Effect of Microphone Orientation

It has been shown that shock wave signatures with similar spikey characteristics on both the bow and tail waves 

can be realized as a result of microphone orientation. Garinther and Moreland (ref. 2.30) investigated several 

transducers that were considered for use in evaluating the hearing hazard of pressure waves that small arms 

produce. Although muzzle blast was foremost in the study, measurements were also made of the shock waves 

associated with the supersonic passage of the riÀe bullet past the microphone, which was oriented at various 

angles from normal (0° incidence) to grazing (90° incidence). The results from BRL 250-kc microphone are 

shown in ¿gure 2.31.

Figure 2.30. Comparison of sonic boom pressure signatures from STS-26 reentry as measured at 10 sites in 

California (adapted from ref. 2.28).
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

48

Figure 2.31(a) shows the shock waves associated with the 7.62 mm riÀe bullet traveling at 2870 feet per second 

with microphones about 1 meter from the shock pattern at 0o

 and 90o incidence to the shocks (normal and grazing, 

respectively). Figure 2.31(b) illustrates how the bow shock reÀects around the simulated transducer, which is 

oriented at about a 45o

 incidence angle to the shock. Note the very large difference between the thickness of the 

shocks as compared to the size (1.20-in. diameter) of the microphone diaphragm. In the case of boom signature 

measurements resulting from the shocks off the aircraft, the reverse is true (i.e., the shocks are usually an order of 

magnitude thicker than the size of the microphone diaphragm).

Figure 2.31(c) and ¿gure 2.31(d) show the signi¿cant difference in the measured N-waves from the bullet shock 

system. The signature measured with the microphone at grazing incidence in ¿gure 2.31(c) results in the expected 

N-wave without distortions due to reÀections or refractions about the transducer. However, at normal incidence, 

the bow and tail shocks are peaked and spikey, similar to what has been observed during sonic boom measurement 

and attributed to atmospheric effects.

However, for the aircraft boom case, the thickness of the shock is much greater than the size of the microphone 

used to measure the signatures. As such, microphone orientation should not play a role in de¿ning the boom 

signature characteristics. In order to establish that the boom signature distortions (spiking and rounding of bow 

and tail shocks) are truly a result of atmospheric inÀuences and are not a result of the orientation of the microphone 

measurement systems, a special boom overÀight test was conducted during the 1966 – 67 sonic boom experiments 

(ref. 2.22).

Figure 2.32 depicts the test setup and resulting boom signature measurements. Six of the Photocon microphone 

systems (ref. 2.31) were arranged on a 4-foot square ground board in a cluster about one foot in diameter and 

isolated from any vibrations. One was Àush mounted with its diaphragm parallel to the ground, four were oriented 

Figure 2.31. ,QÀXHQFHRIPLFURSKRQHRULHQWDWLRQRQEXOOHWVKRFNZDYHVLJQDWXUHDGDSWHGIURPUHI

(a) 7.62 mm-bullet shock waves. (b) ReÀection of bow shock around transducer.

(d) 0° incidence angle 

max. overpressure 166dB.

(c) 90° incidence angle max. 

overpressure 157 dB. 
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

49

about 6 inches above the board with their diaphragms at an incidence angle of 45o to the ground plane in a 

cruciform array parallel and perpendicular to the aircraft ground track. A sixth microphone was located in the 

same plane and with its diaphragm parallel to and facing the ground.

Figure 2.32. Effect of microphone orientation on sonic boom signature shape.

Two passes were made on 2 consecutive days, one in the afternoon with the F-104 at Mach 1.3 and 21,000 feet 

altitude and offset from the microphone array by about 5 miles. The second pass was made in the morning of 

the second day by an F-111 at Mach 1.92 and an altitude of 40,000 feet almost directly overhead of the array. 

Examination of the measured signatures indicate that for the F-104 afternoon Àight, atmospheric inÀuences are 

evident in the measured boom signatures in that they are spikey, whereas for the F-111 morning Àight, when the 

lower layer of the atmosphere were quiescent, near normal N-waves were measured. In both cases, any distortions 

that occured for the bow shock were also present on the tail shock. More importantly, however, is that for each 

Àight, the measurements made by all six microphones are essentially identical regardless of diaphragm orientation. 

Thus, the signature distortions associated with aircraft generated sonic booms result from atmospheric effects. A 

similar microphone orientation checkout test was conducted in 1987 by the U. S. Air Force during the development 

of their digital Boom Event Analyzer Recorder (BEAR) system (ref. 2.32). Once again, six microphones were 

arranged in the same fashion as for the 1967 EAFB tests and the results were similar.

Earlier in this chapter (¿gs. 2.16 and 2.32) it was shown that sonic boom signatures acquired with the microphones 

grouped within a foot or so were essentially identical. It was also shown that as the separation distance between 

microphones increased beyond 50 feet, the boom signatures differed from one another (see ¿gs. 2.17, 2.18, 2.25, 

and 2.26). Some studies conducted by the Environmental Science Services Administration (ESSA) during the 

1966 EAFB National Sonic Boom Program sought to establish a more solid relationship between the atmosphere 

and its inÀuence on sonic boom signatures. Figure 2.33 (ref. 2.33) shows the designed layout of 42 microphone 

measurement systems located near the aircraft ground track and with a spacing of from 12.5 feet to 200 feet along 

with contours displaying the distribution of overpressure patterns for two supersonic overÀights.
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

50

During these tests, it was observed that at the microphone array arranged in concentric circles out to a 100-foot 

radius (microphones 2 through 20 in ¿gure 2.33(a)), the microphones that were within 25 feet of the center of the 

circle (microphones 4, 5, 9, 10, 11, 12, 13, 17, and 18) were correlated (i.e., all the signatures were essentially 

the same). As the distance from the center of the circle increased to 50 feet (microphones 3, 8, 14, and 19) the 

correlation ceased to exist and all the signatures were different from each other.

A similar observation was made during the 2003 SSBD Àight program (ref. 2.34) and is shown in ¿gure 2.34 (ref. 

2.35). It can be seen that the two boom signatures from the F-5E aircraft measured at microphones 1 and 2 are 25 

feet apart and essentially identical in all aspects. 

Figure 2.33. Microphone layout and overpressure patterns acquired during 1967 NSBEO 

ESSA meteorological investigation (adapted from ref. 2.33).

(a) Microphone array for ESSA studies – Site 9.

(c) Distribution of overpressure patterns for Mission

87-1, 50-ft grid array.

(b) Distribution of overpressure patterns for Missions

88-1 and 44-1, 200-ft grid array.
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

51

Signature Deturbing

The fact that atmospheric distortions to the sonic boom signatures affect the bow and tail shocks equally, on 

waveforms of up to 300 msec in duration, allows one to assume that the turbulence structure of the atmosphere is 

essentially frozen during the time period in which the shock propagates through it to the ground. Boom signatures 

measured for the SSBD and F-5E aircraft of about 90 msec in duration are also short enough that the frozen 

turbulence assumption should apply. A deturbing procedure was therefore applied (refs. 2.20, 2.36, and 2.37). The 

process consisted of superposing a clean step function on the rear shock and subtracting that from the measured 

boom following the shock. The resulting difference was then subtracted from both the front and rear shocks. 

Figure 2.35 (from ref. 2.20) shows the results. Figure 2.35(a) shows a measured F-5E boom on the left and the 

same signature with turbulence subtracted on the right. The rear shock (by de¿nition) becomes a simple step. 

With the inÀuence of turbulence on the bow shock removed, the full signature is close to a perfect N-wave. This 

process was found to work for virtually all of the N-wave booms. 

Figure 2.34. Signatures from microphones positioned 25 feet apart (ref. 2.35).

(a) F-5E signatures.

(b) SSBD signatures.

Figure 2.35. ([DPSOHVRIERRPVLJQDWXUHFOHDQXS7KHÀLJKWVRIZHUHDWKUVDQGKUVDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

52

This turbulence subtraction algorithm was applied to the measured SSBD boom shown in ¿gure 2.35(b). The 

turbulence-subtraction analysis showed that the original signature variations were due to turbulence. Removal of 

turbulence results in extremely consistent measured results for the N-wave and shaped boom.

It is interesting to note that sonic boom signature deturbing was ¿rst looked at by Kane and Palmer in 1964 (ref. 

2.1) when they noted that if there is turbulent scattering of the shock wave, the changes of the turbulent structure 

of the atmosphere between the instant of passage between the bow shock wave and the aft shock wave are very 

small (i.e., one can assume that the turbulence is frozen for that time period) and the front and aft shock waves 

should be affected in the same way. Thus, they performed the following experiment to test this deduction. First 

they made a tracing of the distorted N-wave signature. Then, they placed this tracing below the original trace so 

that the axis corresponding to time is parallel to the original N-wave signature, as shown in ¿gure 2.36. Next, the 

trace is translated to the left so that the point where the aft shock wave begins and the front shock wave begins 

coincide vertically. Next, they perform an algebraic-graphical subtraction in which values below the zero ǻpz line 

are treated as negative. This procedure, illustrated in the ¿gure, restored the original form of the N-wave.

2II7UDFN9DULDELOLW\

Signature variability is not only observed along the aircraft Àight track, but also at lateral distances out to and 

beyond the cutoff depending upon the state of the atmosphere, particularly in the lower layers. An illustration of 

such an occurrence is presented in ¿gure 2.37 (ref. 2.9) for steady level Àights of an F-104 at the EAFB test site 

during fairly stable and unstable conditions of the atmosphere. The four Àights were made at about the same Mach 

and altitude conditions.

Figure 2.36. Reconstruction of wave signature by graphical method (adapted from ref. 2.1).
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

53

The lateral spread results shown at the top of the ¿gure represent four Àights under fairly calm surface and lower 

layer conditions. Note that similar waveforms were obtained for about the same distances to each side of the 

airplane ground track and the bow-shock overpressure decreases while the rise time increases (wave becomes 

more rounded) as the lateral cutoff is approached. Beyond this point, the boom signatures lose their identity and 

are observed as a rumbling noise as depicted by the low frequency pressure time histories.

Lateral-spread results, presented in the lower part of ¿gure 2.37, were obtained in the same manner as those in 

the upper half of the ¿gure, only during a day in which the atmosphere was known to be more active, that is, 

high surface winds, cloud cover, and overcast. The results presented are for two steady-level passes of the F-104. 

Solid symbols represent no disturbances observed or measured. Also shown are sketches of the type of pressure 

signatures measured at the various recording stations. The most signi¿cant feature of these latter results are the 

shapes of the signatures. Note that a nominally shaped N-wave does not appear – rather the wave signatures are 

greatly distorted into peaked and rounded waveform shapes with accompanying wide ranges of overpressure. 

In fact, one of the signatures near the lateral cutoff has the appearance of a U-shape (double positive peaks) 

associated with focusing as observed for Mach cutoff (see ¿g. 5.7 of Chapter 5).

Statistical Variations

Peaking and rounding of sonic boom signatures is statistical in nature and occurs as a function of either time or 

distance. A summary of the variations of the on-track overpressures resulting from the atmosphere for steady 

level Àight is given in ¿gure 2.38 (ref. 2.38). This statistical analysis comprises most of the planned sonic boom 

experiments that have been conducted in the United States. Data are included for a wide range of aircraft, a Mach 

number range of 1.2 to 3.0, and an altitude range of about 10,000 to 80,000 feet. A total of 12,406 data samples 

have resulted from the 1,625 supersonic Àights. 

Figure 2.37. Effects of atmosphere on lateral boom signatures (ref. 2.9).
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

54

Plotted on ¿gure 2.38 is a cumulative frequency distribution and histogram for on-track measurements showing 

the probability of equaling or exceeding the ratio of the measured overpressure to the predicted overpressure 

for steady Àight in standard atmosphere with no winds. For this type of presentation, all the data would fall in a 

straight line if the logarithm of the data ¿t a normal distribution. Rounded signatures of the waveform sketched 

in the chart are usually associated with overpressure ratios less than 1.0. Nominal or N-wave signatures are 

observed on the average and peaked signatures of higher overpressures are observed usually at ratios greater 

than 1.0. 

The data indicate that variation in the sonic boom signatures, as a result of the effects of the atmosphere, can 

be expected during routine operations. For example, one boom in a thousand is expected to exceed the nominal 

value by a factor of about 3.0, at least for N-wave designed aircraft.

Effect of Mach Number

It has also been found that sonic boom variability is dependent upon Àight Mach number. Higher Mach numbers 

result in less variability of the N-waves. This is illustrated in ¿gure 2.39 (ref. 2.24), which shows the statistical 

variation observed in the sonic boom overpressures for an F-104 airplane Àying at a constant altitude of about 

30,000 feet at Mach numbers of 1.3 and 1.6 over an 8000-foot linear array of microphones and an illustration 

of the shock-ray patterns for both the low and high Mach number situation as they propagate to the ground. 

Note that for the lower Mach case, the ray path is longer and, thus, spends more time in the lower layers of the 

atmosphere as compared to the higher Mach case. As a result, as will be noted from the probability distributions 

that are shown on the left-hand side of the chart, the longer the dwell time in this layer of the atmosphere the 

greater the variability. As the variability increases, the chance of encountering large excursions and thus higher 

boom levels, on occasion, is increased.

Figure 2.38. 2QWUDFNVWDWLVWLFDOYDULDWLRQDGDSWHGIURPUHI
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

55

Effect of Lateral Distance

A comparison of the variability of the overpressures for a given set of Àight conditions for Àights of the ;B-70 

for locations on track and at a large distance from the Àight track are given in ¿gure 2.40 (ref. 2.15). Data for 

measurement locations about 13 miles off the Àight track (diamond symbols) are compared with those on the 

track (circle symbols) for Àights at an altitude of 60,000 feet and Mach numbers of 1.8 to 2.5.

Figure 2.39. (IIHFWRIDLUFUDIW0DFKQXPEHURQVRQLFERRPYDULDELOLW\)DWIW06/DGDSWHGIURPUHI

Figure 2.40. (IIHFWRIODWHUDOGLVWDQFHRQVRQLFERRPYDULDELOLW\;%DW0DFK±DWIHHWDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

56

In addition to the probability curves, histograms are also included. It can be seen that the probability distribution 

for the measurements obtained at distances out to 13 miles shows larger variability. This, of course, would be 

expected as a result of the longer ray paths traveled by the waves in the lower layers of the atmosphere before 

reaching the lateral measurement stations.

Rise Time Variability

The possibility that the rise times tend to increase with increasing Àight altitude is suggested by the data in 

¿gure 2.41 (ref. 2.39). The various data points are individual rise times (IJMax or IJ1/2) measured on-track when 

aircraft are Àying at a given altitude. Scatter of the data is a clear indication of the effects of turbulence and smallscale atmospheric phenomenon. If the trend indicated by the data is real, then one is confronted with an as yet 

unexplained inconsistency with the generally accepted notions that (1) the magnitude of the rise times is caused 

by atmospheric perturbations, and turbulence in particular (2) the bulk of such perturbations are within 3000 feet 

of the ground and (3) any accumulative creation of ¿nite rise times by higher-altitude variations should be negated 

by nonlinear steepening effects. It will be shown later in these discussions that the inÀuence of atmospheric 

absorption dominated by the molecular relaxation of O2

 and N2 can play a nontrivial role in signature rise time. As 

it stands, the data suggest that N-wave sonic boom signatures produced by aircraft Àying at an altitude of 50,000 

to 60,000 feet will realize about a 3–6 milliseconds rise time under most conditions.

It has been shown that signature variability increases with increasing lateral distance since these ray paths, which 

the shock travels along, spend more time in the lower layers of the atmosphere. Thus, one would expect that 

the signature shock rise time would also increase as lateral distance increases. The plots of the rise time relative 

probabilities shown in ¿gure 2.42 (ref. 2.39) are based on data taken for F-104 airplanes Àying in the altitude 

range of 28,000 feet to 32,000 feet at a Mach number of about 1.5 during the Oklahoma City tests (ref. 2.40) and 

are similar to other rise-time histograms. This particular ¿gure illustrates the general observation that larger rise 

times may be expected when the lateral distance from the ground track is increased. Once again, as was shown 

in the previous ¿gure, rise times, to the half and maximum amplitudes are presented for measurements made on 

the ground track and at lateral locations of 5 and 10 miles. Note that both the mean rise times and the relative 

probability of larger rise times increase as lateral distance is increased. 

Figure 2.41. 9DULDWLRQRIULVHWLPHZLWKDOWLWXGHRQWUDFNDGDSWHGIURPUHI
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

57

-RLQW$FRXVWLF3URSDJDWLRQ([SHULPHQW-$3(6RQLF%RRP([SHULPHQWV

In August 1991, a sonic boom propagation experiment was conducted at the White Sands Missile Range (WSMR), 

New Mexico, as part of the North Atlantic Treaty Organization (NATO) JAPE. The sonic boom propagation 

experiment was added to JAPE to take advantage of the extensive meteorological instrumentation gathered to 

perform the JAPE experiment (refs. 2.41 and 2.42).

The sonic boom propagation experiment consisted of Àying three types of aircraft supersonically over a groundbased microphone array with concurrent measurements of turbulence and other meteorological data. The test 

aircraft were a T-38, F-15, and F-111, and were Àown at speeds of Mach 1.2 and 1.3, and at an altitude of 30,000 

feet above a 16 element, linear microphone array with an inter-element spacing of 200 feet. In 2 weeks of testing, 

57 supersonic passes of the test aircraft were Àown from early morning to late afternoon.

Histograms of the percentage of occurrence of peak bow-shock overpressure and rise time for a T-38 and an F-15 

for low and moderate turbulence conditions are presented in ¿gure 2.43 and ¿gure 2.44, respectively (from ref. 

2.41). Typically, during the WSMR sonic boom experiment there was little cloud cover. Temperature inversions 

with light winds were the norm in the morning. By afternoon the desert Àoor had heated up, the morning inversion 

had been replaced with an increased lapse rate, and the winds had increased in speed. Thus, it is assumed that the 

morning time period was associated with low turbulence and the afternoon time period with moderate turbulence. 

The average (x) and median (M) overpressure, rise time values, standard deviation (σ) skewness (Į3), kurtosis 

(Į4), and the number of date points (n) for each histogram are listed in the histogram legends. Skewness is a 

measure of the degree of symmetry of a distribution and Kurtosis is a measure of the peakedness.

Figure 2.42. Variation of signature rise time with lateral distance (adapted from ref. 2.39).
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

58

(b) Low and moderate turbulence rise time distributions.

Figure 2.44. +LVWRJUDPVRIVRQLFERRPRYHUSUHVVXUHDQGVKRFNULVHWLPHIRU)DLUFUDIWREWDLQHGGXULQJ-$3(UHI

(a) Low and moderate turbulence bow-shock overpressure distributions.

(a) Low and moderate turbulence bow-shock overpressure distributions.

(b) Low and moderate turbulence rise time distributions

Figure 2.43. +LVWRJUDPVRIVRQLFERRPRYHUSUHVVXUHDQGVKRFNULVHIRU7DLUFUDIWREWDLQHGGXULQJ-$3(UHI
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

59

Examination of the results in both ¿gures show that the moderate turbulence overpressure and rise time 

distributions from both T-38 and F-15 Àights are more skewed and thus less peaked than for the low turbulence 

conditions. The bow shock overpressure distributions were skewed positively indicating large positive deviations. 

The majority of measured data indicated that the mean and standard deviation of the bow-shock overpressure 

distributions increased from the low turbulence condition to the moderate turbulence condition. As turbulence 

increased, the difference between the median and the mean increased indicating larger positive overpressure 

deviations. The effect on rise time is more readily seen in the rise time distributions. In general, the moderate 

turbulence rise time distribution mean values were larger by a factor of 4 from the low turbulence conditions and 

the standard deviations were larger by a factor of 3.

The authors noted that little of the extensive meteorological data collected were available for inclusion in these 

data. It should also be noted that the earlier Àight-test results regarding the statistical variations in sonic boom 

overpressure resulting from the atmosphere and shown in ¿gure 2.38 is presented in a different format than the 

JAPE ¿ndings.

Atmospheric Absorption

Absorption of sound by the atmosphere is a process consisting of thermo-viscous dissipation (classical absorption) 

and molecular relaxation that is dominant. Since 99 percent of the atmosphere is composed of nitrogen and 

oxygen, it is the relaxation of these molecules in the presence of water vapor that controls the atmospheric 

absorption of sound. In the absence of turbulence, the rise time of a perfect N-wave is determined by absorption. 

Figure 2.45(a) shows a typical variation of relative humidity with altitude and the ¿gure 2.45(b) variation of 

relaxation frequencies with altitude. Figure 2.45(c) illustrates two ¿ndings. The ¿rst is that the rise time increases 

with decreasing shock overpressure, reÀecting the diminished effect of non-linear steeping. The second is the 

dominance of molecular relaxation relative to classical absorption. 

Figure 2.45. 5ROHRIPROHFXODUUHOD[DWLRQDQGFODVVLFDODEVRUSWLRQRQVRQLFERRPULVHWLPH

(c) Contribution of classical absorption, O2, and N2

relaxation to rise time (ref. 2.45).

(d) Variation of shock rise time with shock

overpressure (ref. 2.43).

(a) Distribution of relative humidity in

atmosphere (ref. 2.43).

(b) O2 and N2 relaxation frequencies (50 percent

RH at ground) (ref. 2.44).
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

60

To validate the =EPH<RUS model, its output was compared to that of the ARAP (Hayes model) program (ref. 

2.47) that has been used for many years to predict sonic booms. ARAP does not include absorption but only 

models nonlinear effects. In order to compare =EPH<RUS with ARAP, the attenuation effects were turned off. 

The comparison, shown in ¿gure 2.46(a), indicates that the =EPH<RUS results agree quite well with ARAP. 

Figure 2.46(b) presents the results from =EPH<RUS propagating the same initial signature to the ground with full 

nonlinear and attenuation effects turned on for zero percent relative humidity at the ground. Note that the general 

N-wave shape is essentially unchanged but the attenuation produced rounding at the bow and tail shocks. Sonic 

booms measured on quiescent days in the desert area, where low humidity is common, do show this shock front 

rounding. In higher humidity areas, the measured signatures display less rounding. Figure 2.46(c) presented an 

interesting ¿nding regarding the dependence of rise time on initial signature shape. In ¿gure 2.45(c) it is noted that 

rise times depend on the magnitude of the shock and, as such, the remaining waveform is relatively unimportant. 

To investigate this, a Àattop initial waveform was selected (¿g. 2.46(c)) and propagated in =EPH<RUS for the 

zero percent humidity case. The amplitude of the initial waveform was reduced so that the bow shock amplitude 

of the waveform at the ground would be comparable to the results in ¿gure 2.46(b). Note that the rise time of the 

ground signature from the initial Àattop signature is at least 1.5 times that of the saw-tooth one shown in ¿gure 

2.46(b), thus, indicating that waveform shape does have a strong inÀuence on rise time.

In 1989, Pierce (ref. 2.45) showed that shock waves below about 0.4 lb/ft2

 would have rise times longer than what 

might be expected of stronger shocks and, hence, would be particularly quiet. This expectation was also suggested 

in the previous two ¿gures. The relaxation theory upon which this is based is suf¿ciently well established so as 

to be standardized (ref. 2.48) and has been successfully applied to sonic boom calculations (ref. 2.49). The results 

agree well with available sonic boom Àight-test data (ref. 2.50).

Note the strong inÀuence of O2 and N2 in increasing shock rise time as compared to classical absorption effects. 

In ¿gure 2.45(d), a comparison of the rise times of measured sonic boom signature overpressures to the steady 

state shock overpressure predicted by the molecular relaxation model is shown. Theory and measurements show 

increasing shock rise times with decreasing shock overpressures. Such rounded, or long rise time boom signatures, 

have been observed on some SR-71 (ref. 2.46) and Shuttle reentry Àights (refs. 2.28 and 2.29) where boom levels 

of 1.0 lb/ft2

 and less were experienced. 

The =EPH<RUS computer model (ref. 2.2) calculates sonic boom distortion during propagation through the 

atmosphere. Non-linear effects, attenuation, dispersion refraction, and wind are accounted for, but not distortion 

due to turbulence. Of particular interest is its ability to include the effects of absorption in the calculation of 

the boom signature. A brief overview of the program outputs is presented in ¿gure 2.46 (ref. 2.2). The initial 

waveforms represent those that would be calculated in the near ¿eld below the aircraft. All of the data are plotted 

to the same scale for comparison.

Figure 2.46. ,QÀXHQFHRIPROHFXODUUHOD[DWLRQDQGDWPRVSKHULFDEVRUSWLRQDQG LQLWLDOVLJQDWXUHVKDSHRQVKRFNULVHWLPHUHI.

(a) Attenuation effects off. (c) Attenuation effects on,

0 humidity.

(b) Attenuation effects on,

0 humidity.
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

61

Sonic boom signatures in available Àight-test data tend, however, to be in the 1 to 2 lbs/ft2 range. Boom signatures 

below 0.4 lb/ft2

 are rare and when generated by conventional aircraft tend to occur near lateral cutoff, where they 

are distorted by the effects of turbulence and ground interference.

In 2004, a series of sounding rocket tests (unrelated to sonic boom research) were conducted. Pre-Àight analysis 

indicated that low-amplitude N-wave booms would occur under the reentry Àight track. The opportunity was 

taken to acquire measurements of the sonic boom signatures to examine weak boom shocks structures after they 

had propagated through a real atmosphere (ref. 2.51). Several NASA Dryden Boom Amplitude and Shape Sensor 

(BASS) sonic boom recorders were deployed within the expected ground footprint and acquired an extraordinarily 

clean 0.2 lb/ft2

 N-wave that provided a shock structure used by Plotkin, Haering, and Murray (ref. 2.51) to 

quantitatively compare with relaxation theory. The results are presented in ¿gure 2.47 (ref. 2.51).

Figure 2.47(a) shows the measured 0.2 lb/ft2 N-wave. Note that the front and rear shock waves have the same 

shape and that the shape qualitatively appears similar to that of absorption on shocks presented in references 2.49 

and 2.50. Figure 2.47(b) shows a detailed comparison of the measured shock structure with a theoretical relaxation 

shock. This is the measured bow shock from the boom shown in ¿gure 2.47(a) with the time scale expanded and 

the computed shock overlaid. The agreement is excellent, con¿rming the expectation that relaxation shock theory 

applies to weak sonic booms in the real atmosphere.

Recently, Baudoin, Coulouvrat, and Thomas (refs. 2.52 and 2.53) noted that although atmospheric absorption 

may have a huge impact on the sonic boom annoyance by reducing the amplitude and increasing the rise time, 

the standard absorption due to the vibrational relaxation of molecular nitrogen and oxygen do not allow for an 

estimate of the inÀuence of clouds where scattering by water droplets occurs. They also pointed out that as clouds 

cover more than 50 percent of the earth¶s surface and that test Àights performed in the former Soviet Union in 

1967–1968 indicated a strong impact. The authors applied an existing model for acoustical propagation in a 

polydispersed air-vapor-droplet suspension by Gubaidullin and Nigmatulin (ref. 1 of ref. 2.52) to conditions 

prevailing in atmospheric clouds to determine the impact of clouds on reducing the amplitude and increasing the 

rise time of sonic boom signatures. Their results show a dramatic increase of sound attenuation and dispersion, 

as shown in ¿gure 2.48.

(a) Measured 0.2 lb/ft2 N-wave sonic boom. (b) Comparison of measured bow shock and rise 

time with computed bow-shock rise time.

Figure 2.47. ([DPSOHRIWKHLQÀXHQFHRIDWPRVSKHULFUHOD[DWLRQRQDORZDPSOLWXGHVRQLFERRPDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

62

The study considered the propagation of a 0.2 second duration N-wave of maximum overpressure of 50 Pascals 

(about 1 lb/ft2

) into a typical cumulus cloud 2000 m high and 2000 m deep and with a water liquid content of 

1 gram/cu meter and mean radius of 10 mm. The calculation is performed with all propagation mechanisms 

(dotted curve), nonlinear effects (dashed curve), and without evaporation and nonlinear effects (dashed dotted 

curve). Examination of the results of ¿gure 2.48 show that after propagating through the cloud layer, the pressure 

maximum is only 64 percent of its initial value and the rise time is increased up to 4.6 msec. The authors noted that 

their results are in accordance with some test Àights performed in the Soviet Union in 1967–1968 that observed a 

smoothing of the wave pro¿le and diminution of about 40 percent of the pressure maximum for similar conditions.

Secondary Booms

Secondary booms (see ¿gures 1.2 and 1.3 in Chapter 1) are an inescapable consequence of supersonic Àight. 

Each of the major sonic boom Àight programs sent secondary booms propagating through the upper atmosphere. 

The secondary booms went essentially unnoticed until the 1977 to 1978 time period, when the Naval Research 

Laboratory (NRL) investigated the East Coast acoustic disturbances (ref. 2.54), which were initially reported 

to be strange and mysterious in origin. The Concorde had entered into commercial service in mid-1976 and 

scienti¿c use was being made of its secondary boom, which was a consistent and known source for determining 

the characteristics of the upper atmosphere (refs. 2.55 and 2.56). Concorde secondary booms thus became more 

evident and complaints to this effect were received. However, in every case of Concorde-generated secondary 

sonic booms, rerouting of the Àight tracks and changes in operating conditions, depending upon atmospheric and 

seasonal variations, mitigated the problem. A more recent study that correlates seasonal and diurnal atmospheric 

Àuctuations of the upper atmosphere to variations in the arrival time, trace velocity, and arrival azimuth of the 

infrasonic signals from Concorde are given in reference 2.57.

The secondary sonic boom carpet and the disturbances experienced within this carpet are not as well de¿ned as 

for the primary sonic boom. Only fragmentary observations and measurements are available. These disturbances 

are known to involve both the upper and lower levels of the atmosphere during propagation, to have very low 

overpressure values, and to have a very low frequency content. Propagation distances greater than 100 miles 

are observed and relatively large ground areas are exposed, but the signi¿cance from a community response 

standpoint has not been established.

Secondary sonic booms, or so-called over-the-top boom disturbances (refs. 2.55, 2.56, and 2.58–2.61), are quite 

distinct from primary booms, not only in the manner in which they are propagated from the aircraft to the ground, 

but also in the way their signatures are shaped. The characteristics of these secondary sonic booms are illustrated 

in ¿gure 2.49 (ref. 2.61). An overall pressure time history from the Concorde secondary boom is shown in ¿gure 

2.49 and is seen to be complex in that numerous disturbances are observed (some 13 minutes or so after passage 

Figure 2.48. ,QÀXHQFHRIFORXGVRQVRQLFERRP1ZDYHDGDSWHGIURPUHI
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

63

of the aircraft) at this particular measurement location over a period of 1.5 minutes with a maximum peak-topeak pressure of about 0.2 lb/ft2

. Three sections of the overall pressure signature at A, B, and C are presented 

with expanded time scales on ¿gure 2.49(b) to ¿gure 2.49(d), to provide an indication of the frequency content of 

these signals. Note also that the fundamental frequency is about 1.5 to 2.0 Hz. For secondary boom signatures, 

the pressure changes very slowly and is in the sub-audible frequency range, and may or may not be heard.

An appreciation of the distinct differences between secondary and primary boom signatures may be obtained 

with the aid of ¿gure 2.50. At the top left of the ¿gure is shown the cruise carpet boom signature from Concorde 

(ref. 2.62) and to the right the resulting secondary boom signature (ref. 2.61). The two signatures are plotted to 

the same pressure and time scales. Note that the Concorde secondary boom signature is considerably different in 

character and lower in overpressure than the primary boom N-wave signature.

(a) Overall time pressure history. (b) Expanded pressure time history A.

(c) Expanded pressure time history B. (d) Expanded pressure time history C.

Figure 2.49. Characteristics of secondary sonic booms (adapted from ref. 2.61).

(a) Primary carpet boom. (b) Secondary carpet boom.

Figure 2.50. Comparison of primary and secondary sonic boom signatures and spectra for Concorde.
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

64

A further indication of the signi¿cant difference between the secondary and primary boom signatures may be 

obtained by comparing their frequency spectra as shown in the lower portion of ¿gure 2.50. Note that the primary 

N-wave boom spectrum (ref. 2.62) contains a considerable amount of energy out beyond 1000 Hz, whereas the 

secondary boom energy (ref. 2.61) is con¿ned to frequencies below about 50 Hz. As such, the secondary boom 

disturbances are in the sub-audible range and observed as mufÀed thumps and low frequency rumbles. As a result, 

secondary booms are dif¿cult to sense outdoors, but noticeable indoors, since buildings respond to these low 

frequencies that are near the natural frequency of vibration of the building structural components.

Currently, three computer programs are capable of secondary sonic boom propagation, TRAPS, =EPH<RUS, 

and PCBoom 6(ref. 2.64). TRAPS (ref. 2.63), added the capability of ray path reversal and secondary booms to 

the Hayes ARAP program (ref. 2.47). A more recent program, =EPH<RUS (ref. 2.2), includes air absorption and 

molecular relaxation effects on sonic boom propagation. The current version of PCBoom (ref. 2.64) computes 

boom signatures at an over-the-top caustic passage and at ground caustic intercepts and also includes absorption 

effects. 

The TRAPS ray tracing was used by Gardner and Rogers (ref. 2.58) to predict the secondary boom levels 

associated with Concorde Àights. The results of this research are presented in ¿gure 2.51 (ref. 2.58). Figure 2.51 

shows the predicted ground pressures for the initially upward and initially downward waves, as a function of 

distance from the ground track. The solid lines show the combined linear and nonlinear results, while the dashed 

lines show the result obtained using nonlinear theory alone. The latter can be considered to be an upper bound for 

the ground pressure. The dominant signal is from the initially downward wave. The highest pressure (about 0.008 

lb/ft2

) will occur about 200 nmi from the ground track. The pressure measured on the ground track is a minimum 

and will be about 0.003 lb/ft2

 for the initially downward wave. This is in contrast to the carpet boom, where the 

pressure is a maximum (about 2.0 lbs/ft2

) along the ground track and decreasing to zero at the lateral cutoff. The 

reason the secondary boom levels are at a minimum on the ground track is because the ray paths along which the 

shocks propagate are less steeply inclined at lateral locations as compared to on-track. Thus, on-track rays extend 

to much higher altitudes, travel longer ray paths, and are subject to more atmospheric attenuation resulting in 

lower pressure amplitudes. The sharp cutoffs, indicated by the vertical dashed lines at about 200 nmi, are due to 

shadow zone formation similar to the lateral cutoff overpressure of the primary carpet. 

Figure 2.51. Variation of secondary sonic boom levels with lateral distance (adapted from ref. 2.58).
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

65

It should be noted that the predicted secondary sonic boom levels are at least an order of magnitude less than those 

that have been observed (ref. 2.61). The difference may be in the dif¿culty of accurately determining atmosphere 

characteristics and wave front angles of propagation. The studies of Pichon et al. and Poling (refs. 2.57 and 2.65) 

respectively, illustrated the impact of weather and Àight conditions on secondary booms. The Blanc-Benon et 

al. (ref. 2.66) signature model was used to predict the amplitude and frequency of the secondary booms. They 

attribute the bursts to the arrivals of direct and indirect rays and the rumble noise to the presence of gravity waves 

or other ¿ne scale effects in the atmosphere. 

It has been shown that secondary booms, sometimes referred to as over-the-top booms, are associated with every 

supersonic Àight (ref. 2.58). The disturbances, which arrive at the ground some 10–15 minutes after passage 

of the aircraft, are known to involve both the upper and lower levels of the atmosphere during propagation. 

Propagation distances of over 100 miles are observed and relatively larger ground areas are exposed and the 

pressures are higher at lateral locations than on-track. Secondary sonic booms are quite distinct from primary 

booms not only in the manner in which they are propagated from the aircraft to the ground but also in the way 

their signatures are shaped. For secondary boom signatures, the pressure changes very slowly and its frequency 

content is in the sub-audible range, both about an order of magnitude lower than for the primary boom. This lack 

of audibility combined with the very low amplitudes makes secondary booms dif¿cult to sense outdoors, but they 

can be noticeable indoors. The secondary sonic boom carpet and the disturbances experienced within it are not as 

well de¿ned as those for the primary boom and only fragmentary observations and measurements are available.

Chapter 2 Summary Remarks

The atmosphere plays a signi¿cant role in establishing the characteristics of the primary sonic boom signature. 

Primary booms result from shocks that propagate through only that part of the atmosphere below the aircraft.

Pressure, temperature, and wind pro¿les can be classi¿ed as macro effects and are responsible for de¿ning the 

intensity, location, and lateral extent of the sonic boom ground footprint. Above Mach 1.5, these macro effects 

have a relatively small effect on boom intensity and signature shape.

Turbulence in the lower layer of the atmosphere has a signi¿cant inÀuence on altering N-wave boom signature 

shape. The peaking and rounding of the boom signatures can be expected during supersonic Àight operations. 

Higher overpressures are observed from peaked signatures and lower values from rounded signatures.

Current sonic boom prediction codes can account for non-standard atmosphere with winds and atmospheric 

absorption but cannot account for the inÀuence of turbulence in the lower layers of the atmosphere.

Aircraft shock waves that propagate through the atmosphere at altitudes higher than the aircraft are responsible 

for the secondary booms, also referred to as over-the-top booms. They are of low amplitude and frequency, 

and therefore dif¿cult to sense outdoors but are noticeable indoors. These disturbances extend well beyond the 

primary boom footprint. As a result, meteorological conditions play an important role in secondary boom long 

distance propagation. Existing prediction codes can de¿ne the ground footprint but underestimate the pressure 

levels.

Chapter 2 References

2.1 Kane, Edward J. and Palmer, Thomas <. Meteorological Aspects of the Sonic Boom. SRDS Report No. 

RD 64-160, FAA, ASTIA No. AD 610463, 1964.

2.2 Robinson, Leick D. A Numerical Model for Sonic Boom Propagation Through an Inhomogeneous, Windy 

Atmosphere. NASA CP-3172, Feb. 1992, pp. 7–30.
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

66

2.3 Coulouvrat, Francois Blumrich, Reinhard and Heimann, Deitrich Meteorologically Induced 

Variability of Sonic Boom of a Supersonic Aircraft in Cruising or Acceleration Phase ISNA 17 AIP Conf. 

Proceedings, Vol. 838, Melville, N< 2005, pp. 579–586.

2.4 Maglieri, D. J. Hilton, D. A. Huckel, V. Henderson, H. R. and McLeod, N. J. Measurements of Sonic 

Boom Signatures From Flights at Cutoff Mach Number. NASA SP-255, Oct. 1970, pp. 243–254.

2.5 Lundberg, W. R. Seasonal Sonic Boom Propagation Prediction. AL/OE-TR-1994-0132, March 1994.

2.6 Dressler, Robert and Fredholm, Nils Statistical Magni¿cations of Sonic Booms by the Atmosphere. FFA 

Rept. 104, Aeronau. Res. Inst. Sweden, 1966.

2.7 Lundberg, Bo K Dressler, Robert F. and Lagman, Sven Atmospheric Magni¿cation of Sonic booms in 

the Oklahoma Tests. FFA Rept. 112, Aeronau. Res. Inst. Sweden, June 1967.

2.8 Haglund, George T. and Kane, Edward J. Flight Test measurements and Analysis of Sonic Boom 

Phenomena Near Shock Wave Extremity. NASA CR-2167, Feb. 1973.

2.9 Maglieri, D. J. Hilton, D. A. and McLeod, N. J. Further Experiments on the Effects of Atmospheric 

Refractions and Aircraft Accelerations on Sonic Boom Ground Pressure Patterns, NASA TN-D 3520, July 1966.

2.10 Onyeowu, Ronald O. Diffraction of Sonic Boom Past the Nominal Edge of the Corridor. J. Acoust. Soc. 

Am., Vol. 58, No. 2, Aug. 1975.

2.11 Hubbard, H. H. Maglieri, D. J. and Huckel, V. Variability of Sonic Boom Signatures With Emphasis on 

the Extremities of the Ground Exposure Patterns. NASA SP-255, Oct. 9–30, 1970, pp. 351–359.

2.12 Pierce, Allan D. Atmospheric Propagation at Larger Lateral Distances From the Flight Track. NASA Conf. 

Pub. 3279, Oct. 1994.

2.13 Coulouvrat, Francois Sonic Boom in the Shadow =one A Geometrical Theory of Diffraction. J. Acoust. 

Soc. Am., Vol. III, No. 1, Pt. 2 of 2, Jan. 2002.

2.14 Walker, E. J. and Doak, P. E. Effects of Ground ReÀections on the Shape of Sonic Bangs. 5th Congres 

International D¶Acoustique, Liege, Sept. 7–14, 1965, paper L55.

2.15 Maglieri, D. J. Sonic Boom Flight Research - Some Effects of Airplane Operations and the Atmosphere 

on Sonic Boom Signature. NASA SP-147, 1967, pp. 25–48.

2.16 Maglieri, Domenic J. and Hubbard, Harvey H. Ground Measurements of the Shock-Wave Noise From 

Supersonic Bomber Airplanes in the Altitude Range from 30,000 to 50,000 Feet. NASA TN D-880, 1961.

2.17 Hubbard, Harvey H. Maglieri, Domenic J. Huckel, Vera and Hilton, David A. Ground Measurements of 

Sonic Boom Pressures for the Altitude Range of 10,000 to 75,000 Feet. NASA TR R-198, 1964.

2.18 Hilton, David A. Huckel, Vera Steiner, Roy and Maglieri, Domenic J. Sonic Boom Exposures During 

FAA Community Response Studies Over a Six-Month Period in the Oklahoma City Area. NASA TN 

D-2539, 1964.

2.19 Hilton, D. A. Huckel, Vera and Maglieri, D. J. Sonic Boom Measurements during Training Operations in 

the Chicago Area. NASA TN D-3655, 1966.

2.20 Plotkin, K. J. Haering, E. A., Jr. Murray, J. E. Maglieri, D. J. Salamone, J. Sullivan, B. M. and Schein, 

D. Ground Data Collection of Shaped Sonic Boom Experiment Aircraft Pressure Signatures. AIAA-2005-

0010, Jan. 2005.
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

67

2.21 Haering, E. Murray, J. Purifoy, D. Graham, D. H. Meredith, K. B. Ashburn, C. E. Stucky, M. Airborne 

Measurements of Shaped Sonic Boom Demonstration Aircraft Pressure Signatures with Comparison to 

CFD. AIAA-2005-0009, 2005.

2.22 Maglieri, D. J. Hilton, D. A. and McLeod, N. J. Summary of Variations of Sonic Boom Signatures 

Resulting from Atmospheric Effects. National Sonic Boom Evaluation Of¿ce Sonic Boom Experiments 

at Edwards Air Force Base. NSBEO-1-67 (Contract AF 49(638) 1758, Stanford Research Inst., July 28, 

1967, Part 1, Annex C, pp. C-1-1 to C-1-125.

2.23 Wetmore, Joseph W. and Reeder, John P. Aircraft Vortex Wakes in Relation to Terminal Operations. NASA 

TN D-1777, 1963.

2.24 Maglieri, Domenic Huckel, Vera Henderson, H. R. and McLeod, Norman, J. Variability in Sonic Boom 

Signatures Measured Along an 8000 Foot Linear Array. NASA TN-5040, 1969.

2.25 Garrick, I. E. and Maglieri, D. J. A Summary of Results on Sonic Boom Pressure Signature Variations 

Associated With Atmospheric Conditions. NASA TN D-4588, 1968.

2.26 Sherlock, R. H. Stout, M. B. Dow, W. G. Gault, J. S. and Swinton, R. S. Storm Loading and Strength 

of Wood Pole Lines and a Study of Wind gusts. Edison Elec. Inst., c. 1936.

2.27 Houbolt, John C. Steiner, Roy and Pratt, Kermit G. Dynamic Response of Airplanes to Atmospheric 

Turbulence Including Flight Data on Input and Response. NASA TR-R-199, 1964.

2.28 Maglieri, Domenic J. Henderson, Herbert R. Stansbery, Eugene G. and Massey, Steven J. A Compilation 

of Space Shuttle Sonic Boom Measurements. NASA CR 2011-217080, April 2011.

2.29 Garcia, Frank J. Jones, Jess H. and Henderson, Herbert H. Correlation of Predicted and Measured Sonic 

Characteristics from the Reentry of STS-1 Orbiter. NASA TP-2475, 1985.

2.30 Garinther, G. R. and Moreland, J. B. Transducer Techniques for Measuring the Effect of Small-Arms 

Noise on Hearing. U.S. Army Tech. Memo. 11-65, July 1965.

2.31 Hilton, D. A. and Newman, J. W., Jr. Instrumentation Techniques for Measurement of Sonic Boom 

Signatures. J. Acoust. Soc. Am. 39, S31-S35, 1966.

2.32 Lee, Robert A. Air Force Boom Event Analyzer Recorder (BEAR) Comparison With NASA Boom 

Measurement System. AAMRL-TR-88-039. July 1988.

2.33 Roberts, C. Johnson, W. Herbert, G. and Hass, W. A. Meteorological Investigations. National Sonic 

Boom Evaluation Of¿ce Sonic Boom Experiments at Edwards Air Force Base, NSBEO-1-67 (Contract 

AF 49 (638), 1758), Stanford Research Inst., July 28, 1967, Part 1, Annex D. DD-D-1 through D-11 (also 

A-10 and A-14).

2.34 Pawlowski, Joseph W. Graham, David H. Boccadoro, Charles H. Coen, Peter G. and Maglieri, Domenic 

J. Origins and Overview of a Shaped Sonic Boom Demonstration Program. AIAA 2005-0005, Jan. 2005.

2.35 Morgenstern, J. M. Arslan, A. Lyman, V. and Vadyak, J. F-5 Shaped Sonic Boom Demonstrator¶s 

Persistence of Boom Shaping Reduction Through Turbulence, AIAA-2005-0012, Jan. 2005.

2.36 Plotkin, Kenneth J. Maglieri, Domenic J. and Sullivan, Brenda M Measured Effects of Turbulence on the 

Loudness and Waveforms of Conventional and Shaped Minimized Sonic Booms. AIAA-2005-2949, May 

2005.
&KDSWHU,QÁXHQFHRIWKH$WPRVSKHUH

68

2.37 Plotkin, Kenneth J. Maglieri, Domenic J. and Sulllivan, Brenda M. Measured Effects of Turbulence 

on the Loudness of Sonic Booms. Proc. of 17th Int. Smp. on Non-Linear Acoustics, AM Inst. of Phys. 

Melville, N<, July 2005, pp. 627–630.

2.38 Maglieri, Domenic J. and Kenneth, J. Sonic Boom, Chapter 10 Aeroacoustics of Flight Vehicles, Theory 

and Practice. NASA RP 1258, Vol. 1 and WDRC TR 80-3052, Aug. 1991.

2.39 Pierce, Allan D. and Maglieri, Domenic J. Effects of Atmospheric Irregularities on Sonic Boom Propagation. 

J. Acoust. Soc. Am., Vol. 51, No. 2, (Part 3), 1972, pp. 702–721.

2.40 Maglieri, Domenic J. and Sothcott, Victor E. Summary of Sonic Boom Rise Times Observed During FAA 

Community Response Studies Over a 6-Month Period in the Oklahoma City Area. NASA CR-4277, April 

1990.

2.41 Willshire, W. L., Jr. and DeVilbiss, D. W. Preliminary Results from the White Sands Missile Range Sonic 

Boom Propagation Experiments. NASA CP-3172, Feb. 1992, pp. 137–150.

2.42 Willshire, William L., Jr. Garber, Donald P. and DeVilbiss, David W. Flight Test Measurements of the 

Effect of Turbulence on Sonic Boom Peak Overpressure and Rise Time. J. Acoust. Soc. Am., Vol. 92, Issue 

4, 1992, pp. 2329–2330.

2.43 Cleveland, Robin O. Hamilton, Mark F. and Blackstock, David T. Effect of Strati¿cation and Geometrical 

Spreading on Sonic Boom Rise Time. NASA CP-3279, Oct. 1994, pp. 19–38.

2.44 Robinson, Leick D. A Numerical Model for Sonic Boom Propagation through an Inhomogeneous, Windy 

Atmosphere. NASA CP-3172, Vol.1, Feb. 1992, pp. 7–30.

2.45 Pierce, Allan D. Weaker Sonic Booms May be Considerable More Quiet. J. Acoust. Soc. Am. 85, 1989,

p. 581.

2.46 Maglieri, Domenic J. Huckel, Vera and Henderson, Herbert R. Sonic Boom Measurements for SR-71 

Aircraft Operating at Mach Numbers to 3.0 and Altitudes to 24,384 Meters. NASA TN D-6923, 1971.

2.47 Hayes, Wallace D. Haefeli, Rudolph C. and Kulsrud, H. E. Sonic Boom Propagation in a Strati¿ed 

Atmosphere With Computer Program. NASA CR-1299, 1969.

2.48 Method for the Calculation of the Absorption of Sound by the Atmosphere. ANSI SI-26-1978, American 

National Standards Institute.

2.49 Chambers, James P. Cleveland, Robin O. Bass, Henry E. Blackstock, David T. and Hamilton, Mark 

F. Comparison of Computer Codes for the propagation of Sonic Booms Through Realistic Atmospheres 

Utilizing Actual Acoustic Signatures. NASA CP 3335, July 1996, pp. 151–175.

2.50 Kang, J. Nonlinear Acoustic Propagation of Shock Waves through the Atmosphere with Molecular 

Relaxation. PH.D. Thesis, The Pennsylvania State University, May 1991.

2.51 Plotkin, K. J. Haering, E. A. and Murray, J. E. Low-Amplitude Sonic Boom From a Descending Sounding 

Rocket. Proc. of 17th Inst. Symp. on Non-Linear Acoustics, AM. Inst. of Phys. Melville N<, July 2005, pp. 

615–618.

2.52 Baudoin, M. Coulouvrat, F. and Thomas, J. L. Absorption of Sonic Boom by Clouds. Proc. of 17th Int. 

Symp. on Non-Linear Acoustics, AM. Inst. of Phys. Melville N<, July 2005, pp. 619–622.

2.53 Baudoin, M. Coulouvrat, F. and Thomas, J. L. Sound, Infrasound, and Sonic Boom Absorption by 

Atmospheric Clouds. J. Acoust. Soc. Am. 130(3), Sept. 2011, pp. 1142–1153.
Chapter 2 ,QÁXHQFHRIWKH$WPRVSKHUH

69

2.54 Dept. of Navy NRL Investigations of East Coast Acoustics Events 2 December 1977 – 15 February 1978, 

March 10, 1978.

2.55 Balachandra, Nambath K. Donn, William L. and Rind, David H. Concorde Sonic Booms as an 

Atmospheric Probe. Sci., Vol. 197, No. 4298, July 1, 1977, pp. 47–49.

2.56 Donn, William L. Exploring the Atmosphere with Sonic Booms. Am. Sci., Vol. 66, No. 6, Nov.–Dec., 

1978, pp. 724–733.

2.57 Pichon, Alexis Le Garces, Milton Blanc, Elisabeth and Barthelemy, Maud Acoustic Propagation and 

Atmospheric Characteristics Derived From Infrasonic Waves Generated by the Concorde. J. Acoust. Soc. 

Am. 2002, pp. 629–641.

2.58 Gardner, John H. and Rogers, Peter H. Thermospheric Propagation of Sonic Booms From the Concorde 

Supersonic Transport. NRL Memo. Rept. 3904, U. S. Navy, Feb. 14, 1979 (Available from DTIC as AD 

A067 201).

2.59 George, A. R. and Kim, <. N. High-Altitude Long Range Sonic Boom Propagation. J. Aircraft, Vol. 16, 

No. 9, Sept. 1979, pp. 637–639.

2.60 Liszka, Ludwik Long-Distance Focusing of Concorde Sonic Boom. J. Acoust. Soc. Am., Vol. 64, No. 2, 

Aug. 1978, pp. 631–635.

2.61 Rickley, Edward J. and Pierce, Allan D. Detection and Assessment of Secondary Sonic Booms in New 

England. FAA-AEE-80- 22, May 1980.

2.62 Holbeche, T. Measurements of Sonic Bangs From the Prototype Concorde 002 During Supersonic 

Development of Flying in the United Kingdom. Royal Aircraft Establishment Tech. Memo. Aero. 1405, 

1972.

2.63 Taylor, A. D. The TRAPS Sonic Boom Program. NOAA Tech. Memo. ERL ARL-87, July 1980.

2.64 Page, J. A. Plotkin, K. J. and Wilmer, C. PCBoom Version 6.6 Technical Reference and User Manual.

Wyle Report WR 10-10, March 2010.

2.65 Poling, Hugh W. Impact of Weather and Flight Condition on Secondary Booms. NASA CP 3335, July 

1996, pp. 136–150.

2.66 Blanc-Benon, Phillipe Dallios, Laurent Scott, Julian Erger, UWE and Allwright, David Ray Theory 

Analysis and Modeling of the Secondary Boom Propagation for Realistic Atmospheric Conditions. ISNA 

17 AIP Conf. Proc., Vol. 838, Melville, N< 2006, pp. 187–192.

&KDSWHU,QÁXHQFHRI0DQHXYHUV

71

CHAPTER 3 INFLUENCE OF MANEUVERS

In this chapter, sonic booms associated with maneuvers of aircraft are discussed including dives, climbout 

pushovers, turns, and linear accelerations. Unlike the carpet booms associated with steady supersonic Àight 

that are dragged along behind the aircraft, maneuver booms are single occurrences, where multiple booms may 

be observed at the ground with boom intensities greater or less than the corresponding carpet boom. Military 

operations may, of course, include all of the above, whereas commercial operations would involve milder turn 

and pushover maneuvers. Both military and commercial Àights must transition from subsonic to supersonic 

speeds and descend and decelerate from supersonic to subsonic speeds. Questions regarding focus booms from 

maneuvering Àight include whether they can be avoided or minimized and controlled to the extent of the focus 

area and magnitude of the focused boom. Descent decelerations are not touched upon in this section since Àight 

planning can eliminate focusing at the ground either by decelerating to subsonic speed at constant altitude or 

scheduling Mach decrease and descent to preclude focusing. This chapter concludes with a discussion of sonic 

booms that can occur from aircraft Àying at relatively low altitudes and high subsonic Mach numbers and in a 

subsonic dive-pull-up maneuver.

Nature of Focus Patterns

Any rapid deviation of a vehicle from steady, level supersonic Àight conditions can produce considerable 

modi¿cations in the location, number, and intensity of the ground shock wave patterns. This maneuvering 

phenomenon is illustrated in ¿gure 3.1 (ref. 3.1), which shows the shock wave ground-intersection patterns for 

two Àight conditions of an aircraft. For simplicity, only the bow shock wave is shown.

At the left, the shock wave ground-intersection pattern for an aircraft in steady, level Àight is shown. The ray 

paths from the aircraft to the ground, represented by the angled lines, are generally parallel to each other and the 

bow shock wave ground-intersection pattern, as represented by the heavy shaded line, is essentially hyperbolic 

in shape. The pattern to the right is for an aircraft experiencing a level lateral acceleration. The ray paths are no 

longer parallel. In fact, in some regions they tend to converge and in others to diverge. Likewise, the shock wave 

ground intersection pattern is no longer hyperbolic and contains some irregularities, including a shock fold in 

which multiple booms would be observed and a cusp formation in which the pressures are higher than for steady 

Àight conditions. Such pressure increases are indicators of focused booms.

Figure 3.1. 1DWXUHRIUD\SDWKVKRFNZDYHJURXQGIRRWSULQWIURPVWHDG\DQGDFFHOHUDWHGÀLJKWUHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

72

Another example of boom focusing due to maneuvering Àight is presented in ¿gure 3.2 (ref. 3.2). Shown on the 

¿gure is a three-dimensional view of both the vertical cross section and the ground pattern for an aircraft in a dive 

of about 20° beginning at Mach 1.2 at 40,000 feet and terminating at about 20,000 feet and Mach 1.6. Only the 

bow shock is illustrated. The ground pattern is symmetric with respect to the Àight path so that only the part on 

the right side of the Àight track is shown. The bow shock that develops into a folded three-shock system in the 

vertical plane spreads laterally when intersecting the ground and extends about 6 miles and results in multiple 

booms over an appreciable ground area. As the aircraft proceeds along the low-altitude level portion of the Àight 

path, the complicated shock pattern produced by the dive hits the ground and vanishes. The ground shock is left 

with a fold that gradually unravels as the aircraft continues so that the end result is the normal hyperbolic-shaped 

ground shock. Everywhere there is a shock, a boom will be observed and wherever a folding of a shock front 

occurs would be a pressure enhancement (focus).

Once it became obvious that supersonic Àight would become commonplace, especially for military aircraft, 

some early cursory Àight experiments were conducted to assess the nature of booms associated with steady and 

maneuvering Àights. In 1959, Kerr (ref. 3.3), in addition to reporting on the booms from steady-level Àight, also 

reported on sonic booms associated with level Àight acceleration from Mach 0.98 to 1.2 at an altitude of 10,000 

feet, supersonic acceleration and deceleration, and a 2-g supersonic turn at Mach 1.5 at 40,000 feet. Hubbard et al. 

(ref. 3.4) reported on 63 supersonic Àights conducted at EAFB in 1961 with emphasis on the inÀuence of lift (i.e., 

aircraft weight) on boom levels. Twenty-three of the Àights dealt with maneuvers. Included were dives, turns, and 

linear accelerations. Increases in boom levels of about 2, 3, and 4 times the boom levels from steady Àight were 

observed for a linear acceleration, pull-up-push-over, and circular turn, respectively (refs. 3.1 and 3.5).

Military Operations

In the next series of ¿gures, boom signature overpressure observations will be shown for various types of maneuvers 

performed by military aircraft and include a dive, climb/pushover, turn and turn entry, and ¿nally longitudinal 

accelerated transition Àight from subsonic and supersonic speeds. Each of these non-steady Àights can result in 

non-uniform sonic boom ground patterns, which could include focus and non-focus regions where boom levels 

may be intensi¿ed or decreased respectively. Most of these military maneuvers are avoidable, especially in the 

case of commercial Àight operations with the exception of the transition focus boom.

Four air combat type maneuvers were studied and included a diving acceleration, a climbout-pushover, constant 

g turn, and a level linear acceleration. Some results of each of these four types of maneuvers will be presented 

in subsequent ¿gures. A major part of the results to be shown were acquired during the Have BEARS Àight-test 

program conducted by the USAF Test Pilot School in April 1994 (ref. 3.6). This study had three main objectives 

– (1) to test the ability of pilots to control the placement of the focus region, (2) to validate prediction methods, 

Figure 3.2. 6FKHPDWLFRIVKRFNZDYHDQGJURXQGSDWWHUQIRUDQDLUFUDIWLQDGLYHUHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

73

and (3) to evaluate the effects of atmospheric turbulence on focusing. An F-16B (similar to the airplane shown in 

¿g. 3.3) served as the test aircraft. 

Dives

For the diving accelerations, performed during the USAF Have BEARS Àight-test program, the F-16B aircraft 

attained stability at Mach 0.9 and an altitude of 20,000 feet. At the maneuver point, the pilot selected full afterburner, 

rolled inverted, and performed a 4-g pull-down to a 30° nose low attitude on the Àight path marker. No course 

corrections were provided after initiation of the maneuver. The maneuver was terminated as the aircraft reached 

Mach 1.2 or descended below an altitude of 13,000 feet. A pro¿le view sketch of the dive maneuver and the ontrack measured results are shown in ¿gure 3.4 (ref. 3.6). Examination of the signature development indicates that 

the focus boom location was somewhere in the region up-track from the target point (about -2000 feet) where 

the signature was observed with an overpressure of 6.0 lbs/ft2

. The maximum overpressure of 7.2 lbs/ft2 occurred 

at the target point, which was in the post-focus region as indicated by the N-wave U-wave signature. Within the 

focus region, the peak overpressure of 7.2 lbs/ft2

 was ampli¿ed over the average carpet boom overpressures of 

about 3.7 lbs/ft2

, which resulted in a focus factor of about 2.0 for the Àight data. 

Figure 3.3. General Dynamics F-16B Fighting Falcon.

86$LU)RUFHSKRWR

Figure 3.4. 0HDVXUHGVRQLFERRPVLJQDWXUHVIURPDLUFUDIWLQDDFFHOHUDWLQJGLYHDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

74

Climbout/Pushover

For the climbout/pushover maneuver performed during the USAF Have BEARS Àight-test program (ref. 3.6), 

the aircraft would start a 10° climb at Mach 1.2 and an altitude of 10,000 feet. At the pushover point, the pilot 

pushed the aircraft over to a load factor of -0.5 g to the level Àight attitude while maintaining constant Mach 

number. The maneuver was terminated as the aircraft reached the level Àight attitude. A pro¿le view sketch of the 

climb/pushover maneuver along the on-track booms measured from this Àight is shown in ¿gure 3.5 (ref. 3.6). 

The maximum peak overpressure was 11.6 lbs/ft2

 and occurred 2000 feet down-track of the predicted focus point 

(target point). This boom was ampli¿ed by a factor of 4 as compared to the average overpressures observed in 

the pre-and post-focus regions. For this Àight, a second signature was not observed in the post-focus region, only 

slight disturbances appeared to trail behind the N-wave.

Figure 3.5. 0HDVXUHGVRQLFERRPVLJQDWXUHVIURPDLUFUDIWLQJFOLPERXWSXVKRYHUDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

75

Figure 3.6 (ref. 3.5) shows a pro¿le and plan view of a constant Mach number pull-up/climb/pushover, which 

was also carried out by NASA and the USAF in the vicinity of Rogers Dry Lake at EAFB. The results presented 

in ¿gure 3.5 for the climbout/pushover maneuver present the boom signatures and focus development along the 

ground track of the aircraft. Focusing can also occur at locations lateral to each side of the ground track, as shown 

in ¿gure 3.6. The Àight path was essentially con¿ned to a vertical plane and had the approximate dimensions 

shown in ¿gure 3.6(a). Radar tracking and weather information were obtained, but ground pressure measurements 

were recorded by only one microphone, which was slightly off the Àight track, as indicated in ¿gure 3.5(b). 

Note that in this case the second signature to arrive had the highest overpressure by about a factor of 3.0. Theory 

predicted multiple booms and normal overpressures in the grayed elliptical region shown on the ¿gure and in a 

similar symmetrically situated region on the other side of the Àight track. The shock waves, which fell within 

these two areas, originated from the pushover and level-out portion of the maneuver.

(b) Plan view of maneuver.

Figure 3.6. 6RQLFERRPVLJQDWXUHVPHDVXUHGQHDUIRFXVUHJLRQIURPFOLPERXWSXVKRYHUPDQHXYHUUHI

(a) Pro¿le view of maneuver.

(c) Measured sonic boom pressure signature.
&KDSWHU,QÁXHQFHRI0DQHXYHUV

76

Turns

For the constant-g turn Àown during the USAF Have BEARS Àight program, a load factor of 4 g was chosen as a 

maximum sustainable load factor for the turn maneuver while trying to maintain Mach 1.2. Before the maneuver, 

as shown in the plan view sketch of the turn maneuver (¿g. 3.7), the aircraft was stabilized at Mach 1.2 and an 

altitude of 10,000 feet. At the start of the turn, the pilot selected full afterburner and initiated a 4-g level turn. The 

maneuver was terminated after a 50° turn.

The Àight path was aligned with the array so that the array would capture the focal line from the steady part of the 

turn and not the superfocus region generated by the initiation of the turn. The measured booms are shown in ¿gure 

3.7 (ref. 3.6). At the ¿rst part of the array, the measured booms were from the steady portion prior to the maneuver 

point. Focusing was measured within a band of 2500 feet about the target point with the maximum overpressure 

measured at 1500 feet from the target. This showed that the focal line was very narrow for this maneuver. The 

maximum overpressure was 8.7 lbs/ft2

. Post-focus signatures or disturbances appeared in both directions. The 

measured focus boom from the turn ampli¿ed the boom by a factor of about 2.5.

Figure 3.7. 0HDVXUHGVRQLFERRPVLJQDWXUHVIURPDLUFUDIWLQFRQVWDQWJWXUQDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

77

As shown in ¿gure 3.7, during a turn maneuver the measurements were in the vicinity of the focus line from the 

steady part of the turn and not near the superfocus generated by the initiation of the turn where two focus lines 

merge. The superfocus region on the ground was very small in area and challenging to capture. A superfocus 

recording was, however, successfully accomplished as part of the French Operation Jericho Carton Àight test (ref. 

3.7). At an altitude of 33,000 feet, a Mirage IV Àew a 2-g turn entry at Mach 1.7. Figure 3.8 shows the measured 

results and supporting focus analysis. 

In ¿gure 3.8(a), the predicted ground shock-interaction and shock folding of the turn entry is presented. At the 

tip of the shock folds, two focus lines develop – one due to the steady portion of the turn and the pseudo focus 

line due to the turn entry. Where those two focus lines join is known as the superfocus location. Also shown 

is the designed ground location of the 4.8 km linear array of 50 microphones with respect to the aircraft path. 

Figure 3.8(b) presents the sonic boom signature measurements. The three vertical lines are located 1 second 

apart. Examination of these signatures suggests that they were obtained between the two focus lines and very 

near the superfocus location. On microphone 18, the maximum value of the overpressure was obtained. From the 

Figure 3.8. 6XSHUIRFXVERRPIURPWXUQHQWU\PDQHXYHUDW0DFKDQGDWDQDOWLWXGHRIIWDGDSWHGIURPUHI

(a) Ground shock intersections. (b) Measured signatures.

(c) Computed focus location.
&KDSWHU,QÁXHQFHRI0DQHXYHUV

78

oscillograph trace of the signature from microphone 18, it can be seen that the ¿rst peak was higher and sharper 

than the second one. The intensity of the overpressure was about 15 lbs/ft2

, which gave a focus factor of about 

9.0. The existence of the two peaks on the bow shock, as opposed to one, indicated that the measurement was 

not at the exact superfocus location. This conclusion is con¿rmed by the signatures from microphones 15 and 19, 

where the existence of several shocks is shown. The conclusion is also con¿rmed by the post-analysis graph of 

this particular Àight given in ¿gure 3.8(c), which shows that the two focus lines cross the measurement line in its 

middle at about 1 or 2 km away from the superfocus. It is important to appreciate that the superfocus inÀuences 

a very small area on the ground on the order of a few hundred feet.

Transition Flight

Supersonic cruise Àight requires that the aircraft transition from subsonic to supersonic speeds and, as such, will 

always have associated with it a focus region. This transition (accelerated Àight) may occur at constant altitude 

or during a climb-acceleration pro¿le. In either case, focusing will always occur. Since all vehicles will generate 

the transition boom, which incidentally is usually the ¿rst boom to reach the ground, a brief review of the nature 

of its occurrence and signi¿cance in terms of boom level is in order.

Figure 3.9 (ref. 3.8) is intended to illustrate the nature of the transition focus boom. An aircraft in level Àight, 

from left to right, accelerates through Mach 1. A uniform atmosphere is modeled so that the rays are straight. As 

the aircraft accelerates, rays converge to focus. The distance to the focal point varies with the aircraft position, 

so the focus is a coalescing of rays on a line called a focus (caustic). Crossing rays away from the caustic 

are separate booms, but a focused boom condition exists where they converge along the caustic. A maximum 

focus boom occurs along the caustic and is of particular interest where it intersects the ground, while multiple 

signatures (at least two – an N-wave and a post-focus U-wave) occur at positions down track. The focus point on 

the ground is very small and is a one-time occurrence; that is, it is not dragged along with the vehicle as is the 

case for the carpet boom. 

While ¿gure 3.9 shows straight rays and a curved caustic, the wave behavior close to the caustic is very similar 

for cutoff caustics shown later in ¿gure 5.5. The governing equations of boom behavior at a focus and a key 

scaling law were developed by Guiraud (ref. 3.9). A key parameter in focus scaling is the curvature of the caustic. 

Another property of the caustic is that it forms an envelope (boundary) of the rays. It is clear from ¿gure 3.9 

that a transition focus caustic forms a boundary between the region where there is no boom and where the boom 

carpet begins.

Figure 3.9. 1DWXUHRIWUDQVLWLRQIRFXVERRPDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

79

The governing equation written by Guiraud (ref. 3.9) is the nonlinear Tricomi equation

 ijyy í (y / R + ijx ) ijxx 0 (3.1)

where ijis the perturbation velocity potential, x is a local coordinate along the caustic, y is a local coordinate 

normal to the caustic, and R is the relative radius of curvature between the caustic and the ray. This equation 

applies locally, within a diffraction layer along the caustic. The ijx

ijxx term is nonlinear, the same second order 

steepening quantity that is represented by Whitham¶s rule (ref. 3.10). The remaining linear terms are hyperbolic 

(supersonic) at positive y and elliptic (subsonic) at negative y, consistent with the caustic forming a boundary. 

There is a subsonic evanescent wave (shown in ¿g. 5.5) on the shadow side.

Guiraud developed a scaling law for a step function shock. Because there is only one length scale, R, involved, 

the scaling law is universal so that a single step shock result (experimental or numerical) can be applied to 

focusing of any single shock. Gill and Seebass (ref. 3.11) and Gill (ref. 3.12) developed a numeric solution for the 

peak factor in Guiraud¶s solution. This was exploited by Plotkin and Cantril (ref. 3.8) to incorporate focal zones 

in a prediction code that evolved into PCBoom (ref. 3.13). Plotkin and Cantril¶s analysis showed that Gill and 

Seebass¶s numeric peak focus result matched the N-wave Àight-test results of Operation Jericho (ref. 3.7) and the 

ballistic range experiments of Sanai et al. (ref. 3.14). 

For N-wave booms, it is common to refer to a focus factor as being the ratio between shock amplitude at the focus 

and shock amplitude for an equivalent carpet boom. This is typically in the range of 2.5 to 5 (refs. 3.7 and 3.15). 

This focus factor should not be confused with the universal peak factor required by Guiraud¶s similitude. 

On-Track

While ¿gure 3.9 shows the transition focus from the perspective of sonic boom rays and is oriented on the caustic, 

¿gure 3.10 shows the transition focus from the perspective of wavefronts and is oriented to the perspective of 

observers on the ground. In the upper portion of the ¿gure is a sketch showing the development of the on-track prefocus, focus, and post-focus carpet boom regions associated with an accelerated Àight of an aircraft transitioning 

from subsonic to supersonic speed. The aircraft is Àying from left to right. Also shown is the development of the 

bow shock and focus caustic line and their intersection with the ground as the aircraft accelerates from Mach 0.9 

to 1.5. The sonic boom pressure signatures that would be observed at various positions along the ground within 

the pre-focus, focus, post-focus, and carpet regions are also shown.

Figure 3.10. 0HDVXUHGERRPRYHUSUHVVXUHVDORQJJURXQGWUDFNIRUDLUFUDIWLQWUDQVLWLRQÀLJKW

0DFKWRDWIHHWDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

80

In the pre-focus region, ahead of the focus caustic line, the nature of the pressure disturbances are low frequency 

noise signatures such as rumbles that increase in amplitude as the focus is approached. Within the focus region, 

which may be on the order of 100 – 200m in width, an observer would experience the intense U-shaped focus 

signature as a loud bang-bang. In the post-focus region that follows the focus, anywhere from 3 to 4 shocks may 

be experienced at intensities less than at the focus and an observer would hear a bang-bang pop-pop. The time 

between these two events increases as the carpet boom region is approached. Once the carpet boom region is 

entered, the U-wave disappears due to atmospheric refraction and an observer experiences only the lower level 

bang-bang of the carpet N-wave.

In the lower portion of ¿gure 3.10 (ref. 3.15) is shown the results of sonic boom ground-pressure measurements 

along the ground track for three longitudinal aircraft accelerations from Mach number Mach 0.9 to about Mach 

1.5 at a constant altitude of 37,000 feet with an array of microphones extending about 23 miles. The data at the 0 

on the abscissa of ¿gure 3.10 represent the so-called focus boom conditions where pressure ampli¿cations occur. 

The data for the three separate Àights were normalized by plotting the highest measured ground overpressure, ǻpo

, 

at this zero position. The direction of the aircraft is from left to right, as indicated by the sketches at the top along 

with corresponding tracings of measured signatures. The data points represent peak overpressures as de¿ned in 

the sketch. The low value points to the left are observed as rumbles. The high points near the center correspond to 

measurements that are very close to the focus point and thus represent what are conventionally described as focus 

booms. To the right of the focus point are two distinct sets of signals that relate to the region of multiple booms. 

For convenience in illustrating the trends of the data, solid and dashed lines are faired through the data points. The 

data points that cluster about the solid curve relate to the bow shock overpressure of the ¿rst signature to arrive, 

in all cases, and this eventually develops into the steady-state signature of the carpet boom. The data points that 

cluster about the dashed curve relate, in all cases, to the bow shock overpressure of the second signature to arrive. 

These values generally decrease as distance increases and eventually this second signature ceases to exist due to 

atmospheric refraction.

The highest overpressures are measured in an extremely localized region. These values are as high as 2.5 times 

the maximum value observed in the multiple-boom region. The main multiple-boom overpressure values are of 

the same order of magnitude as those predicted for comparable steady-state Àight conditions.

The locations of the focus boom and multiple-boom regions are readily predictable provided such information as 

Àight path, altitude, and acceleration rate of the aircraft is available. Based on this experience, it was believed at 

the time that the focus boom could be placed at a position on the ground to within about 5.0 miles of the desired 

location and would be improved if more detailed weather information was available.

During the USAF Test Pilot School 1994 Controlled Focus Boom (ref. 3.16) Project (also called Have BEARS in 

ref. 3.6), a set of transition Àights were performed both under radar guidance and autonomously using on-board 

guidance capabilities within an F-16B aircraft for placement of the focus boom at a ground target.

Figure 3.11 (ref. 3.6) presents a comparison of the predicted and measured signatures along the ground track of 

an F-16 aircraft during transition Àight from Mach 0.9 to 1.2 at a constant altitude of 10,000 feet and under calm 

atmospheric conditions. The predicted signatures shown on the left hand side of the chart were computed from 

PCBoom3 (ref. 3.13) using the aircraft acceleration pro¿le and rawinsonde weather information near the time of 

Àight. Corresponding measured signatures are shown on the right hand side of the ¿gure. The boom signatures 

are aligned in relative time to the leading shock. It will be noted that the ¿rst boom recorded, ¿gure 3.11(b), was 

500 feet up-track of the target point and had a peak overpressure of 10.8 lbs/ft2

. However, the maximum peak 

overpressure of 19 lbs/ft2

 occurred at the target point. Note also the increased separation between the N-wave 

and U-waves with distance from the focus region. In this post-focus region, the N-wave signature boom levels 

(about 6.0 lbs/ft2

) are settling down to the carpet boom values associated with steady Àight at a higher Mach 

number while the U-wave signatures continue to decrease in boom level until they disappear due to atmospheric 

refraction. For this particular Àight, an ampli¿cation (focus factor) of about 3.0 was observed. Good agreement 

existed between the predicted and measured signatures, and boom placement on the target was excellent.
&KDSWHU,QÁXHQFHRI0DQHXYHUV

81

The results presented in ¿gure 3.11 from the USAF Have BEARS Àight-test program (ref. 3.6) have shown that 

this transition focus region can be placed to within plus or minus 1000 feet of the desired location if the vehicle 

performance and atmospheric conditions are known. It would be expected that for maximum focusing to take 

place, the atmosphere must be stable. Atmospheric turbulence, which is random in nature, would tend to upset 

this required in-phase condition and, thus, act to reduce the chances for maximum focusing or even eliminate it in 

some cases (refs. 3.6 and 3.15).

The predicted focus boom region during transition Àight of the SR-71 from Mach 0.9 to about Mach 1.2 at an 

altitude of 30,000 feet in a standard atmosphere is presented in ¿gure 3.12 (ref. 3.17).

Figure 3.11. &RPSDULVRQRIRQWUDFNSUHGLFWHGDQGPHDVXUHGVRQLFERRPVLJQDWXUHVGXULQJWUDQVLWLRQÀLJKWOHYHODFFHOHUDWLRQRI)IURP0DFKWR0DFKDWIWDGDSWHGIURPUHI

(a) Predicted signatures. (b) Measured signatures.
&KDSWHU,QÁXHQFHRI0DQHXYHUV

82

A plan view of the focus region for the aircraft moving from left to right is depicted in the upper right portion of 

the chart. The lower part of the ¿gure shows a pro¿le of the N-wave bow shock overpressures along the airplane 

ground track. It can be seen that the highest overpressures, about 9.0 lbs/ft2

 occur along the focus boom line and 

decrease rapidly as distance along the ground track increases. The nominal, or carpet boom, beyond the focus and 

multiple boom regions and along the ground track is shown to be 2.5 lbs/ft2

. This results in a focus factor along 

the ground track of about 3.5. Other Àight-test measurements suggested that the focus factor can vary from 2.5 to 

5.0. It was also shown that the focus line extended laterally out to the cutoff.

A unique set of Àight experiments regarding focus booms associated with transition Àight at low altitude were 

conducted at Istres, France in 1967 (ref. 3.18). A Mirage IIIB (¿g. 3.13) served as the Àight-test ¿ghter aircraft 

and was Àown at an altitude of 2000 feet (610 m) to minimize the inÀuence of the atmosphere, accelerating from 

Mach 0.97 – 1.06 over a 3 km array of 28 ground microphones spaced some 100 m apart. Results from one of 

the transition Àights are shown in ¿gure 3.14. Bow-shock overpressures are plotted for each of the measured 

signatures, along with 5 measured signatures representing the pre-focus (microphones 3 and 6), focus (microphone 

9), and post-focus (microphones 12 and 15) regions. There are three observations of signi¿cance that deserve 

discussion. First, a maximum overpressure of 28 mbars (about 58 lbs/ft2

) was observed at the focus (microphone 

9). The average overpressure associated with the post-focus region (microphones 12 through 27) is about 5.5 

mbars (about 11.5 lbs/ft2

). This results in a focus factor, on the bow shock, of about 5.0. The second observation 

is that the maximum overpressure is quite localized, drops off to half amplitude during the next 100 m, and 

becomes equal to the carpet boom within the next 300 m. Also, the signatures measured at the focus (microphone 

9) show that the area (impulse) under the positive phase of the signature is much less than that associated with 

an equivalent N-wave of equal amplitude and period. The third observation is the character of the measured 

Figure 3.12. 3UHGLFWHGIRFXVERRPUHJLRQGXULQJ65WUDQVLWLRQÀLJKWGLVWDQFHDORQJ

JURXQGWUDFNPLDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

83

signatures in the pre-focus region as illustrated in the traces from microphones 3 and 6. These types of signatures 

have been observed on airfoils in wind tunnels and aircraft in Àight, wherein the free-stream Àow is at very high 

subsonic Mach number (see, for example, ¿g. 25 of ref. 3.19) but the Àow about the aircraft in some locations 

may be supersonic. Although the bow shock overpressure is 5.6 mbars, as the Àow accelerates about the aircraft, 

the tail shock amplitude increases to about 21 mbars (44 lbs/ft2

).

Figure 3.14. /RZDOWLWXGHWUDQVLWLRQIRFXVERRPPHDVXUHPHQWVDGDSWHGIURPUHI

Figure 3.13. Dassault-Breguet Mirage III.

86$LU)RUFHSKRWR
&KDSWHU,QÁXHQFHRI0DQHXYHUV

84

The cut-off Mach number, where the aircraft speed over the ground is less than the speed of sound at the ground, 

associated with the Mirage IIIB Àights for a standard atmosphere is about 1.02. The focus boom will be associated 

with the transition region from about Mach 0.95 to Mach 1.04. As altitude increases, Mach cutoff also increases 

(Mco at 30,000 ft is about 1.12, while at the tropopause (an altitude of about 36,000 feet) and above Mach cutoff is 

about 1.16). Such subsonic-transonic signatures are usually refracted before reaching the ground.

Lateral Locations

Measurements designed to gain insight into the overpressures and focus factor associated with the laterally 

extended focus line for transition Àight have also been conducted. Figure 3.15 (ref. 3.7) presents this set of 

measurements that were conducted in the 1967 time period in France. To the left of the ¿gure is a schematic 

of the test setup showing the focus region and a set of lateral measurement locations (indicated by the dashed 

lines) where measurements were taken. This lateral displacement was accomplished by offsetting the aircraft 

Àight track from the linear microphone array. The measured results are presented at the right of the ¿gure. Focus 

overpressures are shown as a function of lateral distance from the Àight track. The circles representing each 

measurement include the accelerations associated with each Àight. In an attempt to reduce the data scatter, the 

overpressure ǻp, is shown as the ratio of ǻp/(M2

-1)1/8, where M is the Mach number corresponding to the shock 

wave focusing on the measurement line.

Examination of the results show that the focus overpressures decrease as lateral distance increases and occurs in 

the same fashion as for steady-level Àight. This may suggest that the focus factor remains constant with lateral 

distance out to cutoff. These are the only known published results of this nature and more research is required 

regarding the lateral focus factor. It is expected that the caustic curvature, rather than the distance and acceleration, 

plays a key role in scaling.

Modeling Focus Boom Footprint

Since these experimental data were obtained, considerable progress has been made relative to the state-of-the-art 

of sonic boom modeling (see ref. 3.20). All of the sonic boom models provide signatures at the ground. For many 

applications, the user needs a full footprint of some overall quantity, typically the maximum overpressure on the 

ground. Figure 3.16 (ref. 3.20) shows a schematic footprint (contour chart of peak overpressure) for a focal zone 

corresponding to a transition acceleration maneuver performed in level Àight at a ¿xed acceleration rate.

(a) Plan view of focus region. (b) Measured focus overpressures.

Figure 3.15. Measurements of focus booms at various lateral distances from ground track, rectiOLQHDUÀLJKWRI0LUDJH,9DWIHHWDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

85

At one time, due to computer capabilities, creating a footprint like that shown in ¿gure 3.16 was a signi¿cant 

undertaking. Using the early version of PCBoom3 (ref. 3.16) in the mid-1980s, such a footprint took several 

days to generate. Calculating the boom at enough points on the ground would take one or two (sometimes three) 

overnight computer runs. Runs were pieced together manually and contours were then drawn using a customwritten plotting program. Today, the computations for a footprint, as shown in ¿gure 3.16, take only a few 

seconds from start to ¿nish. 

,QÀXHQFHRI6LJQDWXUH6KDSH

While PCBoom¶s mid-1970s application of the Gill-Seebass shock solution was quite successful for N-wave 

booms, it carried the assumption that each shock was an independent entity and behaved as an isolated step. A 

major advance occurred 25 years later, when Auger and Coulouvrat (ref. 3.21) and Marchiano and Coulouvrat 

(ref. 3.22) obtained a new numeric signature length. An iterative pseudospectral algorithm was used to solve for 

the full boom signature throughout the diffraction zone in the vicinity of the caustic. Their solution showed that 

signature shape, and the interaction between multiple shocks, can have a signi¿cant effect on the focus factor. 

Two cases are presented in ¿gure 3.17 (ref. 3.21) for transition Àight in a standard atmosphere and at a constant 

altitude of about 12 km and an acceleration rate of 0.6 m/sec2

, one assuming the incoming signature to be an 

N-wave (¿g. 3.17(a)) and the other a multi-shock signature of Concorde at the same altitude (¿g. 3.17(b)). For 

the N-wave case, predicted sonic boom pressure time histories are shown for four distances from the caustic. 

The distance is indicated as nondimensional z z/į, where z is distance above the caustic and į is the diffraction 

thickness of the focal zone. The locations include the evanescent shadow zone region (z - 0.5), at the focus 

(z 0), at the edge of the diffraction zone where the N and U-waves are just separate (z 1.0), and outside the 

diffraction zone where the N and U-waves have separated (z 1.5). It can be seen that at the focus location (z = 

0), the maximum bow and tail shock overpressures are about 4.5 times the amplitude of the incoming N-wave 

signature bow and tail shocks. 

Figure 3.16. Transition focus boom footprint showing overpressure contours in the focal zone 

DORQJWKHJURXQGWUDFNDQGODWHUDOO\QRWWRVFDOHUHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

86

In the case of the three-shock Concorde incoming signature (¿g. 3.17(b), the maximum bow shock overpressure 

at z = z( pa

max) is only about twice that of the incoming bow shock pressure. However, it is important to point out 

that the ampli¿cation of the tail shock for the Concorde case is about four times that of the incoming bow shock.

Since it has been shown that boom signature shape can inÀuence transition focus boom levels, the question 

arose as to whether future aircraft designed to exhibit low-boom shaped signatures during cruise Àight would 

also result in lower focus levels during transition from subsonic to supersonic Mach numbers. In order to answer 

this question, a numerical code was developed by Kandil and =heng (ref. 3.23, Appendix 4 3Development and 

Application of a Sonic Boom Focusing Computer Code ́) that would replicate the Auger-Coulouvrat (ref. 3.21) 

results so that one could examine the inÀuence of several shaped boom signatures on transition focus booms.

Computational runs, computed with the full nonlinear Tricomi equation, were made for the case of an incoming 

N-wave and on an incoming three-shock saw-tooth representing a Concorde signature during transition Àight and 

for the same operating conditions as assumed in ¿gure 3.17. The results are presented in ¿gure 3.18 for similar 

shadow zone, caustic, and above caustic locations (z values). Comparison of the predicted focus signatures at the 

Figure 3.17. ,QÀXHQFHRILQFRPLQJVRQLFERRPVLJQDWXUHRQIRFXVERRPGXULQJWUDQVLWLRQÀLJKWUHI

(a) N-wave incoming signature.

(b) Concorde incoming signature.
&KDSWHU,QÁXHQFHRI0DQHXYHUV

87

z position where maximum amplitude occurs, ¿gure 3.17 for z = z ( pa

max) for the Auger-Coulouvrat and ¿gure 

3.18 at z = max for the Kandil code, indicate that the Kandil code does indeed replicate the Auger-Coulouvrat 

results.

Next, the Kandil-=heng numerical code was used to predict the signatures in the vicinity of the transition focus 

boom for four low-boom shaped cruise signatures that included the asymmetrical and symmetrical Àat-top and 

initial shock ramp type. A summary of the focus factors for both the bow and tail shocks for all six incoming 

signatures that were examined is provided in ¿gure 3.19 (ref. 3.23). 

Figure 3.18. 3UHGLFWHGVLJQDWXUHVIRUOHYHOWUDQVLWLRQÀLJKWXVLQJ.DQGLOQXPHULFDOFRGHUHI

(b) Concorde three-shock saw-tooth incoming signature.

(a) N-wave incoming signature.
&KDSWHU,QÁXHQFHRI0DQHXYHUV

88

It can be seen from the ¿gure that the lowest focus factors of the bow shock are associated with the Concorde 

type multi-shock and asymmetric and symmetric initial shock ramp signatures. Note also that the tail shock focus 

factors are greater than the bow shock focus factors for all six incoming signatures with a maximum of about 

5.6 for the symmetric Àat-top incoming signature. In the post focus region all six of the incoming signatures 

considered show that the reÀected waveforms are still U shaped. Although not included in reference 3.23, the 

predicted focus signature for an incoming symmetrical ramp signature of 0.5 lb/ft2

 overpressure, 150 msec period, 

and 30 msec rise times the refracted waveform is also U shaped.

Design Cruise and Incoming Transition Signatures

The next question that arose concerned the relationship, if any, that a shaped signature designed for cruise Àight 

may have with its incoming signature during the transition phase of operation. Bobbitt and Massey (ref. 3.23, 

Appendix 1) provide a simple method for calculating the lift distribution that allows the effective area distribution, 

due to volume at the design Mach number, to be rapidly evaluated. This code permits calculation of the equivalent 

volume at other Mach numbers using the design Mach number volume distribution plus the lift distribution 

methodology. Effective area distributions and F-functions were presented for Mach numbers from 1.8, or 2.0 

down to 1.2 for both asymmetrical Àattop and initial shock ramp type pressure signatures. Mach 1.0 cuts (actual 

geometry) of the area distributions for these two types of signatures are also given. Some results are presented in 

¿gure 3.20.

The design F-function (F) and effective area (Ae

) for an asymmetric Àat-top and initial-shock ramp con¿guration 

at Mach 2.0 along with the same quantities calculated for Mach 1.4 are shown in ¿gure 3.20. It can be seen that 

the F-functions for both Mach 2.0 and Mach 1.4 vary in amplitude as expected but are quite similar in shape. 

Although the effective area distributions at Mach 1.4 show Àuctuations in the aft portions of the Àat-top and ramp 

F-functions, when compared to the Mach 2.0 cruise case they are surprisingly similar. In reference 3.23, it was 

concluded that shaped cruise signatures may be viewed as the incoming signature for the transition Àight case.

Figure 3.19. ,QÀXHQFHRILQFRPLQJVRQLFERRPVLJQDWXUHVKDSHRQIRFXVIDFWRUIRUOLQHDU

acceleration at constant altitude of 12 km at 0.6 m/sec2UHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

89

In an attempt to gain some early insight into the design cruise and incoming transition signatures, the Shaped 

Sonic Boom Demonstrator (ref. 3.24), which generates a nominal Àat-top boom at its design condition, appeared 

to provide an opportunity to measure focusing of a non-N-wave signature. Accordingly, plans were made to 

incorporate a focus condition Àight in the January 2004 SSBE Flight Test Program (ref. 3.25).

There are four types of maneuvers that will generate focal zones and include – (1) Àight near sonic cutoff, (2) 

linear acceleration, (3) turn, and (4) pushover-dive. SSBD¶s shaped minimal boom design point is Mach 1.4 at 

an altitude of 32,000 feet. That eliminated maneuver type (1) as a possibility, since SSBD¶s low amplitude sonic 

boom would end up an N-wave. Maneuver type (2) was not possible because the aircraft¶s acceleration capability 

around Mach 1.4 is limited. That left maneuver types (3) and (4), so PCBoom4 (ref. 3.26) was exercised for turn 

and pushover-dive maneuvers beginning from steady-level Àight at the design condition. It was found that a level 

turn could generate a focus, but would involve bank angles in excess of 40°. The g-load would be within the load 

limits of the aircraft, but the increased induced drag would reduce the aircraft¶s Mach number to less than 1.4.

The pushover-dive focus was examined. It was found that a pushover rate of one degree per second would 

(a) Asymmetric Àat-top con¿guration.

(b) Asymmetric initial-shock ramp con¿guration.

 Figure 3.20. &RPSDULVRQRI)IXQFWLRQVDQGHTXLYDOHQWDUHDGLVWULEXWLRQVIRUWZRFRQ¿JXUDWLRQV

DW0DFKDQG0DFKUHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

90

generate a focus at the ground as the aircraft passed through a Àight path angle of minus one to two degrees. The 

results from Àight 27 are presented in ¿gure 3.21 (from ref. 3.27). 

Figure 3.21(a) illustrates the ground-based microphone array used for the Àight test. The primary linear array is 

12,500 feet long, with sensors located 500 feet apart. The intent was to place the geometric focus at the center of 

the array, near sensor M. Figure 3.21(b) shows the measured boom signatures along the microphone array for the 

pushover event. The plots are in the general format used in reference 3.6. They have been shifted in time so as to 

align the ¿rst shock at each sensor.

Results from Flight 27 indicate that the maximum focus occurs at the E sensor location. The SSBD¶s shaped bow 

shock is not apparent on the boom signatures at the scale of ¿gure 3.21(b) but can be seen in ¿gure 3.21(c) where 

the initial carpet wave from sensor C is plotted at an expanded time scale. The post-focus carpet boom signature 

measured at sensor O, shown at an expanded time scale in ¿gure 3.21(c), which was expected to be a shaped boom, 

is actually an N-wave. Recall that the aircraft was unloaded to 0.25 g until it passed the end of the microphone array. 

(a) Linear array of ground-based microphones.

(c) Recorded boom signature at sensor C. (d) Recorded boom signature at sensor O.

Figure 3.21. 6RQLFERRPVLJQDWXUHVDVVRFLDWHGZLWK66%'SXVKRYHUPDQHXYHU)OLJKWDGDSWHGIURPUHI

(b) Measured boom signatures along microphone array.
&KDSWHU,QÁXHQFHRI0DQHXYHUV

91

The carpet boom is thus from a Àight condition where the lift load is one quarter that corresponds to the minimal 

boom design condition for SSBD. With that light a load (and correspondingly lower coef¿cient of lift) the shaping 

geometry that produced the Àat-top bow shock was lost. 

The focusing maneuver was successful, and it showed, as expected, that this pushover focusing maneuver was at 

a Àight condition that does not yield the design low-boom cruise condition. That lesson is a useful result. Auger 

and Coulouvrat (ref. 3.21) showed that a lower focus factor is realized for the Concorde three-shock signature 

than that of a simple N-wave with only bow and tail shocks. They suggested that a deliberately complex signature 

could provide relief from focus superbooms. The result of this Àight test shows that focus conditions are well 

removed from the shaped minimal boom design point. While the off-design signature for the SSBD was a simple 

N-wave, the possibility of developing a suitable complex boom in the low Mach number transonic acceleration 

region of an operational low-boom supersonic aircraft may be realized. It is of interest to note, however, that 

Bobbitt and Massey (see Appendix 1 of reference 3.23) show that for transition Àight from subsonic to supersonic 

speeds, the off-design signature is similar to that of design cruise Mach numbers as low as 1.2. However, the 

likelihood of realizing similar equivalent area distributions and F-functions of the transition phase of Àight to the 

cruise design condition is yet to be determined.

Dedicated Flight Transition Experiments

Since acceleration to supersonic speed is an unavoidable maneuver for supersonic Àight, the focus boom ground 

footprint associated with this transitioning has always been a serious obstacle to overland operations. It has been 

shown that the booms from transition Àight can result in signi¿cant boom amplitude enhancements in the focal 

zones and that the potential exists for complex multi-signature patterns. Several transition focus boom Àight tests 

have been conducted over the years aimed at de¿ning the nature of this particular maneuver in order to seek ways 

to minimize its impact. A compilation of these nine Àight tests (refs. 3.3, 3.4, 3.15, 3.16, 3.18, and 3.28 – 3.32) 

is presented in table 3.1, beginning with the earliest Àight test, conducted in England in 1959, to the most recent 

Àight test conducted in the United States in 2011. Information that provides an indication of the scope of each 

experiment in terms of Àight conditions, microphone arrangement, and focus factors is also presented in the table.

Table 3.1. Compilation of Transition Flight-Test Experiments
&KDSWHU,QÁXHQFHRI0DQHXYHUV

92

A common factor among the ¿rst eight of the nine transition Àight-test studies was that the studies focused 

on the location of the focus, the condition that generated them, and the peak pressures of the focused N-wave 

signatures. Signature shapes were qualitatively noted, but other than the peak pressures, no comparison to 

theory was made. The ninth and most recent Àight experiment, known as the Superboom Caustic Analysis 

and Measurement Program (SCAMP), had a primary goal of gathering a comprehensive empirical data set 

of focused sonic boom signatures suitable for validation of computer models for predicting sonic boom focal 

zones and signatures, and to apply these models to predict focus booms for low-boom aircraft designs.

SCAMP (ref. 3.32) consisted of 13 supersonic Àights of an F-18, 11 of which had ¿ve to seven supersonic 

transition maneuvers. The objective was to obtain detailed signature data that could be compared to theoretical/

numerical focus models. A variety of acceleration and pushover maneuvers were employed so as to vary caustic 

curvature (ref. 3.33). Forty focal zones were recorded along a 10,000-foot 81-microphone array (refs. 3.34 and 

3.35). Ten focal zone signatures of various types were recorded on a powered glider about 5000 feet above the 

ground array. Two analytic models for focus signatures were evaluated. The ¿rst was a lossy nonlinear Tricomi 

equation (NLTE) solver (ref. 3.36). This was based on the methodology pioneered by Auger, Marchiano, and 

Coulouvrat (refs. 3.21 and 3.22) but extended to include atmospheric absorption. The rise time associated with 

absorption had been shown in ref. 3.8 to be signi¿cant for peak shock overpressures. NLTE results agreed 

very well with measured foci, matching the shock peaks and also the signature shapes throughout the focal 

zone. The second model was a Nonlinear Progressive Wave Equation (NPE) solver (ref. 3.37), a more general 

wave propagation code. NPE provides good qualitative agreement with measured booms, but required external 

scaling and in its current form does not include absorption losses.

The validated NLTE codes was applied to prediction of transition focus for several low-boom aircraft 

con¿gurations (ref. 3.38). Interactions between shocks, similar to those seen in ¿gure 3.17(b), were observed. 

General indications of the effects of Mach number, altitude, and maneuver on focus factor were observed. 

Launch Vehicle Transition Focus Boom

Transition focus booms were also experienced during the launch-ascent phase of mission operations with 

vehicles such as the Saturn-Apollo rocket/capsule combination vehicles and the Space Transportation System 

(STS)/Space Shuttle Orbiter. An illustrated description of the launch-ascent focus boom region is presented in 

¿gure 3.22 (ref. 3.39). The origin of the launch-ascent focus boom region is shown schematically in the ¿gure. 

When, for example, the Saturn-Apollo vehicles and the Space Shuttle ¿rst achieved supersonic velocities, 

they were in nearly vertical Àight and the propagation of the disturbances was upward, away from the ground. 

As the vehicles continued to accelerate and pitch over, the Àight path angle decreased suf¿ciently so that the 

disturbance propagation path intersected the ground surface. The combination of angular and linear acceleration 

rates resulted in a region some 40 nmi or so from the launch site in which the acoustical energy was focused, 

as indicated by the loci of focal areas shown in the pro¿le view presented in ¿gure 3.22(a). These loci de¿ne 

a focus line on the ocean surface that is parabolic in shape as depicted in ¿gure 3.22(b) and extends laterally 

approximately 40 nmi or so to each side of the vehicle ground track out to the lateral cutoffs. Beyond the lateral 

cutoff, the pressure wave is refracted up by the atmosphere and does not intersect the ground. Behind (downrange 

from) the focus line, the post-focus region overpressure peaks originating from different points on the Àight 

path reach the surface at different times, producing signatures with multiple peaks. In front of the focus line (the 

pre-focus region), no sonic boom reaches the ground. The highest peak overpressure is obtained at the focus 

line beneath the Àight path and falls off both laterally from the ground track and downrange from the focus line.
&KDSWHU,QÁXHQFHRI0DQHXYHUV

93

The pre-focus, near-focus, and post-focus signatures observed from measurements acquired during the launchascent of the Saturn-Apollo 17 (ref. 3.39) mission are shown in ¿gure 3.23. Six U. S. Naval vessels were located 

in the Atlantic Ocean directly under the Àight path of the launch vehicle and were positioned to cover the extent 

of the focus region. Note that although two of the measurements were near the focus line, the chart suggests that 

the values measured do not represent the maximum overpressures within the focus line.

(a) Origin of launch-ascent focus boom.

(b) Plan view of launch-ascent focus boom region.

Figure 3.22. 'HVFULSWLRQRIODXQFKDVFHQWIRFXVERRPUHJLRQDGDSWHGIURPUHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

94

Sonic boom signatures representative of those measured within the STS launch-ascent focus region are shown in 

¿gure 3.24 (ref. 3.39) and are similar to those observed from the Saturn-Apollo launch-ascent. Note the change 

in the time scale associated with each set of measured signatures. The uppermost signature was measured at a 

location in the pre-focus region slightly up-track (before) the focus line. The signature shown at the center of 

the ¿gure was measured within the focus line and is seen to consist of a sharp signal shock of large amplitude, 

which may not represent the maximum value. A considerable database on focus booms associated with supersonic 

aircraft suggests that the downrange thickness of the focus line is on the order of a few hundred feet. Down-track, 

behind the focus line, and in the post-focus region the measured signature shown at the bottom of ¿gure 3.24 also 

displays a two-shock trace, the initial shock being attributed to the direct boom and the second the reÀected shock 

arriving at a slightly later time and from a slightly different location along the ascent trajectory.

Figure 3.24. 676ODXQFKDVFHQWVRQLFERRPVLJQDWXUHVZLWKLQIRFXVUHJLRQUHI

Figure 3.23. 6DWXUQ$SROORODXQFKDVFHQWVRQLFERRPVLJQDWXUHVZLWKLQIRFXVUHJLRQUHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

95

It is quite observable that the measured sonic boom ground signatures associated with the Saturn-Apollo and 

STS Shuttle launch ascents are quite different in character than the N-wave shapes associated with aircraft and 

the Space Shuttle Orbiter. Note from ¿gures 3.23 and 3.24 that the boom signatures measured in the post-focus 

region (i.e., down-track of the focus line) consist of an initial bow shock followed by a long expansion similar 

to signatures associated with explosive charges. Thus, only a single boom is observed. In addition, the boom 

signature period is on the order of 4.0 seconds. Although Saturn-Apollo and STS Shuttle vehicles (in their launch 

con¿gurations) were large, the initial shock resulted from the enormous rocket engine exhaust plumes.

Current coastal launch sites allow for the placement of the transition focus region to impact over water. Future 

space exploration efforts may be located at inland launch sites where sonic boom impact must be addressed with 

more consideration of the transition focus region.

Focus Boom Avoidance Charts

During the U.S. SST effort of the mid-1960s and also in preparation for the entry of Concorde into routine 

commercial Àight service, information relating to the avoidance of Àight maneuvers that could cause focus booms 

was obtained. Two examples of focus boom avoidance operational charts are provided in ¿gure 3.25 (refs. 3.7 and 

3.40). Wanner et al. (ref. 3.7) presented an operation chart regarding Concorde operations that avoids focus booms 

during turn maneuvers and is shown in ¿gure 3.25(a). The maximum permissible bank angle in a steady turn for 

Concorde to not produce a focus on the ground is plotted as a function of altitude and Mach number. For a better 

understanding of these limits, the relation between bank angle and rate of change of heading versus Mach number 

is also shown. As an example, at Mach 2, the maximum authorized bank angle is 35° at an altitude of 36,000 feet 

(11 km) and 30° at an altitude of 52,500 feet (16 km). But on the other hand, the limit is much lower for low Mach 

numbers. At 32,800 feet (10 km), the maximum permissible bank angle at Mach 1.3 is only 10°.

(b) Pushover requirements for caustic formation on the ground (ref. 3.40).

Figure 3.25. Examples of focus boom avoidance operational charts.

(a) Maximum authorized bank angle in order to avoid focus during turning maneuvers (ref. 3.7).
&KDSWHU,QÁXHQFHRI0DQHXYHUV

96

A study by Haglund and Kane (ref. 3.40) of maneuvers typical of a large SST-type airplane showed that it is 

possible to perform normal SST Àight operations without producing focus booms except during the transonic 

acceleration phase of Àight. Thus, for commercially operated supersonic aircraft, maneuvers such as pull-up, 

pushovers, sideslips, and abrupt turns at supersonic speeds would be avoided and the proper decelerationdescent schedule would be employed to avoid focusing during decent. Figure 3.25(b) addresses the critical lift 

load factors nL required for a caustic at the ground directly beneath the airplane during pushovers in the 1962 

U.S. Standard Atmosphere with no wind. Note that caustics are most easily produced at the low supersonic 

Mach numbers. At speeds greater than about Mach 2, caustics are impossible to form operationally for an SST 

because of the load factor constraint on commercial Àight. For passenger comfort the lift load factor nL will be 

restricted to 0.5 g in pushovers, while the structural limit load factor minimum is about -0.5 g. A typical Àight 

pro¿le (Mach number-altitude variation) is also shown on the ¿gure. For the operational minimum of 0.5-g load 

factor, caustics could be produced only at Mach numbers between 1.5 and the threshold value. Charts of this 

nature are very important in the operation of supersonic aircraft in order to avoid generating unnecessary focus 

booms during Àight operations. In fact, such information could be integrated into an aircraft¶s onboard Àight 

computer systems.

Haglund and Kane (ref. 3.40) also examined Àight-test data involving acceleration rates of 0.04 g to 0.10 g 

that suggests that a method to alleviate the transonic accelerating caustic is to accelerate rather slowly. They 

concluded, however, that based upon current prediction methods at that time, there was no method available for 

calculating the variation of caustic intensity with acceleration magnitude even though the limited experimental 

data did suggest a pronounced effect of deceleration on caustic intensity. Recently, Auger and Coulouvrat (ref. 

3.21) concluded that, for the limited acceleration rate and altitude examined, these factors had little inÀuence 

on ground track focusing.

When the Space Shuttle Orbiter returned from orbit, most of its atmospheric descent was at supersonic speeds. 

The resultant sonic boom impinged on land areas in the United States, with the sonic boom carpet extending 

to the vicinity of the landing site. Prediction of sonic boom has been routinely performed as part of mission 

planning and these predictions have agreed well with measurements (ref. 3.39). There was some concern that 

maneuvers during the ¿nal stages of supersonic Àight could, under anomalous atmospheric conditions, cause 

a focus boom to occur at some location on the ground. This concern was centered on the portion of descent 

around Mach 3, where the Shuttle made a signi¿cant S-turn. The ¿nding of the Plotkin study of reference 3.41 

indicates it does not appear that sonic boom focusing will occur in the Mach 3 range. Focusing is possible, but 

would require turn rates higher than those normally employed within the Orbiter¶s Àight envelope. However, 

focusing can occur for turns at a Mach number below 2. This is outside the range that was of concern and is 

also in the range where sonic cut-off focusing is normally expected as the vehicle approaches subsonic speeds 

and the boom lifts from the ground.

Figure 3.26 is an example focus condition chart adapted from reference 3.41. The abscissa is turn rate and the 

ordinate is Àight path angle rate. To the right are shown the Mach number, altitude, Àight path angle, and Mach 

rate. These are nominal quantities, corresponding to the center of the ranges seen in several Shuttle-Orbiter 

reentries. The small rectangular area just above the center of the chart represents the Àight envelope at that 

Mach number. The V-shaped lines represent the threshold of focusing. Within the V, no focus occurs. Outside 

(or below) the V, focus will occur. Three V contours are shown, the middle one corresponds to the nominal 

Àight conditions to the right and the other two Vs are focus conditions computed at the extreme values of Mach 

rate. Focus charts similar to ¿gure 3.26 are also presented in reference 3.41 for Mach numbers from 2 to 6 and 

for two atmospheres (the U. S. Standard Atmosphere and the EAFB Range Standard Atmosphere). These charts 

indicate that focusing was not expected to occur for Space Shuttle descent.
&KDSWHU,QÁXHQFHRI0DQHXYHUV

97

As has been shown in the previous ¿gures, sonic boom enhancement can result from a variety of aircraft 

maneuvers. Figure 3.27 is presented as a summary reminder that focus boom regions may be experienced when 

an aircraft performs three of the more common maneuvers and include a longitudinal acceleration, a 90° turn, 

and a pushover maneuver. 

In each maneuver, focus overpressure increases occur in the localized regions suggested by the shaded areas 

in the sketches. It is very important to remember that although the aircraft and shock waves are moving, 

these localized areas on the ground in which pressure enhancements occur are ¿xed and do not move with 

the aircraft. The localized regions, incidentally, are on the order of 1000 feet or less in width (thickness). The 

relative overpressure increases in these focus areas are a function of the type of maneuver and the acceleration 

Figure 3.27. Focus boom regions on ground from three maneuvers.

Figure 3.26. 6SDFH6KXWWOH2UELWHUIRFXVERRPDYRLGDQFHFKDUWIRUGHVFHQWUHI
&KDSWHU,QÁXHQFHRI0DQHXYHUV

98

involved and are noted to be two to ¿ve times the boom carpet values and in some cases, as high as nine at 

so called superfocus locations, which are even smaller in extent. As noted previously, pressure buildups will 

always result for the longitudinal maneuver when the aircraft accelerates from subsonic to supersonic speeds. 

The overpressure increase areas associated with turns and pushover maneuvers can be minimized or avoided by 

reducing acceleration (or decelerating) or by simply avoiding the maneuver.

In scheduled commercial Àight operations, longitudinal acceleration from subsonic to supersonic speeds is the 

only maneuver of signi¿cance from a ground exposure point of view. Focus boom during the deceleration-descent 

phase of Àight can be avoided by proper arrangement of the aircraft Mach-altitude schedule. Recent experience has 

demonstrated that the focus boom region associated with this transition acceleration can be placed to within about 

1000 feet of the designated area. However, experience with normal Concorde operations over a 1-year sampling 

has shown that meteorological induced variations in boom amplitude and focus location are experienced (ref. 

3.42). It is important to note that any randomness of the atmosphere, which brings about waveform distortions, 

may decrease the focus factor value and, for certain situations, may eliminate the focus altogether as observed in 

references 3.15 and 3.16. Such occurrences, combined with a minimum boom design and Àight transition pro¿le, 

could render the focus boom ground footprint to a negligible issue.

Sonic Booms at High Subsonic Mach Numbers

It can generally be stated that as long as the aircraft speed over the ground is less than the speed of sound at the 

ground, boom-less Àights at low supersonic Mach numbers at Àight altitude can be achieved. It is often asserted 

that as long as the aircraft speed is less than Mach 1.00, no sonic booms should be experienced at ground level. 

However, it is known that sonic booms and, at times, damage has resulted from aircraft Àights at relatively 

low altitudes and at high subsonic Mach numbers. Sonic booms were reported to have been observed from the 

subsonic ;P-86 Sabre prototype (ref. 3.43), shown in ¿gure 3.28, during a dive-pull-up maneuver several days 

before Chuck <eager¶s level supersonic Àight in the ;-1 aircraft in 1947 when his support team in the NACA 

tracking van reported they heard what sounded like a distant rumble of thunder (ref. 3.44).

Booms from Low-Altitude Level Flight

Experience, con¿rmed by measurement (ref. 3.31) indicates that booms can be observed at ground level from 

aircraft in steady-level Àight at Mach numbers from about 0.95 to 0.99 at altitudes of about 300 to 2000 feet above 

ground level. This phenomenon is similar to that observed for airfoils in wind tunnels (as shown in ¿g. 3.29(a) 

from ref. 3.19) at high transonic Mach numbers, for which localized shocks occur at the maximum thickness 

(where the Àow accelerates beyond Mach 1.00 and then decelerates across a shock). These shocks extend for 

some distance from the airfoil before dissipating into acoustic disturbances. Extended shocks of this sort are also 

Figure 3.28. 1RUWK$PHULFDQ;36DEUHSURWRW\SH

86$LU)RUFHSKRWR
&KDSWHU,QÁXHQFHRI0DQHXYHUV

99

shown in photographs of ¿ghter aircraft in Àight at high subsonic Mach numbers during low altitude passes such 

as shown in ¿g. 3.29(b) (refs. 3.45 and 3.46). The explanation of why the shock waves are visible is given in 

reference 3.45 (p. 4) as follows

The freestream Àow accelerates to supersonic speeds above and below the wing, causing the Àow to 

condense in the expansion waves in the front portion of the condensation pattern. The aft end of the pattern 

is created by a shock wave through which the Àow is decelerated back to subsonic speeds. The rapid 

temperature rise through the shock causes the condensed Àow to evaporate. 

The aircraft, like the airfoil has a maximum thickness (equivalent cross-sectional area distribution) such that 

the local Àow can be equal to or exceed Mach 1.0 at some given free-stream transonic Mach number. These 

localized shocks have been observed to extend outward and downward as much as 30 airplane body lengths. The 

intensity of the shocks is substantial because of the very low altitudes and the signature (¿g. 3.30), is considerably 

different in nature from the normally observed N-wave-type signature associated with a fully-developed 

supersonic Àow ¿eld (see, for example, the discussion on a similar transonic signature presented in ¿g. 3.14).

Figure 3.30. Character of transonic boom signature.

(a) NACA 16-2122 airfoil in wind tunnel, Mach 0.90 (ref. 3.19). (b) F/A-18F during a high-speed, 

low altitude pass.

861DY\SKRWR13

Figure 3.29. 7UDQVRQLFÀRZ¿HOds.
&KDSWHU,QÁXHQFHRI0DQHXYHUV

100

A detailed analysis of low-altitude transonic Àight-test data (ref. 3.31) has indicated that existing meteorological 

conditions inÀuence the vertical extent of attached shock waves produced at nearly sonic Àight. Aircraft Mach 

number also has a direct inÀuence on the strength and vertical extent of the attached shock waves. The extension 

of these attached shock waves to lower altitude may explain several accidental sonic booms produced by lowaltitude, marginally subsonic aircraft (although Mach meter and altimeter errors may also be responsible). 

Booms from Dive Pull-Up Maneuver

For aircraft in non-level Àight, in a climbing or diving condition, the sonic boom propagation situation can 

change signi¿cantly as compared to that for level Àights. The climb angle always directs or aims the shock 

wave and thus the boom away from the ground, whereas a dive angle directs or aims the shock wave and thus 

the boom toward the ground. The sketches presented in ¿gure 3.31 can be useful in illustrating the inÀuence of 

climb and dive angle on shock propagation. Figure 3.31 shows three aircraft all Àying at the same high subsonic 

Mach number and altitude with the one on the left in level Àight, the one in the center in a climb, and the one 

on the right in a dive. The shock wave and the ray path along which they propagate are also shown in the ¿gure. 

Recall that it was stated earlier in these discussions that the ray always travel perpendicular to the shocks and at 

the local speed of sound. It is quite apparent from the three sketches in ¿gure 3.31 that a climb angle essentially 

rotates the level Àight shock-ray pattern upward, whereas the dive angle rotates the level Àight shock rays 

downward. Another way of stating this from a propagation point of view is that a climb angle acts to effectively 

reduce the level Àight Mach number, whereas a dive angle acts to effectively increase the Mach number.

Now that the inÀuence of dive angle has been presented, a discussion of the possibility of a sonic boom being 

observed on the ground during a high subsonic Mach number (Mach  1.0) dive of an aircraft with a pull-up at 

relatively high altitudes (10,000 to 15,000 feet) is in order. A schematic illustration of such a situation is shown 

in ¿gure 3.32.

Figure 3.31. Nature of shock wave-ray paths of aircraft at a steady Mach number less than 1.0.
&KDSWHU,QÁXHQFHRI0DQHXYHUV

101

The aircraft is assumed to enter the dive from level Àight in a standard atmosphere at about 30,000 feet and Mach 

0.65 at position (1) indicated in ¿gure 3.32. As the aircraft descends during the 15° to 20° dive it accelerates to 

about Mach 0.82 at the bottom of the dive at which time an 8-g pull-up is initiated and the Mach number then 

decreases to 0.75 at position (6). Note that during the dive, local shock waves appear and extend above and 

below the aircraft. The distance the shock waves extend from the aircraft increases as Mach number increases. 

For simplicity, only the ray paths associated with each of the local shocks that extend below the aircraft are 

shown. A similar picture would exist regarding the local shocks that extend above the aircraft. These ray paths 

start out perpendicular to the shock front and then begin refraction upward because of the refraction due to 

increasing temperature as they propagate towards the ground. There is only a short portion of the Àight path 

between positions (3) and (5) where the shocks ¿nd favorable conditions (relative to shock angle-dive angle 

and ray path) to propagate the many thousand feet to the ground. It should be noted that the probability of these 

shocks reaching the ground is enhanced for the case of cooler temperatures at ground level and tailwinds at Àight 

altitude. Likewise, warmer temperatures at ground level and headwinds at altitude would cause the shock to 

refract upward and away from the ground. Such weather situations are more inÀuential in shallower dive angles 

than at steeper dive angles. Interestingly, Barger addressed these issues in a short technical note in 1967 (ref. 3.37).

Chapter 3 Summary Remarks

Rapid deviations of a vehicle from steady-level Àight produce signi¿cant changes in ground shock patterns 

resulting in the observation of multiple booms and focused booms. These booms are one-time occurrences and 

are not dragged along the ground behind the aircraft like carpet booms.

Focus boom regions on the ground are extremely localized with typical focus factors on the order of two to 

¿ve for transition booms. For commercial supersonic Àight operations, most focus booms can be avoided or 

minimized except for the transition focus experienced during acceleration from subsonic to supersonic speeds. 

Placement of these focus booms to within 1000 feet of the desired location has been demonstrated.

The signature shape for transition Àight is shown to have a signi¿cant inÀuence in altering the focus boom levels. In addition, atmospheric turbulence at lower altitudes ( 5000 feet) also seems to diffuse focus boom levels.

Figure 3.32. Schematic illustration of local shock waves and ray paths emanating from an aircraft in 

a 20° dive at Mach < 1.0.
&KDSWHU,QÁXHQFHRI0DQHXYHUV

102

Current prediction codes have matured suf¿ciently such that we can predict maneuver shock patterns on the 

ground and overpressure magnitudes, including focused boom regions.

Sonic booms have been experienced at ground level from relatively low-altitude Àights at Mach numbers less 

than 1.0 and from steep dives from high altitude at high subsonic Mach numbers.

Chapter 3 References

3.1 Maglieri, D. J. and Lansing, D. L. Measured Shock Wave Ground Pressure Patterns From Aircraft in 

Maneuvers. NASA TN D-2370, 1964.

3.2 Lansing, Donald L. Some Effect of Flight Maneuvers on the Distribution of Sonic Booms. Proceedings 

of Symposium on Atmospheric Acoustic Propagation, Vol.1, June 14–15, 1961, pp. 24–43. 

3.3 Kerr, T. H. Experience of Supersonic Flying Over Land in the United Kingdom. AGARD Report 250, 

Sept. 1959.

3.4 Hubbard, Harvey H.; Maglieri, Domenic J.; Huckel, Vera; and Hilton, David A. Ground Measurements of 

Sonic Boom Pressures for the Altitude Range of 10,000 to 75,000 Feet. NASA TR R-198, 1964.

3.5 Lansing, Donald J. and Maglieri, Domenic J. Comparison of Measured and Calculated Sonic-Boom 

Ground Patterns Due to Several Different Aircraft Maneuvers. NASA TN D-2730, 1965.

3.6 Downing, Micah; =amot, Noel; Moss, Chris; Morin, Daniel; Wolski, Ed; Chung, Sukhwan; Plotkin, 

Kenneth; and Maglieri, Domenic J. USAF Flight Investigation of Focused Sonic Booms; Project 3HAVE 

BEARs, ́ NASA CP-3335, July 1996, pp. 259–277.

3.7 Wanner, Jean-Claude; Vallee, Jacques; Vivier, Claude; and Thery, Claude Theoretical and Experimental 

Studies of the Focus of Sonic Booms. J. Acoust. Soc. Am., Vol. 52, No. 1, Pt. 1, July 1972.

3.8 Plotkin, K. J. and Cantril, J. M. Prediction of Sonic Boom at a Focus, AIAA paper 76-2, Jan. 1976.

3.9 Guiraud, J. P. Acoustique Geometrique, Bruit Ballistique des Avions Supersoniques et Focalisation, J. 

Mechanique, Vol. 4, 1965, pp. 215–267.

3.10 Whitham, G. B. On the Propagation of Weak Shock Waves. Journal of Fluid Mechanics, Vol. 1, Part 3, 

Sept. 1956.

3.11 Gill, P. M. and Seebass, A. R. 3Non-Linear Acoustic Behavior at a Caustic An Approximate Solution ́, 

AIAA Progress in Astron. Aeronautics, Nagamatsu, HJ.T. (Ed.). MIT Press, 1975.

3.12 Gill, P. M. 3Nonlinear Acoustic Behavior at a Caustic ́, Ph.D. Thesis, Cornell University, June 1974.

3.13 Plotkin, K. J.; Downing, J. M.; and Page, J. USAF Single Event Sonic Boom Prediction Model PCBoom. 

J. Acoust. Soc. Am., 95(5), Part 2, May 1994, pp. 28–29.

3.14 Sanai, J.; Toong, T. <.; and Pierce, A. D. 3Ballistic Range Experiments on Superbooms Generated by 

Refraction ́ and 3Ballistic Range Experiments on the Super-boom Generated at Increasing Flight Mach 

Numbers ́, J. Soc. Am., 59(3), 1976, pp. 513–524.

3.15 Maglieri, D. J.; Hilton, D. A.; and McLeod, N. J. Further Experiments on the Effects of Atmospheric 

Refractions and Aircraft Accelerations on sonic Boom Ground Pressure Patterns. NASA TN D-3520, July 

1966.
&KDSWHU,QÁXHQFHRI0DQHXYHUV

103

3.16 Downing, Micah; =amot, Noel; Moss, Chris; Morin, Daniel Wolski, E.; Chung, Sukhwan; Plotkin, 

Kenneth; and Maglieri, Domenic J. Measurement of Controlled Focus Booms from Maneuvering 

Aircraft. USAF/AL, AL-OE-WP-TR-1997-0185, Feb. 1998.

3.17 Plotkin, Kenneth J. Sonic Boom Focal =ones from Tactical Aircraft Maneuvers, Journal of Aircraft, Vol. 

30, No. 1, Jan.–Feb. 1993.

3.18 Vallee, J. Operation Jericho-Focalisation, Rapport D¶Edute, CEV, No. 272, Oct. 1967.

3.19 Maglieri, Domenic and Plotkin, Kenneth J. Sonic Boom, Chapter 10, pp. 519-561, Aeroacoustics of 

Flight Vehicles, Theory and Practice. NASA RP 1258, Vol. 1 and WRDC TR 90-3052, Aug. 1991.

3.20 Plotkin, Kenneth J. State of the Art of Sonic Boom Modeling. J. Acous. Soc. Am.111(1), Part 2, Jan. 

2002, pp. 520–536. 

3.21 Auger, T. and Coulouvrat, F. Numerical Simulation of Sonic Boom Focusing. AIAA Jour. Vol. 40, No. 9, 

Sept. 2002, pp. 1726–1734.

3.22 Marchiano, R. and Coulouvrat, F. Numerical Simulation of Shock Wave Focusing at Fold Caustics with 

Application to Sonic Boom. J. Acoust. Soc. Am. 114(4), Pt. 1, Oct. 2003, pp. 1758–1771.

3.23 Maglieri, D. J.; Bobbitt, P. J.; Plotkin, K. J.; Kandil, O. A.; and =heng, ;.; and Massey, S. J Focused 

and Steady-State Characteristics of Shaped Sonic Boom Signatures Prediction and Analysis. NASA CR 

2011-217156, June 2011.

3.24 Pawlowski, J. W.; Graham, D. H.; Boccadoro, C. H.; Coen, P. G; and Maglieri, D. J. Origins and Overview 

of the Shaped Sonic Boom Demonstration Program. AIAA-2005-0005, Jan. 2005.

3.25 Plotkin, K. J.; Haering, E. A., Jr.; Murray, J. E.; Maglieri, D. J.; Salamone, J.; Sullivan, B. M.; and Schein, 

D. Ground Data Collection of Shaped Sonic Boom Experiment Aircraft Pressure Signatures. AIAA 2005-

0010, Jan. 2005.

3.26 Plotkin, K. J. and Grandi, F. Computer Models for Sonic Boom Analysis PCBOOM4, CABoom, 

BOOMap, CORBoom. Wyle Report WR-02-11, June 2002.

3.27 Plotkin, K. J.; Martin, R.; Maglieri, D. J.; Haering, E. A., Jr.; and Murray, J. E. Pushover Focus Booms 

from the Shaped Sonic Boom Demonstrator. AIAA-2005-0011, Jan. 2005.

3.28 Vallee, J. Operation Jericho-Virage, Rapport D¶Etude, CEV, No. 277, May 1969.

3.29 Vallee, J. Operation Jericho-Carton, Rapport D¶Etude, CEF No. 291, May 1973.

3.30 Haglund, George T. and Kane, Edward J. Flight Test Measurements and Analysis of Sonic Boom 

Phenomena Near Shock Wave Extremity, NASA CR-2167, Feb. 1973.

3.31 Haglund, George T. and Kane, Edward J. Analysis of Sonic Boom Measurement Near Shock Wave 

Extremities for Flight Near Mach 1.0 and for Airplane Accelerations. NASA CR-2417, 1974.

3.32 J. Page; K. Plotkin; E. Haering; D. Maglieri; Cowart, R.; Salamone, J.; Elmer, K.; Welge, H.; Ladd, 

J. SCAMP Superboom Caustic Analysis and Measurement Project Overview. AIAA-2013-0930, June 

2013.

3.33 Plotkin, K. and Maglieri, D. SCAMP Experimental Design of a Sonic Boom Focus Flight Test. AIAA2013-0931, January 2013.
&KDSWHU,QÁXHQFHRI0DQHXYHUV

104

3.34 Haering, E.; Cliatt, L.; Plotkin, K.; Maglieri, D.; Delaney, M.; Brown, J. SCAMP Rapid Focused Sonic 

Boom Waypoint Flight Planning Methods, Execution, and Results. AIAA-2013-0932, January 2013.

3.35 Page, J.; Hobbs, C.; Haering, E.; Maglieri, D.; Shupe, R.; Hunting, C.; Giannakis, J.; Franzeska, H.

SCAMP Focused Sonic Boom Experimental Execution and Measurement Data Acquisition. AIAA-2013-

0933, January 2013.

3.36 Salamone, J.; Sparrow, V.; and Cowart, R. SCAMP Solution of the Lossy Nonlinear Tricomi Equation 

for Sonic Boom Focusing. AIAA-2013-0935, January 2013.

3.37 Piacsek, A. SCAMP Application of Nonlinear Progressive-wave Equation to Sonic Boom Transition 

Focus. AIAA-2013-1064, January 2013.

3.38 Elmer, K.; Welge, H.; Salamone, J.; Cowart, R. SCAMP Supersonic Passenger Transport Transonic 

Acceleration Flight Pro¿les with Considerations of Focused Sonic Boom. AIAA-2013-1065, January 

2013. 

3.39 Maglieri, Domenic J.; Henderson, Herbert R.; Massey, Steven J.; and Stansbery, Eugene G. A Compilation 

of Space Shuttle Sonic Boom Measurements. NASA CR-2011-217080, April 2011. 

3.40 Haglund, G. E. and Kane, E. J. Effect of SST Operational Maneuvers on Sonic Boom. J. Acoust. Soc. 

Am., Aug. 1972, pp. 563–568.

3.41 Plotkin, Kenneth J. Potential Sonic Boom Focal =ones From Space Shuttle Reentry. Wyle Research 

Report. WR 89-11, July 1989.

3.42 Coulouvrat, Francois; Blurich, Reinhard; and Heimann, Deitrich Meteorologically Induced Variability of 

Sonic Boom of a Supersonic Aircraft in Cruising or Acceleration Phase. ISNA 17 AIAA Conf. Proc, Vol. 

838, Melville, N<, 2006, pp. 579–586.

3.43 Blackburn, Albert Aces Wild The Race for Mach 1, Scholarly Resources Inc., 1998. 

3.44 <eager, C. and Janos, L. <eager; An Autobiography, Bantam Books, July 1985, p.130.

3.45 Campbell, James F.; Chambers, Joseph R.; and Rumsey, Christopher L. Observation of Airplane Flow 

Fields by Natural Condensation Effects. AIAA 88-0190, Jan. 1988.

3.46 Vapor Condensation Makes F-14 Shockwaves Visible. Aviation Week and Space Technology, Vol. 107, 

No. 21, Nov. 21, 1977, pp. 46–47.

3.47 Barger, Raymond L. Sonic Booms Attributed to Subsonic Flight. AIAA Journal, Vol. 5, May 1967, pp. 

1042–1043.
Chapter 4 In-Flight Flow-Field Signature Measurements

CHAPTER 4 IN-FLIGHT FLOW-FIELD SIGNATURE MEASUREMENTS

Sonic boom prediction techniques bene¿t greatly from the experimental validation of the shock Àow ¿eld 

surrounding an aircraft in supersonic Àight. This validation can be acquired by means of wind tunnel and/or 

Àight tests. In the former, there are limitations due to the fact that measurements are limited to the near- and 

mid-¿elds because of the tunnel test section and model size, as well as the fact that the medium surrounding the 

model does not represent the real atmosphere (i.e., it has uniform free stream conditions). Flight tests, on the 

other hand, provide a real environment and yield both near- and mid-¿eld results along with the all important 

ground measurements. Near-, mid-, and far-¿eld pressure signatures can be measured by probing aircraft or other 

means. In this section, several methods used to describe the Àow ¿eld about an aircraft in supersonic Àight will be 

presented along with a summary of the full-scale in-Àight Àow-¿eld measurement database that has been acquired 

on aircraft over the last 60 years. 

Review of Available Methods

An indication of the various methods used to describe the shock Àow ¿eld about an aircraft in supersonic Àight is 

schematically illustrated in ¿gure 4.1. These methods include probe Àights with instrumented supersonic aircraft, 

airborne measurements using very low-speed instrumented manned or unmanned aircraft, measurements taken 

with transducers located on high mountains, on blimps hovering high above the ground surface, on relatively high 

¿xed towers, and at ground level. Schlieren photography has also been used to qualitatively describe the shock 

Àow ¿eld about an aircraft in supersonic Àight.

Probing the near and mid Àow ¿eld of the shock generating aircraft by means of an instrumented aircraft in 

supersonic Àight passing or being passed at positions above, to the side, and below has been the most widely used 

research method and provides the clearest detail concerning the complex nature of the shock Àow ¿eld near the 

aircraft.

Sonic boom measurements have been made on high mountains, but little, if any, data are available in existing 

literature. Sonic boom signatures have been measured by means of balloon-borne and tower-mounted microphones 

and provide considerable information on signature distortion due to turbulence in the few thousand feet of the 

earth¶s boundary layer, ground reÀection coef¿cients and information regarding the extremities of shock waves 

105

Figure 4.1. 0HWKRGVXVHGWRPHDVXUHVKRFNÀRZ¿HOGDERXWDQDLUFUDIWLQVXSHUVRQLFÀLJKW
Chapter 4 In-Flight Flow-Field Signature Measurements

for Àight operations at Mach cutoff and at lateral cutoff. Ground level measurements make up the majority of the 

sonic boom database.

Airborne and ground-based outdoor Schlieren methods and subsonic airborne in-Àight techniques are recent 

and innovative approaches to de¿ning the aircraft¶s supersonic Àow ¿eld. These techniques are still undergoing 

development.

Application of the in-Àight supersonic Àow-¿eld data acquired through any of the various methods/techniques 

just discussed is valuable for the design of an aircraft having a minimized boom waveform. As indicated in table 

4.1, a description of the supersonic shock Àow ¿eld will provide information on the number, location, and strength 

of the shocks contained in the Àow ¿eld and can also show how many aircraft body lengths (h/O) it takes for these 

shocks to coalesce into their ¿nal form. Qualitative and quantitative information of this nature provides a means 

of validating the present computational Àuid dynamic (CFD) prediction codes out to much larger distances than 

are attainable in wind tunnels using small models. This provides insight into determining when the Àow ¿eld 

about the aircraft has developed such that it is approximately equivalent to a body of revolution when the ray 

tracing sonic boom propagation codes can be properly applied and correctly predict pressure signatures at all 

locations at ground level.

Measurement techniques, such as in-Àight and ground-based Schlieren photography, also provide insight into 

the persistence of a sonic boom signature shock structure as it moves from locations very near the aircraft to 

many body lengths away as the local shocks age (move further away) and coalesce. Although the Schlieren 

observations are only qualitative in nature, they do provide excellent imagery of the shocks from the different 

aircraft components as distance from the aircraft increases. 

The concept and development of the ground-based Schlieren to obtain images of Aircraft in Flight (SAF), see 

¿gure 4.2 (ref. 4.1), was aimed at enhancing the understanding of the structure and development of the supersonic 

Àow system about an aircraft. A photograph of the system is depicted in ¿gure 4.2(a) and a schematic of its set-up 

for viewing aircraft in supersonic Àight is presented in ¿gure 4.2(b). The bottom two photographs, ¿gure 4.2(c) 

and ¿gure 4.2(d), are the results acquired by the ground-based Schlieren showing the shock systems emanating 

from a T-38 and F-18, respectively, in supersonic Àight. In both photographs, the multiple shocks are clearly 

evident to h/O of about 2 to 5 and the exhaust stream boundaries are also well de¿ned.

106

7DEOH6LJQL¿FDQFHRI,Q)OLJKW6XSHUVRQLF)ORZ)LHOG'DWD

s%STABLISHESNUMBERLOCATIONSTRENGTHOFSHOCKS

s$ESCRIBESSHOCKWAVECOALESCENCE

s6ALIDATESPREDICTIONMETHODS

s0ROVIDESINSIGHTINTOWAVEFORMPERSISTENCEAGING

s3OURCEOFINFORMATIONONTURBULENCESCALEWAVEFORMSHAPESHOCK

RISETIME

s$ESCRIBESATMOSPHERICABSORPTION

s-EASUREDNEAR
ANDMID
FIELDSIGNATURESARENOTSIGNIFICANTLY

CONTAMINATEDBYATMOSPHERICINSTABILITIES
Chapter 4 In-Flight Flow-Field Signature Measurements

Whereas the ground-based Schlieren is aimed primarily at providing a visual picture of the shock system above 

and below the aircraft, an airborne aircraft system could provide signi¿cant close-up detail into the structure of 

the shock system surrounding the aircraft including wakes and exhaust systems. Continuing improvements and 

developments on the ground- and airborne-based Schlieren systems will tremendously enhance the database and, 

thus, the ability to properly handle the analysis of the near-, mid-, and far-¿eld sonic boom characteristics of lowboom shaped vehicles.

Subsonic airborne measurement techniques also provide a source of information on atmospheric turbulence as it 

relates to signature distortions and shock rise times. Better de¿nition of the inÀuence of atmospheric absorption 

on shock smoothing (rise time) could also be inferred. Many of the shock Àow-¿eld observation techniques, 

especially the Schlieren photography and subsonic airborne systems, would provide a database regarding the 

initial conditions of the secondary (over-the-top) sonic boom. Finally, in-Àight signature measurements are not 

as likely to be contaminated by atmospheric instabilities that are encountered in measurements at ground level.

%ULHI5HYLHZRI([LVWLQJ'DWDEDVH

A brief summary of the in-Àight supersonic Àow-¿eld database that has been gathered over six decades is provided 

in table 4.2 and includes the test aircraft, location of the Àow-¿eld observation about the aircraft, number of body 

lengths (h/O) from the test aircraft, the technique used, type of results acquired, the time period of the observations, 

and the publication source. An examination of the information contained in the chart indicates that the present 

sonic boom Àow-¿eld database is a result of 13 experiments involving 12 different aircraft – the F-100, F-104, 

B-58, F-106, ;B-70, F-18, SR-71, T-38, F-4, F-5E, SSBD, and F-15 Quiet Spike. The majority of Àow-¿eld 

experiments (identi¿ed in table 4.2) have been conducted using supersonic aircraft with instrumented probes and 

Àying below the test aircraft at distances of from 0.4 to 95 body lengths, and also above and to the side of the test 

aircraft from 1 to 33 body lengths away (refs. 4.1 – 4.17 ).

107

(a) SAF setup on runway at Wallops. (b) Schlieren setup for aircraft in Àight. 

(c) SAF of T-38 at 32,000 ft slant range and Mach 1.1. (d) SAF of F-18 at 60,000 ft slant range and Mach 1.4.

Figure 4.2. 'HVFULSWLRQDQGUHVXOWVIURPJURXQGEDVHG6FKOLHUHQDGDSWHGIURPUHI
Chapter 4 In-Flight Flow-Field Signature Measurements

Airborne measurements using transducers carried aloft on blimps (ref. 4.5) and stationary transducers located on a 

high tower (refs. 4.8 – 4.11) have provided very useful information but are most useful in measuring the far-¿eld 

boom signatures due to their close proximity to the ground. 

The most recent developments in Àow-¿eld de¿nition techniques that can be used to describe the nature of the 

shock-Àow ¿eld generated by an aircraft are the subsonic airborne systems (refs. 4.12, 4.13, 4.15 and 4.16). 

To minimize the non-stationary inÀuences on measurements using sailplanes, their Àights should be Àown 

perpendicular to the generating aircraft Àight track and directly under the aircraft. Subsequent ¿gures provide 

details of measurements made on several of the con¿gurations listed in table 4.2 and include those references (4.2 

– 4.4, 4.6, 4.7, 4.12, and 4.14 – 4.17).

7DEOH,Q)OLJKW6XSHUVRQLF)ORZ)LHOG'DWDEDVH

(DUO\)OLJKW7HVWV

Insight into Nature of Flow Field

The ¿rst in-Àight Àow-¿eld tests undertaken with the objective of determining and measuring the shock-wave 

pressure pattern surrounding an F-100 aircraft in steady-level supersonic Àight was at Edwards Air Force Base 

in 1956 (ref. 4.2). At the time, the Century series jet ¿ghter aircraft, capable of Àying at supersonic speeds with 

ease, were being introduced and there was an urgent need to extend the general knowledge of the shock waves 

that generated the booming noise.

108
Chapter 4 In-Flight Flow-Field Signature Measurements

Time histories of the variation in static pressure caused by the shock waves were obtained by Àying an F-100 

aircraft, instrumented for static pressure measurements, through the shock waves generated by a second F-100. 

Fly-by passes were made to the right of and below the generating aircraft, which was Àying at a speed of Mach 

1.05 and an altitude of 35,000 feet. The separation distance between the two aircraft was varied from about 85 

to 1700 feet. Several passes were also made below the generating aircraft Àying at a speed of Mach 1.05 and an 

altitude of 25,000 feet with the separation distance varying between about 200 and 1000 feet.

The variations of static pressure experienced during the Ày-by¶s were measured by the use of a differential 

pressure transducer and were recorded on a multiple channel oscillograph. A photo panel operated by the pilot 

recorded Mach number and altitude. Pressure transducers were located in the nose compartment of the F-100 and 

were connected to two static holes located on the test nose boom. Provisions were included to permit the pilot 

to close off one side of the pressure cell when the aircraft had been stabilized at the desired Mach number and 

altitude. This established a reference static pressure. During rapid climbs and descents both sides of the pressure 

cell were opened to preclude the possibility of overloading the cell. The separation distance between the aircraft 

was obtained by using a 35-mm movie camera mounted in the canopy of the instrumented aircraft. Continuous 

photographs were made of the shock generating aircraft during the passes. Then, using the known aircraft length, 

camera focal length, and measured image size it was possible to compute the range and azimuth.

Eighteen of the twenty signatures measured from these Àight tests are shown in ¿gure 4.3 (ref. 4.2). The variation 

in signature length is a result of the probing aircraft at different closure rates through the generating aircraft Àow 

¿eld. It can be seen that in the near ¿eld of the aircraft three or four shocks are evident and these are coalescing 

to an N-wave as distance from the aircraft increases. Signature overpressures varied from about 12 lbs/ft2

 at the 

close-in distances to about 2 lbs/ft2

 at the largest distances. Although only the nearest and furthest signatures are 

labeled with bow and tail wave overpressures, all the traces are to the same scale. Note also that in the near ¿eld, 

the tail shock pressures are greater than the bow shock pressures.

109

Figure 4.3. ,QÀLJKWÀRZ¿HOGVLJQDWXUHVPHDVXUHGEHORZDQGWRWKHVLGHRIDQ)DLUFUDIWDW

0DFKDGDSWHGIURPUHI
Chapter 4 In-Flight Flow-Field Signature Measurements

It should be noted that these signatures lack ¿delity in describing the shock rise times as a result of the measurement 

system frequency response. In addition, they were obtained at relatively low Mach numbers, separation distances 

are estimated, and aircraft weight is not provided. However, considerable amounts of information were gained 

from their analysis and include con¿rmation of current prediction codes in calculating the number and strength of 

local shocks and to con¿rm predictions of shock coalescence (ref. 4.18).

Measurements of Near-Field Shocks from Passing Aircraft

In 1960, a series of in-Àight Àow-¿eld probe measurements were made to the side of an F-100, F-104, and B-58 

at distances of from 120 to 425 feet (ref. 4.3). Data were obtained on the F-100 and F-104 at Mach 1.2 and on the 

B-58 at Mach 1.3 to Mach 1.8. The Àow ¿eld to be measured was generated by the lead airplane, which was Àown 

at a pre-selected Mach number. The passing airplane was Àown through this Àow ¿eld at a constant passing rate 

and variations in static pressure were measured by a sensitive pressure transducer mounted in the nose boom of 

the passing airplane. To determine the lateral-separation distance, a motion picture camera was mounted on the 

passing airplane to photograph the lead airplane. The Àight altitude at which these Àight tests were conducted is 

not given in the report nor is the weight of each aircraft. Figure 4.4 presents the measured signatures (ref. 4.3). 

Because of the experimental procedure used, the absolute lengths of the Àow ¿elds were not determined; therefore, 

the measured pressure signatures shown in ¿gure 4.4 are presented in terms of non-dimensional distances between 

the front and rear shocks.

110

Figure 4.4. ,QÀLJKWÀRZ¿HOGVLJQDWXUHVPHDVXUHGWRVLGHRIDLUFUDIWDGDSWHGIURPUHI
Chapter 4 In-Flight Flow-Field Signature Measurements

It can be observed that the measured signature data is a result of readings taken at discrete time intervals from the 

continuous pressure traces obtained with the transducer in the probe aircraft nose boom. As such, details of actual 

shock rise time and shock wave closure at the tail shock are not possible, although the actual number of shocks is 

shown. In addition, calculated boom signatures were also made, as shown by the solid traces on the chart, using 

the Whitham equivalent body analysis (ref. 4.19). Since the character of the signatures is volume dominated, one 

would expect fairly good correlation between prediction and measurements. It should be noted that the normal 

area distributions (i.e., Mach 1.0) were used in the calculations shown on the ¿gure and they suf¿ce for the low 

Mach cases. At the Mach 1.6 and 1.8 conditions for the B-58, large discrepancies were anticipated and observed 

in the vicinity of the tail shock. The correlation was greatly improved by using the area distributions associated 

with the Àight Mach numbers.

Unlike the F-100 signatures, which were made over large distances (¿g. 4.3), information regarding shock 

coalescence from the data in ¿gure 4.4 does not yield much information. However, knowledge and lessons learned 

can be gleaned from data regarding the inÀuence of inlet spillage and nacelle shocks on the boom signature.

Insight into Effects of Aircraft Lift

With the advent of the U. S. SST program, there was a need for in-Àight Àow-¿eld measurements above and below 

a relatively large aircraft in order to assess existing boom prediction codes and their ability to account for both 

lift and volume effects on the sonic boom signature. Shock coalescence was also of interest regarding sonic boom 

signature freezing, a condition where Hayes¶ theory (ref. 4.20) predicts that signature shape beyond the point of 

freezing will persist inde¿nitely below the aircraft to the ground.

In response to the need for insight into the volume and lift effects on boom signatures, a series of in-Àight Àow-

¿eld measurements were conducted at EAFB in 1963 by NASA and the USAF involving the 96.8-foot long B-58 

(shown in ¿g. 4.5) as the boom generating aircraft and a specially instrumented F-106 as the probing aircraft 

(ref. 4.4). The B-58 generating aircraft was Àown at about Mach 1.6 in the altitude range of from 40,000 – 48,000 

feet with gross weights varying from about 83,000 – 115,000 pounds. 

111

)LJXUH ,QDVHULHVRILQÀLJKWÀRZ¿HOGPHDVXUHPHQWLQYHVWLJDWLRQVZHUHFRQGXFWHGDW

(GZDUGV$LU)RUFH%DVHLQYROYLQJWKHIRRWORQJ%VKRZQDERYHDVWKHERRPJHQHUDWLQJDLUFUDIW

DQGDVSHFLDOO\LQVWUXPHQWHG)DVWKHSURELQJDLUFUDIW

86$LU)RUFHSKRWR
Chapter 4 In-Flight Flow-Field Signature Measurements

During the Àight tests, both radar and optical (Askania) tracking were accomplished. The radar plotting-board 

tracks were used for ground control of the airplanes while they were getting into the proper position for the test 

run. The Askania tracking data were used in the data reduction process for determining the speeds and positions 

of the airplanes during the actual recording of data. One Askania network of three stations was used to track the 

generating airplane, and a second Askania network of three stations was used to track the instrumented airplane. 

Accuracy of space positioning was quoted as 1 foot and airplane velocity within an accuracy of 1 foot per 

second. 

Seven penetrations were made and included two probings above the B-58 at distances of from about 1800 – 2000 

feet and ¿ve probings below the aircraft at distances of about 1300 – 9000 feet. Measurements of the boom 

signature were also acquired at ground level. Figure 4.6 presents a schematic of the aircraft and shock Àow ¿eld 

with actual tracings of the measured boom signatures above and below the aircraft Àying at a speed of about Mach 

1.6, an altitude of 48,000 feet, and a gross weight of about 115,000 pounds.

112

)LJXUH ,QÀLJKWVRQLFERRPVLJQDWXUHVPHDVXUHGDERYHDQGEHORZD%DLUFUDIWDGDSWHGIURPUHI
Chapter 4 In-Flight Flow-Field Signature Measurements

Examination of the signatures revealed several signi¿cant features. Below the aircraft at 1355 feet, the pressure 

signature contains four shocks – the bow and tail shocks plus the shocks off the front and rear of the MB-3 pod 

carried under the aircraft. As these shocks propagate downward below the aircraft they coalesce and the signatures 

progress from saw-tooth in character to an N-wave at about 9000 feet. Another obvious observation is that 

aircraft lift effects on boom signatures are evident when comparing the signatures measured above and below the 

aircraft at equal distances, especially in regards to the amplitude and location of the shocks.

The inÀuence of lift on the sonic boom signature was further de¿ned by Àying the B-58 at 83,000 pounds gross 

weight at a lower altitude of 40,000 feet and about the same Mach number. The results of the two measurements 

obtained at about 1800 feet distance are given in ¿gure 4.7. 

Referring to ¿gure 4.7(a), a distinct difference in the above and below measured signatures, as related to the 

aircraft geometry, is evident in terms of the number of shocks. It can also be seen in ¿gure 4.7(b) that, with the 

aircraft at nearly the same lift coef¿cient, the contrast between the two boom signatures measured at nearly the 

same separation distance above and below the aircraft is much greater below the aircraft due to the lift contribution.

Interestingly, with the exception of some unpublished correlations between the close-in measurements and 

prediction, this probing database has not been published before. Part of the reason is that a good geometric and 

wave drag description of the aircraft was not available at the time. Such information is now available (ref. 4.21). 

During the 1966–67 U. S. National Sonic Boom Program (ref. 4.22), the opportunity was taken to obtain in-Àight 

Àow-¿eld measurements on the 185-foot long delta-wing ;B-70 aircraft (see ¿gures 4.8 and 4.9) at EAFB. Sonic 

boom signatures were acquired above and below the ;B-70, which was Àown at an altitude of about 37,000 feet, 

a speed of Mach 1.5, and a weight of about 333,000 pounds. The probing aircraft was an F-104 instrumented with 

the same nose probe used previously on the F-106 probes of the B-58 (ref. 4.4). Six signatures were obtained 

including one measured at about 3000 feet above, but about 7000 feet laterally from the aircraft Àight path 

centerline, and ¿ve signatures below the aircraft at distances of about 2000 feet and 5000 feet. Measurements 

113

Figure 4.7. ,QÀLJKWVLJQDWXUHVPHDVXUHGDERYHDQGEHORZD%DWVLPLODUOLIWFRHI¿FLHQWVDGDSWHGIURPUHI

(a) Aircraft layout to signature character.

(b) Comparison of signatures.
Chapter 4 In-Flight Flow-Field Signature Measurements

were also obtained at ground level. The same precision ground-based radar and optical (Askania) tracking that 

was used to position the B-58 and F-106 probing tests was used for the ;B-70/F-104 probing tests.

These measurements were highlighted at the time of the Àight tests (ref. 4.6). A ¿nal analysis and documentation 

of the results are contained in reference 4.7. Three of the six in-Àight measured signatures are shown in schematic 

form in ¿gure 4.10 along with a signature measured at ground level. 

114

86$LU)RUFHSKRWR

1$6$SKRWR(&1

)LJXUH 'XULQJWKH861DWLRQDO6RQLF%RRP3URJUDPVRQLFERRPVLJQDWXUHV

ZHUHDFTXLUHGDERYHDQGEHORZWKH;%ZKLFKZDVÀRZQDWDQDOWLWXGHRIDERXWIHHWD

VSHHGRI0DFKDQGDZHLJKWRIDERXWSRXQGV

)LJXUH 7KH1RUWK$PHULFDQ;%$9DON\ULHHVFRUWHGE\D%+XVWOHUFKDVH

DLUFUDIWPDNLQJDODQGLQJDSSURDFKDW($)%7KH;%LQQRUPDOÀLJKWFRQ¿JXUDWLRQ

LVVKRZLQJSDLQWMREZHDUUHVXOWLQJIURPWKHULJRUVRIWKHKLJKVSHHGÀLJKWWHVWUHJLPH
Chapter 4 In-Flight Flow-Field Signature Measurements

It can be seen that the mid-¿eld boom signatures are complex and have not yet coalesced to an N-wave at the 

ground (h/Oa 180). Here again, as in the case of the B-58 Àow-¿eld measurements (ref. 4.4) previously discussed, 

the lack of ;B-70 geometric and wave drag descriptions did not allow their use in CFD predictions. Details 

regarding ;B-70 geometry, along with a wave drag description, are now available (ref. 4.21).

Validation of CFD Codes

SR-71 Aircraft

In-Àight Àow-¿eld measurements below the 107-foot long NASA SR-71, shown at the top of ¿gure 4.11, were 

accomplished as part of the NASA HSR Program. NASA Dryden Flight Research Center¶s (DFRC¶s) F-16;L, 

shown at the bottom of ¿gure 4.11, was used as the probing aircraft and was ¿tted with an instrumented nose probe 

that measured the pressure ¿eld. Space positioning and separation distances between the SR-71 and the F-16;L 

(see ¿gure 4.12) were provided through the use of ground-based precision radar and onboard GPS. Figure 4.12 

presents a schematic of the Àow-¿eld measurements. The SR-71 was Àown in the Mach range 1.25 – 1.48 and 

at altitudes of from 31,000 feet to 48,000 feet at gross weights varying from 74,000 pounds to 118,000 pounds. 

F-16;L probe measurements were acquired in the near- and mid-¿eld at distances of about 500 feet to about 

10,000 feet below the SR-71. In-Àight measurements were also obtained at altitudes of about 10,000 feet above 

the ground using the quiet <0-3A Quiet Star, a turboprop-powered glider aircraft, equipped with microphones. 

Boom signatures at ground level were also measured.

115

)LJXUH ,QÀLJKWVRQLFERRPVLJQDWXUHVPHDVXUHGDERYHDQGEHORZWKH;%DLUFUDIWDGDSWHGIURPUHI
Chapter 4 In-Flight Flow-Field Signature Measurements

116

1$6$SKRWR(&

Figure 4.11. 1$6$¶V65DQG);/VKLSÀ\LQIRUPDWLRQRQDVRQLFERRPUHVHDUFKPLVVLRQ

Figure 4.12. 65VKRFNÀRZ¿HOGPHDVXUHPHQWDUUDQJHPHQWLOOXVWUDWLRQ
Chapter 4 In-Flight Flow-Field Signature Measurements

At the time of these Àight experiments, a signi¿cant effort in sonic boom minimization was taking place under the 

HSR program. CFD activities were widespread and there was a need for near-¿eld in-Àight signature measurements 

that would contribute to code validation. In particular, knowledge of how accurately the codes predicted shock 

coalescence as the complex near-¿eld signature propagated to the ground was desired. The effect of inlet nacelle 

shocks, which had been shown in wind-tunnel tests to have a signi¿cant inÀuence on shock coalescence, was 

especially important. Over 105 probe signatures were obtained.

Figure 4.13 shows a schematic of the Àow ¿eld of the SR-71 with measured signatures (ref. 4.12) superimposed at 

various distances below the aircraft at about 500, 2000, 5000, and 8000 feet. The aircraft was Àying at a speed of 

Mach 1.25, an altitude of 31,000 feet, and a gross weight of about 100,000 pounds. A complex sawtooth signature 

was observed at about ¿ve body lengths (a 500 ft) from the aircraft with shocks emanating from the nose and 

canopy followed by a very strong inlet/nacelle wing shock that essentially dominated the front and mid-part of 

the Àow ¿eld out to a distance of about 8000 feet (h/O a 80). Beyond this distance, an N-wave was established and 

continued to the ground.

It is important to note that the SR-71 inlets were designed for full Àow at the design Àight conditions of Mach 

3.0 at an altitude of 80,000 feet. Thus, at the off-design conditions at which the probe measurements were made, 

considerable inlet Àow spillage occurs even though the inlets have a translating centerbody to control the Àow. 

This spilled Àow contributes signi¿cantly to shock strength and shock coalescence.

Figure 4.14 (ref. 4.12) represents the same data as in ¿gure 4.13 but the various signatures are superimposed to better 

visualize the changes with probe separation distances. The ¿gure shows the measured in-Àight SR-71 sonic boom 

signatures where all the bow shocks are aligned. Several trends are noteworthy. As vertical separation between 

the SR-71 and F-16;L probe aircraft was increased, the overall signature length increased, the overpressures 

decreased, and the inlet and canopy shocks moved toward the bow shock. One interesting and unexpected trend 

concerned the plume pressures aft of the tail shock. All of the plumes from each signature collapsed to one curve.

117

Figure 4.13. ,QÀLJKWÀRZ¿HOGPHDVXUHPHQWVEHORZWKH65DLUFUDIWDGDSWHGIURPUHI
Chapter 4 In-Flight Flow-Field Signature Measurements

A comparison of Àight-test data and the computated pressure signatures by Fouladi (ref. 4.23) are presented in 

¿gure 4.15 for the SR-71. The MDBOOM code (ref. 4.24) was used to propagate the computed signature to the 

distance at which the Àight measurements were made.

The comparison shows reasonable agreement, particularly in the ¿rst half of the signature. The pressure peak in 

the inlet region was under-predicted in the computed signature. This may have been due to the lack of modeling 

of some features such as by-pass doors on the engine in the CFD computations.

118

Figure 4.14. 'DWDSUREHVIRUDQ65DW0DFKDQGDQDOWLWXGHRIIHHWDGDSWHGIURPUHI

)LJXUH &RPSDULVRQRIPHDVXUHGDQGSUHGLFWHGLQÀLJKW65ERRPVLJQDWXUHDGDSWHGIURPUHI
Chapter 4 In-Flight Flow-Field Signature Measurements

F-5E Inlet Spillage Shock Measurements (ISSM)

The F-5E Tiger II in-Àight probe measurements Àight-test program of 2002 was conducted to de¿ne the supersonic 

Àow ¿eld below the F-5E at various distances and with particular emphasis on the performance of the aircraft¶s 

inlets and the amount of air spillage associated with certain Àight conditions. This effort was given the name the 

Inlet Spillage Shock Measurements (ISSM) test and provided information that was crucial to the design of the 

Shaped Sonic Boom Demonstrator (SSBD), a modi¿ed version of the F-5E Tiger II that would produce a Àattop 

boom signature (ref. 4.25) and is subsequently discussed. The success of the SSBD program depended on the 

accuracy of CFD as a predictive tool and thus high correlation was necessary between the measured and predicted 

signatures on the F-5E.

The ISSM test was conducted at EAFB using an instrumented NASA F-15B aircraft to probe the F-5E Àow ¿eld 

(see ¿g. 4.16) at a nominal Mach number of 1.4 at an altitude of about 32,000 feet. 

Fifty-six pressure signatures were collected during four Àight tests. Of the 56 pressure signatures collected, four 

met the criteria for CFD validation based upon the criteria used in determining acceptable signatures. These four 

criteria were

1. Small vertical separation distance from the F-5E (optimally 50 to 200 feet)

2. Fairly constant separation distance

3. Fairly steady-state Àight conditions for the F-5E (no maneuvers by the F-5E)

4. F-15B generally directly beneath the F-5E (no large off-track variation of the relative Àight paths)

Some results are presented in ¿gure 4.17 (ref. 4.14) that show a comparison of signature 47, measured 94 feet 

below the aircraft, with CFD predictions assuming three inlet mass-Àow conditions, one 10 percent greater and 

10 percent less than the design case of 58.6 lbs/sec.

119

1$6$SKRWR(&

)LJXUH $QLQVWUXPHQWHG1$6$)%DLUFUDIWSUREHVDQ)(VXSHUVRQLFÀRZ¿HOGRQDQ,QOHW6SLOODJH6KRFN

0HDVXUHPHQWV,660ÀLJKWWHVWKLJKDERYHWKH0RMDYH'HVHUWDW(GZDUGV$LU)RUFH%DVH&DOLIRUQLDLQ
Chapter 4 In-Flight Flow-Field Signature Measurements

Two major ¿ndings were evident. The CFD results matched the measured signature in regard to the number, 

location, and magnitude of the shocks, especially of the nose, inlet, and wing shocks and it was also established 

that the pressure signature was not signi¿cantly sensitive to the inlet mass Àow. The inlet and wing shocks moved 

aft and decreased in amplitude as mass Àow was increased and moved forward and increased in magnitude as 

mass Àow was decreased. Comparing the location of the computed shocks with the measured Àight-test data 

showed that the nominal value of 58.6 corrected mass Àow (CMF) matched best, which validated the pre-test 

prediction of inlet mass Àow. Such ¿ndings assured con¿dence that the modi¿cations to the SSBD design would 

provide the desired Àat top signature.

Shaped Sonic Boom Demonstrator (SSBD) Aircraft

In 1988, a 2-day Sonic Boom Workshop (ref. 4.26) was held to assess the state of the art in sonic boom physics, 

methodology, and understanding and to determine areas in which additional sonic boom research was needed. 

Three priority research areas were identi¿ed – (1) establishing the criteria for an acceptable sonic boom waveform, 

(2) designing a viable aircraft to a desired shaped waveform, and (3) quantifying the atmospheric effects on shaped 

waveforms. Maglieri, Sothcott, and Keefer (ref. 4.27) suggested a fourth need – demonstrating the persistence of 

shaped boom signatures to the ground from an aircraft Àying in the real atmosphere. Recognition of this latter need 

led to the SSBD program (ref. 4.25), which utilized an F-5E aircraft modi¿ed as shown in ¿gure 4.18 to produce a 

120

WUDQVODWHGLQDIWDGDSWHGIURPUHI

Figure 4.17. )(SUHVVXUHVLJQDWXUHFRPSDULVRQIRUYDULRXVLQOHWPDVVÀRZUDWHV6LJQDWXUH&)'
Chapter 4 In-Flight Flow-Field Signature Measurements

Àat-top shaped signature at the ground. Modifying the F-5E aircraft to produce a Àat-top bow shock was found to 

be the most straightforward modi¿cation to the aircraft and such a signature would be more distinguishable after 

propagating the large distance between the aircraft and the ground. Additional discussion of signature shaping for 

boom minimization will be presented in Chapter 5.

A detailed Àight program to describe the near-mid and far-¿eld boom signatures associated with the baseline F-5E 

and SSBD aircraft (see ¿g. 4.19) was conducted at EAFB in 2002–2004 (refs. 4.14, 4.15, and 4.16 respectively). The 

measurement setup was similar to that involved during the SR-71 boom measurements (¿g. 4.12), except that the 

F-15B was used to probe the near- and mid-¿eld (from about 1.5 to 15 body lengths below the aircraft) and an L-23 

sailplane was used to obtain measurements of the incident and reÀected signature in the far ¿eld 6000 to 8000 feet 

above the ground. An illustration of the F-5E and SSBD Àow ¿eld measurement arrangement is shown in ¿gure 4.20.

121

1$6$SKRWR(&

1$6$SKRWR

)LJXUH 6KDSHG6RQLF%RRP'HPRQVWUDWRU66%'DLUFUDIW

)LJXUH 7KH6KDSHG6RQLF%RRP'HPRQVWUDWRU66%'DLUFUDIWWRS

SHUIRUPVDUHVHDUFKÀLJKWZKLOHD861DY\)(ÀLHVFKDVH
Chapter 4 In-Flight Flow-Field Signature Measurements

Both aircraft were Àown at a design Mach number of 1.4 and at an altitude of about 32,000 feet. Aircraft gross 

weight at the time of probing was about 13,000 pounds. A total of 56 in-Àight pressure signatures were obtained 

on the F-5E (ref. 4.14) and 68 on the SSBD (ref. 4.15).

An illustration of the characteristics of the signatures observed for the SSBD aircraft is presented in ¿gure 4.21 

(ref. 4.15). Three signatures are shown – one measured in the near-¿eld at about 80 feet below the aircraft, one 

measured using the L-23 sailplane Àying at about 5500 feet above the ground, and one at ground level.

122

)LJXUH ,OOXVWUDWLRQRIWKH)(DQG66%'VKRFNÀRZ¿HOGPHDVXUHPHQWDUUDQJHPHQW

Figure 4.21. ,QÀLJKWÀRZ¿HOGPHDVXUHPHQWVEHORZ66%'DLUFUDIWDGDSWHGIURPUHI
Chapter 4 In-Flight Flow-Field Signature Measurements

The modifications to the F-5E aircraft were designed to alter regions just downstream of the bow-shock portion 

of its N-wave ground signature into a flat-top shape while leaving the aft portion of the N-wave signature 

unaltered. Comparison of the SSBD near-field signature (shown in fig. 4.21) with that of the unmodified 

F-5E (shown in fig. 4.17) illustrates the nature of the change that results in the SSBD near-field signature 

shape. Note that from the inlet shock rearward, both the F-5E and SSBD near-field measured signatures 

are essentially the same. The character of the SSBD near-field signature behind the bow shock, however, is 

altered as a result of the reshaping of the F-5E forebody. Such a change in the near-field signature results in 

the nearly flat-top shape observed in figure 4.21 for the far-field at the sailplane location and at ground level.

A more detailed look at the SSBD near-¿eld signature is provided in ¿gure 4.22. Figure 4.22 shows the signature 

below the SSBD measured in Àight from the NASA F-15B probe aircraft at about 80 feet below the SSBD, which 

is Àying at Mach 1.4 and an altitude of 32,000 feet. Also shown in ¿gure 4.22 is a computed signature from a 

CFD calculation at the same separation distance. The source of each shock is identi¿ed including – the bow, 

forebody, canopy, inlet, leading-edge extension, wing leading edge, wing trailing edge, horizontal tail leading 

edge, recompression shock, and the expansion caused by the exhaust plume.

The design modi¿cations were such as to provide for a strong bow shock that would prevent the following shocks, 

especially from the inlet, leading-edge extension (LE;), and wing leading edge, from moving forward as the 

signature propagated towards the ground. The two shocks located between the bow and inlet shock are associated 

with the slight ramp up of the nose forebody just ahead of the canopy and the canopy shock. Other minor features 

of the aircraft such as the airdata probe at the nose, nose gear doors, and total temperature probes were not included 

in the CFD analysis. On the whole, however, the computed pressure signature captured all of the measured shocks 

and at the correct locations. An excellent match was also observed for the maximum overpressures at the inlet, 

wing, and tail shocks. This provided further evidence that the design changes to the SSBD were proper in that the 

desired initial Àat-top signature was observed in the far ¿eld. Results similar to those of ¿gure 4.22 are derived in 

reference 4.28 as well as ground signatures. 

123

Figure 4.22. 66%'SUHVVXUHVLJQDWXUHFRPSDULVRQEHWZHHQÀLJKWWHVWDQG&)'DQDO\VLVIRUVHSDUDWLRQ

GLVWDQFHDERXWIHHWEHORZWKHDLUFUDIWaERG\OHQJWKVDGDSWHGIURPUHI
Chapter 4 In-Flight Flow-Field Signature Measurements

The reshaping of the SSBD was focused on assuring that the shaped Àat-top boom signature would result at a 

location directly below the aircraft. It was also believed that the shaping inÀuence would extend to some distances 

laterally to each side of the aircraft. In order to assess the robustness of the design changes, near-¿eld Àow-¿eld 

probe measurements were made at several azimuthal angles below and to the side of the SSBD.

In ¿gure 4.23 (ref. 4.15) the near-¿eld measurement of an in-Àight signature at about 85 feet below and 45° 

to the side of the aircraft is presented. In comparing this signature to that measured directly below the SSBD

(¿g. 4.22) it is ¿rst noted that they have similar shock structures. Closer examination shows that the shock 

structure is different on the forebody region and the inlet shock has become more dominant at the 45° location. 

Measurements made at ground level and off track about 20° indicate that the bene¿t of the shaping effect was still 

evident. These measurements suggest that designing minimum shaped signatures must include consideration of 

off-track locations out to lateral cutoff.

F-15B Quiet SpikeTM Aircraft

From April 2004 to February 2007, Gulfstream and NASA DFRC engaged in a Àight-test program to validate 

the technical feasibility of the Quiet SpikeTM (ref. 4.29), a Gulfstream-patented sonic boom mitigation device. 

The Quiet Spike was adapted to the NASA F-15B Àight research aircraft and a total of 32 research Àights were 

conducted between August 2006 and February 2007. 

The arrangement and description of the Gulfstream Quiet Spike adapted to the NASA F-15B is presented in 

¿gure 4.24 (ref. 4.29). The NASA F-15B Quiet Spike Àight research aircraft, with the spike fully extended, is 

shown in ¿gure 4.24(a), ¿gure 4.24(b) provides details of the Quiet Spike geometry, and ¿gure 4.24(c) shows 

the F-15B Quiet Spike Àight research aircraft in Àight with the Quiet Spike fully retracted and extended. These 

Àight tests had two objectives – the ¿rst was to assure the structural integrity of the Quiet Spike design throughout 

its operating envelope and the second was to acquire a description of the supersonic Àow ¿eld near the aircraft 

associated with the Quiet Spike in its fully extended mode.

124

Figure 4.23. 1HDU¿HOGVRQLFERRPVLJQDWXUHPHDVXUHGDWDERXWIHHWEHORZDQG°WRWKHVLGHRI

WKH66%'DLUFUDIWDGDSWHGIURPUHI
Chapter 4 In-Flight Flow-Field Signature Measurements

The Quiet Spike was designed such that the series of weak shocks generated by each of the telescoping sections 

would not coalesce into an N-wave but propagate to the ground in parallel fashion. When the Quiet Spike is 

integrated into a low-boom designed con¿guration it provides the appropriate equivalent area distribution that 

would result in a shaped signature at the ground having an initial ramp shape rather than the abrupt N-wave shock 

(see for example refs. 4.30 and 4.31).

125

1$6$SKRWR('

1$6$SKRWR(' 1$6$SKRWR('

(a) NASA F-15B 836 with fully extended Quiet Spike installed and prepared for SMI testing.

(b) Quiet Spike geometry.

(c) NASA F-15B 836 and Quiet Spike during ¿rst Àight and ¿rst extension Àight.

Figure 4.24. $UUDQJHPHQWDQGGHVFULSWLRQRIWKH*XOIVWUHDP4XLHW6SLNHTMDGDSWHGWRWKH1$6$

)%ÀLJKWUHVHDUFKDLUFUDIWDGDSWHGIURPUHI
Chapter 4 In-Flight Flow-Field Signature Measurements

In December 2006, over 30 near-¿eld probe measurements using the NASA F-15 837 aircraft were made below, 

to the side of, and above the test aircraft Àying at a speed of Mach 1.4 and an altitude of 40,000 feet at distances 

from about 95 to 630 feet to con¿rm the Quiet Spike aerodynamic shaping theory and the coalescence rates of the 

canopy, wing, and inlet shocks on the front end of the F-15B Quiet Spike con¿guration as the shocks propagate 

away from the aircraft.

Because of the strength and persistence of the F-15B shock Àow ¿eld behind the three shock system from the 

Quiet Spike, it was predicted that the Quiet Spike¶s bow shock minimization would not be observable on the 

ground. CFD analysis had shown that the series of shocks from the Quiet Spike would persist to a suf¿cient 

distance from the F-15B aircraft before being overtaken by the F-15B Àow ¿eld. However, the CFD analysis 

also predicted that the bene¿t could be realized on the ground signature when the Quiet Spike is incorporated on 

a low-boom shaped vehicle.

In ¿gure 4.25 (ref. 4.17), an F-15 Quiet Spike near-¿eld signature, measured 95 feet below the aircraft, and a 

comparison with a hybrid CFD calculation are presented. Each of the major shocks associated with the Quiet 

Spike and F-15B Àow ¿eld are also identi¿ed.

The comparison of measured and predicted shocks, the location of the shocks, and magnitude of the shocks are 

excellent, with the exception of the events following the wing trailing-edge shock. In addition, the three shocks 

off the Quiet Spike (stages 1, 2, and 3) are clearly evident and generated as designed. Results of the probing test 

and CFD calculations con¿rmed that parallel propagation of the Quiet Spike weak shocks persisted out to 10 body 

lengths below the F-15. 

In addition to the near-¿eld probing directly below the F-15 Quiet Spike aircraft, off-track measurements were 

also made. These measurements were obtained in order to quantify the Quiet Spike shock strength as a function 

of azimuthal position since the Quiet Spike was designed to have steeper sloping transitions on the top side of the 

conical transitions than on the bottom (see ¿g. 4.24). Early analyses showed that weak shock waves generated by 

the lesser sloping design on the bottom of the spike would propagate downward and persist into the mid ¿eld to 

achieve the desired ground signature.

126

)LJXUH )%4XLHW6SLNHQHDU¿HOGVLJQDWXUHPHDVXUHGIHHWEHORZWKHDLUFUDIWDQGD

FRPSDULVRQZLWKK\EULG&)'FDOFXODWLRQDGDSWHGIURPUHI
Chapter 4 In-Flight Flow-Field Signature Measurements

Sixteen off-track signatures were measured, four of which are presented in ¿gure 4.26 (ref. 4.17) – one measured 

below the aircraft at a distance of about 377.5 feet, one at about 45° to the side 279.5 feet, one at about 90° to the 

side and 426.6 feet, and one at about 115° to the side and above the aircraft at 484.3 feet.

Note that at about 380 feet below the aircraft, the measured signature exhibits the expected three shocks associated 

with the Quiet Spike design, but the third shock is being overridden by the F-15B nose shock at this distance. A 

similar situation is observed at the 45° position. At the position nearly abreast and above the aircraft, only the ¿rst 

and second Quiet Spike shocks are evident. Large changes in the character of the F-15B shock system are evident, 

as expected, as one moves from observations below, to the side of, and above the vehicle due to both geometric 

and lift changes.

The Quiet Spike has proven that it can play a signi¿cant role in achieving the desired area distribution for a 

low-boom vehicle. Since the Quiet Spike is being carried throughout the Àight mission, it would be of interest 

to examine whether Quiet Spike could play a bene¿cial role at off-design conditions, in particular during the 

transition phase of Àight to minimize the focus boom signature.

Flow-Field Database Utilization

Before concluding this chapter, it is useful to brieÀy review the utilization of all the in-Àight Àow-¿eld probe 

measurements that have been acquired over the past 50 years in validating/updating the prediction codes. 

Shown in ¿gure 4.27 are the sketches of the planforms of the eight aircraft for which in-Àight boom signatures 

were obtained. Below these sketches is an indication as to whether the signatures were measured in the near, mid, 

or far ¿eld. This is followed by a listing of the known individuals who have made use of the database, the number 

of signatures utilized, and whether the correlations with theory have been made and published.

127

)LJXUH )%4XLHW6SLNHQHDU¿HOGVLJQDWXUHVPHDVXUHGEHORZWRWKHVLGHRI

DQGDERYHWKHDLUFUDIWDGDSWHGIURPUHI
Chapter 4 In-Flight Flow-Field Signature Measurements

Boom theory was in its infancy and CFD for sonic boom did not exist in 1956 when Mullens (ref. 4.2) completed 

the measurements on the F-100 aircraft. The primary objective of these measurements was to gain knowledge into 

the nature of the shock Àow ¿eld surrounding an aircraft at supersonic speeds and extend the general knowledge 

of the shock waves that produce the booming noise. Even though the 1960 measurements on the F-104 were 

focused on examining the inÀuence of the supersonic Àow ¿eld on the stability and control of other aircraft, Smith 

(ref. 4.3) did show that the signatures calculated using the Whitham equivalent body analysis (ref. 4.19) correlated 

well with the measured signatures (ref. 4.3). 

By the time that Àow-¿eld measurements were conducted on the B-58 and ;B-70 (1963 and 1966, respectively), 

sonic boom theory was greatly advanced as a result of the U. S. SST effort and although CFD was well underway 

it was not focused on the sonic boom arena. Here again, the primary objective of these two measurement efforts 

was to establish the inÀuence of lift on sonic boom and although Carlson and Morris applied existing boom 

codes for comparison with the measured signatures and showed good correlation, the results were never formally 

published.

It was not until the late 1980s and 1990s that a renewed effort was launched to quantitatively describe the nearand mid-¿eld Àow ¿elds from aircraft in supersonic Àight for use in con¿rming the newly developed CFD sonic 

boom prediction codes. This effort began with the SR-71 sonic boom Àight program of 1995 (ref. 4.12) in concert 

with the NASA HSR Program (ref. 4.32) with increased emphasis stemming from the DARPA QSP effort (ref. 

4.33) and followed by the F-5/SSBD and Quiet Spike Àight programs (refs. 4.25 and 4.29) of 2002 to 2004 and 

2006, respectively.

128

)LJXUH8WLOL]DWLRQRILQÀLJKWÀRZ¿HOGPHDVXUHGVLJQDWXUHVZLWKSUHGLFWLRQFRGH
Chapter 4 In-Flight Flow-Field Signature Measurements

&KDSWHU6XPPDU\5HPDUNV

Knowledge of the Àow ¿eld surrounding a supersonic aircraft is paramount to the veri¿cation of prediction codes 

and to the design of an aircraft with an acceptable sonic boom signature. Description of the shock Àow ¿eld is 

needed to provide information on the number, location, and strength of the shock ¿eld and describes how the 

shocks coalesce into ¿nal form in the far-¿eld ground signature. 

Several techniques are available to measure the Àow ¿eld around a supersonic aircraft. These include probing 

the near and mid Àow ¿elds by means of an instrumented aircraft; the use of instrumented sailplanes, blimps, and 

towers to describe the far-¿eld signatures; and airborne and ground-based Schlieren photography methods that 

can provide useful qualitative information.

Probing the near and mid Àow ¿eld of the shock generating aircraft by means of an instrumented aircraft in 

supersonic Àight has been the most utilized Àight research method and provides the clearest detail as to the 

complex nature of the shock Àow ¿eld near the aircraft.

Sonic boom signatures measured in the far ¿eld by means of airborne microphones provide considerable 

information about signature distortion from turbulence in the last few thousand feet near the ground.

&KDSWHU5HIHUHQFHV

4.1 Weinstein, L.; Stacy, K.; Vieira, J.; Haering, E., Jr.; and Bowers, A. Imaging Supersonic Aircraft Shock 

Waves. Journal of Flow Visualization and Image Processing, Vol. 4., No. 3, 1997, pp. 189–1990.

4.2 Mullens, Marshall E. A Flight Test Investigation of the Sonic Boom. AFFTC TN 56-20, Air Research 

and Development Command, U. S. Air Force, May 1956.

4.3 Smith, Harriet J. Experimental and Calculated Flow Fields Produced by Airplanes Flying at Supersonic 

Speeds. NASA TN-D 621, 1960.

4.4 Maglieri, Domenic J.; Ritchie, Virgil S.; and Bryant, John F., Jr. In-Flight Shock Wave Pressure 

Measurements Above and Below a Bomber Airplane at Mach Numbers from 1.42 to 1.69. NASA TN-D1968, Oct. 1963.

4.5 Maglieri, Domenic J. Sonic Boom Flight Research, Some Effects of Airplane Operations and the 

Atmosphere on Sonic Boom Signatures. NASA SP-147, 1967, pp. 25–48.

4.6 Maglieri, D. J.; Huckel, V.; Henderson, H. R.; and Putnam, T. Preliminary Results of ;B-70 Sonic Boom 

Field Tests During National Sonic Boom Evaluation Program. National Sonic Boom Evaluation Of¿ce

Sonic Boom Experiments at Edwards Air Force Base. NSBEO-1-67 (Contract AF 49(638)-1758, Stanford 

Research Institute, July 28, 1967. Part II, Annex C, pp. C-II-1 to C-II-17.

4.7 Maglieri, Domenic J.; Henderson, Herbert R.; and Tinetti, Ana F. Measured Sonic Boom Signatures 

Above and Below the ;B-70 Airplane Flying at Mach Number 1.5 and 37,000 Feet. NASA/CR 2011-

217077, April 2011.

4.8 Maglieri, Domenic J.; Hilton, David A.; Huckel, Vera; and Henderson, Herbert R. Measurements of 

Sonic Boom Signatures From Flight at Cut-Off Mach Number. NASA SP-255, Oct. 1970, pp. 243–254.

4.9 Hubbard, H. H.; Maglieri, D. J.; and Huckel, V. Variability of Sonic Boom Signatures With Emphasis on 

the Extremities of the Ground Exposure. NASA SP-255, Oct. 1970, pp. 351–359.

4.10 Haglund, George T. and Kane, Edward Analysis of Sonic Boom Measurements Near Shock Wave 

Extremities for Flight Near Mach 1.0 and for Airplane Accelerations. NASA CR-2417, 1974.

129
Chapter 4 In-Flight Flow-Field Signature Measurements

4.11 Haglund, George T. and Kane, Edward, Jr. Flight Test Measurements and Analysis of Sonic Boom 

Phenomena Near Shock Wave Extremity. NASA CR-2167, Feb. 1973.

4.12 Haering, Edward A., Jr.; Ehernberger, L. J.; and Whitmore, Stephen A. Preliminary Airborne Measurements 

for the SR-71, Sonic Boom Propagation Experiment. NASA TM 104307, Sept. 1995.

4.13 Stansbery, Eugene; Baize, Daniel; and Maglieri, Domenic J. In-Flight Technique for Acquiring Mid- and 

Far-Field Sonic Boom Signatures. NASA CP-1999-209699, Dec. 1999, pp. 249–268.

4.14 Meredith, K.; Dahlin, J.; Graham, D.; Haering, E.; Maline, M.; and Page, J. Flight Test Measurement and 

Computational Fluid Dynamics Correlation of F-5E Off-Body Pressures. AIAA-2005-0006, Jan. 2005.

4.15 Haering, E.; Murray, J.; Purifoy, D. D.; Graham, D. H.; Meredith, K. B.; Ashburn, C. E.; Stucky, J. Airborne 

Measurements of Shaped Sonic Boom Demonstration Aircraft Pressure Signatures with Comparison to 

CFD. AIAA 2005-0009, Jan. 2005.

4.16 Plotkin, K.; Haering, E.; Murray, J.; Maglieri, D.; Salamone, J.; Sullivan, B.; and Schein, D. Ground Data 

Collection of Shaped Sonic Boom Demonstration Aircraft Pressure Signatures. AIAA 2005-0010, Jan. 

2005.

4.17 Howe, D. C.; Waithe, K.; and Haering, E. A. Quiet SpikeTM Near Field Flight Test Pressure Measurements 

with Computational Fluid Dynamics Comparison. AIAA 2008-0128, Jan. 2008.

4.18 Hicks, Raymond M. and Thomas, Charles L. A Preliminary Report on Shock Coalescence. NASA SP255, Oct. 1970, pp. 297–305.

4.19 Whitham, G. B. The Flow Pattern of a Supersonic Projectile. Computational Pure and Applied 

Mathematics, Vol. V, No. 3, Aug. 1952, pp. 301–348.

4.20 Hayes, Wallace D.; Haefeli, Rudolph C.; and Kulsrud, H. E. Sonic Boom Propagation in a Strati¿ed 

Atmosphere, With Computer Program. NASA CR-1299, 1969.

4.21 Tinetti, Ana F.; Maglieri, Domenic J.; Driver, Cornelius; and Bobbitt, Percy J. Equivalent Longitudinal 

Area Distributions of the B-58 and ;B-70-1 Airplanes for use in Wave Drag and Sonic Boom Calculations. 

NASA/CR-2011-217078, March 2011.

4.22 National Sonic Boom Evaluation Of¿ce Sonic Boom Experiments at Edwards Air Force Base. 

NSBEO-1-67 (Contract AF 49(638)-1758), Stanford Research Institute, July 28, 1967.

4.23 Fouladi, Kamran CFD Predictions of Sonic-Boom Characteristics for Unmodi¿ed and Modi¿ed SR-71 

Con¿gurations. NASA CP-1999-209699, Dec. 1999, pp. 219–236. 

4.24 Plotkin, K. J. Calculation of Sonic Boom From Numerical Flow-Field Solutions MDBOOM Version 2.2, 

Wyle Research Report WR 92-14, July 1992.

4.25 Pawlowski, J. W.; Graham, D. H.; Boccadoro, C. F.; Coen, P. G.; Maglieri, D. J. Origins and Overview of 

the Shaped Sonic Boom Demonstration Program. AIAA 2005-0005, Jan. 2005.

4.26 Darden, C. M.; Powell, C. A.; Hayes, W. D.; George, A. R.; and Pierce, A. D. Status of Sonic Boom 

Methodology and Understanding. NASA CP3027, Jan. 19–20, 1988.

4.27 Maglieri, D. J.; Sothcott, V. E.; and Keefer, T. N., Jr. Feasibility Study in Conducting OverÀight 

Measurements of Shaped Sonic Boom Signatures Using the Firebee BQM-34E, RPV. NACA CR189715, 

Feb. 1992.

130
Chapter 4 In-Flight Flow-Field Signature Measurements

4.28 Kandil, Osama A.; Ozcer, Isik A.; Sheng, ;udong; and Bobbitt, Percy J. Comparison of Full Potential 

Propagation-Code Computations with the F-5E 3Shaped Sonic Boom Experiment ́ Program. AIAA 2005-

0013.

4.29 Cowart, R. and Grindle, T. An Overview of the Gulfstream/NASA Quiet SpikeTM Flight Test Program. 

AIAA 2008-0123, Jan. 2008. 

4.30 Howe, D. C. Improved Sonic Boom Minimization with Extendable Nose Spike, AIAA 2005-1014, Jan. 

2005.

4.31 Howe, D. C. Sonic Boom Reduction Through the Use of Non-Axisymmetric Con¿guration Shaping. 

AIAA 2003-0929, Jan. 2003.

4.32 Committee on High Speed Research, ASEB, NRC U.S. Supersonic Commercial Aircraft Assessing 

NASA¶s High Speed Research Program, National Academics Press, March 1958.

4.33 Wlezien, R. and Veitch, L. Quiet Supersonic Platform. AIAA Paper 2002-0143, Jan. 2002.

131

Chapter 5 Approaches to Sonic Boom Minimization

133

CHAPTER 5 APPROACHES TO SONIC BOOM MINIMIZATION

This chapter presents a review of sonic boom minimization approaches through aircraft operations, aircraft shaping, 

and alterations of the airstream around an aircraft. Aircraft operations include changes in Àight altitude and Mach 

number, increasing Àight path angle, Àying at cut-off Mach number where the speed of the aircraft over the 

ground is less than the speed of sound at the ground, tailoring the Àight path during cruise, and Àying an unsteady 

Àight path as a form of active control. Aircraft shaping includes changing the con¿guration planform such that 

the volume and lift distributions and propulsion integration are arranged in such a manner as to produce a ground 

signature that is either a substantially reduced N-wave or typically a non-N signature with increased rise time 

and/or reduced overpressure. The goal is to soften the boom’s loudness to the point where it is not objectionable, 

potentially not even heard. This is considered to be the most common approach to boom minimization, and is 

discussed in detail in Chapter 7. 

The most extreme approaches to boom minimization alter the airstream surrounding the aircraft so as to increase 

its effective length and ¿neness ratio. The goal is similar to shaping, but is accomplished without a physical 

aerodynamic body. Other exotic approaches that have been investigated include propulsion-airframe integration 

schemes and unique arrangements of vehicles to essentially increase the equivalent vehicle length or shield the 

shocks from ground observers. Each of these minimization approaches are designed to alter the boom signature 

intensity and shape and in some cases perform supersonic Àights that are referred to as boomless. It is appropriate, 

therefore, to begin with a brief discussion of the term “boomless”.

Boomless Flight

Throughout most of the studies related to boom minimization via shaping and particularly airstream alterations, 

the term “boomless Àight” is mentioned. A brief discussion of the meaning of this term and how it translates in 

terms of boom loudness and building response follows.

Schematic of Flight Situation

In ¿gure 5.1, two aircraft Àight situations are schematically shown that will aid in discussion of boomless Àight. 

The situation to the left of ¿gure 5.1 is for an aircraft Àying steady-level at a low supersonic Mach number such 

that its speed over the ground (Vg

) is less than the speed of sound at the ground (ag). Thus, the aircraft is Àying 

at a speed below Mach cutoff (MCO) – that is, the Àight Mach number at which the shocks terminate and reÀect 

back upwards. Acoustic disturbances are only observed if the termination point is within a few hundred feet of 

the ground. Thus, Àights below MCO can be classed as boomless even though they are obviously not shock free.

Figure 5.1. 8QGHUVWDQGLQJWKHPHDQLQJRIERRPOHVVÀLJKW
Chapter 5 Approaches to Sonic Boom Minimization

134

It will be shown later on in this chapter that the practical range for MCO Àight (i.e. where the shocks do not reach 

the ground, ¿g. 5.1) is in the Mach 1.01 to Mach 1.3 range and that, at the shock termination, a caustic (focus) 

condition exists wherein the boom overpressures can be as much as 3.0 times the boom levels generated by the 

aircraft Àying at the same altitude at Mach numbers above cutoff Mach number MCO. 

The schematic to the right of ¿gure 5.1 is for the case of very long and slender (a600 to 900 feet) aircraft having 

very high ¿neness ratios of about 60 to 80 as compared to about 16 to 20 for supersonic transport designs and 8 

to 10 for subsonic aircraft. The ¿neness ratio is de¿ned as the fuselage length divided by the fuselage maximum 

diameter. High ¿neness ratios are desirable for supersonic vehicles in order to reduce wave drag. Acquiring such 

extreme lengths had been the focus of the majority of the airstream alteration (phantom body) concepts, which 

will be discussed later in this chapter. The Àight Mach number of these studies ranges from about 1.4 to 3.0. The 

resulting boom signature at the ground is no longer the classical N-wave but one with very long shock rise times, 

almost approaching a sine-wave. Since the ear responds to rapid changes in pressure, a signature of the sort shown 

on the right side of ¿gure 5.1 would be less likely to be heard by outdoor observers. Once again, as for the MCO

case, a long vehicle producing a ¿nite rise time signature is boomless Àight (only for outdoor observers – as will 

be shown on the next ¿gure) but not shock free Àight.

Boom Responses

Sonic booms are experienced by people both outdoors and indoors, and, as will be discussed in Chapter 8, their 

responses can differ considerably. In fact, it has been found that objections to booms can be greater for those 

observing them indoors as compared to outdoors. The thrust of all sonic boom minimization activities is to 

design an aircraft that produces a boom signature with a shape and maximum overpressure that is acceptable both 

outdoors and indoors.

Loudness (the magnitude of the sound) is one measure of boom acceptance. The inÀuence of altering the sonic 

boom signature’s shape on observed loudness is presented on the left hand portion of ¿gure 5.2 (ref. 5.1). Relative 

loudness is shown for four boom signatures, all having the same maximum overpressure of 1.0 lb/ft2

. They have 

varying levels of the initial shock strength from 1.0 lb/ft2

 (for the N-wave) to 0.125 lb/ft2 followed by ramps up to 

the maximum  ̈p = 1.0 lb/ft2

. Note that the initial shock on the left has zero rise time. It is apparent that decreasing 

the initial shock strength decreases loudness. Because the human ear responds to rapid changes in pressure, 

humans consequently hear only the actual shock. Note that there is an 18 dB reduction in loudness for a shaped 

signature having a 0.125 lb/ft2

 initial shock (with 1.0 lb/ft2 maximum level) as compared to the N-wave having 

an initial shock of 1.0 lb/ft2 (also the maximum level). If one carries the rise time analogy a step further to a sine 

wave signature of the same amplitude and period as the N-wave, it would be inaudible outdoors. The sine wave 

signature would not be heard indoors either. It should be noted that even though these experiments were done on 

subjects outdoors and indoors with windows opened and closed, the subjects were only rating boom loudness. 

The indoor signatures that subjects were exposed to were re-shaped as compared to the outdoor signature in order 

to account for the changes due to transmission losses through the building walls and windows. Subjects were 

not exposed to the other stimuli experienced indoors, such as building vibrations and rattling, that also cause 

annoyance.
Chapter 5 Approaches to Sonic Boom Minimization

135

To the right side of the ¿gure is a schematic illustrating a building structure response to an N-wave and sine wave 

of the same overpressure level and duration. Also shown on the schematic is an outdoor and indoor observer. 

Outdoors, the observer would not hear the sine wave signature because of its extremely low frequency but 

de¿nitely would hear the booms from the N-wave. Indoors, the observer would respond to the building vibration 

and rattling of windows and bric-a-brac, etc., for either the N-wave or sine wave. In Chapters 8 and 9 of this 

publication, it will be shown that a sine wave is more ef¿cient exciting a building structure than an N-wave. 

Therefore, when shaping a boom signature to reduce loudness, it is also desirable to reduce its overpressure and 

increase rise time.

Boom Minimization through Aircraft Operations

In this section, sonic boom minimization by means of altering aircraft Àight operations will be reviewed and 

include the demonstrated bene¿ts associated with Àight altitude and Mach number, those resulting from altering 

Àight path angle and the no boom cut-off Mach number Àight operation. Two additional aircraft operations aimed 

at reducing the boom observed at the ground will also be discussed, both of which may be considered beyond the 

realm of current practice – Ferri’s tailoring the aircraft Àight path (ref. 5.2) and Crow’s active control – unsteady 

Àight path (ref. 5.3). 

InÀuence of Altitude and Mach Number

Aircraft Àight altitude and Mach number play a signi¿cant role in determining the magnitude of the boom as shown 

in ¿gure 5.3 (ref. 5.4). Figure 5.3(a) shows the relative boom attenuation as a function of the Àight altitude for two 

aircraft in steady-level Àight at the same Mach number – (1) a lightweight ¿ghter whose boom is due primarily 

to its volume and (2) a heavyweight bomber whose boom is due primarily to the weight (lift) it is carrying. The 

sonic boom of an aircraft is made up of the boom generated by its volume and the boom generated by the lift it 

carries. Thus, aircraft size and weight play a signi¿cant role in establishing boom intensity. The attenuation is, of 

course, a function of both altitude (H) and atmospheric pressure at the Àight altitude (Pa

) and at the ground (Pg). It 

can be seen that increasing altitude will result in signi¿cant attenuations of the boom depending upon the amount 

of volume and lift carried by the vehicle.

Another view on the inÀuence of increasing altitude at a constant Mach number and weight is shown in ¿gure 

5.3(b). Overpressure is plotted as a function of Àight altitude. Two curves are shown, one for volume only and 

the other for lift only. The plot shows that for a ¿xed Mach number at low altitudes, the volume contribution 

is dominant. As the airplane is Àown at higher altitudes and at a given Mach number, the angle of attack must 

increase in order to maintain the lift equal to the weight, thus producing a stronger shock wave.

Figure 5.2. Sonic boom loudness and building response (adapted from ref. 5.1).
Chapter 5 Approaches to Sonic Boom Minimization

136

The variation of shock strength with Mach number is given in ¿gure 5.3(c). In the case of the lower-weight 

vehicle where the boom intensity is primarily due to its volume, the shock strength increases with increasing 

Mach number. For the heavyweight vehicle where the boom intensity is primarily due to the lift it is carrying, 

shock strength increases with Mach number up to about a value of 1.5 and then begins to decrease. The decrease 

is due to the fact that as speed is increased, the vehicle angle of attack decreases in order to maintain the same lift. 

This, in turn, reduces the vehicle drag and thus the boom due to vehicle volume. Thus, the effect of speed for the 

lift contribution is somewhat different than that for the volume contribution for a ¿xed weight. 

In addition to the inÀuences of changes in altitude and Mach number discussed above, both also play a key role in 

the design of aircraft for low-boom shaped signatures, as will be addressed later in this section.

Flight Path Angle

Another operational procedure that can be used to minimize the boom at ground level is through the use of Àight 

path angle (Ȗ) to delay its arrival until the aircraft has reached higher altitudes. Figure 5.4 has been assembled to 

illustrate this situation.

(b) Contribution of aircraft lift and volume on boom level. 

(a) Sonic boom attenuation with altitude.

(c) InÀuence of Mach number on boom level. 

Figure 5.3. ,QÀXHQFHRIDOWLWXGHDQG0DFKQXPEHURQVRQLFERRPUHI
Chapter 5 Approaches to Sonic Boom Minimization

137

Figure 5.4(a) illustrates two aircraft (both Àying at constant Mach number) – one in level Àight (Ȗo) and the other

at a given Àight path angle (Ȗc

). Only the bow shock waves are shown. For the level Àight case Ȗo, the Machaltitude is such that the speed of the aircraft over the ground is greater than the sound speed at the ground and 

the bow shock reaches the ground and is observed at the ground. In the climb case Ȗc

, the climb angle is selected 

so that as the aircraft passes through the same altitude, the bow shock becomes normal to the ground causing it 

to terminate before reaching the ground. The Àight path angle Ȗ can be viewed as an effective change in Mach 

number, positive climb angles being bene¿cial regarding boom minimization on the ground while negative climb 

angles (dives) are detrimental.

The theoretical cut-off Mach (MCO) for various climb and descent angles for a standard atmosphere with no winds 

and also for a standard day 40°F are provided in ¿gure 5.4(b) (ref. 5.5). It can be seen that an aircraft in a 20° 

climb in a standard atmosphere with the proper Mach schedule can delay booming the ground until it reaches 

about Mach 1.55 at the tropopause (36,000 feet).

In order to determine experimentally whether cut-off Mach number is affected in a manner indicated by the 

equation shown on ¿gure 5.4(c), a Àight investigation was conducted involving level Àight followed a short time 

later by one that included a pull-up and climb maneuver (ref. 5.6). The Mach number was 1.4 for level Àight, but 

varied from the 1.4 planned Mach to between 1.4 and 1.34 in the 10° climb maneuver. The Àight paths for the two 

test Àights, taken from the radar plot board, are shown in ¿gure 5.4(c) along with the ray paths for both the level 

and climbing Àights represented by the dot-dash and dashed lines respectively. In ¿gure 5.4(d), the calculated MCO 

is shown as a function of Àight path angle for Àights at various altitudes in a standard atmosphere. Also shown is 

(a) Schematic of shock-ray pattern. (c) Aircraft level and climb Àight pro¿les and ray paths.

(b) Predicted Mco with climb angle. (d) Measured results. 

)LJXUH (IIHFWRIFOLPEDQJOHRQFXWRII0DFKQXPEHUDGDSWHGIURPUHIVDQG
Chapter 5 Approaches to Sonic Boom Minimization

138

the calculated MCO for the atmosphere on the test day. The climb test data point is also shown and is seen to be in 

good agreement with prediction.

Climb angle has been used during military operations to delay the arrival of the transition focus boom to a more 

suitable location further down the Àight track along with its corresponding lower overpressures as a result of the 

higher altitude at which the boom is produced.

Mach Cut-Off Operations

It has been suggested that overland supersonic operations be Àown at so-called cut-off Mach numbers, that is, 

relatively low Mach numbers at which the aircraft shocks and thus booms do not reach the ground. This might 

be accomplished by operating a conventional SST at low supersonic speeds, by developing a low Mach number 

SST (ref. 5.7), or by designing an advanced low-boom supersonic transport. However, as noted in the previous 

discussion on boomless Àight, at the termination of the shocks during Mach cutoff (MCO), a caustic (focus) 

condition exists wherein the boom overpressure can be as much as 3 times the boom level generated by the 

aircraft Àying at the same altitude at a high Mach number. This caustic is carried along with the aircraft during 

the entire Àight at MCO.

Figure 5.5 shows the focusing situation caused by refraction when steady Àight is just below the MCO. As shown 

in ¿gure 5.5(a), the rays are curved and the caustic is straight. A bow shock is shown illustrating how it appears to 

be reÀected from the caustic. The reÀection corresponds to rays continuing after passing their tangent point along 

the caustic. Notice that the rays approach their tangent point and the area between the consecutive rays decrease 

and approach zero at the caustic. Figure 5.5(b) shows a more detailed view of the Mach cut-off caustic, from a 

pressure signature perspective, showing the types of waveforms expected. The N-wave signature to the left has 

not yet reached the caustic, and far above it will be a conventional boom. Since the ray tube area at the caustic is 

zero, geometric acoustics state that the pressure goes to in¿nity. The caustic is an edge and violates the geometric 

acoustics condition since the gradient length scale of P is large compared to wavelength, so diffraction serves 

to limit the signature amplitude at the caustic. Diffraction tends to limit low frequencies more than high, so the 

bow and tail shocks amplify more than the expansion portion of the N-wave boom signature, hence, an incoming 

N-wave will transform into a U-wave shape at the caustic (its maximum). The other waves have interacted with 

the caustic, with the post-focus U-wave reÀected and low frequency evanescent waves passing below the caustic.

(b) Pressure signatures in the vicinity of a Mach cut-off caustic.

(a) Mach cut-off caustic.

Figure 5.5. )RFXVGXHWRVWHDG\OHYHOÀLJKWDW0DFKFXWRII0CO 
Chapter 5 Approaches to Sonic Boom Minimization

139

A pictorial of the sonic boom behavior for steady-level Àight near Mach cutoff (MCO) is illustrated in ¿gure 5.6. 

The shock pro¿les in four conditions of Àight are shown and include operations at MCO near MCO, slightly above 

MCO, and well above MCO. At MCO, the bow and tail shocks terminate and reÀect back on themselves prior to 

reaching the ground, since the speed of the aircraft over the ground is less than the sound speed at the ground. 

Booms are also not observed at locations lateral to the aircraft ground track for MCO Àight. An acoustic disturbance 

may be observed at a few hundred feet below the shock extremities. As the Mach number is increased, the bow 

and tail shocks propagate further down towards the ground to the point where they may touch the ground. In this 

case, a U-shaped focus boom signature is experienced. It can have up to three times the intensity of the boom from 

a steady Àight at a high Mach and at the same altitude. Such a focus or caustic could be experienced throughout 

much of the MCO Àight mission. This focus signature will also be observed a very short distance lateral to the 

track, as illustrated by the sketch. At Mach numbers slightly above and well above MCO, the boom signature and 

intensity is approaching that associated with the normal carpet boom and is N-wave in character with the lateral 

extent of the boom being about 1 mile in width for each 1000 feet of Àight altitude. The plot of overpressure with 

Àight Mach number, shown at the top of ¿gure 5.6, positions these various Àight Mach conditions and clearly 

shows the pressure buildups for operations near MCO. The risk of operating below MCO is that if the Mach number 

inadvertently exceeds the cutoff condition, there can be an extensive focus boom region on the ground.

In the 1970 time period, a series of Àight-test experiments (ref. 5.8) were conducted by NASA, the Atomic 

Energy Commission (AEC), the National Oceanic and Atmospheric Administration (NOAA), the USAF, and the 

Department of Transportation (DOT)/Federal Aviation Administration (FAA) to investigate the nature of sonic 

booms at Àight operations at Mach cutoff (MCO). Use was made of the 1500-foot high Bare Reactor Experiments, 

Nevada (BREN) tower at the AEC test site Jackass Flats, Nevada to locate microphones every 100 feet from 

ground level to the top. Microphones were also located at 200-foot spacing on the ground along the Àight track. 

)LJXUH 3LFWRULDORIVRQLFERRPEHKDYLRUIRUOHYHOÀLJKWQHDU0DFKFXWRII
Chapter 5 Approaches to Sonic Boom Minimization

140

Flights of F-104 aircraft, vectored and tracked by ground-based precision radar crews, were made at an altitude 

of 33,700 feet and at speeds near MCO ranging from about 1.1 to 1.3 (based upon atmospheric sounding data near 

Àight times) over the tower such that the shocks terminated somewhere within the 1500-foot tower height. Flights 

were also made at Mach numbers well above MCO. The results are presented in ¿gure 5.7 (refs. 5.8, 5.9, and 5.10) 

and include schematics of the ray-path and shock ¿eld diagrams, signature shapes, and boom level.

Figure 5.7(a) shows the ray paths for a Àight where the aircraft speed over the ground Vg

 is greater than the sound 

speed, ag, at the ground and also where it is less than MCO. The aircraft is shown moving in a direction from right 

to left and, for simplicity, only the bow wave is shown. In the case where Vg

 > a

g

, the bow shock wave extends to 

the ground and is reÀected upward. As the disturbances that form this shock wave are emitted from the aircraft, 

they travel toward the ground along ray paths indicated by the solid lines. These rays intersect the ground and are 

reÀected upward, as illustrated by the dotted lines. Note that two consecutive rays are essentially parallel and tend 

to converge only slightly as they approach the ground. When Vg

< a

g

, the bow shock extends downward below 

the aircraft until its speed becomes less than the speed of sound at the ground and reÀects back on itself before 

reaching the ground. Note that the rays have a greater curvature and are totally refracted at an altitude above the 

ground. The areas between adjacent rays, as indicated by the shaded region, decrease until they theoretically 

approach zero where the rays become tangent and the ray tube area between them goes to zero, where boom 

pressures are expected to markedly increase. Thus, a caustic, or line focus, is formed where the rays become 

tangent at the cut-off altitude.

(a) Ray-shock diagrams.

(b) Details of shock-wave structure at M > MCO.

(c) Details of shock-wave structure at M (d) Variation of overpressure. CO.

Figure 5.7. 1DWXUHRIVRQLFERRPIRUVWHDG\ÀLJKWQHDUFXWRII0DFK0coDGDSWHGIURPUHI
Chapter 5 Approaches to Sonic Boom Minimization

141

Sketches of sonic boom signatures measured on the tower and ground for the Àight at Mach 1.3 (M > MCO) are 

shown in ¿gure 5.7(b). At the top of the tower, both incident and reÀected N-wave signatures are observed. 

The incident and reÀected signature are similar in shape and are about equal in amplitude. At ground level, 

these two signatures are coincident and only a single signature is observed and depending on the ground surface 

characteristics, could have about twice the amplitude of the free air pressure signatures. At the top of the tower, 

therefore, one would observe four distinct booms, whereas at ground level only two booms would be observed 

and they would be twice the intensity of the free air boom.

For the case of the grazing condition (MCO), shown in ¿gure 5.7(c), at the top of the tower, a normal N-wave 

signature was measured that included the incident bow and tail shocks and their reÀections. At midtower, which 

was the approximate location of the shock wave extremity, it is noted that a U-shape (caustic) signature is measured 

for which the amplitudes are larger than those associated with N-wave signatures observed in the supersonic Àow 

region. Near the base of the tower, below the shock extremity, the signatures are rounded or sinusoidal in shape 

and indicate acoustic disturbances.

The overpressures associated with the BREN tower signatures are presented in ¿gure 5.7(d). A theory curve is 

also shown (refs. 5.11–5.15). At Mach < 1.10, very low boom levels were measured, and these were associated 

with the acoustic type of signature. At Mach numbers above 1.10, normal N-wave types of signatures were 

observed from which the pressure increased gradually with increasing Mach number as predicted by theory. Near 

Mach 1.10, U-shape waveforms were generally observed. The U-shaped measured caustic signatures generally 

indicate overpressure enhancement compared to those associated with the higher Mach numbers. The highest 

enhancement factor measured is 3. On a ¿nal note, the shock wave was found to be quite sensitive at its extremity 

to local atmospheric conditions (winds, turbulence, etc.).

The range of Mach numbers and altitudes over which operations at cut-off Mach number can be performed is 

shown in ¿gure 5.8. Looking ¿rst at the case of a standard atmosphere with no winds (¿g. 5.8(a), ref. 5.16) for 

steady-level Àight at Mach numbers to the left of the MCO line will result in no booms reaching ground, whereas 

Àights at Mach numbers to the right of the line will result in booms reaching the ground. The highest speed at 

which the aircraft could operate above the tropopause, in a standard atmosphere with no wind without producing 

booms at the ground, is about Mach 1.16. In a real atmosphere, variations in the effective speed of sound do exist 

because of temperature and winds, as shown in ¿gure 5.8(b) and ¿gure 5.8(c) (refs. 5.17 and 5.12). Note that cutoff Mach numbers of as high as 1.5 are possible with a 200-knot headwind at altitude. Conversely, with a 50-knot 

tailwind at the aircraft, Àights above the tropopause would have to be Àown at Mach < 1.05. Climb or descent 

angles would also permit an increase or decrease in MCO, respectively.
Chapter 5 Approaches to Sonic Boom Minimization

142

Flight near MCO played an important role as to whether a sonic boom was observed at the ground from Chuck 

<eager’s famous ;-1 (¿g. 5.9) Àight of October 14, 1947, in which he was the ¿rst person to pilot an aircraft 

that broke the sound barrier in level Àight. According to his book (ref. 5.18, p. 130), the ;-1 was in level Àight at 

42,000 feet and achieved Mach 1.07 during the Àight. He stated that a sonic boom was observed on the ground 

by his test group. This boom was the ¿rst ever produced by an aircraft in level Àight and supposedly the ¿rst ever 

generated by an aircraft. Shock wave booms have been produced by projectiles, riÀes, and cannons long before 

aircraft booms were observed. With respect to the ;-1 boom, in looking back on it and what is known today 

regarding MCO, it would have been fortunate that it was observed, since for a standard atmosphere (no wind), the 

cutoff Mach number for level Àight at 42,000 feet is about 1.16. The ;-1 only attained Mach 1.07. Thus, no boom 

would be observed at ground level because of atmospheric refraction. If the atmosphere was non-standard (i.e., 

cooler temperatures) and there was a tailwind gradient of at least 50 knots at altitude, then the predicted Mach 

cutoff would have been about 1.06. Thus, at Mach 1.07, a sonic boom would have been observed, and since it was 

so near to cutoff, it would sound more like a rumble than a distinct double boom. <eager noted that the NACA 

tracking van reported a distant rumble of thunder. However, records show that the Àight was heading northwest 

over Victorville and upper air weather soundings taken at Bakers¿eld, California on that day show that the winds 

at altitude were from the northwest at 50 knots. Thus, <eager’s ;-1 would have encountered headwinds and 

not tailwinds, and as such the Mach cutoff would have been more like 1.24, resulting in the shocks terminating 

without even reaching the ground.

(a) MCO in standard atmosphere (no wind).

(c) Effect of winds. (b) Effect of temperature.

)LJXUH ,QÀXHQFHRIWHPSHUDWXUHDQGZLQGJUDGLHQWVRQ0DFKFXWRIIDGDSWHGIURPUHIVDQG
Chapter 5 Approaches to Sonic Boom Minimization

143

Two points should be made about boomless Àight operations. Boomless Àight is independent of aircraft 

con¿guration and is a function of the aircraft operating conditions and the atmosphere. Aircraft con¿guration 

is, of course, important from the standpoint of ef¿ciency of operation at these low Mach numbers; for example, 

Àying a high Mach cruise design at the off-design MCO is less desirable than Àying an aircraft designed to operate 

at Mach 1.15. In either case, boomless Àight operations, unlike the stationary focus from an aircraft maneuver, 

always result in a continuous caustic or focal line where the overpressures can be higher than those of the steady 

Àight boom from the aircraft Àying at the same altitude but at the higher cruise Mach number. Therefore, in order 

to assure the shocks and thus the boom for Àight at MCO will terminate at some safe height above ground level, a 

margin of safety in the form of reduced Mach number is required (refs. 5.9 and 5.10). A practical range of MCO

above the tropopause Àight is probably no greater than 1.3. Studies have been conducted in the past (see ref. 5.19) 

and are continuing to examine the possibility of overland boomless Àight operations involving the Mach cut-off 

concept as a means of decreasing travel time. 

Tailoring Flight Path

Since overland supersonic Àights would include operations over heavily populated areas, Ferri (ref. 5.2) examined 

the possibility of substantially reducing the sonic boom when Àying over cities. As illustrated in ¿gure 5.10(a), 

reducing the aircraft lift can be accomplished by means of a maneuver. An airplane Àying at high velocity could 

perform a pull-up maneuver of a few degrees before reaching the point where its cruise sonic boom level will be 

minimized and then Ày a lower lift trajectory to effectively reduce the boom over the selected point. The airplane 

could then Ày for several miles producing a signal that is substantially reduced.

Figure 5.9. 2Q2FWREHU&KXFN<HDJHUSLORWHGWKH%HOO;SDVWWKH

VRXQGEDUULHUH[FHHGLQJ0DFKLQOHYHOÀLJKW

&
Chapter 5 Approaches to Sonic Boom Minimization

144

The distance over which the reduced boom levels would be realized is given in ¿gure 5.10(b) as a function of 

Mach number and for different values of, the pull-up or pushover maneuver angle and for varying values of N, and 

the ratio of the aircraft CL during the maneuver to the cruise CL. The maneuver starts at an altitude of 40,000 feet 

(see ¿g. 5.10(a)) where the airplane makes a pull-up maneuver of _ degrees and then Àies a trajectory at constant 

CL, equal to N times the CL for cruise, with constant velocity. The airplane ¿rst increases altitude, then descends, 

and reaches 40,000 feet again at the same angle _. The maximum altitude reached is given in ¿gure 5.10(c). Two 

values of initial angle of the trajectory have been considered – one corresponding to _ = 5° and the second to _ = 

10°. The maximum value of the discontinuous  ̈p produced by the sonic boom decreases strongly when the Àight 

altitude decreases and CL decreases. 

The maneuver therefore can alleviate substantially the disturbances produced by sonic boom. For example, initial 

 ̈p for the CL corresponding to the two-thirds of the horizontal value at an altitude of 40,000 feet can be as low 

as 0.4 lb/ft2

 and ramping up to about 0.8 lb/ft2, as shown by the signature in ¿gure 5.10(d). The boom signature 

corresponds to an airplane having a weight of 460,000 pounds and a length on the order of 300 feet. The takeoff 

weight of the airplane is between 650,000 and 700,000 pounds. Whether or not tailoring cruise Àight path to 

include pull-up pushover maneuver to reduce lift and thus ǻp as the aircraft approaches populated areas is yet to 

be evaluated as being practical or usable.

Active Control-Unsteady Flight Path

Figure 5.11 presents some results of a study by Crow and Bergmeier (ref. 5.3) of sonic booms produced by aircraft 

in non-steady Àight. The goal was to ¿nd whether “slosh”, a non-steady source phenomena where the longitudinal 

(c) Maximum  ̈h reached.

)LJXUH /RFDOUHGXFWLRQRIVRQLFERRPE\PDQHXYHULQJDLUFUDIWDGDSWHGIURPUHI

(a) Schematic of pull-up maneuver. (b) Distance over which boom is reduced.

(d) Resulting boom signature.
Chapter 5 Approaches to Sonic Boom Minimization

145

Àow of lift back and forth from the middle of the aircraft to the nose and tail, and surge, a periodic acceleration 

of the aircraft along its Àight path, can scramble or attenuate sonic booms heard by listeners on the ground as 

schematically is illustrated in ¿gure 5.11(a). Such source phenomena would constitute active sonic boom control. 

Active sonic boom control must somehow prevent the pressure waves generated by a supersonic aircraft from 

coalescing into compact and coherent wave at large distances. The control methods must work for listeners located 

anywhere on the ground.

The ¿rst example of a periodic source is slosh. An aircraft with three lifting surfaces could implement slosh by 

oscillating control surfaces at the three trailing edges with the canard and tails synchronized and the wing 180° 

out of phase. Alternatively, an elongated delta or quarter sine wing could have piezoelectric leading edges capable 

of bending into S-shapes, thereby altering the longitudinal distribution of cambers. Figure 5.11(b) displays sonic 

booms arising from periodic slosh. The darker curve is the boom at zero phase, while the red dashed curve is the 

boom of the steady source. It was concluded from the plot that slosh alters the boom profoundly but does not 

reduce its pressure level.

The second example of a periodic source is surge – a periodic acceleration of the aircraft along its Àight path. 

In principle, engine thrust variations could implement surge. A deliberately excited phugoid oscillation could 

do so also, with the complication of small periodic changes in altitude. Neither mode of implementation was 

recommended for commercial supersonic transports. Sonic booms from the surging aircraft are stretched and 

attenuated, as shown in ¿gure 5.11(c). The sonic boom of the steady source (red dashed line) has collapsed into 

waves of low amplitude resembling broad band noise. The waves seem oddly complicated in view of their origin 

from a simple aircraft undergoing a simple sinusoidal surge.

As stated by Crow and Bergmeier (ref. 5.3, p. 108), “Unfortunately the assumed surge amplitude is anything 

but practical; its position oscillates at an amplitude of 400 feet and frequency of 0.5 Hz. The amplitude of speed 

oscillations is 1257 ft/sec, so the speed varies from 73 ft/sec to 3257 ft/sec in the course of a cycle. Acceleration 

oscillations have amplitudes of 3948 ft/sec2

, about 123 times the acceleration of gravity.”

Figure 5.11. $FWLYHVRQLFERRPFRQWUROXVLQJQRQVWHDG\ÀLJKWDGDSWHGIURPUHI

(a) Periodic Àight pro¿le.

(b) Sonic boom from a sloshed lift distribution. (c) Sonic boom from an aircraft subject to extreme 

periodic surge.
Chapter 5 Approaches to Sonic Boom Minimization

146

The authors also point out that the speed and acceleration amplitudes diminish as the frequency falls, but so too 

does the ef¿cacy of surge as a means of reducing sonic boom intensity. At a frequency of 0.1 Hz, the amplitude of 

acceleration is 4.9 times gravity, but the sonic boom is hardly changed from the case of steady Àight. Surge with 

more moderate accelerations shifts the boom back and forth without chopping it to pieces. The phase-averaged 

boom is still weak, but the weakness reÀects only boom displacements, not intensity reductions that a listener 

would notice.

In this section, ¿ve approaches to sonic boom minimization through the use of Àight operations have been discussed 

including – (1) the inÀuence of altitude and Mach number, (2) Àight path angle, (3) Mach cut-off operations, (4) 

tailoring the Àight path, and (5) active control-unsteady Àight path. The ¿rst three approaches are considered to 

be practical while the last two may be considered beyond the realm of current practice. Increasing altitude, using 

a climbing Àight path angle, operating at speeds that are less than the speed of sound at the ground, and MCO can 

play a role in reducing the boom levels at the ground. Other than Àight below MCO eliminating the boom at the 

ground (or making it worse if cutoff condition is slightly exceeded), these Àight parameters do not change the 

character of the boom. In 1965, McLean (ref. 5.20) pointed out that booms propagating to the ground could be 

“mid ¿eld” and not necessarily asymptotic far-¿eld N-waves. That led to the development of the concept of the 

mainstream approach to boom minimization. 

Boom Minimization through Aircraft Shaping

Following McLean’s concept of mid-¿eld signatures, considerable research efforts have been made aimed at 

reducing or eliminating sonic boom by shaping. These efforts have been classi¿ed as two types of studies – (1) 

aerodynamic modi¿cation studies and (2) exotic con¿guration studies. As stated by Seebass and George (ref. 5.21, 

pp. 687–688), “We will call aircraft con¿gurations that leave total enthalpy of the Àow essentially unchanged 

aerodynamic con¿gurations. ... Con¿gurations that change the total enthalpy of a signi¿cant fraction of the Àow 

past them, as well as those that rely on physics beyond our comprehension, we will term exotic con¿gurations.” 

In this section, minimization by way of aerodynamic modi¿cations that leave the total enthalpy of the Àow 

essentially unchanged will be discussed. A presentation of several con¿gurations/planforms that have been set 

forth aimed at minimizing the sonic boom and the role that the aircraft volume and lift distribution play in shaping 

the vehicle boom signature is included. Substantial quantitative analysis of shaping has utilized Whitham’s 

equivalent body concept. Chapter 7 presents details of the application of this concept to shaping, together with 

an extensive review of shaping con¿guration studies. A brief review of this concept is presented in this chapter. 

This is followed by a discussion of the role two con¿guration components, wing planform and wing dihedral, 

play in boom minimization. Application of the various boom approaches aimed at designing low-boom concepts 

is presented as applied to numerous supersonic transport and supersonic business jet concepts.

Con¿guration/Planform

The concepts illustrated in ¿gure 5.12 involve vehicle shaping for boom minimization. Their objective is generally 

to reduce the amplitude of the shock waves either by stretching an N-wave signature and trading length for 

amplitude, or to create a non-N-shape such as a Àat-top or ramp.
Chapter 5 Approaches to Sonic Boom Minimization

147

The Busemann biplane concept of 1935 (¿g. 5.12, top left) is a concept where for one speci¿c Mach number at 

zero lift, the wave drag can be made zero with no external shock waves (ref. 5.22). Twenty years later (ref. 5.23), 

Busemann noted that no satisfactory solution for the lifting case depicted has yet been devised. The ring wing 

(ref. 5.24) is essentially the Busemann wing wrapped around a contoured fuselage. It is also ineffective for the 

lifting case. A practical version of the supersonic biplane with reduced booms has been investigated by Ferri (ref. 

5.2) and is a unique way to increase the effective lifting length of the vehicle. In the mid 1960s, McLean (ref. 

5.25) noted that for supersonic transports of practical length, the signature at the ground need not be the far-¿eld 

N-wave. He observed that the mid-¿eld region could extend several hundred body lengths. One could envision 

a large (500-foot long) SST Àying low enough to be within the near ¿eld. If the volume and lift distributions are 

optimized, the sonic boom signature could be a sine wave and, thus, not easily observed by a person outdoors. 

Several wing con¿gurations that were examined by Hunton in regards to the effect of wing planform, dihedral, 

and camber on sonic boom (ref. 5.26) are shown in the center left of ¿gure 5.12. The oblique wing was a concept 

developed in Germany in 1942 and Àight proven during the 1980s in the form of the subsonic AD-1 by NASA 

under the direction of Jones (ref. 5.27). Li, Seebass, and Sobieczky (ref. 5.28) noted that this con¿guration was 

designed to Ày ef¿ciently at subsonic speeds and also overland at Mach numbers of 0.9 to 1.10 where there is no 

sonic boom at the ground. This concept combines the volume and lift distributions to have a long lifting length 

and to alter boom signature both below the aircraft and at lateral distance from the ground track. Early studies 

(ref. 5.29) suggested that the oblique wing concepts may be limited to aMach 1.4. Speeds higher than Mach 

1.4 are possible with more wing sweep, but, as stated in reference 5.28 (p. 754), “the wing’s control becomes 

increasingly dif¿cult with 60° being judged acceptable in previous studies.” 

Figure 5.12. %RRPPLQLPL]DWLRQFRQFHSWVLQYROYLQJYHKLFOHVKDSLQJ
Chapter 5 Approaches to Sonic Boom Minimization

148

A recent novel idea for a 70-passenger supersonic transport, shown at the middle right of ¿gure 5.12, having 

an operational range of 2000 nmi, that is claimed to achieve low sonic boom and high subsonic and supersonic 

performance is the supersonic Bi-Directional (SBiDir) Àying wing (ref. 5.30). This Mach 1.6 vehicle, which has a 

wing loading of 15.3 lbs/ft2

, is said to achieve its high ef¿ciency subsonically and supersonically by performing a 

mode change from subsonic to supersonic and vice versa using one of two options – (1) to turn the engines through 

a mechanical system or (2) by using the aerodynamic forces on the wing to turn the airplane under the engines. 

They considered the latter since it was found to be the most energy ef¿cient method. Pfenninger’s long-range 

supersonic laminar Àow design (ref. 5.31), shown in the lower right of ¿gure 5.12, incorporated highly swept 

strut-braced wings and was to offer high cruise L/D’s and low sonic boom overpressures. Several multiple wing 

con¿gurations studied by Northrop Grumman (ref. 5.32) during the Defense Advanced Research Projects Agency 

(DARPA)/Quiet Supersonic Platform (QSP) program (ref. 5.33) are shown at the bottom left of ¿gure 5.12. These 

highly unconventional vehicle concepts were thought to be more accommodating in ful¿lling the QSP goals and 

requirements, particularly in the 6000-nmi range. This DARPA effort was aimed at advancing the technologies 

necessary to enable the development of ef¿cient and environmentally acceptable overland supersonic aircraft. So 

there are a multitude of supersonic aircraft concepts, but most except for the Concorde and various ¿ghter aircraft 

have not evolved enough in terms of their design maturation to determine their viability. 

Volume and Lift Distribution

Sonic boom signature minimization through aircraft shaping is based upon the equivalent body concept established 

by Whitham and Walkden (refs. 5.34 and 5.35) and is illustrated in ¿gure 5.13 (ref. 5.36). The message to be 

conveyed is that for sonic boom purposes, if the actual airplane wind-tunnel model shown in the upper left of the 

¿gure is replaced by an equivalent body of revolution (upper right) having the same effective area distribution 

(Ae

) as shown by the center plot, then similar sonic boom signatures will result. The two sonic boom signatures 

shown at the bottom of the ¿gure con¿rm the validity of the theory. Some slight variations are noted to exist 

between the tail shock recompression (negative) phase of the waveform, but these are primarily a result of the 

body-sting support termination.

Figure 5.13. ,OOXVWUDWLRQRIWKHHTXLYDOHQWERG\FRQFHSW0DFK&L KO DGDSWHGIURPUHI
Chapter 5 Approaches to Sonic Boom Minimization

149

Illustrations of some general signature characteristics and airplane shaping considerations for sonic boom 

minimization are illustrated in ¿gure 5.14. Three equivalent area distributions (Ae

) and the resulting far-¿eld 

boom signatures are shown in the lower part of the ¿gure. All of the past and current supersonic aircraft, which 

are not designed for boom minimization, have their volume and lift arranged in such a manner as to produce an 

N-wave on the ground. Designs where the aircraft volume and lift are arranged so as to produce a smooth optimum 

progression of Ae

 from the nose to the maximum value result in a boom signature that can either be a Àat-top or 

an initial shock ramp type waveform as illustrated by the two top Ae

 curves. Note that very little change in Ae (at 

the nose and near the maximum value) is necessary to change from a Àat-top to an initial shock-ramp signature. 

In order to reduce the overpressure for a given design, the equivalent area must be spread so as to increase the 

slenderness ratio as illustrated by the three sketches shown in the lower part of ¿gure 5.14. It will be noted that the 

N-wave signature is associated with an Ae

 development that is irregular resulting in the classical N-wave. As the 

Ae

 development is smoothed and stretched out over a longer length with a lesser Ae maximum, a Àat-top (plateau) 

signature of reduced  ̈p results. Spreading Ae

 smoothly over an even longer length and even lower Ae maximum 

could result in a ¿nite rise time signature approaching a sine wave. As will be shown later in this section, vehicle 

length on the order of 500 feet or greater would be required for this latter case. Two important lessons learned 

from the discussion are that the signature overpressure is set by the maximum area carried and the signature shape 

is determined by the shape of the Ae curve.

Vehicle Shaping – Wind-Tunnel Results

The area shaping concept was ¿rst validated by Carlson et al. in 1966 on two models tested in the wind tunnel 

(ref. 5.36) that had equivalent area distributions similar to the N-wave signature and Plateau (asymmetric Àat-top) 

signature depicted in ¿gure 5.14. The test results are provided in ¿gure 5.15. Measured sonic boom signatures for 

two vehicle con¿gurations are shown for various distances from the models – one vehicle con¿guration consisting 

of a basic body designed to produce an N-wave signature in the far ¿eld and another vehicle con¿guration 

)LJXUH Relationship of signature shapes to vehicle area development.
Chapter 5 Approaches to Sonic Boom Minimization

150

consisting of a modi¿ed body designed to produce a Àat-top signature in the far ¿eld. Signature measurements at 

2.5, 5, and 10 body lengths (h/l) from the model illustrate the development of the waveforms for the two models. 

Note that the basic con¿guration signature sketches shown to the left, which result in an N-wave in the far ¿eld, 

still retain the multiple saw-tooth shock characteristic out to 10 body lengths. However, the signatures shown on 

the right side of ¿gure 5.15 are produced by a model, that was designed to produce a Àat-top signature in the far 

¿eld, and show Àat-top waveforms at all three measurement positions. Tunnel test section/model size constraints 

limit the furthest measurement – in this case, to 10 body lengths from the model. Measurements at larger h/l 

either require smaller models, which then begin to lose geometric ¿delity, or larger tunnels. Wind-tunnel model 

near-¿eld signatures of the type shown in ¿gure 5.15 are then inserted into a sonic boom prediction program and 

propagated to distances/body lengths equivalent to full-scale aircraft Àying at cruise altitudes.

Vehicle Shaping – Flight Test Results

Although theory, supported by wind-tunnel measurements, predicted that a shaped signature from a real aircraft 

would persist to the ground while propagating through the real atmosphere, the consensus of the technical 

community was that this process would have to be demonstrated.

In 2002, Northrop Grumman had the opportunity to demonstrate this area shaping concept on an existing aircraft 

to produce a shaped sonic boom signature. This aircraft modi¿cation and test was designed to produce a Àat-top 

signature on the ground and thus, if successful, would con¿rm that a shaped signature would persist through a 

real atmosphere to the ground. This program (ref. 5.37), named Shaped Sonic Boom Demonstrator (SSBD), was 

carried out as part of DARPA’s QSP program (ref. 5.33). Theory predicted that a shaped wave would persist to 

300 – 600 body lengths. Wind-tunnel measurements similar to those of ¿gure 5.15 have been acquired on models 

designed to have shaped waveforms out to the walls of the test section, some 20 body lengths. 

To demonstrate persistence, only the positive phase of the aircraft’s N-wave needed to be modi¿ed. This is 

fortunate, since modifying the complete N-wave signature would be virtually impossible. An initial study had 

shown that it was feasible to modify the F-5E series aircraft to produce a shaped boom signature in a relatively 

short time frame and at a reasonable cost. Detailed boom analysis, including CFD, provided the required design 

modi¿cations. A brief view of both aircraft and the shaping change along with the measured Àight-test signatures 

are given in ¿gure 5.16 (ref. 5.37) and ¿gure 5.17 (refs. 5.38, 5.39, and 5.40). Referring to ¿gure 5.16, on the 

left side of the ¿gure is shown the basic F-5E Tiger II aircraft and its associated equivalent area distribution (Ae

)

Figure 5.15. 0HDVXUHGVRQLFERRPVLJQDWXUHVRQDEDVLFDQGPRGL¿HGHTXLYDOHQWERG\RIUHYROXWLRQ

LQWKHZLQGWXQQHO0DFK&L

±DGDSWHGIURPUHI
Chapter 5 Approaches to Sonic Boom Minimization

151

which is known to produce an N-wave at the ground. To the right of the ¿gure is shown the SSBD aircraft with its 

re-shaped equivalent area distribution (Ae

) designed to produce a Àat-top signature at the ground.

In-Àight probings of the F-5E and SSBD were performed to describe the near- and mid-Àow ¿eld below each 

aircraft. Signature measurements were also acquired in the far ¿eld using a sailplane Àying at about 6,000 ft above 

ground level and with microphones at ground level. The results of these Àight tests are given in ¿gure 5.17 (refs. 

5.38, 5.39, and 5.40).

For both the F-5E and SSBD, the near-¿eld signatures contain several shocks from the various components 

of each aircraft. The results of the modi¿cations to the SSBD are evident when comparing the front portion of 

the signatures to that of the F-5E. Note too that the three shocks at the rear of the signature are similar since no 

changes were made to the aft end of the F-5E. At ground level, the F-5E signature has developed into a classical 

N-wave and the SSBD signature has developed into the Àat-top wave as designed. In ¿gure 5.18, the ground 

measured boom signatures for the F-5E and SSBD are compared. The aircraft were Àying about 45 seconds apart 

at about the same altitude, Mach number, and Àight track.

)LJXUH 0RGL¿FDWLRQRI)(LQWRWKH6KDSHG6RQLF%RRP'HPRQVWUDWRU66%'DGDSWHGIURPUHI

Figure 5.17. ,QÀLJKWDQGJURXQGPHDVXUHPHQWRIVKRFNÀRZ¿HOGEHORZWKH)(DQG66%'

DGDSWHGIURPUHIVDQG
Chapter 5 Approaches to Sonic Boom Minimization

152

([KDXVW$IW6KRFN,QWHUDFWLRQ±)OLJKW7HVW5HVXOWV

Current prediction codes take into account the aircraft engine exhaust Àow and include it as an area addition in 

developing the equivalent area distribution (Ae

) for given Àight conditions. In some con¿gurations, because of 

engine placement, the exhaust inÀuences the Ae during its rise to the maximum area – an undesirable feature. 

Other con¿gurations have the exhaust adding beyond Ae max can smooth the area distribution and reduce the 

aft shock, which can be a desirable feature relative to its inÀuence on the far-¿eld boom signature. 

Sonic boom measurements were acquired on the ;-15 hypersonic research aircraft (¿g. 5.19(a)) and are reported 

in reference 5.41. An interesting set of data was obtained concerning the inÀuence of the ;-15 aft Àow ¿eld, 

speci¿cally the exhaust plume and speed brake deployment, on the sonic boom signatures. The results are 

shown in ¿gure 5.19(b). 

)LJXUH )LUVWPHDVXUHPHQWRIDVKDSHGVRQLFERRPUHI
Chapter 5 Approaches to Sonic Boom Minimization

153

Two sets of boom signatures are presented – the signatures on the left are for the ;-15 without the rocket engine 

thrusting and speed brakes retracted, and the signatures on the right are for the aircraft with the rocket engine 

thrusting at 50 percent and its four speed brakes deployed. The boom signatures from the seven microphones 

separated by about 100 feet have been drawn to the same overpressure and time scale. The important point to 

be made regarding the two sets of signatures relates to the manner in which the tail shock (recompression wave) 

returns to ambient pressure. For the non-thrusting case and speed brakes retracted, shown to the left, the bow and 

tail (recompression) shock fronts have rapid recoveries. As such, two cracks or booms were heard. In the case 

(b) Effects of ;-15 rocket engine plume and speed brakes at Macha4 and altitude of about 70,000 feet (adapted from ref. 5.41).

86$LU)RUFHSKRWR

(a) North American ;-15 hypersonic research aircraft.

Figure 5.19. 7KH1RUWK$PHULFDQ;K\SHUVRQLFUHVHDUFKDLUFUDIWDQGLQÀXHQFHRIURFNHWHQJLQHSOXPH

DQGVSHHGEUDNHVRQ;VRQLFERRPVLJQDWXUHV
Chapter 5 Approaches to Sonic Boom Minimization

154

of the engine thrusting 50 percent and speed brakes deployed (shown to the right of the ¿gure), the tail shock 

recovery is very gradual with a considerably longer rise time. This stretching of the negative phase of the boom 

signature is due to the inÀuence of exhaust plume and wake from the speed brakes, which are acting to increase 

the effective length of the vehicle. An observer would hear only a single crack associated with the bow shock in 

this latter case.

The results of ¿gure 5.19(b) suggest that consideration be given to examining the possibility of favorably altering 

the aft shock Àow-¿eld exhaust design to minimize the inÀuence of the tail shock regarding people and building 

response. For the current vehicle designs that produce N-wave signatures in the far ¿eld on the order of 1 lb/ft2

to 3 lbs/ft2

, the inÀuence of the engine exhaust Àow plays a second order role in the boom intensity and signature 

shape. However, in the design of low-boom shaped signature vehicles, the exhaust Àow will play a more important 

role. A more in-depth discussion on the inÀuence of engine exhausts on boom signatures is provided in Chapter 7.

Wing Planform

Shocks due to volume effects are minimized by having volume distributions that are as close to optimum as 

possible. In Chapter 7 of this publication, the virtues of volume distributions that provide a fast pressure recovery 

followed by a shock are discussed. Lift distributions can also be used to control the strength and location of shocks 

by means of planform changes, wing section thickness, wing twist, and wing camber and dihedral. It is important 

to note that the volume and lift contributions to the effective area distribution are superimposed such that the two 

contributions must be optimized together to obtain the optimum results. An interesting set of wind-tunnel tests 

of various wing con¿gurations was conducted in the mid 1960s (ref. 5.26) to examine wing con¿gurations that 

were to some extent unconventional at the time in order to search out possible new design concepts for boom 

minimization that may have been overlooked in earlier studies. 

Shown in ¿gure 5.20(a) (ref. 5.26) are sketches of wing con¿gurations examined. Each had been selected to feature 

some particular arrangement of the wing shock system – such as intersecting, curved, or vertically displaced 

shocks to explore various shock system combinations. In addition to these symmetrical con¿gurations, the arrow 

wing was also tested with a cambered airfoil section and the delta wing studied with wing dihedral of 10°.

A summary of the overpressure characteristics measured for these various wings in the presence of the simple body 

is provided in ¿gure 5.20(b). Maximum peak overpressures resulting from the wing as a function of lift coef¿cient 

are presented for 12 wings for Mach 1.4 and at a distance of four body lengths. The assigned numbers, in addition 

(a) Study con¿gurations. (b) Summary of wing peak overpressures.

)LJXUH ,QÀXHQFHRIZLQJFRQ¿JXUDWLRQVRQVRQLFERRP0DFKKO DGDSWHGIURPUHI
Chapter 5 Approaches to Sonic Boom Minimization

155

to identifying the curves, can be seen to indicate the general progression of overpressure from the highest to the 

lowest level at the approximate lift coef¿cient for transition Àight of 0.15. Also shown is a table on the right that 

is intended to summarize, in somewhat gross terms, the measure of success in which the characteristics of these 

several wings could be predicted by theory at the time.

The principle conclusions that were drawn from the study are as follows

 1. A relatively large spread in overpressures was obtained for this series of wings ranging from the unswept 

trapezoidal down to the highly sweptback arrow and the limits of this spread were predicted by theory.

 2. Camber for the arrow wing was advantageous at the higher lift coef¿cients and warranted further detailed 

study. This effect was not predicted by theory.

 3. The variation in lift effectiveness on the overpressure, as evidenced by the differences in the slopes of the 

curves, is quite large and preliminary estimates of these effects were generally successful.

 4. Wing dihedral on the delta con¿guration showed a surprisingly large reduction of the overpressure, which 

was predicted with only fair success.

Wing Dihedral

Sonic boom minimization, when realized to its fullest extent, will include consideration of the complete ground 

footprints. Thus, minimum boom concepts will attempt to not only reduce boom levels directly below the aircraft 

but also laterally to each side of the ground track out to cutoff. Wing dihedral has been shown to be effective in 

providing boom relief for both on- and off-track locations, as shown in ¿gure 5.21.

Figure 5.21. ,QÀXHQFHRIGLKHGUDORQERRPUHGXFWLRQ
Chapter 5 Approaches to Sonic Boom Minimization

156

The idealized ray propagation patterns for a Àat wing and one with dihedral, illustrating the inÀuence of dihedral, 

are shown at the top left of ¿gure 5.21. In the top right of the ¿gure, the inÀuence of dihedral on a large SST 

type concept (ref. 5.42) is shown. As can be seen, dihedral angle is an extremely important design consideration. 

Dihedral angle is de¿ned as shown in the sketch of the rear view of the con¿guration at its design attitude. A 

dihedral angle of 0°would result in an on-track shock strength of about 1.25 lbs/ft2

. Increasing the dihedral angle 

to about 9.5° permits the trailing edge of the wing tip to lie in the same horizontal plane as the wing apex such that 

when developing the equivalent area distribution, Ae, the 9.5° dihedral is equivalent to about a 40-foot increase 

in the wing overall length. This results in a 28-percent reduction on-track shock strength to about 0.9 lb/ft2

. Increased 

dihedral could lead to greater gains. However, as wing dihedral increases, so too does the aircraft roll-yaw coupling 

increase leading to aircraft stability problems. There is thus a strong incentive for solution of the problem of rollyaw coupling for wings with large positive dihedral. In the lower part of ¿gure 5.21 are two sketches that describe 

the lateral distribution of sonic boom overpressures. The solid line curve represents the expected falloff of ǻp 

with lateral distance out to the lateral cutoff due to atmospheric refraction of the shock waves. The dashed curve 

suggests a more uniform redistribution of the overpressures through the use of wing dihedral. Since the lateral 

cutoff is independent of the vehicle con¿guration and only a function of the aircraft operating conditions and the 

atmosphere (ref. 5.12), then the normal  ̈p distribution represented by the solid line can be considered as being 

Àexible and since boom levels are less off track than under the aircraft, a Àattening of the curve would provide for 

more uniform boom levels laterally across the ground boom footprint. Reduced levels are experienced under the 

aircraft and increased levels laterally.

An informative set of wind-tunnel tests relative to anhedral and dihedral were conducted as part of the wing 

con¿guration studies presented on ¿gure 5.20 (ref. 5.26) and the results are shown in ¿gure 5.22. Three models 

were tested (as shown by three curves on the left side of the ¿gure) – (1) a Àat wing, (2) a wing with 10° anhedral, 

and (3) a wing with 10° of dihedral at Mach 1.7 and a lift coef¿cient of 0.2. First note the small silhouette of 

the test con¿guration, which is scaled to show the relative size and distance of the model from the probe station 

located at ground level as tested in the wind tunnel that is equivalent to a distance of 4.5 body lengths. Also shown 

on the left are the peak overpressures measured as a function of lateral to vertical distance ratio for the three values 

of wing dihedral.

It can be seen that for í10° anhedral, higher overpressures are experienced over those for the Àat wing (0°). On 

the other hand, for 10° of dihedral a signi¿cant reduction in overpressure is realized as compared to the Àat wing. 

Also note, however, that these separated curves are nearly parallel, which was interpreted to mean that the effect 

of dihedral in these tests is attributed primarily to a volume effect, presumably from the vertical displacement of 

the wing volume and not to any favorable lift effect since the lift coef¿cient was the same.

The curves on the right of ¿gure 5.22 are intended to show the attenuation of the centerline maximum overpressures 

for the three wings out to large distance ratios that are commensurate with Àight. Note that at an h/l of 50 or more, 

N-waves begin to form and at h/l of 200 or so, representative of Àight altitudes for SST size con¿gurations, 

the effects of anhedral and dihedral are no longer evident. These results have been derived from the measured 

centerline signatures on the assumption that these near-¿eld characteristics, measured at an h/l = 4.5 would remain 

orderly out to any distance. At the time of these tests, this assumption was questioned and it was recommended 

that further experimental investigation was needed (i.e., measurement at greater h/l’s). It is now understood, as 

will be shown in the next ¿gure, that care must be exercised during boom minimization efforts that near-¿eld 

signatures must be extended to much larger h/l’s for certain con¿gurations before propagating them to the ground. 

This is especially true for those con¿gurations designed to alter the lateral distribution of the pressures on the 

ground. 
Chapter 5 Approaches to Sonic Boom Minimization

157

As an integral part of the NASA HSR program, an assembly of present and past sonic boom experts in the areas of 

boom generation, propagation, predicting, and effects met to establish the state-of-the-art needs and opportunities 

regarding boom minimization (ref. 5.43). In an overview of theoretical aspects of sonic boom, W. D. Hayes 

provided considerable insight into the concerns regarding lateral redistribution and axisymmetry. 

Hayes ¿rst made the point that when sonic booms are calculated at an azimuthal angle other than at 90° (ontrack) under the Àight path, a rough approximation of the cosine of the azimuthal angle often is used as a factor 

to correct the lift contributions. For accuracy, the actual cuts for volume and lift at that azimuthal angle should 

be determined and the canonical procedure for predicting the sonic boom should be followed. Predictions and 

minimization calculations are most often done at an azimuthal angle of 90°, since boom levels are most often a 

maximum there. The lateral distribution of the boom should be accurately calculated when the Àight track boom 

has been minimized, since those off track may be larger.

In reference 5.43 (p. 12), Hayes further stated

...Ray-tracing or linear theory methods are only valid where the Àow can be assumed to be locally 

axisymmetric, therefore, the nonlinear codes like MMOC must be modi¿ed to calculate in all azimuthal 

directions. Flow ¿eld codes would have to calculate further radially than they do currently so they could 

match the ray-tracing codes. Otherwise, experimental data for extrapolating from the near ¿eld to the mid 

¿eld would have to be obtained from tests of wind tunnel models in large tunnels.

In reference 5.44, Bobbitt, Kandil, and <ang looked at the effects of wing dihedral on sonic boom using the 

3-D-Full-Potential Propagation code of reference 5.45. The motivation for this study was the perception that the 

bene¿cial effects of dihedral may have been underestimated in the past due, in part, to the de¿ciencies of the 

propagation codes in use. Test cases included three 60° delta wings, two with dihedral of 15° and 20° and the 

third was straight (Àat, no dihedral). One delta wing has a 5 percent biconvex airfoil section and a second was 

slab sided. The lift coef¿cient was maintained at the same value for both the plain (straight) and dihedral wings 

by varying angle of attack. Some results of this study are presented in ¿gure 5.23 (ref. 5.44) for the straight 

delta wing (no dihedral) with a chord of 60 feet and similar delta wings with dihedrals of 15° and 20°. The Àight 

conditions are for Mach 2 at 50,000 feet and at lift coef¿cients of 0.077.

Figure 5.22. 0HDVXUHGDQGSUHGLFWHGHIIHFWVRIDQKHGUDODQGGLKHGUDORQVRQLFERRPUHI
Chapter 5 Approaches to Sonic Boom Minimization

158

Figure 5.23(a), which shows the on-track variation of the initial (bow) shock strength with altitude, in contrast 

with the results in ¿gure 5.22, indicates that the bene¿ts of dihedral persist all the way to ground from 50,000 

feet (833 body lengths). Figure 5.23(b) and ¿gure 5.23(c) show the variation of the initial (bow) shock strength 

and trailing (tail) shock strength, respectively, as a function of lateral distance from the Àight track. It can be seen 

that for the initial (bow) shock (¿g. 5.23(b)), the strength of both straight and 15° dihedral wing decrease with 

lateral distance and the difference in their strength also decreases. The trailing (tail) shock for the straight wing 

(¿g. 5.23(c)) also decreases as lateral distance increases. For the 15° dihedral wing, the reduction in the trailing 

shock on track is much larger than that realized on the initial (bow) shock and this bene¿cial effect only persisted 

to about half the lateral distance realized for the bow shock. This indicates that there is a lift effect as well as a 

volume effect.

It should be noted that the lateral extent of the sonic boom footprint for the given Àight conditions is about 

135,000 feet lateral to the ground track. Thus, the lateral extent of the results in the ¿gure (40,000 feet) suggests 

that the effects of dihedral beyond 40,000 feet and out to lateral cutoff for the cases shown are small.

Wing dihedral has been shown to be effective in providing boom relief for both on- and off-track locations on the 

ground. Reductions of from 18 percent to 28 percent of the on-track boom levels have been predicted for vehicles 

having 10-15° dihedral and continue at lesser bene¿ts out to about 1/3 of the distance to lateral cutoff. Dihedral 

does not inÀuence the extent of the lateral cut-off distance, which is independent of vehicle con¿guration and is 

only a function of altitude, Mach number, and the atmosphere. 

(b) Variation of initial (bow) shock strength with 

lateral distance. 

(c) Variation of trailing (tail) shock strength 

with lateral distance.

(a) Variation of initial (bow) shock strength below wings.

Figure 5.23. (IIHFWRIZLQJGLKHGUDORQVRQLFERRPRYHUSUHVVXUHIRUDGHOWDZLQJKDYHSHUFHQWELFRQYH[VHFWLRQDQG

IRRWFKRUGÀ\LQJDW0DFKDWIHHWDQGD&L

 DGDSWHGIURPUHI
Chapter 5 Approaches to Sonic Boom Minimization

159

Low-Boom Concepts

In principle, an aircraft can be designed to produce almost any type of sonic boom signature. Such a design, if it 

is to Ày supersonic over land, must result in a viable aircraft with an acceptable low-boom shaped signature. It 

is known that aircraft con¿guration and technology advances are key players in attaining such a vehicle. Aircraft 

size (which is driven by the number of passengers) where boom levels tend to decrease as the vehicle decreases 

in size is also a key factor in producing a viable aircraft design that generates a low-boom shaped signature. 

Thus, a 10-passenger supersonic business jet has a much better chance of producing an acceptable boom than a 

300-passenger commercial transport.

One illustration of the signi¿cance of aircraft con¿guration on sonic boom minimization is given in ¿gure 5.24 

(ref. 5.42). Sonic boom levels are shown as a function of aircraft weight at the beginning of cruise for four 

transcontinental vehicles of equal lengths of 290 feet with planforms varying from a delta-wing vehicle with tail to 

a tailless highly swept arrow wing with a canard. Sketches are used to show modi¿ed effective area developments 

and signatures corresponding to each of the four con¿gurations. 

An important consideration that often arises in discussions of sonic boom minimization is the advantage that 

can be taken of across-the-board technology advances. As such, each of the four design point airplane weights 

were also evaluated for combined empty weight and speci¿c fuel-consumption reductions of 10 to 20 percent, 

as shown in ¿gure 5.24. Overpressures of 1.0 lb/ft2

 and less are usually associated with the highly swept arrow 

wing planforms. It can be seen that, although technology advances offer appreciable gains in terms of reduced 

sonic boom level, these gains are not comparable with those potentially attainable through the employment of 

low-boom design approaches.

In the following sections, several con¿guration studies will be presented for supersonic transports and supersonic 

business jet size vehicles.

Supersonic Transports

In 1972, Kane conducted a study (ref. 5.46) to determine if an airplane designed to produce a low-boom shaped 

signature represented a feasible supersonic transport. It was found that, in principle, sonic boom designed 

con¿gurations represent a potentially realistic concept assuming technology advances. Two goals were chosen, 

a high-speed  ̈p = 1.0 lb/ft2

 or less for a supersonic cruise of Mach 2.7, an altitude of 55,000 feet (¿g. 5.25), and 

a mid-Mach  ̈p = 0.5 lb/ft2

 for a supersonic cruise of Mach 1.5 and altitude of 45,000 feet (¿g. 5.26).

)LJXUH 6LJQL¿FDQFHRIDLUFUDIWFRQ¿JXUDWLRQDQGZHLJKWRQVRQLFERRPPLQLPL]DWLRQ0DFKIW

QPL3$;DGDSWHGIURPUHI
Chapter 5 Approaches to Sonic Boom Minimization

160

(a) Con¿guration layout.

(b) Design point area distribution.

(c) Predicted boom signatures.

Figure 5.25. &KDUDFWHULVWLFVRIORZVRQLFERRPVXSHUVRQLFWUDQVSRUWFRQFHSW±KLJKVSHHGGHVLJQ0DFKO IW

design ǻS 07: OEV3$; FRQVWDQWDOWLWXGHFUXLVHRIIWDGDSWHGIURPUHI

(a) Con¿guration layout.

(b) Design point area distribution.

(c) Predicted boom signatures.

)LJXUH &KDUDFWHULVWLFVRIORZVRQLFERRPVXSHUVRQLFWUDQVSRUWFRQFHSW±0LG0DFKGHVLJQ0DFKO IW

design ǻS OEIW2

 07: OEV3$; FRQVWDQWDOWLWXGHFUXLVHRIIWDGDSWHGIURPUHI
Chapter 5 Approaches to Sonic Boom Minimization

161

The high-speed design goal was achieved with a blended arrow wing con¿guration with dihedral and with podmounted engines at the wing trailing edge, shown in ¿gure 5.25(a). A folding canard was also used at low speed. 

An overall equivalent area distribution based on the design point is shown in ¿gure 5.25(b) and follows the 

desired 3/2 power law slope to provide a Àat-top signature for cruise altitude of about 60,000 ft. The nose of the 

area envelope was blunted to reduce the amount of fuselage ahead of the wing. This aircraft was designed to have 

the capability of carrying 151 passengers 3220 nmi.

In ¿gure 5.25(c), the estimated sonic boom signatures are as shown for the Mach 2.7 constant altitude cruise at 

beginning, middle, and end of cruise. Two observations may be made. Although the  ̈p = 1.0 lb/ft2

 design goal 

was achieved, the signature shocks have not completely coalesced and, as such, the Àat-top signature was not 

realized. Also, the tail shocks (recompressions) at the beginning and mid cruise were somewhat greater than 1.0 

lb/ft2

. It was stated (ref. 5.46) that the most critical problem with this con¿guration was the stability at subsonic 

speeds and low weights.

The Mach 1.5 design of the 1972 Boeing study (ref. 5.46) had a goal of  ̈p = 0.5 lb/ft2

 (24 N/m2) for a Àight at 

Mach 1.5 and an altitude of 45,000 feet. Figure 5.26 (ref. 5.46) presents the characteristics of this concept. The 

mid Mach was chosen because preliminary data indicated that a reasonable size and weight aircraft could be 

designed to produce cruise boom signatures of 0.5 lb/ft2

. 

The design was also a blended arrow-wing con¿guration with dihedral and with pod-mounted engines on the 

wing trailing edge shown in ¿gure 5.26(a). In ¿gure 5.26(b), the design point equivalent area (Ae

) distribution, 

which was to follow the quadratic law in shape in order to produce a ramp signature, is shown. Note that the 

airplane is quite slender at the nose to maintain the front shock  ̈p within the design criteria and this led to the 

arrow wing and an up-loaded (not normal) horizontal tail for longitudinal balance and trim.

Sonic boom signatures calculated for this baseline airplane are shown in ¿gure 5.26(c) for beginning, middle, 

and end of cruise; all at constant Mach and altitude. All three signatures are of the ramp type where the initial 

bow shock is about 0.25 lb/ft2

 ramping to almost 2.0 lbs/ft2 at beginning cruise and to about 1.0 lb/ft2 at end of 

cruise. In addition, the tail (recompression) shock is about 0.75 lb/ft2

 and could not be reduced further without 

some extreme aft body contouring and attendant drag increase. The aircraft would have been capable of carrying 

180 passengers 3220 nmi.

As mentioned earlier in this section, a reduction in sonic boom loudness outdoors (via ramp signature with 

large shock rise time) without a reduction in maximum overpressure,  ̈p, may not reduce annoyance of indoor 

observers as compared to an N-wave of equal maximum overpressure. A ¿nal observation is that this Mach 1.5 

con¿guration is designed to have a lower boom than the high-speed design of the previous ¿gure by being longer 

and Àying at a lower altitude and Mach number. It is important to point out that, as shown in this study, the slope 

of the aircraft equivalent area distribution (the 3/2 power, 5/2 power, quadratic, linear, etc.) establishes the desired 

shaped boom signature. Also, as will be noted in Chapters 6 and 7 of this publication, the slope of Ae buildup 

depends upon the Mach number, Àight altitude, and airplane length, l. The larger the aircraft length (l), the more 

linear the buildup of the equivalent area distribution (Ae

) must be. As distance from the aircraft increases, ramp 

type signatures will, as they propagate to the ground, want to develop into N-waves. Thus, ramp signatures may 

be more compatible to long aircraft Àying at low-Mach altitude. Flat-top signatures, on the other hand, usually 

allow aircraft to Ày at high altitude, which in turn dictates higher Mach numbers. 

In sonic boom minimization, the total length of the airplane has proven to be a design parameter of extreme 

importance. Ferri (ref. 5.2) took advantage of the fact that the required length of the airplane can be interchanged 

with the height of the airplane. This tradeoff suggested a biplane concept, one having wings that do not interfere 

at supersonic speeds and do not choke at transonic speeds, with potential to minimize the boom.

Figure 5.27 (ref. 5.2) presents a possible biplane con¿guration and corresponding predicted boom signature at 

the ground. This vehicle is also designed to Ày at a lower Mach-altitude cruise such that the desired near-¿eld 
Chapter 5 Approaches to Sonic Boom Minimization

162

signature is realized at ground level. As such, the aircraft is long (290 feet) and slender with the upper wing 45 

feet above the fuselage centerline. Cruise is at Mach 1.5 and an altitude of 40,000 feet.

Figure 5.27(b) illustrates the boom signature predicted for the biplane concept. Note that it is a ramp type with 

an initial shock  ̈p of 0.3 lb/ft2

 ramping to about 0.45 lb/ft2. Here again, as noted on the previous Boeing midMach design (¿g. 5.26), the tail (recompression) shock has a  ̈p = 0.6 lb/ft2

. However, if the calculated signature 

would be realized in actuality (i.e., rear shock does not recompress to ambient pressure but gradually trails away 

to ambient pressure) then an outdoor observer would only hear a boom of about 0.4 lb/ft2

. Here again, indoor 

observers would experience the annoyance of the 0.6 lb/ft2

 recompression shock.

As mentioned earlier in this section, Àight altitude and airplane weight play key roles in the determination of the 

sonic boom signature. Figure 5.28 (ref. 5.2) illustrates the inÀuence of these two parameters. Figure 5.28(a) shows 

the predicted boom signatures for a biplane con¿guration Àying at altitudes of 40,000 feet and 60,000 feet at 

Mach 2.7. The airplane is 300 feet long and is similar in shape to the con¿guration shown in the previous ¿gure. 

Note that both signatures are ramp type with initial shocks of  ̈p = 0.3 lb/ft2

 for a Àight at an altitude of 40,000 

feet and  ̈p = 0.4 lb/ft2

 for an altitude of 60,000 feet. Both signatures then ramp up to about 0.6 lb/ft2 and 0.8 lb/ft2, 

respectively. More importantly, the boom signature for the vehicle Àying at the lower altitude has a lower boom 

level and shorter length than at an altitude of 60,000 feet due to lift effects. 

(b) Sonic boom signature.

(a) Possible biplane con¿guration. 

Figure 5.27. 3RVVLEOHELSODQHFRQ¿JXUDWLRQDQGSUHGLFWHGERRPVLJQDWXUH0DFKDWIWO IW

Zcruise OEV3$;PLOHUDQJHDGDSWHGIURPUHI

(a) Effect of Àight altitude. (b) Effect of airplane weight. 

)LJXUH ,QÀXHQFHRIDOWLWXGHDQGFUXLVHZHLJKWRQERRPVLJQDWXUHVDGDSWHGIURPUHI
Chapter 5 Approaches to Sonic Boom Minimization

163

Some interesting comments made by Ferri (ref. 5.2) regarding this situation reveal that if the equivalent area 

distribution selected on the basis of sonic boom optimization requires too large a fuselage in the front part of the 

vehicle, the requirement can be satis¿ed by using highly swept-back wings. However, if the Àight Mach number 

increases at constant altitude or the Àight altitude decreases for the same Mach numbers, then the maximum 

fuselage cross section permitted corresponding to the total area distribution selected decreases. As a consequence, 

solutions are obtained that do not have practical applications because the permissible fuselage is too small. 

Because the cross section and volume of the fuselage required for a vehicle are dictated by the mission, the 

apparent advantage from the point of view of reduced sonic boom of low-altitude Àight (below 40,000 feet), as 

indicated by generalized optimization studies, cannot be achieved when realistic requirements of volume, area, 

and length of the fuselage are introduced even if the large reduction of airplane performance, due to the decrease 

of Àight altitude, could be accepted. 

Airplane weight and hence wing lift can exert a powerful inÀuence on the sonic boom signature. Predicted 

signatures for three airplanes at Mach 2.7 and a cruise altitude of 60,000 feet having the same length (300 feet) 

and same distribution of cross-sectional area but at cruise weights of 230,000 pounds, 340,000 pounds, and 

460,000 pounds are shown in ¿gure 5.28(b) (ref. 5.2). The con¿guration is a double-delta planform with canard. 

Note that the signatures, at least at the lower weights, are Àattop in character as dictated by the area development 

for this con¿guration. It can be seen that a decrease in weight decreases substantially the  ̈p. In fact, a halving of 

the weight decreases the bow shock by about 40 percent.

It has been shown thus far that cruise boom levels on the order of 1.0 lb/ft2

 or less may be possible for SST-size 

concepts that are on the order of 300-feet long, weigh about 600,000 to 700,000 pounds at takeoff, and have 

¿neness ratios (length divided by equivalent diameter based on Ae

) of about 30. Concorde was about 200-feet 

long and weighed about 400,000 lbs at takeoff, and had a ¿neness ratio of about 20. 

6XSHUVRQLF%XVLQHVV-HWV

It is of interest to also look at a vehicle of smaller size and weight with regard to sonic boom. In 1995, a study 

was made (ref. 5.47) to provide a compilation of all documented supersonic business jet activities from 1963 to 

1995 by universities, industry, and NASA. One of the con¿guration studies, conducted in the 1986 time period, 

documented the effects of emerging technology on a dual use Business/Interceptor Supersonic Cruise Jet. A threeview of the study con¿guration is shown in ¿gure 5.29.

Figure 5.29. &RQYHUWLEOH%XVLQHVV,QWHUFHSWRUVXSHUVRQLFFUXLVHDLUFUDIWFRQ¿JXUDWLRQ0DFKO IW

DOW IW3$; 5DQJH QPL07: OEVUHI
Chapter 5 Approaches to Sonic Boom Minimization

164

This 1986 study was initiated to assess the feasibility of an eight-passenger, supersonic cruise long-range business 

jet aircraft that could be converted into a military missile carrying interceptor. The baseline passenger version 

had a Àight crew of two with cabin space for four rows of two passenger seats plus baggage. The ramp weight 

was 61,600 pounds. Range was 3,622 nautical miles at Mach 2.0 cruise. Balanced ¿eld take-off distance was 

6,600 feet and landing distance was 5,170 feet at 44,737 pounds. The passenger section from aft of the Àight crew 

station to the aft pressure bulkhead in the cabin was modi¿ed for the interceptor version. Bomb-bay type doors 

were added and volume was suf¿cient for four advanced air-to-air missiles mounted on a rotary launcher. One of 

the main constraints established for this study was that the external geometry of the concept would be retained so 

the aerodynamic performance would be the same for both missions. No attempt was made to design this vehicle 

for minimum boom. Wing loading was about 63 lbs/ft2

 and the L/D at mid cruise about 7.0. This aircraft had a 

¿neness ratio of about 17 and the N-wave boom signature at mid cruise was about 0.9 lb/ft2

.

When boom minimization becomes a ¿rst order concern, the vehicle design requires an entirely different 

approach that may incorporate unique features in order to achieve the low-boom goal. For example, variable 

swept aft wings were employed on several SSBJ concepts discussed in reference 5.47 and more recently by 

Gulfstream (ref. 5.48). A study by the Japan Aerospace Exploration Agency found that a variable swept forward 

wing was considered to be a suitable con¿guration for an SSBJ (ref. 5.49). A most interesting and unique effort by 

Gulfstream Aerospace Corporation and their desire to bring a quiet civil supersonic aircraft to market involved a 

con¿guration employing their quiet nose spike, as shown in ¿gure 5.30 (refs. 5.50 – 5.53) to acquire a low-boom 

equivalent area distribution. Figures 5.30(a) and 5.30(b) show the vehicle with the nose spike in the deployed and 

stowed position. 

Gulfstream’s efforts began in 2004 with CFD analyses followed by wind-tunnel tests in the NASA Unitary Tunnel 

(ref. 5.51). These results con¿rmed that a ramp-shaped boom signature would result at ground level as indicated 

by the near- and far-¿eld ground signature results shown in ¿gures 5.30(c) and 5.30(d). A full-scale Àight version 

of the Quiet Spike was then adapted to the NASA F-15B and in-Àight and near-¿eld probe measurements were 

acquired in 2006 that further con¿rmed its performance (ref. 5.50). See also ¿gures 4.24 – 4.26 in Chapter 4 of 

this publication for additional details of the quiet nose spike.

(c) Wind-tunnel/CFD near-¿eld signatures. 

(a) High-speed concept with deployed quiet spike. (b) Low-speed concept with stowed quiet spike. 

(d) Propagated wind-tunnel/CFD ground signatures. 

)LJXUH $*XOIVWUHDPVXSHUVRQLFEXVLQHVVMHWFRQFHSWHPSOR\LQJ4XLHW6SLNHDGDSWHGIURPUHIVDQG
Chapter 5 Approaches to Sonic Boom Minimization

165

A ¿nal note of interest regarding the Quiet Spike cited in Chapter 4 is whether it could play a bene¿cial role at 

off-design conditions, in particular during the transition phase of Àight to minimize the focus boom signature. 

Howe (ref. 5.54) has shown that placement of the engines above the wing can bene¿t the sonic boom by partially 

shielding the inlet shocks thereby inÀuencing shock coalescence to allow shaped signatures to reach the ground. 

A detailed discussion of engine placement is presented in Chapter 7. 

In this section, boom minimization by way of aerodynamic modi¿cations that leave the total enthalpy of the 

Àow essentially unchanged was discussed. A presentation of several con¿gurations/planforms aimed at boom 

minimization, a discussion of the role that the volume and lift distribution of an aircraft play in shaping the boom 

signature, and a brief review of the equivalent body of revolution concept were included. Wind-tunnel and Àighttest results were presented that con¿rm the persistence of a shaped signature from an aircraft to the ground. It was 

shown that wing dihedral plays a role in reducing the boom intensity on track and redistributing the boom levels 

on each side of the aircraft ground track to provide a more uniform boom exposure pattern. Several low-boom 

concepts of supersonic transports and supersonic business jets were shown and discussed that demonstrate that 

low-boom shaped signatures can be produced by properly arranging the aircraft volume and lift distributions to 

acquire the desired equivalent area distribution (Ae

).

Boom Minimization through Exotic Concepts

The previous discussion addressed aircraft con¿gurations that leave the total enthalpy (a measure of the total 

energy of a thermodynamic system) of the Àow essentially unchanged and assigned them the term “aerodynamic 

con¿gurations” (ref. 5.21). In the remainder of this section, discussion will be focused on con¿gurations or 

techniques that change the total enthalpy of a signi¿cant fraction of the Àow past them as well as those that rely 

on physics beyond present comprehension and assign them the term “exotic concepts”. Four such concepts are 

illustrated in ¿gure 5.31. These concepts include – (1) those that alter the airstream (phantom body) to increase 

the effective length through heat or mass addition as per Miller and Carlson (refs. 5.55 and 5.56), Batdorf (refs. 

5.57 and 5.58), and Swigart and Lubard (ref. 5.59), as shown in ¿gure 5.31(a), and (2) those that employ shock 

refraction from arti¿cial changes in acoustic impedance as per Rethorst et al. (ref. 5.60) and Henderson (ref. 5.61), 

as shown in ¿gure 5.31(b), and (3) the Resler (ref. 5.62) concept, which examined the premise of eliminating the 

boom due to lift through thermodynamic processes by achieving a reduced area stream tube as shown in ¿gure 

5.31(c) (accomplished by the incorporation of special engine designs), and (4) the concept examined by Galanis 

(ref. 5.63), who calculated some of the practical consequences of the streamtube area reduction method and the 

heat or mass addition phantom body concept as well as the Goethert and Gruska scheme (ref. 5.64, ¿g. 5.31(d), 

pp. 2.157 – 2.180) of using the lift component of a deÀected exhaust jet to increase the lifting length of the vehicle 

and thus reduce the boom.
Chapter 5 Approaches to Sonic Boom Minimization

166

Heat or Mass Addition

The phantom body exotic concept shown in ¿gure 5.31(a) has been the exotic concept most aggressively 

researched and studied. The nature of the airstream alterations required to produce the phantom body in order 

to achieve the highly desirable ¿nite rise time signature will be discussed along with an estimate of the power 

requirements necessary to attain the low overpressure and large shock rise times for boomless signatures. Use 

of a thermal ¿n as a means of altering the airstream will be discussed.

Airstream Alteration

An effective area development (solid line curve) of an airplane that would produce an N-wave as well as a phantom 

body area development (dashed curve), resulting from a combination of the airplane and altered airstream, are 

depicted in ¿gure 5.31(a). These area developments would also produce a boomless signature on the airplane 

ground track. The difference between the area development of the phantom body and that of the airplane de¿nes 

the required airstream alterations that must be created using a carefully controlled heat or force ¿eld extending 

well ahead of and behind the airplane. At ground positions away from the Àight track, the airplane effective area 

development assumes a different shape and magnitude. Thus, boom elimination at all ground positions would 

require a carefully controlled azimuthally as well as longitudinally altered airstream. As will be shown in a later 

¿gure, the phantom body must be much longer than the actual aircraft in order to acquire the desired ¿nite rise 

time signature. However, if the vehicle slenderness ratio is not increased, the added effective area produced by 

the phantom body will actually increase the maximum sonic boom overpressure over that of the basic airplane.

In ¿gure 5.31(a), it was noted that the phantom body length is the primary factor upon which the sonic boom 

signature characteristics as well as the power requirements depend. Figure 5.32 (ref. 5.55) shows how the rise 

time IJ increases and the maximum ground overpressure  ̈ pmax decreases as the phantom body area development 

(c) Streamtube area reduction (ref. 5.62). 

(a) Heat or mass addition (ref. 5.55). (b) Shock refraction (ref. 5.60). 

(d) Lifting component of deÀected exhaust jet (ref. 5.64). 

Figure 5.31. 6RPHH[RWLFFRQFHSWVIRUERRPPLQLPL]DWLRQ
Chapter 5 Approaches to Sonic Boom Minimization

167

is stretched out. In selecting a reasonable body length, no values less than 900 feet are considered because lengths 

less than that do not produce a ¿nite rise time. As expected, the power requirements increase with increasing 

length. The desired rise time is the primary factor for de¿ning the necessary phantom body length and the 

maximum power requirements. A rise time of 30 msec and a corresponding body length of 975 feet were chosen 

for the example to provide a near minimum power requirement while offering signi¿cant sonic boom bene¿ts and 

a margin against possible adverse effects of atmospheric distortion (i.e., nonlinear shock steepening). 

The results of studies reported in reference 5.55 indicate that power requirements become less for lower Mach 

numbers, but not to the extent that the scheme appears to be more practical. For high Mach numbers, which are 

more attractive from an economic standpoint, the power requirements are greater. For a given Mach number, power 

requirements are not signi¿cantly less at altitudes above or below those normally selected for cruise economy.

The requirements for elimination of the front shock (i.e., obtaining signi¿cant shock rise time) has been 

examined by Lipfert (ref. 5.65) and the results are shown in ¿gure 5.33. It can be seen that in order not to 

exceed the baseline aircraft overpressure, a phantom body length of about 550 feet is required as compared to 

the 298-foot length of the actual aircraft. Note too that a shock rise time of only 0.10 seconds (100 msec) is 

acquired. Thus, it is necessary to triple the aircraft length in order to achieve a ¿nite rise time without increasing 

the overpressure. Large penalties in terms of increases in effective area and signature impulse are also incurred. 

On ¿rst impression, it would appear the airstream alteration concept has been applied to an N-wave designed 

aircraft with already undesirable lift and volume characteristics. It would be of interest to apply the concept to 

a con¿guration that has already been minimized through aircraft shaping.

Figure 5.32. 3KDQWRPERG\OHQJWKFRQVLGHUDWLRQDGDSWHGIURPUHI
Chapter 5 Approaches to Sonic Boom Minimization

168

Thermal Fins

The thermal ¿n (refs. 5.57 and 5.59) is one of many approaches that have been proposed regarding airstream 

alterations to produce a phantom body and may be described with the aid of ¿gure 5.34. The unique features of 

the thermal ¿n are the direct burning of fuel to produce the heat ¿eld and the introduction of the heat below the 

airplane itself. Batdorf (ref. 5.57, p. 336) points out that “with direct burning of jet fuel, the power requirements 

for bow shock elimination are not necessarily prohibitive” and that “locating the heat ¿eld below the airplane 

would be attractive from the standpoint of airplane thermal environment and safety.” 

)LJXUH 7KHUPDO¿QFRQFHSWUHI

Figure 5.33. )URQWVKRFNHOLPLQDWLRQUHTXLUHPHQWVUHI
Chapter 5 Approaches to Sonic Boom Minimization

169

As stated by Miller (ref. 5.55, p. 337)

The conceptual single thermal ¿n arrangement illustrated at the center of ¿gure 5.34 is compared with 

an un-implemented axial distribution of heating and cooling shown at the left. Because the thermal ¿n 

as presently conceived provides for heat addition only, the airplane must be reshaped and the phantom 

body forepart must be extended an additional 27 ft to provide an airstream that requires no heat removal. 

For the single thermal ¿n, no signi¿cant increase in power over the basic axial concepts is required. 

With direct burning during the supersonic portion of a coast-to-coast Àight, it is estimated that power 

requirements can be met with about a 20-percent increase in onboard fuel. It should be noted that the 

single thermal ¿n would be effective in eliminating only the bow shock, and the tail shock would 

remain unless some means is provided for properly shaping the rear portion of the phantom body. 

The possibility of employing a second thermal ¿n for tail shock suppression was considered and is 

illustrated on the right in the ¿gure. Estimates indicate that total shock elimination employing thermal 

¿ns would require about 60 percent additional onboard fuel, with no account being taken of the weight 

and performance penalties of the system.

It is obvious that the thermal ¿n that must extend about 80 feet below the airplane would pose severe if 

not insurmountable problems related to aircraft performance, stability, structure, and weight. 

Six models were used in the wind-tunnel test program conducted in the NASA Langley 4- by 4-foot Supersonic 

Wind Tunnel as illustrated in ¿gure 5.35. The design and construction of models, data reduction, analysis, and 

reporting was conducted by Aerospace Corp. (ref. 5.66) under contract to NASA.

The test program was divided into two parts. The ¿rst part consisted of testing the four non-lifting bodies shown 

diagonally across the top of the ¿gure. The basic model in this series was a 10-inch long body of revolution having 

an effective area development representative of an SST at cruise speeds. The second model was essentially an 

isentropic spike modi¿cation of the basic model with an additional length of 6 inches, which was designed to 

produce a ¿nite rise time signature. Each of the remaining two models in this series had a vertical ¿n extending 

about 4 inches below the model nose. The ¿n models were designed to have identical effective area developments 

and thus produce identical signatures as the isentropic spike model. The solid mechanical ¿n was about 40 percent 

larger than the thermal ¿n – this difference being simulated by means of hot gas ejection. The second part of the 

test program involved the testing of two lifting wing-body models shown at the lower left of the ¿gure. The basic 

wing body model produced a lift-induced sonic boom pressure signature with shocks. The wing-body model 

Figure 5.35. 0RGHOVIRUZLQGWXQQHOSURJUDPUHI
Chapter 5 Approaches to Sonic Boom Minimization

170

with the thermal ¿n was designed to suppress the shocks. In the actual tests, the wing-body model con¿guration 

included the solid ¿n rather than the thermal ¿n with Àow.

For each of the models, signatures were measured at Mach 2.01 for a minimum of two model-probe separation 

distances. The thermal ¿n model design incorporated instrumentation necessary for measuring the properties of 

the gas being emitted. Some of the results of the experimental program carried out in the NASA Langley 4- by 

4-foot Supersonic Wind Tunnel at Mach 2.01 to investigate the validity of the heat-¿eld concept for sonic boom 

alleviation are presented in ¿gure 5.36 (ref. 5.66). To the left of the ¿gure are shown three of the six con¿gurations 

that were tested and included the basic body of revolution (¿g. 5.36(a)), having a nominal length of 10 inches 

and representative of a 1/360 scale SST con¿guration; the basic body plus solid ¿n (¿g. 5.36(b)) designed so that 

the slope of the area distribution at the test Mach number follows the 5/2 power law so as to provide the ¿nite 

ramp signature; and the basic body and so-called thermal ¿n (¿g. 5.36(c)) in which about 40 percent of the solid 

¿n model is replaced by a heat ¿eld designed to have an area distribution equivalent to that of the basic body and 

solid ¿n. The heat ¿eld is generated by passing nitrogen through a 1/8-inch diameter heating tube that continues 

through the model into a nozzle whose exit plane is at the rear of the ¿n. In order to accommodate the 1/8-inch 

heating tube in the ¿n section, the scale of the thermal ¿n model was increased by a factor of 1.5 over its solid 

counterpart. Hence, the basic body portion of the thermal ¿n model has a nominal length of 15 inches.

(a) Basic body of revolution.

(d) Pressure distribution – basic body.

(b) Basic body and solid ¿n.

(e) Pressure distribution – basic body and solid ¿n. 

(c) Basic body and thermal ¿n. (f) Pressure distribution – basic body and thermal ¿n.

)LJXUH :LQGWXQQHOUHVXOWVIRUWKHUPDO¿QFRQFHSWDGDSWHGIURPUHI
Chapter 5 Approaches to Sonic Boom Minimization

171

The resulting pressure signatures for all three models are shown on the right hand side of ¿gure 5.36. Figure 

5.36(d) presents the measured and calculated signature for the basic body at a distance of two body lengths (h/l 

= 2.0). Good agreement existed between the measured and predicted signatures, which is typical of an N-wave 

design aircraft. The measured and predicted signature (¿g. 5.36(e)) for the basic body and solid ¿n, also at two 

body lengths, displayed the ¿nite rise time signature associated with a 5/2 power law shaped area distribution. 

Again, good correlation existed between theory and measurement. The important question is whether any local 

compression regions will cause a shock wave to develop. Two such regions are seen in the signature shown in 

¿gure 5.36(e) – one at the beginning and one toward the end of the linear pressure rise region. When the signature 

was measured at three body lengths, no signi¿cant steepening occurred for the compressive region at the beginning 

and the one toward the end of the linear region has nearly disappeared. It was noted that even if shock waves 

developed from these compressions, they would account for no more than 10 percent of the total pressure rise.

The measured signature for the basic body plus thermal ¿n (¿g. 5.36(f)) shows the results of passing heated 

nitrogen through the ¿n at the design mass Àow rate and temperature (ref. 5.66). Note the large expansion and 

subsequent recompression (ax-ȕr = 6 in.). This portion of the signature corresponds to disturbances generated 

by the nozzle region of the ¿n, expansion being generated by the growing area de¿cit through the nozzle region, 

and the recompression caused by this de¿cit becoming constant at the end of this region. Visual examination of 

the model after the test indicated that the nozzle slot did not remain constant in width during the test, but bowed 

at the center when the Àow was turned on, giving a mass (and hence area) de¿cit in the lower region of the ¿n. 

This is the probable cause of the expansion recompression region noted in the signature. Further, note the two 

points marked cold Àow and no Àow. These points were obtained by turning the heater power and then the nozzle 

Àow to the off position. In this manner, the effects of the Àow and heat are separated and it is seen that they both 

contribute about equally to the overpressure at this point.

)RUZDUG6ZHSW.HHO

The concept of an isentropic spike projected by energy addition was revisited during the DARPA/QSP program. 

A detailed numerical investigation to further advance the keel concepts of Batdorf and Swigart using high ¿delity 

computational methods in the application of aft-axis volume control for sonic boom mitigation was performed 

by Marconi, Bowersox, and Schetz in 2003 (ref. 5.67). It was also based on Marconi’s earlier work of 1998 (ref. 

5.68). Two equivalent bodies of ¿neness ratio 17.1 and 10.1 having a 5/2 spike area distribution and a forward 

swept solid and thermal keel were investigated at Mach 2.4. The computations were made assuming a vehicle of 

85 feet in length Àying at an altitude of 57,000 feet.

Four speci¿c goals were pursued – (1) examining both on- and off-track boom mitigation, (2) developing 

techniques for a design of thermal keel heating distributions, (3) examining the use of alternate keel orientations 

(length and shape) to minimize overall size, and (4) producing tailored ground signatures for single and multiple 

keel Àow ¿elds. A depiction of the forward swept keel and some numerical results are presented in ¿gure 5.37 

(ref. 5.67).
Chapter 5 Approaches to Sonic Boom Minimization

172

Figure 5.37(b) illustrates the signi¿cant bene¿t of vehicle length ampli¿cation resulting from the addition of 

off-axis volume. In the optimum case of a keel swept forward normal to the Mach plane, a keel length L can be 

used to produce the same effect as a spike of length Mach x L. Sweeping the keel forward so that its leading 

edge is perpendicular to the free-stream Mach line also results in the minimum length of the device. Figure 

5.37(b) also shows the predicted sonic boom ground pressure signatures for the baseline body, the baseline body 

with the phantom spike, and the forward swept thermal keel for both an on-track and 40° off-track location.

The ¿rst observation is that all of the modi¿ed signatures are more acceptable than the baseline body as a result 

of the increased shock rise times for the 5/2 spike and thermal keel at q = 0° and the two lower amplitude shocks 

on the thermal keel at q= 40°. Note the on-track signature from the thermal keel closely matches the 5/2 power 

area distribution having a spike signature rise time of about 35 msec and is also lower in overall magnitude. 

The off-track keel signature displays two small shocks but lacks the bene¿cial rise time of the spike and thermal 

keel on track.

It is of interest to note that in this study (ref. 5.67), the improvements from thermal keel having a 101 ¿neness 

ratio body were not as bene¿cial as for the thermal keel having a 171 ¿neness ratio body. Recall that the 

¿neness ratios of most of the SST and supersonic business jets (SSBJs) is in the 17 to 19 range with some of 

the QSP concepts being as high as 22.

)RFXVHG0LFURZDYH(QHUJ\

Another concept of an isentropic spike projection by energy addition funded under the 2000 DARPA/QSP 

program was the work of Miles et al. at Princeton University (ref. 5.69). This study explored the possibility of 

achieving signi¿cant reductions of sonic boom by combining dynamic aft-body energy addition and/or near-

¿eld shock focusing with vehicle shape optimization. Various antenna con¿gurations were analyzed to establish 

their ability to focus microwave energy to the required ¿eld strengths. One example is shown in ¿gure 5.38 

(ref. 5.69), suggesting a four-array con¿guration mounted under the aircraft, which focuses the 49 megawatts of 

microwave energy about 46 meters ahead of the vehicle. They also note that this location can be rapidly moved 

by changing the relative phases of the transmitting elements.

(b) Predicted ground signature comparisons.

(a) Pressure distribution – basic body and thermal ¿n.

Figure 5.37. 6FKHPDWLFRIIRUZDUGVZHSWNHHOFRQFHSWDQGJURXQGVLJQDWXUHFRPSDULVRQVIRUDERG\¿QHQHVV

UDWLRDVSLNHDQGWKHUPDONHHORQDQGRIIÀLJKWWUDFNDGDSWHGIURPUHI
Chapter 5 Approaches to Sonic Boom Minimization

173

Shock Refraction

The Rethorst concept, which employed shock refraction from arti¿cial changes in acoustic impedance to alter 

the airstream, was ¿rst examined in the mid-1960s during the U.S. SST Program (ref. 5.60). In the mid-1980s, 

Rethorst’s Vehicle Research Corporation (VRC) claimed to have discovered a practical approach for no or lowboom supersonic Àight and patented the concepts shown in ¿gure 5.39. Note that two engine arrangements are 

proposed for a basically similar aircraft con¿guration – one of underwing pods as shown in ¿gure 5.39(a) and the 

other of tail-mounted pods as shown in ¿gure 5.39(c). For each case, a very large circular ring is located forward 

near the cockpit to provide a sheet of air that envelopes the complete vehicle. The wing/jet system is shown in 

¿gure 5.39(b).

)LJXUH 0RGHORIPLFURZDYHIRFXVLQJWRDPHWHUGLDPHWHUVSRWPHWHUVEHORZWKHDLUFUDIWZLWKIRXUPHWHU

PXOWLHOHPHQWDUUD\VHPLWWLQJDW*+]DQGORFDWHGRQWKHXQGHUVLGHRIWKHDLUFUDIWDVVKRZQLQWKHGLDJUDP

7KHDUUD\VGHOLYHU0:WRWKHEUHDNGRZQUHJLPHUHI
Chapter 5 Approaches to Sonic Boom Minimization

174

As described in the patent, the system discharges a portion or all of the propulsive jet, usually fan air, as a 

planar sheet below and apart from the wing, thereby providing a variable energy Àow. The jet sheet comprises a 

pneumatic shield to contain the underwing pressure, reÀecting the compression waves generated by the forward 

concave-down wing underside upwards against the contracting aft portion of the wing, producing a lift and thrust 

component. As shown in ¿gure 5.39(b), an asymmetric nozzle with an internal upper surface acoustic source is 

located below the wing. A review of the 1992 Rethorst supersonic aircraft shock wave Energy Recovery Patent 

(ref. 5.70) is provided in ¿gure 5.39(c). Essentially, all who have examined this concept agree that minimization 

and even elimination of the boom due to aircraft volume can be accomplished. However, eliminating boom due 

to lift is not possible.

Exhaust Jet Sheet DeÀection

Another application of the aircraft engine exhaust was investigated in the early 1970s by Goethert and Gruska 

(ref. 5.64, pp. 2.157 – 2.180). Some results are provided in ¿gure 5.40. Their research showed that a slot-type 

engine exhaust has the unique capability of shifting lift from the solid surfaces of the wing to the region behind 

the wing. The critical lift is produced by wing pressures and the lift forces produced by the engines. There is no 

lift on the engine or wing wake. Due to lift produced by the engines, the angle of attack can be reduced and the 

level of pressure on the wing reduced. These results were developed for two dimensional Àow conditions. Not 

only is there a shifting (reduction) of the lift on the main wing and an associated reduction of the sonic boom, but 

also favorable effects on the performance of the aircraft in certain Àight regimes (usually at relatively high Mach 

numbers). It was shown that slotted nozzle engine exhausts have the unique capability to shift lift from the solid 

surface of the wing to the region behind the wing, with the resulting increase in lifting length and reduction in 

boom intensity.

(c) Patent review (tail mounted engines).

Figure 5.39. 6KRFNUHÀHFWLRQIURPDUWL¿FLDOFKDQJHVLQDFRXVWLFLPSHGDQFHDGDSWHGIURPUHIVDQG

(a) Boomless con¿guration with underwing engines.

(b) Wing/jet system with shock wave energy recovery mechanism.
Chapter 5 Approaches to Sonic Boom Minimization

175

In ¿gure 5.40(a) and ¿gure 5.40(b), it is shown that the sonic boom signature spreads over a larger distance and 

has a smaller pressure peak when the lifting surface has a larger chord; that is, when lift is spread over a larger 

distance in the Àight direction. The study showed that the distribution of the lift in the Àight direction can occur 

not only by means of stretching the wing chord, but also by having part of the total lift produced by the deÀected 

exhaust of the jet engine(s) as illustrated in ¿gure 5.40(c). The deÀected jet exhausts produce lift, thus reducing 

the lift required of the wing.

Virtually no mention has been made of the boom reductions to be realized with the concept nor the penalties 

associated with its implementation. It was stated that at Mach 3 the jet Àap would be identical in effectiveness to 

a mechanical Àap with a Àap chord of about 35 percent of the main wing.

Other Unique Exotic Minimization Schemes

In 1972, Lipfert (ref. 5.65) conducted a study that considered all identi¿able means of altering the Àow near the 

aircraft that could improve the boom at ground level and to include a realistic assessment of the penalties incurred 

by these various means. It was shown that weight penalties of the order of the baseline aircraft were incurred but 

that smaller weight penalties would result if one could create a precursor signal that would warn of the impending 

boom and, as such, reduce the startle effect. In ¿gure 5.41(a), two approaches are put forth relative to this concept 

(i.e., to create a precursor disturbance) – (1) the use of a small drone aircraft or (2) a laser focused to a remote 

upstream spot. 

(a) Two-dimensional Àat plate at small angle of attack.

(b) Lift on two-dimensional wings at various chord lengths 

and same lift.

(c) Jet Àap principles. 

)LJXUH 6RQLFERRPPLQLPL]DWLRQE\PHDQVRIGHÀHFWHGH[KDXVWMHWVDGDSWHGIURPUHI

( ) À i il
Chapter 5 Approaches to Sonic Boom Minimization

176

However, as will be shown in Chapters 8 and 9, although startle plays a signi¿cant role in outdoor response, a 

precursor signal warning of the impending boom does not necessarily condition the observer to the oncoming 

boom. For example, even though one anticipates thunder following a lightning strike, he or she is still startled. 

Likewise, in the case of aerial ¿reworks, one expects a loud boom following a mortar shell burst at altitude, but 

is still startled by the burst. 

Several other methods for boom reduction have been set forth by Batdorf (ref. 5.57) and Swigart and Lubard (ref. 

5.59) and include the use of a continuous in-line train of explosive pellets that are ignited upon launch from the 

aircraft, as depicted in ¿gure 5.41(b) and the use of a powered tethered drone. The fuel for propulsion and heating 

of this drone would be supplied through the tether as shown in ¿gure 5.41(c).

The concept of a penalty aircraft, put forth by Lipfert (ref. 5.65) and shown in ¿gure 5.41(d), calls for the use of 

a penalty aircraft that would Ày in close proximity to the baseline aircraft (so that the sonic booms interfere) and 

relieve the necessity of increasing the baseline aircraft gross weight. The additional weight would be borne by 

the penalty aircraft and its lift distribution would be tailored to provide, in part, the desired low-boom signature. 

A logical question arises as to the bene¿ts to be gained from such an arrangement. Obviously, both aircraft must 

maintain position in three dimensions very accurately and for the complete range of the mission. While this 

scheme was not considered quantitatively, the favorable trend may be seen by considering Seebass’s criterion (ref. 

5.21) that indicated doubling of the weight (W, baseline plus trailing penalty aircraft) and length (l, baseline plus 

trailing penalty aircraft) results in a reduction of the boom.

(d) Penalty aircraft. (ref. 5.65)

(b) In-line train of explosives. (refs. 5.57 and 5.59)

(c) Power-tethered drone. (ref. 5.59)

(a) Pre-cursor mini warning boom. (ref. 65)

)LJXUH 2WKHUXQLTXHH[RWLFPLQLPL]DWLRQWHFKQLTXHV
Chapter 5 Approaches to Sonic Boom Minimization

177

Overview of Exotic Concepts

A listing of the various exotic schemes relating to sonic boom minimization, that have been discussed are listed 

in table 5.1. Included is a listing of the individuals, the approximate time of their entry into the ¿eld, reference 

to the work, and the mechanism involved. In the discussions following table 5.1, assessment of these activities 

is presented and include those by Lipfert (ref. 5.65), Miller and Carlson (ref. 5.56), and Seebass and George (ref. 

5.21).

Table 5.1. Brief Overview of Exotic Concepts to Minimize Sonic Boom

In a controversial paper written in 1968, Cahn and Andrews (ref. 5.71) proposed an electrostatic scheme of creating 

reduced shock wave strength by means of static charges. Their proposed research method was then analyzed by 

Cheng and Goldberg (ref. 5.72), who assigned unit weight penalties for the electrical equipment required for the 

scheme. Apparently, their analysis did not include a realistic assessment of the effects of the electrical forces on 

the boom signature.

Chuan’s patent (ref. 5.73) dealt with mass removal from the airstream through air condensation into the aircraft 

boundary layer. This would affect a fractional reduction of the boom due to volume but provide no bene¿t to the 

portion due to lift.

Both heat and force ¿elds were considered in the Miller-Carlson study (ref. 5.56). However, in order to completely 

cancel the shocks, it was found necessary to both add heat in some regions and remove it in others. Larger quantities 

of heat may readily be added through combustion, but no such potentially light-weight mechanisms existed for 

cooling. In earlier discussions of references 5.57, 5.58, 5.59 and 5.66, a thermal keel was proposed as a means 
Chapter 5 Approaches to Sonic Boom Minimization

178

of altering the airstream and forming a phantom body. Wind-tunnel tests were conducted and demonstrated the 

concept. The propulsive and control implications of this scheme were not considered.

Another class of boom alleviation was concerned with streamtube contraction by the propulsion system. Resler 

(ref. 5.62) noted that a negative volume effect could be used to cancel a portion of the lift effect if an engine 

could be designed with exit cross-sectional area less than the inlet. His approach may be considered as an extreme 

application of the phantom body concept in which a constant area body would be created by streamtube reduction 

only. If this could be accomplished, no disturbance of any kind would be felt outside the phantom body boundaries. 

It was also noted that the drag for a given lift using this scheme is three times what it would be for an ordinary 

wing with the same lift. Galanis (ref. 5.63) examined the concomitant engine requirements, concluding that a new 

cycle with airstream cooling was required using the fuel as a heat sink. Rethorst’s concept (ref. 5.60) was similar 

in that power plant streamtube contraction was also required, albeit implicitly. Also, both concepts involved wing 

con¿gurations with lift from the top surface only. Such wings provide only half the lift at the same wave drag.

Newman (cited in ref. 5.64, p. 1.4) conducted a brief assessment of using air liquidation to suppress the boom. It 

was found early on that the additional power required to maintain large external surfaces at cryogenic temperatures 

in high Mach number Àow ¿elds was excessive and the work was discontinued. Kohl (cited in ref. 5.64, pp. 

2.127 – 2.156) advanced the idea to use current or future lasers to deÀect the airÀow about the aircraft and thus 

create a phantom body. The laser beam would be focused at distances of 100 feet or more ahead of the aircraft. 

Interest has also risen regarding the use of plasmas for boom minimization; the reasoning being if plasmas reduce 

drag, then it might be possible to delay the onset of sonic booms. Kunhardt et al. conducted a series of shock tube 

experiments to obtain shock wave modi¿cation data by the use of plasmas (ref. 5.74). Goethert and Gruska (ref. 

5.64, pp. 2.157 – 2.180) proposed employing the lifting component of deÀected jet exhausts to essentially increase 

the aircraft lifting length to spread the boom signature and thereby decrease the overpressure. Marconi, Bowersox, 

and Schetz (ref. 5.67) recently revisited the Batdorf-Swigart thermal keel approach by way of a forward-swept 

keel and Miles et al. (ref. 5.69) revisited the Kohl laser approach by way of a microwave focusing array mounted 

under the aircraft.

In this section, minimization and elimination of the sonic boom by means of con¿guration or techniques that 

change the total enthalpy of a signi¿cant fraction of the Àow past them as well as those that rely on physics beyond 

present comprehension and classify them as “exotic concepts” have been discussed. Included are the alteration of 

the airstream about a vehicle to create a phantom body through the use of heat or mass addition, those that employ 

shock refraction from arti¿cial changes in acoustic impedance, those that achieve streamtube reduction through 

aerodynamic means, and those that use the lift component of a deÀected exhaust jet to increase vehicle lifting 

length. Other unique exotic minimization schemes include electro-aerodynamics, cryogenic cooling, focused 

laser or microwave beams, and use of plasmas.

Support for these exotic schemes began in the late 1960s and early 1970s as part of the U.S. SST effort and the 

schemes were revisited in the early 2000s as part of the DARPA/QSP effort. In general, it was found that all of 

the above approaches to boom minimization or elimination carried with them large penalties in terms of either 

large increases in power amounting to more than the aircraft’s propulsion power output or a weight increase of 

the order of the baseline gross weight, or drag increases, for a given lift of about three times that for an ordinary 

wing with the same lift. 

Chapter 5 Summary Remarks

Boom reduction through aircraft operations can be obtained by increasing altitude, use of a climbing Àight pro¿le, 

and Àying at speeds that are less than the sound speed at the ground. Achieving Mach cutoff (MCO) is generally 

limited to Mach < 1.3 depending upon winds and temperatures.

Sonic boom minimization by means of aircraft shaping to produce non-N-wave shaped signatures has been shown 

to be feasible and validated in wind tunnels and in full-scale Àight. Recent developments in CFD codes allow 
Chapter 5 Approaches to Sonic Boom Minimization

179

for the proper management of the aircraft volume, lift distributions, and engine exhaust Àows so as to yield the 

equivalent area distribution (Ae

) required to produce a low-amplitude shape boom signature at ground level.

Wing planform and dihedral has been shown to be effective in providing boom relief for both on- and off-track 

locations on the ground. Dihedral does not play a role in establishing the boom lateral cut-off distance that is 

independent of vehicle con¿guration and only depends on altitude, Mach number, and atmospheric conditions. 

Engine/nacelle locations above the wing provide partial shielding of the inlet shocks and alter the coalescence of 

the near-¿eld shocks.

Numerous studies have been conducted involving exotic concepts – those that change the total enthalpy of the 

Àow as well as those that rely on physics beyond present comprehension. In general, all of these schemes have 

large power, weight, or drag penalties.

Chapter 5 References

5.1 Shepherd, K. P.; Sullivan, B. M.; Leatherwood, J. D.; and McCurdy, D. A. Sonic Boom Acceptability 

Studies. First Annual High Speed Research Workshop, NASA CP-10087, Part 3, April 1992, pp. 1295 

–1311.

5.2 Ferri, Antonio Airplane Con¿gurations for Low Sonic Boom. NASA SP-255, Oct. 1970, pp. 255 – 275.

5.3 Crow, Steven C. and Bergmeier, Gene G. Active Sonic Boom Control. NASA CP-3335, July 1996, pp. 

68 – 111.

5.4 Kane, Edward J. and Sigalla, Armand Effect of Sonic Boom on Supersonic Transport Design and 

Performance. Fifth Conference on Applied Meteorology of the American Meterological Society; 

Atmospheric Problems of Aerospace Vehicles, March 2-6, 1964, Atlantic City, NJ. Also available as 

Boeing Doc. D6-8614, Feb. 1964.

5.5 Patterson, Donald W. Sonic Boom Limitations on Supersonic Aircraft Operations. Aero/Space Engineering, 

July 1960, pp. 22–24 and pp. 40 – 45.

5.6 Lina, Lindsay J. and Maglieri, D. J. Ground Measurements of Airplane Shock Wave Noise for Mach 

Numbers to 2.0 and Altitudes to 60,000 Ft., NASA TN-D-235, 1960.

5.7 Bradley, E. S.; Johnson, W. M.; and Von Keszycki, C. H. Passenger Transport at Low Supersonic Speeds. 

AIAA paper No. 69-776, 1969.

5.8 Maglieri, D. J.; Hilton, D. A.; Huckel, V.; Henderson, H. R.; and McLeod, N. J. Measurements of Sonic 

Boom Signatures from Flights at Cutoff Mach Number. NASA SP-255, Oct. 1970, pp. 243 – 254.

5.9 Haglund, George T. and Kane, Edward J. Flight Test Measurements and Analysis of Sonic Boom 

Phenomena Near Shock Wave Extremity. NASA CR-2167, Feb. 1973.

5.10 Haglund, George T. and Kane, Edward J. Analysis of Sonic Boom Measuements Near Shock Wave 

Extremities for Flight Near Mach 1.0 and for Airplane Accelerations. NASA CR-2417, 1974.

5.11 Seebass, R. Nonlinear Acoustic Behavior at a Caustic. NASA SP-255, Oct. 1970, pp. 87 – 120.

5.12 Randall, D. G. Methods for Estimating Distributions and Intensities of Sonic Bangs. R	M, No. 3113, 

British A.R.C., 1959.

5.13 Friedman, Manfred P. and Chou, David C. Behavior of the Sonic Boom Shock Wave Near the Sonic 

Cutoff Altitude. NASA CR-358, 1965.
Chapter 5 Approaches to Sonic Boom Minimization

180

5.14 Thery, C. Refraction Atmospherique et ReÀection au Sol Des Bangs. AGARD Conf., Proc. No. 42, May 

1969.

5.15 Guiraud, J. P On the Intensity Value of Sonic Boom in the Neighborhood of a Caustic. C.R.H. Acad. Sci., 

Vol, 256, No. 8, Feb. 18, 1963 (A63-16929).

5.16 Maglieri, Domenic J. and Plotkin, Kenneth J. Aeroacoustics of Flight Vehicles Theory and Practice. 

NASA RP 1258, Vol, 1 and WRDC TR 90-3092, Aug. 1991, pp. 519 – 561.

5.17 Kane, Edward J. and Palmer, Thomas <. Meteorological Aspects of the Sonic Boom. SRDS Report No. 

RD 64-160, FAA, ASTIA No. AD 610 463, 1964.

5.18 <eager, Chuck <eager An Autobiography. A Bantam Book, July 1985, p. 130.

5.19 Perley, Richmond Design and Demonstration of a System for Routine Boomless, Supersonic Flights. 

Report No. FAA-Rd-77-72, April 1977.

5.20 McLean, F. E. Some Non-Asymptotic Effects on the Sonic Boom of Large Airplanes. NASA TND-2877, 

June 1965.

5.21 Seebass, R. and George, A. R. Sonic Boom Minimization. Jour. Acous. Soc. of Am., Vol. 51, 1972, pp. 

686 – 694.

5.22 Busemann, A. Aerodynamischer Auftrieb bei Uberschallgeswindigkeit, Volta Congress, 1935, pp. 315–

347.

5.23 Busemann, A. The Relation Between Minimizing Drag and Noise at Supersonic Speeds, High-Speed 

Aeronautics. Polytechnic Institute of Brooklyn, Brooklyn, N<, 1955.

5.24 Baals, Donald D. and Foss, Willard E., Jr. Assessment of the Sonic Boom Problems for Future AirTransport Vehicles. Jour. Acous. Soc. of Am., Vol. 39, No. 5, part 2, 1966, pp. S-73-S80.

5.25 McLean, Edward F. Con¿gurations Designed for Speci¿ed Pressure Signature Characteristics. NASA 

SP-180, May 1968, pp. 37 – 45.

5.26 Hunton, Lynn W. Current Research in Sonic Boom. NASA SP-180, May 1968, pp. 57–66.

5.27 Sims, Alex G. and Curry, Robert E. Flight Characteristics of the AD-1 Oblique-Wing Research Aircraft. 

NASA TP-2223, March 1985.

5.28 Li, P.; Seebass, R.; and Sobieczki, H. The Sonic Boom of an Oblique Flying Wing. CEAS/AIAA-95-107, 

June 1995.

5.29 Kulfan, Robert M. High-Transonic-Speed Transport Aircraft Study - Summary Report. NASA CR-2465, 

Sept. 1974.

5.30 Espinal, Daniel; Im, Hongsik; Lee, Brian; Dominquez, Joanna; Sposoto, Hannah; Kinard, Daniel; and 

=ha, Ge-Cheng Supersonic Bi-Directional Flying Wing, Part II Conceptual Design of a High Speed Civil 

Transport. AIAA Paper 2010-1393.

5.31 Pfenninger, Warner and Vemuru, Chandra S Design Aspects of Long Range Supersonic LFC Airplanes 

with Highly Swept Wings. SAE paper 881397, Oct. 1988.

5.32 Komadina, S. and Drake, A. Development of a Quiet Supersonic Aircraft with Technology Applications 

to Military and Civil Aircraft. AIAA paper 2002-0519, Jan. 2002.
Chapter 5 Approaches to Sonic Boom Minimization

181

5.33 Wlezien, R. and Veitch, L. Quiet Supersonic Platform. AIAA Paper 2002-0143, Jan. 2002.

5.34 Whitham, G. B. The Flow Pattern of a Supersonic Projectile, Commun. Pure and Appl. Math, Vol. V, No. 

3, 1952, pp. 301–348.

5.35 Walkden, F. The Shock Pattern of a Wing-Body Combination, Far from the Flight Path. Aero. Quarterly, 

Vol. I;, May 1958, pp. 164–194.

5.36 Carlson, Harry W.; McLean, Edward F.; and Shrout, Barrett L. A Wind Tunnel Study of Sonic Boom 

Characteristics for Basic and Modi¿ed Models of a Supersonic Transport Con¿guration. NASA TM 

;-1236, 1966.

5.37 Pawlowski, Joseph W.; Graham, David H.; Boccadora, Charles H.; Coen, Peter G.; and Maglieri, Domenic 

J. Origins and Overview of a Shaped Sonic Boom Demonstration Program. AIAA 2005-0005, Jan. 2005.

5.38 Meredith, K.; Dahlin, J.; Graham, D.; Haering, E.; Maline, M.; and Page, J. Flight Test Measurement and 

Computational Fluid Dynamics Correlation of F-5E Off-Body Pressures. AIAA-2005-0006, Jan. 2005.

5.39 Plotkin, K.; Haering, E.; Murray, J.; Maglieri, D.; Salamone, J.; Sullivan, B.; and Schein, D. Ground 

Data Collection of Shaped Sonic Boom Demonstration Aircraft Pressure Signatures. AIAA-2005-0010, 

Jan. 2005.

5.40 Haering, E.; Murray, J.; Purifoy, D. D.; Graham, D. H.; Meredith, K. B.; Ashburn, C. E.; and Stucky, 

J. Airborne Measurements of Shaped Sonic Boom Demonstration Aircraft Pressure Signatures and 

Comparisons to CFD. AIAA-2005-0009, Jan. 2005.

5.41 Green, Karen S. and Putnam, Terrill W. Measurements of Sonic Booms Generated by an Airplane Flying 

at Mach 3.5 and 4.8. NASA TM-;-3126, Oct. 1974.

5.42 Carlson, Harry W.; Barger, Raymond L.; and Mack, Robert J. Application of Sonic Boom Minimization 

Concepts in Supersonic Transport Design. NASA TN D-7218, 1973.

5.43 Darden, Christine M.; Powell, Clemans A.; Hayes, Wallace D.; George, Albert R.; and Pierce, Allan D.

Status of the Sonic Boom Methodology and Understanding. NASA CP 3027, 1988.

5.44 Bobbitt, P. J.; Kandil, O. A.; and <ang, =. The Bene¿cial Effects of Wing Dihedral on Sonic Boom. AIAA 

2003-3273, May 12–14, 2003.

5.45 Kandil, O. A.; <ang, =.; and Bobbitt, P. J. Prediction of Sonic Boom Signature Using Euler-Full-Potential 

CFD with Grid Adaptation and Shock Fitting. AIAA 2005-2543, June 2002.

5.46 Kane, Edward J. A Study to Determine the Feasibility of a Low Sonic Boom Supersonic Transport. 

NASA CR-2332, Dec. 1972.

5.47 Maglieri, Domenic J. A Compilation and Review of Supersonic Business Jet Studies from 1963 through 

1995. NASA CR-2011-217144, May 2011.

5.48 Woltz, R. A Summary of Recent Supersonic Vehicle Studies at Gulfsteam Aerospace. AIAA Paper 2003-

0558, Jan. 2003.

5.49 Harinouchi, Shigeru Conceptual Design of a Low Sonic Boom SSBJ. AIAA Paper 2005-1018, Jan. 2005.

5.50 Cowart, R. A. and Grindle, T. An Overview of the Gulfstream/NASA Quiet Spike Flight Test Program. 

AIAA-2008-0123, Jan. 2008.
Chapter 5 Approaches to Sonic Boom Minimization

182

5.51 Howe, D. C.; Simmons, F., III; and Freund, D. Development of the Gulfsteam Quiet Spike for Sonic 

Boom Mitigation, AIAA 2008-0124, Jan. 2008.

5.52 Howe, D. C. Improved Sonic Boom Minimization with Extendable Nose Spike, AIAA 2005-1014, Jan. 

2005.

5.53 Howe, D. C.; Waithe, K.; and Haering, E. A. Quiet SpikeTM Near Field Flight Test Pressure Measurements 

with Computational Fluid Dynamics Comparison. AIAA 2008-0128, Jan. 2008.

5.54 Howe, D. Engine Placement for Sonic Boom Mitigation. AIAA 2002-0148, Jan. 2002.

5.55 Miller, David Status of Research on Boom Minimization through Airstream Alteration. NASA SP-255, 

Oct. 1970, pp. 325-340.

5.56 Miller, D. S. and Carlson, H. W. A Study of the Application of Heat or Force Fields to the Sonic Boom 

Minimization Problem. NASA TN D-5582, Dec. 1969.

5.57 Batdorf, S. B. A New Approach to the Alleviation of the Sonic Boom. Aerospace Corporation Rept. No. 

ATR-70 (S9990)-1, Sept. 1969.

5.58 Batdorf, S. B. An Alleviation of the Sonic Boom by Thermal Means. AIAA Paper 70-1323, 1970.

5.59 Swigart, R. and Lubard, S. Sonic Boom Studies. Aerospace Corporation Rept. No. ATR-69 (S8125)-1, 

May 1969.

5.60 Rethorst, S.; Alperin, M.; Behrens, W.; and Fujita, T. Reduction of Shock Wave Strength by Means of 

Nonuniform Flow. AFFDL-TR-69-62, Pt. 1, 1-103, 1969.

5.61 Henderson, L. F. On Shock Impedance. Journal of Fluid Mechanics, 40, 1970, pp. 731–732.

5.62 Resler, E. L., Jr. Reduction of Sonic Boom Attributed to Lift. NASA SP-180, May 1968, pp. 99–106.

5.63 Galanis, N. T. Power Plant Design for the Reduction of the Sonic Boom Generated by Supersonic 

Transport Aircraft. Ph.D. Thesis, Cornell University, June 1970.

5.64 Goethert, B. H. Fundamental Research on Advanced Techniques for Sonic Boom Suppression. Rept. 

FAA-RD 73-4, University of Tennessee, Nov. 1972.

5.65 Lipfert, R. W. An Analytical Study of Some Possible Sonic Boom Alleviation Schemes. AIAA Paper 72-

653, June 1972.

5.66 Swigart, Rudolph J. Veri¿cation of the Heat-Field Concept for Sonic Boom Alleviation. AIAA Journal of 

Aircraft, Vol. 12, NO. 2, 1975, pp. 66–71.

5.67 Marconi, F.; Bowersox, R. D. W.; and Schetz, J. A. Sonic Boom Alleviation Using Keel Con¿gurations. 

AIAA Journal of Aircraft, Vol. 40, No. 2, March–April 2003.

5.68 Marconi, F. An Investigation of Tailored Upstream Heating for Sonic Boom and Drag Reduction. AIAA 

Paper 98-0333, Jan. 1998.

5.69 Miles, R.; Martinelli, L.; Macheret, S.; Shneider, M.; Girgis, I.; =aidi, S.; Mans¿eld, D.; Siclari, M.; 

Smereczniak, P.; Kashuba, R.; and Vogel, P. Suppression of Sonic Boom by Dynamic Off-Body Energy 

Addition and Shape Optimization. AIAA Paper 2002-0150, Jan. 2002.

5.70 <oung, Robert W. Supersonic Aircraft Shock Wave Energy Recovery (5,241,846), Review of Acoustical 

Patents. J. Acoust. Soc. Am., 95(3), March 1994, p. 1700.
Chapter 5 Approaches to Sonic Boom Minimization

183

5.71 Cahn, M. S. and Andrew, G. M. Electro-Aerodynamics in Supersonic Flow. AIAA Paper No. 68-24, Jan. 

1968.

5.72 Cheng, S. and Goldburg, A. An Analysis of the Possibility of Reduction of Sonic Boom by ElectroAerodynamic Devices. AIAA paper No. 69-38, Jan. 1969.

5.73 Chaun, R. L. Sonic Boom Amelioration. U.S. Patent 3510095.

5.74 Kunhardt, E.; Saeks, R.; Mankowski, J.; and Suchomel, C. One Dimensional Shock Characteristics in 

Weakly Ionized Gases. AIAA Paper 99-4941, Nov. 1999.

Chapter 6 Theoretical Considerations and Applications

185

CHAPTER 6 THEORETICAL CONSIDERATIONS AND APPLICATIONS

This chapter addresses the theoretical developments since the mid 20th century relevant to the analysis of sonic 

booms. It begins with the early ideas of Whitham, Landau, Walkden and other scientists based on linear theory with 

nonlinear corrections and ends with an analysis of hypersonic theory based primarily on blast wave methodology. 

Also presented are the methods for calculating the propagation of pressure signatures based on Whitham’s 

F-function and Thomas’s waveform parameter method. Research utilizing Whitham’s F-function method led to 

the development of the “age parameter” and a phenomenon that became known as “freezing”. These theoretical 

factors are discussed in detail in this chapter.

Since most near-¿eld Àow calculations made today use CFD codes based on Euler equations, the dif¿culties of 

matching these data to the linear far-¿eld propagation codes are presented. In addition, the lateral variations of 

sonic booms as well as the lateral extent of sonic booms on the ground are discussed. Finally, several theory and 

experiment comparison plots are presented that indicate how well the predictive methods work.

Fundamental Boom Theory

Early speculation was that sonic booms were associated with a Doppler singularity at Mach 1 (engine noise 

bunching up as the sound barrier was broken). Researchers soon realized that sonic booms were the same 

phenomenon as ballistic waves, the properties of which had been understood for some time, quanti¿ed through 

the work of DuMond et al. (ref. 6.1), Whitham (refs. 6.2 and 6.3), and others, including Landau’s work on the 

asymptotic form of weak shock waves (ref. 6.4). Building on this work and on Hayes’s linearized Àow theory (ref. 

6.5), the basics of sonic boom analysis were laid down by Whitham (refs. 6.2 and 6.3), Walkden (ref. 6.6), Warren 

(refs. 6.7 and 6.8), Randall (ref. 6.9), and others. Contributions and improvements have been made over the years 

by a host of researchers and were documented in several summary papers (see refs. 6.10 to 6.15). 

The Whitham theory is based on the concept that linear theory provides the correct ¿rst order values along a 

characteristic, but the location of the linear theory characteristics is correct only to the zeroth order. He developed 

a procedure to correct the characteristic location to the ¿rst order, thus obtaining a uniform ¿rst order solution – 

which is formally equivalent to second order. The Whitham methodology began with the acoustic solution for the 

Àow ¿eld around a supersonic projectile.

 (1)

which is often written as

 (2)

where Ȥ is the location on the axis of the equivalent body of the Mach plane translated ¿eld point, where

a = Speed of sound

F = Source function

M = Mach number = U/a

p

a

 = ambient pressure

 

 
Chapter 6 Theoretical Considerations and Applications

186

įp = p - pa

r = radial coordinate

U = free stream velocity

x = axial coordinate parallel to Àight path

ȕ = 

Ȗ = ratio of speci¿c heat

Ȥ = x - ȕr

The meaning of the coordinate Ȥ = x - ȕr is sketched in ¿gure 6.1. Lines of constant Ȥ are simply the Mach waves 

originating at axial position x along the body.

Equations (1) and (2) are essentially the acoustic propagation of a locally axisymmetric source. This generally 

means that r is far enough from a vehicle that near-¿eld cross-Àow effects have become negligible, and that the 

amplitudes are small enough that propagation is linear.

The F-function in equations (1) and (2) for an axisymmetric body is related to its geometry by 

 

 (3)

where A is the cross sectional area of the body and $ƍƍ( x )denotes the second derivative. The area A is the normal 

projection of cuts made at the Mach angle (i.e., slices along lines of Ȥ). For slender bodies, A is often approximated 

by the cross-sectional area.

Equations (2) and (3) are written for an axisymmetric vehicle. They can apply to a non-axisymmetric vehicle if the 

Àow ¿eld is such that it can be considered as locally axisymmetric, i.e., at any given azimuthal angle ș the Àow 

behaves as if it was axisymmetric, so equation (2) can be generalized to 

 (4)

)LJXUH &RRUGLQDWHV\VWHPDQGGH¿QLWLRQRI Ȥ.

 
Chapter 6 Theoretical Considerations and Applications

187

Walkden (ref. 6.6) determined the ș dependence for a wing-body combination, accounting for the volume of the 

fuselage, the volume and lift of the wing, and interference between the body and wing. Walkden’s result for the 

F-function can be written in terms of a single volume term, including any interference effects and a single lift term 

including lift interference effects as 

 

 (5)

Lƍ(x,ș) can be approximated by cosșLƍ(x) and written so that the ș direction component of total integrated lift from 

the leading edge up to station x is de¿ned as 

 

 (6)

and the ƍ and Ǝ indicate ¿rst and second derivatives with respect to x, where 

ș = direction component of lift, it is zero in head down direction

q = free stream dynamic pressure = ò ȡ82

ȡ = ambient density

L(x,ș) = lift on a spanwise strip per unit chordwise length 

Av

(x,ș) = longitudinal area distribution

The Av

Ǝ term is the volume contribution in equation (5) and is determined by the cross sections measured 

by cutting planes aligned with the Mach angle. The L term is the contribution due to lift as noted and 

should really be determined along Mach cutting planes. Except for extremely slender wing planforms, 

the use of equation (6) based on the longitudinal lift distribution is a more serious approximation than 

the use of simple cross sections for volume cuts. The numerator of the integral in equation (5) before 

differentiation is referred to as the effective area Ae

.

 (7)

Thus, equation (4) for įp(x, ș) uses F from equation (3) with Ae replacing A. 

 (8)

As noted earlier, for a slender body, Av

(x,ș) can be approximated by the normal cross-sectional area at station 

x. For an aircraft in level flight or in a coordinated turn, lift is normal to the wing span head up and ș is 

zero in the head down direction. Total lift is the integral of cosșLƍ(x) over the vehicle length. The cosine 

form for the azimuthal direction is a reasonable, practical approximation, much like normal area cuts rather 

than Mach cuts, but it should be remembered that the lift portion of equation (7) is best performed along 

Mach cuts at each ș. It should also be remembered that the volume and lift components properly include the 

interference components identified by Walkden (ref. 6.6).

 

 

 
Chapter 6 Theoretical Considerations and Applications

188

A typical build up of lift and volume contributions to an Ae distribution is shown in ¿gure 6.2 for an SST (ref. 

6.16) with a 300-foot-long fuselage (actual length).

Early researchers (refs. 6.1 and 6.2) found that the far-¿eld decay of shock strength in a uniform atmosphere 

follows a r-3/4 law. Whitham (refs. 6.3 and 6.17) derived the following expression for the far-¿eld shock jump

 (9)

where pa and ca are the ambient pressure and speed of sound, Ȗ is ratio of speci¿c heats and S is the geometrical

acoustic ray-tube area. Whitham noted that S could be further generalized to include acoustic impedance

and refraction.

The integration limit IJo

 is the value of IJ that makes F(IJo) = 0 and a maximum. This usually 

corresponds to the initial positive phase of the F-function. As pointed out in references 6.17 and 6.18, for a 

uniform atmosphere, 6aVaU and equation (9) yields the r-3/4 behavior. The uniform atmosphere form of the 

Whitham-Walkden-Randall theory (refs. 6.3, 6.6, and 6.9) is thus

 (10)

or

 (11)

 

)LJXUH (TXLYDOHQWDUHDGLVWULEXWLRQFRUUHVSRQGLQJWRDLUSODQHFRQ¿JXUDWLRQ

0DFKV\PPHWU\SODQHFXWVUHI

 
Chapter 6 Theoretical Considerations and Applications

189

where is used in equation (11) instead of Pa (eq. (10)) to approximate the effect of the acoustical impedance 

differences in the atmosphere between the ground and the aircraft.

A more general formulation of boom theory includes the actual ray tube area, S, as contained in equation (9) and 

acoustical impedance rather than approximating it with p. If atmospheric winds are included, then the impedance 

and ray tube area factors are combined into the general form derived by Blokhintzev (ref. 6.19). Additionally, in 

the general theory, the upper limit of the F-integral is IJ(s), rather than the IJ0

, so that mid-¿eld as well as far-¿eld 

booms can be computed. The general theory is presented later in this chapter.

A further representation of equation (10) is found in reference 6.11

 (12)

where

 (13)

and Kr

 is the ground reÀection factor normally taken as 1.9 or 2.0.

In subsequent publications (refs. 6.20 and 6.21) equation (11) evolved into

 (14)

where K

p

 is a factor accounting for the difference between uniform atmosphere propagation and propagation in the 

real atmosphere. The shape factor Ks

 includes both volume and lift contributions while he, the effective altitude, 

accounts for the effect of Àight-path and ray-path-azimuth angles on propagation distance. Signature duration is 

determined in a similar fashion and is given by

 (15)

where Kt is a factor, similar in concept to K

p

, that adjusts for propagation in a real atmosphere and is given in 

reference 6.21, and ca

 is the speed of sound at the aircraft’s altitude.

In addition to laying out the calculation procedure for ǻpPD[ and ǻt, reference 6.21 provided several illustrative 

boom calculations. Figure 6.3, from reference 6.21, depicts some typical results that show good agreement of ǻpPD[

and ǻt predictions with experiment. A note of caution is in order – the method of reference 6.21 only applies to 

conventional aircraft that yield N-wave sonic boom signatures as opposed to tailored minimum boom signatures. 

 

 
Chapter 6 Theoretical Considerations and Applications

190

A further cautionary note – equation (8) properly applies to con¿gurations that have smooth shapes (i.e., without 

slope discontinuities). Reference 6.3 discusses an F-function integral, denoted as the h function, that applies to 

both smooth and non-smooth area distributions and is more accurate in the latter case.

Signature Evolution

Equations (1), (2), and (4) do not require that F be obtained from equations (5) or (8) since it is simply an acoustic 

source function. The only requirement is that the wave have locally plane wave behavior, such that Ȥ is the 

appropriate combination of x and r and that amplitude changes over gradient scales that are large compared to the 

signal wavelength. Whitham (ref. 6.17) wrote a general form of equation (1) in simpler form as

 (16)

where B is a generalization of r to represent any slowly varying amplitude change and IJ is a time based equivalent 

of Ȥ. Whitham wrote S rather than B, specifying that S could be a constant (plane wave), V (propagation distance, 

cylindrical wave), or V

 (propagation distance squared, spherical wave). He also noted that S could represent a 

general ray tube area and could include acoustic impedance variations. B is used here to represent that general 

form. Ray tracing, ray tube area and acoustic impedance, based on Blokhintzev’s theory (ref. 6.19), will be 

discussed later in this section.

In equation (16) the time based variable

 

 (17)

represents phase along a ray that is normal to the wavefronts sketched in ¿gure 6.1, where s is the propagation 

distance along the ray and a is the ambient sound speed. F(IJ) and F(Ȥ) are not the same function, since one is 

a function of time and the other of length, but both forms are used in the literature with length units generally 

applied to external scaling of both forms. The arrival time of wavefront of phase IJ is t = IJ + VD. If the propagation 

medium has varying sound speed a0

, the arrival time generalizes to

)LJXUH &RUUHODWLRQRISUHGLFWLRQVZLWKPHDVXUHPHQWVFRYHULQJDUDQJHRIDLUSODQHW\SHVUHI
Chapter 6 Theoretical Considerations and Applications

191

 (18)

The appearance of N-waves at the ground, rather than near-¿eld waves that closely mimic the aircraft con¿guration, 

is a consequence of propagation not actually being linear. Whitham (refs. 6.2 and 6.3) proposed that the linear 

solution gave the correct wave amplitude to ¿rst order, but that the wave shapes (or ray arrival times) were only 

correct to the zero order. A uniformly valid ¿rst order solution could be obtained by adjusting propagation speed 

to ¿rst order. a0

 in equation (18) is replaced with a0 + įD + įX, where įD is the perturbation to sound speed and įu 

is the local volume velocity associated with the acoustic wave. From the acoustic equations, these are 

 (19)

so that

 (20)

Equation (17) for the arrival time is updated to

 (21)

which can be written as

 (22)

where

 (23)

is denoted the age parameter. This is equivalent to the age variable de¿ned throughout the course of sonic boom 

theory development. Hayes (ref. 6.12) has noted that Landau (ref. 6.4) ¿rst presented this for a uniform medium 

(where it was just the distance), and Whitham was the ¿rst to present it for a non-uniform medium (ref. 6.22). 

Hayes et al. (ref. 6.23) wrote the age variable, with different notation than used here, for downward ray propagation 

in a horizontally strati¿ed atmosphere.

 

 

 

 

 

 
Chapter 6 Theoretical Considerations and Applications

192

Applying the age parameter to equation (16)

 (24)

so that wavefront IJ arrives early by the amount ȁ F(i.e., the age parameter times its F-function waveform steepens as sketched in ¿gure 6.4 for three successive times).

If continued inde¿nitely, geometric construction of steepening leads to triple valued regions, as sketched in ¿gure 

6.4(c). When the waveform slope approaches vertical, however, a shock wave will form, as sketched in ¿gure 6.5. 

The wave speeds up behind a weak shock and is given by linearizing the Rankine-Hugoniot equations, and (for 

zero pressure before it) is

 (25)

where ǻp is the shock pressure, and T(V) is the phase of the wavefront about to enter it. Note that a weak shock’s 

speed increment above ambient is half that of the increment for an isentropic compression wave of the same 

strength. This leads to the area balance algorithm for ¿tting shocks to a folded-over construction such as ¿gure 

6.4, wherein the folded-over region is replaced with a shock such that the area of the waveform is preserved. This 

is illustrated in ¿gure 6.6.

)LJXUH 1RQOLQHDUGLVWRUWLRQRIERRPVLJQDWXUH(DFKSRLQWDGYDQFHVE\ȁ)

)LJXUH 6KRFNIRUPDWLRQDWZDYHIURQW7(S1)
Chapter 6 Theoretical Considerations and Applications

193

The arrival time T(V) at distance V of the shock for a simple waveform as shown in ¿gures 6.4-6.6 is given by 

equation (26) with T(V) replacing IJ (see equation (22))

 (26)

If equation (26) is differentiated once with respect to V, it gives dtshock/GV, which is the reciprocal of the shock speed 

given by equation (25). Whitham combined these equations, obtaining a differential equation for T(V), which he 

then integrated to obtain

 (27)

Equation (27) provides F behind the shock, hence the shock pressure. This is an implicit relation, since 7V

appears as a limit to the integrand of F on the right hand side. Whitham (ref. 6.17) noted that at large distances 

most of the original F-function will be engulfed in the shock, and 7V will be very close to IJ0

, the zero at the end 

of the positive phase of the F-function. In the far-¿eld, the shock overpressure will thus be

 (28)

Because only a small portion of the original F-function is left, the shock will be followed by a linear expansion, 

hence an N-wave shape, with positive duration given by the advance time to the shock, which he found to be

 (29)

)LJXUH 6KRFN¿WWLQJE\DUHDEDODQFH

 

 

 
Chapter 6 Theoretical Considerations and Applications

194

For plane, cylindrical, and spherical waves the asymptotic behavior is

 Plane

 Cylindrical (30)

 Spherical

 Plane

Cylindrical (31)

 Spherical

The cylindrical results are the well known r-1⁄2 law, so that the amplitude of an N-wave boom decays more rapidly 

than the r-1⁄2 decay of a cylindrical acoustic wave. Note that the additional 1⁄4 power results from the slope of the 

N being absorbed into the shock. The shock of a Àat-top boom discussed in the minimization chapter decays at 

the acoustic rate of r-1⁄2, and the shock of a ramp boom would decay slower than r-3⁄4 since the portion of the wave 

entering the shock has an upward slope.

Not all booms are asymptotic in the far-¿eld, and many real world F-functions are complex with multiple shocks 

possible. The area-balancing rule illustrated in ¿gure 6.6 can be used to locate shocks. Figure 6.7 illustrates how 

this can be done, either after steepening the signature (top sketch) or before steepening (bottom sketch). Either 

way the shock position is iterated until the areas are balanced.

Iterative shock balancing can be tedious to implement, particularly if there are multiple shocks in a signature. A 

general algorithm for shock ¿tting was developed by Middleton and Carlson (ref. 6.24) and by Hayes (ref. 6.23). 

In this method, a function S is de¿ned that is the integral of the F-function

 (32)

The function is computed for the age-strained IJ, i.e., IJ í F ȁ, as illustrated in ¿gure 6.8.

 

 

 

 

 

 

)LJXUH 6KRFN¿WWLQJE\DUHDEDODQFLQJ

 
Chapter 6 Theoretical Considerations and Applications

195

Because S is the integral of F, it represents areas of F, so area balancing is equivalent to places where F crosses 

itself. Note in ¿gure 6.8 that triple valued regions of F correspond to regions where S reverses its direction, then 

after progressing in the original direction crosses itself. Shocks are located where forward-running segments 

of S cross. Middleton and Carlson (ref. 6.24) de¿ne the algorithm, and provide step-by-step procedures for its 

implementation. Those steps include rules for dealing with situations where there can be multiple overlaps in a 

region. Hayes et al. (ref. 6.23) shed further rigor on the underlying mathematics in their presentation.

An alternate method of aging a signature and managing shock formation is the waveform parameter method 

developed by Thomas (refs. 6.25 and 6.26). In that method, the signature is divided into several segments and 

shocks, as shown in ¿gure 6.9. The per-segment quantities that de¿ne the waveform parameters are shown in the 

¿gure. Thomas’s implementation works directly with the pressure signature, rather than the F-function, but that 

is just a matter of scaling and (despite the title of ref. 6.25) is an equivalent de¿nition. Thomas’s method uses 

Whitham’s rule to compute the advance of each xi

 in the signature, and the corresponding lengths Ȝi and slopes Pi. 

The shock jumps ǻpi

 are computed by a generalization of the process Whitham used to compute the shock jump 

for an N-wave. The software implementation of this method advances the signature at nominal time or distance 

steps along a ray. If a shock forms within a step, or if two segments coalesce within a step, the step is shortened to 

match the shock formation or coalescence point. The waveform parameters are reformulated to include the new 

shock and/or to eliminate the merged segment, and the process continues.

A weakness of Thomas’s original implementation is that the code only expected one shock formation or coalescence 

at a time. If a complex signature with a large number of points is speci¿ed, there is an increasing chance that two 

such events could happen simultaneously, causing a failure of the calculation. This becomes a problem when using 

CFD data as F-function inputs, since such solutions tend to have numerous points on a ¿ne mesh, increasing the 

likelihood of simultaneous coalescences. This is an issue for the Thomas code and its descendants, which included 

earlier versions of PCBoom (ref. 6.27). A multi-coalescence update was made to a proprietary code (ref. 6.28). 

)LJXUH 6KRFN¿WWLQJE\FURVVLQJVRIWKH6IXQFWLRQ

)LJXUH 5HSUHVHQWDWLRQRIERRPVLJQDWXUHE\ZDYHIRUPSDUDPHWHUV
Chapter 6 Theoretical Considerations and Applications

196

Signature Aging and Shock Coalescence

Early sonic boom analyses concentrated on far-¿eld signatures and the Landau-Whitham result that N-waves were 

inevitable. There was a major conceptual advance in 1965 when McLean (ref. 6.29) pointed out that N-wave booms 

were not inevitable. He noted that when real atmosphere effects (derived in the next section) were considered, 

the boom at the ground would not be far ¿eld, but would be mid-¿eld and did not have to be an N-wave. This 

signature freezing phenomenon was further explained by Hayes (ref. 6.12) and explored by Seebass (refs. 6.10 

and 6.30) and George (ref. 6.31). Hayes de¿ned an age variable (ref. 6.23) that in an isothermal atmosphere 

reaches an asymptotic value at a distance of ʌH/2 where H is the scale height of an isothermal atmosphere.

While the term freezing was coined, ¿gures 6.10 and 6.11 from reference 6.25 show that, for both uniform and 

standard atmospheres, an example two-shock signature from an aircraft at an altitude of 60,000 feet never freezes. 

There is a distinct difference in the rate of coalescence as both signatures move continuously toward an N-wave. 

The interest is, of course, in the boom at the ground, and not what it would be if it propagated inde¿nitely. It 

would appear that if that same airplane had been Àying at lower altitude, say at 45,000 feet, then the two-shock 

con¿guration would have reached the ground yielding a smaller ǻpmax.

)LJXUH (IIHFWRIDWPRVSKHULFJUDGLHQWVRQVKRFNFRDOHVFHQFHIRUDQRJHHZLQJ

DW0DFKDQG& UHI

)LJXUH (IIHFWRIDWPRVSKHULFJUDGLHQWVRQZDYHDPSOLWXGH IRUDQRJHHZLQJ

DW0DFKDQG&L

 UHI
Chapter 6 Theoretical Considerations and Applications

197

While true freezing does not occur in the real atmosphere (refs. 6.32 – 6.38) and the phenomenon might better 

be called chilling, it is important to note that mid-¿eld signatures are the rule for larger aircraft. By controlling 

shock-strength, pressure-recovery rates (see ¿g. 6.12), and altitude, non-N-wave signatures on the ground can be 

achieved.

Pressure Signature Propagation in a Real Atmosphere

The theory development presented in equations (16) through (32) has been for propagation through a uniform 

atmosphere, although the potential for atmospheric gradients has been discussed and the parameter B introduced in 

equation (16) provides a place for those effects. Atmospheric gradients are addressed by the method of geometrical 

acoustics. The formulation employed is that of Blokhintezev (ref. 6.19), which addresses wind, sound speed, and 

density gradients. An equivalent simpler derivation for a windless atmosphere, following that of Of¿cer (ref. 6.39) 

is presented in detail below, with Blokhintzev’s full result shown afterwards.

Ray Tracing

Consider propagation through an atmosphere with variable ambient sound speed and density, with no wind

velocity and neglecting gravitational buoyancy. The wave equation is 

 (33) 

where p now is termed the acoustic overpressure Įo and ȡo are the ambient sound speed and density.

A solution is sought of the form

 (34)

)LJXUH (IIHFWRIVORSHEHKLQGZLQJVKRFNRQFRDOHVFHQFHDW0DFKUHI

 
Chapter 6 Theoretical Considerations and Applications

198

where

Ȧ = frequency 

 D = ¿xed reference sound speed 

 3(x,y,z) = amplitude function 

 :(x,y,z) = wavefront function

t í :/a is a generalization of the earlier phase relation t - s/a, and P is a generalization of the 1/¥B amplitude 

relation (see eq. 16).

Substituting equation (34) into equation (33) and separating the real and imaginary parts, the following two 

equations are obtained

 

 (35)

 (36)

Note that the only terms dependent on Ȧ are on the right hand side of equation (35). Those terms are of the order 

(Ȝ/L)2

, where Ȝ is the wavelength of the signal and L is the scale length of atmospheric gradients and amplitude 

changes. If the short wavelength limit, Ȝ<<L, is taken, equation (35) becomes

 (37)

so that there is no frequency dependence, and the system is non-dispersive. Equation (35) is the eikonal equation, 

familiar from geometrical optics, and states that the gradient of W is proportional to the local index of refraction. 

Propagation is along geometrical rays orthogonal to wave fronts W.

Since equation (34) is written for a harmonic wave, the Ȝ<<L limit is really taken as Ȧ ĺ . Keller (ref. 6.40) 

presented an alternate derivation written in terms of shocks, where taking the shock thickness as small (formally 

Ȝ<<L) yielded the same result as the harmonic formulation. Because sonic booms are shocks, some authors (e.g., 

Friedman, Kane, and Sigalla in ref. 6.41) cite Keller rather than Blokhintzev. Once a ray ¿eld is computed, 

may be written where is the unit vector ¿eld representing ray direction. Equation (36) may be 

written as

 (38) 

 

ǻ

:
Chapter 6 Theoretical Considerations and Applications

199

which has the form of a continuity equation. De¿ning a ray tube as a bundle of rays, equation (38) integrates to

 (39)

where S is the ray tube area. Figure 6.13 is a sketch of a ray tube and its cross sectional area (note that S is not 

the same as the function de¿ned in equation (32)). Notations in sonic boom literature are not entirely consistent. 

A is often used for ray tube area, and should be not confused with A used for body cross sectional area in the 

F-function de¿nition. The quantity ȡ0

a0 is the acoustic impedance, and equation (39) represents conservation of 

energy within a ray tube.

When winds are present, the acoustic equations are considerably more complex. The acoustic velocity, density, 

and sound speed perturbations do not fall out until the short wave limit is taken. Because of convection, the ray 

paths do not necessarily coincide with wave normals. Blokhintzev derived the eikonal and amplitude for an 

inhomogeneous moving medium, and obtained (with notation slightly different from that used here)

 (40)

 (41)

where

 (42)

Equation (41) integrates to

 (43)

along a ray tube de¿ned by trajectories

 (44)

)LJXUH 5D\WXEHDQGUD\WXEHDUHD

 

 

 

 
Chapter 6 Theoretical Considerations and Applications

200

It is straightforward to match equations (2) and (16) to equation (39) or (43) to obtain the proper form of the 

generic amplitude 1/¥B. Rays can be traced by any of the familiar methods from optics, including Fermat’s 

principle and Snell’s law. Ray tracing begins with an initial ray on a ray cone generated at any given time at the 

aircraft. Figure 6.14 illustrates a ray cone and an initial ray at azimuth ࢥ) Note that ࢥ is about the aircraft’s roll 

axis, as is body-oriented azimuth ș as in equation (4), but is relative to earth referenced down rather than aircraft 

coordinates. The two angles differ by the bank angle).

The independent variables for selecting a ray are aircraft time t and the azimuth ࢥ. In software implementations 

of boom theory, it is typical to use four rays, separated by small increments in t and ࢥ. There are two widespread 

styles in use. The ¿rst is that in the ARAP program (ref. 6.23), where differential relations are developed for the 

ray path and ray tube area. Those relations are in the form of quadratures, which then are evaluated numerically. 

The second is that used in the Thomas program (ref. 6.26) where each ray is traced numerically and the ray tube 

areas obtained by differences between them.

As might be surmised by the division of theory within this chapter, numeric implementation of sonic boom theory 

is modular. Figure 6.15 shows the logical Àow. For a given point on the aircraft’s Àight path, the F-function is 

obtained from aerodynamics and geometry. Geometry and area rule are set off in the chart since the F-function (or 

initial p vs s signature, depending on scaling tastes) can come from any suitable source, such as CFD. Rays are 

traced, depending only on the Àight path kinematics and the atmosphere. Ray tube areas and the age parameter 

are part of the ray tracing analysis, which is independent of the vehicle source characteristics. Finally, the initial 

signature is merged with ray tracing and aging to obtain the boom signature at the ground or any location along 

the ray path. Figure 6.16 shows the same process in graphical format.

)LJXUH 5D\FRQHDWWLPHt DQGLQLWLDOUD\DWD]LPXWKࢥ.

)LJXUH /RJLFDOÀRZRIVRQLFERRPFDOFXODWLRQ
Chapter 6 Theoretical Considerations and Applications

201

Pressure Signature Propagation Codes

As noted earlier, there are several methods/computer codes available for predicting the evolution of an aircraft’s 

pressure signature as it propagates to the ground through a real strati¿ed atmosphere. One of the most used codes 

in the United States for many years, when F-function methodology was dominant, was the Hayes code (refs. 6.23, 

6.42, and 6.43). Rao (ref. 6.44) formulated a methodology for maneuvering aircraft in a homogeneous atmosphere 

and Randall (ref. 6.45) for steady-state Àight in a strati¿ed atmosphere. 

The Hayes code was based on geometrical acoustics as derived by Blokhintsev (ref. 6.19). Details of the method 

are given in reference 6.23; the computer code (often called the ARAP code) is also described in this reference. 

There are other propagation codes based on the Hayes methodology that go by various names. Improved user 

friendly inputs are typical; some may have a more accurate maneuver capability. Another propagation code 

based on ray tracing concepts was documented in references 6.46 and 6.47 by Friedman et al. As with 

the Hayes code, this program allowed for flight paths that are curved, climbing, or diving. Example 

results were given for the effects on sonic boom of some atmospheric effects as well as flight path 

curvature and acceleration.

An alternate method with limited utility was formulated by Schorling (ref. 6.48). He noted that while the ray 

tracing codes include the effects of nonlinear distortions they are essentially linear in nature and are not adequate 

for handling such nonlinear effects as shock focusing or cut-off Mach number. In his method of characteristics 

based on analysis, the nonlinear system of partial differential equations for supersonic Àow were solved for large 

distances by using a perturbation method developed by Tsien Poincarp, Lighthill, and Kuo (see ref. 6.49). The 

analysis of reference 6.48 was for a homogeneous atmosphere; reference 6.50 extends this work to a strati¿ed 

atmosphere.

Another propagation code (and its derivatives) frequently used today is the Thomas code (refs. 6.25 and 

6.26). The Thomas code is based on geometrical acoustics as derived by Blokhintsev (ref. 6.19) but does not 

use an F-function to represent the near-field signature. In reference 6.25 (p. 206), Thomas asserts that,

The approach used is to describe the waveform of the sonic boom wave by several waveform parameters 

and then to obtain equations for the parameters as functions of time. This approach has the advantages 

that (1) the theory is simpler and more intuitive than the Whitham theory, (2) it provides a more 

convenient method for extrapolating experimental signatures because the pressure signature is dealt 

with directly, rather than through the use of an F-function, and (3) shock locations are determined by 

a much neater method than the classical area balancing technique used in F-function extrapolations.

As noted earlier, Thomas’s wave parameter formulation is actually a generalization of Whitham’s analytic 

formulation summarized in equations (20) – (27). His initial waveform corresponds to beginning with 

the left hand side of equation (1) rather than the right hand side, which is appropriate if the F-function 

itself has not been computed or directly measured. The formulation of the method is rather elegant, but 

in some situations lends itself to complexity in practical implementation.

)LJXUH 6RQLFERRPJHQHUDWLRQSURSDJDWLRQDQGHYROXWLRQ
Chapter 6 Theoretical Considerations and Applications

202

The effects of aircraft acceleration and atmospheric temperature, pressure, and wind gradients are included in 

the theory and in the computer program (ref. 6.26). Several other codes with the acronym SHOCKN and THOR, 

developed at the University of Mississippi and University of Texas respectively, are described and applied in 

reference 6.51.

One of the most widely used codes is PCBoom (ref. 6.27). It originated as an extension of the Thomas code, with 

algorithms to compute signatures within focal zones. It has evolved into a multi-featured program, accepting a 

variety of source de¿nition types and computing complete footprints. The current version also computes overthe-top booms and accounts for the actual ellipsoidal earth, rather than Àat earth. Because of the instabilities 

of the waveform parameter method for complex signatures, the current version of PCBoom has abandoned the 

waveform parameter in favor of the age parameter and Middleton-Carlson shock ¿tting. PCBoom retains the 

feature of beginning with įp at a reference r rather than the F-function.

Siclari (ref. 6.52) and Fouladi (ref. 6.53) compared ground pressure signatures calculated with an early version 

of MDBOOM (ref. 6.54) and Thomas (ref. 6.26). As seen in ¿gures 6.17 and 6.18, the MDBOOM code yielded 

a higher ǻp and longer signatures than that of Thomas. This indicates that the mid-¿eld pressure signature did 

not decay as fast with the MDBOOM prediction as the near-¿eld decay of the Thomas code. Siclari also states 

that MDBOOM results show signi¿cantly less sensitivity to extrapolation distances in comparison to the Thomas 

code. Certainly the vertical distance from the aircraft where the propagation code is matched to the Euler solution 

is critical. Nevertheless, the differences are puzzling since MDBOOM is also based on the Thomas methodology. 

The signatures compared in both references 6.52 and 6.53 are those for the symmetry plane (on track) of conceptual 

con¿gurations. It would be useful to have a comparison of these methods for a con¿guration where real data 

exists, such as shown in ¿gure 6.3, for the Carlson methodology.

)LJXUH &RPSDULVRQRI0'%220DQG7KRPDV$1(7SUHGLFWLRQVRIJURXQGSUHVVXUHVLJQDWXUHVUHI

(a) OPT5 wing-body. (b) MOD446 wing-body.
Chapter 6 Theoretical Considerations and Applications

203

There are several codes based on the Thomas code methodology in circulation, so apparently MDBOOM was 

based on a different version than that used by Siclari. It is worth noting that the equations in references 6.25 and 

6.26 differ from each other, one being based on signature time and the other on signature length.

One area where most of these propagation codes break down is when a focus exists. Factors that are neglected 

(diffraction and nonlinear effects) in the development of geometric acoustics become important and limit 

pressures at these singularities to ¿nite values. Three types of focused booms and the maneuvers that produce 

them are detailed in reference 6.55 along with the methodology required to predict their geometry and magnitude. 

Modi¿cations to a version of the Thomas code were made to include the focused boom, or caustic geometry 

analysis, and example calculations are given. Other analyses of the booms of maneuvering aircraft are given 

in references 6.56 to 6.59. Related studies of the sonic boom behavior near a caustic are discussed and listed in 

reference 6.55. See Chapter 3 for additional discussion of the effect of maneuvers on sonic boom.

The most used boom codes employed in the United States do not consider the secondary or over-the-top 

booms. Gardner and Rogers (ref. 6.60) provide details of a nonlinear theory for the long-range propagation 

of sonic booms through the thermosphere. Results are presented for the case of the Concorde SST in straight, 

level, and steady flight at an altitude of 17.5 kilometers and a speed of Mach 2. Taylor (ref. 6.61) describes the 

TRAPS code that added secondary boom capability to the ARAP (or Hayes) code. =EPH<RUS (ref. 6.62) 

is another code that has secondary boom capability and includes absorption effects as well. A comparison 

of the two aforementioned codes (refs. 6.61 and 6.62) is given in reference 6.63, which examined the impact 

of weather and flight conditions on the secondary boom (see also discussion in Chapter 2). It is interesting 

that while both TRAPS and =EPH<RUS account for the passage of an over-the-top boom through a caustic, 

neither actually computes boom signatures at a caustic. The current version of PCBoom (ref. 6.64) does 

compute boom signatures at an over-the-top caustic passage and at ground caustic intercepts and also 

includes absorption effects.

)LJXUH &RPSDULVRQRIWKHJURXQGSUHVVXUHVLJQDWXUHVRIWKHEDVHOLQHFRQ¿JXUDWLRQ0'%220YHUVXV7KRPDV

%RHLQJEDVHOLQHFRQ¿JXUDWLRQUHI
Chapter 6 Theoretical Considerations and Applications

204

The Near-Field/Mid-Field Dilemma

It is convenient to break down the volume of air surrounding a supersonic aircraft into three regions – a near ¿eld, 

a mid ¿eld, and a far ¿eld (see ¿gure 6.19). The near ¿eld may be calculated using linear theory or, most likely 

today, using a CFD code based on the Euler equations. In the near ¿eld, Euler equation case, the actual geometry 

would have been modeled including the fuselage, wing, tail, and engines. Normally in treating the engine, 

boundary conditions are placed on the inlet and exhaust planes to calculate the Àow around and downstream of 

the engines. In some cases, investigators have allowed Àow through the engine but no energy is added. Reference 

6.65 by Siclari and Fouladi is an example of the former procedure.

In the use of Euler equations for near-¿eld calculations there will normally be nonlinear and non-axisymmetric effects. To 

get to a radial location where the CFD solution can be properly matched to locally axisymmetric ray tracing propagation 

codes, the Euler calculation may have to extend out to the far ¿eld. Today high-¿delity Euler-equation calculations 

beyond a billion points or nodes, and the extension of a high ¿delity calculation to the far ¿eld is possible, but not yet 

practical for general use. The original Whitham formulation modeled source and propagation as a single zone. Using 

CFD for the near ¿eld becomes a two-zone problem, and attention must be paid to matching the zones. 

Another more accurate option would be to use a three-zone formulation, where a mid-¿eld code that matches the CFD 

calculations at a small radius can continue propagation out to the far-¿eld locally axisymmetric region, where ray tracing 

codes like ARAP (ref. 6.23) or Thomas (ref. 6.26) would complete the propagation. Real near-¿eld Àow ¿elds are not 

locally axisymmetric or linear, so the CFD calculation must be matched to a mid-¿eld code that models similar Àow 

physics.

Shock Smearing and Fitting

When calculating the near ¿eld of an aircraft using a CFD Euler code, one will ¿nd that the shock jumps are 

consistent with the Rankine-Hugoniot equations. With this constraint there are shocks of different shape and 

strength followed by pressure recoveries of different strengths (rates of recovery). Normally, CFD calculations are 

made with grids that are stretched radially as one moves to the outer boundaries, since the Àow gradients become 

smaller, and far-¿eld boundary conditions can be imposed. Outer boundaries are typically placed one to two body 

lengths from the centerline depending on the Mach number and shape. Solution schemes are generally of the 

shock capturing variety. All of this combines to smear the shocks and reduce their maximum pressure jumps from 

their proper value at the outer boundary. Figures 6.20 and 6.21 from references 6.66 and 6.65, respectively, show 

the smearing of shocks caused by the solution algorithms and grids and how the smearing becomes worse as the 

radial distance is increased (¿g. 6.21). It should be noted that the HFLO3 (¿g. 6.20) calculations, at an h/l of 0.25, 

involve an adaptive grid and the AIRPLANE calculations used a high resolution unstructured grid.

)LJXUH 5DGLDOEUHDNGRZQRISUHVVXUHYDULDWLRQVIURPQHDU¿HOGWRIDU¿HOG
Chapter 6 Theoretical Considerations and Applications

205

Shock ¿tting schemes are another option and have been available for many years. However, they are not 

normally used or needed where the primary interest is the pressures on the con¿guration itself. Whether a 

)LJXUH &RPSDULVRQRI$,53/$1(DQG+)/QHDU¿HOGSUHVVXUHVLJQDWXUHV0DFKĮ , KO UHI

)LJXUH 1HDU¿HOGSUHVVXUHVLJQDWXUHVIRUWKH$PHV0RGHOGHVLJQUHI
Chapter 6 Theoretical Considerations and Applications

206

procedure can be formulated to recover an accurate ¿nite shock jump at the near-¿eld boundary from a smeared 

one is not clear. Lacking a shock ¿tted Euler (or Navier-Stokes) code it is desirable to use a grid that conforms 

as close as possible to the shocks and to have as high a concentration of grid points in the vicinity of the shocks 

as can be accommodated. The latter is desirable since shock jumps are usually resolved in three or four grid 

points. The use of a grid adaptation scheme in an Euler code with a shock capturing solution algorithm is one 

way of further improving resolution. The combination of shock capturing and shock ¿tting is the preferred or 

ideal approach. The latter provides a procedure for explicitly computing the jump conditions across shocks. It 

locates the shocks and treats them as boundaries between regions where the solution is regular. Moretti (ref. 6.67) 

developed a method known as Àoating shock ¿tting where shocks Àoat during the iterative calculation. Several 

papers treating the Euler equations with shock ¿tting have been published over the years (refs. 6.68 to 6.71) and 

the technique is fairly well established. Shock ¿tting has also been applied to various versions of the potential 

equations for both transonic and supersonic Àows (refs. 6.72 and 6.73). Where the near-¿eld shocks are smeared 

(not ¿tted) one would like to employ a mid-¿eld calculation that starts as close to the aircraft as possible. This 

places strong demands on the matching method of a two-zone scheme.

Mid-Field Pressure Propagation Methods

Page and Plotkin (ref. 6.74) describe a shock ¿tting Euler code (SCRAM) that has been coupled with the multipole 

linear scheme of George (ref. 6.75). The multipole pressure ¿eld is matched to the CFD solution at some radius 

and converts it to an equivalent locally axisymmetric source, so that a ray tracing code can be applied to take the 

pressure pulse to the ground. While this is clearly a more accurate method to propagate the pressure signature 

than connecting the ray tracing code directly to the CFD solution, there is still a concern. The multipole method 

still assumes the sources are concentrated along the vehicle axis, so the further one can take the CFD solution 

(larger radial distance) into the mid ¿eld where the ratio of wingspan to distance is small, the more accurate 

will be the multipole solution. While reference 6.74 presents the multipole results only for a simple triangular 

wing con¿gurations and the SCRAM code, it has been successfully applied in various studies to more complex 

con¿gurations and other CFD codes. Application of the multipole mid-¿eld methodology, along with the SCRAM 

Euler code, to a complex canard con¿guration is discussed in reference 6.76. Improvement to the multipole 

scheme by Morgenstern was noted by Siclari in reference 6.52 (p. 158). There are other papers, though seldom 

referenced, that describe the multipole approach to boom minimization authored by <. S. Pan. In references 6.77 

and 6.78, he developed the propagation equations and applied them to the calculation of the Àow about several 

bodies of revolution.

Another methodology that would serve as a mid- to far-¿eld propagation methodology or as a near-¿eld to ground 

methodology was given in reference 6.79. This methodology was based on the full potential equation (FPE) 

and matched to the near-¿eld Euler solution point for point to the full potential solution, across three planes of 

data, thus capturing the lateral and radial gradients as well as shock jumps. While the FPE did not duplicate 

Euler equation results exactly, the difference is small. The method uses both grid adaptation and shock ¿tting to 

maintain accurate shock-pressure jumps and is capable of calculating the propagation of the three-dimensional 

pressure wave all the way to the ground. For example, calculations for ground pressure signatures for delta wings 

with biconvex and slab-sided sections Àying at Mach 2.01 and an altitude of 52,000 feet are given in reference 

6.79. The method has also been used to show the merits of dihedral wings in reference 6.80. FPE code predictions 

for a delta-wing con¿guration have also been compared to the experimental data of Cliff (ref. 6.66) and to Àight 

data for a modi¿ed F-5 in reference 6.81.

At the start of the calculation, the FPE method discussed in reference 6.79 uses an interpolation routine that 

determines the Àow variables on the unstructured grid of the FPE propagation codes from those of the structured 

grid of the near-¿eld Euler calculation. Reference 6.82 has added an additional interpolation routine that enables 

an unstructured grid near-¿eld Euler calculation (ref. 6.83) to be used. This modi¿cation was demonstrated in 

reference 6.82 for a double-cone con¿guration along with experimental data comparisons. 

In the utilization of a FPE methodology for a mid-¿eld code, or extending the near-¿eld Euler calculation to the far 
Chapter 6 Theoretical Considerations and Applications

207

¿eld, there is a question of where to initiate the far-¿eld ray tracing code calculation. While the pressure signature 

calculated by the mid-¿eld or Euler codes is normally input, and continuity of its magnitude is preserved, the 

radial gradient may not be preserved. Lacking a theoretical prescription, the mid-¿eld or Euler calculation can 

be extended to several different radial distances, then exercising for each distance the far-¿eld propagation code 

to see if the starting location, or match point, makes a difference in the ground signature. At the radial distance, 

where a further increase in radial location of the match point has only a trivial effect on the ground signature, one 

should assume a proper match point has been found.

Another mid-¿eld possibility is that of Hicks and Mendoza in reference 6.84. While its title purports to predict 

the sonic boom from experimental near-¿eld results, the method could be used to extrapolate near-¿eld Euler 

calculations based on Whitham’s F-function, which in turn is based on his h-function (ref. 6.3) and is capable 

of calculating the pressures of bodies with discontinuities in the shape of their area and lift distributions. The 

method is illustrated using experimental results for an ;B-70 model (see ¿g. 6.22) taken at two radial positions of 

r/l of 1.0 and 4.5 and lift coef¿cients from 0.04 to 0.19 as illustrated in ¿gures 6.23(a) and 6.23(b). A comparison 

of the calculated ground signature for the ;B-70 (¿g. 6.22) at Mach 1.8 and an r/l of 280, using wind-tunnel 

pressure signatures measured at an r/l = 1.0 (¿g. 6.23) is compared with Àight data in ¿gure 6.24.

)LJXUH 0RGHODQGUHODWHGWHVWHTXLSPHQWLQVWDOOHGLQWKHE\IRRWZLQGWXQQHOUHI

PRGHOURWDWHGIURPUXQQLQJSRVLWLRQ

)LJXUH :LQGWXQQHOWHVWUHVXOWVIRUDQ;%PRGHOUHFRUGHGDWWZRUDGLDOSRVLWLRQVRIUOYDU\LQJOLIWFRHI¿FLHQWVUHI

(a) r/L = 1

(b) r/L = 4.5
Chapter 6 Theoretical Considerations and Applications

208

The Àight data was obtained from an ;B-70 airplane test at Edwards Air Force Base using an average of three 

separate pressure signatures for the airplane. These measured results were the only data available a Mach 1.8 

where the ground track of the aircraft was suf¿ciently close to the ground measurements.

As can be seen, the agreement between the wind-tunnel derived data taken at an r/l of 1.0 and the Àight pressure 

signature is good except for the small discrepancy in the location of the rear shock. This discrepancy is primarily 

attributed to two factors. First, no attempt was made to simulate the Àow of hot exhaust gases in the windtunnel tests. Second, the sting support used with the wind-tunnel model was too short to allow for an accurate 

measurement of the decay of the pressure signature downstream of the rear shock (see ¿g. 6.22). In order to 

balance area for the determination of the rear shock strength and location on the experimental F-function at an 

r/l of 290, it was necessary to extrapolate the wind-tunnel pressure signatures of ¿gure 6.23 downstream for 

several model lengths. As a mid-¿eld code, the question of where to make the match with the ray tracing code is a 

concern, just as for the FPE or Euler equation solutions. However, the F-function methodology used in reference 

6.84 is capable of calculating the pressure signature all the way to the ground.

Lateral Variation and Extent of Sonic Boom Signatures

Considerable attention has been given to de¿ning the lateral variation and extent of the primary boom carpet for 

steady Àights of aircraft at various Mach numbers and altitudes. References 6.41, 6.85, 6.86 provide equations 

for the former, but Kane and Palmer in reference 6.87 did a simple analysis that was based on the result that, in 

a uniform atmosphere, the magnitude of an N-wave sonic boom varies inversely as the 3⁄4 power of the distance 

from the airplane to the ground. 

)LJXUH &RPSDULVRQRIÀLJKWDQGZLQGWXQQHOGHULYHGSUHVVXUHVLJQDWXUHVDWUO DQG0DFKUHI

)LJXUH *HRPHWU\QRPHQFODWXUHXVHGIRUGLVWDQFHFDOFXODWLRQ

 Given (45)
Chapter 6 Theoretical Considerations and Applications

209

the expression for ǻp at some lateral position relative to ǻp under the Àight track is

 (46)

Equation (46) can be rewritten using equation (45) as 

 (47)

where

 (48)

and the F-function is de¿ned by equation (5). See equations (9), (10), and (11) for the relationship of ,IJo,ș) to ǻp. 

A plot of equation (47) for the lateral variation of the boom strength compared to those calculated by the method 

of references 6.41, 6.85, and 6.86 is shown in ¿gure 6.26. As reference 6.87 (p. 8) notes,

The above results indicate that in the standard atmosphere, the variation of boom strength 

with lateral distance may be very closely approximated by equation (47) with ǻp under Àight 

track being obtained by the methods of the ¿rst section of this chapter. The lateral distribution of 

sonic boom strength predicted by this method should be suitable for most routine calculations.

In the early stages of sonic boom studies, concern was expressed regarding the nature of sonic boom exposure 

patterns near the lateral cutoff. It was believed by some (ref. 6.88 and 6.89) that boom focusing would occur at 

the lateral extremities of the primary boom carpet as a result of atmospheric refraction during steady-level Àight. 

Some boom prediction codes, based on linear acoustic theory, show rapid increases in boom level as a result of 

ray tube areas going to zero at the lateral cutoff (ref. 6.90). However, in 1959, Randall (ref. 6.9) developed the 

following equation for the lateral cutoff for altitudes below the tropopause (a36,000 feet).

 

)LJXUH 9DULDWLRQRIERRPVWUHQJWKZLWKODWHUDOGLVWDQFHIRU866WDQGDUG$WPRVSKHUHLQDGDSWHGIURPUHI
Chapter 6 Theoretical Considerations and Applications

210

(49)

and with V = aa

M

(50)

Where

h = altitude

a

g

 = speed of sound at the ground

aa

 = speed of sound at the altitude of Àight

V = velocity of airplane at Àight altitude

Randall evidently derived the equation required for above the tropopause but did not provide its equation (ref. 

6.9). A plot of the variation of the cutoff distance with Mach number for altitudes up to 65,000 feet is provided in 

¿gure 6.27.

In 1964, Kane and Palmer (ref. 6.87) developed lateral cutoff equations that, for altitudes below the tropopause, 

are the same as Randall’s equation. For altitudes above the tropopause (36,000 feet) and below 65,000 feet, 

reference 6.87 adds an additional term to equation (50) so that \PD[ becomes

(51)

)LJXUH /DWHUDOVSUHDGRIVRQLFEDQJVSURGXFHGE\DQDLUFUDIWLQVWHDG\OHYHOÀLJKWPHDVXUHGIURPÀLJKWWUDFN

DGDSWHGIURPUHI
Chapter 6 Theoretical Considerations and Applications

211

where a36 indicates the value of the speed of sound a at 36,000 feet (the tropopause) and h is the altitude above 

36,000 feet. A plot of equations (50) and (51) (ref. 6.87) is given in ¿gure 6.28. This plot contains the same type of 

data as in ¿gure 6.27 but in a different format. An equation that gives the value of \max for altitudes above 65,000 

feet was also provided in reference 6.87.

In the 1960s and 1970s, special effort was taken to obtain a more accurate pressure distribution near the extremity 

of the shock wave pattern on the ground (refs. 6.91 and 6.92). Some sample data are shown in ¿gures 6.29, 

6.30, and 6.31. Particular emphasis was placed on the cut-off region where a grazing condition exists because of 

atmospheric refraction, as suggested by the ray-path sketch at the top of ¿gure 6.29. As evident from equation 

(50) and (51) the lateral cut-off point is independent of aircraft type and is only a function of the aircraft altitude, 

the Mach number, and the characteristics of the atmosphere below the aircraft (ref. 6.9).

)LJXUH /DWHUDOORFDWLRQRIVRQLFERRPFXWRIILQ866WDQGDUG$WPRVSKHUHUHI

)LJXUH 0HDVXUHGODWHUDOVSUHDGSDWWHUQVIRUD¿JKWHUDLUFUDIWDWWZRGLIIHUHQWDOWLWXGHVUHI
Chapter 6 Theoretical Considerations and Applications

212

Flights were made at altitudes of 52,200 feet and 37,200 feet and Mach numbers of 2.0 and 1.5, respectively, 

during quiescent atmospheric conditions and the results are compared with theory in the data plots of ¿gure 6.29. 

The results from the Àight at 52,200 feet and a Mach number of 2.0 show that the pressures generally decrease as 

lateral distance increases (solid symbols indicate that no boom was observed). The fact that measurements were 

obtained beyond the theoretically predicted cut-off distance led to more de¿nitive studies at 37,200 feet and a 

Mach number of 1.5. These data, which were obtained from four Àights involving various lateral displacement 

distances of the airplane from the overhead position, are similar and, in fact, beyond the predicted cut-off distance 

of 15 miles zero signals are indicated. Note that a ¿gure similar to ¿gure 6.29 was also used in the discussion of 

atmospheric effects in Chapter 2. 

A better understanding of this phenomenon may be obtained from examination of measured waveforms taken at 

two different altitudes, as seen on the right hand side of ¿gure 6.29. Sharply de¿ned shock-wave type signatures 

exist generally for the region predicted by the calculations. Near the predicted lateral cutoff the rise times are 

noticeably longer. At distances beyond the predicted cutoff the signatures lose their identity and associated 

observations indicate the existence of rumbles, as previously described. These rumbles are noise that emanates 

from the extremity of the shock wave beyond the cutoff as it propagates through the air in the vicinity of the 

measuring stations.

Data similar to those shown in ¿gure 6.29 were obtained on a large supersonic aircraft, the ;B-70, at two altitudes 

and Mach numbers, and are presented in ¿gure 6.30 (ref. 6.91). In ¿gure 6.30, overpressure measurements are 

plotted as a function of lateral distance to each side of the ground track. The data at the top of the ¿gure relate to 

four Àights made at 37,000 feet and a Mach number of 1.5. The data at the bottom are taken from 13 Àights at an 

altitude of 60,000 feet and a Mach number range of 1.8 to 2.5. The data points are coded to represent the averages 

of from 3 to 40 microphones as indicated on the ¿gure. Also shown are calculated curves using the generalized 

theory of references 6.9, 6.21, and 6.93 for a standard atmosphere where the centerline values are determined 

using the latter two references. The cut-off points due to atmospheric refractions are shown as vertical dashed 

lines (ref. 6.9). It can be seen that the overpressures are a maximum on the track and decrease with increasing 

lateral distance as predicted generally by theory. The measured and calculated values of overpressure are in good 

agreement with the exception of the region near the lateral cutoff where the measured data falls below the theory. 

This discrepancy is due in part to the fact that only the areas from the Mach cutting planes for locations directly 

below the aircraft (symmetry plane) were utilized in the theory and lift was assumed to fall off as cosine ș.

)LJXUH 6RQLFERRPRYHUSUHVVXUHVIRUWKH;%DLUFUDIWDVDIXQFWLRQRIODWHUDOGLVWDQFHIRU

WZRGLIIHUHQWÀLJKWFRQGLWLRQVUHI
Chapter 6 Theoretical Considerations and Applications

213

Another set of lateral spread measurements acquired for the SR-71 aircraft at altitudes from about 50,000 feet to 

80,000 feet are presented on ¿gure 6.31 (from ref. 6.94). Each symbol represents an individual mission, the solid 

symbols represent the average of the measurements obtained on 15 to 46 microphones and the open symbols the 

average of the measurements obtained from 3 to 10 microphones. The circle symbols represent data from Àights 

made during the November 1966 to January 1967 time period for which atmospheric conditions observed to be 

somewhat more quiescent than those represented by the diamond symbols which were made during the June 1966 

time period. Once again, overpressures are a maximum on track and decrease with increasing lateral distance, as 

predicted by theory (refs. 6.9 and 6.93).

Comparisons of the calculated and measured lateral extent of the sonic boom patterns as a function of aircraft 

altitude and Mach number for steady Àight in a standard atmosphere are given in ¿gure 6.32 (refs. 6.18 and 6.95). 

The data points represent averages of several measurements involving various aircraft. The width of the sonic 

boom carpets on the ground increase with increasing altitude and Mach number. For example, at an altitude of 

20,000 feet and Mach 1.5 the total width of the pattern is about 22 nmi. At 60,000 feet and Mach 2.0 the pattern 

width is about 55 nmi. The two sketches at the top of the chart illustrate the fact that supersonic Àights at low 

altitudes result in narrow carpets having higher overpressures, whereas at higher altitudes the carpet widths are 

much broader and the ground overpressures are lower. In this chart, good agreement exists between measured and 

calculated values. Note that the entire width of the ground signature is plotted in ¿gure 6.32 and not the semi span 

as in ¿gure 6.27 and 6.28. Also, nautical miles are used in ¿gure 6.32 and statute miles in ¿gures 6.27 and 6.28.

)LJXUH 6RQLFERRPRYHUSUHVVXUHVDVDIXQFWLRQRIODWHUDOGLVWDQFHIRUYDULRXVDOWLWXGHUDQJHVIRUWKH650DFK

QXPEHUUDQJHVIURPWRUHI

(a) Altitude range 15,088 to 15,240 meters.

(b) Altitude range 21,245 to 21,580 meters.

(c) Altitude range 22,311 to 22,890 meters.

(d) Altitude range 23,226 to 24,384 meters.
Chapter 6 Theoretical Considerations and Applications

214

Additional discussion of the boom lateral variation and cutoff is given in Chapter 2. Included in these 

discussions are other works of signi¿cance regarding sonic boom beyond the lateral cutoff (in the shadow 

zone), including diffraction effects (refs. 6.96 through 6.99).

Hypersonic Sonic Boom Methodology

By 1970, there was an increased interest in the prediction of sonic booms at hypersonic speeds. Threedimensional Euler or Navier-Stokes methodology was available at that time, but not the computers to run 3-D 

nonlinear codes, hence, analytical or empirical solutions were required. In 1970, A. Richard Seebass, while 

at the Boeing Scienti¿c Research Laboratory developed a method for hypersonic strong-shock propagation 

based, in part, on blast wave theory. Seebass noted that an instantaneous release of energy per unit radian, 

E, produces a shock wave with a shock pressure rise ǻp for the strong shock regime (ref. 6.100 by Sakarai)

 (52)

where po

 is the ambient pressure, Ȗ is the ratio of speci¿c heats, r is the radial distance of the shock from the 

origin and effective radius

 (53)

The numerical constants a and E have the values of 0.877 and 0.989 respectively for Ȗ = 1.4. 

Realizing that for large values of r that ǻp a U-3/4, equation (52) was modi¿ed to 

 (54)

)LJXUH :LGWKRISULPDU\VRQLFERRPSDWWHUQRQJURXQGDGDSWHGIURPUHIVDQG

 

 
Chapter 6 Theoretical Considerations and Applications

215

where

   (55)

and

 (56)

With the above values for a, E, and for Į and ȕ, and with the effective radius R set equal to (D/2ʌpo

 )1/2 equation 

(54) becomes

 (57)

Since there is a great variation of the drag, ', with Mach number, Seebass found it convenient to

rewrite equation (57) using

 (58)

and with a non-dimensional area in the drag equation as the body cross section ʌd2

/4. Using equation (58) for 

drag, equation (57) becomes

 (59)

Equation (59) can also be cast in a somewhat different and more accurate form by noting that to go from 

a homogeneous atmosphere to an isothermal atmosphere (see ref. 6.10) the following equation applies

 (60)

where ș is the angle between the normal to Àight path trajectory and the vertical (see ¿g. 6.33). For an 

isothermal exponential atmosphere with , equation (60) becomes

 (61)

 

 

 

 

 
Chapter 6 Theoretical Considerations and Applications

216

Con¿ning one’s interest in equation (57) to cases where and where 

 , equation (57) becomes

 (62)

If one sets in equation (62) and inserts it in into equation (61) with r

equal to h, the atmospheric scale height + = 25,000 feet, Sg

 = 2116 lbs/ft2, ' normalized by 105, and ș = 0, and 

a ground reÀection factor of 2.0, it becomes

 (63)

This is identical to the equation Seebass derived except for the multiplicative factor, which he set at 4.2 instead 

of 3.83. It is also similar to that given by Seebass and George in a later paper (ref. 6.101, p. 8). A plot of ǻp as a 

function of K+ using Seebass’ 4.2 factor is given in ¿gure 6.34. Note that it is a drag dominated result and for an 

aircraft where Mach is large and Mach xIJ is the order of 1, where IJ is the slenderness ratio.

)LJXUH 6NHWFKGH¿QLQJV\PEROVXVHGWRDQDO\]HÀLJKWWUDMHFWRU\RIK\SHUVRQLFYHKLFOHV

 

 

 

 
Chapter 6 Theoretical Considerations and Applications

217

A second version of ¿gure 6.34 is given in reference 6.101 (p. 8) that includes plots of the impulse as well as 

the overpressure. A third version of this ¿gure is contained in reference 6.18. Plotkin has added the overpressure 

and impulse for a nominal 400,000 pound supersonic transport (HST) at Mach 2.7 to that of reference 6.101 (see 

¿gure 6.35). It tends to make the point that a hypersonic transport may be more boom friendly than a supersonic 

transport (SST). However, it has been pointed out in reference 6.18 that the theory is a volume only model 

that does not account for vehicle lift. Almost 40 percent of the boom from an SST such as Concorde is due to 

lift. The drag-dominated theory implicitly assumes a short body, which results in short signature durations and 

correspondingly lower impulse.

M. N. Plooster, also during the 1970 time period (see ref. 6.102), investigated the shocks resulting from an 

instantaneous energy release along a line in a quiescent atmosphere. He utilized an empirical relationship 

between shock overpressure and radius suggested by Jones, Goyer, and Plooster (ref. 6.103) of the form

)LJXUH &UXLVHRYHUSUHVVXUHYHUVXVDOWLWXGHIRUK\SHUVRQLFYHKLFOHVUHI

)LJXUH 2YHUSUHVVXUHDQGLPSXOVHDVIXQFWLRQRIDOWLWXGHIRUGUDJGRPLQDWHGK\SHUVRQLFYHKLFOH

$FRQYHQWLRQDO667LVVKRZQIRUFRPSDULVRQUHI
Chapter 6 Theoretical Considerations and Applications

218

 (64)

where

 (65)

 (66)

 (67)

 (68)

For air with Ȗ = 1.4, Jones, in reference 6.104, ¿nds E § 3.94 in the equation for Ro

.

Substituting the above de¿nitions into equation (64) yields

 (69)

This equation approaches as and for large it approaches , 

for the strong and weak shock solutions, respectively.

With Eo

 = ', Ro becomes 0.85156 ('/po)1/2 and equation (69) can now be written as

 (70)

Setting

 (71)

 

 

 

 

 

 

 

 
Chapter 6 Theoretical Considerations and Applications

219

equation (69) can be recast as

 (72)

Thus, for a homogeneous atmosphere and large UG

 (73)

For and equation (72) can be simpli¿ed to

 (74)

Jones, Goyer, and Plooster (ref. 6.103) assumed c a 1. However, to agree with the results of Pan and Sotomayer 

(ref. 6.105) and Tiegerman (ref. 6.106), c should be 0.844 and to agree with Seebass equal to 0.545. In reference 

6.102, Plooster noted that equation (64) could better approximate the strong shock solution at small radii by 

including a į-1 factor in the de¿nition of ȕ. This accounts for the ef¿ciency that the system utilizes the input 

energy (to produce shock waves) at substantially less than 100 percent ef¿ciency. 

Consequently, the equation for ȕ is

 (75)

With a value of c of 0.95 and į = 2.62, equation (68) for ǻSSo

 with the above modi¿cation, becomes

 (76)

and is plotted and compared to data from three primacord tests in ¿gure 6.36. As evident from the ¿gure, the 

modi¿ed ǻp equation gives a very accurate representation of the experimental results.

 

 

 

 
Chapter 6 Theoretical Considerations and Applications

220

Using the de¿nitions of Ȝ and Ro, given by equations (67) and (68), equation (76) may be written in terms of 

more physical quantities as

(77)

If it assumed that and 

Equation (77) becomes

(78)

for a homogeneous atmosphere.

For an isothermal atmosphere, equation (78) is substituted in equation (60) and with C' replaced by its de¿nition 

from equation (58) for large r (r = h), it becomes

(79)

with + = 25,000 feet, pg

 = 2116 lbs/ft2, ș = 90° and a ground reÀection factor of 2.0. Equation (79) is identical 

to equation (63) of Seebass, except for the multiplicative factor.

)LJXUH 5DGLDOGHSHQGHQFHRIVKRFNZDYHRYHUSUHVVXUHIURPGHWRQDWLRQRIORQJFKDUJHVRIKLJKH[SORVLYH3ULPDFRUG

7KHFXUYHWKURXJKWKHGDWDSRLQWVLVIURPHTXDWLRQUHI
Chapter 6 Theoretical Considerations and Applications

221

Pan and Sotomayer (ref. 6.105) presented the results of an approximate method, based on hypersonic small disturbance theory, for calculating the sonic boom strength , normalized position IJ and positive phase duration 

l

x

. The equations they gave for these quantities are

 (80)

 (81)

 (82)

where

 (83)

 (84)

and

 (85)

with Co being the speed of sound of the undisturbed Àow, Ro

 being a characteristic radius (E/EȖpo)1/2, E being 

the energy released per unit length of the line source, and E =  for air with Ȗ = 1.4. Note that equation 

(80), for ǻSSo

, has a different form from Plooster’s equation (64) and Seebass’ equation (54). With the above 

de¿nitions and setting

 (86)

or

 (87)

 

 

 

 

 

 

 
Chapter 6 Theoretical Considerations and Applications

222

equations (80), (81), and (82) can be written as

 (88)

 (89)

 (90)

Note that the 0.243 factor in equation (88) is at variance with the factor used in reference 6.106, which has it as 

0.306, but is consistent with equation (80) and the de¿nition of Ro

. The 0.306 factor was required by Pan and 

Sotomayer (ref. 6.105) to make it compatible with the Plooster data (¿g. 6.36) for a ǻp/po

 = 0.1, i.e., so that at 

 = 5.628 (or Ȝ = 8.933), equals 0.1. Thus, 

 (91)

Also, note that the 0.343 factor in equation (80) must be increased to 0.433 to be consistent with equation (91). 

A plot of ǻSSo

 from equation (91) along with those of Seebass (equation (59)) and Plooster’s (equation (77)) is 

given in ¿gure 6.37. 

 

 

 

 

 
Chapter 6 Theoretical Considerations and Applications

223

In 1975, Tiegerman’s thesis entitled “Sonic Booms of Drag Dominated Hypersonic Vehicles” (ref. 6.106) 

was published. This thesis, which built on Seebass’s formulation, contains the background and development 

of the hypersonic far-¿eld theory for sonic booms. Like the earlier investigations, it relies on similar 

length and time scales. The equation for ǻp/po

 for a homogeneous atmosphere that Tiegerman derived is

(92)

where A1 = 0.6079 and R is given by .

 (93)

and with

(94)

)LJXUH 9DULDWLRQRIǻSSRZLWKUG0¥&' 

 
Chapter 6 Theoretical Considerations and Applications

224

R can be recast as

 (95)

Using this de¿nition, equation (92) for ǻp/po

 becomes

 (96)

The value of A2

 was given as -0.55 when second order terms were included. However, reference 6.106 also 

states that it should be positive, so its value was never conclusively established although it was discussed in 

some detail.

If , then

 

 (97)

showing again the (UG)-3/4 behavior in the far ¿eld for a homogeneous atmosphere. A second 

and interesting form of equation (92) can be developed for the case where ,

 (98)

using equation (93) for R equation (98) for ǻp/po

 becomes

 (99)

 

 

 

 

 

 

 
Chapter 6 Theoretical Considerations and Applications

225

With Seebass’ equation (60), the homogeneous atmosphere equation above for ǻSSo can be converted to the 

following one for the pressure jump on the ground (r = h) in an isothermal atmosphere

(100)

In this derivation pg

 was set equal to 2116 lbs/ft2, + to 25,000 feet, and a ground reÀection factor of 2.0 was 

employed. Equation (100) is the same as that prescribed by Seebass (eq. (63)) except for the multiplicative 

factor, which is 2.46 versus 3.83. If the same empirical factor is used for Tiegerman’s equation (96) as for Pan’s 

equation (91), i.e., 0.306, and if A2

 is set equal to -1.8569, equation (96) becomes

(101)

As for equations (77) and (91) with , equation (101) will yield a of 0.1.

A plot of this equation versus those of Plooster’s, Pan’s, and Seebass’ is provided in ¿gure 6.37 and labeled 

Tiegerman. As is evident from this ¿gure, all of the ǻp equations for the homogeneous atmosphere (with 

the empirical corrections) reduce to essentially the same result. In reference 6.106, Tiegerman also derived 

equations for the axial and radial lengths of the positive phase (Lx

 and Lr) for a homogeneous atmosphere. The 

equations are

(102)

Using

(103)

 
Chapter 6 Theoretical Considerations and Applications

226

with the reference area de¿ned as , equation (102) for Lx and Lr becomes

 (104)

With B2 = A2 and using the same empirical value for A2 as for equation (101), i.e., -1.8569, equation (104) becomes

 (105)

Recall that the main virtue of this empiricism (the value of A2) was it enabled the agreement of ǻSSo with the 

data of Plooster. Except for the B2

 term, equation (104) for Lx0 is essentially the same as Pan and Sotomayer’s 

equation (90).

Equations for an Lx

 and the positive phase impulse ,

x for an isothermal atmosphere were also given in reference 

6.106. They are listed below in a slightly different form.

 (106)

 (107)

In deriving these formulas, + was set equal to 25,000 feet, pg to 2116 lbs/ft2 and the speed of sound ag to 1117 ft/sec.

Tiegerman’s result was recast as an effective F-function and incorporated into PCBoom (ref. 6.27) for two 

applications – the boom generated by high altitude under-expanded rocket plumes and the boom generated by 

blunt reentry bodies. This was used to very successfully predict the boom from a re-entering comet probe (ref. 

6.107) with predicted and measured peak overpressures agreeing within 1 percent and arrival time within 1.25 

seconds.

To date, the combinations of Euler and FPE codes have not been applied to a hypersonic case. The strong shock 

extrapolation procedure of reference 6.108 may prove useful in extrapolating the high amplitude sources to a 

radius where ray tracing codes can continue propagation to the ground. Finally, there is not an analytical method 

at hypersonic speeds for calculating sonic boom parameters that includes lift. The various methods documented 

for drag dominated vehicles have different forms, but for large radial distances reduce to essentially the same 

results when they are empirically matched to the Plooster data and the excellent agreement of a Tiegerman-based 

prediction to the measured Stardust reentry boom data (ref. 6.107).

 

 

 
Chapter 6 Theoretical Considerations and Applications

227

Boom Predictions and Correlations with Experiment

Up until the late 1980s, boom prediction methodology was primarily F-function based. Near-¿eld pressures provided by the F-function were fed into the Hayes or Thomas ray-tracing propagation codes to determine the ground 

pressure signatures. Since that time, the use of Euler CFD codes has been the preferred method for near-¿eld 

calculations. The ingredients contained within F-function-based sonic boom prediction codes, i.e., equivalent 

axisymmetric-body methods, along with the CFD approach, are schematically illustrated in ¿gure 6.38. Also indicated is the use of near-¿eld wind-tunnel data. In this latter case, due to the lack of three-dimensional data, the 

calculation must proceed directly to the ray-tracing propagation code.

For the Euler or Navier-Stokes codes, a computational grid is required. Ideally, the code will have an adaptive 

grid capability to concentrate the grid in the vicinity of shocks, or a shock ¿tting routine, since shock jumps tend 

to smear as distance from the con¿guration increases (noted earlier). In most cases, Euler equation codes are used 

since, for vehicles at cruise conditions, viscous effects are second order. Boom predictions using this technology 

are included throughout subsequent sections.

The path for the F-function approach begins with the geometry of the vehicle that is converted into a numerical 

model. Area developments for the desired Mach number and azimuth angle are obtained through use of a computing 

program, which is also used in the evaluation of airplane wave drag. Lift development is also normally provided 

by a computer program. The resulting equivalent area distributions evolve into the Whitham F-function and then 

into the near-¿eld signature. This near-¿eld signature is then input to the atmospheric propagation program (raytracing) or a mid-¿eld propagation code that better accounts for nonlinear or three-dimensional effects. The output 

of this latter program is then input to the ray-tracing code providing the detailed sonic boom signatures at ground 

level for standard or actual (non-standard) atmospheres. A third path is indicated where the Ks

, Kp, and Kt factors 

are obtained using the Carlson methodology of reference 6.21.

The wind-tunnel path in the sonic boom prediction program was developed in order to use the near-¿eld signatures 

measured on small sonic boom models. These models, in themselves, provide the same inputs as the primary path 

(geometry, volume, lift, etc.). This alternate path is particularly valuable when sonic boom information is required 

for non-standard con¿gurations, for vehicles operating at extreme conditions, and particularly at relatively high 

Mach numbers. 

It should be noted that the most frequently used sonic boom prediction method in use today has been developed 

and improved upon over several decades. The basic Whitham (ref. 6.3) method has been enhanced by the works 

of many individuals, including Carlson (ref. 6.21), Hayes (ref. 6.23), Thomas (ref. 6.26), and Plotkin (ref. 6.54). 

Application of computer programs by the authors to essentially all classes of vehicles for both steady and nonuniform Àight operations in standard or non-standard atmosphere has provided good correlation with actual 

measured signatures. 

)LJXUH ,QJUHGLHQWVRIVRQLFERRPSUHGLFWLRQSURJUDPV
Chapter 6 Theoretical Considerations and Applications

228

Correlation of Boom Predictions for Aircraft

A considerable amount of theory/experiment correlations work has been done using Àight-test data. The bulk of 

the signatures measured in the usual Àight-test programs display some form of deviation from nominal or average 

signatures as a result of atmospheric disturbances (discussed in Chapter 2). However, complete sets of relatively 

disturbance-free signatures have been obtained by some programs in which a deliberate attempt was made to 

minimize these factors by selection of test site, season, and time of day.

An interesting set of signatures for the 55-foot long Lockheed F-104 Star¿ghter supersonic jet ¿ghter is shown in 

¿gure 6.39 (ref. 6.109). Note the wide variety of altitudes and Mach numbers at which the various Àight tests were 

conducted. For the on the deck Àight at 60 feet (h/l a 1), the signature is very complex and the overpressure is of 

the order of 100 lbs/ft2

. Except for the bow shock (where the measured peak overpressure at the bow shock was 

clipped when the measurement system was over-driven), the signature shape is well represented by the theory. It 

is also evident that the signature approaches a simple N-wave as altitude (and h/l) is increased. At 48,000 feet (h/l

a 873) an N-wave has formed and the overpressure is less than 1 lb/ft2

. The agreement of theory and experiment 

is good except in the vicinity of the tail wave, where the predicted signature has a longer period (ǻt). In the above 

discussion, h and l are the symbols for the respective altitude and aircraft length.

Far-¿eld ground signatures for Mach numbers near 3.0 for the ;B-70 and the SR-71 were also obtained. Figure 

6.40 shows an experiment/theory comparison (ref. 6.110) for the ;B-70 at a Mach number of 2.84, an altitude of 

70,300 feet, and a gross weight of 304,500 pounds. Data for three microphones are plotted and compared to the 

predicted signature. All show that the theory predicts the shock strengths very well but that the predicted signature 

length exceeds that of the measurement. Since the bow shock was made to line up with the experimental one, it 

is not clear if the difference in signature length is a front or back-end problem or simply a theory shortcoming. It 

is worth noting that the weight, and thus the lift, is substantial. The magnitude of the measured bow shocks range 

from 1.6 lbs/ft2

 to 1.9 lbs/ft2 and the signature length is about 0.30 sec.

)LJXUH 0HDVXUHGDQGSUHGLFWHGVRQLFERRPVLJQDWXUHVIRU)DLUFUDIWRQWUDFNUHI
Chapter 6 Theoretical Considerations and Applications

229

There are also Àight measurements for the SR-71 aircraft at a Mach number of 3.0 and an altitude of 80,000 feet 

(refs. 6.94 and 6.111). Figure 6.41 shows this measurement as well as those for Mach numbers of 1.35 and 2.0. 

All of the theoretical predictions are in agreement with experiment both for the shock jumps and the length of 

signature. However, the SR-71 is a smaller and lighter (80,000 to 100,000 pounds) aircraft than the ;B-70 and 

effectively more slender at 105 feet in length. It is also noteworthy that the earlier calculations (¿gs. 6.29 - 6.31)

for the wind-tunnel models were made using Whitham’s F-function near-¿eld methodology as interpreted by 

Carlson, McLean, and Shrout (ref. 6.93) and the Àight prediction for the SR-71 was based on the F-function, plus 

Hayes’ propagation code (ref. 6.23), calculations.

Bodies of Revolution

As Mach numbers increase beyond 3 or 4, the linear methods normally used for sonic boom predictions begin to 

have problems. In the near ¿eld, where nonlinear effects are most important and become increasingly so as Mach 

number increases, linear lifting-surface methods and Whitham’s F-function methodology start to break down. 

With the near-¿eld predictions becoming more inaccurate the mid- and far-¿eld estimates also suffer. It should 

be noted, however, that the sharper (pointed) and more slender a con¿guration, the higher the Mach number and 

radial distance may be before these methods falter.

)LJXUH 6RQLFERRPVPHDVXUHGE\WKUHHPLFURSKRQHVIRUWKH;%0DFKK IHHWUHI

)LJXUH0HDVXUHGDQGSUHGLFWHGVRQLFERRPVLJQDWXUHIRUWKH65DLUFUDIWRQWUDFNDGDSWHGIURPUHI

1$6$SKRWR(&
Chapter 6 Theoretical Considerations and Applications

230

Some evidence of these problems can be seen in reference 6.112, which contains data for some slender bodies of 

varying bluntness (see ¿g. 6.42) for Mach numbers from 1.41 to 4.63. They are de¿ned by simple raxn

 equations, 

where the n values used are 1.0, 0.5, and 0.25 as noted by the equations on the ¿gure. Bow-shock pressures, in 

the form of , and impulses for these bodies are plotted as a function of n in ¿gures 6.43 and 6.44.

The pressure-parameter plots for Mach numbers of 2.96, 3.83, and 4.63 show fair agreement for all Mach number 

and n values. The impulse plot, on the other hand, shows that the predictions deteriorate with increasing Mach 

number and bluntness. This reÀects the differences in the lengths of the positive phase of the pressure signatures. 

Note that all of these data are for zero angle of attack. 

)LJXUH 0RGHOVZLWKHTXDWLRQVIRUPRGHOUDGLLUHI

)LJXUH 9DULDWLRQRIPD[LPXPRYHUSUHVVXUHSDUDPHWHUZLWKEOXQWQHVVSDUDPHWHUKO UHI
Chapter 6 Theoretical Considerations and Applications

231

Whitham’s method (ref. 6.3) is used for these pressure-signature and shock-strength predictions for a smooth 

body. However, for a conical forebody with its sharp shoulder, the authors applied the non-smooth-body equation 

of Whitham (also ref. 6.3). They also looked at the effects of the effective lift and boundary layer, as shown in 

¿gure 6.45. The former is due to the asymmetric pressures on the Mach-cut planes. It is evident from the ¿gure 

that the non-smooth method provided a better result in the aft regions of the signature and that the addition of the 

boundary layer improved the agreement of the theoretical bow-shock strength with experiment.

)LJXUH 9DULDWLRQRIVLJQDWXUHLPSXOVHSDUDPHWHUZLWKEOXQWQHVVSDUDPHWHUUHI

)LJXUH &RPSDULVRQRIVPRRWKERG\SURJUDPZLWKOLIWDQGQRQVPRRWKERG\SURJUDPZLWKDQGZLWKRXWERXQGDU\OD\HU

0RGHO0DFKKO UHI
Chapter 6 Theoretical Considerations and Applications

232

Diamond Cross-Section, Body and Wing Body

Normally, at hypersonic Mach numbers, one expects to see the predicted impulse of signatures to be larger than 

those measured. This is attributed primarily to the fact that most signatures contain lift effects and lifting effects 

on signature length are generally not as well predicted as volume effects. Several models were tested in 1970 

and reported in reference 6.113 that shed some light on this phenomenon. In this paper, Àow ¿eld surveys of two 

con¿gurations, shown in ¿gure 6.46, were carried out. One con¿guration consisted of a body with a diamond 

cross-section and a leading-edge sweep of a 80° (model A), while the other con¿guration consisted of a body 

with a wing of 64.5° sweep (model B). Figures 6.47 and 6.48 give pressure distributions for these models in the 

form of (ǻp)(KO)

3/4 for three Mach numbers (2.3, 2.96, and 4.63). Data for both non-lifting and lifting attitudes is 

provided.

)LJXUH 6RQLFERRPWHVWPRGHOV$OOGLPHQVLRQVDUHQRQGLPHQVLRQDOL]HGZLWKUHVSHFWWRPRGHO

OHQJWKORIFPLQUHI

)LJXUH ([SHULPHQWDODQGWKHRUHWLFDOSUHVVXUHVLJQDWXUHVIRUPRGHO$DWVHOHFWHGYDOXHVRI0DQG&LKO UHI
Chapter 6 Theoretical Considerations and Applications

233

The theoretical predictions were made using Whitham’s methodology as interpreted by reference 6.93. Figure 

6.47 for model A shows for CL = 0 that the theoretical pressures agree quite well with experiment for all three 

Mach numbers. At a CL a 0.1, the magnitude of the measured and predicted pressures are still in good agreement, 

however, the signature-length predictions become progressively worse as Mach number increases. While the 

difference in signature length between the theoretical prediction and experiment for Mach numbers 2.3 and 2.96 

might be minimized by accounting for viscous effects, the difference at a Mach number of 4.63 is clearly a failure 

of the quasi-linear method. Figure 6.48 for model B shows similar data but the predictions of the magnitude of 

the pressure parameter at CL = 0 deteriorate as the Mach number increases from 2.3 to 4.63. Curiously, for the 

lifting calculation at a CL a 0.1, the magnitude of the pressure parameter is fairly well predicted but the signaturelength predictions exceed the measured ones as for model A. 

Apollo Capsule

In the area of ground sonic boom measurements, there is also data for the Apollo capsule during the atmospheric 

entries of Apollo 15 and Apollo 16 (refs. 6.114 and 6.115). Application of the prediction methodology of reference 

6.21 to these cases are shown in ¿gure 6.49. Illustrative theory/experiment comparisons for four Mach numbers 

from 1.75 to 15.0 are plotted. Predictions for the magnitudes of the bow, or leading, shocks range from fair to 

good. Signature length estimates are generally longer than those measured. However, the effective length of the 

capsule due to Àow separation over the after body was not accounted.

)LJXUH ([SHULPHQWDODQGWKHRUHWLFDOSUHVVXUHVLJQDWXUHVIRUPRGHO%DWVHOHFWHGYDOXHVRI0DQG&LKO UHI
Chapter 6 Theoretical Considerations and Applications

234

Similar calculations for Apollo 15 and Apollo 16 were carried out at the Ames Research Center (ARC) during the 

early 1970s and documented in references 6.116 and 6.117. The wind-tunnel data was obtained on a 0.016-scale 

model of the Apollo 15 command module (¿g. 6.50) at Mach numbers from 1.5 to 10 in the Jet Propulsion 

Laboratory (JPL) supersonic and hypersonic wind tunnels and were reported in reference 6.117. Data for Mach 

numbers of 1.16 and 4.57 and an h/l of 2.85 are shown in ¿gure 6.51. Bank angles consistent with the Àight 

conditions at those Mach numbers were used. The tunnel signature for Mach 1.16 was obtained by extrapolating 

the data of reference 6.118 from Mach 1.5. This extrapolation is justi¿ed because the signature parameters have 

been found to change very little between these Mach numbers. It was also necessary to interpolate between the 

bank angles for which data were presented in reference 6.118 to obtain the signatures shown in ¿gure 6.51.

)LJXUH &RUUHODWLRQRISUHGLFWLRQVZLWKPHDVXUHPHQWVPDGHGXULQJUHHQWULHVRI$SROORDQGUHI

)LJXUH ,QVWDOODWLRQSKRWRJUDSKVKRZLQJDQ$SROORFDSVXOHPRGHOLQLQFK6XSHUVRQLF:LQG7XQQHODWWKH

-HW3URSXOVLRQ/DERUDWRU\UHI
Chapter 6 Theoretical Considerations and Applications

235

Calculation of the ground overpressures required the determination of the point-of-origin on the Àight path of 

the pressure signals received by the sensors located on two ships (USS .DZLVKLZL and USS 2NLQDZD) positioned 

north of Hawaii. With the point-of-origin determined, the propagation methodology of Thomas (refs. 6.25 

and 6.26) was utilized to calculate the ground signatures shown in ¿gure 6.49. Comparison of the calculated 

pressure signatures (extrapolated from wind-tunnel data) with the measured ones shown on ¿gures 6.52(a) for 

Mach 1.16 and ¿gure 6.52(b) for Mach 4.57 indicate good agreement – similar to those shown earlier for the 

Carlson technique. Only the positive portion of the wind-tunnel signature has been shown at Mach 1.16, since 

shock-wave reÀections from the Àoor of the wind tunnel prevented the recording of the full pressure signature 

at the lowest Mach number of the test described in reference 6.118. The possible effects of temperature and 

winds on these measurements are discussed in reference 6.116. Apollo command module wind-tunnel data is 

also contained in reference 6.108 along with a method for extrapolating strong shock waves.

)LJXUH $SROOR&RPPDQG0RGXOHZLQGWXQQHOSUHVVXUHVLJQDWXUHVUHI

)LJXUH $SROOR&RPPDQG0RGXOHZLQGWXQQHOLQÀLJKWFRUUHODWLRQUHI
Chapter 6 Theoretical Considerations and Applications

236

Saturn V Launch Vehicle

Booms produced by the Apollo ascent vehicles, shown schematically in ¿gure 6.53, have also been measured and, 

in a few cases, have been compared to predictions. Reference 6.114 provides Apollo 15 measured signatures (see 

¿g. 6.54) from the two ship stations shown in the schematic of ¿gure 6.55. The ¿rst signature, measured aboard 

the USS Salinan, is for a Mach number of 6.07 and an altitude of a209,000 feet. The second was measured aboard 

the USS $XVWLQ and is for a Mach number of 16.13 at an altitude of 586,392 feet. The Mach 6.07 measurement was 

for the S-1C vehicle con¿guration while a Mach number of 16.13 was measured for the S-11 stage. As noted, no 

predictions were made of the pressure signatures for these two cases. Similar data is described in reference 6.115 

for the Apollo 16 mission. Ascent measurements for the Àight were made at three ship stations. As in Apollo 15, 

no predictions were made of the pressure signatures.

)LJXUH 6FKHPDWLFGLDJUDPRI$SROOR6DWXUQ9ODXQFKYHKLFOHDQGUHHQWU\YHKLFOHFRQ¿JXUDWLRQVUHI

)LJXUH 0HDVXUHGVRQLFERRPVLJQDWXUHVGXULQJDVFHQWDVUHFRUGHGDWSRVLWLRQVNPDQGNPIURPWKH

ODXQFKVLWHDORQJWKH$SROORJURXQGWUDFNUHI

(a) Measured on USS Salinan, Overhead Conditions Velocity = 2210 m/sec and Altitude = 63,422 meters.

(b) Measured on USS $XVWLQ, Overhead Conditions Velocity = 4762 m/sec and Altitude = 178,778 meters.
Chapter 6 Theoretical Considerations and Applications

237

From a measurement standpoint, Apollo 17 (ref. 6.119) was more detailed than Apollo 15 and Apollo 16, having a 

total of six measuring stations. Figure 6.56 (ref. 6.119) shows the relative ship locations. Signatures from these six 

stations are given in ¿gure 6.57 (ref. 6.119). These stations were located to lie within the focus regions associated 

with the Àight path angle and acceleration pro¿le of the space vehicle during ascending Àight. Listed in the ¿gure 

are the velocity and the altitude of the launch vehicle recorded along the Àight path at the time that the initial sonic 

boom was generated for each of the measurement stations.

)LJXUH6FKHPDWLFVKRZLQJVKLSSRVLWLRQIRUGDWDDFTXLVLWLRQGXULQJODXQFKDQGUHHQWU\UHI

)LJXUH6FKHPDWLFVKRZLQJVKLSSRVLWLRQIRUGDWDDFTXLVLWLRQGXULQJDVFHQWUHI
Chapter 6 Theoretical Considerations and Applications

238

In contrast to the Apollo 15 and Apollo 16 data, predictions of the shock overpressures were made and are shown 

in ¿gure 6.58. This ¿gure was taken from reference 6.119, which, in turn, was taken from reference 6.120. 

Clearly, the agreement is quite remarkable. No indication is given in these references of the methodology used to 

obtain results, but most likely they utilized the experimental data of references 6.108 and 6.121, the strong shock 

propagation procedures of reference 6.108 and the wave form propagation method of Thomas (refs. 6.25 and 

6.26).

)LJXUH6RQLFERRPVLJQDWXUHVPHDVXUHGGXULQJDVFHQWRI$SROORDVUHFRUGHGDWVWDWLRQVWRUHI

)LJXUH 2YHUSUHVVXUHGDWDDVDIXQFWLRQRIGRZQUDQJHGLVWDQFHDVPHDVXUHGLQWKHIRFXVERRPUHJLRQGXULQJ

DVFHQWRI$SROORUHI
Chapter 6 Theoretical Considerations and Applications

239

Space Shuttle

Pressure signature measurements and boom predictions for early versions of the Shuttle and booster date back to 

the early 1970s. For example, references 6.122, 6.123, and 6.124 contain data on early straight- and delta-wing 

orbiter concepts. Reference 6.125 contains data and sonic boom predictions for a Ày-back booster and orbiter 

shown in ¿gure 6.59. Tests were conducted with and without a solid exhaust plume simulation. Figure 6.60 shows 

a Schlieren for Mach numbers of 3.0 and 4.0 of the ascent con¿guration with the simulated exhaust plume and 

the strong shock that the latter generates. Boom predictions and correlations were made using Thomas’ method 

and the near-¿eld measured pressures contained in the report. An illustrative example is given in ¿gure 6.61 for 

the Àight conditions listed in the legend, where Į is the angle of attack, ࢥ is bank angle, and Ȍ is heading angle. 

It gives the variation of ǻPmax with the rate of change of Àight path angle, for the launch con¿guration with and 

without plume and the Ày-back booster without plume. For values beyond a -0.5 deg/sec, there is a focus region. 

The label “trajectory value” is the value for the example trajectory given in the paper at a Mach number of 3.0. 

The other plots provided in reference 6.125 illustrate the effects of Àight path angle and its rate of change.

)LJXUH 6KDGRZJUDSKVWDNHQGXULQJWHVWVLQ-3/PHWHULQFKVXSHUVRQLFZLQGWXQQHOĮ UHI

(a) Launch con¿guration with simulated plume (Mach 3). (b) Launch con¿guration with simulated plume (Mach 4).

)LJXUH )O\EDFNERRVWHUDQGRUELWHUFRQ¿JXUDWLRQVUHI
Chapter 6 Theoretical Considerations and Applications

240

Subsequent to the publication of reference 6.124, the Space Shuttle Orbiter was heavily modi¿ed. As a result of 

these design modi¿cations, a wind-tunnel investigation that used a 0.0041 scale model of the latest (¿nal) Space 

Shuttle Orbiter (see ¿gure 6.62) to determine the effects on the ground overpressure characteristics due to changes 

in the geometry and the aerodynamic characteristics of the Orbiter was conducted. The results of the investigation 

were presented in 1975 in a paper (ref. 6.126, p. 1) written by Mendoza. The abstract for this paper states,

Pressure signatures for a 0.0041-scale model of a space shuttle orbiter were measured in a wind tunnel at 

Mach numbers from 1.30 to 3.02. The model was tested at 10° and 25° angles-of-attack and roll angles 

were varied from 0° to 180° in 30 degree increments. Comparisons of sonic boom levels were made for 

a delta-wing con¿guration and for the latest space shuttle orbiter, which were assumed to have identical 

lengths and entry trajectories.

Calculations were made for two trajectories (actually two modi¿ed trajectories) using the waveform method of 

reference 6.126. These trajectories, shown in ¿gure 6.63, are for space shuttle entry and cover a range of Mach 

numbers from 2.7 down to 1.2. A comparison of sonic boom footprints for the Space Shuttle and earlier versions 

of the shuttle for trajectory A are shown in ¿gure 6.64. Figure 6.64 shows that the longest delta-wing space shuttle 

had the highest pressure and the 32.6 m delta wing shuttle the lowest. Similar results for trajectory B are given in 

reference 6.126.

)LJXUH 7KHVFDOHPRGHORIWKHODWHVW6SDFH6KXWWOH2UELWHUUHI

)LJXUH 6RQLFERRPGXULQJDVFHQWĮ GHJUHHVࢥ GHJUHHV  GHJUHHVVHFRQGUHI
Chapter 6 Theoretical Considerations and Applications

241

)LJXUH &RPSDULVRQVRIWKHVRQLFERRPIRRWSULQWVIRUWKHYDULRXVVSDFHVKXWWOHYHKLFOHVKr 

IRUWUDMHFWRU\$¿JDUHI

)LJXUH 6SDFH6KXWWOHHQWU\WUDMHFWRU\SDUDPHWHUVUHI

(a) Trajectory A. (b) Trajectory B.
Chapter 6 Theoretical Considerations and Applications

242

Variations of the maximum ǻp with Mach number for the two modi¿ed trajectories in ¿gure 6.63 for the shuttle 

orbiter and for delta-wing and straight-wing orbiters are provided in ¿gure 6.65. It is evident that the trajectory 

B of ǻp values are larger than those for trajectory A and that the latest orbiter ǻp values are higher than those of 

the delta-wing version. The highest value is for the straight-wing orbiter with a ǻp of 95 N/m2 at a Mach number 

of 1.2 (see ref. 6.122).

The 1973 paper by Holloway et al. treated both the shuttle orbiter and ascent vehicle booms (see ref. 6.120). Also, 

it analyzed both Western Test Range (WTR) and Kennedy Space Center (KSC) launches. Thomas’ methodology 

(ref. 6.26) used in these calculations was augmented by the near-¿eld strong shock extrapolation procedure of 

reference 6.108. Figure 6.66 (adapted from ref. 6.120) shows the ground-track overpressure variation during 

shuttle ascent.

As shown earlier for the Apollo ascent (¿g. 6.58), there is a focal region followed by a rapid decline in overpressure. 

Maximum pressures at the focus may be in excess of 200 n/m2

 (4.0 lbs/ft2). Focused energy may be expected to 

extend to about 45 nmi on either side of the ground track. The general characteristic of the focus zone is that it is 

longest near the ground track and becomes narrow near the outer edge. Analysis of the Saturn V data from Apollo 

17 suggests that the longitudinal extent of the focal zone will be less than 2 nmi at its widest point.

Overpressures during orbiter entry are plotted in ¿gures 6.67 and 6.68 (ref. 6.120). The lateral distributions, 

pictured in ¿gure 6.67, have the typical bell shape and are a maximum at a Mach number of 2.0. Figure 6.68, a 

plot of the maximum values, shows that the overall maximum is around 1.4 lbs/ft2

 and occurs at a range to landing 

of a 30,000 feet. Further details are given in reference 6.120. 

)LJXUH *URXQGWUDFNVRQLFERRPOHYHOVIRUWKUHHRUELWHUFRQ¿JXUDWLRQVUHI

)LJXUH *URXQGWUDFNRYHUSUHVVXUHYDULDWLRQGXULQJVKXWWOHDVFHQWDGDSWHGIURPUHI
Chapter 6 Theoretical Considerations and Applications

243

The near-¿eld pressure signatures of the space shuttle launch and orbiter vehicle were further studied by Ashby 

in 1979 in reference 6.127 (p. 7),

Static-pressure signatures parallel to the Àight path of the launch and entry con¿gurations of the spaceshuttle 

were measured in the Langley 20-inch Mach 6 tunnel in air at selected distances from the Àight path. The 

launch con¿guration, consisting of an equivalent body of revolution (representing the orbiter and external 

fuel tank) with a solid exhaust gas plume attached, was tested at an angle of attack of 0°. The entry 

con¿guration (Orbiter alone) was tested over an angle-of-attack range from 10° to 40°.

The simulated plume body represents the area distribution of the gaseous exhaust plume plus the mixing region 

between the plume inner shock and the external Àow. Its shape and size were determined in a manner described 

in reference 6.128.

Figure 6.69(a) shows the dimensions and shape of the launch con¿guration model as well as that of the orbiter 

(¿g. 6.69(b)). A schematic of the test setup is shown in ¿gure 6.70. Measured values of ǻp/p are tabulated in the 

paper for a range of azimuths from 68.5° to 180° at an h/Oof 10.65 and a Mach number of 6.0. Plots and calculated 

signatures are given for azimuth angles of 150° and 90°. A plot of the 150° data and predictions based on the 

methods of references 6.129 and 6.130 are presented in ¿gure 6.71. Experimental pressures were determined 

using both static and pitot probes at an h/l of 10.65.

)LJXUH 2UELWHUHQWU\RYHUSUHVVXUHYDULDWLRQDORQJWKHJURXQGWUDFNUHI

)LJXUH /DWHUDORYHUSUHVVXUHYDULDWLRQGXULQJRUELWHUHQWU\UHI
Chapter 6 Theoretical Considerations and Applications

244

(a) 0.000456-scale model of equivalent body of revolution (orbiter and external fuel tank) with 

solid exhaust gas plume (Mach 6).

)LJXUH 'HOWDZLQJ6SDFH6KXWWOH2UELWHUWHVWPRGHO$OOOLQHDUGLPHQVLRQVDUHLQPLOOLPHWHUVUHI

(b) 0.0041-scale model of 0898 orbiter.

)LJXUH 6FKHPDWLFRIWHVWVHWXSUHI
Chapter 6 Theoretical Considerations and Applications

245

The computations were carried out for the geometry illustrated in the key. The geometry has a cylindrical wake 

downstream of the plume. Data for both forward and reverse traverses are also provided. It is noteworthy that 

the static probe sensed the pressure bump (bow shock) ¿rst and its measured maximum value is about twice 

that of the pitot probe. A similar relationship exists between the calculated pressures jump and the static probe 

measurements. If one assumes that the static probe measurement is the most accurate, then it would appear that 

the actual viscous expansion about the simulated plume model was greater than that of the inviscid calculation 

(refs. 6.129 and 6.130) for the model with the cylindrical wakes.

The presentation of the orbiter experimental results in reference 6.127 is more extensive than the presentations 

of experimental results for the ascent vehicle. The experimental results for the geometry presented in ¿gure 6.69 

are provided for the lower symmetry plane (0° azimuth angle) and angles of attack of 10°, 20°, 30°, and 40°. 

The computer code had limitations in how far downstream and radially the Àow could be computed. As stated in 

reference 6.127 (p. 6),

The computer program would not run far enough downstream for the shock to be at the required h/l, and 

could not compute the Àow ¿eld for angles of attack greater than 25°. Since only the Àow ¿eld of the 

windward surface is of interest, the upper surface can be judiciously contoured to make the program run 

for an angle of attack of 30°, but only for a small distance beyond the length of the con¿guration. To make 

the program run the required distance for the shock to be at the desired h/l, an established experimental 

observation was utilized. It has been shown (refs. 6.131 and 6.132) for a delta wing con¿guration at angles 

of attack above 20°, a body of revolution generated by the lower surface contour in the plane of symmetry 

has, at an angle of attack of 0°, approximately the same Àow ¿eld as the delta wing con¿guration does in 

that plane. Therefore, such an equivalent body of revolution was used in the program to calculate the Àow 

¿eld for an angle of attack of 30°. 

This prediction is shown in ¿gure 6.72 and is in good agreement with the pitot probe measurements, but much 

lower than those for the more accurate static probe. Neither probe is able to account for the large Àow angles 

present in the Àow ¿eld at such high angle of attack and small h/Ovalues. Present-day Euler codes do not have 

these limitations.

)LJXUH 3UHVVXUHVLJQDWXUHVIRUVFDOHPRGHORIHTXLYDOHQWERG\RIUHYROXWLRQRUELWHU

DQGH[WHUQDOIXHOWDQNZLWKVROLGH[KDXVWJDVSOXPH0DFKDWWZRPHULGLDQDODQJOHVRI

)LOOHGV\PEROVDUHIURPIRUZDUGWUDYHUVH2ULJLQVZHUHVKLIWHGIRUSORWWLQJĮ UHI
Chapter 6 Theoretical Considerations and Applications

246

Reference 6.133 focuses on correlations of ground measured pressure data with sonic boom predictions for the 

space shuttle STS-1 orbiter during reentry. Forty-four sonic boom pressure signatures recorded at 11 locations 

during the reentry of the Orbiter &ROXPELD are compared to signatures extrapolated from Àight altitudes 

using near-¿eld wind-tunnel pressure data for Mach numbers of Mach 1.23 to 5.87. Pressure signatures were 

recorded by microphones positioned at ground level and simulated ear level near the descent ground track along 

the California corridor. Only the ground level data was used for the theory/experiment correlations. Station 

locations, meteorological data, signature duration, and shock-rise-time information are tabulated in ref. 6.133.

The ground signature measurements taken at the 11 stations are shown in ¿gure 6.73. While all are N-wave type 

signatures, several of the leading shocks have rounded peaks (instead of sharp corners) and the last two, for Mach 

numbers of 1.40 and 1.23, have a spiked shock. The time duration of the signatures vary from 0.693 second at 

Mach 5.87 to 0.375 second at Mach 1.23.

)LJXUH 3UHVVXUHVLJQDWXUHVDORQJSODQHRIV\PPHWU\RIVFDOHPRGHORIWKH%RUELWHUDWDQDQJOHRIDWWDFNRI°. 

)LOOHGV\PEROVDUHIURPIRUZDUGWUDYHUVH2ULJLQVZHUHVKLIWHGIRUSORWWLQJࢥ UHI
Chapter 6 Theoretical Considerations and Applications

247

The sonic boom predictions were made using Thomas’ extrapolation methodology (ref. 6.26) and the wind-tunnel 

data from references 6.126 and 6.127. Mach number, angle of attack and h/l combinations used in the reference 

6.126 tests are provided in the table included with ¿gure 6.74 below. Roll angles ranged from 0° to 180° in 30° 

increments. Tests were at a Mach number of 6.0 and the h/l was 1.176 (ref. 6.127). Angles of attack ranged from 

10° to 40° and roll angles from 0° to 68.5° or 90° depending on whether the data was taken by the pitot probe 

or static pressure probe, respectively. The estimated roll angle and angle-of-attack variation with Mach number 

during the reentry of the STS-1 orbiter are given in ¿gure 6.74. In order to make ground sonic boom predictions 

for the Àight conditions of the signatures of ¿gure 6.73 interpolations and extrapolations of the data (i.e., roll 

angle, angle of attack, and Mach number) contained in the above references were required. With these data, 

Thomas’ wave-form propagation code was used to make predictions of all 11 signatures shown in ¿gure 6.73.

)LJXUH 0HDVXUHGVRQLFERRPVLJQDWXUHVUHFRUGHGDWPHDVXUHPHQWVLWHVORFDWHGXQGHUDQGODWHUDOWR

WKH676UHHQWU\JURXQGWUDFNDGDSWHGIURPUHI
Chapter 6 Theoretical Considerations and Applications

248

M 1.30 1.64 2.21 2.61 3.02

Į 10° 10° 10° 10°/ 25° 25°

h/l 1.55 and 1.36 1.36 1.36 1.36 and 0.99 0.99

Since most of the wind-tunnel data are limited to the positive phase of the signatures, predictions were only made 

for the positive phase. Two examples are provided in ¿gure 6.75; one for station 0 at a Mach number of 5.87 and 

the other for station 3 at a Mach number of 2.97. The agreement of the prediction with experiment is good in both 

cases, as it was for the other 9 cases (not shown). 

)LJXUH 3UHGLFWHGDQGPHDVXUHGVRQLFERRPVLJQDWXUHVIRUWKH6SDFH6KXWWOHDW0DFKDQGDQGUHVSHFWLYH

DOWLWXGHVRIDQGPHWHUVUHI

)LJXUH (VWLPDWHGUROODQJOHDQGDQJOHRIDWWDFNGXULQJUHHQWU\RI676RUELWHUUHI
Chapter 6 Theoretical Considerations and Applications

249

The authors of reference 6.133 also calculated the lateral distributions of the maximum pressures at the ground for 

the 11 stations. As with the longitudinal distributions, the results for stations 0 and 3 are shown in ¿gure 6.76. It is 

apparent that the roll angle at station 0 (Mach 5.87) (see ¿gure 6.74) is about +45°, while that at station 3 (Mach 

2.97) is approximately -40°. Also, the angle of attack at station 0 is a 25.5° and 16.25° at station 3. Thus, one 

would assume that the character of the ground signature at station 0 would be quite different from that at station 

3. This is clari¿ed in ¿gure 6.76. Also note that the lateral extent of the ground signatures for station 0 is slightly 

greater than that for station 3 with Mach number and altitude effects tending to offset one another.

)LJXUH /DWHUDOGLVWULEXWLRQRIUHHQWU\RYHUSUHVVXUHVDORQJVKRFNJURXQGLQWHUVHFWLRQVUHI
Chapter 6 Theoretical Considerations and Applications

250

Peak Overpressure Predictions

Numerous studies aimed at de¿ning the peak amplitudes (overpressures) of the signatures for primary boom 

carpets for a wide range of vehicles and Àight conditions have been conducted. A summary of the results from 

these studies for generally quiescent atmospheric conditions is depicted in ¿gure 6.77 (ref. 6.134). Predicted and 

measured on-track sonic boom overpressures are plotted as a function of altitude for several aircraft of various 

sizes and weights (including Concorde) and for Apollo and Shuttle launch and reentry vehicles. The data represent 

predominately on-track measurements (i.e., those within  3 nmi of the vehicle ground track).

It can be seen that the predicted trend of decreasing sonic boom overpressure with increasing altitude is reÀected 

in the aircraft data up to 80,000 feet, in the Apollo capsule measurements up to 174,000 feet, and in the Space 

Shuttle Orbiter results up to altitudes of about 250,000 feet. The two Space Shuttle Orbiter data points at altitudes 

of about 195,000 feet and 250,000 feet were at offset distances of about 33 nmi and 75 nmi respectively. Note that 

the larger the vehicle, the greater the overpressure, varying from about 3.5 lbs/ft2

 for the large ;B-70 to about 1.0 

lb/ft2

 for the smaller F-104 ¿ghter at the same altitude and to 0.2 lb/ft2 for the even smaller Apollo capsule. Space 

Shuttle Orbiter overpressures vary from about 2.5 lbs/ft2

 at 70,000 feet to about 0.7 lb/ft2 at 129,000 feet. In all 

cases, the data, particularly for the Space Shuttle Orbiter, closely match the data obtained from the performance 

of aircraft in Àight tests over the past four decades.

The sonic boom overpressures measured during the launch-ascent of the Saturn-Apollo vehicle and Space 

Shuttle do not include overpressures very near or on the focus line. In addition, the ascent boom data are 

plotted at the approximate altitude at which the boom originated. Previous plots, similar to figure 6.77 

(ref. 6.134), are plotted at altitudes corresponding to the vehicle overhead position.

In general, the measured overpressures for the launch and ascent portion of spacecraft flights indicate the 

same trend of decreasing pressure with increasing altitude. However, the magnitudes of the overpressure 

values during ascent are much greater than those of the reentry vehicle. Since the launch vehicle is 

considerably larger than the reentry vehicle, higher boom levels can be expected. The largest portion of the 

overpressure from launch vehicles results from the “effective body” produced by the rocket exhaust plume. 

It is noteworthy that disturbances from Apollo rockets in space were measured at ground level for the vehicle 

operating at altitudes up to about 600,000 feet (ref. 6.135). Simplified methods for prediction of spacecraft 

launch and reentry sonic booms are discussed in references 6.21, 6.136, 6.137, and 6.138.

Chapter 6 Summary Remarks

The Whitham F-function methodology is still useful in the estimation of sonic booms of supersonic aircraft 

whether in an exact or semi-empirical scheme. In supersonic design and analysis, the use of F-function methods 

)LJXUH 6XPPDU\RIPHDVXUHGDQGSUHGLFWHGVRQLFERRPRYHUSUHVVXUHVQHDUWKHJURXQGWUDFNIRUYDULRXV

DLUFUDIWDQGVSDFHFUDIWUHI
Chapter 6 Theoretical Considerations and Applications

251

prior to the application of Euler-equation CFD codes can lead to a better understanding of the Àow ¿eld and its 

shocks, and thus to more meaningful and ef¿cient Euler calculations.

With today’s computer capabilities, Euler or Navier-Stokes CFD codes can be used to de¿ne a con¿guration’s 

Àow¿eld out to where near-¿eld effects are small. Ideally, one would use shock-¿tted Euler codes for near-

¿eld calculations to eliminate shock-smearing, and thus provide more accurate shock pressure jumps at large 

radial distances. If computer limitations do not allow the Euler CFD code calculations to extend out to where 

near-¿eld effects are small, several other options are available. The use of George’s multipole analysis for the 

mid-¿eld calculations, closely coupled with the CFD can affect an overall improvement as demonstrated by 

Page and Plotkin. A second and more accurate option would be the use of a mid-¿eld code based on the fullpotential equation. With this approach, lateral gradients of the Àow quantities can be matched at the interface 

with the near-¿eld code calculations and accuracy improved.

Understanding how the pressure signature aging and freezing during its propagation to the ground is useful in 

the design of low-boom supersonic aircraft. The magnitude of the pressure gradients following shocks in the 

near ¿eld dictates their subsequent strength, including those in the ground pressure signature (sonic boom).

Numerous ray tracing codes are available for the prediction of the pressure signatures, or sonic boom, on the 

ground. All are based on geometrical acoustics as derived by Blokhintsev. Some are F-function dependent, 

while others use Thomas’ waveform approach. All treat the steady-state, or constant-velocity, boom. Several 

can predict the focused booms that result from maneuvers and acceleration, as well as non-standard atmospheres 

with winds. Several computer codes are capable of calculating the secondary, or over-the-top booms. Only a 

few propagation codes treat the effect of air absorption. 

Wind-tunnel and Àight data from low Mach numbers to near orbital speeds are presented along with predictions 

based primarily on methods developed for supersonic application. At hypersonic speeds, the boom intensities 

are fairly well predicted, but predicted signature lengths are usually longer than measured. Hypersonic boom 

methodology is based primarily on blast wave theory and consequently applies to drag-dominated vehicles. 

Chapter 6 References

6.1 DuMond, W. M.; Cohen, E. R.; Panofsky, W. K. H.; and Deeds, E. A Determination of the Wave Forms

 and Laws of Propagation and Dissipation of Ballistic Shock Waves. J. Acoust. Soc. Am. 18, 1946, pp.

 97–118.

6.2 Whitham, G. B. The Behavior of Supersonic Flow Past a Body of Revolution Far from the Axis. Proc. 

 Roy-Soc. A. Vol. 201. No. 1064, March 1950, pp. 89–109.

6.3 Whitham, G. B.  The Flow Pattern of a Supersonic Projectile. Communications on Pure and Applied 

Math, Vol. V, No. 3, Aug. 1952, pp. 301–348.

6.4 Landau, L. On Shock Waves at Large Distances from the Place of Their Origin. J. Phys. USSR, Vol. 9, 

No. 6, 1945, pp. 496–500.

6.5 Hayes, W. D. Linearized Supersonic Flow. Thesis, California Institute of Technology, 1947; Reprinted 

as North American Aviation Report AL-222; Available as Princeton University AMS Report 852, 1968.

6.6 Walkden, F. The Shock Pattern of a Wing-Body Combination, Far from the Flight Path. Aero. Quarterly, 

Vol. I;, May 1958, pp. 164–194.
Chapter 6 Theoretical Considerations and Applications

252

6.7 Warren, C. H. E. Sonic Bangs A Qualitative Explanation. R.A.E. Tech. Note Aero. 2192, ARC 15,540. 

Sept. 1952.

6.8 Warren, C. H. E. Addendum and Corrigenda to Above. R.A.E. Tech. Note. Aero 2192a. A.R.C. 15,541. 

Oct. 1952.

6.9 Randall, D. G. Methods for Estimating Distributions and Intensities of Sonic Bangs. ARC Technical 

Rept. R	M No. 3113, Aug. 1959.

6.10 Seebass, R. Sonic Boom Theory. Journal of Aircraft, Vol. 6, No. 3 (May-June 1969), pp. 177–184.

6.11 Carlson, H. W.; Mack, R. J.; and Morris, O. A. Sonic Boom Pressure-Field Estimation Techniques. J. 

Acoust. Soc. Am., Vol. 39, Number 5, Part 2, 1966, pp. 510–518.

6.12 Hayes, Wallace D. Brief Review of the Basic Theory. Sonic Boom Research, A. R. Seebass, ed., NASA 

SP-147, 1967, pp. 3–7.

6.13 Carlson, H. W. and Maglieri, D. J. Review of Sonic-Boom Generation Theory and Prediction Methods. 

J. Acoust. Soc. Am., Vol. 51, No. 2 (Part 3), 1972, pp. 675–685.

6.14 Darden, Christine M., et al. Status of Sonic Boom Methodology and Understanding. NASA CP 3027, 

Jan. 1988.

6.15 Plotkin, K. J. and Maglieri, D. J. Sonic Boom Research History and Future. AIAA-2003-3575, Orlando, 

FL, June 23, 2003.

6.16 Ferri, Antonio and Schwartz, Ira R. Sonic Boom Generation, Propagation, and Minimization. AIAA 

Paper No. 72-194, Jan. 1972.

6.17 Whitham, G. B. On the Propagation of Weak Shock Waves. Journal of Fluid Mechanics, Vol. 1, pt. 3, 

Sept. 1956.

6.18 Maglieri, D. J. and Plotkin, K. J. Aeroacoustics of Flight Vehicles Theory and Practice. NASA RP1258, 

Vol. 1 and WRDC TR 90-3052, Aug. 1991, pp. 519–561.

6.19 Blokhintzev, D. I. The Propagation of Sound in an Inhomogeneous and Moving Medium1. J. Acoust. Soc. 

Am., Vol. 18, 1946, pp. 322–328 Also “Acoustics of Non-Homogeneous Moving Medium,” Gostekhiazat, 

Moscow, USSR, 1946 (translated as NACA TM-1946).

6.20 Jackson, C. M. and Carlson, Harry W. Nomograms for Determining Sonic Boom Overpressure. Journal 

of Aircraft 3, 1966, pp. 74–76.

6.21 Carlson, Harry W. Simpli¿ed Sonic Boom Prediction. NASA TP 1122, March 1978.

6.22 Whitham, G. B. The Propagation of Weak Spherical Shocks in Stars. Communications of Pure Applied 

Math, Vol. 6, 1953, pp. 397–414.

6.23 Hayes, W. D.; Haefeli, R. C.; and Kulsrud, H. E. Sonic Boom Propagation in a Strati¿ed Atmosphere 

With Computer Program. NASA CR-1299 (1968).

6.24 Middleton, W. D. and Carlson, H. W. A Numerical Method for Calculating Near-Field Sonic Boom Pressure Signatures. NASA TN D-3082, 1965.

6.25 Thomas, Charles L. Extrapolation of Wind-Tunnel Sonic Boom Signatures without Use of a Whitham 

F-Function. NASA SP-255, 1970, pp. 205–217.
Chapter 6 Theoretical Considerations and Applications

253

6.26 Thomas, Charles L. Extrapolation of Sonic Boom Pressure Signatures by the Waveform Parameter Method. NASA TN D-6832, June 1972.

6.27 Plotkin, K. J. PCBoom3 Sonic Boom Prediction Model - Version 1.0e, Wyle Research Report

WR 95-22E, October 1998.

6.28 Plotkin, K. J. and Page, J. A. MDBOOM and MDPlot Computer Programs for Sonic Boom Analysis and 

Design. Wyle Research Report WR 02-02, Aug. 2002.

6.29 McLean, F. E. Some Non-Asymptotic Effects on the Sonic Boom of Large Airplanes. NASA TN D-2877, 

June 1965.

6.30 Seebass, R. Minimum Sonic Boom Shock Strengths and Overpressures. Nature 221 (1969), pp. 651–653.

6.31 George, A. R. Lower Bounds for Sonic Booms in a Mid¿eld. AIAA Journal 7, 1542 (1969).

6.32 Hicks, Raymond M. and Thomas, Charles L. A Preliminary Report on Shock Coalescence. NASA SP 

255, Oct. 1970, pp. 297–305.

6.33 Cleveland, R. O. and Blackstock, D. T. Waveform Freezing of Sonic Booms in the Atmosphere. J. Acoust. 

Soc. Am. 92 (4) (A), 1992, pp. 23–31.

6.34 Cleveland, R. O.; Hamilton, M. F.; and Blackstock, D. T. Effect of Strati¿cation of the Atmosphere on 

Sonic Boom Propagation. Proceedings of the 6th International Conference on Long-Range Propagation. 

Ottawa, Canada (1994), pp. 59–76.

6.35 Plotkin, K. J. On the Aging of Sonic Booms. J. Acoust. Soc. Am. 93 (1993), p. 2407 (A).

6.36 Cleveland, R. O. Propagation of Sonic Booms through a Real, Strati¿ed Atmosphere. Ph.D. Dissertation. Department of Mechanical Engineering, the University of Texas at Austin (1995).

6.37 Cleveland, R. O. Effects of Atmospheric Strati¿cation on Sonic Boom Propagation. J. Acoust. Soc. Am. 

97, 3257 (A) (1995).

6.38 Cleveland, Robin O. and Blackstock, David T. Waveform Freezing of Sonic Boom Revisited. NASA CP 

3335. Vol. I, July 1996, pp. 20-40.

6.39 Of¿cer, C. B. Introduction to the Theory of Sound Transmission, with Application to the Ocean, McGrawHill, New <ork, 1958.

6.40 Keller, J. B. Geometric Acoustics. I. The Theory of Weak Shock Waves, Journal of Applied Mechanics, 

25(8), 1955, pp. 938–947.

6.41 Friedman, M. P.; Kane, E. J.; and Sigalla, A. Effects of Atmosphere and Aircraft Motion on the Location 

and Intensity of a Sonic Boom. AIAA Journal 1 (6), 1963, pp. 1327–1335.

6.42 Haefeli, R. C. Effects of Atmosphere, Wind, and Aircraft Maneuvers on Sonic Boom Signatures. NASA 

CR 66756, April 1969.

6.43 Hayes, Wallace D. and Runyan, Harry L., Jr. Sonic Boom Propagation through a Strati¿ed Atmosphere. 

J. Acoust. Soc. Am., Vol. 51, No. 2 (Part 3) 1972, pp. 695–701.

6.44 Rao, P. S. Supersonic Bangs. Aeronautics Quarterly 7 (1956), pp. 21–44 and pp. 135–155.

6.45 Randall, D. C. Sonic Bang Intensities in a Strati¿ed, Still Atmosphere. Journal of Sound Vibrations 8 

(1968), pp. 196–214. Also RAE Tech. Rept. No. 66002 (1966).
Chapter 6 Theoretical Considerations and Applications

254

6.46 Friedman, M. P.; Kane, E. J.; and Sigalla, A. Effects of Atmosphere and Aircraft Motion on the Location 

and Intensity of a Sonic Boom. AIAA Journal, Vol. 1, No. 6, June 1963, pp. 13–27 and pp. 1327–1335.

6.47 Friedman, Manfred P. A Description of a Computer Program for the Study of Atmospheric Effects on 

Sonic Booms. NASA CR-157, February 1965.

6.48 Schorling, Michael Calculation of Supersonic Flows at Large Distances from Slender Lifting Bodies. 

NASA TN D-6446, August 1971.

6.49 Tsien, H. S. The Poincarp-Lighthill-Kuo Method. Vol. IV of Advances in Applied Mechanics, H. L. 

Dryden and Theodore Von Kjrmjn, eds., Academic Press, Inc., 1956, pp. 281–349.

6.50 Schorling, Michael A Nonlinear Theory for Sonic-Boom Calculations in a Strati¿ed Atmosphere. NASA 

TN D-7105, March 1973.

6.51 Chambers, James P.; Cleveland, Robin O.; Bass, Henry E.; Blackstock, David T.; and Hamilton, Mark 

F. Comparison of Computer Codes for the Propagation of Sonic Booms through Realistic Atmospheres 

Utilizing Actual Acoustic Signatures. NASA CP 3335, July 1996, pp. 151–175.

6.52 Siclari, Michael J. Sonic Boom Prediction and Minimization of the Douglas Reference OPT5 Con¿guration. 

NASA/CP-1999-209520, December 1999, pp. 138–161.

6.53 Fouladi, Kamran Langley’s Computational Efforts in Sonic Boom Softening of the Boeing HSCT. NASA/

CP-1999-209520, December 1999, pp. 47–72.

6.54 Plotkin, K. J. Calculation of Sonic Boom from Numerical Flow Field Solutions MDBOOM, Version 2.2, 

Wyle Research Report WR-92-14, July 1992.

6.55 Plotkin, Kenneth J. and Cantril, Jerry M. Prediction of Sonic Boom at a Focus. AIAA Paper No. 76-2, 1976.

6.56 Barger, Raymond L. Some Effects of Flight Path and Atmospheric Variations on the Boom Propagated 

from a Supersonic Aircraft. NASA TR R-191, 1964.

6.57 Lansing, Donald L. Application of Acoustic Theory to Prediction of Sonic Boom Ground Patterns from 

Maneuvering Aircraft. NASA TN D-1860, October 1964.

6.58 Lansing, Donald L. and Maglieri, Domenic J. Comparison of Measured and Calculated Sonic-Boom 

Ground Patterns Due to Several Different Aircraft Maneuvers. NASA TN D-2730, April 1965.

6.59 Onyeowu, R. O. A Numerical Study of the Effects of Aircraft Maneuvers on the Focusing of Sonic 

Booms. UTIAS Report No. 192, November 1973.

6.60 Gardner, John H. and Rogers, Peter H. Thermospheric Propagation of Sonic Booms from the Concorde 

Supersonic Transport. NRL Memorandum Report 3904 (February 14, 1979).

6.61 Taylor, A. D. The TRAPS Sonic Boom Program. NOAA Technical Memo ERL ARL-87, July 1980.

6.62 Robinson, L. D. Sonic Boom Propagation through an Inhomogeneous Windy Atmosphere. Ph.D. 

Dissertation, Department of Physics, The University of Texas at Austin (1991).

6.63 Poling, Hugh W. Impact of Weather and Flight Condition on Secondary Booms. Baize, Daniel G., Editor. 

NASA CP 3335, July 1966, pp. 136–150.

6.64 Page, J. A.; Plotkin, K. J.; and Wilmer, C. PCBoom Version 6.6 Technical Reference and User Manual, 

Wyle Report WR 10-10, March 2010.
Chapter 6 Theoretical Considerations and Applications

255

6.65 Siclari, M. J. and Fouladi, Kamran A CFD Study of Component Con¿guration Effects on the Sonic Boom 

of Several High-Speed Civil Transport Concepts. NASA CP 10133, Vol. II, Ames Research Center (May 

12-14, 1993), pp. 277–300.

6.66 Cliff, Susan E. On the Design and Analysis of Low Sonic Boom Con¿gurations. NASA CP 10133, Vol. 

II, Ames Research Center (May 12-14, 1993), pp. 37–80.

6.67 Moretti, G. Thoughts and Afterthoughts about Shock Computations. Poly Technical Institute of Brooklyn, PIBAL Report 72-37, December 1972.

6.68 Salas, Manuel D. Shock Fitting Method for Complicated Two-Dimensional Supersonic Flows. AIAA 

Journal, Vol. 14, No. 5, May 1976.

6.69 Verhoff, A. and O’Neil, P. J. A Natural Formulation for the Numbered Solution of the Euler Equations. 

AIAA Paper 84-0163, January 1984.

6.70 Hartwich, P. M. Fresh Look at Floating Shock Fitting. AIAA Journal, Vol. 29, No. 7, 1991, pp. 1084–

1091.

6.71 Hartwich, Peter M. Comparison of Coordinate-Invariant and Coordinate-Aligned Upwinding for the 

Euler Equations. AIAA Journal, Vol. 32, No. 9, September 1994.

6.72 Hafez, M. M. and Murman, E. M. A Shock Fitting Applied to Relaxations of Transonic Small-Disturbance Equations. AIAA Journal, Vol. 15, No. 6, 1977, pp. 786–793.

6.73 Hafez, M. M. and Murman, E. M. A Shock Fitting Algorithm for the Full Potential Equation. AIAA Paper 

77-632 (1977).

6.74 Page, Juliet A. and Plotkin, Kenneth J. An Ef¿cient Method for Incorporating Computational Fluid 

Dynamics into Sonic Boom Prediction. AIAA Paper 91-3275, 1991.

6.75 George, A. R. Reduction of Sonic Boom by Azimuthal Redistribution of Overpressure, AIAA Paper No. 

68-159, 1968.

6.76 Camacho, Peter CFD Analysis of the MDC Mach 2.4/1.8 Low Boom Wind Tunnel Model. NASA CP 

10133, Vol. II, May 1993, pp. 169–194.

6.77 Pan, <. S.; A Method for Wind Tunnel Investigations of Sonic Boom Based on Large Models. AIAA 

Journal, Vol. 10, No. 11, 1972, pp. 1408–1414.

6.78 Pan, <. S.; Wang, K. T.; and Varner, M. O. Extension of the Current Sonic Boom Theory and Development 

of a Wind Tunnel Testing Method Based on Large Models. Fundamental Research on Advanced Techniques 

for Sonic Boom Suppression. Goethert, Dr. B. H., Editor, Report FAA-RD 73-4, University of Tenn., 

November 1972.

6.79 Kandil, O. A.; <ang, =.; and Bobbit, P. J. Prediction of Sonic Boom Signature Using Euler-Full Potential 

CFD with Grid Adaptation and Shock Fitting. AIAA 2002-2543, June 2002.

6.80 Bobbitt, P. J.; Kandil, O. A.; and <ang, =. The Bene¿cial Effects of Wing Dihedral on Sonic Boom. AIAA 

2003-3273-CP, May 2003.

6.81 Kandil, Osama A.; Ozcer, Isik A.; Sheng, ;udong; and Bobbitt, Percy J. Comparison of Full Potential 

Propagation-Code Computations with the F-5E “Shaped Sonic Boom Experiment” Program. AIAA 2005-

0013, 2005.
Chapter 6 Theoretical Considerations and Applications

256

6.82 Kandil, Osama and Ozcer, Isik A. Sonic Boom Computations for Double-Cone Con¿guration Using 

CFL3D, FUN3D, and Full-Potential Codes. AIAA 2006-0414, 2006.

6.83 Anderson, W. K. and Bonhaus, D. L. An Implicit Upwind Algorithm for Computing Turbulent Flows on 

Unstructured Grids. Computers and Fluids, Vol. 23, No. 1, 1994, pp. 1–22.

6.84 Hicks, R. M. and Mendoza, J. P. Prediction of Aircraft Sonic Boom Characteristics from Experimental 

Near Field Results. NASA TM ;-1477, 1967.

6.85 Kane, E. J. Propagation of Sonic Boom through a Non-Uniform Atmosphere. Boeing Doc. D6-

8979, May 1962.

6.86 Brown, J. R. Sonic Boom Propagation –Nonhomogeneous Atmosphere, TA-90. Boeing Doc. DC2315TN, September 1964.

6.87 Kane, Edward J. and Palmer, Thomas <. Meteorological Aspects of the Sonic Boom. SRDS Report No. 

RD 64-160, FAA, ASTIA No. AD 610463, 1964.

6.88 Dressler, Robert and Fredholm, Nils Statistical Magni¿cations of Sonic Booms by the Atmosphere. FFA 

Rept. 104, Aeronautical Research Institute of Sweden, 1966.

6.89 Lundberg, Bo K.; Dressler, Robert F.; and Lagman, Sven Atmospheric Magni¿cation of Sonic Booms in 

the Oklahoma Tests. FFA Rept. 112, Aeronautical Research Institute of Sweden, June 1967.

6.90 Haglund, George T. and Kane, Edward J. Flight Test Measurements and Analysis of Sonic Boom 

Phenomena Near Shock Wave Extremity. NASA CR-2167, February 1973.

6.91 Maglieri, D. J. Sonic Boom Flight Research – Some Effects of Airplane Operations and the Atmosphere 

on Sonic Boom Signature. NASA SP-147, 1967, pp. 25–48.

6.92 Maglieri, D. J. and Hilton, D. A. Experiments on the Effects of Atmospheric Refraction and Airplane 

Accelerations on Sonic Boom Ground Pressure Patterns. NASA TN D-3520, July 1966.

6.93 Carlson, Harry W.; McLean, Edward F.; and Shrout, Barret L. A Wind Tunnel Study of Sonic Boom 

Characteristics for Basic and Modi¿ed Models of a Supersonic Transport Con¿guration. NASA TM 

;-1236, 1966.

6.94 Maglieri, Domenic J.; Huckel, Vera; and Henderson, Herbert R. Sonic Boom Measurements for SR-71 

Aircraft Operating at Mach Numbers of 3.0 and Altitudes to 24,384 Meters. NASA TN D-6823, 1971.

6.95 Kane, Edward J. Some Effects of the Atmosphere on Sonic Boom. NASA SP-147, April 12, 

1967, pp. 49–63.

6.96 Hubbard, H. H.; Maglieri, D. J.; and Huckel, V. Variability of Sonic Boom Signatures with Emphasis on 

the Extremities of the Ground Exposure. NASA SP-255, October 1970, pp. 351–359.

6.97 Onyeowu, Ronald O. Diffraction of Sonic Boom Past the Nominal Edge of the Corridor. J. Acoust. Soc. 

Am., Vol. 58, No. 2, August 1975.

6.98 Pierce, Allan D. Atmospheric Propagation at Larger Lateral Distances from the Flight Track. NASA CP 

3279, October 1994, pp. 99–122.

6.99 Coulouvrat, Francois Sonic Boom in the Shadow =one A Geometrical Theory of Diffraction. J. Acoust. 

Soc. Am., Vol. III, No. 1, Pt. 2 of 2, January 2002.
Chapter 6 Theoretical Considerations and Applications

257

6.100 Sakarai, A. On the Propagation and Structure of Blast Waves, I and II, J. Phys. Soc., Japan 8 and 9, 1953 

and 1954, pp. 662–669 and pp. 256–266.

6.101 Seebass, A. R. and George, A. R. Sonic Boom Reduction through Aircraft Design and Operation. AIAA 

Paper No. 73-241, 1973.

6.102 Plooster, Myron N. Shock Waves from Line Sources. Numerical Solutions and Experimental Measurements. Phys. of Flds., Vol. 13, No. 11, Nov. 1970.

6.103 Jones, D. L.; Goyer, G. A.; and Plooster, M. N. Shockwave from a Lightning Discharge. Journal of 

Geophysical Res. 73, 3121, 1968.

6.104 Jones, D. L. The Energy Parameter B for Strong Blast Waves, NBS TN 155, July 1962. 

6.105 Pan, <. S. and Sotomayer, W. A. Sonic Boom of Hypersonic Vehicles. AIAA Journal, Vol. 10, 

No. 4, 1972.

6.106 Tiegerman, B. Sonic Booms of Drag Dominated Hypersonic Vehicles. Ph.D. thesis, Cornell Univ., 1975.

6.107 Plotkin, K. J.; Franz, R. J.; and Haering, E. A., Jr. Prediction and Measurement of a Weak Sonic Boom 

from an Entry Vehicle (A). J. Acoust. Soc. Am., Vol. 120, Paper 2a PA3, 2006, p. 3077.

6.108 Hicks, Raymond M.; Mendoza, Joel P.; and Thomas, Charles L. Pressure Signatures for the Apollo 

Command Module and the Saturn V Launch Vehicle with a Discussion of Strong Shock Extrapolation 

Procedures. Ames TM ;-62,117, April 6, 1972.

6.109 Carlson, Harry W. Experimental and Analytic Research on Sonic Boom Generation at NASA. NASA 

SP-147, 1967, pp. 9–23.

6.110 Kane, Edward The Boeing Company, Private Communication to D. J. Maglieri. March 15, 1967.

6.111 Carlson, H. W. and Maglieri, D. J. Review of Sonic Boom Generation Theory and Prediction Methods. 

J. Acoust. Soc. Am., Vol. 51, No. 2(Part 3), 1972, pp. 675–685.

6.112 Shrout, Barrett L.; Mack, Robert J.; and Dollyhigh, Samuel M. A Wind-Tunnel Investigation of SonicBoom Pressure Distributions of Bodies of Revolution. NASA TN D-6195, April 1971.

6.113 Miller, David S.; Morris, Odell A.; and Carlson, Harry W. Wind-Tunnel Investigation of Sonic Boom 

Characteristics of Two Simple Wing Models at Mach Numbers from 2.3 to 4.63. NASA TN D-6201. April 

1971.

6.114 Hilton, David A.; Henderson, Herbert R.; and McKinney, Royce Sonic Boom Ground Pressure 

Measurements from Apollo 15. NASA TN D-6950, 1972.

6.115 Henderson, Herbert R. and Hilton, David A. Sonic-Boom Ground Pressure Measurement from the 

Launch and Reentry of Apollo 16. NASA TN D-7606, 1974.

6.116 Hicks, Raymond M.; Mendoza, Joel P.; and Garcia, Frank Jr. A Wind Tunnel-Flight Correlation of Apollo 

15 Sonic Boom. Ames TM ;-62,111, SSPD 71, Jan. 28, 1972.

6.117 Garcia, Frank, Jr.; Hicks, Raymond M.; and Mendoza, Joel P. A Wind Tunnel Flight Correlation of 

Apollo 16 Sonic Boom. NASA TM ;-62,073, SSPD-90, Feb. 5, 1972.

6.118 Mendoza, Joel P. and Hicks, Raymond M. Wind Tunnel Pressure Signatures for an 0.016 Scale Model of 

the Apollo Command Module. NASA TM ;-62,047, July 14, 1971.
Chapter 6 Theoretical Considerations and Applications

258

6.119 Henderson, Herbert R. and Hilton, David A. Sonic-Boom Measurements in the Focus Region during the 

Ascent of Apollo 17. TN D-7806, Dec. 1974.

6.120 Holloway, Paul F.; Wilhold, Gilbert A.; Jones, Jess H.; Garcia, Frank, Jr.; and Hicks, Raymond M. Shuttle 

Sonic Boom – Technology and Predictions. AIAA Paper No. 73-1039, 1973.

6.121 Hicks, R. M. and Mendoza, J. P. Pressure Signatures for a 0.0053 Scale Model of the Saturn V - Apollo 

Launch Vehicle with Simulated Exhaust Plumes. NASA TM ;-62, 129, July 23, 1973.

6.122 Hicks, R. M.; Mendoza, J. P.; and Levy, L. L., Jr. An Investigation of Sonic Boom for Straight- and DeltaWing Space Shuttle Orbiters. NASA TM ;-62, 030, April 1971.

6.123 Hicks, R. M. and Mendoza, J. P. Wind-Tunnel Pressure Signatures for a Delta Wing Space Shuttle Vehicle. 

NASA TM;-62,040, May 1971.

6.124 Hicks, Raymond M. and Mendoza, Joel P. Wind-Tunnel Pressure Signatures for a Delta Wing Space 

Shuttle Vehicle and a Space Shuttle Fuel Tank. NASA TM ;-62,119, April 1972.

6.125 Hicks, Raymond M. and Mendoza, Joel P. A Brief Study of the Space Shuttle Sonic Boom during Ascent. 

NASA TM ;-62,050, July 23, 1971.

6.126 Mendoza, Joel P. Wind Tunnel Pressure Signatures for a 0.0041-Scale Model of the Space Shuttle Orbiter. 

NASA TM ;-62,432, May 1975.

6.127 Ashby, George C. New-Field Boom Pressure Signatures for the Space Shuttle Launch and Orbiter 

Vehicles at Mach 6. NASA TP-1405, April 1979.

6.128 Hicks, Raymond M. and Mendoza, Joel P. An Investigation of the Feasibility of Simulating Gaseous 

Exhaust Plumes with Solid Bodies in Sonic Boom Studies. NASA TM;-62,62131, 1973.

6.129 Marconi, Frank; Salas, Manuel; and <aeger, Larry Development of a Computer Code for Calculating the 

Steady Super/Hypersonic Inviscid Flow Around Real Con¿gurations. Vol. I, Computational Technique. 

NASA CR-2675, 1976.

6.130 Marconi, Frank and <aeger, Larry Development of a Computer Code for Calculating the Steady Super/

Hypersonic Inviscid Flow Around Real Con¿gurations. Vol. II, Code Description. NASA CR-2676, 1976.

6.131 Keyes, J. Wayne and Ashby, George C., Jr. Calculated and Experimental Hinge Moments on a TrailingEdge Flap of a 75 Degree Swept Delta Wing at Mach 6. NASA TN D-4268, 1967.

6.132 Ashby, George C., Jr. and Helms, Vernon T., III Flow Field Surveys on the Windward Side of the NASA 

040A Space Shuttle Orbiter at 31-Degree Angle of Attack and Mach 20 in Helium. NASA TM ;-3560, 

1977.

6.133 Garcia, Frank J.; Jones, Jess H.; and Henderson, Herbert H. Correlation of Predicted and Measured Sonic 

Characteristics from the Reentry of STS-1 Orbiter. NASA TP-2475, 1985.

6.134 Maglieri, Domenic J.; Henderson, Herbert R.; Massey, Steven J.; and Stansbery, Eugene G. A Compilation 

of Space Shuttle Sonic Boom Measurements. NASA CR2011-217080, April 2011.

6.135 Cotton, Donald and Donn, William L. Sound from Apollo Rockets in Space. Science, Vol. 171, No. 3971, 

Feb. 12, 1971, pp. 565–567.

6.136 Carlson, Harry W. and Mack, Robert J. A Study of the Sonic-Boom Characteristics of a Blunt Body at a 

Mach Number of 4.14. NASA TP-1015, 1977.
Chapter 6 Theoretical Considerations and Applications

259

6.137 Ashby, George A Study of Sonic Boom Characteristics of a Blunt Body at a Mach Number of 6. NASA 

TP-1787, 1980.

6.138 Carlson, Harry W. and Mack, Robert J. A Wind-Tunnel Study of the Applicability of Far-Field Sonic 

Boom Theory to the Space Shuttle Orbiter. NASA TP-1186, June 1978.

Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

261

CHAPTER 7 SONIC BOOM MINIMIZATION FOR VARIOUS 

AERODYNAMIC CONFIGURATIONS

In this chapter, minimization methods based on the Whitham F-function are discussed, as well as results based 

on the more complex optimization schemes employing CFD Euler codes. In addition, the utility of having a fast 

pressure recovery (rapid expansion) following an initial shock as well as embedded shocks is discussed. Also 

presented in this chapter, in some detail, are the effects of engine nacelles and engine exhausts on sonic booms. 

Finally, a section in this chapter is devoted to a discussion of the features of numerous supersonic jet concepts 

proposed and promoted in publications over the years as well as the 300-passenger commercial aircraft designs 

conceived in the NASA SCAR and HSR programs.

F-Function Boom Minimization

The minimization of sonic boom by theoretical methods started with the development of the ¿rst propagation 

equation and included linear aerodynamics and homogeneous atmosphere techniques. Most researchers credit L. 

B. Jones (ref. 7.1) with the ¿rst analytical approach. It is based on equation (5) of Chapter 6, using the Whitham/

Walkden area rule F-function integral. Jones noted that by treating this equation as an Abel integral equation and 

since $ƍv

(x) and L(x) are continuous in the range of o  x  l its inverse is

 a = speed of sound

F = source function

 M = Mach number = U/a

U = free stream velocity

x, y = axial coordinate parallel to Àight path

ơ = 

L(x) = lift on a spanwise strip per unit chordwise length

Av

(x) = longitudinal variation of cross-sectional area

q= free stream dynamic pressure = 1/2 r U 2

r = ambient density

The ƍ and ƍƍ indicate ¿rst and second derivatives with respect to x. Note that this methodology is based on the 

smooth-body form of the F-function.

Integrating equation (1) (which assumes axial symmetry) yields

and when integrated again with respect to x gives 

(1)

(2)
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

262

with the total lift, L, given by

where l is the length of the aircraft.

Since Ae

(0) = 0, the left hand side of equation (3) can be designated as the effective area Ae.

Equation (3) is the basis for Jones’ (refs. 7.1, 7.2, and 7.3) minimum-boom analyses. Jones (ref. 7.2) determined 

that the far-¿eld minimum N-wave shock pressure jump for lift at any distance is given by the lift distribution 

except near the origin. For a non-lifting body with a given base area, the area distribution yielding the minimum 

pressures jump was obtained as

The optimum lift and area distributions for other constraints are given in tables 7.1 and 7.2, respectively, from 

reference 7.2. Optimums for combined lift and area distribution are given in table 7.3 also from reference 7.2.

In these tables, the following additional symbol de¿nitions apply

V = volume of aircraft

J = 

xo

 = location of the zero of Whitham’s F-function

xcp = location of center of pressure

(3)

(4)

(5)

(6)
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

263

Table 7.1. Non-Lifting Bodies (ref. 7.2)

Table 7.2. Lifting Wing Without Volume (ref. 7.2)

7DEOH*HQHUDO&RQ¿JXUDWLRQUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

264

Jones’s minimization results are for far-¿eld booms. With N-waves considered to be inevitable, his near-¿eld 

signatures are in the form of delta function pulses, so that shock waves would quickly form. This exploited the 

dissipation of energy by the shocks and their higher decay rate of 1/r3/4 versus 1/r1/2 for isentropic acoustic waves. 

However, while shock and/or impulse could be minimized, this class of signatures would have shocks that were 

not expected to be acceptable to the public.

A major conceptual advance occurred in 1965 when Mclean (ref. 7.4) pointed out that the boom from a large aircraft 

Àying at normal operational altitude in the real atmosphere would not reach asymptotic far-¿eld conditions. The 

boom would thus not necessarily be an N-wave, so that shapes other than N-waves became possible. The concept 

of mid-¿eld shaped booms was born.

Figure 7.1 shows a range of the types of mid-¿eld signatures that could be considered if the goal is to reduce 

shock overpressure. Compared to a regular N-wave shown in ¿gure 7.1(a), Jones’s solutions yielded N-waves 

with lower peak pressures (¿gure 7.1(b)). A sine-like boom shown in ¿gure 7.1(c) would remove the audible 

high frequency energy. While shock formation may be avoidable, aging tends to generate signatures with linear 

segments. Therefore, a signature like the shockless boom shown in ¿gure 7.1(d) may be more feasible to generate. 

If a shock is unavoidable, minimum shock (¿gure 7.1(e)) or Àat-top (¿gure 7.1(f)) booms are expected to be 

favorable. Psychoacoustic experiments reviewed in Chapters 8 and 9 have shown that shaped booms, particularly 

ramp (shockless or minimum shock) are indeed quieter than N-wave booms. 

Another signi¿cant advancement occurred in the late 1960s, when George (ref. 7.5) developed a basic quantitative 

approach to minimized shaped-boom design. He noted that Jones’s delta function solution for a minimum 

asymptotic N-wave was optimal at any N-wave distance. Once that existed, there could be a further pressure 

signature behind this solution as shown in ¿gure 7.2. In the ¿gure, ȁ is the age parameter, F1

 and F2 are the 

F-function valves at those two points, I0

 is the positive impulse of the pressure signature t, t0, and T0 are time, and 

IJ is the shock rise time. 

(b)

(a)

(c)

Figure 7.2. Aging of a Spiked Ramped Signature (adapted from ref. 7.5).

Figure 7.1. Ground overpressure signatures.

(a)

(d)

(b)

(e)

(c)

(f)
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

265

The signature at the aircraft begins with a spike according to Jones’ N-wave solution as shown in ¿gure 7.2(a). 

There can be an additional signature behind this solution, but with compression regions having small enough 

slopes such that they will not steepen into shocks. When the signature is partially aged as shown in ¿gure 7.2(b), 

the spike has steepened into a partial N-wave, with the expansion of the partial N-wave sketched as a dashed line. 

At the fully aged design point (¿g. 7.2(c)), the bow spike has decayed to match the isentropic wave behind it and 

the forward part of a ramp minimum shock boom has evolved.

George and Seebass completed the theory with the aft part of the boom and showed that their solution yielded the 

minimum possible shock pressures for a given weight aircraft (refs. 7.6, 7.7, and 7.8) with the optimal F-function 

given by equation (7a) and sketched in ¿gure 7.3 (ref. 7.8). 

Here A, B, C, and D are constants yet to be determined and į(y) is the delta function. The corresponding equivalent 

area development using equation (3) is

where 1(Ȝ) is the unit step function.

A key part of their solution was that the F-function was de¿ned algebraically as shown in equation (7a). When this 

solution was applied to the inverse Abel transform (equation (3)), the result is also algebraic as shown in equation 

7(b).

Mid-¿eld shaped methodology became the workhorse of boom minimization and was used and extended in studies 

such as references 7.9, 7.10, and 7.11. Reference 7.9 includes an excellent review of minimization studies from 

the 1960s through the early 1970s, spanning the time from before the concept of shaping through the ¿rst few 

years of the George-Seebass Theory. Darden’s Reference 7.10 contains a practical application of the methodology 

and serves as the basis of systematic shaping studies.

The methodology of Darden (ref. 7.10) has the ability to de¿ne either Àat-top or ramp pressure signatures for a 

real atmosphere. Figure 7.4 (ref. 7.10) depicts the effective area distribution, F-function, and pressure signature 

and associated quantities that must be speci¿ed or determined. 

Figure 7.3. Whitham F-function for minimizing various signature parameters (adapted from ref. 7.8).

(7a)

(7b)
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

266

Darden’s F-function is de¿ned below, where for B = 0 a Àat-top signature results, and for B  0 a ramp-type 

signature or N-wave may result, depending on the values of l, yf

 and H.

 F(y) y

2yH/yf (0 < y < yf/2) (7a)

(2y/yf -- 1) - H(2y/yf - 2) (yf

/2 < y < yf) (7b)

B(y - yf

) + C (yf

 < y < l) (7c)

B(y - yf

) - D (l < y < l) (7d)

In these equations, H, B, C, D, and l are unknown coef¿cients, which are determined by the cruise conditions of 

the aircraft, by nose length, by the prescribed ratio of bow to rear shock strength, and by the type of signature 

being minimized.

Substituting equations (7) for the F-function into equation (3) for Ae yields 

where 1(x - yf

/2) and 1(x- yf) and [Ȝ are Heaviside unit step functions.

(8)

Figure 7.4. ,OOXVWUDWLRQRIWKHWKHRUHWLFDOFRQFHSWVRIQHDU¿HOGVRQLFERRP(ref. 7.10).
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

267

A critical parameter is the width of the forward spike, yf, and its effect on the initial pressure jump, impulse, and 

drag. Figure 7.5 from reference 7.10 shows that as yf

 is increased, drag goes down and the Àat-top pressure levels, 

and ramp maximum pressures increase. For the conditions given in the legend of ¿gure 7.5, most of the drag 

bene¿ts are realized by the time yf /l has reached a value of 0.05. It should be noted that reference 7.10 also includes 

a description of a computer code that calculates the Whitham F-function and the corresponding equivalent area 

distribution, which produce the minimum overpressure (Àat-top) or minimum-shock (ramp) signatures.

The results given in ¿gure 7.5 are for an altitude, h = 60,000 feet, and an aircraft length of l = 300 feet or an h/l

of 200. A 100-foot long aircraft Àying at an altitude of 50,000 feet yields an h/l of 500. Few papers present results 

for h/l values beyond 300. The work of Hague and Jones (ref. 7.12) is an exception. Figure 7.6 (ref. 7.12) shows 

that as h/l increases, the shape of body that produces the minimum pressure jump changes. 

Figure 7.5. (VWLPDWHGGUDJLQFUHPHQWVDVVRFLDWHGZLWKFRQ¿JXUDWLRQFKDQJHVIRUVRQLFERRPPLQLPL]DWLRQ0DFK 

K P IW: NJOEVO PIWUHI

Figure 7.6. (IIHFWRIGLVWDQFHRQVLQJOHSRZHUDUFVROXWLRQVZLWKOHQJWKDQGEDVHFRQVWUDLQHG0DFK UHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

268

For power law bodies (i.e., r = AxN), the exponent N that yields the minimum Ƌp decreases from ~0.75 at an h/l

of 10 to ~0.3 at an h/l of 700. Of course, Mach number as well as the constraints imposed will have an effect on 

the minimum shape. Clearly for con¿gurations on the order of 100-foot length, like small business jets, and with 

h/l values approaching 500, this is a phenomenon that needs to be understood and used to the greatest advantage.

An even further modi¿cation of the optimum F-function,which might be termed a hybrid, was made by Hagland 

and Mack (refs. 7.13 and 7.14), as shown in ¿gure 7.7, that has both Àat-top and ramp features following the initial 

shock. The effect of hot and cold days on the length of the nose spike to achieve a given pressure level behind 

the initial shock is discussed in reference 7.14. Additional modi¿cations to this initial area development (nose 

geometry) are given by Mack in reference 7.15, which illustrates the options available using the F-function for 

maintaining a near-optimum pressure distribution.

The Rapid Pressure Recovery/Expansion

Referring back to equations (5) and (6), we see that the derivative of Av

(x) (i.e., dAv(x)/dx from equation (6) 

and L(x) from equation (5) of Jones’ minimum boom analysis both have the same behavior. The front-loaded 

lift distribution (eq. (5)) and the blunt body (eq. (6)) resulting from this behavior yield a strong shock followed 

by a rapid recovery/expansion. This has certain advantages as can be seen from the pressure jump equation from 

Thomas (ref. 7.16) for a uniform atmosphere where Ƌp varies inversely as m, the rate of change of pressure 

recovery/expansion. Clearly, the more negative the value of m (note that m is negative in the sketch of ¿g. 7.8) 

the faster the pressure jump decreases. This same phenomenon applies for embedded shocks as well, such as those 

from a nacelle or inlet shock.

Aside from the advantage of a rapid shock-strength reduction, the fast recovery of an embedded shock also 

reduces its ability to move forward and coalesce with the bow shock. Hicks and Thomas (ref. 7.17) studied this 

effect along with the effect of several other parameters on shock coalescence using the uniform atmosphere 

equations of reference 7.16. Figure 7.9 shows the faster the pressure recovery of the wing shock, the lower the 

convergence with bow shock.

Figure 7.7. +DJOXQGPRGL¿HGHTXLYDOHQWDUHDV)IXQFWLRQDQGSUHVVXUHVLJQDWXUHDGDSWHGIURPUHI

Figure 7.8. 7\SLFDO1ZDYHVRQLFERRP
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

269

Minimization of Sonic Boom Using Various Optimization Schemes

The minimization of sonic booms using F-function methodology was discussed in the previous section of this 

chapter and will be addressed to a lesser degree in the next section, entitled “The Effect of Engine Nacelles on Sonic 

Booms”. While sonic booms can be minimized using F-function methodology and effective area distributions, 

they are calculated and minimized more precisely using the Euler-equations, real aircraft geometries, and a 

mathematical optimization technique. However, there are studies that use an optimizer in combination with the 

F-function and linear-lifting methodology, or Euler-equation, Àow-¿eld solutions. Numerous papers have been 

published over the past decade using these approaches. Some of these papers will be discussed in the following 

pages.

One of the ¿rst studies to use the Euler equation, along with an optimizer, also utilized the F-function (see ref. 7.18). 

However, the optimization technique, named NPSOL (see ref. 7.19), did not operate directly on the con¿guration’s 

geometry but on the F-function, de¿ned initially by nine variables. The number was later increased from 9 to 10 

variables because the Àat-top F-function originally sought was not feasible with the volume constraints imposed. 

Consequently, a combination Àat-top and ramp F-function was required. This type of F-function is plotted and the 

segments labeled in ¿gure 7.10.

In Cheung’s method (ref. 7.18), the F-function is extracted from the near-¿eld pressure signature (usually at one 

body length) and the associated effective-area distribution from this F-function. The procedure was applied to the 

Boeing 911 con¿guration shown in ¿gure 7.11 with the wing geometry ¿xed. 

)LJXUH (IIHFWRIVORSHEHKLQGZLQJVKRFNRQFRDOHVFHQFH0DFK DGDSWHGIURPUHI

Figure 7.10. &RPELQDWLRQÀDWWRSDQGUDPSVLJQDWXUHUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

270

Thus, the fuselage area distribution was actually the target of the optimization. Figure 7.12 gives a plot of the 

original effective area distribution and the one that resulted from the optimization procedure (modi¿ed). A similar 

optimization could have been done with the lift distribution using camber as a variable.

The sonic boom improvement that resulted from the modi¿cation to the Ae

 distribution is evident in the plot 

of ¿gure 7.13. It shows that the second shock at a time of ~0.12 second has been eliminated and a near Àat-top 

signature was achieved. 

Figure 7.12. (TXLYDOHQWDUHDGLVWULEXWLRQVIRURULJLQDODQGPRGL¿HG%RHLQJFRQ¿JXUDWLRQUHI

Figure 7.13. 2ULJLQDODQGPRGL¿HGVRQLFERRPVLJQDWXUHVIRUWKH%RHLQJFRQ¿JXUDWLRQKO 0DFK 

Ơ $OWLWXGH IWDGDSWHGIURPUHI

Figure 7.11. %RHLQJFRQ¿JXUDWLRQUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

271

The optimizer NPSOL (ref. 7.19) was used by Siclari (ref. 7.20) where fuselage volume and camber distributions 

were optimized for four different con¿gurations. The Euler calculations were carried out by a very ef¿cient multiblock three-dimensional ¿nite volume marching code (MIM3DSB). In addition, as noted in reference 7.20 and 

later in this chapter, a unique grid topology is used to accurately capture shocks several body lengths downstream 

of the aircraft. Additional details of MIM3D are given in reference 7.21. Once the pressures are determined, those 

below the aircraft become input to a waveform parameter propagation code (ref. 7.16) that extrapolates these 

near-¿eld signatures to the ground through a speci¿ed atmosphere. 

The design system used in reference 7.20 for optimizing one or more geometric features of an aircraft concept is 

depicted in ¿gure 7.14. This system seeks to minimize the objective function in terms of its derivative and not the 

function itself. There may be local minima, which may not be the best solution, and there may be cases when the 

solutions are not smooth. Therefore, there has to be operator involvement, particularly in selecting and changing 

the initial estimate. Cubic splines are used to describe the geometric design variables such as fuselage volume 

distribution or camber. The number of design variables might be as little as three or as many as 15. The gradient 

based optimization method will require one or two evaluations of the objective function for each design variable 

depending upon whether one-sided or central derivatives are used to evaluate the objective function gradients. 

Hence, for example, if 10 design variables are used, the design methodology will require 10 to 20 CFD runs to 

evaluate the objective function gradients. If 10 global iterations of the design method are implemented, this could 

add up to 100 to 200 CFD runs.

One of the four con¿gurations analyzed in reference 7.20 was the LB18-10B, pictured in ¿gure 7.15. It was 

designed using F-function techniques to have a ramp sonic boom signature when cruising at Mach 1.8 and at 

an altitude of 48,600 feet. When subjected to CFD analysis, the near-¿eld pressure signatures in ¿gure 7.15 are 

the result. These signatures, for h/l values of 0.5, 1.0, and 2.0 are also used to produce the ground sonic boom 

signatures shown on the right side of the ¿gure. Clearly, these signatures are not ramp type, although the pressure 

level is comparable to that of the target ramp signatures.

Figure 7.14. &)'VRQLFERRPGHVLJQV\VWHPUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

272

Four separate design computer runs were made using different fuselage stations and target ramp pressures (see 

¿gure 7.16). Overall, these design runs required over 100 CFD runs. Fuselage cross-sections are ellipses and 

the major and minor axes were design variables. The starting or initial signature for each run, along with the 

¿nal signature and the target ramp signatures, are plotted for each run. Run 4 resulted in an excellent wavy 

approximation of the target ramp.

Due to computation time, the grid used for the production runs was not the ¿nest possible. So, a ¿ner grid 

calculation of the run 4 con¿guration was performed. Sonic booms using the near-¿eld signatures at h/l = 1.0 

and 2.0 for the ¿nest grid are shown in ¿gures 7.17 and 7.18. In ¿gure 7.17 for an h/l of 1.0, the ¿nest grid 

calculation is compared to the one using the production or design grid. 

Figure 7.15. &)'DQDO\VLVRIQHDU¿HOGDQGH[WUDSRODWHGJURXQGVLJQDWXUHVIRUWKH/%%DGDSWHGIURPUHI

Figure 7.16. )XVHODJHYROXPHPRGL¿FDWLRQVDQGWDUJHWVLJQDWXUHVIRUWKH/%%FRQ¿JXUDWLRQDGDSWHGIURPUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

273

Note that the ¿nest grid analysis yields higher amplitude oscillations than that of the lower resolution design grid. 

Nevertheless, they are smaller in amplitude than that of the original signatures (see ¿g. 7.18) and, consequently, 

are a better approximation of the target ramp signature. Thus, the optimization procedure did reduce the magnitude 

of the sonic boom produced by the LB18-10B con¿guration. Similar results are given in reference 7.20 for the 

other con¿gurations.

The F-function was also used in reference 7.22 by Makino et al. to provide an optimum target near-¿eld pressure 

at an h/l of 2.0. The axial distribution of fuselage radii is perturbed in their scheme to minimize the difference in 

the calculated and target near-¿eld pressures. The near-¿eld Àow calculations were made using a fully 3-D Euler 

CFD code. The optimization method is based on the least-squares technique of Lee and Eyi (ref. 7.23). The lowboom con¿guration fuselage depicted in ¿gure 7.19 is the prime subject of the minimization effort, particularly 

the aft part. 

Figure 7.17. &RPSDULVRQRIJURXQGVLJQDWXUHVIRUFUXGHGHVLJQDQG¿QHJULGDQDO\VLVRIPRGL¿HG/%%H[WUDSRODWHGIURPKO 0 Ơ $OWLWXGH IWUHI

Figure 7.18. &RPSDULVRQRIJURXQGVLJQDWXUHVIRUPRGL¿HGDQGRULJLQDO/%%FRQ¿JXUDWLRQH[WUDSRODWHG

IURPKO DGDSWHGIURPUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

274

Initially, this con¿guration had an equivalent area distribution close to the designed optimum and where the small 

differences from the optimum are beyond an x of 70 meters (see ¿g. 7.20).

However, the shock they produced at a time of ~125 msec on the ground signature (see ¿g. 7.21) is far from 

optimum. Application of the minimization process eliminated this shock and resulted in the near Àat-top optimized 

ground signature shown in ¿gure 7.21.

)LJXUH /RZERRPFRQ¿JXUDWLRQUHI

Figure 7.20. (TXLYDOHQWGLVWULEXWLRQVUHI

Figure 7.21. Optimized ground pressure signature (adapted from ref. 7.22).
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

275

The equivalent area that resulted from the optimization (volume plus lift) is plotted in ¿gure 7.22 and shows an 

increase in the area of the fuselage over most of its length. Figures 7.21, 7.22, and 7.23 demonstrate that there are 

effects that F-function methods do not account for that must be overcome to achieve a real optimum. Thus, the 

nonlinear Euler equations, when coupled to an optimization scheme with the necessary logic, can produce a more 

realistic low-boom con¿guration.

Makino et al. (ref. 7.22) also applied the least-squares optimizer to a simple delta-wing/body con¿guration with 

excellent results. Finally, loudness calculations were made for the initial and optimized ground pressure signatures 

of the low-boom con¿guration, which showed a 2dBA reduction (77.4 versus 79.4) for the latter.

An entirely different optimization scheme is used in reference 7.24 to reduce the sonic boom of a slightly swept 

wing con¿guration appropriate for a supersonic business jet. An adjunct method is used that was originally 

developed (see ref. 7.25) to optimize the shape, pressure distribution, and associated aerodynamic coef¿cients of 

a con¿guration. It was later extended in reference 7.26 to calculate non-co-located sensitivities. It is this capability 

that was applied in reference 7.24 to the sonic boom reduction problem. The remote inverse adjunct approach 

developed in reference 7.24 modi¿es the true geometry not by altering its planform but its current shape grid point 

by grid point. Gradients are calculated for each point on the surface of the wing and fuselage, and modi¿cations 

are made based upon a simple steepest descent algorithm.

Figure 7.22. 2SWLPL]HGHTXLYDOHQWDUHDGLVWULEXWLRQVUHI

Figure 7.23. Optimized fuselage geometry (ref. 7.22).
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

276

The business jet con¿guration studied is shown in ¿gure 7.24. As stated in reference 7.24 (p. 5),

It was sized to accommodate between 6 to 8 passengers with a gross takeoff weight of 100,000 pounds and 

a fuselage length of 100 feet. The supersonic Àight condition at which all designs were calculated is Mach 

1.5. The fuselage is cylindrical and the maximum diameter occurs at 31% measured from the nose of the 

fuselage. The wing has a biconvex wing section with a 7.125 degrees leading edge sweep, an aspect ratio 

of 3.0 and a taper ratio of 0.218.

The Àight altitude was not given, but based on some of the discussions, is probably around 50,000 feet. As stated 

in reference 7.24 (p. 6),

The root airfoil is a 3% thick biconvex airfoil and the tip is 1.5%. The biconvex pro¿le in the center sections 

was obtained by interpolating between the root and tip. The airfoils were constructed to accommodate 

thick spars at the 10 and 80% chord locations. The baseline wing does not have geometric twist. The 

computational mesh has eight blocks with 193x49x33 nodes on a C-H grid. The fuselage has 25 points in 

the cross-streamwise direction and 144 points in the streamwise direction. The wing contains 97 points in 

the streamwise direction and 17 sectional cuts in the spanwise direction.

Calculations were made with and without a lift constraint. The target pressure distribution was obtained by rescaling the initial calculated near-¿eld pressure distribution. Figure 7.25 shows the initial and ¿nal wing-root 

airfoil geometries for the unconstrained lift case. However, the wing thickness is constrained. To maintain the 

wing thickness distribution, the upper surface pro¿le is modi¿ed to maintain the spar locations at the 10 percent 

and 80 percent chord locations. At the end of each design cycle, the minimum permissible thickness constraint is 

imposed at each chordwise cut between the 10 percent and 80 percent chord locations. 

Figure 7.24. %XVLQHVVMHWFRQ¿JXUDWLRQVWXGLHGLQUHIHUHQFH
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

277

The shape modi¿cations, illustrated by the root airfoil modi¿cation in ¿gure 7.25, yield a 40 percent reduction 

in the wing shock and a 35 percent reduction in the trailing shock of the near-¿eld pressure distribution shown 

in ¿gure 7.26. Different scales are used for the ordinate and abscissa in ¿gure 7.25 to better show the shape 

change. On the ground (¿g. 7.27), there is about a 23 percent reduction in the wing shock. Since lift is not 

constrained, CL is reduced from 0.1 to 0.073. When the wing lift coef¿cient is constrained at a value of 0.1, the 

geometry modi¿cation that results is less than that for the unconstrained lift (as seen in ¿g. 7.28). However, ¿gure 

7.29 shows that the fuselage near-¿eld peak pressure has been reduced by almost 18 percent of its initial value. 

The wing peak pressure was reduced by 22 percent as opposed to the 4 percent reduction in the unconstrained 

case. With the wing lift coef¿cient constrained at 0.1, the angle of attack rose from 1.62° to 2.39° and the drag 

coef¿cient increased from 0.00568 to 0.00574. Modest decreases on the order of 10 percent were obtained for the 

fuselage, wing, and trailing shocks of the ground signature (see ¿g. 7.30).

Figure 7.25. ,QLWLDODQG¿QDOURRWDLUIRLOVDW0 DGDSWHGIURPUHI1RWHWKHGLIIHUHQFHLQRUGLQDWHDQGDEVFLVVDscales.

Figure 7.26. 6RQLFERRPUHGXFWLRQWDUJHWLQLWLDODQG¿QDOQHDU¿HOGSUHVVXUHGLVWULEXWLRQDIWHUGHVLJQF\FOHV

0DFK Į GHJOLIWQRWFRQVWUDLQHGDGDSWHGIURPUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

278

Figure 7.27. 6RQLFERRPUHGXFWLRQLQLWLDODQG¿QDOJURXQGVLJQDWXUHVDIWHUGHVLJQF\FOHV0DFK 

Į °OLIWQRWFRQVWUDLQHGDGDSWHGIURPUHI

Figure 7.28. ,QLWLDODQG¿QDOURRWDLUIRLOV0DFK DGDSWHGIURPUHINote the 

GLIIHUHQFHLQRUGLQDWHDQGDEVFLVVDscales.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

279

)LJXUH 6RQLFERRPUHGXFWLRQWDUJHWLQLWLDODQG¿QDOQHDU¿HOGSUHVVXUHGLVWULEXWLRQDIWHUGHVLJQF\FOHV

0DFK  Ơ °&L

 DGDSWHGIURPUHI

Figure 7.30. 6RQLFERRPUHGXFWLRQ±LQLWLDODQG¿QDOJURXQGVLJQDWXUHVDIWHUGHVLJQF\FOHV0DFK 

Ơ °, CL

 DGDSWHGIURPUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

280

A 2008 paper by Li, Shields, and Le (ref. 7.27) introduced a computer program named BOSS (Boom Optimization 

using Smoothest Shape modi¿cations). As noted in reference 7.27 (p. 1381), BOSS,

was intended to help designers ¿nd the right con¿guration among the in¿nite number of possible 

con¿gurations that are equally good using any numerical ¿gure of merit. BOSS uses the smoothest shape 

modi¿cation strategy for modifying the fuselage radius distribution at 100 or more longitudinal locations 

to ¿nd a smooth fuselage shape that reduces the discrepancies between the design and target equivalent 

area distributions over any speci¿ed range of effective distance.

The authors also noted in reference 7.27 (p. 1381) that using BOSS “within a few hours, a designer can either 

generate a realistic fuselage shape that yields a supersonic con¿guration with a low-boom ground signature or 

quickly eliminate any con¿guration that cannot achieve low-boom characteristics with fuselage shaping alone.”

Further details of the BOSS methodology are given in ref. 7.27.

In the authors’ sonic boom minimization efforts, F-function technology is employed using equivalent area 

distributions for lift and Mach cuts to acquire the area distributions (see equation 3). The fuselage has circular 

cross-sections and is de¿ned by 120 equally spaced longitudinal locations. The vertical and horizontal tails and 

engine nacelles are accounted for in the volume distribution.

The starting con¿guration for the BOSS minimization study is shown in ¿gure 7.31. Boom considerations were 

not employed in its design. It has a take-off weight of 100,000 pounds, a balanced ¿eld length of 7000 feet, and 

a cruise Mach number of 1.8. The nacelles are located atop the wing and based on Howe’s analysis (ref. 7.28) in 

a near-optimum location. The equivalent area distribution is given in ¿gure 7.32(a) along with its lift and volume 

components. Also shown is the hybrid signature target (i.e., a compromise between low-drag and low-boom area 

distributions). As one might expect, the sonic boom of the performance low-drag concept, ¿gure 7.32(b), is not 

anywhere near the desired optimum.

Figure 7.31. 7KUHHYLHZGHSLFWLRQRIDVXSHUVRQLFEXVLQHVVMHWFRQFHSWGHVLJQHGIRURSWLPXPSHUIRUPDQFHUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

281

A second con¿guration was developed and is depicted in ¿gure 7.33.

As noted in reference 7.27 (p. 1390),

The ¿nal Ae

 distribution in ¿gure 7.34(a) is a low-boom area distribution derived by a designer, via a trialand-error approach using planform modi¿cations and fuselage shaping in succession, to best match the 

unmatchable target area distribution. This process usually takes several days to complete.

Clearly, a better approximation of the target hybrid equivalent area distribution was achieved (see ¿g. 7.34(a)) as 

well as the ground ramp-type signature shown in ¿gure 7.34(b). The resulting low-boom fuselage shape (dashed 

lines) is plotted in ¿gure 7.35. Note the difference in the ordinate and abscissa scales. 

Figure 7.32. (TXLYDOHQWDUHDGLVWULEXWLRQDQGJURXQGVLJQDWXUHRIDORZGUDJVXSHUVRQLFFRQFHSWDGDSWHGIURPUHI

(a) Comparison of equivalent areas. (b) Comparison of ground signatures.

Figure 7.33. 7KUHHYLHZGHSLFWLRQRIDORZERRPVXSHUVRQLFEXVLQHVVMHWFRQFHSWUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

282

Subsequently, the linear methodology and BOSS were applied to modify the fuselage shape in order to better 

approximate the hybrid ramp target signature. The resulting equivalent area distribution or numerical optimum 

(¿g. 7.36) shows the close agreement achieved with the hybrid target equivalent area distribution. The sonic boom 

signature achieved relative to the hybrid target is shown on the right side of ¿gure 7.36. It is evident that this is 

an improvement over that of the low-boom concept of ¿gure 7.34(b). Figure 7.36 gives the fuselage shape for the 

numerical optimum that evolved compared to that for the low-boom con¿guration. With its irregularities it is not 

as practical as the low-boom shape but, with its optimum ramp signature, does point the way to further re¿nement.

The use of BOSS to analyze and optimize the sonic boom signatures of a con¿guration through the modi¿cation 

of its fuselage geometry was demonstrated in reference 7.27. As stated in reference 7.27 (p. 1381),

Figure 7.34. (TXLYDOHQWDUHDGLVWULEXWLRQDQGJURXQGVLJQDWXUHRIORZERRPVLJQDWXUHVDGDSWHGIURPUHI

Figure 7.35. 6LGHYLHZRIORZERRPIXVHODJHDQGQXPHULFDOO\RSWLPXPIXVHODJHDGDSWHGIURPUHI

(a) Comparison of equivalent areas. (b) Comparison of ground signatures.

Figure 7.36. (TXLYDOHQWDUHDGLVWULEXWLRQDQGJURXQGVLJQDWXUHRIDQXPHULFDOO\RSWLPXPFRQFHSWDGDSWHGIURPUHI

(a) Comparison of equivalent areas. (b) Comparison of ground signatures.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

283

To summarize, BOSS allows one to examine the differences between the design and target equivalent 

areas, decide which part of the design equivalent area curve needs to be modi¿ed, choose a desirable rate 

for the reduction of the discrepancies over the speci¿ed range, and select a parameter for smoothness 

control of fuselage shape.

Then BOSS “will then generate a fuselage shape based on the designer’s inputs in a matter of seconds.”(ref. 

7.27, p. 1381) Further, as stated in reference 7.27 (pp. 1394-1395), “If the generated solution is not acceptable, 

the designer can work on a different part of the equivalent area curve, change the rate of reduction, or relax the 

smoothness control until a desirable solution is found.”

Minimization of the sonic boom of a supersonic jet without consideration of its aerodynamics, the mission 

constraints, structure, take-off and landing distances, cabin volume, etc., normally yields an optimistic result. 

Studies that examine boom-minimum designs as well as performance-based designs always show higher booms 

for the latter. Understanding and applying practical constraints and performance goals in the design of a low-boom 

aircraft is highly desirable. As stated by Choi, Alonso, and Kroo in reference 7.29 (p. 1), they have utilized a

Multi-disciplinary aircraft synthesis tool (PASS) that incorporates highly-tuned low-¿delity models of all 

the relevant disciplines and computes the complete mission pro¿le of the aircraft, and a hierarchical multi-

¿delity environment for the creation of response surfaces for aerodynamic performance and sonic boom 

loudness (BOOM-UA) that attempts to achieve the accuracy of an Euler-based design strategy.

Some of the factors considered in PASS are – drag estimation, weights and c.g., propulsion, low-speed analysis 

(including takeoff and landing), and mission analysis.

CFD tools used include the A502/Panair and AirplanePlus Àow solvers, the Centaur Mesh Generation System, 

and the PCBoom software (an early version of ref. 7.30) for propagation of the acoustic signatures. Details of the 

PASS system are given in the paper as well as a discussion of the accuracy of the A502/Panair code relative to 

AirplanePlus Euler solver. Another feature of reference 7.29 is that it concentrates on minimizing the loudness 

of the sonic boom (in dBA) rather than the maximum shock strength in lbs/ft2

. The baseline con¿guration from 

reference 7.29 was a design that fell short of the desired range (4500 nmi) by almost 1000 miles. Its geometry 

is provided in ¿gure 7.37 with other pertinent details listed in table 7.4. A reduced target range of 4000 nmi was 

established. To achieve this range, the weight was increased and with it the target balanced ¿eld length, which 

was increased from 5000 feet to 6500 feet.

Figure 7.37. 6XPPDU\RIEDVHOLQHFRQ¿JXUDWLRQDGDSWHGIURPUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

284

7DEOH5HVXOWVRI3$665HVSRQVH6XUIDFH$QDO\VLVRIWKH%DVHOLQH&RQ¿JXUDWLRQUHI

Range 3,650 nmi

BFL 5,482 ft

MTOGW 92,018 lbs

Ground signature (dBA) 86.15

A PASS optimization was carried out using the new targets. The resulting performance and aircraft geometry 

details are listed in table 7.5. The near-¿eld pressure distributions and ground boom signatures of the baseline and 

optimum con¿gurations are given in ¿gure 7.38. It is obvious from ¿gure 7.38(b) that the initial shock strength 

of the ground signature of the optimized design was increased by about 10 percent from that of the baseline. On 

the other hand, the mid-¿eld shock at 60 msec is reduced signi¿cantly leading to a loudness reduction from 86.15 

dBA to 78.87 dBA.

7DEOH5HVXOWVRI3$66UHVSRQVHVXUIDFHRSWLPL]DWLRQIRUERRPPLQLPL]DWLRQUHI

Performance

Cruise Mach 1.6

Range 4,000 nmi

BFL 6,500 ft

MTOGW 97,130 lbs

Ground signature (dBA) 78.87

Wing and Tail Geometry

Wing reference area 1,155 ft2

Wing aspect ratio 4.2

Wing quarter-chord sweep 55°

Leading edge extension 0.55

Trailing edge extension 0.026

Wing root leading edge 0.23

Root section t/c 3.0 percent

Break section t/c 2.56 percent

Tip section t/c 2.0 percent

Figure 7.38. &RPSDULVRQRIRSWLPL]HGDQGEDVHOLQHGHVLJQVDGDSWHGIURPUHI

(a) Near-¿eld pressure distribution. (b) Ground boom signature.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

285

However, Choi, Alonso, and Kroo (ref. 7.29) were not satis¿ed with the wing geometry and some additional 

changes were implemented. As they note in reference 7.29 (p. 13),

Minor reductions in reference area (from 1,155 ft2

 to 1,100 ft2), aspect ratio (from 4.2 to 3.7) and sweep 

(55° to 54°) were manually applied to the above (optimum) design to return the wing to a more reasonable 

shape. The resulting con¿guration suffered only a modest gain in boom strength, while still managing to 

meet all other constraints, as can be seen in table 7.6 and ¿gure 7.39.

Table 7.6. Results of PASS + Response Surface Optimization for Boom Minimization with 

6PDOO0DQXDO0RGL¿FDWLRQVUHI

Range 4,021 nmi

BFI 6,255 ft

MTOGW 95,000 lbs

Ground signature (dBA) 80.3

Wing and Tail Geometry

Wing reference area 1,100 ft2

Wing aspect ratio 3.7

Wing quarter-chord sweep 54°

Leading edge extension 0.23

In addition to the boom minimization, reference 7.29 presented the results for a case where take-off gross weight 

is minimized. It increased the loudness level of the ground pressure signature by 4.6 dBA and decreased the 

TOGW by 253 pounds.

Finally, reference 7.29 presents the results of an array of computational tools that have been integrated and applied 

in such a way that a multi-disciplinary optimization can be performed with numerous constraints. An interesting 

difference between this study and most others that attempt boom minimizations is that it keys on loudness rather 

than bow- and/or trailing-shock strengths. Another interesting aspect is that this study starts with a design that is 

more performance than boom oriented. However, if one starts with a lower boom design, like one based on linear 

optimization theory, it might yield a con¿guration with a lower boom and still have the range required.

In summary, several sonic boom reduction schemes exist that vary in complexity and utilize different optimization 

methodologies. Some use a combination of linear and nonlinear (Euler) Àow codes, while others rely entirely 

on Euler codes. Most studies only treat the aerodynamic characteristics and sonic booms of their con¿gurations. 

However, some studies also treat the structural and mission consequences of going from a performance to a lowboom design.

)LJXUH %RRPRSWLPL]HGFRQ¿JXUDWLRQSOXVVPDOOPDQXDOPRGL¿FDWLRQVDGDSWHGIURPUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

286

The Effect of Engine Nacelles on Sonic Booms

One of the most complex and challenging problems faced by designers of civil supersonic aircraft is the placement 

of the engines. Large 300-passenger transports studied in NASA’s SCAR, HSCT, and HSR programs generally 

had four engines – two mounted on each side, under the wing, and near the trailing edge. Supersonic business jet 

(SBJ) concepts are usually powered by two engines, placed below the wing in some con¿gurations and above the 

wing or on the vertical tail in others. Depending on the location, the engines may cause an increase in strength of 

the bow or trailing shocks of the sonic boom signature or produce discrete shocks somewhere in between. The 

wing geometry, fuselage shape and/or engine locations can be con¿gured such that they will do the least damage 

to the effective area distribution and the resulting sonic boom at the cruise Mach number. It is important to note 

that when a con¿guration is optimally designed with the engines in place, engine relocation may cause additional 

shocks to appear in the near-¿eld and ground signatures that did not previously exist.

The magnitude of the shocks produced by the engines will depend on their size as well as the details of the inlet 

and the exit. Also, the exhaust plume may have a signi¿cant effect on the shocks produced depending primarily 

on the pressure ratio. Exhaust effects will be discussed in detail in the next section. The Àow spillage from engines 

that are not operating at optimal conditions can also enhance the strength of the shock or shocks emanating from 

the forward portion of the engine nacelle. It is normally assumed in analytical studies, at the design conditions, 

that the engines are operating without spillage. Pylons that hold the engines to the wing or fuselage are usually 

accounted for, particularly in the CFD studies already performed.

Several theoretical studies using F-function methodology or Euler CFD codes have been conducted that examine 

propulsion integration problems. In most cases, the engine’s geometry is idealized as well as that of the inlet and 

exhaust Àows. In the following discussion, a description of some of these studies will be provided.

F-Function Methodology

F-function methods for sonic boom prediction, which were prevalent in the 1950s and 1960s, rely on the effective 

area distribution of a con¿guration (see equations (5) and (7) of Chapter 6). The latter, in turn, is derived using 

Mach cuts of the proposed geometry or from an analytical method aimed at producing an optimal distribution 

(refs. 7.6 and 7.10). One of the ¿rst methods used to analyze the incremental effects of engines was based on a 

combination of the F-function and linear-potential-theory methodologies and documented in reference 7.31. In 

this reference, a computer code is described that calculates

• The interference pressures and associated lift and drag on a wing adjacent to a nacelle

• The calculation of the local wing camber (reÀex) required to cancel out all, or a portion of, the 

interference effect of a nacelle

A schematic of the nacelle-wing interference problem is shown in ¿gure 7.40(a). A typical result is also shown in 

¿gure 7.40(b), including the nacelle-induced pressure ¿eld and the wing deformation or reÀex required to cancel 

out this effect. The small plot in the right-hand corner shows the original trailing-edge geometry along with that 

of the reÀexed surface.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

287

The integrated or force effect of the interference pressures is illustrated by the lift-drag polar shown in ¿gure 7.41

along with the associated moment coef¿cient. It is evident that at low CL there is a drag penalty while at design CL

there is none. The effect on moments of the interference pressures is to make them more negative, as indicated in 

the Cm vs CL plot on the right side of ¿gure 7.41.

(a) Pictorial representation of nacelle-wing interference problem (shaded area indicates interference region).

Figure 7.40. 6NHWFKRIQDFHOOHZLQJLQWHUIHUHQFHSUREOHPSUHVVXUH¿HOGDQGUHÀH[HGVXUIDFHWRFDQFHORXWWKH

induced pressure (ref. 7.31).

(b) Nacelle pressure ¿eld at surface of twisted and cambered wing and reÀex surface required for 

100 percent cancellation. 
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

288

Several papers contain analyses that highlight the adverse effects of the engine nacelles on sonic boom signatures. 

In a study by R. Mack (ref. 7.32), the issue of nacelle integration was addressed and provided an improved 

analysis, which contained all of the pieces that go into an F-function including the isolated and interference effects 

of nacelles. Figure 7.42 from this study (ref. 7.32) shows the con¿guration used to illustrate the method (¿g. 7.42 

(a)) as well as its effective area distribution (¿g. 7.42(b)) and associated F-function (¿g. 7.42(c)). Note that the 

nacelle effects are not included in the F-function plotted in ¿gure 7.42(c). Figure 7.43 shows the effective areas 

due to the interference lift produced by the nacelles, the corresponding F-function, and incremental effect that 

the interference lift of the nacelles has on the con¿guration’s F-function distribution.

Figure 7.41. $HURG\QDPLFFKDUDFWHULVWLFVRIWZLVWHGDQGFDPEHUHGZLQJQDFHOOHFRPELQDWLRQIRUSHUFHQWUHÀH[

(adapted from ref. 7.31).

Figure 7.42. 7KUHHYLHZGHSLFWLRQRIWKHFRQFHSWXDODLUFUDIWLWVHIIHFWLYHDUHDGLVWULEXWLRQV

and associated F-function (ref. 7.32).

(b) Effective area distribution. (c) F-function.

(a) Conceptual aircraft.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

289

The additional effective area created by the volume effects of the nacelles is illustrated in ¿gure 7.44 along with 

the associated F-function distribution. The result of adding all component F-functions together is given in ¿gure 

7.45. This ¿gure can be compared to the distribution shown in ¿gure 7.42 to see the large incremental effect the 

nacelles had on the basic F-function.

Figure 7.43. Effective area due to wing-nacelle interference and the corresponding F-function as well as the total 

FRQ¿JXUDWLRQ)IXQFWLRQLQFOXGLQJWKDWGXHWRWKHLQWHUIHUHQFHOLIWUHI

Figure 7.44. Equivalent area and F-function for an isolated nacelle (ref. 7.32).

Figure 7.45. )IXQFWLRQRIDOODLUFUDIWFRPSRQHQWV7KHGDVKHGOLQHVVKRZWKH)IXQFWLRQEHIRUHWKHLQFUHPHQWV

IURP¿JXUHZHUHDGGHGUHI

(b) F-function due to wing nacelle interference.

(c) Total con¿guration F-function.

(a) Effective area due to wing nacelle interference.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

290

While the F-function effects of the nacelle shocks may be strong, they are usually followed by a rapid recovery. 

As noted earlier in this chapter, the shock strengths diminish very rapidly when followed by a rapid recovery so 

that the effect of the nacelle shock on the F-function may not be indicative of its effect on the sonic boom.

F-function distributions for a slightly different con¿guration (¿g. 7.46), with and without nacelles, are shown in 

¿gure 7.47 (ref. 7.33). This con¿guration is for cruise at Mach 1.8 overland and 2.4 over water, thus, the prime 

concern for the boom is at Mach 1.8. The large peak in the F-function at an x of 275 feet, due to the nacelles, is 

clearly on the down slope or expansion region of the F-function, which helps minimize the adverse effects of the 

engines on the sonic boom ground signature, as seen in ¿gure 7.48. The F-function distribution in ¿gure 7.47 is 

for the start of cruise at Mach 1.8.

Figure 7.46. 0DFK &RQ¿JXUDWLRQ general arrangement (ref. 7.33).

Figure 7.47. 0'%220SUHGLFWHG)IXQFWLRQDW0DFKEHJLQQLQJRIFUXLVHDGDSWHGIURP
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

291

A different engine installation is illustrated in ¿gure 7.49 along with its F-function (ref. 7.34). The four engines 

are mounted on the aft end of the fuselage (see ¿g. 7.49 (a)) and produce incremental effects to the F-function 

(see ¿g. 7.49 (b)) that are lower than those seen on most wing-mounted engine con¿gurations. The sonic boom 

signature created by this concept Àying at Mach 1.8 at an altitude of 48,000 feet and a start of cruise weight of 

618,000 pounds is shown in ¿gure 7.50 along with the ramp-type ideal signature. The small shock at an (x - ơh/l) 

of 0.6 is due to the engines and its low magnitude is a result of the optimal location of the engines.

Figure  Three-view depiction and Whitham F-function of the complete HSCT-10B wind-tunnel model (adapted from 7.34).

Figure 7.48. 0DFK&RQ¿JXUDWLRQJURXQGXQGHUWUDFNZDYHIRUPDW0DFKEHJLQQLQJRIFUXLVHUHI

(a) Front and top view of the HSCT-10B wind-tunnel model.

(b) Whitham F-function.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

292

In reference 7.35, Cliff documented an analysis of three supersonic cruise con¿gurations using CFD codes with 

both structured and unstructured grids. The con¿gurations were analyzed without engines and with four or three 

engines. A drawing of the con¿guration, designated LBWT, is shown in ¿gure 7.51. The symmetry-plane grids 

for this con¿guration are shown in ¿gures 7.52 and 7.53, with the former for the HFLO structured-grid code and 

the latter for the unstructured-grid AIRPLANE code. AIRPLANE unstructured, surface grids for the empennage 

of three- and four-engine versions of the LBWT are shown in ¿gures 7.54 and 7.55.

Figure 7.50. 3UHGLFWHGJURXQGOHYHOSUHVVXUHVLJQDWXUHIURPWKH+6&7%FUXLVLQJDW0 K IHHWDQG

VWDUWRIFUXLVHZHLJKWRIDERXWSRXQGVUHI

Figure 7.51. LBWT wind-tunnel model (ref. 7.35).
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

293

Figure 7.52. HFL04 computational grid (ref. 7.35).

Figure 7.53. AIRPLANE unstructured tetrahedral grid for the LBWT without engines (ref. 7.35).
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

294

Near-¿eld pressure signatures at an h/l of 1/3 for the LBWT con¿guration with three and four nacelles using these 

grids are plotted in ¿gure 7.56. The incremental effects of the three and four engines on the pressure near x = 16 

inches are quite evident. When these pressure signatures are propagated to the ground from an altitude of 60,000 

feet and a Mach number of 2.0, the result is depicted in ¿gure 7.57.

Figure 7.54. AIRPLANE unstructured surface grid for the LBWT with three nacelles (ref. 7.35).

Figure 7.55. AIRPLANE unstructured surface grid for the LBWT with four nacelles (ref. 7.35).
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

295

This ¿gure shows that both three and four engine concepts cause increases to the maximum pressure with the 

latter raising the level from ~1.1 lbs/ft2

 (no engines) to 1.6 lbs/ft2. Similar results for a canard version of LBWT 

(LBWC) and for the con¿gurations without the empennage (LBW) are given in reference 7.35.

Another study, documented in the same workshop proceedings (ref. 7.21), also looked at the incremental effects 

of engine installations. The relative sonic boom merits of ¿ve con¿gurations were explored using a very ef¿cient 

3-D Euler, ¿nite-volume marching code (MIM3DSB) perfected by Siclari and Fouladi. As they stated in reference

7.21 (p. 227),

In addition, a unique grid topology is used to accurately capture shocks several body lengths downstream 

of the aircraft. This unique grid topology has been sometimes referred to as the “donut grid” and consists 

of modeling the inner boundary downstream of the aircraft as a Mach cone surface. This approach takes 

advantage of the Mach cone characteristics associated with supersonic Àow and reduces grid spreading 

and the resultant smearing of shock waves that would occur with the use of a normal relaxation method 

type of grid.

Near-¿eld signatures were extrapolated to the ground using the Thomas wave-form parameter method

(ref. 7.16).

Figure 7.56. $,53/$1(QHDU¿HOGSUHVVXUHVLJQDWXUHVIRUWKH/%:70DFK Į °,KO DGDSWHGIURPUHI

Figure 7.57. Ground pressure signatures for the LBWT using AIRPLANE/ANET/ADDRISE computational data 

H[WUDSRODWHGIURPKO 0DFK Į °K IHHWDGDSWHGIURPUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

296

The planform geometry of the ¿ve concepts (ref. 7.21), along with the cruise-Àight conditions utilized is given 

in ¿gure 7.58 with the front-view geometries shown in ¿gure 7.59. These designs were sized for carrying 300 

passengers 5000 nautical miles and are 300-feet long. Sample results will be given here for the Langley LB16 and 

the Ames Model 3 con¿guration.

Figure 7.58. 3ODQIRUPYLHZRI&)'JHRPHWU\PRGHOVIRU¿YHORZERRPDLUFUDIWUHI

)LJXUH )URQWYLHZRI&)'JHRPHWU\PRGHOVIRU¿YHORZERRPDLUFUDIWUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

297

As stated by Siclari and Fouladi in reference 7.21 (p. 231),

The nacelles are treated in a similar fashion for all ¿ve con¿gurations. The inlet face is treated as a 

discontinuity in the geometry and the assumption is made that all of the mass Àow encompassed by the 

inlet face is captured with no spillage. The internal geometry of the engine nacelles was not modeled. 

The engine exits are also treated as discontinuities and grid points lying within the engine exhaust area 

are assigned free-stream values. This was done in order to approximately simulate Àow-through nacelles. 

More realistic engine exhaust conditions can also be simulated by MIM3DSB.

The MIM3DSB realistic engine exhaust condition simulations will be demonstrated in the next section with the 

aid of reference 7.36. The type of grid used to calculate the characteristics of these con¿gurations is illustrated by 

the cross section of the grid, used for the Langley LB16 design (¿g. 7.60) and the Ames Model 3 design (¿g. 7.61).

Lift, drag, and moment coef¿cients along with L/D are calculated for each con¿guration and both near-¿eld and 

ground-pressure signatures were determined. The authors noted that to adequately describe the geometry of the 

¿ve aircraft designs, including the nacelles, 7 to 11 axial grid blocks were typically required. Three grid blocks 

were needed to model a staggered pair of nacelles.

The effect of nacelles on the near- and far-¿eld pressure signatures for the Langley LB16 design at Mach 1.6 

and h = 45,000 feet is given in ¿gure 7.62. Shown on the left hand side of the ¿gure are the near-¿eld pressure 

distributions at a distance of 300 feet below the aircraft (h/l = 1) for the nacelle on and off con¿gurations. It can be 

seen that, even at the close-in distances, the incremental effects of the engines are to reduce the shock that occurs 

without the engines. Similarly, on the ground (¿g. 7.62 right side), the shock due to the nacelles is much weaker 

than of the nacelles-off shock and the bow or trailing shocks as well. This is an indication that the engines were 

well placed and that the geometry was properly tailored.

Figure 7.60. *ULGVDQGEORFNLQJVWUXFWXUHIRUWKH/DQJOH\/%GHVLJQDGDSWHGIURPUHI

Figure 7.61. *ULGVDQGEORFNLQJVWUXFWXUHIRU1$6$$PHV0RGHODGDSWHGIURPUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

298

A plot similar to ¿gure 7.62 is given for the NASA Ames Model 2 and is shown in ¿gure 7.63. This con¿guration, 

like LB16, has an arrow wing with four engines placed to provide as smooth an area distribution as possible. 

However, at Mach 2 the results are not the same. The incremental pressure due to the engines at a distance of 300 

feet is higher than the incremental pressure without engines and, consequently, there is adverse impact on the 

ground pressures (¿g. 7.63).

Calculations for the Ames Model 3 geometry (see ¿g. 7.64) at Mach 1.68 show near-¿eld and ground pressure 

signatures due to engine installation that are similar in magnitude to those of the LB16 design at Mach 1.6, 

indicating that the engine integration task produced better results at the lower Mach number.

Figure 7.62. (IIHFWRIQDFHOOHVRQWKHQHDUDQGIDU¿HOGVLJQDWXUHVRIWKH/DQJOH\/%GHVLJQ;LVWKHORFDWLRQRI

the initial shock (ref. 7.21).

Figure 7.63. (IIHFWRIQDFHOOHVRQWKHQHDUDQGIDU¿HOGSUHVVXUHVLJQDWXUHVIRUWKH$PHVPRGHOGHVLJQ

0DFK Ơ °, h = 54,286 feet (ref. 7.21).
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

299

A few of the studies that address the sonic boom of supersonic business jets focus on the incremental effects of 

engine installation. In 2002, however, Howe (ref. 7.28) speci¿cally focused on the engine placement problem 

using a generic wing-fuselage geometry and engines placed at three locations above the wing and the same three 

longitudinal locations below the wing. Adjustments to the wing and fuselage geometries were made to achieve the 

near-optimum area distribution shown in ¿gure 7.65. A schematic of the wing-fuselage and the engine longitudinal 

placements is shown in ¿gure 7.66. The ground signature for the baseline geometry is plotted in ¿gure 7.67 and 

shows an initial Ƌp/p, for a standard atmosphere of 0.00032 and a peak Ƌp/p of 0.00034, which convert to a Ƌp 

of 0.677 lb/ft2

 and 0.72 lb/ft2 for a sea level pressure of 2116 lbs/ft2.

Figure 7.64. (IIHFWRIQDFHOOHVRQWKHQHDUDQGIDU¿HOGSUHVVXUHVLJQDWXUHVRIWKH$PHV0RGHOGHVLJQ

0DFK  Ơ K IHHW;LVWKHORFDWLRQRIWKHLQLWLDOVKRFNDGDSWHGIURPUHI

Figure 7.65. %DVHOLQHFRQ¿JXUDWLRQDQGHTXLYDOHQWDUHDGLVWULEXWLRQVUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

300

Near-¿eld Àow calculations were made using the OVERFLOW solver (ref. 7.37) where grid blocks for nacelles or 

other components are embedded and point-to-point alignment is not required. Far-¿eld pressure-wave propagations 

are made using Thomas’ waveform parameter method (ref. 7.16). Figure 7.68 shows a view from the underside 

of the wing of the OVERFLOW grid, including the block containing the nacelle. As stated by Howe in reference 

7.28 (p. 6), it shows the position of a

... large block which is added to resolve the near ¿eld pressures below the con¿guration for later signature 

extraction and sonic boom propagation. This block is swept along the Mach angle and has grid points 

clustered in the vicinity of the shocks and strong pressure gradients. Also, this block extends down past 

one body length below the con¿guration and intersects both the nose block and the under nacelle block to 

avoid smearing the solution by the more coarsely gridded wing/body or outer blocks.

About 10 million grid points were used for the under-wing nacelle con¿gurations and 11 million for the over-wing 

nacelles. Pressure-wave propagation calculations were made starting with the Euler solution at one body length 

below the fuselage.

Figure 7.66. Inlet/nacelle axial positions (ref. 7.28).

Figure 7.68. Overall view of the OVERFLOW grid (ref. 7.28).

Figure 7.67. %DVHOLQHZLQJERG\JURXQGVLJQDWXUHDGDSWHGIURPUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

301

Two inlet geometries, an external compression inlet and a mixed compression inlet, were utilized for each of 

the six engine locations. The differences in geometry of these engine inlets (¿g. 7.69) produced different shock 

strengths and patterns and thus cause different interference effects, drags, and lifts as well as sonic booms. Near-

¿eld pressure and sonic booms for the mid-axial position of the external compression engine are given in ¿gures 

7.70 and 7.71, respectively. Clearly, in this location, the under-wing location of the nacelle produces the stronger 

shock. This carries over to the ground signature where the under-wing nacelle shock has coalesced with the bow 

shock to form a slightly higher ǻp/p than that produced by the over-wing nacelle location (¿g. 7.71 (a)).

)LJXUH Inlet geometry comparison (ref. 7.28).

Figure 7.70. 1HDU¿HOGSUHVVXUHFRPSDULVRQIRUH[WHUQDOFRPSUHVVLRQLQOHWDGDSWHGIURPUHI

Figure 7.71. External and mixed compression inlet ground signatures (ref. 7.28).

(a) External compression signatures. (b) Mixed compression signatures.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

302

Ground pressure signatures for the mixed compression inlet seen in ¿gure 7.71(b) are similar to those for the 

external compression inlet with the exception that the under-wing nacelle’s shock does not quite coalesce with 

the bow shock. The Àight conditions and con¿guration data for these calculations are given below in table 7.7.

7DEOH)OLJKW&RQGLWLRQVDQG&RQ¿JXUDWLRQ'DWDIRU)LJXUHVWKURXJK

Mach number 2.20

Altitude 56,000 ft

Wing Area 1800 ft2

Fuselage length 140 ft

Weight 101,000 lbs

A low-boom supersonic business jet (SBJ) con¿guration was designed and analyzed by Mack and the results are 

documented in reference 7.38. It has its engines mounted on the vertical tail, a canard for take-off rotation, and a 

wing with a curved (versus straight-line segments) leading edge. Several different canards and canard locations 

were studied to improve the take-off characteristics and meet the 6000-foot take-off distance speci¿cation. The 

three-view depiction in ¿gure 7.72 is the SBJ with the original canard. Other canard geometries and locations

were examined in reference 7.38 to increase rotation rate and decrease take-off distance. The effective area 

distribution of this con¿guration is shown in ¿gure 7.73 along with the target low-boom distribution (dashed 

line). Xe is the effective distance along the longitudinal direction.

Figure 7.72. 7KUHHYLHZGHSLFWLRQRIORZERRP6%-FRQFHSWUHI

Figure 7.73. 6XPPHGHTXLYDOHQWDUHDVH[FOXGLQJQDFHOOHVRIWKH6%-FRQFHSWVKRZQDERYH0DFK 

Wc

 OEVDQGK IHHWUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

303

The F-function for the nacelles was calculated by the method of reference 7.31 and is plotted in ¿gure 7.74 where 

y is the spanwise direction or Whitham F-function effective length parameter. When this is added to the basic 

wing-fuselage F-function the result is shown on the left of ¿gure 7.75. Note that the increment due to the nacelle 

starts at a y value of around 100 feet. A slightly better result might have been achieved had the nacelles and the 

start of the expansion been a bit closer. Mack notes in reference 7.38 (p. 18),

Ideally, the nacelle volume F-function would be added to the fuselage-wing-¿n volume and wing-lift 

F-function at the longitudinal distance where the fuselage-wing F-function expansion began. However, the 

nacelles off F-function in ¿gure 7.75(b) shows the ideal was not completely achieved. Better agreement 

between the SBJ concept’s wing/fuselage/¿n/nacelle F-function and its theoretically ideal F-function 

might have been achieved by expending more effort in the fuselage tailoring and/or by using more stations 

in the volume and lift distribution.

Nevertheless, the ground pressure signature for the con¿guration with and without nacelles, plotted in ¿gure 7.76, 

does not show a large increment due to the nacelles. There is a small increase in the tail shock and a small shock 

at an (x-ơh)/le of 0.3.

Figure 7.74. )IXQFWLRQRIWKHQDFHOOHIRUWKHFRQFHSW¶VORZE\SDVVUDWLRHQJLQHUHI

Figure 7.76. 3UHGLFWHGJURXQGVLJQDWXUHVIURPWKH6%-FRQFHSWZLWKWKHFDQDUGDW]HUROLIW0DFK 

Wc

 OEVDQGK IWUHI

Figure 7.75. 1DFHOOHRQDQGQDFHOOHRII)IXQFWLRQVRIWKH6%-FRQFHSWDWEHJLQQLQJRIFUXLVH$VZHOODV

QDFHOOHVRII)IXQFWLRQFRPSDUHGWRWKDWRILGHDOORZERRPFRQFHSWUHI

(a) Comparison of nacelle-on and nacelle-off 

F-functions.

(b) Comparison of ideal and calculated F-functions – 

nacelles off.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

304

In summary, there are published studies that address the effect of nacelles on sonic booms. Sample results from 

some of these studies have been presented. It is clear that the incremental effect of engine nacelles on the sonic 

boom produced by a supersonic cruise aircraft is highly dependent on the aircraft’s geometry and the locations 

of engine nacelle placement. Changes in wing planform and fuselage longitudinal area distributions can usually 

be made to reduce the adverse effects of an engine installation. Using F-function equivalent area distributions 

to make adjustments to the area distribution and/or locate nacelles can be most useful in a qualitative sense. 

Generally, these adjustments should be validated and ¿ne-tuned using CFD.

The Effect of Engine Exhausts on Sonic Booms

The origin of the trailing or rear shock of a sonic boom is substantially more complicated than that of the leading or 

bow shock. This is due to the geometric complexity of the rear areas of most con¿gurations. Vertical and horizontal 

tails, engines, wing trailing edges, and the aft portion of fuselages all contribute to establishing the aft portion 

of the boom signature. Most of these aircraft components are usually accounted for in sonic boom predictions 

whether the Àow ¿eld analysis is made using the Euler equations or the linear effective area F-function approach. 

However, there is one item that is frequently ignored independent of the method used – the contribution of engine 

exhaust plume. This is most likely because engine exhaust is not part of the aircraft’s geometric de¿nition and an 

accurate calculation of the plume shape, for a real engine, may be beyond most analysts’ capabilities. During the 

1950s and 1960s, the convenient assumption was usually made that the effective exhaust shape was cylindrical. 

However, there were methods available for estimating the effective boundary of jets exhausting into a supersonic 

stream (refs. 7.39 to 7.41). Reference 7.42, published in 1969, documented the ¿rst study that analyzed both the 

real and effective (solid body) shape of jet plumes, as well as their possible effect on sonic booms. Experimental 

data for a series of seven nozzles was provided (see ¿gure 7.77 for details) along with calculations for the inviscid 

jet boundary using the linear method of reference 7.43. Also, the jet equivalent solid body shapes were calculated 

using the method detailed in the study.

Figure 7.77. Details of nozzles. All dimensions are in cm except as noted. Areas are in cm2 (ref. 7.42).
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

305

Figure 7.78 shows illustrative jet-equivalent solid shapes for nozzle 4 and for a series of pressure ratios. The solid 

body plumes shown in this ¿gure were used for the near-¿eld pressure signature calculations shown in ¿gure 7.79. 

These calculations were made for two aircraft con¿gurations – a podded engine ¿ghter and a four-engine supersonic 

transport. Results for Mach 2.2 and a range of pressure ratios up to 2.326 are given in ¿gure 7.79 (ref. 7.42).

Figure 7.78. &RPSDULVRQRIMHWHTXLYDOHQWVROLGERG\ZLWKLQYLVFLGMHWERXQGDU\IRUMHWVH[KDXVWLQJIURPQR]]OHDW

VHYHUDOMHWVWDWLFSUHVVXUHUDWLRV0DFK DGDSWHGIURPUHI

)LJXUH (IIHFWRIMHWSOXPHRQVRQLFERRPSUHVVXUHVLJQDWXUHRISRGGHGHQJLQH¿JKWHUDLUSODQHDQG

VXSHUVRQLFWUDQVSRUWDLUSODQHZLWKQR]]OH0DFK  (adapted from ref. 7.42).

(a) Fighter airplane with two podded engines. (b) Supersonic transport airplane with four podded engines.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

306

Putnam and Capone note in reference 7.42 (p. 17) that these calculations,

Indicate that there is considerable effect on the trailing-shock-wave system resulting from the jet plume 

with the effects increasing with jet pressure ratio. However, these effects are a near ¿eld effect, and 

calculations of the far ¿eld N-wave pressure signatures indicated that for the cases considered there 

would be no effect of the jet plume.

There are no data or sonic boom signatures given to support this conclusion.

Additionally, in 1992 Barger studied the exhaust problem mentioned in reference 7.44 using the numerical 

technique of Salas (ref. 7.45) for plume shape calculations. Most of his results were for the low-boom design 

con¿guration depicted in ¿gure 7.80. Sonic booms were computed for this con¿guration at several Mach numbers 

with both cylindrical and computed plume shapes. The calculated plume and shock for Mach 2.1 and an altitude 

of 55,000 feet is shown in ¿gure 7.81. No numbers are given for the pressure ratios or for the Mach number ratio 

Mj

/M for this plume.

Figure 7.80. 6XSHUVRQLFFUXLVHORZVRQLFERRPGHVLJQUHI

Figure 7.81. &RPSXWHGSOXPHVKDSHIRUÀLJKWDW0DFK DQGDOWLWXGHRIIHHWUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

307

F-function methodology was used for the boom calculations and is given along with the sonic boom pressure 

distributions in ¿gure 7.82 for both cylindrical (¿g. 7.82(a)) and calculated plumes (¿g. 7.82(b)). Clearly, the 

calculated plume provided a signi¿cant hump in the F-function beyond an x/L of 0.7 and it, in turn, caused an 

increase in the strength of the secondary shock from 1.2 to ~1.8 lbs/ft2 (¿g. 7.82(b)). This increase caused the 

secondary shock to become the dominant noise source. After analyzing the results for altitudes of 45,000, 55,000, 

and 60,000 feet, Barger (ref. 7.44, p. 4) concluded that “for Àight at altitudes above 60,000 ft, the plume effects 

were dominant; but for altitudes below 55,000 ft, they were signi¿cant but not dominant.”

The results of a third study, carried out by Siclari, attempted to determine the effect of real exhaust plumes on the 

sonic boom of a con¿guration was published in 1992. In his Euler-equation calculations, discussed in reference 

7.36 (p. 187), Siclari stated that,

The inlets were initiated by assuming that all of the mass entering the face of the engine is swallowed or 

zero spillage is assumed. The exhaust of each nacelle was simulated by injecting mass into the Àow and 

by assuming the Àow was no longer isoenergetic. In other words, the enthalpy downstream of the engines 

was no longer assumed to be constant. The actual engine operating conditions for the Mach 2 aircraft 

obtained from NASA and used in the computation were as follows

ȡj ȡ = 0.4796

Vj /V = 1.697

Pj /P = 1.0

The exhaust pressure ratio for the Mach 2 aircraft is matched with freestream. These conditions lead to 

exhaust jets with approximately a 2.4 Mach number.

Near-¿eld and ground sonic boom pressure signatures for the Mach 2 con¿guration are plotted on the left side of 

¿gure 7.83 and show minimal effects on both. The bow and trailing shocks are not affected and the mid-signature 

shock that the plumes create is much less than that of the bow shock.

Figure 7.82. )IXQFWLRQVDQGJURXQGOHYHOVLJQDWXUHVIRUORZERRPFRQ¿JXUDWLRQZLWKF\OLQGULFDOMHWDQG

FRPSXWHGSOXPHVKRZQLQ¿JXUH0 DQGDOWLWXGHRIIHHWDGDSWHGIURPUHI

(a) Cylindrical jet. (b) Computed sonic boom for plume of ¿gure 7.81.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

308

Calculations were also made in reference 7.36 at Mach 3 for the con¿guration shown on the right side of ¿gure 

7.83. The operating conditions for the engine were

ȡj ȡ = 0.3904

Vj /V = 2.686

Pj /P = 1.048

The jet plume is slightly under expanded and the jet exit Mach number for these conditions was computed as 4.92.

In reference 7.36 (p. 190), Siclari notes that “As a result of these conditions (i.e., under expanded jet and higher 

exhaust (Mach number)), it is expected that the engine exhaust for the Mach 3 aircraft will have a greater effect on 

the pressure ¿eld below the aircraft.” As seen in ¿gure 7.83, the effect of the plumes on the near-¿eld and ground 

sonic boom signatures is much larger. Both the bow and trailing shocks of the sonic boom are increased. Note that 

the cruise altitude for the Mach 3 case is 65,000 feet, while the cruise altitude for Mach 2 is 55,000 feet. 

Calculated Results for Initial Slope and Contours of Jet Plumes

Both of the cases described above had static pressure ratios close to 1.0. As pressure ratio increases for the same 

Àight conditions, the plume will be larger and the shock it generates will be stronger. Figure 7.78 for nozzle 4 

illustrates the effect of increases in pressure ratio on plume size (¿g. 7.84 from ref. 7.43 may be even more useful) 

since it highlights the initial slope of the plume. The latter calculations are for Ƣj

 = Ƣ = 1.4 and with the jet Mach 

Figure 7.83. &RPSDULVRQRIKO DQGH[WUDSRODWHGJURXQGVLJQDWXUHVIRUERWKÀRZWKURXJKQDFHOOHVDQG

QDFHOOHVZLWKHQJLQHH[KDXVWVLPXODWLRQIRUWKH0DFKDQG0DFKFRQ¿JXUDWLRQVUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

309

number equal to 2.0. The pressure ratio ranges from ~0.25 to 5.5 and Mach numbers from 2 to 9. As stated by 

Englert in reference 7.43 (p. 16),

The exact results were obtained by use of Prandtl-Meyer expansion curves for the expanding Àow on 

one side of the jet boundary and by use of two-dimensional shock charts on the compression side of the 

boundary. A unique solution Ș(0) is obtained, which yields continuity of pressure and velocity direction 

across the jet boundary.

It is also possible to calculate the exact values by solving the cubic equations for P2 /Pj

 and P2 /P simultaneously. 

Calculated values for M = 2 of the exact initial slope are given in ¿gure 7.84 from reference 7.43 (solid lines) and 

are represented by the square symbols in the equation derived in the next section of this Chapter. As observed, the 

square symbols and the solid lines yield identical results. Even using only the terms up to Ș(0)2

 (i.e., eliminating 

the cubic term) provides a good approximation of Pj /P as seen by the circular symbols on ¿gure 7.84. Finally, the 

linear equation results from reference 7.43 yield a good approximation of the exact Ș(0) up to pressure ratios of 

2.5. Whether these results are based on linear potential theory or exact theory, one can appreciate that for pressure 

ratios of 5 and 6 and plume initial slopes on the order of 0.25 (14°), the substantial impact exhaust plumes can 

have on the trailing shock of sonic booms.

All of the theoretical results for jet plume shapes discussed were for air as the constituent gas, both for the exhaust 

and free-stream Àows. The effect of real exhaust gases was not illustrated. The linear equation for the initial slope 

of the plume that produced (the dashed lines in ¿gure 7.84) can also be used to get some idea of the effects of the 

exhaust gas on the initial slope and shape of the plume. The equation for Ș(0) from reference 7.43 can be rewritten 

using the equation of state and the equation for the speed of sound as

While this is a linear result, it is most useful in a qualitative sense. Figure 7.85, derived from the above equation 

for M = 2 and Ƣj = 1.32 shows (as expected) the strong dependence of the initial slope of the plume (i.e., Ʀ(0) on 

Figure 7.84. &RPSDULVRQ RIOLQHDUL]HG DQG H[DFWLQLWLDO VORSHV RIMHW ERXQGDU\1R]]OHH[LW DQG VWUHDP

VSHFL¿FKHDWUDWLRVƢj

 and Ƣ QR]]OHZDOODQGERDWWDLODQJOHV 0j = 2 (ref. 7.43).

(9)

β

1+

0
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

310

the value of the pressure ratio Pj /P ). Jet Mach number increases cause a decrease in plume slope while a realistic 

(reduced) ratio of the jet speci¿c heats (i.e., 1.4 to 1.32) causes an increase. 

First and second order solutions of the linear potential equation for the shape of the plume are derived in reference 

7.43. The ¿rst order solution is given by

These equations are slightly different in form, but equivalent to, those of reference 7.43. 

Note that z is the distance measured from the nozzle exit. As can be seen, the controlling exhaust gas parameters 

other than Pj /P are and . A plot of the above equation for rb

/ro versus z as well as that for the second

Figure 7.85. ,QLWLDOVORSHVRIMHWSOXPHVYHUVXVHQJLQHH[KDXVWIUHHVWUHDPSUHVVXUHUDWLRIRU0 Ƣj 

(10)

(11)

(12)

(13)

(14)
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

311

order is given in ¿gure 7.86 for M = Mj = 2.0 and a range of pressure ratios. Note that the ¿rst order solution 

varies little from that of the second, particularly for pressure ratios less than ¿ve. In reference 7.43 (p. 20), 

Englert notes that “The difference between the simpler solution (equation for rb

/ro above) and characteristics 

and experimental data was within 10 percent over the range investigated.” Thus, it is clear that for sonic boom 

calculations, based on the F-function methodology, the ¿rst order Englert equation is suf¿cient.

It is also of interest to compare the plume shape with the exact Ș(0) in equation(10) to those calculated by the 

characteristics method. Figure 7.87 (ref. 7.43) shows such a comparison using data from three separate papers 

(refs. 7.41, 7.46, and 7.47). Clearly, there is excellent agreement between the two methods, particularly for the two 

lower jet Mach number cases. It is evident, then, that the linear plume-shaped equation with the exact Ș(0) gives 

results comparable to characteristic equations for the plume shape just downstream of the nozzle for supersonic 

Mach numbers.

Figure 7.87. -HWFRQWRXUIRUVXSHUVRQLFH[WHUQDOÀRZDGDSWHGIURPUHI

Figure 7.86. &RPSDULVRQRI¿UVWDQGVHFRQGRUGHUWKHRU\IRUMHWVKDSH1R]]OHH[LWDQGVWUHDPVSHFL¿FKHDW

UDWLRV Ƣj

 and Ƣ 1R]]OHH[LWDQGVWUHDP0DFKQXPEHUV0j and 0 DGDSWHGIURPUHI

(a) Mj = 2.29, M = 3.0, pj/p  = 2.0, nozzle wall 

angle = 12°, boattail angle = 0°.

(b) Mj

 = 2.38, M = 3.24, pj/p  = 8.96, nozzle wall 

angle = 12.5°, boattail angle = 9°.

(c) Mj

 = 3.0, M = 3.0, pj/p  = 12.23, nozzle wall 

angle = 12.5°, boattail angle = 0°.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

312

Finally, all the analyses and data shown were for simple nozzles with uniform Àow out of the nozzles. Plumes and 

associated shock systems for real engines with real exhaust gases, internal mixers, cowls with serrated trailing 

edges, by-pass air, and plugs have not been published in the open literature. The utility of the calculation methods 

for simple nozzles for approximating the plumes and shocks for the more complicated real engines has not been 

demonstrated.

Calculation of Exact Ș(0)

The equations de¿ning the ratios of P2 /Pj and P2 /P (see ¿g. 7.88) are given below.

With A, B, C, D, E and F de¿ned by

Figure 7.88. 6NHWFKVKRZLQJSOXPHSOXPHVKRFNDQGSUHVVXUHV

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

313

Combining equations (15) and (16) yields 

Solutions to this equation yields the required Ș(0) and is given below

Where p and x are normally negative. The quantities p and x are determined through a series of equations starting 

with p, q, and r.

(23)

(28)

(29)

(30)

(31)

(32)

(27)

(26)

(25)

(33)

(24)
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

314

&RQ¿JXUDWLRQ'HVLJQ$QDO\VHV&RQFHSWV

The use of ¿nite difference techniques to solve the three-dimensional Euler equations and full potential equation 

dates back to the 1960s. Wings, bodies, and wing-body con¿gurations were treated in the 1970s using primarily 

single block grids. Improvements in grid technology, solution algorithms, and computers combined in the 1980s 

to allow the treatment of complex con¿gurations (including nacelles, pylons, empennages, etc.) in a matter of 

hours. Purely supersonic Àows that allowed the use of simple marching schemes could be solved in minutes. 

In addition, with the increased speed and storage capability of the large mainframe computers, the complexity 

of the Navier-Stokes could be accommodated and viscous effects assessed. The application of CFD and grid 

codes during the 1970s and 1980s seems to have been primarily to aircraft design analyses with an emphasis on 

aerodynamic characteristics.

Sonic boom analyses requiring a near-¿eld signature for insertion in the Thomas propagation code, produced in 

1972, could have bene¿tted from the application of CFD. However, the ¿rst concerted effort to take advantage 

of this fast improving technology started in the late 1980s. Several AIAA papers appeared in 1990 and 1991 (see 

refs. 7.48 to 7.52) and a handful of CFD sonic boom papers form the basis of Volume II of the Proceedings of 

the 1992 Sonic Boom Conference (ref. 7.53). Sonic boom workshops were also held in 1993 (ref. 7.54), 1994 

(ref. 7.55), and 1995 (ref. 7.56) with each succeeding session producing design and methodology advancements. 

NASA Langley Research Center (LaRC), NASA Ames Research Center (ARC), Douglas, Lockheed, Grumman, 

and Boeing were the major participants.

Large Supersonic Commercial Transport Jet Studies

Most of the basic con¿guration geometries proposed for large supersonic commercial jets are contained in the 

¿rst two NASA workshops (refs. 7.53 and 7.54). They are all either arrow-wing or cranked delta-wing designs. 

Subsequent workshops contain additional improvements to those con¿gurations through trial and error or 

analytical optimization. Boom reduction to existing con¿gurations is termed boom softening (see refs. 7.57 and 

7.58). Comparisons of the maximum boom of several con¿gurations following optimization are presented in 

reference 7.20. Performance assessments of several candidate con¿gurations are contained in references 7.59 

and 7.60. Figure 7.89 gives a sample result from the performance assessments of reference 7.59. It shows all of 

the con¿guration planforms and the characteristics table based on a 12,000-foot take-off ¿eld length constraint. 

Assessment of changes in various geometric features is the subject of other published studies. For example, table 

7.8 lists some of the options studied by Morgenstern in reference 7.61.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

315

Table 7.8. Boom Softening Options (ref. 7.61)

Boom Softening Options

Small modi¿cations

 Different trim/tail loading

 Wing dihedral

 Fuselage camber

 Outboard wing sweep (also in planform study)

 Increased wing area

Moderate Modi¿cations

 Planform variations from planform study

 Canard/3-surface

 Fuselage length

 Shaping of front shock using area/lift distribution

)LJXUH 3HUIRUPDQFHDVVHVVPHQWVRIVL[VXSHUVRQLFFUXLVHORZERRPFRQ¿JXUDWLRQVUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

316

A summary of Haglund’s assessment on sonic boom reduction possibilities of the Boeing HSCT based on his 

optimization studies presented in reference 7.60 is as follows

1. The greater potential for sonic boom reduction rests on the tailoring of the lift distribution by modi¿cations 

to the wing planform and size. Promising modi¿cations include increased wing size (decreased wing 

loading), and increased wing slenderness, which may be achieved through increased wing leading-edge 

sweep and/or reduced span.

2. Wing dihedral shows promise for sonic boom reduction, but the adverse effects on the aerodynamics and 

structure must be understood and minimized.

3. The modi¿cations that are most bene¿cial for reduced sonic boom aggravate the low-speed, take-off ¿eld 

length, and community noise problems.

4. The constraint imposed by the need for very small or no performance penalty is a severe one and will 

limit the range of boom-softening modi¿cations.

5. For the 1080-444 con¿guration, with aggressive boom-softening and signi¿cant wing modi¿cations, 

about 0.4 lb/ft2

 reduction in maximum over-pressure was achieved (from 2.97 to 2.57 lbs/ft2). This is at 

the expense of a 1 percent penalty in MUTATOR.

6. Technology advances that result in greater ef¿ciencies in structures and propulsion will translate directly 

into reduced sonic boom provided that these advances produce a reduction in wing loading.

These conclusions also apply to the majority of the optimization results of other studies and, more importantly, 

provide a guide to current studies.

Finally, in order for the reader to get a better idea of the con¿guration geometries and analyses, sample geometries 

and results for large commercial jets are presented in the following sub-sections from references 7.53 and 7.54, 

along with a few comments to further de¿ne the content of the technical papers. In the last subsection, similar 

results for business jets are presented.

Supersonic Commercial Jets

The following sub-section contains depictions of the con¿guration concepts reported in NASA CP 3173 and NASA 

CP 10133 (refs. 7.53 and 7.54, respectively), along with a few sample result charts. The names of the authors, 

their af¿liation, and a short list of comments to further indicate what is in the published study are provided for 

each con¿guration. NASA CP-1999-209699 (ref. 7.55) and NASA CP-1999-209520 (ref. 7.56) contain additional 

con¿guration studies. Other references report on further optimization of con¿gurations in refs. 7.53 and 7.54. The 

four NASA reports are a valuable resource for anyone interested in the minimization of sonic boom and the tools 

utilized to perform this type of research.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

317

&RQ¿JXUDWLRQ6XSHUVRQLF$LUSODQH'HVLJQ2SWLPL]DWLRQ0HWKRGIRU$HURG\QDPLF

Performance and Low Sonic Boom

Authors Samson H. Cheung and Thomas A. Edwards

Organization NASA Ames Research Center, Moffett Field, California

Report High Speed Research Sonic Boom, NASA CP 3173, Vol. II, Feb. 1992, pp. 31-44.

Comments • Camber optimized to improve L/D (3.75%)

• Euler version of UPS3D used for Àow ¿eld calculation, NPSOL code for 

optimization

• Darden F-function procedure for modest boom improvement

• Mach 1.7, L = 330 ft, h = 44,000 ft

• Boeing model 1080-911
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

318

&RQ¿JXUDWLRQ&)'3UHGLFWLRQVRI1HDU)LHOG3UHVVXUH6LJQDWXUHVRID

Low-Boom Aircraft

Authors Kamran Fouladi and Daniel Baize

Organization Lockheed Engineering and Sciences Company, Hampton, VA

NASA Langley Research Center, Hampton VA

Report High Speed Research Sonic Boom. NASA CP 3173, Vol. II, Feb. 1992, pp. 119-136.

Comments • Hybrid signature design

• Low-boom arrow wing

• On and off-track signature

• Near-¿eld and ground signatures

• M = 1.6, h = 47,000 ft

• Near ¿eld calculated using MIM3DSB Euler-marching code

• Grid resolution a possible problem
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

319

&RQ¿JXUDWLRQ&RPSXWDWLRQDO([SHULPHQWDO$QDO\VLVRI7KUHH/RZ6RQLF%RRP

&RQ¿JXUDWLRQVZLWK'HVLJQ0RGL¿FDWLRQV

Author Susan E. Cliff

Organization NASA Ames Research Center, Moffett Field, CA

Report High Speed Research Sonic Boom. NASA CP 3173, Vol. II, Feb. 1992, pp. 89-116.

Comments • Three low-boom con¿gurations – two Mach 2.0 and one Mach 3.0

• Euler with structured and unstructured grids (Team and Airplane codes)

• Theory and experiment for near ¿eld

• Nacelle effects studies

• Notes importance of grid resolution
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

320

&RQ¿JXUDWLRQ/RZ6RQLF%RRP'HVLJQDQG3HUIRUPDQFHRID0DFK2YHUODQG

High Speed Civil Transport

Author John M. Morgenstern

Organization McDonnell Douglas Corporation, Douglas Aircraft Company, Long Beach, CA

Report High Speed Research Sonic Boom. NASA CP 3173, Vol. II, Feb. 1992, pp. 55-64.

Comments • Canard con¿guration optimization

• Various wing planforms, wing twist and camber, horizontal and vertical tails, 

canards fuselage and nacelle location studied

• Ramp signature

• Mach 2.4/1.8, L = 330 ft

• On- and off-track signatures for M = 1.8 and M = 1.2
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

321

&RQ¿JXUDWLRQ7ZR+6&70DFK/RZ6RQLF%RRP'HVLJQV

Authors George T. Haglund and Steven S. Ogg

Organization Boeing Commercial Airplane Group, Technology and Product Development/

Aerodynamics Engineering, Seattle, WA

Report High Speed Research Sonic Boom. NASA CP 3173, Vol. II, Feb. 1992, pp. 65-88.

Comments • Low sonic boom concepts for wind-tunnel study

• Two low-boom concepts, ramp and Àat top, and baseline studied

• Blended Wing Body philosophy

• Leading and trailing edge Àaps vary for climb out and approach

• Low-boom designs at M = 1.7 and 44,000-foot altitude

• Suggestions for improved performance and low boom
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

322

&RQ¿JXUDWLRQ6RQLF%RRP3UHGLFWLRQIRUWKH/DQJOH\0DFK

/RZ%RRP&RQ¿JXUDWLRQ

Author Michael D. Madson

Organization NASA Ames Research Center, Moffett Field, CA

Report High Speed Research Sonic Boom. NASA CP 3173, Vol. II, Feb. 1992, pp. 157-174.

Comments • Langley Mach 2 low-boom con¿guration

• TranAir full-potential code use for near-¿eld predictions

• Theory experiment comparisons (on track)

• On- and off-track predictions with/without nacelles
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

323

&RQ¿JXUDWLRQ*URXQG6LJQDWXUH([WUDSRODWLRQRI7KUHH'LPHQVLRQDO1HDU)LHOG

&)'3UHGLFWLRQVIRU6HYHUDO+6&7&RQ¿JXUDWLRQV

Author M. J. Siclari

Organization Grumman Corporate Research Center, Bethpage, New <ork

Report High Speed Research Sonic Boom. NASA CP 3173, Vol. II, Feb. 1992, pp. 175-200.

Comments • Utilizes a multi-block Euler marching code developed by author. Includes innovative 

 grid scheme for better shock resolution.

• NASA Mach 2 and 3 concepts as well as Boeing 911 low boom (Mach 1.7 

con¿guration) studied

• Larger effect of real-exhaust on Mach 3 con¿guration boom (h = 65,000 ft) than on 

Mach 2 con¿guration (h = 55,000 ft)

• Higher pressures off track than on track shown for Mach 2 concept
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

324

&RQ¿JXUDWLRQ/RZ%RRP$LUFUDIW&RQFHSWZLWK$IW)XVHODJH0RXQWHG

Engine Nacelles

Author Robert J. Mack

Organization NASA Langley Research Center, Hampton, VA

Report High Speed Research Sonic Boom. NASA CP 10133, pp. 17-36.

Comments • Mach 1.8/2.4 concept developed using Haglund Hybrid F-function

• TOGW 662,000 lbs, 328.4-foot length

• Aft fuselage mounted engines

• Start of cruise altitude = 49,300 ft, end of cruise altitude = 67,000 ft
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

325

&RQ¿JXUDWLRQ2QWKH'HVLJQDQG$QDO\VLVRI/RZ6RQLF%RRP&RQ¿JXUDWLRQV

Author Susan E. Cliff

Organization NASA Ames Research Center, Moffett Field, CA

Report High Speed Research Sonic Boom. NASA CP 10133, Vol. II, May 1993, pp. 37-80.

Comments • Low-boom design with three or four engines and with canard or horizontal tail

• Developed using HFL03, HFL04, and airplane codes. The latter uses an unstructured 

grid, while the HFL codes use structured meshes

• Cruise Mach numbers of 2.0 and cruise altitudes of 34,286 ft and 49,249 ft for tail 

and canard con¿gurations, respectively

• Boom, loudness, and performance results for various nacelle combinations

• See also Cliff et al. paper in NASA CP-1999-209699
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

326

&RQ¿JXUDWLRQ/RZ6RQLF%RRP6WXGLHVDW%RHLQJ

Author George T. Haglund

Organization Boeing Commercial Airplane Group, Advanced Development, HSCT Aerodynamics

Report High Speed Research Sonic Boom. NASA CP 10133, Vol. II, May 1993, pp. 81-94.

Comments • Effort to improve Boeing 910 and 911 concepts using improved linear 

 methodology

• Modi¿ed model designed 935 and 936 are hybrid and Àattop designs, respectively

• Still concern for drag and weight penalties, rear shock strength, balance, trip and 

low-speed performance

• One 1.0 lb/ft2 Àat top achieved

• See also Haglund paper in NASA CP-1999-209699
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

327

&RQ¿JXUDWLRQ$0DFK/RZ6RQLF%RRP+LJK6SHHG

Civil Transport Concept

Authors Daniel G. Baize and Peter G. Coen

Organization NASA Langley Research Center, Hampton, Virginia

Report High Speed Research Sonic Boom. NASA CP 10133, Vol. II, May 1993, pp. 125-

142.

Comments • Appears to be further re¿nement of con¿guration of Fouladi and Baize (CP 3173)

• Ramp F-function design

• Minimized effect of nacelle integration
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

328

&RQ¿JXUDWLRQ$&)'6WXG\RI&RPSRQHQW&RQ¿JXUDWLRQ(IIHFWVRQWKH6RQLF

Boom of Several High Speed Civil Transport Concept

Authors M. J. Siclari and Kamran Fouladi

Organization Grumman Corporate Research, Bethpage, New <ork

Lockheed Engineering and Sciences Company, Hampton, VA

Report High Speed Research Sonic Boom. NASA CP 10133, Vol. II, May 1993, pp. 227-

300.

Comments • Comparison of 5 con¿guration using Siclari-developed Euler code and grid 

 topology.

• Near- and far-¿eld (boom) pressures as well as aerodynamic characteristics 

predicted and analyzed

• Pressure results given for nacelles on and off

• Results show error in ground pressures that can result from extrapolating from 

near-¿eld pressures too close to airplane (e.g., less than one body length)

• Extensive documentation, only a few sample results given here
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

329
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

330
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

331

Supersonic Business Jet Studies

There is general agreement that the ¿rst supersonic cruise aircraft to be produced for civil use will be a supersonic 

business jet (ref. 7.62). Over the past 45 years, conceptual studies have yielded business jets weighing from 8,400 

to 134,000 pounds and having fuselage lengths from 40 to 135-feet long. A brief summary of several published 

business jet studies is presented in the following pages.

A design concept study of a small supersonic cruise vehicle by the University of Colorado in 1963 (ref. 7.63) was 

the ¿rst published study of such a vehicle. It is the smallest vehicle of the small supersonic cruise vehicle types 

to be proposed, having a 40-foot long fuselage and is by far the lightest, weighing in at 8,400 pounds at take-off 

ground weight (TOGW) (see ¿gure 7.90).

Up until recent years, the largest by weight (134,000 pounds TOGW) was a cranked arrow-wing concept 

developed in a study by Fairchild/Sweringen in 1982 (ref. 7.64). The baseline con¿guration for this study, 

shown in ¿gure 7.91, has three engines. Business jet concepts were also developed under this study by Douglas, 

British Aerospace, and Lockheed. Their con¿gurations give rise to the ranges for the various quantities provided 

in the adjacent table.

In addition to the University of Colorado and Fairchild/Sweringen con¿gurations mentioned above (¿gs. 7.90

and 7.91), the characteristics of 23 business jet concepts, along with sketches of their geometries, are given in 

reference 7.64 by Maglieri. These concepts are typical of the con¿gurations proposed in the 1970s and 1980s, and 

similar in most respects to those still being studied. More recent supersonic business jet studies are documented 

in the following pages.

)LJXUH 8QLYHUVLW\RI&RORUDGRFRQ¿JXUDWLRQUHI

)LJXUH Fairchild/SweringenEDVHOLQHUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

332

Recent Supersonic Business Jet Studies

Since the publication of reference 7.64, there have been numerous studies that have produced low-boom supersonic 

cruise concepts of business jet size. One of the more signi¿cant efforts was DARPA’s Quiet Supersonic Platform 

(QSP) program (ref. 7.65), which was directed towards a dual use (commercial and military) 100,000-pound 

class aircraft. A goal of 0.3 lb/ft2

 was set by DARPA for the initial shock of the sonic boom. Several conceptual 

con¿gurations are shown in reference 7.65, including the one pictured in ¿gure 7.92. The QSP system goals 

versus those of the Concorde are also shown in ¿gure 7.92.

Komadina and Drake (ref. 7.66) describe a design approach that produced a dual-relevant vehicle concept that 

could be con¿gured to satisfy the QSP Program goal of either a civilian business jet or a military strike aircraft. 

The geometry of the design is shown in ¿gure 7.93 along with the design requirements in table 7.10 for the 

military strike version as well as those for the business jet and dual-relevant concepts.

)LJXUH Quiet supersonic platform concept and design goals (ref. 7.65).

)LJXUH Dual-relevant vehicle (7.66).
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

333

7DEOH9HKLFOH'HVLJQ5HTXLUHPHQWVUHI

DARPA, QSP Military Strike Business Jet Dual Relevant

Sonic boom 0.30 lb/ft2 n/a very low 0.30 lb/ft2

TOGW 100,000-lb class fallout 100,000-lb class 100,000-lb class

Range 6000 nm QSP Consistent 4k - 6k nm 6000 nm

Cruise speed M = 2.4 QSP Consistent M > 1.8 M = 2.2

Payload 20% TOGW QSP Consistent 6k - 8k lbs 20,000 lbs

TO/Landing noise Stage 3 Stage 3 Stage 4 Stage 3

Cruise L/D 11 n/a n/a 11

Cruise TSFC 1.05 n/a n/a 1.05

Engine T/W 7.5 n/a n/a 7.5

Takeoff BFL n/a 8000 ft 6500 ft 7000 ft

X-wind land n/a 30 kts 30 kts 30 kts

Cruise Altitude n/a > 60k ft 45k - 65k ft 60k - 65k ft

Note that the overall length of the design shown in ¿gure 7.93 is approximately 170 feet. Figure 7.94 shows the 

equivalent area distribution and sonic boom signature of this con¿guration. Although several QSP system goals 

were established, the QSP had only one requirement that the initial shock strength be no greater than 0.3 lb/ft2

(ref. 7.65). Note that in ¿gure 7.94, the initial shock is ~0.3 lb/ft2

 but the maximum positive and negative shock 

strength is around 0.5 lb/ft2

.

)LJXUH (TXLYDOHQWDUHDDQGVRQLFERRPVLJQDWXUHIRUGXDOUHOHYDQWYHKLFOHUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

334

The concepts developed in the QSP Program were designed to produce Àat-top or ramp-type signatures. This 

concentration was the result of down-selecting from an initial slate of approaches that included concepts from 

unconventional (e.g., airÀow modi¿cation) through the George-Seebass theory that had been the mainstay of 

conventional shaping analysis. The con¿guration studies included design exercises that veri¿ed a low-boom 

aircraft could be built. A follow on to the DARPA QSP Program was the Shaped Sonic Boom Demonstrator 

(SSBD) Àight-test program that proved the persistence to the ground of a Àat-top pressure signature. There were 

both DARPA and NASA components of this Àight program and they are discussed in reference 7.67 and detailed 

in Chapter 5 of this publication.

A more recent SSBJ con¿guration design is discussed in reference 7.38 by Mack and shown in ¿gure 7.95. It is 

noteworthy for its smooth, curved leading edge and its combination Àat-top/ramp F-function de¿nition. Near-¿eld 

experimental pressure data is given for an h/l of 1.36. A sonic boom goal of 0.5 lb/ft2

 was achieved.

A study by Briceno et al. of the Georgia Institute of Technology (ref. 7.68) using a response surface methodology 

produced the optimized design of ¿gure 7.96. The impact of 17 separate con¿gurations, mission, aerodynamics, 

and environmental factors on 13 technologies are evaluated, along with the ability of 1025 separate con¿gurations 

to meet the design goals/constraints. After the aircraft was sized, PBOOM (ref. 7.69) was used to calculate the 

sonic boom signature of the aircraft. For the optimized design initial shock strength of 0.68 lb/ft2

 was calculated 

versus the goal of 0.5 lb/ft2

.

A market study and accompanying environmental assessment were described in a 2003 AIAA paper by Wolz (ref. 

7.70). The resulting Quiet Supersonic Jet (QSJ) con¿guration is shown in ¿gure 7.97 as well as its geometric and 

weight characteristics.

)LJXUH 7KUHHYLHZGHSLFWLRQRIWKH/DQJOH\ORZERRPZLQGWXQQHOPRGHOZLWKODUJHQDFHOOHVUHI

)LJXUH Georgia Tech Design (ref. 7.68).
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

335

In reference 7.70 (p. 8), Wolz concluded that

• The QSJ will be well suited for a multitude of different civil and military missions.

• Establishing and meeting environmental standards for sonic boom, engine exhaust emissions, and 

airport noise are critical.

• Progress must be made to advance aerodynamic, propulsion, and structural system performance. Step 

improvements in all of these areas are needed to achieve the market-driven design requirements of a 

viable QSJ.

Further con¿guration studies by Gulfstream have led to the development of the Quiet Spike, discussed in Chapter 

4 (see ¿gures 4.24 – 4.26) and Chapter 5 (see ¿gure 5.30). This is a retractable nose extension that allows aircraft 

length in supersonic Àight to be longer than would be practical for ground and subsonic operations. The spike 

consists of telescoping sections where the diameters and lengths of the segments are such that the shocks from 

each step do not coalesce, but (when smoothed by atmospheric absorption during propagation to the ground) 

closely approximate an ideal shockless ramp shape. 

Horinouchi of the Japan Aerospace Exploration Agency presented an AIAA paper in 2005 (ref. 7.71) that, in 

many respects, is similar to the study discussed by Wolz in reference 7.70. A mission study for both a supersonic 

business jet and small supersonic transport is described, along with payload and cabin size requirements. Other 

targets are given in table 7.11 below.

7DEOH7DUJHW5HTXLUHPHQWVIRU6XSHUVRQLF%XVLQHVV-HWDQG6PDOO6XSHUVRQLF7UDQVSRUWUHI

Cruise speed Mach 1.8 – 2.2

Range 3,500 nmi (as a minimum)

Payload 2 crew plus 8 passengers

Runway length 7,000 ft

Sonic Boom 0.3 – 0.5 lb/ft2

)LJXUH %DVHOLQH46-FRQ¿JXUDWLRQUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

336

A unique feature of reference 7.71 is its examination of a variable geometry forward swept wing along with a 

cranked arrow wing (see ¿gure 7.98).

Aside from the obvious low-speed advantages of the variable geometry forward swept wing con¿guration, 

reference 7.71 points out a possible sonic boom mitigation advantage as well. Below, ¿gure 7.99 shows the effect 

area development of both cranked arrow and variable geometry forward swept wing con¿gurations, and provides 

evidence of the potential for sonic boom mitigation bene¿ts.

)LJXUH &UDQNHGDUURZDQGYDULDEOHJHRPHWU\IRUZDUGVZHSWZLQJVVWXGLHGLQUHIHUHQFH

)LJXUH 0DFKFXWVIRUVZHSWEDFNDQGIRUZDUGVZHSWZLQJVDGDSWHGIURPUHI

(a) SSBJ-1 cranked arrow wing. (b) SSBJ-2 variable geometry forward-swept wing.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

337

Another paper that examined the virtue of a swept forward wing vis-a-vis that of an aft-swept wing is that of 

Hunton et al. (ref. 7.72). Figure 7.100, from this paper, shows the experiment results for three lift coef¿cients, 

compared to theoretical predictions for both aft-swept and forward-swept wings.

(a) Aft-swept wing.

)LJXUHDZLWKIROORZLQJSDJH Comparison of experimental and theoretical pressure signatures for an 

DIWVZHSWDQGIRUZDUGVZHSWZLQJFRQ¿JXUDWLRQDW0DFKDGDSWHGIURPUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

338

Whitham’s F-function methodology is used in the prediction of the pressure signature including an extrapolation 

procedure due to Hicks and Mendoza (ref. 7.73). The latter does not include the real atmosphere effects on shock 

coalescence as derived by Hayes, Haefeli and Kulsrud (ref. 7.74) or Thomas (ref. 7.16). Overall, the theory and 

experiment agreement at an h/l of 3.6 is good with the best results obtained for the aft-swept wing and the lower 

lift coef¿cients. At an h/l of 130, also shown in ¿gure 7.100, sonic boom signatures for both the Whitham-based 

and extrapolation methods and they yield slightly different results for bow and wing shock strengths and wing 

shock locations. 

(b) Forward-swept wing.

)LJXUHEZLWKSUHYLRXVSDJH Comparison of experimental and theoretical pressure signatures for an 

DIWVZHSWDQGIRUZDUGVZHSWZLQJFRQ¿JXUDWLRQDW0DFKDGDSWHGIURPUHI
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

339

Chapter 7 Summary Remarks

Boom minimization techniques based on Whitham’s F-function are a valuable ¿rst-order tool in the conceptual 

design of low-boom supersonic aircraft. More complex con¿gurations can be studied and boom reduction 

schemes can be utilized by applying the Euler CFD codes with numerical optimization. Several codes have 

been developed that automate the trade studies between boom minimization and performance, and deliver 

signi¿cant design improvements.

Minimization of the boom due to the forward part of a supersonic cruise aircraft is relatively straightforward due 

to the fact that the fuselage and the canopy are the main elements involved. The geometry of these components 

are relative simple and concentrated near the axis of the vehicle. On the other hand, the minimization of the 

aft shock, or boom, is a much more dif¿cult task since the wing volume and lift, the empennage, aft fuselage, 

engines and engine exhaust plumes all contribute. The placement of the engine, and its exhaust plume relative 

to the other components, is critical to obtaining the lowest boom.

A variety of large supersonic commercial transport con¿gurations and, more recently, supersonic business jet 

con¿gurations have been studied over the years. In general, lower boom con¿gurations have been achieved 

when the engines are integrated into the aircraft above the wing. In addition, the lower boom con¿gurations 

tend to have higher drag than high-performance designs.

Chapter 7 References

7.1 Jones, L. B. Lower Bounds for Sonic Bangs. J. Roy. Aeron. Soc. 65, 1-4 (1961).

7.2 Jones, L. B. Lower Bounds for Sonic Bang in the Far-Field. Aeron. Quart. XVIII, Pt. 1, 1-21 (1967).

7.3 Jones, L. B. Lower Bounds for the Pressure Jump of the Bow Shock of a Supersonic Transport. 

The Acoustical Quarterly, Vol. XXI, Feb. 1970.

7.4 McLean, F. E. Some Non-Asymptotic Effects on the Sonic Boom of Large Airplanes. NASA TN D-2877, 

June 1965.

7.5 George, A.R., Lower Bounds for Sonic Booms in the Mid¿eld, AIAA Journal, Vol. 7, No.8, Aug. 1969, pp. 

1542–1545.

7.6 George, A. R. and Seebass, R. Sonic Boom Minimization Including Both Front and Rear Shocks. AIAA J. 

9, 2091-2093 (1971).

7.7 Seebass, R. Minimum Sonic Boom Shock Strengths and Overpressures, Nature 221, 651-653 (1969).

7.8 Seebass, R. and George, A. R. Sonic-Boom Minimization. J. Acoust. Soc. Am., Vol. 51, No. 2 (pt. 3), Feb. 

1972, pp. 686–694.

7.9 Carlson, H. W., Barger, R. L, and Mack, R. J., Application of Sonic-Boom Minimization Concepts in 

Supersonic Transport Design, NASA TN D-7218, June 1973.

7.10 Darden, Christine M. Sonic Boom Minimization with Nose-Bluntness Relaxation. NASA TP 1348, 

Jan. 1979.

7.11 Mack, Robert J. and Darden, Christine M. Wind-Tunnel Investigation of the Validity of a Sonic-BoomMinimization Concept. NASA TP 1421. October 1979.

7.12 Hague, D. S. and Jones, R. T. Application of Multivariate Search Techniques to a Design of Low Sonic 

Boom Overpressure Body Shapes. NASA SP 255, Oct. 1970, pp. 307–323.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

340

7.13 Haglund, George T. High Speed Civil Transport Design for Reduced Sonic Boom. Boeing Doc. No. Do55430, NASA Cont. No. NAS1-18377, (1991).

7.14 Mack, Robert J. and Haglund, George T. A Practical Low-Boom Overpressure Signature Based on 

Minimum Sonic Boom Theory. NASA CP-3173, Vol. II, Feb. 1992, pp. 15 –30.

7.15 Mack, Robert J. Additional F-Functions Useful for Preliminary Design of Shaped Signature, Low-Boom, 

Supersonic-Cruise Aircraft. NASA CP-1999-209699, Dec. 1999, pp. 1–12.

7.16 Thomas, Charles L. Extrapolation of Wind-Tunnel Sonic Boom Signatures without Use of a Whitham 

F-Function. NASA SP 255, 1970, pp. 205–217.

7.17 Hicks, Raymond M. and Thomas, Charles L. A Preliminary Report on Shock Coalescence. NASA SP 255, 

Oct. 1970, pp. 297–305.

7.18 Cheung Samson Design Process of Ames Wind-Tunnel Model 3. NASA CP 10133, Vol. II, 1993, pp. 

95–124.

7.19 Gill, P. E.; Murray, W.; Saunders, M. A.; and Wright, M. H Users Guide for NPSOL (version 4.0) A 

FORTRAN Package for Nonlinear Programing. TR SOL 86-2, Jan. 1986, Dept. of Ops. Res., Stanford 

University.

7.20 Siclari, Michael J. The Analysis and Design of Low Boom Con¿gurations Using CFD and Numerical 

Optimization Techniques. NASA CP-1999-209699, Dec. 1999, pp. 107-128.

7.21 Siclari, M. J. and Fouladi, Kamran A CFD Study of Component Con¿guration Effects on the Sonic Boom 

of Several High-Speed Civil Transport Concepts. NASA CP 10133, Vol. II, May 1993, pp. 227–300.

7.22 Makino, <.; Aoyama, T.; Iwamiya, T.; Watanuki; and Kubota, H. Numerical Optimization of Fuselage 

Geometry to Modify Sonic-Boom Signature. Journal of Aircraft, Vol. 36, No. 4, pp. 668–674.

7.23 Lee, D. K. and Eyi, S. Aerodynamic Design via Optimization. Jour. of Aircraft, Vol. 29, No. 6, 1992, pp. 

1012–1019.

7.24 Nadarajah, Siva K.; Jameson, Antony; and Alonso, Juan J. Sonic Boom Reduction Using an Adjoint 

Method for Wing-Body Con¿gurations in Supersonic Flow. AIAA 2002-5547, Sept. 2002.

7.25 Nadarajah, S. and Jameson, A. A Comparison of the Continuous and Discrete Adjoint Approach to 

Automatic Aerodynamic Optimization. AIAA 2000-0667, Jan. 2000.

7.26 Nadarajah, S.; Jameson, A.; and Alonso, J. An Adjoint Method for the Calculation of Remote Sensitivities 

in Supersonic Flow. AIAA 2002-0261, Jan. 2002.

7.27 Li, Wu; Shields, Elwood; and Le, Daniel Interactive Inverse Design Optimization of Fuselage Shape for 

Low-Boom Supersonic Concepts. Jour. of Aircraft. Vol. 45, No. 4, July–Aug. 2008, pp. 1381–1397.

7.28 Howe, D. Engine Placement of Sonic Boom Mitigation. Gulfstream Aero. Corp. AIAA Paper 2002-0148, 

Jan. 2002.

7.29 Choi, Seongim; Alonso, Juan J.; and Kroo, Ilan M. Multi-Fidelity Design Optimization of Low-Boom 

Supersonic Business Jets. AIAA 2004-4371, Sept. 2004.

7.30 Page, J. A.; Plotkin, K. J.; and Wilmer, C. W. PCBoom Version 6 Technical Reference and User Manual. 

Wyle Research Report WR 09-20, Aug. 2009.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

341

7.31 Mack, Robert J. A Numerical Method for Evaluation and Utilization of Supersonic Nacelle-Wing 

Interference. NASA TN 5057, March 1969.

7.32 Mack, Robert J. Some Consideration of the Integration of Engine Nacelles into Low Boom Aircraft 

Concepts. NASA CP-3173, Vol. II, Feb. 1992, pp. 221–236.

7.33 Morgenstern, John M. Low Sonic Boom Design and Performance of Mach 2.4/1.8 Overland High Speed 

Civil Transport. NASA CP-3173, Vol. II, Feb. 1992, pp. 55–64.

7.34 Mack, Robert J. Wind-Tunnel Overpressure Signatures from a Low-Boom HSCT Concept with AftFuselage-Mounted Engines. NASA CP-1999-209699, Dec. 1999, pp. 59-72.

7.35 Cliff, Susan E. On the Design and Analysis of Low Sonic Boom Con¿gurations. NASA CP 10133, Vol. II, 

May 1993, pp. 37–80.

7.36 Siclari, M. J. Ground Signature Extrapolation of Three-Dimensional Near-Field CFD Prediction for 

Several HCST Con¿gurations. NASA CP 3173, Vol. II, 1992, pp. 175–200.

7.37 Buning, P. G. et al. OVERFLOW User’s Manual, Version 1.8f, NASA Langley Research Center, 1998.

7.38 Mack, Robert J. A Supersonic Business-Jet Concept Designed for Low Sonic Boom. NASA TM 2003-

212435, Oct. 2003.

7.39 Wang, C. J. and Peterson, J. B. Spreading of Supersonic Jets from Axially Symmetric Nozzles. Jet Prop., 

Vol. 28, No. 5, May 1958, pp. 321–328.

7.40 Henson, J. R. and Robertson, J. E. Methods of Approximating Inviscid Jet Boundaries for Highly 

Underexpanded Supersonic Nozzles. AEDC-TDR-62-7 (Contract No. AF-40(6))-800/S/A 24(61-73)) 

Arnold Eng. Dev. Ctr., May 1962.

7.41 Love, Eugene S. An Approximation of the Boundary of a Supersonic Axisymmetric Jet Exhausting into a 

Supersonic Stream. Jour. of Aero. Sci., Vol. 25, No. 2, Feb. 1958, pp. 130–131.

7.42 Putnam, Lawrence E. and Capone, Francis J. Experimental Determination of Equivalent Solid Bodies to 

Represent Jets Exhausting into a Mach 2.20 External Stream. NASA TN D-5553, Dec. 1969.

7.43 Englert, Gerald W. Operational Method of Determining Initial Contour of and Pressure Field about a 

Supersonic Jet. NASA TN D-279, 1960.

7.44 Barger, Raymond L. Comparison of Jet Plume Shape Predictions and Plume InÀuence on Sonic Boom 

Signature. NASA TP 3172, 1992.

7.45 Salas, Manuel D. The Numerical Calculation of Inviscid Plume Flow Fields. AIAA Paper No. 74-523, 

June 1974.

7.46 Englert, Gerald W. and Luidens, Roger W. Wind-Tunnel Technique for Simultaneous Simulation of 

External Flow Field about Nacelle Inlet and Exit Airstreams at Supersonic Speeds. NACA TN 3881, 1957.

7.47 Love, Eugene S. and Grigsby, Carl E. Some Studies of Axisymmetric Free Jets Exhausting from Sonic and 

Supersonic Nozzles into Still Air and into Supersonic Streams. NACA RM L54L31, 1955.

7.48 Cheung, Samson H.; Edwards, Thomas A.; and Lawrence, Scott L. Application of CFD to Sonic Boom 

Near and Mid Flow-Field Prediction. AIAA Paper 90-3999, 1990.

7.49 Siclari, Michael J. and Darden, Christine M. CFD Predictions of the Near-Field Sonic Boom Environment 

for Two Low Boom HSCT Con¿gurations. AIAA Paper 91-1631, 1991.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

342

7.50 Cliff, Susan E. and Thomas, Scott D. Euler/Experiment Correlations of Sonic Boom Pressure Signatures. 

AIAA paper 91-3276, 1991.

7.51 Madson, Michael D. Sonic Boom Predictions for Three Generic Models Using a Solution Adaptive FullPotential Code. AIAA Paper 91-3278, 1991.

7.52 Haglund, George T. HSCT Designs for Reduced Sonic Boom. AIAA paper 91-3103.

7.53 NASA CP 3173, High Speed Research Sonic Boom, Vol. II, Feb. 25–27, 1992.

7.54 NASA CP 10133, High Speed Research Sonic Boom, Vol. II, May 12–14, 1993.

7.55 NASA CP 1999-209699, Dec.1999, High Speed Research 1994 Sonic Boom Workshop.

7.56 NASA CP-1999-209520, 1995 NASA High-Speed Research Program Sonic Boom Workshop, Dec. 1999.

7.57 Cheung, Samson Sonic Boom Softening of Reference-H, NASA CP-1999-209699, Dec. 1999, pp. 89-106.

7.58 Mack, Robert J. Boom Softening and Nacelle Integration on an Arrow-Wing High Speed Civil Transport 

Concept NASA CP-1999-209520, Dec. 1999, pp. 121–137.

7.59 Baize et al. A Performance Assessment of Eight Low Boom, High Speed Civil Transport Concepts. NASA 

CP-1999-209699, Dec. 1999, pp. 149-170.

7.60 Haglund, George T. Potential for Sonic Boom Reduction of the Boeing HSCT. NASA CP-1999-209520, 

Dec. 1999, pp. 96–120.

7.61 Morgenstern, John M. Potential for Sonic Boom Reduction of the 2.4 H5085 Arrow Wing HSCT. NASA 

CP-1999-209520, Dec. 1999, pp. 162–175.

7.62 National Research Council, Commercial Supersonic Technology – The Way Ahead, National Academy 

Press, Washington, DC, 2001.

7.63 Wood, K. D. Aerospace Vehicle Design, Vol. I, Aircraft Design. Johnson Publishing, Co., Boulder, CO, 

1963, pp. 41–61.

7.64 Maglieri, Domenic J. Compilation and Review of Supersonic Business Jet Studies from 1963 through 

1995. NASA CR 2011-217144, May 2011.

7.65 Wlezien, R. and Veitch, L. Quiet Supersonic Platform Program. AIAA Paper 2002-0143. Jan. 2002.

7.66 Komadina, Steve and Drake, Aaron Development of a Quiet Supersonic Aircraft with Technology 

Applications to Military and Civil Aircraft. AIAA Paper 2001-0519, Jan. 2002.

7.67 Pawlowski, Joseph W.; Graham, David H.; Boccadero, Charles H.; Coen, Peter G.; and Maglieri, Domenic 

J. Origins and Overview of a Shaped Sonic Boom Demonstration Program. AIAA 2005-0005, Jan. 2005. 

7.68 Briceno, Simon I.; Buonan, Michael A.; Fernandez, Ishmael; and Mavris, Dimitri A Parametric Exploration 

of Supersonic Business Jet Concepts Utilizing Response Surfaces. AIAA Paper 2002-5828, Oct. 2002.

7.69 Coen, Peter Development of a Computer Technique for the Prediction of Transport Aircraft Flight Pro¿le 

Sonic Boom Signatures. Master’s Thesis. GWU, 1991.

7.70 Wolz, R. A Summary of Recent Supersonic Vehicle Studies at Gulfstream Aerospace. AIAA 2003-0558, 

Jan. 2003.

7.71 Horinouchi, Shigeru Conceptual Design of a Low Sonic Boom SSBJ. AIAA 2005-1018, Jan. 2005.
Chapter 7 6RQLF%RRP0LQLPL]DWLRQIRU9DULRXV$HURG\QDPLF&RQ¿JXUDWLRQV

343

7.72 Hunton, Lynn W.; Hicks, Raymond M.; and Mendoza, Joel P. Some Effects of Wing Planform on Sonic 

Boom. NASA TN D-7160, 1973.

7.73 Hicks, Raymond M. and Mendoza, Joel P. Prediction of Aircraft Sonic Boom Characteristics from 

Experimental Near Field Results. NASA TM X-1477, 1967.

7.74 Hayes, W. D.; Haefeli, R. C.; and Kulsrud, H. E. Sonic Boom Propagation in a Strati¿ed Atmosphere, with 

Computer Program. NASA CR-1299, 1969.

Chapter 8 Response to Sonic Booms

345

CHAPTER 8 RESPONSE TO SONIC BOOMS

This chapter begins with a description of the factors involved in boom exposure, including both human and 

building response. Outdoor and indoor stimuli include audible, vibratory, and visual cues. A discussion of damage 

complaints, relative to primary and secondary structural members, is given as a function of the range of boom 

exposure levels. Human response to booms includes startle, rattle, annoyance, effects on sleep, and long-term 

effects on health. Other effects of sonic booms are addressed including those on animals, terrain (avalanches and 

landslides), and other aircraft.

Factors Involved in Sonic Boom Exposures

There is considerable concern about the manner in which people and structures respond to sonic booms and 

how such responses will affect the acceptance of overland supersonic operations. The nature of the sonic boom 

response problem is illustrated in ¿gure 8.1 (ref. 8.1). The sketch at the top of the ¿gure suggests two different 

situations for people. In one case, the person is outdoors and is directly exposed to the shock waves. In the other 

case, the shock waves impinge on the building with the person inside the building. The building then acts as a 

¿lter that establishes the nature of the stimuli reaching the inside observer. The ingredients of this indoor exposure 

situation are included in the chain diagram at the bottom of the ¿gure. The sonic-boom-induced excitation, which 

causes the building to vibrate, may arrive either through the air or through the ground. It is generally conceded 

that the air path is the more signi¿cant one in most cases and is thus designated the primary path on the ¿gure. The 

ground transmission path is considered secondary and has not been found to be signi¿cant. Building vibrations 

can be perceived directly by the observer either through direct contact with the structure or visually, particularly 

in the case of window vibrations. A person may also observe vibration-induced noise, for example rattling of 

windows or, in the extreme case, associated super¿cial damage of the structure.

Loading on Buildings

A building is subjected to a variety of loading effects when a sonic boom wave pattern sweeps over it as illustrated 

in ¿gure 8.2 (ref. 8.1). Shown schematically at the top of the ¿gure is the N-wave pressure signature on the ground 

from a full-size N-wave supersonic transport. The pressure loading on the building, as the N-wave sweeps over 

it, at positions 1, 2, 3, and 4 is illustrated at the bottom half of the ¿gure.

Figure 8.1. Factors involved in sonic boom exposures (adapted from ref. 8.1).
Chapter 8 Response to Sonic Booms

When the boom signature is at Position 1, the building would ¿rst be forced laterally as a result of the initial 

positive pressure loading on the front surface. Then, as the boom signature moves over the building (Position 2), 

it would then be forced inward from all directions, then pulled outward as the signature moves over it (Position 

3) and ¿nally displaced laterally again (Position 4) because of the negative pressures acting on the back surface. 

These loadings, which would be applied within a time period of about 0.1 to 0.3 second, can result in complex 

transient vibrations of the building.

The response of the structure will also depend upon the shape of the signature. Insight can be obtained through 

a simpli¿ed analysis that represents a building as a single degree of freedom, a spring mass system. A measure 

of structural response to transient inputs is the Dynamic Ampli¿cation Factor (DAF), which is the ratio of the 

maximum dynamic displacement to the displacement due to a static force (ref. 8.2). The higher the DAF, the 

greater the response of the structure to the transient input (the boom signature in this case). Figure 8.3 (refs. 8.2 

and 8.3) illustrates the inÀuence of signature shape on the DAF.

346

Figure 8.2. Factors involved in sonic boom exposures (adapted from ref. 8.1).

Figure 8.3. ,QÀXHQFHRIVRQLFERRPVKDSHRQG\QDPLFDPSOL¿FDWLRQIDFWRUDGDSWHGIURPUHIVDQG
Chapter 8 Response to Sonic Booms

347

Shown are the calculated DAFs on an undamped system plotted against the ratio of the duration of the signature, 

T, to the period of the oscillation 2ʌ/Ȧo

 for four signature shapes that include an N-wave; a half-cosine wave, 

which is similar to a Àattop signature; a triangular wave, which is representative of a ¿nite rise time signature; and 

a sine wave. All signatures have the same maximum overpressure and duration.

The following discussion applies when the duration of the signature is roughly equal to the natural period of 

oscillation. It should also be noted that the effect of signature shape on complex buildings is more subtle (ref. 

8.4 and 8.5) than the single degree of freedom analysis of ¿gure 8.3. In this ¿gure, the minimum value of 2.0 

of the DAF is associated with the N-wave and the maximum value of about 3.0 is associated with the sine wave 

signature. This ¿nding would be expected since the structure has inertia and would take some time to respond 

to the N-wave. On the other hand, since the sine wave signature loading begins gradually, the structure will 

be driven more ef¿ciently. The DAF curve for the ¿nite rise time signature will increase as rise time increases 

and eventually reach the sine wave value. The half cosine (Àat-top) signature curve gives a DAF about midway 

between the N-wave and sine wave. The majority of the sonic boom database relating to structural response is for 

N-wave type signatures of overpressures of greater than 1.0 lb/ft2

. Experimental data and analysis for N-wave and 

shaped signatures in the overpressure range of from about 0.2 lb/ft2

 to about 1.4 lbs/ft2 provide considerably more 

insight into this question and will be discussed later in the next section.

The interaction of the structural components of the building as a result of the loading events is signi¿cant to the 

response of people indoors. The measured modal response of the Àoor, walls, and rooms of a two-story residencetype structure is presented in ¿gure 8.4 (ref. 8.1). In the case illustrated for Àoor vibrations, it can be seen that a 

preferred phase relationship exists because of the manner in which interior wall structures are arranged. In regard 

to the wall structure, it was found that the panels between the vertical studs vibrated in a preferred manner such as 

that shown in the bottom left hand of the ¿gure. Higher panel mode frequencies were also noted to exist and to be 

important. The sketch on the right-hand side of the ¿gure suggests an interaction of the structure of the building 

and the enclosed air cavities within the rooms and attic spaces.

Sonic Boom Stimuli

Inside the building, a person is exposed to a rather complex series of stimuli, including auditory, visual, and 

vibratory inputs. The nature of the auditory and vibratory inputs is illustrated in ¿gure 8.5 (ref. 8.1). The top trace 

is the measured outdoor pressure time history. This signature is of the N-wave type, but it differs slightly from an 

N-wave in some of its details, as do many of the boom signatures measured outdoors as a result of atmospheric 

inÀuences. The three bottom traces represent corresponding indoor exposure stimuli. The topmost of these traces 

represents the pressure variation inside the building owing to vibratory motions of the building and the cavity 

resonances. Although this is a pressure disturbance, it generally occurs in a frequency range that is not audible to 

Figure 8.4. 0HDVXUHGPRGDOUHVSRQVHVIRUDWZRVWRU\UHVLGHQFHW\SHVWUXFWXUHUHI
Chapter 8 Response to Sonic Booms

humans. The audible portion of this signal, as measured with a separate microphone system, has the characteristic 

shape of the middle trace and is an order of magnitude lower in amplitude. The audible portion of the pressure 

signal is associated with the rattling of the building structure and furnishings. Finally, the bottom trace represents 

the vibration of the Àoor that would be sensed by a person either directly or through the furniture. A person 

indoors, therefore, can be inÀuenced because of an auditory, vibratory, or visual cue such as the movement of 

bric-a-brac on shelves and window movement. The indoor exposure situation is not understood well enough to 

permit the relative importance of each of these stimuli to be determined, although it was believed that in certain 

situations each one is signi¿cant. Presently, it is understood that the indoor pressure signature is composed of two 

parts, one due to the transmission of the boom and the other due to secondary sources such as rattles, squeaks, etc. 

Both parts are audible and their ratio depends on the characteristics of the structure.

Human and building response is directly related to the frequency spectrum of the sonic boom signature. This is 

illustrated in ¿gure 8.6, which shows the effect of boom signature time duration on the energy spectra of two sonic 

boom N-waves having the same overpressures but differing markedly in their time duration. The frequency ranges 

that are most important for human outdoor response and building response are indicated. It should be noted that 

these spectra result from N-waves with instantaneous (zero) shock rise times.

348

Figure 8.5. Outside and inside exposure stimuli due to sonic booms (ref. 8.1).

Figure 8.6. (IIHFWVRIWLPHGXUDWLRQRQWKHHQHUJ\VSHFWUDRIVRQLFERRP1ZDYHVDQGWKHLU

VLJQL¿FDQFHUHJDUGLQJUHVSRQVHVDGDSWHGIURPUHI
Chapter 8 Response to Sonic Booms

349

Relative amplitudes of the component frequencies are shown in ¿gure 8.6 by means of the spectrum envelope 

curves. Data for the short-duration wave from a small vehicle are shown by the curve of short dashes and those 

for the long-duration wave from an SST size vehicle are indicated by the solid curve. Although not shown in the 

¿gure, these spectrum envelopes continue out to higher frequencies. It is important to note that in each case the 

curves are tangent to a 6 dB per octave line that serves as a spectrum envelope for both waves. Examination of the 

¿gure shows that the relative amplitudes of the high frequency components from about 30 Hz - 1000 Hz are the 

same for the two signatures, which vary markedly in time duration. It is thus suggested that the human responses 

for outside exposure would be approximately the same from an overÀight of a 350-foot SST size vehicle or a 

small vehicle. On the other hand, the low frequency components of the two signatures, which inÀuence building 

response, vary markedly as a function of time duration. In particular, the low-frequency amplitudes from about 

1 Hz - 20 Hz are considerably greater for an SST size vehicle boom signature of longer time duration. This result 

suggests that structural components having low vibration frequencies (e.g., larger building structures) would be 

excited by the SST size vehicle signature of longer duration and would not be signi¿cantly inÀuenced by the much 

smaller vehicle’s signature.

As indicated earlier, N-wave signatures having large rise times (IJ) and of the same amplitude (ǻp) and duration 

(ǻ T) as a zero rise time N-wave will reduce outdoor, indoor, and building response because their spectral content 

is much reduced compared to that of an N-wave. This is illustrated with the aid of ¿gure 8.7 (from ref. 8.4), 

which presents the envelopes of three frequency spectra (1) one for a symmetrical N-wave of zero rise time, (2) 

the second for a symmetrical N-wave with an 8 msec rise time, and (3) the third for a symmetrical delayed ramp 

signature having an 8 msec rise to 0.5 lb/ft2

 followed by a 35 msec rise to 1.0 lb/ft2. All three signatures have 

maximum boom levels (ǻp) of 1.0 lb/ft2

 and a total duration (ǻT) of 350 msec.

It is evident that all three spectra peak in the sub-audible range of about 3 Hz (approximately the reciprocal of the 

signature period) and the levels decrease with frequency above this value. As previously mentioned for the ideal 

N-wave of zero rise time (¿gure 8.6), the decay is 6dB/octave. The N-wave with 8 msec rise time has an initial 

decay of 6dB/octave that transitions to 12 db/octave at a frequency determined by the rise time (40 Hz for this 

example). Note the signi¿cant decrease in amplitude with frequency for the 8 msec rise time N-wave as compared 

to the zero rise time N-wave. For the delayed ramp signature with an 8 msec rise time on the initial shock, the 

spectrum shape is similar to the 8 msec N-wave spectrum but with a reduced amplitude of 6 dB due to the initial 

shock strength being 0.5 lb/ft2

 rather than 1.0 for the N-wave. Since the human ear is very sensitive to the higher 

frequencies, it follows that signatures with increased rise times will be more acceptable outdoors than zero rise 

time N-waves. Indoor response would also be expected to be more acceptable as a result of reduced building 

response associated with the reduced amplitudes at the lower frequencies for the shaped signatures. However, 

since shaped signatures were shown to increase the dynamic ampli¿cation factor (see ¿g. 8.3) over that predicted 

for an N-wave the bene¿ts may be offset. An analytical study (ref. 8.5) on the effect of sonic boom shaping on 

booms heard indoors suggests otherwise and will be discussed later in the next section.

ǻS= 1.0 lb/ft2, 

ǻ7= 350 msec

Figure 8.7. )UHTXHQF\VSHFWUDRIV\PPHWULFDOVRQLFERRPVLJQDWXUHVDGDSWHGIURPUHIVDQG
Chapter 8 Response to Sonic Booms

Structural Response

The relation between sonic booms and damage has the same complexity as the relation between sonic booms 

and structural response: a rigorous relationship depends on the frequency content of the boom and the frequency 

response of the structure. A practical, simple measure of the boom (for correlation with damage) would be the 

energy content in frequencies around the fundamental response frequency of structures, since this is where the 

greatest response occurs (refs. 8.6 and 8.7). For this reason, boom impulses, the area under the positive phase of 

the signature, as well as peak overpressures, are often reported. The fundamental frequency response of single 

frame residential buildings is typically 10 to 30 Hz (ref. 8.8). For the boom signature shown in ¿gure 8.7, the 

energy spectral density at the dominant frequency of about 3 Hz is proportional to the overpressure times duration 

squared (ref. 8.9). Thus, boom impulse might be a reasonable estimation of structural response (refs. 8.10 and 

8.11).

The vast majority of experience with sonic booms has been with N-waves of about 100 to 300 msec in duration. 

Usually only the overpressure has been reported or correlated with damage. One would, however, expect the 

relation between impulse, spectra, and overpressure to be fairly consistent for booms of such similar shapes 

(N-waves). As will be shown later in this section, care must be taken when these data associated with N-wave 

signatures are applied to signi¿cantly different types of boom signatures. However, these correlations of boom 

damage with overpressure are self-consistent and well worth examining.

Damage Complaints

Experience has shown that supersonic Àights over communities have resulted in complaints regarding damage 

caused by sonic booms. The nature of the reported damage is fairly well represented in ¿gure 8.8, which shows 

the percent of complaints with which certain types of damage are mentioned (ref. 8.12). Plaster cracks, the type of 

damage reported most frequently, are mentioned in 43 percent of the complaints. Other reported damage includes 

cracks in window glass, walls, and tile. Structures reportedly damaged by sonic booms are mostly brittle surfaces 

and are secondary structural components. 

Induced Damage

The majority of damage surveys have included all complaints made during the period of overÀight, regardless 

of whether the damage was actually caused by sonic booms. During the St. Louis studies (ref. 8.12), wherein 

about 10 booms per month over a 7-month period were experienced, prompt investigations of the alleged damage 

350

Figure 8.8. Sonic boom damage complaints (ref. 8.12).
Chapter 8 Response to Sonic Booms

351

by architectural and engineering personnel indicated that only about 20 percent of the reported damage was 

considered likely to have been caused by a sonic boom. The remaining damage was considered to be due to 

natural causes, such as changes due to temperature, humidity, and aging. The results of such an engineering 

investigation are given in ¿gure 8.9 (ref. 8.1). The overpressure range is indicated on the horizontal scale and 

the number of valid damage incidents per Àight per million people is shown on the vertical scale. The four bars 

indicate the number of damage incidents associated with four different exposure areas (varying lateral distance 

from the ground track from 0 to 18 miles) for which the ranges of overpressure are indicated. It is obvious that 

the higher rate of occurrence was associated with the higher range of overpressures experienced at locations on 

or near the aircraft ground track. It may be signi¿cant that no damage incidents occurred for exposures below 

about 0.8 lb/ft2

 at the furthest lateral region, although it should be noted that a smaller number of data samples 

was available in this range. It is also important to note that the boom signature shapes at these lateral locations, 

in addition to having lower overpressures, can also have different frequency spectra due to increased shock rise 

times than those on or near the ground track.

Damage Studies

In this section, brief summaries of the activities and ¿ndings regarding damage studies relating to plaster cracking, 

window breakage, and wall accelerations of conventional structures associated with N-wave sonic boom signatures 

will be presented. Some discussion will also be presented that addresses damage to buildings that are irreplaceable 

because of their historic nature.

In 1998, the USAF funded Haber and Nakaki (ref. 8.13) to review sonic boom damage to conventional structures. 

Concern regarding sonic boom damage to unconventional structures was also an important issue for the USAF and 

resulted in the summary work of Sutherland, Brown, and Goerner (ref. 8.14). In their assessment, unconventional 

structures involved historic national monuments or archaeological structures, Indian caves with ancient petroglyph 

drawings, older historic buildings, wells or large open water tanks, and radio telescopes/antenna. Ref. 8.14 contains 

a bibliography for the response of unconventional structures to sonic boom. Haber et al (ref. 8.15) describe the 

creation of a comprehensive database of the literature on the response of structures to noise and sonic boom. That 

database was incorporated into an archive denoted “International Bibliography On Noise” (IBON). IBON was not 

maintained and is no longer available.

Plaster Cracking

Archival information on the cracking of plaster has been documented from extensive building vibration studies 

made in connection with quarry blast operations (ref. 8.16). These 1942 data, summarized in ¿gure 8.10 (ref. 

8.17) as measured ceiling displacements versus response frequency, are still relevant today even though building 

designs, construction, and material have changed.

Figure 8.9. Sonic boom induced damage incidents for various overpressure ranges (adapted from ref. 8.1).
Chapter 8 Response to Sonic Booms

The envelope of the cross-hatched region encompasses the data points for which some plaster damage occurred 

during several building vibration tests. Associated 1-g and 0.1-g acceleration lines are shown for reference. The 

envelope indicates that the lowest amplitude at which damage occurs falls off as frequency increases and seems 

to follow roughly a constant acceleration line. Experience with buildings exposed to quarry blasting for which 

the acceleration amplitudes did not exceed 0.1 g resulted in no observable damage. The data points shown on 

the ¿gure correspond to observations made during several sonic boom Àight test programs and are associated 

with conditions of no observable damage. The limited sonic boom results are roughly consistent with the above 

vibration studies. The quarry blast vibration tests also produced many data points for which no damage occurred 

in the frequency range 5 to 40 Hz and at displacement amplitudes up to 0.3 inch. De¿nitive data on plaster damage 

are dif¿cult to evaluate because of the many contributing factors such as variations in design, construction method, 

state of repair, environment, etc. (refs. 8.7 and 8.16). Approximately 40 such contributing factors relating to wall 

and ceiling cracks are listed in ref. 8.16.

The 1964-65 White Sands sonic boom overÀights provided additional data regarding the cumulative crack length 

of plaster on wood lath in a two-story structure that occurred over a period of about 3 weeks of testing (ref. 8.18). 

Results are presented in ¿gure 8.11 (taken from reference 8.2). Two curves are shown, one indicating the crack 

length growth for the no boom case and one associated with exposures to sonic booms. For the sonic boom case, 

nominal overpressures of 5 lbs/ft2

 were imposed the ¿rst 20 days and then increased in 2 lbs/ft2 increments each 

day up to a maximum of 19 lbs/ft2

.

352

Figure 8.10. 6XPPDU\RIUHVXOWVIURPSODVWHUYLEUDWLRQWHVWVUHI

Figure 8.11. &XPXODWLYHFUDFNOHQJWKRISODVWHURQZRRGODWKREVHUYHGGXULQJVRQLFERRPWHVWVUHI
Chapter 8 Response to Sonic Booms

353

For the no boom case (upper curve), two slopes are noted. The greater slope was attributed to the sizable changes 

in temperature between daytime and nighttime. The lower curve, representing the boom case, has two slopes 

also. The lesser slope almost parallels the no-boom case. However, after about 22 days of boom exposure, when 

the boom levels increase, the slope of the curve increases more rapidly than for the non-boom case. The authors 

concluded that for the two-story structure tested, the sonic booms caused damage when their level became greater 

than 11 lbs/ft2

.

In the early 1990 time period, the USAF funded a large-scale experimental and analytical effort on cumulative 

plaster damage (ref. 8.19). In these tests, full-scale plaster walls (8 ft by 10 ft) were subjected to many thousands 

of simulated booms of overpressures ranging from about 2 lbs/ft2

 to 20 lbs/ft2. Three walls, including ¿xtures to 

simulate the boundary conditions that would exist in the actual structure of the ceiling, roof, and sidewalls were 

tested. Two were designated strong plaster wall and one weak plaster wall. Some of the results of these tests by 

Haber (ref. 8.20) are presented in ¿gures 8.12 and 8.13.

Figure 8.12. 7RWDOFUDFNOHQJWKLQVWURQJSODVWHUZDOOYHUVXVQXPEHURIVLPXODWHGERRPVUHI

Figure 8.13. 1XPEHURIFUDFNVLQZHDNSODVWHUZDOOYHUVXVQXPEHURIERRPVUHI
Chapter 8 Response to Sonic Booms

Total crack length versus number of simulated booms for the strong plaster wall is given in ¿gure 8.12. Two 

curves are shown, both for observations of cracks above the window, with the lower curve designating major 

cracks and the upper curve designating all cracks except major ones. The tests consisted of 5000 simulated 20 lbs/

ft2

 N-wave booms followed by 5000 booms of 1.8 lbs/ft2.

Both curves show that crack length increases as the number of booms increases, with major cracks being initiated 

after some 200 booms and increase rapidly with increasing number of booms to a break point at about 1000 

booms. At this point, the data fall in a horizontal line indicating no further damage.

A plot of the number of cracks versus number of booms for the weak plaster wall is given in ¿gure 8.13 (from ref. 

8.20). Four damage levels were de¿ned to include tiny, slight, moderate, and large. For these tests, the test article 

wall was subjected to three sequences of 5000 simulated booms of 20 lbs/ft2

. The upper curve shows the number 

of observable cracks, regardless of size, and reaches a maximum of 25 after 5,000 booms. The other curves on the 

¿gure illustrate the number of cracks of various sizes. It is apparent that less than ¿ve cracks were observed with 

a size greater than tiny.

The key results of this study, as stated by the author of reference 8.20 (pp. 6-7), are as follows:

 1. In the absence of stress raisers, pre-existing stresses, or pre-existing damage, no evidence was found 

 for sonic boom damage at overpressures up to 20 lbs/ft2

.

 2. Sonic booms or blast loads do cause progressive damage to plaster walls.

 3. Sonic booms can produce cumulative damage given the right combinations of pre-existing stress and 

 damage.

 4. Damage to plaster from sonic booms is a result of the combined stresses introduced by the sonic 

 booms together with environmental stresses.

As noted by Haber (ref. 8.20, p. 1):

 Three concepts of cumulative damage are found in the literature: (1) any progressive damage from repeated

 sonic booms; (2) sonic boom damage in excess of that produced by environmental factors; and (3) sonic 

boom damage from repeated booms at an increasing damage rate.

Previous studies also established that plaster crack extensions can occur under repetitive sonic boom loads.

As revealed by Haber (ref. 8.20, p.7), the present experimental study indicated that the sonic boom contribution

to plaster damage occurs in three ways:

• Plaster that has been damaged by water or other factors may be weaker than well-maintained, properly 

constructed plaster. Sonic booms are one of many factors that may generate stress levels that can damage 

weakened plaster.

• Other natural and manmade forces may raise existing stress levels within plaster. Sonic booms may then 

act as a triggering mechanism for plaster failure.

• Plaster stress levels may be raised by other factors. The sonic boom levels may not be suf¿cient by 

themselves to trigger damage. They may, however, subject the plaster to fatigue cycles so that failure 

occurs when combined with pre-stresses and other cyclic stressors.

Window Breakage

Concern for glass window damage has existed long before the sonic boom issue came into being. In a 1964 paper 

by McKinley (ref. 8.21), it was noted that when a window pane has been abraded to the point of obscurity by 

weathering and diligent housekeeping, its strength to a uniform load is reduced to about half its original value. 

354
Chapter 8 Response to Sonic Booms

355

Table 8.1 (ref. 8.21) indicates that it requires a loading of some 3000 lbs/in2 to 30,000 lbs/in2, depending on the 

type of loading and glass, to break large panes of glass.

Table 8.1. The Relationship of Load to Breaking Strength of Glass (ref. 8.21)

Typical Breaking Strength of Large Panes

 (Normal Surface Quality, As Glazed), lbs/in.2

Type of Loading Approx. Load 

Duration

Regular

Plate Glass

Regular

Window Glass

Heat Strengthened

Fully Tempered 

(Herculite)

Sonic booms, 

blastsa 0.1 sec 6000 6600 15,000 30,000

Wind gusts 5-10 sec 5500 6050 13,750 27,500

Fastest mile 

windb 1 min 4000 4400 10,000 20,000

Long-term 2 hours, inde¿-

nite 3000 3300 7500 15,000

a

 The complex nature of these loads requires special engineering study when design criteria are to be established.

b

 The term “fastest mile” denotes the average wind velocity over a 1-min period.

McKinley goes on to say that state and local building codes require glass of suf¿cient strength to resist wind loads 

to which outdoor walls are exposed. Figure 8.14, taken from reference 8.21, shows the recommended thickness 

of polished glass to meet wind load requirements.

The author points out that wind direction, local terrain, building geometry, and the position of the window in a 

facade may have considerable inÀuence on the effective pressure to which glass in a particular opening may be 

exposed.

Note: Solid lines are recommendations 

based on minimum thickness. Normal 

surface depreciation is taken into 

consideration. Shading suggests the 

possible performance of glass with newly 

formed surfaces. Velocities are averages 

for a 1-minute period. Support deÀection 

not more than 1/175 of span at design 

load. Four edges glazed weather tight.

Figure 8.14. 5HFRPPHQGHGWKLFNQHVVRISROLVKHGSODWHJODVVWRPHHWZLQGORDGUHTXLUHPHQWV±IRXUVLGHVVXSSRUWHG

VKRUWVLGHORQJVLGHQRWOHVVWKDQUHI
Chapter 8 Response to Sonic Booms

The 1960 USAF-NASA Project Little Boom Àight-test experiments (ref. 8.22) included a study of window 

damage resulting from sonic booms of from about 5 lbs/ft2

 to 94 lbs/ft2 overpressure and the ¿ndings are reported 

by Maglieri, Huckel, and Parrott (ref. 8.22) and Parrott (ref. 8.23). A series of test windows of plain and colonial 

style, most mounted in cubicles but some standing alone, were oriented under and lateral to the aircraft ground 

track. Some of the plain windows were tested statically and the results are given in ¿gure 8.15 (refs. 8.22 and 

8.23). The open symbols represent the typical behavior of a plain window. The solid symbols represent window 

failures that occurred in the 140 to 160 lbs/ft2

 range.

The results of similar tests on the colonial style windows resulted in considerably larger deÀections for the same 

applied static pressure and the static breaking loads were about half that for plain windows. It was found that the 

wood mullions cracked before the glass failed. During the Àight test program, 214 test windows were exposed 

to a range of sonic boom overpressures produced by two different aircraft (F-104 and F-105). The results are 

presented in ¿gure 8.16 (refs. 8.22 and 8.23).

356

Figure 8.15. 0D[LPXPZLQGRZGHÀHFWLRQDVVWDWLFSUHVVXUHORDGLQJLVLQFUHDVHGWRZLQGRZIDLOXUHLQGLFDWHGE\

VROLGV\PEROV (refs. 8.22 and 8.23).

Figure 8.16. 6XPPDU\RIUHVXOWVIURPZLQGRZEUHDNDJHWHVWVUHIVDQG
Chapter 8 Response to Sonic Booms

357

More windows were damaged by airplane A, a Lockheed F-104 Star¿ghter, than for airplane B, a Republic F-105 

Thunderchief, and no window damage occurred for airplane B at boom levels below 40 lbs/ft2

. While it appears 

that no damage occurred below an overpressure of 20 lbs/ft2

, it is to be noted that no windows were exposed to 

airplane A at boom levels below 20 lbs/ft2

.

The ability of airplane A to cause more damage at equal overpressures can be traced to a detail in the pressure 

signatures; namely the duration of the initial positive overpressure (referred to earlier as the positive impulse), 

which is somewhat greater than that for airplane B. Consequently, an attempt was made to correlate the available 

experimental glass breakage data for plain windows with the detailed characteristics of the initial positive phase 

of the pressure signature. These results are given in ¿gure 8.17 (refs. 8.22, 8.23, 8.7, and 8.2).

The ordinate represents a normalized loading parameter, where (a) and (t) are the window longest dimensions and 

glass thickness, respectively, and ǻp the peak overpressure. The abscissa represents the duration of the positive 

phase of the boom signature (Ș) times the natural frequency of the window Ȧo

. A damage boundary, taken from 

reference 8.7, is also shown. The solid symbols represent about 50 incidents of window glass breakage due to 

sonic booms from the low altitude tests.

It is to be noted that all but one of the damage data points for these square windows fall in the theoretical damage 

region. The only damage point to fall below the curve is associated with the 1959 sonic boom tests at Wallops 

Island, Va. (ref. 8.24), where a large plate glass store-front window was cracked at its lower left corner after a 

boom level of about 1.75 lbs/ft2

. This window, however, was believed to be pre-stressed in its mounting and made 

it vulnerable to damage from several loading inputs. 

Hershey, Higgins, and Magrab (ref. 8.25) addressed the question of sonic boom glass breakage by posing a design 

question. As stated in reference 8.25 (p. 1009), the authors asked “what is the probability that a load having a 

certain statistical variation will cause a material having strength that varies in another statistical manner to fail"” 

They developed a response probability density function technique in a statistical model to estimate probability of 

glass breakage from sonic booms as a function of nominal boom levels and duration, aircraft Àight path, window 

size, and whether the glass was in good condition or cracked. It was estimated that there would be 1.1 breaks per 

million panes in good condition boomed at a nominal overpressure of 1 lb/ft2

. The author’s noted that this agreed 

well with sonic boom claim data of 0.6 breaks per million panes boomed (ref. 8.25, p.1009).

Based on these ¿ndings, one can assume that window damage is generally predictable based on loading and 

structural information. It would also appear that damage to windows that are properly installed and well mounted 

Figure 8.17. 6XPPDU\RIZLQGRZJODVVEUHDNDJHGXHWRVRQLFERRPVUHIVDQG
Chapter 8 Response to Sonic Booms

would not be expected from sonic booms resulting from normal high altitude supersonic Àights. However, 

window breakage has occurred and will continue to occur, even at relatively low-boom levels (e.g., see ref. 

8.15) due mostly to improper installation, weathering, aging, and previous cracking. In the same manner, glass 

of insuf¿cient strength is weeded out to some degree by windstorms whenever they occur (McKinley, ref. 8.21). 

It should be expected that windows that are in disrepair or improperly installed will be weeded out as a result of 

sonic booms from supersonic operations overland.

Wall Damage

The peak values of measured stresses in a vertical stud due to various types of loading have been measured and 

the positive or negative value, whichever is higher, is plotted as stress versus peak overpressure in ¿gure 8.18 

(ref. 8.17).

Peak stress values are shown for sonic boom overpressures from 0.3 lb/ft2

 to about 3 lbs/ft2, and the maximum 

stress is about 60 lbs/in2

. This is small compared to the design load stresses for the building and is of the same order 

of magnitude as the stress induced by such a common occurrence as a door closing. Also shown for comparison 

with this ¿gure are data from explosive charges and rocket noise loadings. For extrapolated comparable peak 

overpressures for sonic booms, the stress response is somewhat lower for the explosive loading than for the sonic 

boom loading. The responses due to rocket engine noise at comparable peak pressures are markedly lower than 

those for the sonic boom. This is probably because most of the acoustic energy in the noise from the rocket was 

at frequencies above the natural frequency of the building components. Such results as those in ¿gure 8.18 would 

suggest that there should be no concern for damage to primary structures due to sonic boom pressure loadings in 

the range shown.

During the National Sonic Boom Program (ref. 8.26), peak acceleration amplitudes resulting from sonic booms 

associated with the F-104, B-58, and XB-70 aircraft were measured on a one-story residence structure and are 

presented as a function of overpressure in ¿gure 8.19 (ref. 8.1).

358

Figure 8.18. Peak vertical stud stresses as a function of peak overpressure for 

YDULRXVW\SHVRIH[FLWDWLRQUHI
Chapter 8 Response to Sonic Booms

359

The acceleration amplitudes are either positive or negative whichever is the largest for a particular test. The sonic 

boom outdoor overpressure value is the average of outdoor ground overpressures measured for that particular 

Àight by an array of ¿ve microphones spaced 100 feet apart. Data were obtained from overhead Àights and from 

Àights displaced about 5 miles laterally. The horizontal cross-hatched line at the top of the ¿gure represents the 

1.0 g structural damage line shown in ¿gure 8.10. It can be seen that acceleration amplitudes vary from about 

0.1 g to about 0.7 g and that despite considerable scatter there is a general trend of increased wall acceleration 

level with increased overpressure. There seems to be no signi¿cant difference between overhead and lateral data 

points. There is thus the suggestion that the possible differences in wave angle and signature rise time due to 

the offset distance were not signi¿cant with regard to this particular measurement of building response. For the 

residence-type structure of the test, the dominant vibration responses were in a frequency range such that similar 

acceleration amplitudes were measured for both small, medium and large aircraft even though their signature 

durations ranged from 100 msec to 300 msec.

It is interesting to observe that if one were to extrapolate a line through the data set until it intersects the 1-g 

structural damage line, the resulting overpressure would be about 10 lbs/ft2

. As suggested by Clarkson and Mayes 

(ref. 8.2) and based on the extensive series of overÀight tests, building structures in good repair should not be 

damaged at boom overpressures less than about 11 lbs/ft2

. Clarkson and Mayes also recognized that considerable 

loading variability occurs owing to atmospheric effects, and the residual strength of the structure varies according 

to usage and natural causes. The extreme statistical data required to predict the probability of damage to residential, 

commercial, and historical buildings are not available and cannot be obtained in a laboratory or limited overÀight 

program.

Another perspective on the acceleration levels shown in ¿gure 8.19 is presented in ¿gure 8.20 (ref. 8.2) where 

they are compared with those experimentally determined (ref. 8.27) for other common events.

Figure 8.19. Maximum building wall acceleration amplitudes as a function of overpressure for 

WKUHHGLIIHUHQWDLUSODQHVUHI

Figure 8.20. 0D[LPXPZDOODFFHOHUDWLRQLQGXFHGE\YDULRXVGLVWXUEDQFHVUHI).
Chapter 8 Response to Sonic Booms

In ¿gure 8.20, the ranges of measured wall acceleration for a sonic boom, subsonic aircraft, ground transportation, 

and miscellaneous household activities are represented by the vertical bars. The transient acceleration for a 2 lbs/

ft2 sonic boom overpressure is seen to exceed those observed for subsonic aircraft, trucks, and trains. The boom 

induced accelerations are comparable to those associated with loud hi-¿ operations. Subsonic aircraft operations 

at about 1000 feet and heavy trucks and trains produce accelerations that are much lower in amplitude.

Damage to Historical Structures

In addressing the sonic boom issue regarding historical or unconventional structures (ref. 8.14), Sutherland et 

al. included historic natural monuments or archaeological structures, Indian caves with important older historic 

buildings, wells or large open water tanks, and radio telescopes/antenna. A ¿eld investigation concerning the 

vulnerability of Indian pictographs and petroglyphs to sonic booms from supersonic Àights within the USAF 

Valentine Military Operating Area in Nevada was conducted and reported by Battis (ref. 8.28). It was demonstrated 

that damage is improbable for sonic boom levels of up to 5 lbs/ft 2

 and signature durations from 100-200 msec. 

With regards to booms affecting satellite communication earth-station aerials, Duffy and Hatton (ref. 8.29), in 

their theoretical and empirical study, indicate that there was no damage or any interference with the facility under 

simulated booms of up to 6 lbs/ft 2

 and durations of 250 msec.

In Europe, concerns focused on the potential damage to older buildings that are irreplaceable because of their 

historic connections; in particular, the many churches, cathedrals, and public and residential buildings that are 

several centuries old. Because of their ages, these buildings are generally in a poor structural state of repair 

compared with modern buildings. Windows were of predominant concern, especially the leaded stained glass 

windows that differ from ordinary windows. Also included were ornate plaster ceilings and walls with frescos and 

statues, which are all vulnerable to impulsive movements of the structure. 

To assess the vulnerability of such structures, the Royal Aircraft Establishment (RAE), Farnborough, England, 

initiated a series of studies (ref 8.30) to measure the existing environment. Measurements were made of the 

response of major structural elements such as windows, walls, columns, ceilings, and spires of a range of cathedrals 

to their everyday noise and vibration environment. This included organ notes, bells, traf¿c, wind loading, thunder, 

and an arti¿cial impulsive sound produced by a small explosive charge. In addition, several subsonic aircraft 

Àyovers were performed. Typical results of this survey are shown in ¿gure 8.21 (ref. 8.2). The limited overÀight 

measurements that were made show that the predicted sonic boom response levels (see ref. 8.30) are greater than 

those produced by the normal environment. 

360

Figure 8.21. 5HVSRQVHRIFDWKHGUDOZLQGRZVWRWUDQVLHQWSUHVVXUHVUHI
Chapter 8 Response to Sonic Booms

361

The indications are that cathedral windows have more fatigue strength in reserve, but a de¿nitive statement on this 

problem will require much more knowledge of the effects of other long-term natural forces such as settlement, 

temperature and humidity variations, weathering, etc.

An important aspect of the potential sonic-boom-induced damage problem as supported by the extensive N-wave 

signature database is illustrated schematically in ¿gure 8.22 (ref. 8.1). The number of damage incidents for a given 

type of structure increases as the overpressure increases, and this is particularly evident at the higher overpressure 

values. Also shown in ¿gure 8.22 is a schematic illustration of the amplitude distribution of the overpressures. Even 

though the nominal, or predicted, overpressure for a given aircraft at speci¿c Àight conditions may have a value 

that is lower than that at which building damage might be expected there is a distribution of pressure amplitudes 

such that a small percentage of them occur in the relatively high overpressure range. These high overpressure 

values, which occur occasionally because of either atmospheric effects or focus booms due to maneuvers, may 

be suf¿cient to trigger incipient damage in existing structures. It is obvious that shaped boom signatures having 

much lower nominal overpressure values and therefore more favorable probability distribution of overpressures 

are desirable in that it reduces the probability of causing building damage. However, low amplitude shaped boom 

signatures do not assure that the triggering of damage can be completely avoided, especially in structures in need 

of repair.

The need to assure that future vehicles are designed to provide low amplitude shaped boom signatures that minimize 

the possibility of damaging structures and reducing annoyance were highlighted by the National Research Council 

2001 study of reference 8.31 and in the DARPA 2002 QSP effort (ref. 8.32). Low-boom shaped signatures would 

shift the nominal value shown in ¿gure 8.22 to the left. Shaped signatures whose spectra contain reduced levels of 

energy at the higher frequencies are expected to reduce the scatter due to atmospheric inÀuences, thereby reducing 

the spread of the pressure load bell-shaped curve. Shifting the nominal overpressure to a lesser magnitude and 

tightening the pressure load distribution curve would signi¿cantly reduce the probability of building damage.

Building Response to Low Amplitude and Shaped Booms

In 2005, NASA, recognizing that little (if any) data existed regarding the response of structures and people in 

and out of doors to sonic boom levels of less than 1.0 lb/ft2

, initiated a series of low-boom Àight tests at EAFB, 

California. Two series of low amplitude sonic boom tests were conducted in June 2006 and July 2007 to evaluate 

indoor/outdoor human response, structural acoustic building response and the effects of atmospheric turbulence 

for low amplitude sonic booms in the overpressure range of 0.1 to 0.6 lb/ft2

. In each test, a single family ranch-style 

home, one of older construction for the 2006 tests and a newer construction for the 2007 tests, was instrumented 

with numerous microphones and accelerometers.

Figure 8.22. 1DWXUHRIVRQLFERRPLQGXFHGGDPDJHSUREOHPDGDSWHGIURPUHI
Chapter 8 Response to Sonic Booms

The June 2006 tests (ref. 8.33) consisted of 112 booms during 6 Àight days providing 14 conventional N-wave 

type signatures of nominal levels of about 1.4 lbs/ft 2

 from straight and level Àyovers of an F/A-18 (shown in 

¿gure 8.23) and 98 low-amplitude rounded type signatures of nominal levels of 0.1 lb/ft 2

 to 0.6 lb/ft 2 generated 

by the F/A-18 performing a specially designed dive maneuver. The July 2007 tests (ref. 8.34) involved 72 booms 

over 5 Àight days and consisted of 42 conventional N-wave types and 30 low-amplitude signatures. Example low 

overpressure signatures from two Àights (Dive Numbers 3 and 5) are presented in ¿gure 8.24 (ref. 8.35).

Each signature represents a ground-level measurement from microphones spaced about one mile apart over six 

miles with one microphone placed 1 mile off track. It can be seen that the signatures vary in amplitude from about 

0.2 lb/ft 2

 to 1.0 lb/ft 2 and vary in waveform from a near N-wave to one approaching a sine wave. Signature rise 

times signi¿cantly increase as maximum overpressure decreases, as much as 40 msec for one signature. The 

inÀuence of atmospheric turbulence is also evident on both the bow and tail shocks of all signatures shown.

A sample of the building response data obtained during the 2006 tests is presented in ¿gure 8.25 (ref. 8.33). Wall 

acceleration time histories are shown for two sonic boom overÀights; one from the F-18B in level Àight producing 

an N-wave of a little over 1.0 lb/ft 2

 and the other being a low-boom signature of a little less than 0.20 lb/ft 2 

resulting from the dive maneuver Àight.

362

Figure 8.23. ,Q-XQHDQG-XO\1$6$FRQGXFWHGORZVRQLFERRPÀLJKWWHVWVRIDQ)$%

+RUQHWDWWKH1$6$'U\GHQ)OLJKW5HVHDUFK&HQWHU')5&LQ&DOLIRUQLD

1$6$SKRWR(&

Figure 8.24. *URXQGOHYHOVRQLFERRPPHDVXUHPHQWVIURPWKH)$%DLUFUDIWLQDVXSHUVRQLF

low-boom dive maneuver (ref. 8.35).
Chapter 8 Response to Sonic Booms

363

Note that the level Àight boom signature time history, shown to the left in ¿gure 8.25, has the remnants of the 

post-focus signature resulting from the acceleration to steady Mach occurring about 1.5 sec behind the carpet 

boom signature. The low-boom signature, shown on the right side of the ¿gure, is followed by the expected postfocus boom about 1.0 sec later resulting from the dive maneuver. It can be observed that, in each case, the wall 

acceleration persists for about 1.0 sec following the boom arrival before damping out. In addition, it is interesting 

to note the differences in the nature of the wall acceleration time histories resulting from the normal N-wave 

boom, the low-amplitude N-wave signature followed by the post-focus boom. In the case of the 1.0 lb/ft 2

 N-wave, 

the envelope of the wall acceleration peaks to  0.1 g and then decreases as time increases. One can also observe 

the very small response due to the refracted signature. The envelope of the wall response to the low boom N-wave 

type signature is about constant in amplitude whereas for the U-shape focus boom signature having the same 

overpressure, the wall acceleration builds to a maximum and then decreases as time increases.

Peak wall acceleration, whether positive or negative, measured at various locations on the single family ranchstyle houses during the 2006 and 2007 tests as a function of outdoor sonic boom levels from the low-boom dive 

maneuvers and also from the straight and level Àights of the F-18 aircraft are presented in ¿gure 8.26 (refs. 8.33 

and 8.34). These results are unique in that they ¿ll in the large gap in the existing database as is evident in ¿gure 

8.19.

Figure 8.25. 7LPHKLVWRULHVRIWUDQVGXFHUUHVSRQVHVRIDQRXWGRRUPLFURSKRQHDQGDZDOOPRXQWHG

accelerometer for a normal amplitude and a low amplitude sonic boom (ref. 8.33).

(a) 2006 tests on old house (ref. 8.33). (b) 2007 test on new house (ref. 8.34).

Figure 8.26. Maximum building wall acceleration amplitudes as a function of sonic boom

overpressure (adapted from refs. 8.33 and 8.34).
Chapter 8 Response to Sonic Booms

It can be seen that wall accelerations observed in the 2006 tests (¿g. 8.26(a)) ranged from about 0.05 for boom 

levels of 0.2 lb/ft 2

 up to about 0.2g at boom levels of about 1.2 lbs/ft 2. For the 2007 tests (¿g. 8.26(b)) slightly 

lower wall accelerations were observed and expected due to construction differences between the two houses.

It was shown in ¿gure 8.24 that as the boom levels from the dive maneuvers decreased in level, the signature 

became more rounded with shock rise times increasing to about 40 msec. Since one would expect that rounded 

signatures would drive the structure more ef¿ciently than an N-wave of equal amplitude and period, based on 

inertia considerations alone (see ¿gure 8.3), one would also expect to see some sort of non-linearity in the variation 

of wall acceleration with sonic boom levels in the 0.2 lb/ft 2

 to 0.6 lb/ft 2 range. However, the variation appears 

fairly linear, which is consistent with the results in ¿gure 8.19 where the differences in wall acceleration resulting 

from the overhead Àights to those resulting from Àights that were offset about 5 mi lateral to the Àight track were 

not signi¿cant. This ¿nding was somewhat unexpected since the 5 mi offset Àights produced signatures with 

larger rise times as compared to the on-track signatures and the angle of incidence at which the shock encounters 

the structure is also quite different.

A recent analysis was performed by Plotkin, Sizov, and Morgenstern (ref. 8.5) that describes the indoor perception 

of various shaped sonic boom signatures as compared to conventional N-waves. This study was aimed at 

determining which sonic boom shapes are best for minimizing the indoor perception and compare their indoor 

bene¿t for guidance in selecting the most acceptable low-boom signature shape.

The ¿ve low-boom shaped signatures, representative of those being considered by the technical community, 

are shown in ¿gure 8.27 (ref. 8.5) and include a Àat-top, ramp, and three multi-shock ramp approximations, 

together with a reference N-wave. Analyses of loudness, low frequency content, building tactile vibration, and 

rattle threshold were performed for each boom signature at six amplitudes. Building response was modeled as a 

single-degree-of-freedom (SDOF) system, with displacements governed by the Duhamel integral.

Wall accelerations as a function of peak overpressure for all six signatures are presented in ¿gure 8.28 (ref. 8.5).

364

Figure 8.27. 7\SHVRQLFERRPVLJQDWXUHVFRQVLGHUHGDGDSWHGIURPUHI
Chapter 8 Response to Sonic Booms

365

These results indicate that, at any given outdoor overpressure level, shaped signatures with larger rise times such 

as ramp1, ms1, and ms3 result in a lower wall acceleration than those resulting from an N-wave. Clarkson and 

Mayes (ref. 8.2) presented a summary of some measured responses of large windows and vertical studs due to 

N-wave type sonic boom loadings in the form of dynamic ampli¿cation factors. These results showed that the 

predicted values are generally conservative and, in particular, for the case of no damping encompass all of the 

measured data. In addition, it has been shown that the pressure loading on a building is lower for a signature 

having a longer rise time than for an equivalent N-wave in that the former has less energy at the higher frequencies 

(see ¿gure 8.7) resulting in lower excitation of the structure.

In the section just concluded, discussions on structural response to sonic booms have been presented. Findings 

regarding damage complaints, induced damage, damage studies and building response to low amplitude shaped 

boom signatures were included. The majority of the data base is associated with N-wave signatures of amplitudes 

in the 1.0 lb/ft 2

 to 3.0 lbs/ft 2 range with damage being con¿ned to brittle surfaces and secondary structural 

components such as plaster and window cracks. Damage to those components is generally predictable based upon 

loading and structural information. As such, damage resulting from sonic booms from nominal high altitude Àight 

would not be expected for structures in good repair. 

In general, the vast majority of the sonic boom building response and damage to conventional and historical 

structures was acquired during the 1960s and 1970s in connection with the U.S. SST program effort and was a 

requirement to the environmental impact statements by the Department of Defense (DoD) for designating military 

operating areas (MOA’s) in remote areas of the U.S. No controlled tests or analyses have been conducted on 

cluster homes as would be found in residential areas, nor have analyses or testing been conducted on high-rise 

structures or enclosed stadiums, all of which are of different design and construction methods with new materials.

Recent studies, analysis and full-scale overÀight experiments indicate that low-amplitude shaped sonic boom 

signatures are more acceptable than N-waves of equal amplitude and duration regarding building response and 

indoor annoyance. It is shown that the pressure loading on a structure is lower for a signature having a longer rise 

time and thus has less energy at the higher frequencies resulting in lower excitation of the structure.

Figure 8.28. 3UHGLFWHGSHDNDFFHOHUDWLRQRIZDOOIRUYDULRXVVRQLFERRPW\SHVDQGDPSOLWXGH

FRPSDUHGZLWKYLEUDWLRQWKUHVKROGUHI
Chapter 8 Response to Sonic Booms

Human Response

The majority of the current database regarding sonic boom acceptability is based upon laboratory and overÀight 

testing that was generated in the mid 1960s and early 1970s as part of the U.S. SST and Concorde development 

programs. The majority of these tests focused mainly on N-wave type sonic boom signatures in the range of about 

1.0 lb/ft 2

 to about 3.0 lbs/ft 2. Von Gierke and Nixon (ref. 8.36) provide an excellent review of the methods and 

results of these laboratory studies, controlled ¿eld studies, and uncontrolled overÀight ¿eld studies on individual 

subjects, groups, and communities. The authors also stated that although much has been learned, it is possible that 

human responses measured during that time period may differ somewhat from those in the future. Indeed, that is 

likely the case since human attitudes are always in a state of change. Since the U.S. SST program was canceled 

and the Concorde was ultimately con¿ned to over water operations, there was little opportunity or motivation for 

further studies. In the 1990s there was a renewed interest engendered by the potential for boom shaping and this 

period saw a Àurry of activity on both laboratory and ¿eld studies.

As a result of this renewed interest, an extensive database has been generated by NASA regarding human responses 

to much lower level shaped sonic boom signatures, which include laboratory, in-home, and ¿eld studies. Sullivan 

(ref. 8.37) noted that laboratory studies have very good control over the sound stimuli that subjects hear but 

require a very abnormal listening environment. An in-home study, where sounds are played through loud-speakers 

in people’s homes, improves the realism of the environment but at the same time reduces control over the sound 

¿eld. Finally, ¿eld studies provide for a completely normal environment but suffer from very poor knowledge 

of the precise details of the sound exposure. Sullivan also states that the acceptability of, or annoyance, caused 

by a sound is affected by many factors. In a laboratory situation, while some of these factors are under control, 

others may be missing. Thus, laboratory studies allow sounds to be compared in a relative sense rather than in an 

absolute one. The in-home study moves closer to absolute measurements and the ¿eld studies measure absolute, 

real reactions. A compilation of the studies, complete with details of the ¿ndings, is provided by Leatherwood et 

al. (ref. 8.38).

The earliest studies on human response to sonic booms relied on overpressure as the parameter to describe a sonic 

boom. This was a reasonable approach since for an N-wave it represents the amplitude of the signature. However, 

the earliest laboratory studies established that the rise time of the signature was also important in determining 

human perception of sonic boom waveforms. The rise-time determines the mid- and high-frequency content of 

the signature. This is the frequency range of maximum sensitivity for human hearing. Thus, the use of various 

metrics, such as A-weighted sound exposure level and loudness-based metrics, has come into being.

However, there is a characteristic of sonic booms and other impulsive sounds – their low frequency content – that 

is able to vibrate buildings and create rattling sounds that must also be considered. All ¿eld studies of sonic booms 

have identi¿ed these phenomena as being important contributors to annoyance. As a result, C-weighted sound 

exposure level is used to assess high-energy impulsive sounds. The C-weighting emphasizes low frequencies 

relative to other metrics in an attempt to incorporate the effects of structural vibrations and the accompanying 

rattling of objects.

There is no consensus within the regulatory and scienti¿c community regarding appropriate metrics and levels 

for sonic boom assessment. In large part this is due to the widespread prohibition of overland supersonic Àight 

that resulted from the experience gained in the 1960s; an outright ban that required no consideration of metrics 

or levels. Despite this, there have been various proposals and attempts to develop assessment methods for sonic 

booms and other impulsive sounds. The general consensus is that selection of a ¿nal metric and level can not 

happen until a demonstration vehicle having a low-amplitude shaped signature is Àown to assess its community 

acceptance. 

An indication of some of the noise metrics that are being assessed is given in table 8.2. Leatherwood et al. 

(ref. 8.38) evaluated ¿ve of these metrics, the Àat-weighted sound exposure level (FSEL), C-weighted sound 

exposure level (CSEL), A-weighted sound exposure level (ASEL), Stevens Mark VII Perceived Level (PL), and 

=wicker loudness level (=LL). The Leatherwood et al. (ref. 8.38) laboratory study was designed to: (1) quantify 

366
Chapter 8 Response to Sonic Booms

367

loudness and annoyance response to a wide range of shaped sonic boom signatures and (2) assess these ¿ve noise 

descriptors as estimators of sonic boom subjective effects.

Table 8.2. Noise Metrics, Symbols, and Abbreviations

DNL Day-Night Average Sound Level, dB

DNL(A) Day-Night Average Sound Level, calculated using A-weighted sound pressure level, 

dB

DNL(C) Day-Night Average Sound Level, calculated using C-weighted sound pressure level, 

dB

DNL(PL) Day-Night Average Sound Level, calculated using perceived noise level, dB

ZLLd Zwicker Loudness Level (diffuse ¿eld), dB

ZLLf Zwicker Loudness Level (frontal ¿eld), dB

PL Perceived Level (Stevens Mark VII procedure), dB

PNL Perceived Noise Level, dB

ASEL A-weighted Sound Exposure Level, dB

CSEL C-weighted Sound Exposure Level, dB

FSEL Flat-weighted Sound Exposure Level, dB

Based on the simulator studies, of the ¿ve metrics involved, Perceived Level (PL) proved to be the best choice for 

comparing booms with different shapes and amplitudes (see ref. 8.38). It was clearly a good metric for outdoor 

listening conditions and there are also some indications that it worked quite well indoors.

Loudness and Annoyance

For the outdoor situation, loudness and annoyance are a direct function of the sonic boom signature spectrum (see 

¿gs. 8.6 and 8.7). The sonic boom spectrum is de¿ned by the signature shape, amplitude, and period or duration. 

Early laboratory studies involving N-waves revealed that perceived loudness or annoyance of sonic booms is 

primarily related to the peak overpressure and shock rise time (refs. 8.39, 8.40, 8.41, and 8.42). Peak overpressure 

is the dominant contributor, since the higher the boom level, the greater the judged loudness. Increasing rise times 

reduce loudness and annoyance, whereas signature duration had little inÀuence as indicated in ¿gure 8.29 (ref. 

8.36).

Figure 8.29. 5HODWLYHORXGQHVVDQGDQQR\DQFHYHUVXVERRPVLJQDWXUHULVHWLPHDQGGXUDWLRQ/DERUDWRU\

IUHH¿HOGMXGJHPHQWVDGDSWHGIURPUHI
Chapter 8 Response to Sonic Booms

It is seen that an increase in shock rise time from 1 msec to 10 msec decreases loudness and annoyance by about 

13 dB. It should be noted that the ¿ndings presented in the ¿gure are for a reference boom level of 1.6 lbs/ft2

. 

Similar results were observed at boom levels of 0.8 lb/ft2

 and 2.4 lbs/ft2.

The procedure for loudness calculations has been applied to not only classical N-waves but also to low-boom 

shape signatures. For non N-wave shaped signatures, Niedzwiecki and Ribner (ref. 8.43) and Shepherd and 

Sullivan (ref. 8.44) showed that loudness is not only controlled by rise time and overpressure, but is also highly 

dependent upon the characteristic of the initial shock. They showed that loudness of booms could be reduced by 

replacing N-wave signatures with symmetrical signatures that achieved peak overpressure in two pressure steps 

instead of one. As can be seen from ¿gure 8.7, booms shaped in this manner would contain signi¿cantly less highfrequency energy and be less loud then an N-wave of identical front shock rise time and maximum overpressure. 

This is illustrated in ¿gure 8.30 (ref. 8.44), which shows the calculated loudness level of a shaped sonic boom 

signature observed outdoors.

The signature, shown to the left, has a duration of 350 msec and a peak overpressure (B) of 50 N/m 2

 (about 1 

lb/ft 2

) with an initial rise time of 2 msec (from zero to point A) with a secondary rise time from point A to point 

B, which is varied from 2 msec to 50 msec. Note that for a small value of the initial shock (A), say 6.25 N/m 2 

(about 0.13 lb/ft 2) and large secondary rise time (B) of say 40 msec, one realizes a reduction of about 16 dB in 

loudness as compared to a Àat-top or N-wave signature of amplitude 50 N/m 2

 (A = B = 50 N/m 2) and a rise time 

of 2 msec. For an initial shock (A) of 25 N/m 2

 and a rise time of 2 msec and a secondary shock rise time of 40 

msec, one only realizes a reduction of about 7 dB in loudness compared to a Àat-top or N-wave signature of 50 

N/m 2

 and a rise time of 2 msec. Thus, if the initial shock rise time is small, then it is desirable to keep the initial 

shock amplitude small (zero to A) and have a large secondary rise time from A to B. Conversely, if the secondary 

rise time is shorter than the initial rise time, then the pressure rise from A to B will control the loudness.

Shepherd and Sullivan (ref. 8.44) also made estimates of the loudness of sonic booms as they would be observed 

indoors of a building with windows open and also closed. However, as the authors noted, this assessment of 

indoor levels made no attempt to include the effects of structural vibrations or secondary acoustic radiation due to 

vibration-induced rattling of objects. Results of their study are illustrated in ¿gure 8.31 (ref. 8.44).

368

Figure 8.30. &DOFXODWHGORXGQHVVOHYHORIVKDSHGERRPVIRURXWGRRUOLVWHQLQJFRQGLWLRQVZLWKSHDNRYHUSUHVVXUHRI1P2, 

duration of 350 msec and initial rise time of 2 msec (adapted from ref. 8.44).
Chapter 8 Response to Sonic Booms

369

In ¿gure 8.31(a), the two curves of noise reduction were derived from measured data for a range of houses, both 

with windows open and closed. These noise reduction values were applied to the same range of booms described 

in ¿gure 8.30.

As can be seen from ¿gure 8.31(b), the trends of all the curves are similar for both cases of windows opened and 

closed. The authors also showed that there is a 10 dB decrease in loudness between the outdoor case and indoors 

with windows open.

Startle

Loudness calculations for sonic booms do not include the potentially important phenomena of startle to the 

outdoor observer and building vibration and rattle sounds that are experienced in an indoor listening environment. 

The outdoor observer not only experiences the audible aspects of the disturbance, but can also be startled. For 

example, during a thunderstorm when one observes lightning it is expected that thunder will follow. Despite 

this, thunder may still be startling. Sonic booms are, on occasion, said to sound like distant thunder. As shown 

in ¿gure 8.32, the pressure signature of thunder is signi¿cantly different than that of an N-wave sonic boom 

signature. Ribner and Roy (ref. 8.45) modeled the lightning strike as a tortuous line emitting N-shaped pressure 

waves from points all along its length as illustrated in ¿gure 8.32. Although emitted simultaneously, they arrive 

sequentially according to distance: the received pressure signature is essentially a convolution of an N-wave with 

a channel-shape function. Thus, the thunder spectrum approximates an N-wave spectrum modulated by another 

due to channel tortuosity.

Figure 8.31. (VWLPDWHVRIWKHORXGQHVVRIVKDSHGVRQLFERRPVKHDUGLQGRRUVZLWKSHDNRYHUSUHVVXUHRI1P2, duration 

of 350 msec and initial rise time of 2 msec (adapted from ref. 8.44).

(a) Noise reduction for typical residential structures. (b) Loudness levels of shaped booms for indoor 

listening conditions with windows open and closed.
Chapter 8 Response to Sonic Booms

Another example of experiencing startle is associated with ¿rework displays. Although observers are aware of, 

and are expecting, a loud burst following some aerial displays, they are still startled when the impulse noise 

reaches them. It is of interest to note that the overpressure levels associated with some of these aerial bursts are 

as high as 15 lbs/ft 2

, as shown in ¿gure 8.33 (ref. 8.46).

Figure 8.33. :DYHIRUPFKDUDFWHULVWLFVRIWKUHHGLIIHUHQWLPSXOVLYHQRLVHVUHI

Figure 8.32. 0HDVXUHGSUHVVXUHWLPHKLVWRU\RIWKXQGHUDGDSWHGIURPUHI

1$6$SKRWR*31

370
Chapter 8 Response to Sonic Booms

371

In Àight tests involving sonic boom measurements it has been found that even though the boom arrival times at the 

measurement locations were estimated to within 1 sec, the outdoor observer still experienced some startle when 

hearing the boom. Thus, a startle factor is inherent in the loudness and annoyance studies involving impulsive 

type disturbances.

Figure 8.34 (ref. 8.4) shows a summary of the types of interference including house shaking, being startled, 

sleep disturbance, interference with conversation, and interference with radio/television listening noted by 

respondents queried during the tests of community reaction to sonic booms conducted during the SST program 

in the 1960s (refs. 8.36 and 8.47). As indicated, house shaking was the most frequently cited type of interference 

from these exposure tests, with the startle factor close behind. The peak sonic boom pressures involved were in 

the range of 1.2 lbs/ft 2

 for the Oklahoma City tests (ref. 8.47) and less than 3.1 lbs/ft 2 for the St. Louis (ref. 8.48) 

tests. Obviously, reducing overpressure would reduce the percentage of those annoyed by these various factors, 

especially the startle, rattle, vibration, and damage concerns.

Rattle

Schomer (ref. 8.49) states that one cannot overestimate the role that noise-induced rattle plays in sonic boom and 

blast noise annoyance. Figure 8.35 (ref. 8.49) shows the number of respondents annoyed by interference caused 

by artillery and street traf¿c noise to their normal daily experiences. These include sleep, rest/relaxation, care/

concentration, radio/television, conversation, being startled and frightened and observing rattling.

Figure 8.34. 7\SHVRILQWHUIHUHQFHIURPVRQLFERRPFRPPXQLW\UHVSRQVHWHVWVUHI

Figure 8.35. 1XPEHURIUHVSRQGHQWVLQGLFDWLQJDQQR\DQFHWRWKHIDFWRULQGLFDWHGUHI
Chapter 8 Response to Sonic Booms

As can be seen, the prevalence of high annoyance to rattles was twice the rate of annoyance to startle, the second 

highest factor. Schomer also states that in contrast, speech interference and interference with listening to radio and 

television, two factors that depend on loudness, were 1/7th to 1/10th as important.

Sleep Interference

Von Gierke and Nixon (ref. 8.36) stated that sleep interference from nighttime booms could be a major determinant 

to public acceptance. They cite the laboratory 1968 and 1970 works of Lukas and Kryter (refs. 8.50 and 8.51) 

who examined the effects of simulated booms on sleep for boom levels of from 0.63 lb/ft 2

 to 2.5 lbs/ft 2 and 

included age groups from 7 to 72 years of age. As stated by von Gierke and Nixon, all sonic booms in these 

laboratory studies were adequate stimuli for awakening subjects during their rapid eye movement (REM) state 

of sleep. REM is a normal stage of sleep that is characterized by the rapid movement of the eyes and occupies 20 

to 25 percent of an adult’s total sleep or some 100 minutes of a night’s sleep. The study showed that 70 year old 

subjects were more likely to be awakened than younger subjects. They also noted that long-term effects on sleep 

of repeated nightly exposure to sonic booms are not known.

Two items of note should be mentioned at this point in the discussion. Although sleep interference is normally 

associated with nighttime sonic booms, there are those that work during nighttime hours and sleep during the 

day who would also be inÀuenced by sonic booms. Second, no signi¿cant distinction is made regarding sleep 

interference in any of the major sonic boom community overÀight programs of the past, some of which involved 

night time booms. For example, during the 1961-62 St. Louis overÀights (ref. 8.12) in which interviews were 

conducted concerning 76 Àights performed over a 7-month period, 45 of the total occurred between 9 P.M. 

and 4 A.M. The Oklahoma City overÀight program (ref. 8.52), which ran from February 1964 through July 

1964, involved no nighttime booms. All 1225 supersonic Àights occurred between about 7 A.M. and 4 P.M. U.S. 

Air Force training Àights over the Chicago area (ref. 8.53) during January-March 1965 involved a total of 49 

supersonic runs, 22 of which boom measurements were obtained. Of these 22 Àights, all occurred between about 

12:30 P.M. and 3:45 P.M. Only damage complaints were reported. The two-phase National Sonic Boom Program 

at EAFB (ref. 8.26) that ran from June 1966 to November 1967 consisted of a total of 569 Àights, all of which took 

place between 7 A.M. and 5 P.M. To summarize, there has been essentially no ¿eld tests with nighttime booms, 

with the exception of the 1961-62 St. Louis overÀights, and thus there is little information available.

Acceptability

It has been shown that loudness and annoyance play an important role in establishing sonic boom acceptance. 

However, as pointed out by Von Gierke and Nixon (ref. 8.36), the acceptability of sonic booms must also include 

physiological, psychological, and sociological responses to regular commercial supersonic Àights overland. They 

also state that based on the integrated results of past sonic boom overÀight programs in the United States, United 

Kingdom, and France, a level of acceptable sonic boom exposure in the community has not been established, 

although some estimates of acceptable boom levels are in the range 0.1 to 0.75 lb/ft 2

. Further, they point out 

that the wide variation in stimuli, immediate environs, and response behavior due to socio-psychological factors 

suggest that the concept of a range of acceptable levels is perhaps more appropriate than a single-value guideline. 

As such, a brief review of the past community overÀight ¿ndings is in order.

A community survey was conducted at Edwards AFB in the 1966-1967 time period (ref. 8.26) that compared the 

attitudes of 793 persons toward sonic boom exposures prior to and during a special test period of boom activity 

that was increased over typical boom activity usually experienced by the residents. Prior to the test, the exposure 

was 4 to 8 booms per day at a mean overpressure level of 1.2 lbs/ft 2

. During the tests (a 1-month period) 289 

booms were generated at a mean peak overpressure level of 1.7 lbs/ft 2

. 

372
Chapter 8 Response to Sonic Booms

373

An additional ¿nding from the study indicated that more than 50 percent of the respondents had experienced the 

4 to 8 boom exposure schedule for over a year. Some adaptation to sonic boom exposure was suggested when one 

is exposed regularly on a daily basis to sonic booms, since 60 percent found the boom more acceptable after being 

regularly exposed to it before the tests. Ten booms per day at an overpressure level of 1.7 lbs/ft 2

 was unacceptable 

for these respondents, as it was for the Oklahoma City residents (ref. 8.47).

Another survey of community reaction to sonic boom was conducted over six major metropolitan areas in the 

United States (Atlanta, Dallas, Denver, Chicago, Minneapolis, and Los Angeles) in relation to routine Air Force 

training Àights in supersonic SR-71 aircraft (ref. 8.54). The boom exposures from the SR-71 overÀights varied 

from an average number of one to three booms every 3 days at mean peak overpressures ranging from less than 

1 lb/ft 2

 to 2 lbs/ft 2. About 5000 pre-exposure, 500 during exposure, and 100 post-exposure personal interviews 

were completed. The post exposure interviews were taken from 4 to 5 months after the sonic booms had ceased. 

Although the different methodology limits comparisons, several ¿ndings are consistent with those of previous 

community studies. For example, respondents had a negative attitude towards sonic booms and the attitude 

increases rapidly in strength with increasing number of booms per day. Booms were ranked at the top of the 

most unwanted list of sounds. Ninety percent of complaintants owned their own homes and felt that the booms 

damaged their homes.

The NASA HSR Program (ref. 8.55) required a revisiting and reassessment of previous sonic boom community 

overÀight results in an attempt to establish the feasibility of overland supersonic Àight. In order to update the 

database, a study was funded to examine the response of communities in a vicinity of Nellis AFB, Nevada (1992-

93 time period) and Edwards AFB, California (1995 time period) to sonic booms associated with normal training/

testing operations (ref. 8.56). A summary of these along with other ¿ndings is given in ¿gure 8.36 (ref. 8.57).

The percentage of the population highly annoyed by N-wave type sonic booms of various levels calculated using two 

metrics, the overpressure in lbs/ft 2

 together with number of booms per day and the day-night average C-weighted 

sound level, is plotted in ¿gure 8.36. C-weighting was selected by the Committee on Hearing, Bioacoustics, and 

Biomechanics (CHABA) (ref. 8.58) under the constraints that included common availability on standard sound 

level meters. LCdn is a cumulative aggregation based on the equal energy hypothesis, accounting for the number 

of events as well as their level. Also plotted in ¿gure 8.36 is the CHABA curve (ref. 8.58), subsequently adopted 

by the American National Standards Institute (ANSI) (ref. 8.59) that provides an assessment of high-energy 

impulsive sounds with respect to residential communities. Examination of the data plotted in ¿gure 8.36 shows 

that the early US-SST cruise boom level design target of 1.5 lbs/ft 2

 is predicted to result in 10 to 30 percent of the 

population being highly annoyed by 1 to 8 booms/day, respectively. However, at boom levels of 0.3 lb/ft 2

 to 0.5 

lb/ft 2

, the annoyance numbers are reduced to about 1 to 5 percent for the 1 to 8 booms/day.

Figure 8.36. 3UHGLFWHGDQQR\DQFHIURPVXSHUVRQLFÀ\RYHUVFRPSDUHGWRFRPPXQLW\

REVHUYDWLRQV1 QXPEHURIERRPVGD\DGDSWHGIURPUHI
Chapter 8 Response to Sonic Booms

The impulsive sounds addressed by CHABA include explosions, quarry blasts, artillery and gun¿re, as well as 

N-wave sonic booms. The C-weighting metric selected is quite insensitive to rise time and mostly controlled 

by the magnitude of the overpressure and signature duration. As a result, it does not account for difference 

between the various types of impulsive sounds. For sonic booms, it does not recognize the reduced loudness of 

a shaped signature of the same overpressure and period but with a larger shock rise time. Studies using sonic 

boom simulators have shown that Perceived Level (also referred to as PLdB) is a better metric for assessing the 

loudness of N-wave and shaped signature booms observed outdoors and possibly indoors also (see table 8.2 and 

ref. 8.38). An illustration of the CSEL and PLdB sensitivity to rise time and signature shape is presented in ¿gure 

8.37. 

Figure 8.37 shows two notional cruise boom signatures having the same overpressure (0.3 lb/ft 2

) and period (150 

msec). The top signature is an N-wave having a shock rise time of 3 msec. The bottom signature is a delayed 

ramp-type shaped signature having an initial shock rise time of 3 msec from 0 to 0.1 lb/ft 2

 followed by a 15 msec 

rise time to the maximum overpressure of 0.3 lb/ft 2

. To the right of each signature are the calculated CSEL and 

PLdB. The CSEL metric indicates that the shaped signature (88.1 dB) is 4.1 dB lower in loudness level than the 

N-wave (92.2 dB). On the other hand, the PLdB metric shows the shaped wave (77.9 dB) is 9.9 dB quieter in 

loudness as compared to the N-wave (87.8 dB). It is obvious that the CSEL metric does not reÀect the reduced 

loudness of shaped signatures having increased shock rise times. Thus, a shaped signature would always be more 

acceptable than an N-wave signature represented in ¿gure 8.36 with the same overpressure and duration.

The Nellis and Edwards study (ref. 8.56) was a combined social survey and noise measurement program involving 

14 communities that have been regularly exposed to sonic booms for many years. A total of 1573 interviews of 

community residents were completed. The least exposed communities averaged one measurable boom in 20 days 

and had less than one boom that was over 2.0 lbs/ft 2

 in 100 days. The most exposed communities averaged 2 booms 

per day with about 1 boom per week over 2.0 lbs/ft 2

. The average number of booms per day of all overpressures 

for Nellis and Edwards was about 0.6 at a arithmetic mean overpressure of about 0.7 lb/ft 2

. Examination of the 

¿gure 8.36 shows that the reactions in the Edwards region, where supersonic Àight operations are controlled and 

primarily of a research nature, are consistent with previous results, and fall on the ANSI/CHABA curve. On the 

other hand, the Nellis results indicate more severe reactions and fall well above the ANSI/CHABA curve. The 

author of the study stated that several potential explanations were explored, but none were able to satisfactorily 

explain the difference in reaction between the two communities.

374

Figure 8.37. &RPSDULVRQRIWKH&6(/DQG3/G%ORXGQHVVQRLVHPHWULFVIRUDQ1ZDYHDQGVKDSHGZDYHERRPVLJQDWXUH
Chapter 8 Response to Sonic Booms

375

These Nellis and Edwards sonic boom surveys (ref. 8.56) found that there were three aspects of sonic booms 

that were most disturbing, namely, being startled, noticing rattles and vibrations, and fearing the possibility of 

structural damage. This ¿nding is consistent with previous community overÀight ¿ndings (as will be shown 

on the next ¿gure). Respondents report that the vibrations are not restricted to hearing rattles but also include 

noticing houses shake. A little over half of the startled respondents report that their startle reactions have not 

lessened from the time when they ¿rst heard the booms. More people fear the possibility of damage than believe 

that booms have thus far damaged their property.

Figure 8.36 is one interpretation of the available data relating residents’ annoyance to their boom exposure. 

Another viewpoint on this question is provided by the data presented in ¿gure 8.38 (refs. 8.57 and 8.60).

Percentage acceptance on a probability scale is shown for a range of sonic boom overpressure levels. The straight 

lines marked Leyman and Wyle are two interpretations of the available data with particular emphasis on the 

1966-67 Edwards results. Based on the assumption that percentage acceptance is equivalent to the inverse of 

highly annoyed, the lines marked Kryter-Schultz outdoors, Kryter-Schultz indoors, and ANSI are included for 

comparison.

The Kryter-Schultz outdoor line, which represents 16 booms per day exposure, is nearly coincident with the Wyle 

line. On the other hand, the ANSI and Kryter-Schultz indoor lines are in close agreement. Both data sets have 

markedly different slopes such that for sonic boom exposures less than 2.0 lbs/ft 2

, the ANSI and Kryter-Schultz 

indoor lines would predict a lower rate of acceptance than do the Wyle and Kryter-Schultz outdoor lines. The 

Wyle interpretation (ref. 8.60) suggests that sonic booms with a peak pressure on the order of 0.8 lb/ft 2

 would be 

expected to be acceptable about 95 percent of the time. The Wyle report further noted that it remains to be shown 

if shaped sonic booms would be expected to follow the same trend.

A ¿nal caution is in order before leaving this ¿gure. The results of the 1992-93 Nellis and 1995 Edwards 6-month 

surveys, shown previously, are not included on this ¿gure. Although the Edwards results would be close to the 

ANSI curve, the Nellis results would not be consistent with any of the curves, since annoyance was found to be 

far higher than in other studies.

Effects on Human Health

In an effort to determine if sonic boom exposure posed a threat to human health, the U.S. Air Force funded a study 

in the mid 1980s to examine long-term exposure to sonic booms and health data. The ¿ndings are presented in 

references 8.61 and 8.62. This study took place in the state of Nevada, since military supersonic operations have 

been carried out within its boundaries over a longer time than in any other area within the United States. Volume I 

Figure 8.38. Predicted sonic boom acceptance (refs. 8.57 and 8.60).
Chapter 8 Response to Sonic Booms

(ref. 8.61) presents the estimates of the sonic boom environment from 1969 to 1983. Although sonic booms were 

encountered as far back as 1955, the 1969 starting date was consistent with practical start dates for medical record 

acquisition. The subjects of this study were the residents of Nevada. Volume II (ref. 8.62) presents the results 

of the epidemiological study, which, as stated by the authors, “was built entirely on a state-wide epidemiologic 

evaluation of mortality for Nevada residents from 1968 to 1983, supplemented by hospital discharge morbidity 

data.” The study results indicated that no evidence was found to prove the existence of adverse health effects due 

to exposure to sonic booms.

Animal Responses

The proposed introduction of commercial supersonic transport travel in the early 1960s focused attention on the 

possible effects of sonic booms on animals. Earlier sonic boom damage claims associated with USAF training 

Àights reÀected that a small percentage of these involved animals. Concerns included possible changes in egg 

production from hatcheries, milk production of dairy herds, animal and bird reproduction, and stampeding and 

trampling. During the 1966 National Sonic Boom Program, conducted at EAFB, Casady and Lehman (ref. 8.63) 

conducted some preliminary investigations of the effects of booms on farm animal behavior for the purpose of 

deciding which common domestic and commercial animal species should be studied in greater detail at a later 

time.

Ten animal installations were selected and included a race horse breeding farm, two beef feeder lots, two turkey 

ranches, two chicken ranches, one sheep ranch, one commercial dairy, and one pheasant farm. The animal 

population of these installations was about 100 horses, 10,000 beef cattle, 125,000 turkeys, 35,000 chickens, 150 

sheep, 320 dairy cattle, and 50,000 pheasants. About 104 booms over 3 weeks were experienced during morning 

hours Monday through Friday over a 3-week period. It was found that except for the avian species, the behavioral 

reactions to the sonic booms were considered minimal. In the case of the avian species, the most visible reactions 

occurred as a result of low-level subsonic Àights, where noise was the disturbing factor. 

One of the most commonly quoted evidences that sonic booms harm wildlife resulted from the 1969 study by 

Austin, Robertson, and Woolfender (ref. 8.64). Even though their evidence was admittedly circumstantial, they 

concluded that sonic booms had caused mass hatching failure of Sooty Terns on the Dry Tortugas, Florida. 

To explain the cause of failure, Austin, Robertson, and Woolfender considered and rejected many possible 

explanations, including predators, food shortages, pesticides, humans walking on the rookery, and abnormal 

weather conditions. An unusual growth of underbrush might also have been a contributing factor. They also 

discovered that although sonic booms were a common occurrence on the Dry Tortugas at the time, unusually 

intense booms were heard during the May nesting time period by the residents of the nearby National Park 

Service Station who stated that they were intense enough to shatter windows. As noted in the 1991 paper by 

Bowles, Aubrey, and Jehl (ref. 8.65), this hatching failure of the Sooty Terns was particularly startling since the 

Brown Noddies, nesting in the bushes in the same area Àedged normal numbers. 

In response to the ¿ndings above, the United States Air Force funded Bowles, Aubrey, and Jehl (ref. 8.65) to 

conduct a series of experiments to determine whether it was possible for very intense booms to crack eggs or 

damage embryos. They were also to review the literature on eggshell strength and resistance to accelerative 

damage. Since extremely low altitude Àight required to produce the intense sonic booms would not be practical 

over the Dry Tortugas, the blasts were from small explosive pest-control devices to produce the test impulses. 

Although the overpressure levels associated with these test impulses (over 170 dB re: 20mPa) equalled and 

exceeded the 120 lbs/ft 2

 sonic boom level from an aircraft Àying at Mach 1.2 and an altitude of 90 feet, they 

differed from aircraft generated booms in several ways: the pressure time history was not N-wave in shape, the 

signature duration and shock rise times were shorter and the resulting noise spectrum is shifted to a much higher 

frequency range than that of an actual boom signature. 

Test results showed that none of the infertile eggs developed cracks of any kind and several deliberately cracked 

eggs did not show sign of further damage. All remaining eggs hatched and there was no signi¿cant difference 

between controlled and exposed eggs hatchability, date, or weight.

376
Chapter 8 Response to Sonic Booms

377

In 1994, Bowles, Knobler, and Seddon (ref. 8.66) conducted another series of experiments to determine whether 

very high amplitude simulated sonic booms of long duration (period) could affect development of eggs and to 

measure egg resonance frequencies. Chicken eggs were used and are somewhat larger than Sooty Tern eggs. As a 

result, they were expected to have a greater tendency to resonate when exposed to sonic booms than Sooty Tern 

eggs. Use was made of the Bolt, Beranek, and Newman (BBN) Sonic Boom Test Facility that generated N-waves, 

via large speakers, of up to 30 lbs/ft 2

 and duration of 100 msec, which closely simulates the sonic booms from 

an F-4E aircraft Àying at M = 1.1 and altitudes of from 800 to 17,000 feet above the ground. Their ¿ndings did 

not provide any evidence of physical damage to egg shells such as cracking, or excessive embryonic deaths as a 

result of exposure to intense simulated sonic booms.

The 2002 study by Ting, Garrelick, and Bowles (ref. 8.67) was the ¿rst analytical study conducted to support 

the empirical work of Bowles, Knobler, and Seddon (ref. 8.66) by providing a mathematical analysis of avian 

eggs to sonic booms. Their study focused on chicken eggs since published data indicated that the structure and 

dimensions for eggs of a variety of bird species, including the Sooty Tern, are similar. The sonic boom was 

represented by an N-wave of 0.15 sec duration and two Àight Mach numbers were chosen, Mach 1.2, the case 

most closely simulating an actual ¿ghter aircraft Àight, and the worst case of where the shock front would be 

parallel to the long axis of the egg resulting from an aircraft Àying at an in¿nite Mach number. Peak eggshell 

stress and peak embryo acceleration were chosen as primary damage metrics. The authors also proposed a third 

criterion, the maximum allowable concentrated radial force that may be applied to the egg. The results of their 

analytical study indicated that no damage was predicted with any of the response metrics until sonic boom 

overpressures reached 250 lbs/ft 2

 assuming Àights at in¿nite Mach number. The maximum peak overpressure 

thus far recorded for an F-4E Àight at M = 1.2 and 95 feet above ground level was 144 lbs/ft 2

. Their calculations 

of the boom level required for damage to eggs assuming Àight at M = 1.2 was 460 lbs/ft 2

; some 100 times greater 

than the sonic boom that would be associated with commercial supersonic operations. They thus conclude that 

even under the most extraordinary circumstances, sonic booms from practical aircraft maneuvers do not pose a 

threat to avian eggs.

It is curious that the Air Force devoted that much effort to assessing whether booms could crack eggs, since 

Austin et. al no evidence of physical damage but speculated more booms causing nest A controlled study on 

the effects of real and simulated sonic booms on farm-raised mink was conducted by Travis et al. in 1970 with 

funding from the FAA (ref. 8.68). These tests took place at three sites in Alaska. The conclusion drawn from these 

studies is that exposure of farm-raised mink to intense booms during whelping season had no adverse effect on 

their reproduction or behavior.

A comprehensive review of reports and studies of animal response to sonic booms was provided by Bell (ref. 8.69) 

in which he addresses USAF data relative to the reactions of domestic animals, mink, wild animals, and birds. He 

stated that, to date, it is dif¿cult to make detailed interpretations of the effects of sonic booms on different animal 

species. Further, if aircraft are to continue Àying supersonically over either populated or wilderness areas, further 

studies of the effect on animals should be conducted. He also stated that it may be necessary to utilize telemetrytype instrumentation to discern the impact of sonic booms on wildlife in its native habitat. In 1975, Lynch and 

Speake (ref. 8.70) conducted such a study involving 20 wild turkey hens equipped with transmitters and subjected 

them to both real and simulated booms. Their results indicated that sonic booms do not initiate any abnormal 

behavior in wild turkeys that would result in decreased productivity.

A more recent literature search of information pertaining to animal hearing and the effects of aircraft noise and 

sonic boom on domestic animals and wildlife can be found in reference 8.71. This effort, conducted by Manci 

et al. of the National Ecology Research Center was a joint effort of the U. S. Air Force/U.S. Fish and Wildlife 

Service. Of the 60 species addressed, about one third were exposed to impulsive type noise (real and simulated 

booms, recorded thunderclaps, blasting, cannon ¿re, and exploding paper bags). Two hundred references were 

provided.
Chapter 8 Response to Sonic Booms

Other Responses

Seismic

During the U.S. SST activities of the 1960s and 1970s, there was a concern that sonic booms produced by aircraft 

moving at supersonic speeds would apply moving loads to the Earth’s surface. Such a concern was expressed, 

even though it was known that the majority of the energy of the N-wave would be reÀected due to the much higher 

sound speed (about 6500 ft/sec) in the ground, resulting in ground motions that might cause damage to residential 

structures, trigger earthquakes, and precipitate incipient avalanches or landslides in areas that are stressed to 

within a few percent of instability.

An extensive experimental database was established by Cook, Goforth, and Cook (ref. 8.72) and Goforth and 

McDonald (ref. 8.73) as part of the U.S. National Sonic Boom Program at EAFB, California (ref. 8.26), and 

involved 178 steady-level supersonic overÀights for four aircraft: the F-104, B-58, SR-71, and XB-70. Five 

velocity-sensing seismographs were used and buried 1 m deep in the clay of a small dry lake bed and also on 

a nearby outcrop of quartz monzonite basement rock. Eight supersonic Àights of the B-58 were also conducted 

over the Tonto Forest Seismological Observatory (TFSO) in Arizona, where a seismometer array, 9 km wide, was 

used to study the energy distribution outside and inside the sonic boom ground footprint and possibly focusing 

effects along the ground track of the aircraft. Three B-58 supersonic Àights were Àown over the Uinta Basin 

Seismological Observatory (UBSO) in Utah where seismometers were available at depths to 8000 feet to study 

attenuation with depth. These latter two locations afforded geology different than that at EAFB. The nature of the 

measured seismic signals associated with the B-58 sonic boom signatures measured at the ground for locations at 

EAFB, TFSO, and UBSO are presented in ¿gure 8.39 (ref. 8.72).

It can be seen that similar sonic boom N-waves resulted in very different seismic waveforms at each of the ¿ve 

locations. This effect, as stated in reference 8.72, is primarily due to the variation of the elastic parameters of the 

earth. Particle velocities vary from 113 ȝ/sec to slightly over 230 ȝ/sec. It was also observed that there was a rapid 

vertical attenuation at the USBO site, the maximum particle velocity at 13.4 m was only 1.3 percent of that near the 

surface. In all cases, the greatest particle velocities occurred in the two sharp downward peaks, which coincided 

with the bow and tail shock of the sonic boom N-wave. Regardless of aircraft type, the maximum particle velocity 

was roughly proportional to the boom overpressure, as shown in ¿gure 8.40 (ref. 8.72) for XB-70 overÀights.

378

Figure 8.39. 9DULDWLRQRIVHLVPRJUDPVZLWKYDULDWLRQRIJHRORJLFDOSURSHUWLHVUHI
Chapter 8 Response to Sonic Booms

379

The largest particle velocity measured during these tests was 340 ȝ/sec at a boom level of 2.5 lbs/ft 2, which 

amounts to less than 1 percent of the seismic damage threshold for residences established by the Bureau of Mines 

(ref. 8.74), which is 2.0 in/sec or 50,800 ȝ/sec.

During these measurements, forerunner waves were always seen at high gain settings. According to the authors, 

these waves had frequencies of the order of 2 Hz and amplitudes of 5 to 10 ȝ/sec and began as much as 7 seconds 

before the arrival of the sonic boom. Higgins (ref. 8.75) observed, during sonic boom tests, the continuous songs 

of birds in the ¿eld were completely silenced 4 to 8 seconds prior to the arrival of the audible boom.

As noted in reference 8.72, present quantitative theories for the major seismic effects agree reasonably well with 

the experiments. Underground effects of a sonic boom from aircraft are essentially con¿ned to the top few meters 

of the ground and decrease rapidly with depth. Thus, the triggering of earthquakes by sonic booms is considered 

quite unlikely because earthquake foci are located at depths of at least 1 km. For aircraft traveling at hypersonic 

speeds above Mach 6.5 (i.e., faster than the speed of sound in the ground, 6500 ft/sec), this conclusion may 

no longer hold in that the shocks would no longer be con¿ned to the top few meters of the ground and would 

propagate to greater depths. 

Little experimental data exists regarding the effects of sonic booms in areas prone to avalanches and landslides. In 

March 1965, a sonic boom study was conducted near Leadville, Colorado to determine the effects of sonic boom 

overpressures on snow avalanches (ref. 8.76). Some 18 supersonic overÀights producing measured overpressures 

of from 1.15 lbs/ft 2

 to 5.02 lbs/ft 2 were generated and resulted in no avalanche activity. On one of the supersonic 

overÀights, no measured overpressure was recorded but predictions based on the aircraft altitude and Mach 

number placed the overpressure at 10.35 lbs/ft 2

. Forest Service personnel rated the avalanche hazard as low 

during the test period, resulting in the recommendation that further testing be conducted during periods of high 

avalanche hazard.

It is of interest to note that, in recent years, large existing seismograph networks have been used by Kanamori 

et al. (ref. 8.77) and Qamar (ref. 8.78) to detect sonic booms from aircraft and meteors. The seismic network in 

Southern California routinely detected booms from aircraft, such as the SR-71 and spacecraft such as the Shuttle 

Orbiter, and provide a unique opportunity to study the long-range propagation of primary and secondary sonic 

booms, as was done by Cates and Sturdevant (ref. 8.79). In addition to providing information on the vehicle 

ground speed, the array also provides information on the ground pressure patterns and vehicle altitude.

An interesting comparative study was made by Goforth and Rasmussen (ref. 8.80) of the frequency of occurrence, 

Figure 8.40. 9DULDWLRQRIVRQLFERRPOHYHOWRSHDNHDUWKSDUWLFOHYHUWLFDOYHORFLW\&OD\/DNH%HGUHI
Chapter 8 Response to Sonic Booms

severity, and spectral content of ground motions resulting from earthquakes and other natural and man-made 

sources with the motions generated by sonic booms. The data were recorded at the two seismic stations in Arizona 

and Utah and covered a period from 1963 through 1968. Of the 180,000 earthquake arrivals, some produced 

ground velocities of some 50 micron/sec. Quarry blast construction sites, oil well drilling and heavy river runoffs 

produced ground velocities less than about 10 microns/sec. No seismic signatures were observed due to thunder; 

possibly due to instrumentation response. Nuclear blasts from the Nevada test site produce peak ground velocities 

in excess of 50 microns/sec.

Marine Life

As was the case for booms impacting the earth, because of the large mismatch of the speed of sound in air (1116.4 

ft/sec) and water (4800 ft/sec), the effect of sonic booms from vehicles in level Àight at supersonic speeds over 

lakes and oceans was expected to be minimal since about 99 percent of the impinging energy would be reÀected. 

Even so, there was a concern that certain sea life, especially marine mammals that spend most of their time in 

the ¿rst few hundred meters of the ocean, would be impacted by the sonic booms from commercial supersonic 

operations over water. A substantial database regarding this topic assuming a Àat ocean surface was developed 

during the U.S. National Sonic Boom Program of the mid-1960s by Cook, Goforth, and Cook, and reported on 

in reference 8.72. Sawyers (ref. 8.81) and Cook (ref. 8.82) provided an analytical theory that was experimentally 

veri¿ed by Waters and Glass (ref. 8.83). Since then, substantial progress has been made regarding the penetration 

of sonic booms into the ocean to include realistic ocean surface, in homogeneous and arbitrary shaped waveforms, 

and a brief overview of these developments has been made by Sparrow (ref. 8.84).

The nature of the underwater sonic boom situation can be illustrated with the aid of ¿gure 8.41 (ref. 8.84), which 

shows the predicted underwater waveforms at depths of 4, 16, and 64 meters from an F-15 sonic boom signature 

of about 1.7 lbs/ft 2

 measured at the surface.

Examination of the results of ¿gure 8.40 show that sonic booms do not penetrate very far beneath the ocean’s 

surface and the waveforms become increasingly rounded as depth increases. Also, as noted by Sparrow (ref. 

8.84), the inÀuence of focusing due to wind waves on the ocean and the effect of bubble plumes never increased 

or decreased the sound levels by more than 1.5 dB over those seen in a homogeneous Àat ocean. 

More recently, Sohn et al. (ref. 8.85) have performed careful ¿eld measurements of the sonic booms from an F-4 

aircraft penetrating into the ocean at depths to 67 meters. Some measured and theoretically predicted pressure 

380

Figure 8.41. Underwater predicted waveforms from sonic booms (ref. 8.84).
Chapter 8 Response to Sonic Booms

381

time histories are given in ¿gure 8.42 (ref. 8.85) for Àight altitudes of 2000 feet and 20,000 feet above the water 

surface for Mach numbers of 1.07 and 1.26, respectively, show excellent agreement. For both Àights it can be 

seen that the sonic booms do not penetrate to a signi¿cant depth, 7 meters in the cases shown, before becoming 

increasingly rounded, evanescent in character, as depth increases.

Recently, an interesting study was conducted by Wang et al. (ref. 8.86) on the inÀuence of extremely high sonic 

boom levels generated by low altitude Àight of a supersonic cruise missile over the ocean surface. Overpressures 

of over 400 lbs/ft 2

 were estimated at the ocean surface, about 50 times greater than was found in traditional 

studies. At a depth of 100 feet, they calculate that the maximum overpressure had fallen to about 1.44 lbs/ft 2

, 

which is typical of the ocean surface conditions of traditionally high altitude studies.

It is worth noting that sonic booms will penetrate into water only when the boom shock wave angle, with respect 

to the water surface, is less than about 13.2° from the vertical, or faster than Mach 4.4 for a vehicle in level Àight. 

The Intrieri and Malcolm experiments (ref. 8.87) were measured on an acoustic shock wave propagating into the 

water from projectile speeds above Mach 4.4. Sparrow also noted that an aircraft Àying over the ocean at Mach 

1.2 and diving at an angle steeper than 43.2° from level Àight would produce a propagating wave into the ocean 

since the aircraft bow shock wave angle with respect to the water surface would be less than 13.2°.

Cook, Goforth, and Cook (ref. 8.72) compared the underwater pressure spectrum of a typical sonic boom signature 

overpressure of 2.5 lbs/ft 2

 and a period of 100 msec from a Mach 1.5 Àight with those of normal ambient noises, 

in sea stage 3 (moderate waves) and heavy ship traf¿c. Figure 8.43, taken from reference 8.72, is typical of the 

results in which the authors state that sonic boom pressures can be expected to momentarily exceed the ambient 

noise levels by up to 50 dB from the surface to depths of a few hundred feet between frequencies of 0.5 Hz to a 

Figure 8.42. &RPSDULVRQRIPHDVXUHGVROLGOLQHDQGSUHGLFWHGGDVKHGOLQHSUHVVXUHWLPHKLVWRULHVRIVRQLF

ERRPSHQHWUDWLRQIURPWZRÀLJKWVLQWRZDWHURIGHSWKVRIPPPPDQGPDGDSWHGIURPUHI
Chapter 8 Response to Sonic Booms

few hundred Hz. As such, sea life will be subjected to detectable amounts of momentary overpressures from the 

passage of the boom.

However, they further state that experiments in clear seawater with an underwater seismic pulse (electric sparker) 

have shown that the most sensitive small ¿sh (anchovies and menhaden) are not stunned outside a radius of 1 

meter from the spark of 2100 lbs/ft 2

, about 600 times typical sonic boom overpressure levels.

Kemp has shown through experiments with explosive charges that oysters, blue crabs, and shrimp are less 

vulnerable to sonic booms than are ¿sh (ref. 8.88). It is clear from the above ¿ndings that sonic booms from 

normal operations of supersonic aircraft will not harm these animals. In the early 1970s, the FAA in conjunction 

with the Department of Interior sponsored a program to conduct a ¿eld and lab study of the effects of sonic booms 

on ¿sh and ¿sh eggs during critical stages of development. Rucker (ref. 8.89) reported that egg and small hatched 

¿sh mortalities from eggs exposed to booms produced by military aircraft at overpressures up to 4.16 lbs/ft 2

caused no increase in mortality as compared to those for control groups of eggs spawned at the same time.

One of the potential launch sites for the Space Shuttle was Vandenberg Air Force Base in California. It was 

obvious that the sonic booms generated by the Shuttle launch would impact the California Channel Islands, 

which provide habitat for numerous forms of sea life. A 1980 study by Bowles and Stewart (ref. 8.90) was 

conducted to observe the effects of sonic boom disturbances to the pinnipeds and birds of San Miguel Island. 

They noted that dramatic disturbances can lead to an increased mortality rate for the habitat observed.

More recently, Perry, Boness, and Insley (ref. 8.91) conducted a study on the effects of Concorde sonic booms 

on breeding gray seals and harbor seals on Sable Island, Canada. These data were collected during the time 

period from January 1997 through May 1998. It is of interest to note that although the Concorde routinely

passed the island on its daily trans-Atlantic Àights, their reactions to these booms had never been documented. 

The study results showed relatively minor or no effects of the Concorde booms on breeding harbor and gray 

seals. It was also noted that they were unable to measure effects of sonic booms on animals in the water. They 

further state that the fact that booms penetrate water, there is the potential to affect animals that are in the water 

foraging or moving between foraging areas and breeding grounds.

382

Figure 8.43. Comparison of underwater sound pressure spectrum levels for a sonic boom and 

ambient noise (ref. 8.72).
Chapter 8 Response to Sonic Booms

383

Effect on Other Aircraft

A concern expressed during the U.S. SST studies of the mid-1960s related to the inÀuence of sonic booms 

and associated shock waves on other aircraft. It was generally agreed that for subsonic aircraft due to the 

combination of high closure speeds and large separation distances, the effects would be negligible. For the case 

of a supersonic aircraft passing another aircraft Àying supersonically, it was felt that adverse effects may be 

realized when the closure speeds are quite low and separation distances extremely small.

In 1963, the question of possible shock wave effects from a supersonic aircraft as it passes over a small subsonic 

aircraft was investigated. Two light aircraft, a small twin engine Beechcraft and a single engine Piper Cub, were 

instrumented with accelerometers and were overÀown by an F-104 aircraft that produced sonic booms from 

1.0 lb/ft2

 to 16.0 lbs/ft2. Accelerations of the instrumented aircraft were also measured when it was parked on 

the ground and during maneuvering Àights. Typical results of the sonic booms on the light aircraft are shown in 

¿gure 8.44 (refs. 8.92 and 8.93).

Acceleration levels for sonic boom induced levels experienced by the aircraft on the ground are observed to 

be approximately 0.3 g’s whereas the aircraft in cruise experienced an appreciably smaller acceleration. By 

comparison, the accelerations when taxiing over a rough runway or in air turbulence are both shown in ¿gure 

8.44 and the latter accelerations are greater than those experienced during the sonic boom overÀights. One 

observer in the aircraft noted that the estimated 16 lbs/ft2

 sonic boom was heard in cruise Àight as a mufÀed 

sound and that the only visible effect on the aircraft was a slight movement of the window and vertical climb 

indicator. As a result of these tests, it was generally concluded that sonic booms do not constitute a hazard for 

other aircraft in Àight or on the ground.

Figure 8.44. 6RQLFERRPHIIHFWVRQOLJKWDLUSODQHVDGDSWHGIURPUHIVDQG
Chapter 8 Response to Sonic Booms

A limited experimental investigation was made on a subsonic transport and similar ¿ndings were observed (ref. 

8.94). The supersonic aircraft was Àown in a passing maneuver about 500 feet to the side and also below the 

transport-type airplane. Since the passing rates were very high, no airplane motion was expected. In both cases, 

the subsonic transport-type airplane experienced nothing more than a slight bump, with the airplane motions 

and loads being negligible. The only loading of concern would be the load induced by the Àow ¿eld as it passes 

over the airplane. Thus, the pressure loading at separation distances of 100 feet or greater does not appear to be 

signi¿cant.

During the 1956 Àight test to measure the pressure ¿eld surrounding an F-100 aircraft in supersonic Àight at 

separation distances of from 2 to 33 body lengths (ref. 8.95), Mullens noted that during each supersonic pass the 

pilot of the overtaking aircraft said his aircraft was yawed considerably toward the other aircraft. Although no 

data were obtained at higher Mach numbers, pilot comments indicated that higher speed Ày-by’s could lead to 

considerable dif¿culty. It was also stated that aside from a risk of collision, it was known from similar tests by 

the NACA that vertical tail loads could become dangerously high (ref. 8.95). In 1959, Jordan (ref. 8.94) reported 

that at supersonic speeds, appreciable motions can be induced in an aircraft Àying in close proximity to another 

aircraft. Some results of this Àight test are presented in ¿gure 8.45 (ref. 8.94) for a lateral separation distance of 

100 feet (about 2 body lengths) at M = 1.3 and an altitude of 32,000 feet. The supersonic passing maneuver is 

illustrated in ¿gure 8.45(a). Several passes were made to the side of the generating aircraft at various separation 

distances, closure rates, altitudes, and a Mach number of about 1.2. An indication of supersonic pressure ¿eld 

surrounding the generating aircraft can be found in reference 8.96.

Figure 8.45. )RUPDWLRQÀ\LQJDWVXSHUVRQLFVSHHGVDGDSWHGIURPUHI

(a) Supersonic passing maneuver.

(b) Time history of supersonic pass.

(c) Effect of passing rate on sideslip angle.

384
Chapter 8 Response to Sonic Booms

385

Figure 8.45(b) presents a time history of the shock Àow-¿eld overpressure along with the corresponding responses 

of the aircraft including sideslip angle (ȕ), lateral acceleration (ny

), and vertical tail shear load (Fy) as the aircraft 

passes through the Àow ¿eld. It can be seen that a maximum side-slip angle, ȕ, of 5.4° was produced and the 

lateral acceleration, ny

, at the aircraft center of gravity reached a maximum value of  0.7 g. The vertical tail shear 

loads (Fy

), which are seen to be a function of sideslip angle, were approximately 50 percent of the design limit. 

The vertical tail loads attributed to the shock passage over the tail were less than 10 percent of the design limit. 

The inÀuence of the time to pass through the shock Àow ¿eld on sideslip angle (ȕ) is shown in ¿gure 8.44(c). 

At a slow passing rate, the yawing moment changes gradually and the aircraft tends to trim out and maintain a 

yawed attitude. The time to pass has an effect on the maximum sideslip angle, since the yawing-moment input is 

somewhat sinusoidal in shape and passing rates near the natural period of the airplane (about 2 sec) results in a 

dynamic response 2 to 3 times greater than for the static case. The fast passing rate resulted in negligible airplane 

motion and, thus, in relatively small vertical tail loads. 

In addition to the formal tests on the effect of booms on aircraft, various subsonic vehicles have been used as 

platforms for elevating microphones above the ground surface in several Àight tests described in Chapters 2 and 

4. Numerous in-Àight Àow ¿eld probing tests have also been conducted and discussed in Chapter 4. No problems 

with the aircraft or aircrew occurred during any of those tests.

Observations from Intense Boom Levels

With the introduction of the Century series of military aircraft (F-100, F-101, F-102, F-104, F-105, and F-106) 

in the late 1950s and early 1960s, Àights at supersonic speeds were easily obtainable. So too were Àights at 

supersonic speeds at very low altitudes wherein very high sonic boom overpressures would be experienced. Two 

concerns became evident. The ¿rst related to the question as to whether these intense booms could be used for 

a variety of tactical purposes, from disabling sensitive electronic equipment to clearing mine ¿elds, and second, 

that these overpressures would be high enough to harm humans. Two Àight tests aimed at addressing those two 

concerns were conducted in 1960 during the joint NASA-USAF study Little Boom at Indian Springs, Nevada 

(ref. 8.22) and the 1965 U.S. Air Force Àight maneuvers Joint Task Force II at Tonapah, Nevada (ref. 8.97). 

Altitudes from about 300 feet down to 50 feet above ground level were Àown and overpressures as high as 120 

lbs/ft2

 and 144 lbs/ft2, respectively, were recorded.

With regard to the use of intense booms for tactical purposes, it was found that although numerous test windows 

were broken, little effect was observed on various ground equipment including a transport aircraft and Mace 

missile weapons system, the latter designed for operation under conditions of 864 lbs/ft2

 blast loadings. The 

primary reasons for this were that although the overpressures were high, the measured particle velocity behind 

the boom signature shocks was quite low (the order of 5 to 15 ft/sec), as compared to an explosive charge of equal 

overpressures and the exposure time was very short relative to the inherent inertia of the systems being exposed.

Regarding the question as to whether intense boom would harm humans, evidence suggests that effects on humans 

are limited to annoyance, startle, and sleep disturbance. During the very low-altitude supersonic Àight tests in the 

Little Boom project, about 50 people, including experienced bioacoustic observers, were exposed to sonic boom 

overpressures of up to 120 lbs/ft2

 without any harm. Similar observations were made during the Tonapah Àight 

tests where a 144 lbs/ft2

 boom level was recorded. Speci¿c auditory observations made during these overÀight 

programs are listed in table 8.3 (ref. 8.98).

 
Chapter 8 Response to Sonic Booms

Table 8.3. Observed and Predicted Auditory Responses to Sonic Booms

 (Summary of all observations reported, from ref. 8.98)

Nature of Auditory Response Sonic Boom Experience or Prediction

Rupture of tympanic membrane None expected below 720 lbs/ft2

 None observed up to 144 lbs/ft2

Aural pain None observed up to 144 lbs/ft2

Short temporary fullness, tinnitus Reported above 95 lbs/ft2

Hearing loss: permanent None expected from frequency and intensity of boom

 occurrence

Hearing loss: temporary None measured

 (1) 3-4 hours after exposure up to 120 lbs/ft2

 (2) immediately after boom up to 30 lbs/ft2

Stapedectomy No ill effects reported after booms up to 3.5 lbs/ft2

Hearing aids No ill effects reported after booms up to 3.5 lbs/ft2

Chapter 8 Summary Remarks

The vast majority of the community response database is for N-wave signatures having overpressures in the 

1.0 lb/ft2

 to 3.0 lbs/ft2 and durations of 100 msec to 300 msec. For this boom level range, 13 to 33 percent of 

the population was highly annoyed. Residences reported that startle, rattle, and vibrations and the possibility of 

damage are the most disturbing aspects of sonic booms. Little data exists on community response to nighttime 

booms, so the long-term effects on sleep are unknown.

The majority of the database regarding building response is associated with single dwelling structures. Little 

information exists regarding sonic boom effects on other modern structures and clustered homes in communities, 

or new design and construction methods and materials.

Sonic boom damage is con¿ned to brittle materials and secondary structures in terms of plaster and window 

cracks. Damage is not likely to result from the normal sonic booms of high altitude operations for structures in 

good repair.

Seismic ground motions induced by some booms from supersonic Àight are less than 1 percent of the damage 

threshold for residential structures. Booms have not triggered earthquakes but may precipitate incipient avalanches 

or landslides in areas already unstable. Sonic booms have been shown to have little effect on domestic and wild 

animals and aquatic life.

A level of acceptability of sonic booms has yet to be determined and may only be established by Àying a

demonstrator aircraft having a low-amplitude shaped signature over communities. Low-amplitude shaped 

signatures are shown to minimize annoyance both outdoors and indoors.

386
Chapter 8 Response to Sonic Booms

387

Chapter 8 References

8.1 Hubbard, Harvey H. and Mayes, William H.: Sonic Boom Effects on People and Structures. NASA SP147, April 1967, pp. 65–76.

8.2 Clarkson, B. L. and Mayes, W. H.: Sonic-Boom Induced Building Structure Responses Including Damage. 

J. Acoust. Soc. Am., Vol. 51:742-757, 1972.

8.3 Cheng, D. H. and Benveniste, J. E.: Dynamic Response of Structural Elements Exposed to Sonic Booms. 

NASA CR 1281, March 1969.

8.4 Brown, D. and Sutherland, L. C.: Evaluation of Outdoor-to-Indoor Response to Minimized Sonic Booms. 

NASA CR-189643, June 1992.

8.5 Plotkin, Kenneth J.; Sizov, Natalia V.; and Morgenstern, John M.: Examination of Sonic Boom 

Minimization Experienced Indoors. AIAA Paper 2008-57, Jan. 2008.

8.6 Cheng, D. H. and Benveniste, J. E.: Transient Response of Structural Elements to Traveling Pressure 

Waves of Arbitrary Shape. Int. J. Mech. Sci., Vol. 8, No. 10, Oct. 1966, pp. 606–618.

8.7 ARDE Associates: Response of Structures to Aircraft Generated Shock Waves. WADC Tech. Rept. 58-

169, U. S. Air Force, Apr. 1959. (Also available from ASTIA as AD-229-463L.)

8.8 Sutherland, Louis C.: Low Frequency Response of Structures. WR 82-18, Wyle Lab., May 1982.

8.9 <oung, J. R.: Energy Spectral Density of the Sonic Boom. J. Acoust. Soc. Am., Vol. 40, Number 2, 1966, 

pp. 496–498.

8.10 Maglieri, Domenic J. and Hilton, David A.: Signi¿cance of the Atmosphere and Aircraft Operations on 

Sonic Boom Exposure. NASA SP-83, May 1965, pp. 245–256.

8.11 Seebass, R. and George, A. R.: Sonic Boom Minimization. J. Acoust. Soc. Am., Vol. 51, pp. 686–694, 

1972.

8.12 Nixon, C. W. and Hubbard, H. H.: Results of USAF-NASA-FAA Flight Program to Study Community 

Responses to Sonic Booms in the Greater St. Louis Area. NASA TN D-2705, May 1965.

8.13 Haber, Jerald and Nakaki, David: Sonic Boom Damage to Conventional Structures. SAF HSD-TR-89-001, 

Feb. 1989.

8.14 Sutherland, Louis D.; Brown, Ron; and Gorener, Dawn: Evaluation of Potential Damage to Unconventional 

Structures by Sonic Booms. USAF HSD-TR-90-021, April 1990.

8.15 Haber, Jerald; Nakaki, David; Taylor, Craig; Knipprath, George; Kapparam, Vijay; and Legg, Mark: 

Effects of Aircraft Noise and Sonic Boom on Structures. USAF HSD-TR-89-002, Feb. 1989.

8.16 Thoenen, J. R. and Windes, S. L.: Seismic Effects of Quarry Blasting. U.S. Dept. of the Int., Bureau of 

Mines. Bulletin 442, 1942.

8.17 Mayes, W. H. and Edge, P. M., Jr.: Effects of Sonic Boom and Other Shock Waves on Buildings. Material 

Research and Standards, Vol. 4, No. 11, Nov. 1964, pp. 588–593.

8.18 Blume, John A. and Associates: Structural Reaction Program. National Sonic Boom Study Project. FAA 

Rept. SST 65-15, Vol. 1, April 1965.
Chapter 8 Response to Sonic Booms

8.19 Haber, Jerald M. and See, Alex: Cumulative Damage Plaster Tests. USAF AL/OE-TR 1994-0127, Oct. 

1993.

8.20 Haber J.: Cumulative Sonic Boom Damage to Plaster. AIAA 93-4446, Oct. 1993.

8.21 McKinley, R. W.: Response of Glass in Windows to Sonic Booms. Materials Research and Standards, Vol. 

4, No. 11, Nov. 1964, pp. 594–600.

8.22 Maglieri, Domenic J.; Huckel, Vera; and Parrott, Tony L.: Ground Measurements of Shock Wave Pressure 

for Fighter Airplanes Flying at Very Low Altitudes and Comments on Associate Response Phenomena. 

NASA TN D-3443, 1966 (formerly NASA TM X-611, 1961). 

8.23 Parrott, T. L.: Experimental Studies of Glass Breakage Due to Sonic Booms. Sound-Its Uses and Control, 

May–June 1962.

8.24 Maglieri, Domenic J.; Hubbard, Harvey H.; and Lansing, Donald L.: Ground Measurements of the ShockWave Noise from Airplanes in Level Flight at Mach Numbers to 1.4 and at Altitudes to 45,00 Feet. NASA 

TN D-48, Sept. 1959.

8.25 Hershey, Robert L.; Higgins, Thomas H.; and Magrab, Edward B.: Application of the Response Probability 

Density - Function Technique to Predicting the Probability of Sonic-Boom Glass Breakage. J. Acoust. 

Soc. Am., Vol. 55, No. 5, May 1974, pp. 1009–1017.

8.26 National Sonic Boom Evaluation Of¿ce: Sonic Boom Experiments at Edwards Air Force Base. 

NSBEO-1-67 (Contract AF 49(638)-1758, Standford Res. Inst. July 28, 1967.

8.27 Carden, H. D.; Findley, D. S.; and Mayes, W. H.: Building Vibrations Due to Aircraft Noise and Sonic 

Boom Excitation. Presented at Symp on Machinery Noise, ASME Annual Mtg., Los Angeles, CA, Nov. 

16–21, 1969.

8.28 Battis, J. C.: Siesmo-Acoustic Effects of Sonic Booms on Archeological Sites. Valentine Military 

Operations Area. A. F. Geophysics Laboratory. AFGL-TR-83-0304, Nov. 1983, AD A139581.

8.29 Duffy, P. S. J. and Hatton, J. D.: Concorde Over Goonhilly. The Post Of¿ce Electrical Engineers, July, Vol. 

64(3), 1971, pp. 172–176.

8.30 Warren, C. H. E.: Recent Sonic-Bang Studies in the United Kingdom. J. Acoust. Soc. Am., 51:783-789, 

1972.

8.31 National Research Council: Commercial Supersonic Technology: The Way Ahead, Nat. Act. Press, Wash. 

DC, 2001.

8.32 Wlezien, R. and Veitch, L.: Quiet Supersonic Platform. AIAA Paper 2002-0143, Jan. 2002.

8.33 Klos, J. and Buehrle, R. D.: Vibro-Acoustic Response of Buildings Due to Sonic Boom Exposure, June 

2006 Field Test, NASA TM-214900, Sept. 2007.

8.34 Klos, J.: Vibro-Acoustic Response of Buildings Due to Sonic Boom Exposure: July 2007 Field Test. 

NASA TM-2008-215349, Sept. 2008.

8.35 Haering, E. A., Jr.; Smolka, J. W.; Murray, J. E.; and Plotkin, K. J.: Flight Demonstration of Low 

Overpressure N-Wave Sonic Booms and Evanescent Waves. Proc. of 17th Int. Symp. on Nonlinear 

Acoustics, Am. Inst. of Physics, Melville, N<, July 2005, pp. 647–650.

8.36 von Gierke, Henning E. and Nixon, Charles W.: Human Response to Sonic Boom in the Laboratory and 

the Community. J. Acoust. Soc. Am. 51, 766-782, 1972.

388
Chapter 8 Response to Sonic Booms

389

8.37 Sullivan, Brenda M.: Research on Subjective Response to Simulated Sonic Booms at NASA Langley 

Research Center. Proc. of 17th Int. Symp. on Nonlinear Acoustics, Am. Inst. of Physics, Melville, N<, 

July 2005, pp. 659–662.

8.38 Leatherwood, Jack D.; Sullivan, Brenda M.; Shepherd, Kevin P.; McCurdy, David A.; and Brown, Sherilyn 

A.: Summary of Recent NASA Studies of Human Response to Sonic Booms. J. Acoust. Soc. Am. 111 (1), 

Pt. 2, Jan. 2002, pp. 586–598. 

8.39 Harel, J. R. P. and Zepler, E.: The Loudness of Sonic Booms and Other Impulsive Sounds. J. Sound 

Vibration, 1965, pp. 249–256.

8.40 Shepherd, L. J. and Sutherland, W. W.: Relative Annoyance and Loudness Judgments of Various Simulated 

Sonic Boom Waveforms. NASA CR 1192, 1968.

8.41 Johnson, D. R. and Robinson, D. W.: Procedure for Calculating the Loudness of Sonic Bangs. Acustica 

21, 307–318, 1969.

8.42 Niedzwiecki, A. and Ribner, H. S.: Subjective Loudness of N-Wave Sonic Booms. J. Acoust. Soc. Am. 64, 

1617–1621 (1978).

8.43 Niedzwiecki, A. and Ribner, H. S.: Subjective Loudness of “Minimized” Sonic Boom Waveforms.” J. 

Acoust. Soc. Am. 64, 1622–1626 (1978).

8.44 Shepherd, K. P. and Sullivan, B. M.: A Loudness Calculation Procedure Applied to Shaped Sonic booms. 

NASA TP 3134, 1991, pp. 1–10.

8.45 Ribner, Herbert S. and Roy, Dipankar: Acoustics of Thunder: A Quasilinear Model for Tortous Lightning. 

J. Acoust. Soc. Am., 72(6), Dec. 1982, pp. 1911–1925.

8.46 Maglieri, Domenic J. and Henderson, Herbert R.: Noise From Aerial Bursts of Fireworks. J. Acoust. Soc. 

Am., Vol. 54, No. 5, 1973, pp. 1224–1227.

8.47 Borsky, P. N.: Community Reactions to Sonic Booms in the Oklahoma City Area. National Opinion Res. 

Ctr., AMRL Rept. TR-65-37, Repts. I and II, 1965.

8.48 Nixon, C. W. and Borsky, P. N.: Effects of Sonic Booms on People: St. Louis, Missouri, 1961–1962. 

Aerospace Medical Res. Lab. Rept., AMRL-Rept. TR-65-196, 1965.

8.49 Schomer, Paul D.: Some Important Factors in Community Response to Sonic Booms, Noise-Con. 2004, 

July 12–14, 2004.

8.50 Lukas, J. S. and Kryter, K. D.: A Preliminary Study of the Awakening and Startle Effects of Simulated 

Sonic Booms. NASA CR-1193. Sept. 1968.

8.51 Lukas, J. S. and Kryter, K. D.: Awakening Effects of Simulated Sonic Booms and Subsonic Aircraft Noise 

on Six Subjects 7 to 72 years of Age. NASA CR-1599, May 1970.

8.52 Hilton, David A.; Huckel, Vera; Steiner, Roy; and Maglieri, Domenic J.: Sonic-Boom Exposures during 

FAA Community Response Studies over a Six-Month Period in Oklahoma City Area. NASA TN D-2539, 

1964.

8.53 Hilton, David A.; Huckel, Vera; and Maglieri, Domenic J.: Sonic Boom Measurements during Training 

Operations in the Chicago Area. NASA TN-D-3655, Oct. 1966.

8.54 Tracor Inc.: Public Reactions to Sonic Booms. NASA CR-1665, Sept. 1970.
Chapter 8 Response to Sonic Booms

8.55 National Research Council: U.S. Supersonic Commercial Aircraft – Assessing NASA’s High Speed 

Research Program, Nat. Acad. Press, Washington, DC, 1997.

8.56 Fields, James M.: Reactions of Residents to Long-Term Sonic Boom Noise Environments. NASA CR 

201704, June 1997.

8.57 Hubbard, Harvey H. and Shepherd, Kevin P.: Comparisons of Methods for Predicting Community 

Annoyance Due to Sonic Booms. NASA TM 110289, Nov. 1996.

8.58 Anonymous: Assessment of Community Response to High Energy Impulsive Sounds. Rept. of Working 

Group 84, CHABA, Nat. Aca. Press, Washington, DC, 1981.

8.59 Anonymous: American Standard Method for Assessment of High Energy Impulsive Sounds with Respect 

to Residential Communities. ANSI S12.4, 1986. 

8.60 Brown, David and Sutherland, L. C.: Sonic Boom (Human Response and Atmospheric Effects) OutdoorTo-Indoor Response. Proceedings of the First Annual High-Speed Research Workshop, NASA CP 10087, 

Part 3, April 1992, pp. 1345–1363.

8.61 Kamerman, C. S.; Sutherland, L.; and Plotkin, K.: Exploratory Study of the Potential Effects of Exposure 

to Sonic Boom on Human Health, Vol. 1, Sonic Boom Environment. AAMRL-TR-86-020, June 1986.

8.62 Anton-Guirgis, H.; Culver, B. D.; Wang, S.; and Taylor, T. H.: Exploratory Study of the Potential Effects 

of Exposure to Sonic Boom on Human Health, Vol. 2, Epidemiological Study. AAMRL-TR-86-020, June 

1986.

8.63 Casady, R. B. and Lehman, R. D.: Response of Farm Animals to Sonic Booms. Sonic Boom Experiments 

at EAFB, NSBE 0-1-67 Interim Rept., Annex H, Sept. 1966.

8.64 Austin, O. L., Jr.; Robertson, W. B., Jr.; and Woolfender, G. E.: Mass Hatching Failure in Dry Tortugas 

Sooty Terns. Proc. Int. Ornithological Cong. 15:627, 1970.

8.65 Bowles, A. E.; Aubrey, F. T.; and Jehl, J. R.: The Effect of High Amplitude Impulsive Noise on Hatching 

Success. A Reanalysis of Sooty Tern Incident. Noise and Sonic Boom Impact Technology Program, OLAC HSD/<AH Rept. No. HSD-TP-91-0006, 1991.

8.66 Bowles, A. E.; Knobler, M.; and Seddon, M. E.: Effects of Simulated Sonic Booms on the Hatchability 

of White Leghorn Chicken Eggs. Occupational and Environmental Health Directorate, AL-OETR-1994-0179.

8.67 Ting, Carina; Garrelick, Joel; and Bowles, Ann: An Analysis of the Response of Sooty Tern Eggs to Sonic 

Boom Overpressures. J. Acoust. Soc. Am. 111(1), Part 2, Jan. 2002, pp. 562–268. 

8.68 Travis, Hugh F. et al.: An Interdisciplinary Study of the Effects of Real and Simulated Sonic Booms on 

Farm-Raised Mink (MUSTELA Vison). FAA Eq.-72-2, Aug. 1972.

8.69 Bell, Wilson B.: Animal Response to Sonic Booms. J. Acoust. Soc. Am. 51, 758–765, 1972.

8.70 Lynch, Thomas E. and Speake, Dan W.: The Effect of Sonic Boom on the Nesting and Brood Rearing 

Behavior of the Eastern Wild Turkey. Rept. No. FAA-RD-75-2, Jan. 1975.

8.71 Manci, Karen M.; Gladwin, Douglas N.; Villella, Rita; and Cavendish, Mary G.: Effects of Aircraft Noise 

and Sonic Booms on Domestic Animals and Wildlife. A Literature Synthesis. AFESC TR 88-14, June 

1988.

390
Chapter 8 Response to Sonic Booms

391

8.72 Cook, J. C.; Goforth, T.; and Cook, R. K.: Seismic and Underwater Responses to Sonic Boom. J. Acoust. 

Soc. Amer. 51, 729–741, 1972.

8.73 Goforth, T. and McDonald, J.: Seismic Effects of Sonic Booms. NASA CR-1137, 1968.

8.74 Duvall, W. I. and Fogelson, D. C.: Review of Criteria for Estimating Damage to Residences from Blasting 

Vibrations. TN 23, U.7, NO. 5963, U.S. Dept. of the Interior, Bureau of Mines, 1962.

8.75 Higgins, Thomas H.: The Response of Songbirds to the Seismic Compression Waves Preceding Sonic 

Booms. Report No. FAA-RD-74-78, May 1974.

8.76 Lillard, D. C.; Parrott, T. L.; and Gallagher, D. C.: Effect of Sonic Booms of Varying Pressures on Snow 

Avalanches. FAA Rept. SST 65-9 AD 468 794, August 1965.

8.77 Kanamori, H.; Mori, J.; Sturtevant, B.; Anderson, D.; and Heaton, T.: Seismic Excitation by Space Shuttles, 

Shock Waves 2, 89–96, 1992.

8.78 Qamar, A.: Seismic Excitation by Atmospheric Disturbances: The Dec. 1992 Space Shuttle and a Fireball 

in Jan. 1989. SSA Abstract, April 1993.

8.79 Cates, Joseph E. and Sturtevant, Bradford: Seismic Detection of Sonic Booms. J. Acoust. Soc. Am. 111(1), 

Pt. 2, Jan. 2002, pp. 614–628.

8.80 Goforth, Tom T. and Rasmussen, Robert K.: Study of the Characteristics of Seismic Signals Generated by 

Natural and Cultural Phenomena. NASA CR 132606, Jan. 1974.

8.81 Sawyers, K. N.: Underwater Sound Pressure from Sonic Booms. J. Acoust. Soc. Am., 523–524, 1968.

8.82 Cook, R. K.: Penetration of a Sonic Boom Into Water. J. Acoust. Soc. Am., 47, 1430–1436, 1970.

8.83 Water, J. and Glass, R. E.: Penetration of Sonic Boom Energy Into the Ocean: An Experimental Simulation. 

Hydrospace Research Corp., Final Rept. on Contract FA-70-WAI-185, HRC TR 288, June 1970, available 

from NTIS/DTIC as AD 711 963.

8.84 Sparrow, Victor W.: Review and Status of Sonic Boom Penetration into the Ocean. J. Acoust. Soc. Am. 

111(1), Pt. 2, Jan. 2002, pp. 537–543.

8.85 Sohn, R. A.; Vernon, R.; Hildebrand, J. A.; and Webb, S. C.: Field Measurements of Sonic Boom Penetration 

into the Ocean. J. Acoust. Soc. Am. 107, 3073–3083 (2000).

8.86 Wang, J. C. T.; Moody, D. M.; Grif¿ce, C. P.; Edwards, J. R.; and Hashad, A. A.: Sonic Boom and 

Underwater Sound Pressure Induced by Low-Altitude Ramjet Cruise Missiles. AIAA Paper 2006-413, 

Jan. 2006.

8.87 Intrieri, P. and Malcolm, G.: Ballistic Range Investigation of Sonic-Boom Overpressures in Water. AIAA 

J.11, 510–516, 1973.

8.88 Kemp, R. J., Jr.: Do Seismographic Explosives Affect Marine Life", Texas Game and Fish Austin, TX, 14, 

No. 9, 11–13, Sept. 1956.

8.89 Rucker, Robert R.: Effect of Sonic Boom on Fish,” Rept. No. FAA-RD-73-29, Feb. 1973.

8.90 Bowles, A. and Stewart, B.: Disturbances to the Pinnipeds and Birds of San Miguel Island, 1979-1980. 

Potential Effects of Space Shuttle Sonic Booms on the Biota and Geology of the California Channel 

Islands: Res. Repts., edited by J. R. Jehl, Jr. and C. F. Cooper, (Cent. Mar. Stud., San Diego State Un. and 

HSWRI, San Diego, CA, pp. 99–137.
Chapter 8 Response to Sonic Booms

8.91 Perry, Elizabeth A.; Boness, Darryl J.; and Insley, Stephen J.: Effects of Sonic Booms on Breeding Gray 

Seals and Harbor Seals on Sable Island, Canada. J. Acoust. Soc. Am. 111(1) Part 2, Jan. 2002, pp. 599–

609.

8.92 Powers, John O.; Sands, J. M.; and Maglieri, Domenic J.: Survey of United States Sonic Boom OverÀight 

Experimentation. Aircraft Engine Noise and Sonic Boom. FDP-PEP, CP 12, AGARD 1969, pp. 15–1 to 

15–35.

8.93 Maglieri, Domenic J. and Morris, Garland J.: Measurements of the Response of Two Light Airplanes to 

Sonic Booms. NASA TN D-1941, 1963.

8.94 Jordan, Gareth H.: Some Aspects of Shock Wave Generation by Supersonic Airplanes. AGARD Rep. 251, 

North Atlantic Treaty Organization, Dec. 1959.

8.95 Mullens, Marshall E.: A Flight-Test Investigation of the Sonic Boom. AFFTC TN 56-20, Air Res. and 

Dev. Command, US Air Force, May 1956.

8.96 Smith, Harriet J.: Experimental and Calculated Flow Fields Produced by Airplanes Flying at Supersonic 

Speeds. NASA TN-D 621, 1960.

8.97 Nixon, C. W.; Hille, H. K.; Sommer, H. D.; and Guild, Elizabeth: Sonic Booms Resulting from Extremely 

Low Altitude Supersonic Flight: Measurements and Observations on Houses, Livestock and People. 

AMRL-TR-68-52, USAF, Oct. 1968.

8.98 von Gierke, H. E.: Effects of Sonic Boom on People: Review and Outlook. J. Acoust. Soc. Am. 39, 

543–550, 1966.

392
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

393

CHAPTER 9 SONIC BOOM SIMULATION DEVICES AND TEST TECHNIQUES

Without question, sonic boom simulation devices have ful¿lled a wide variety of sonic boom research needs that 

have led to a more complete understanding of sonic boom generation, propagation prediction, and responses. The 

development of experimental simulation techniques to generate sonic boom type disturbances have complemented 

the place of complex, lengthy, and costly supersonic Àight operations. 

In this section, we will review the simulation methods/devices listed in table 9.1, indicating the speci¿c sonic 

boom issues they address and highlighting some of the experimental ¿ndings. The speci¿c sonic boom issues to be 

discussed include validation of sonic boom design and prediction codes, the inÀuence of atmospheric variability 

on boom signature distortions, quantifying focus boom intensities, underwater studies, sonic boom reÀection and 

refraction by buildings and topography, indoor-outdoor subjective response, and building response.

In 1970, Edge and Hubbard (ref. 9.1) provided a review of the characteristics of the facilities and techniques of 

simulating sonic booms. Table 9.1 (ref. 9.1) lists the categories of simulators addressed along with an indication 

of research applications for each.

Table 9.1. Categories of Sonic Boom Simulators and their Research Application (from ref. 9.1)

Simulator 

Categories

Research Applications

Generation Propagation Response

Wind Tunnels x x

Ballistic Ranges x x

Spark Discharge x

Loudspeakers x

Piston Systems x

Shock Tubes x x

Explosives x x

Air Modulator Valves x x

The Edge-Hubbard summary of sonic boom simulators was updated in 1986 by Shepherd and Powell (ref. 9.2), 

who summarized the current status of boom simulators that might be used in future studies of the effects of booms 

on people, animals, and structures. Their study was con¿ned to simulators in the United States and Canada, and 

indicated which of the simulators were fully operational, which required modest or major investment to bring to 

operational status, and those no longer in existence.

A majority of the sonic boom simulation devices listed in table 9.1 were not utilized beyond their initial 

application. However, recent and current activities in seeking vehicle designs having low-boom, non-N-wave 

shaped signatures required the continued use of several of these simulation devices. Wind-tunnel testing is still 

necessary for acquiring near-¿eld pressure signatures for validation of the CFD codes used in numerous advanced 

vehicle designs and their shaped signatures. Loudspeaker test chambers, piston systems, and explosive charges 

have been utilized to assess the outdoor and indoor subjective response to these signatures and to establish the role 

of the visual, vibratory, and noise stimuli on indoor subjects. Building response studies utilizing linear charges, air 

modulation, and piston-driven devices and loudspeakers have also been carried out.

Validation of Sonic Boom Design and Predictive Codes

Measurements of the Àow ¿eld characteristics surrounding the Àight of a supersonic aircraft play a key role in the 

continuous development and validation of the design codes used to develop aerodynamically ef¿cient low-boom 

vehicles of the future. The in-Àight measurements of the pressure ¿eld about various aircraft presented in Chapter 
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

394

4 of this publication were very instrumental in con¿rming the validity of past sonic boom prediction codes being 

applied to aircraft not designed for low sonic booms. The most recent Àight tests involving the modi¿ed F-5E 

aircraft into the SSBD added additional credibility of the predictive codes for non-N-wave designs.

Although full-scale Àight-test Àow-¿eld measurements will continue to be required for ¿nal con¿rmation of theory, 

such tests follow rather than lead the way. Small model testing in wind tunnels has long played a signi¿cant role in 

establishing the sonic boom characteristics of speci¿c aircraft con¿gurations and, thus, in the development of sonic 

boom design methodology and predictive codes. Another simulation technique – the use of a ballistic range to launch 

aircraft models – has also been examined. Each of these two simulation techniques will be brieÀy reviewed.

Wind Tunnels

Wind-tunnel studies of the sonic boom phenomenon have been conducted for over 50 years beginning with 

Carlson’s work (ref. 9.3) in 1959 in the NASA LaRC 4- by 4-foot Supersonic Wind Tunnel. Since then, sonic 

boom wind-tunnel testing has been conducted in several NASA supersonic facilities, including the LaRC 4- by 

4-foot Unitary Plan Supersonic Wind Tunnel, ARC 9- by 7-foot Supersonic Wind Tunnel, the 20-inch Mach 6 

Tunnel, and the GRC 8- by 6-foot and 10- by 10-foot wind tunnels. Presently, the ARC 9- by 7-foot Supersonic 

Wind Tunnel and the GRC 8- by 6-foot Supersonic Wind Tunnel are the primary NASA facilities being used for 

sonic boom testing by NASA. 

The success of sonic boom wind-tunnel tests is dependent upon the quality of the tunnel Àow characteristics 

within the test section, the size and geometric ¿delity of the model being tested, the devices and methods used 

to acquire the pressure measurements, and the manner in which the model is supported in the wind-tunnel test 

section. A schematic of a sonic boom wind-tunnel test setup of the mid-1960 time period is shown in ¿gure 9.1 

(ref. 9.4).

During the past 50 years, wind-tunnel testing techniques have helped de¿ne the test model size, manner in which the 

model is mounted, and pressure measurement sensors necessary to describe the boom signatures about the model. 

These techniques were ¿rst set forth in 1967 by Carlson and Morris (ref. 9.4). They also advanced the methods 

used to minimize the inÀuences of non-uniform and non-steady tunnel test conditions, model and measurement 

probe vibrations, and boundary-layer effects on the measured pressure signatures. In addition, they formulated 

procedures to adjust and correct the measurements. A typical measured pressure signature and its adjusted value

is presented in ¿gure 9.2 (ref. 9.4).

Figure 9.1. Wind-tunnel test setup of the mid-1960 time period (ref. 9.4).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

395

The procedure for adjusting the measured signature, which has been smeared as a result of those inÀuences, was 

to project a line along the expansion portion of the boom signature to the amplitude where the areas contained 

within the lower and upper parts of the initial shock were equal. As noted by the authors, the signature for this 

example was deliberately chosen to accentuate the departure from the N-wave shape. They further stated that such 

a departure from that of an N-wave is present to some degree in all tunnel signature measurements. In this section, 

discussions will be provided that address each of these concerns and include test section Àow quality, models, 

pressure measurements, and model support.

Test Section Flow Quality

The tunnel measurement system for a sting-mounted model, as shown in ¿gure 9.1, includes the geometric angle 

of attack, static and total pressures, and Mach number. As with any supersonic tunnel there are non-uniformities 

in all these quantities with the most uniform Àow, hopefully, in the region where sonic boom models are mounted. 

Unlike wind-tunnel force tests, nonuniformities across the entire test section are of concern in regards to where in 

the test section the measurement probes are located. Measurements of the Àow angle, Mach number, and pressure 

can be different due to the lateral, vertical, and longitudinal gradients of Àow angle and Mach number across the 

test section.

A calibration of the Àow qualities of a supersonic tunnel is always made prior to test operations. The NASA LaRC 

Unitary Plan Supersonic Wind Tunnel had two test sections that were used for many sonic boom model tests. Test 

section 1 was designed for testing at Mach numbers of 1.46 to 2.86 and test section 2 for Mach numbers of 2.30 

to 4.63. The test sections are 4-feet wide (y) by 4-feet high (z) and 7-feet long (x). Reference 9.5 by Jackson et 

al. contains plots of the aforementioned non-uniformities for both test sections one and two. An example of the 

lateral and longitudinal variations of test section 1 in Mach number, M, and the Àow angle ࣄv

 (measured in the 

vertical plane, deg) is presented in ¿gure 9.3 (ref. 9.5).

Figure 9.2. Typical measured sonic boom pressure signature of the mid-1960 time period (ref. 9.4).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

396

The surveys were made very near the horizontal centerline along the Àow path at a distance y = 2.25 in. and y = 0 

in. for Mach number and Àow-path angle respectively. As observed in ¿gure 9.3(a), the longitudinal Mach number 

variation across the test section centerline for a nominal tunnel Mach setting of 2.16 ranged from 2.11 to 2.18. 

The longitudinal variation of Àow angle for a nominal Mach setting of 1.97 ranged from 0° to 1.6°. Such 

variations were also observed at different Mach and Reynolds numbers. As observed from this and other 

measurements for sonic boom testing, knowledge of the test section non-uniformities are very important as to 

determining whether to test, at what test conditions, and where to place the model and measurement devices.

Models

Wind-tunnel models have generally ranged in size from 1⁄4-inch to 30 inches in length depending upon the size 

of the wind-tunnel test section and the desire to acquire near-, mid-, or far-¿eld Àow conditions. A photograph of 

four 1-inch sonic boom models, shown in ¿gure 9.4 (ref. 9.1), demonstrates the challenge between the size and 

¿delity of sonic boom models.

For these models, pressure measurements were obtained at various distances from the sonic boom models ranging 

from about 1 to 50 body lengths. Larger models allow for more exacting geometric features such as Àow-thru nozzles 

and exhaust simulation, put less demand on the measurement devices, provide higher test Reynolds numbers, and 

allow for more versatility of the model support. Flow-¿eld measurements are usually restricted to distances close to 

the model (the near ¿eld) at about one to ¿ve body lengths (h/l).

Figure 9.3. 0DFKQXPEHUDQGÀRZSDWKDQJXODULW\GLVWULEXWLRQVLQWKH1$6$/D5&8QLWDU\3ODQ6XSHUVRQLF

Wind Tunnel test section (adapted from ref. 9.5).

(a) Mach number variation, M=2.16. (b) Flow-path angle variation, M=1.97.

Figure 9.4. Small sonic boom wind-tunnel models tested in the wind tunnel (ref. 9.1).

1$6$SKRWR&RXUWHV\RI+DUU\&DUOVRQ
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

397

Smaller models allow for Àow-¿eld measurements far from the model (mid- to far-¿eld) at about 5 to 50 body 

lengths (h/l) and are more prone to Àow-¿eld contamination and model vibrations. In addition, Àow-¿eld 

measurements become more challenging as the measurement devices become large compared to the size of the 

model.

An extreme example of the inÀuence of model size and perhaps vibration on three measured sonic boom signatures 

is presented in ¿gure 9.5 (ref. 9.4).

All three signatures were obtained at equal non-dimensionalized distances from models of a supersonic transport 

varying in size of 1-inch, 1/2-inch, and 1/4-inch. It can be seen that as model size decreases, the signature becomes 

more rounded. Recall that in order to acquire signatures further from the model into the mid- and far-¿eld, smaller 

models were necessary. The results shown in ¿gure 9.5 established that because of the deleterious effect of model 

size and vibration, and boundary layer buildup, models of 1/4-inch would no longer be used.

A comparison of the sonic boom signature measured in a wind tunnel from a 1-inch model of the B-58 aircraft 

with the ground measured signature of the full-scale 97-foot long aircraft in Àight, is given in ¿gure 9.6 (ref. 9.4). 

When the appropriate adjustments are made to the wind-tunnel signature, good agreement is established between 

wind-tunnel and Àight results.

Figure 9.5. Effect of model size on measured signatures (adapted from ref. 9.4).

Figure 9.6. &RUUHODWLRQRIZLQGWXQQHODQGÀLJKWPHDVXUHGERRPVLJQDWXUHVUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

398

The techniques employed to investigate the sonic boom phenomenon using wind tunnels have experienced little 

change in the past 50 years. Sting-mounted models and slender cone measurement probes and the associated 

signature adjustment methods were still in use in the early 2000 time period by Mack and Kuhn (ref. 9.6) for their 

sonic boom tests, as shown in ¿gure 9.7.

Shock smearing was still being experienced by Mack and Kuhn on their 10-inch long low-boom con¿guration 

shown in ¿gure 9.8 (ref. 9.6).

However, as model size increases and measurements are acquired closer to the model, the accuracy and ¿delity 

of the measurements improve considerably, as illustrated in ¿gure 9.9 (ref. 9.7). Figure 9.9 shows the test setup 

in the NASA GRC 8- by 6-foot Supersonic Wind Tunnel and the measured and predicted near-¿eld sonic boom 

signature at an h/l distance of 1.5 for the 2.49-foot SSBD model.

These tests also provided for model inlet Àow-through nacelle effects. The model was mounted in the inverted 

position in the tunnel, as shown in ¿gure 9.9, and attached to the tunnel sting support via a steel strut that replaced 

the vertical tail.

Figure 9.7. Wind-tunnel test setup of the early 2000 time period along with measured and corrected bow shock (ref. 9.6).

Figure 9.8. Three-view of LQFK6/6/(PRGHODQGUHVXOWVIURPZLQGWXQQHOWHVWVRIWKHHDUO\WLPHSHULRG

6/6/(PRGHODW0 &/

&/FUXLVH DQGK LQFKUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

399

3UHVVXUH0HDVXUHPHQW3ODWH

Prior to 1960, the use of a stationary boundary-layer bypass plate was the preferred instrument for measuring 

Àow-¿eld pressure on sonic boom wind-tunnel models primarily because of its simplicity. A schematic of the 

wind-tunnel test setup that utilized a measurement plate and was used by Carlson (ref. 9.3) is depicted in ¿gure 

9.10.

Figure 9.9. 6FKHPDWLFRI66%'VRQLFERRPWHVWVHWXSLQ1$6$*5&E\IRRW6XSHUVRQLF:LQG7XQQHOVKRZLQJ

model and measurement probe locations with measured and predicted results (adapted from ref. 9.7).

(a) SSBD model probe setup.

(b) Measured versus predicted centerline pressures for SSBD at design lift coef¿cient (M=1.367, CN=0.90, h/l=1.5, ij=0°).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

400

Measurements were obtained at pressure ori¿ces on the surface of the plate. It was usually assumed that this Àat 

plate would act as a perfect reÀector producing a doubling of the pressure ratio ǻp/p. In a subsequent test of this 

assumption, Carlson (ref. 9.8) conducted a systems check by obtaining measurements of the pressure ¿eld of the 

same model, ¿rst with the reÀection plate and then with a small static probe. The results of this comparison are 

given in ¿gure 9.11 (ref. 9.8).

Figure 9.10. Description of wind-tunnel test section setup using stationary boundary-layer plate (ref. 9.3).

Figure 9.11. &RPSDULVRQRISUHVVXUHPHDVXUHPHQWVPDGHZLWKDUHÀHFWLRQSODWHDQGZLWKD

small static pressure probe (ref. 9.8).

(a) Schematic of tunnel test setup.

(a) Measurements made with a plate. (b) Measurements made with a probe.

(b) Planview of boundary-layer bypass plate.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

401

The results indicated that, in general, the assumption of 2.0 as a reÀection factor was substantiated. However, 

there is considerably more smearing of the onset of the bow shock due to shock-boundary-layer interaction as 

compared to that measured using the small static pressure probe. Because there was more boundary-layer smearing 

of the measured signature using the plate, subsequent wind-tunnel sonic boom Àow-¿eld pressure measurements 

were made using slender conical probes.

3UHVVXUH0HDVXUHPHQW3UREHV

Use of a slender conical pressure measurement probe of the type shown in ¿gure 9.12 (ref. 9.9) to de¿ne the shock 

Àow ¿eld about a model in the wind tunnel has continued for the past 50 years with only slight variations as to 

the half cone angle, which varied from 1° to 2°. Four static pressure ori¿ces were circumferentially spaced about 

90o

 apart about half way from the tip of the 0.2-inch diameter conical probe. 

The static pressure ori¿ces were arranged to lie in a Mach 1.4 plane originating from the model for the tests of 

reference 9.10 and in a Mach 2.92 plane for the tests of reference 9.11. This latter paper stated that the earlier tests 

(ref. 9.9), over a greater range of Mach angles, did not reveal any signi¿cant effects of the difference between the 

Mach angle and the vertically aligned ori¿ces.

The long slender conical probe shown in ¿gure 9.12 was used for the tests shown in ¿gures 9.6 and 9.8, as well 

as the SSBD tests of ¿gure 9.9. The higher stiffness of the large model, along with the more rigid model sting 

support arrangement, minimized model vibration effects on the signature measurements. However, there were 

still traces of shock smearing, smoothing, or rounding of the shocks in the measured signature. This was believed 

to be associated with the measurement probe; speci¿cally, the shock off the tip of the conical probe, the boundary 

layer buildup from the probe tip to the measuring ori¿ces, and the associated shock-boundary layer interaction 

(mentioned earlier) in the vicinity of the probe static ori¿ces.

In 1959, Carlson (ref. 9.12) used a miniature conical probe in the LaRC 4- by 4-foot Supersonic Wind Tunnel 

to study the actual Àow about wing-body combinations relative to store launches at supersonic speeds. The 

miniature conical probe was used again by Putnam and Capone in 1969 (ref. 9.13) in the 4- by 4-foot Supersonic 

Wind Tunnel to obtain local Mach, Àow angle, and pressures in the Àow ¿eld surrounding a cold jet exhausting 

into supersonic Àow. A sketch showing the details of this conical probe are given in ¿gure 9.13 (refs. 9.12 and 

9.13). The ¿ve pressure ori¿ces of the probe were connected to ¿ve Baldwin gages having a range of 15 lbs/in2

.

Figure 9.12. *HRPHWU\RIFRQLFDOKDOIDQJOHFRQHSUHVVXUHSUREHUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

402

It is important to note that in each of these two tests, the Carlson model size was on the order of 3 ft in length 

with about 2-ft span and the Putnam-Capone jet nozzles were about 6 inches in diameter and 45 inches in length. 

Measurements were made at distances of from about 1 inch to 2 inches below the wing-body models and from the 

exhaust exit to about one nozzle diameter downstream for the jet Àow tests. Some measured results are presented 

in ¿gure 9.14(a) for the Carlson wing-model tests and in ¿gure 9.14(b) for the Putnam-Capone jet nozzle tests.

Figure 9.14 shows that the conical probe is capable of sharply de¿ning the initial shocks for both cases shown 

and that no rounding or smoothing of the shock is visible. In 2009, Bobbitt designed a conical probe, shown in 

¿gure 9.15 (ref. 9.14), for use in both wind-tunnel tests and Àight to more completely and qualitatively describe 

the supersonic Àow ¿eld surrounding a model or aircraft. 

Figure 9.13. Detail of conical probe utilized in 1959 and 1969 wind-tunnel tests (refs. 9.12 and 9.13).

Figure 9.14. )ORZ¿HOGSUHVVXUHVLJQDWXUHVREWDLQHGZLWKWKHFRQLFDOSUREHVLQDQGLQWKH1$6$/D5&

4- by 4-foot Supersonic Wind Tunnel.

(a) Mach number variation, Mach 2.16 wing-body centerline and 2.1 inches below wing at Mach 2.01 (ref. 9.12).

(b) Pressure signature measured on jet nozzle 

exhausting into Mach 2.2 Àow Z/D = 1.0 (ref. 9.13).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

403

The version shown in ¿gure 9.15 is for Àight applications, a wind-tunnel version would be much smaller in 

diameter. The conical probe consists of miniature gages that measure static and total pressures from which Mach 

number and Àow angle are obtained using the Euler equation solutions. The conical probe also contains a total 

temperature gage that will allow one to obtain sound speed and, thus, freestream velocity. Acceleration can be 

obtained by taking the time derivative of the velocity. The conical probe has several advantages over current 

probes as it can determine local Mach number, Àow angle, total pressure and temperature, static pressure, velocity 

and speed of sound.

Some results of measurements acquired with the conical probe during wind-tunnel tests in the NASA LaRC 4- by 

4-foot Supersonic Wind Tunnel (ref. 9.14) are presented in ¿gure 9.16. It can be seen that the comparison between 

the conical probe values and wind-tunnel settings regarding tunnel Mach number (¿g. 9.16(a)), pressure (¿g. 

9.16(b)), and angle of attack (¿g. 9.16(c)) are in agreement.

Figure 9.15. 6FKHPDWLFRIFRQLFDOSUREHZLWKWRWDOWHPSHUDWXUHJDJHWRSURYLGHIUHHVWUHDPSUHVVXUH0DFKQXPEHU

DQJOHRIDWWDFNDQGIUHHVWUHDPYHORFLW\VWDWLFWHPSHUDWXUHDQGVSHHGRIVRXQGUHI

Figure 9.16. &RPSDULVRQRIFRQLFDOSUREHPHDVXUHPHQWVZLWKWXQQHOVHWWLQJVDGDSWHGIURPUHI

(a) Probe versus wind-tunnel Mach number.

(b) Probe versus wind-tunnel pressure. (c) Probe versus wind-tunnel angle of attack, Mach 1.6.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

404

In 1993, Bobbitt (ref. 9.9) invented a new type of wedge probe for use in acquiring sonic boom signatures in the 

wind tunnel and also for measuring the sonic boom signatures in the Àow ¿eld surrounding an aircraft in Àight. 

This device, shown in ¿gure 9.17 (ref. 9.9), provides for the measurement of the Àow-¿eld pressure signatures in 

the wind tunnel free from shock and boundary layer inÀuences.

The wedge probe also provides Àow Mach number and Àow angularity. Initial tests of the wedge probe, using a 

sidewall mount, was conducted in the NASA LaRC 4- by 4-foot Supersonic Wind Tunnel and the results were 

compared with the wind-tunnel free-stream measurements. These comparisons are shown in ¿gure 9.18 (ref. 9.9) 

and the correlation of the pressure and Mach number is excellent.

Figure 9.17. 6XSHUVRQLFZHGJHWRSURYLGH0DFKDQJOHRIDWWDFNDQGVWDWLFSUHVVXUHDGDSWHGIURPUHI

Figure 9.18. &RPSDULVRQRIZHGJHSUREHPHDVXUHPHQWVZLWKWXQQHOVHWWLQJVDGDSWHGIURPUHI

(a) Pressure measurements, lbs/ft2. (b) Mach number measurements.

(c) Flow angle measurements.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

405

A larger-scale version of the wedge probe was built and tested in the NASA LaRC 4- by 4-foot Supersonic 

Wind Tunnel. Some results of measurements acquired with the wedge probe during wind-tunnel tests in the 

NASA LaRC 4- by 4-foot Supersonic Wind Tunnel (ref. 9.14) are presented in ¿gure 9.19. It can be seen that 

the comparison between the wedge probe values and wind-tunnel settings regarding tunnel Mach number (¿g. 

9.19(a)), pressure (¿g. 9.19(b)), and angle of attack (¿g. 9.19(c)) are well correlated. 

The conical and wedge probes were also installed on the NASA F-15B 836 testbed aircraft (ref. 9.14). They were 

located under the aircraft and mounted on the Centerline Instrumentation Pod (CLIP), as shown in ¿gure 9.20. 

This arrangement was part of a structural integrity test of the probes. In the ultimate application of these probes, 

they would be mounted on the aircraft noseboom for the determination of all the free stream Àow quantities.

A sketch of the pro¿le of this aircraft with major shocks emanating from the various components, which one 

would expect to occur, is shown in ¿gure 9.21. As can be seen from the sketch, depending on whether the CLIP 

shock is ahead of, or behind the probes, there will be at least three or four strong shocks ahead of the probes. Thus, 

there is no possibility that the probes there can measure anything resembling free stream quantities. There are, 

however, measurements of some of these quantities by the airplane system and comparisons can be made to 

show the differences.

Figure 9.20. &ORVHXSRIZHGJHDQGFRQLFDOSUREHPRXQWHGRQWKH1$6$)&/,3

1$6$SKRWRV('OHIW('DERYH

Figure 9.19. &RPSDULVRQRIZHGJHSUREHDQGZLQGWXQQHOIUHHVWUHDPÀRZTXDOLWLHVDGDSWHGIURPUHI

(a) Probe versus wind-tunnel Mach number measurements.

(b) Probe versus wind-tunnel pressure measurements. (c) Probe versus wind-tunnel angle of attack, degrees, Mach 1.6.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

406

In ¿gure 9.22 (ref. 9.14) are shown the measurements as a function of time for Mach number, total pressure, and 

angle of attack as measured by the conical and wedge probes along with similar measurements acquired with the 

aircraft system. The data were recorded during acceleration from Mach 1.3 to Mach 1.9 and deceleration from 

Mach 1.9 to Mach 1.3 at a constant altitude of 48,000 feet. Mach number data for the Àight (see ¿g. 9.22(a)) shows 

the earlier time passage of the shocks off the CLIP edges over the wedge probe at ~116 seconds versus that for the 

conical probe at 150 seconds. Passage of these shocks in the other direction occurs at 320 seconds and 350 seconds 

for the conical and wedge probes respectively. There is also the pressure-gauge saturation limit for the wedge probe 

that was set at 10 lbs/in 2 that starts around 250 seconds and lasts until ~300 seconds (see ¿gs. 9.22(a), (b), and (c)). 

Apparently, the 10 lbs/in 2 gauges in the conical probe were just below the saturation value set for those gages.

Figure 9.21 Sketch of F-15B aircraft showing the shocks off the various aircraft components ahead of 

the clip (adapted from ref. 9.14).

Figure 9.22. &RPSDULVRQRIFRPSXWHGWLPHYDULDWLRQRI0DFKQXPEHUWRWDOSUHVVXUHDQGDQJOHRIDWWDFN

for the conical and wedge probes (adapted from ref. 9.14).

(a) Mach number. (b) Total pressure.

(c) Angle of attack.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

407

The total pressure is essentially the same for the two probes (¿g. 9.22(b)) consistent with the physics of Àuid Àow 

where no energy has been added or subtracted. Angle of attack for the two probes is plotted in ¿gure 9.22(c). The 

differences mirror those of Mach number where the shock passage at times of 100 and 325 sec produce spikes in 

the variation of angle of attack.

A signi¿cant feature of both the wedge and conical probes is that the measurement of Mach, angle-of-attack, 

pressure, and velocity are essentially instantaneous. As such, Àow-¿eld surveys, whether in wind tunnels or in 

full-scale Àight, can be completed very rapidly thereby minimizing the inÀuence of tunnel Àow variations or 

aircraft motions on the measured pressure signature.

3UHVVXUH0HDVXUHPHQW5DLOV

Slender conical measurement probes of the type shown in ¿gure 9.12 are capable of acquiring pressure measurements 

with minimal Àow interference, but obviously limit test measurements to a single location at a time. These singular 

measurements can limit test productivity and result in the measurement of a pressure signature over longer test times 

where changing tunnel conditions may occur. Researchers have developed and tested pressure measurement rails 

with closely spaced pressure taps over the length of the rail to measure a complete Àow-¿eld pressure signature. 

In a 2008 test in the ARC 9 - by 7-foot Supersonic Wind Tunnel, researchers investigated the use of pressure 

measurement rails versus the more traditional slender conical probes, as shown in ¿gure 9.23 (ref. 9.15).

(a) Conical (2° half-angle cone) probe measurements (on- and off-track).

(b) Pressure measurement rail.

Figure 9.23. 3UHVVXUHVLJQDWXUHPHDVXUHPHQWGHYLFHVPRXQWHGRQWKHIRUZDUGZLQGRZEODQNDW

WKH$PHVE\IRRW6XSHUVRQLF:LQG7XQQHODGDSWHGIURPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

408

While pressure measurement rails can address many of the limitations of singular conical probes, these devices 

can also introduce new measurement challenges such as Àow interferences from the rail, pressure lag to the 

pressure sensors and longer tubing length required, and challenges with creating and determining a consistent 

reÀection factor along the length of the rail. Conclusions from the 2008 tests at the ARC 9- by 7-foot Supersonic 

Wind Tunnel (ref. 9.15) indicated that while the pressure rails were far more ef¿cient with respect to test time 

than the single conical probes, the probe data appeared to be less sensitive to tunnel Àow variations such as 

humidity. Single probe data was more affected by non-uniformities in the Àow¿eld during the longer test run and 

test ef¿ciency due to the longer test times required. The results of the 2008 sonic boom study has led to a greater 

understanding of the issues related to pressure measurement rails. 

In 2010, an improved pressure measurement rail called the RF 1.0 (reÀection factor 1.0) rail was developed and 

is shown in ¿gure 9.24 (ref. 9.16). Pressure signatures are measured on the apex of the rounded tip pressure rail 

with 420 axial static pressure ori¿ces (0.015-inch diameter) along the length of the rail to obtain the sonic boom 

pressure signature. The rail was designed to have minimal Àow disturbance and no reÀection factor due a small 

edge radius (0.1-inch diameter), and minimize the reÀections of the model signatures from the tunnel wall by the 

large standoff distance (14 inches). 

Initial comparisons obtained in a 2008 test and presented in ¿gure 9.25 (ref. 9.16) show reasonably good agreement 

between the RF 1.0 rail data, probe data, and CFD results for the forward pressure signature. Results for the aft 

signature are less conclusive, but the RF 1.0 rail appears to agree better with the CFD predictions than probe data. 

Final evaluation of the RF 1.0 rail and improvement of the test technique utilizing this rail are ongoing. 

Figure 9.24. 5)SUHVVXUHUDLOPRXQWHGRQWKHDIWZLQGRZEODQNDWWKH1$6$$5&E\IRRW6XSHUVRQLF:LQG7XQQHOUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

409

Model Support

The amount of effort that has been directed towards the reduction of the leading (bow) shock of a sonic boom 

signature as compared to the trailing (tail) shock is a natural consequence of an airplane’s geometry. There are 

no control surfaces or engines up front on most supersonic cruise con¿gurations, thus, the distribution of the 

fuselage’s cross-sectional area and wing’s lift and volume are the controlling elements. Due to the proximity 

of the model support and sting, an aft-end problem arises in wind-tunnel tests that are carried out to measure 

the pressure signatures below an aircraft. Exacerbating the problem is the fact that in order to make pressure 

measurements close to mid-¿eld h/l’s of 5 to 10, where nonlinear effects are small, the model’s length must be 

much less than the height of the tunnel (or if the wings are mounted vertically, much less than the width of the 

tunnel). Ferri and Wang (ref. 9.17) examined the effects of stings on pressure signatures to show that signi¿cant 

unrealistic effects can occur. Figure 9.26 from reference 9.17 gives an illustration of the modi¿cation that a sting 

can inÀict on the rear shock of a pressure signature when propagated to the ground.

Figure 9.25. /%:7&RQ¿JXUDWLRQLQ1$6$$5&E\IRRW6XSHUVRQLF:LQG7XQQHOUHI5)UDLOGDWDFRPSDUHGWR

FRQLFDOSUREHGDWDDQGDQG&)'UHVXOWV

Figure 9.26. (IIHFWRIVWLQJRQDIDU¿HOGVLJQDWXUHUHI).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

410

One exception is the use of a sting, or stings, that have the geometry of the effective shape of the exhaust. In 

this case, the sting must be hollow to allow the Àow from the Àow-through nacelles on the aircraft model to pass 

through. Since each different engine has a different effective exhaust shape at a prescribed Àight condition, the 

use of an exhaust-shaped sting has its limitations. Employing a series of stings representing different exhaust 

geometries could be an option. Simulation of the exhaust plumes associated with the ascent phases of Àight of the 

Saturn V and Shuttle rocket-powered vehicles, as shown in ¿gure 9.27 (refs. 9.18 and 9.19), present a much easier 

task relative to sting mounting arrangement.

Figure 9.27. 6WLQJH[KDXVWSOXPHVLPXODWLRQWHFKQLTXHGXULQJWHVWVLQ-3/LQFK6XSHUVRQLF:LQG7XQQHO

(a) Model of Saturn V with simulated exhaust plume in JPL 20-inch tunnel (ref. 9.18).

(b) Shadowgraph of Shuttle launch con¿guration with simulated plume at Mach 4 (ref. 9.19).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

411

There are wind-tunnel model mounts, other than ordinary stings, that may be used and are less intrusive with 

respect to the trailing shock and plume. As designers began to focus efforts on improved aft signatures and 

measurement of these aft signatures, the use of blade mounts for low-boom wind-tunnel models has emerged, as 

shown in ¿gure 9.28 (ref. 9.20). 

Design of the blade mount becomes an integral part of the model design to minimize the effects of the blade 

mount on the aft signature of the wind-tunnel model. To date, blade mounts tend to exit the top of the model and 

swept with the Mach lines as much as possible to minimize the effect of the blade on both the off-body acoustic 

signature and model/mount interference effects. As one might expect, blade mounts are used to minimize crosssectional area of the blade while meeting the structural requirements of the test facility. Data from the 2008 test 

of the Gulfstream wind-tunnel model with a blade mount are shown in ¿gure 9.29 (ref. 9.20). Schlieren imagery 

and near-¿eld pressures support the use of the blade mount and con¿rm that the aft features of the model were 

captured in the under-track signature.

(a) Three-view drawing of wing-body-vertical low-boom aircraft 

concept with a blade mount.

(b) Installation at the NASA LaRC 4- by 4-foot 

Supersonic Wind Tunnel.

Figure 9.28. *XOIVWUHDPZLQGWXQQHOPRGHORIORZERRPDLUFUDIWFRQFHSWZLWKDEODGHPRXQWUHI

Figure 9.29. 6FKOLHUHQDQGQHDU¿HOGVLJQDWXUHGDWDRI*XOIVWUHDPZLQGWXQQHOPRGHOZLWKEODGHPRXQWUHI

1$6$SKRWR
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

412

Due to the shift between the sting and model axis of revolution, test techniques must be adapted to obtain off-track 

measurements via adjustments to the wind-tunnel model angle of attack and roll angle in the tunnel. Overall, 

the use of blade mounts for low-boom models is likely to continue as an improved approach to achieve better 

understanding of the aft shock and plume features, and improve the ¿delity of aft shock and plume modeling.

Ballistic Range – Free Flight Models

Another means of avoiding the trailing shock interference problems associated with sting-mounted wind-tunnel 

models is to launch free-Àight models into a ballistic range. Such a simulation technique allows for much larger 

models, thus improving con¿guration ¿delity and, in conjunction with a large ballistic range, allow for Àow-

¿eld de¿nition at larger distances from the model trajectory and permit the use of stationary microphones. The 

ability to vary the medium within the ballistic range is also a possibility as regards to investigating atmospheric 

inÀuences or focusing effects.

A schematic of a light gas gun-ballistic range is shown in ¿gure 9.30 (ref. 9.21). The major components are the 

pump tube, launch tube, an 8-foot diameter blast receiver tank and a range tank. A light gas gun, designed to 

generate high velocities, is used to propel the models at Mach numbers greater than 3. A large diameter piston is 

used to force a gas, helium or hydrogen, through a smaller diameter barrel containing the model aircraft enclosed 

in a sabot that breaks away after it leaves the barrel. The piston is powered by gun powder and a rupture diaphragm 

is used as the valve. At Mach 3 and lower, the gun is not used as a light gas gun. The range tank was 10 feet in 

diameter and 100 feet long and it operated at pressures of 10 atmospheres or evacuated to 3 mm Hg.

Three shadowgraph stations were available to record simultaneous horizontal and vertical shadowgraphs of the 

contour of the model and its angular orientation. Transducers were also located within the range tank downstream 

of the shadowgraph stations. A typical arrangement of the microphones can be seen in ¿gure 9.31 (ref. 9.21).

Figure 9.30. Sketch of light gas gun – ballistic range setup (adapted from ref. 9.21).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

413

The model size was chosen to be compatible with the 38-mm diameter launch tube. A view of a delta-wing model 

and its components, along with the three sabot designs used to launch the models, is shown in ¿gure 9.32 (ref. 

9.21). The models (¿g. 9.32(a)) had a length of about 2.0 inches and a span of about 1.3 inches. Considerable 

testing was performed to establish the best sabot design. The cantilever designs 10 and 12, shown in ¿gure 

9.32(b), failed completely in that the model was destroyed before it entered the range tank. It was found that Sabot 

11, depicted in the center of ¿gure 9.32(b), gave successful results with minimum contact with the model.

Tests were conducted to assure there would be no danger of sabot impact damage to the transducer. The most 

promising results were obtained by launching the models into the range tank at low pressures. An example is 

shown in ¿gure 9.33 (ref. 9.21). Because of the optical arrangement of the shadowgraph system, a double image 

of the model, as seen in the upper portion of ¿gure 9.33, is sometimes acquired depending upon the model 

location in the ¿eld of view. The model Àight was noted to be remarkably smooth with no observable pitch, yaw, 

or roll when the sabot was fully clear of the model.

Figure 9.31. Test arrangement and microphone locations (ref. 9.21).

(a) Ballistic model components and completed model. (b) Delta-wing model sabots.

Figure 9.32. 3KRWRJUDSKVRIGHOWDZLQJPRGHODQGVDERWGHVLJQVXVHGLQEDOOLVWLFUDQJHWHVWVDGDSWHGIURPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

414

Considerable effort was expended on the selection of the proper transducer and its mounting arrangement. Of all the 

commercially available transducers, it was found that the capacitance type transducer was best suited for the research. 

An oscillograph trace of the sonic boom signature from the delta-wing model is provided in ¿gure 9.34 (ref. 9.21).

The signature period observed in ¿gure 9.34 is on the order of 175 ȝsec with an overpressure level of about 65 

lbs/ft2

. A slight ringing can be observed at the bow and tail shocks and a bow shock rise time of about 10 ȝsec is 

noted, both attributed to the transducer limitations.

In ¿gure 9.35, shadowgraphs of ballistic range shots of the delta-wing model are shown representing a successful 

launch, shown in ¿gure 9.35(a), as compared to an unsuccessful launch shown to the right in ¿gure 9.35(b). 

The results from both the horizontal and vertical shadowgraph views of the successful Àight showed that the 

model Àight trajectory experienced no pitch or yaw (¿g. 9.35(a)) and although some roll was recorded, good 

pressure signatures were obtained. On the other hand, when similar launches were repeated (see ¿g. 9.35(b)) a 

roll rate of 300 deg/sec was recorded. It was concluded that the motion of the delta-wing models, which varied 

from smooth to highly erratic oscillatory in nature, was not attributable to model tolerances, sabot design, or 

light-gas gun tolerances. Attempts were made to arrest the models at the end of Àight in order to minimize 

model fabrication costs, by using varying thicknesses of urethane foam. However, it was found that the model 

structural integrity could not be maintained.

Figure 9.33. 6KDGRZJUDSKRIGHOWDZLQJODXQFKDQGVDERWEUHDNDZD\VKRW0DFKWDQNHYDFXDWHGWRPP+J

(adapted ref. 9.21).

Figure 9.34. 2VFLOORJUDSKWUDFHRIVRQLFERRPVLJQDWXUHIURPGHOWDZLQJPRGHO6KRW0DFKDGDSWHGIURPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

415

Testing of the wing-body models in the ballistic range was found to be impractical for several reasons, the 

foremost among them was the problem of launching stable Àights. Model integrity relative to model recovery 

would be costly. Model size was such that a short duration N-wave signature (about 0.175 msec) would limit 

model geometric integrity and require transducers with very high frequency response.

However, some limited testing was conducted to explore the possibility of launching bodies of revolution 

representing the equivalent area distributions, Ae

, of several shaped sonic boom signatures. It will be shown 

in the following section on modeling turbulence inÀuences on sonic boom N-wave signatures that useful 

experiments on turbulence effects on shaped signatures could be acquired by launching bodies of revolution in 

the ballistics range.

Signature Distortions by Turbulence

Certain sonic boom issues are both dif¿cult and costly to resolve by means of full-scale supersonic overÀights 

and could require a lengthy time period to establish a credible research database. One such issue is the inÀuence 

of the atmosphere on sonic booms, especially its turbulent nature in the initial 5000 feet of the earth’s surface. 

Distortions of sonic boom signatures result in boom levels that are much greater than the predicted levels or 

much less.

Recall from Chapter 2, it took some 1625 supersonic Àights and over 12,000 boom measurements, over about 

a quarter of a century, to acquire a suf¿cient database to establish the statistical variation of N-wave sonic 

booms. However, these results, which were obtained in speci¿c areas of the United States, do not necessarily 

represent world-wide conditions of turbulence. More importantly, they apply only to N-wave type signatures 

and, except for the few Àights of the SSBD, no database on the inÀuence of turbulence on low-boom shaped 

signatures is available. It is possible that this particular sonic boom issue could be assisted through groundbased experimental simulation.

Experiments simulating turbulence effects have been performed in the past using a variety of techniques 

but always involving N-wave signatures. In this section, several different simulation techniques used in the 

past will be addressed, including – the use of ballistic ranges and projectiles to generate the N-wave and jet 

Àows to simulate turbulence, use of a gas-¿lled soap bubble to refract and defract N-waves produced by spark 

discharges, use of a shock-tube horn-type sonic boom generator in conjunction with an air jet to simulate 

turbulence, shock-tube actuator and grid generated turbulence, ¿ring projectiles into the real atmosphere, and 

use of a spark discharge to provide the N-wave and a fan-plenum chamber with slot jet discharge to simulate 

turbulence. Some of the key ¿ndings and limitations of each of these techniques will be presented.

(a) Steady Àight. (b) Unsteady Àight.

Figure 9.35. Shadowgraphs of delta-wing launch in ballistic range (adapted from ref. 9.21).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

416

Ballistic Range – Projectiles and Duct Flow Turbulence

The earliest model experimental study regarding the inÀuence of turbulence in the lower layer of the atmosphere 

was performed by Bauer and Bagley in 1970 (ref. 9.22). The boom signature measurements with turbulence are of 

two basic types, those generated by jet interaction and those generated by thermal interaction. Every attempt was 

made to relate the model results to the full-scale Àight measurements regarding shock thickness, turbulent scale, 

and sonic boom signature overpressure and period. In fact, the authors dedicate an entire section of the report on 

scaling laboratory sonic boom work.

Their experimental setup, shown in ¿gure 9.36 (ref. 9.22) utilized the ballistic range at the McDonnell Douglas 

Aerophysics Laboratory at El Segundo, Calif. The range was enclosed within a barricade wall, with inside 

dimensions of 23 feet by 22 feet, and with a ceiling height of more than 10 feet. Sonic boom signatures were 

generated by ¿ring projectiles at Mach numbers from about 1.5 to 3.0. Pressure signature measurements were made 

at three positions at approximately 6-inch spacing along a ground plane 15 feet below the projectile trajectory. 

Turbulence was generated from a jet Àow duct exiting across the ground plane. Shadowgraph pictures were also 

obtained. A series of projectile shapes were used, as shown in ¿gure 9.37 (ref. 9.22), and included 22, 30, and 46 

caliber bullets and three machined projectiles of 0.22, 0.457, and 1.5 inches in diameter.

Figure 9.36. 6FKHPDWLFRIEDOOLVWLFUDQJHVHWXSVKRZLQJUDQJHWDQNEDUULFDGHMHWÀRZGXFWJURXQGSODQHDQGPHDVXUHPHQW

locations (view looking in the +z direction) (ref. 9.22).

Figure 9.37. %XOOHWDQGSURMHFWLOHVKDSHVXVHGLQH[SHULPHQWPHDVXUHPHQWLQLQFKHVUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

417

Projectile A was launched from a ballistic range light gas gun and the other projectiles and bullets were riÀe 

launched. The Mach number was controlled by varying the powder charges. For the 15-foot distance at which 

measurements were taken, the ground plane reÀected overpressure ranged from about 17 to 72 lbs/ft2

. Signature 

lengths were the order of 160 ȝsec to 800 ȝsec. The authors noted that the A projectile, which was more dangerous 

and dif¿cult to ¿re, also generated overpressures many times larger than the full-scale values observed from 

full-scale Àight tests and had a rather low sensitivity to turbulence because of the mismatch between the shock 

thickness and the model turbulence generated.

The duct that provided Àow near the ground plane was 24 inches by 24 inches and was termed the “24-inch 

nozzle”. Four other nozzles were designed and attached to the end of the duct nozzle and these are depicted in 

¿gure 9.38. Each of the four nozzles has different contraction ratios and size, each producing different turbulence 

structures. The 4-inch nozzle terminated in a grid made up of 3/4-inch dowels on 4-inch centers. The 6-inch 

nozzle used a honeycomb grid with 6-inch cells. Two high-speed nozzles were designed, one that exited above the 

ground plane and the other at the ground plane. Flow velocities of from 82 ft/sec to about 240 ft/sec were acquired 

depending upon the nozzle inlet size. 

The authors noted that the design of the thermal generator presented a unique challenge regarding the upward 

velocity of the natural convection of the heated air possibly acting as a shear layer rather than a thermal interaction 

with the sonic boom. They ¿nally designed the generator shown in ¿gure 9.39 (ref. 9.22). Two such thermal 

generators were built and used in the experiments and were located in the z plane at 20 inches normal to the barrier 

Àoor and about 7 inches and 13 inches in the x and y axis respectively. Experiments related to the thermal work 

were also performed using a rising column of helium instead of heated air. The helium was injected vertically 

upward from a 0.031-inch nozzle attached to the plenum chamber. The low molecular weight of the helium was 

expected to alter the boom signature in much the same way as the hot air. The authors state that the advantage of 

the helium setup was in the small size of the nozzle compared to the large size of the thermal generator.

Figure 9.38. 6NHWFKHVRIYDULRXVÀRZGXFWQR]]OHVUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

418

Some sonic boom measurements with and without turbulence generated by jet interaction are presented in ¿gure 

9.40 (ref. 9.22) for microphones I and II spaced 6 inches apart along the ground plane. As expected for the no duct 

Àow case (¿g. 9.40(a)) the two measured no turbulence signatures retain their N-wave shape and have nearly the 

same overpressure of about 18 lbs/ft2

 and periods of 170 ȝsec. On the other hand, the N-wave signatures that have 

passed through the turbulence (¿g. 9.40(b)) are distorted and vary in character from a peaked, almost spiked, to 

rounded wave forms with the overpressures varying from about 25 lbs/ft2

 down to about 12 lbs/ft2. The distortions 

observed on the bow shock are repeated at the tail shock. Such activity is essentially replicating full-scale Àight 

experience in the real atmosphere.

Figure 9.39. Thermal generator design (ref. 9.22).

(a) No duct Àow. (b) Turbulent duct Àow.

Figure 9.40. Sonic boom signatures from 0.22-caliber bullet at Mach 3 (adapted from ref. 9.22).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

419

The probability distributions of the sonic boom signature overpressure and bow-shock rise time from many 

measurements on a 0.22-caliber bullet traveling at Mach 3.0 through three levels of duct Àow generated turbulence 

are given in ¿gure 9.41 (ref. 9.22). The authors stated that the slopes of the data regarding overpressure variability 

(¿g. 9.41(a)) are generally less than corresponding data at Mach 1.6 for full-scale Àight results. This would 

indicate that the experimental turbulence intensity created longer perturbations in the model scale than for fullscale results. Examination of the probability distribution of rise-times, shown in ¿gure 9.41(b), indicate that for 

N-waves, turbulence increases the rise time and this ¿nding is consistent with other model experiments and full-scale 

Àight results. Sonic boom signatures measured with and without thermal interactions are presented in ¿gure 9.42 

(ref. 9.22). The projectile was a 0.46-caliber bullet at Mach 2.16.

(a) Overpressure. (b) Rise time.

Figure 9.41. 3UREDELOLW\GLVWULEXWLRQVRIRYHUSUHVVXUHDQGULVHWLPHIURP

caliber bullet at Mach 3.0 (adapted from ref. 9.22).

(a) No jet Àow – no thermal. (b) Thermal generator on.

Figure 9.42. Sonic boom signatures from 0.46-caliber bullet at Mach 2.16 (adapted from ref. 9.22).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

420

For the no-jet thermal case, ¿gure 9.42(a), relatively clean N-wave type signatures are observed with overpressures 

of about 32 and 38 lbs/ft, and a period of 310 ȝsec, both twice the values associated with the 0.22-caliber bullet 

(see ¿g. 9.40). When the thermal generators are operating (¿g. 9.42(b)), the signatures vary from slightly peaked 

to rounded. In all of the thermal tests using generators or helium, none of the signatures were as peaked or spiked 

as compared to when the N-wave signature passed through the duct Àow turbulence. Similar results were also 

observed during full-scale Àight tests in the desert when it was determined that the non-steadiness lower layer 

of the atmosphere was predominately a result of thermal turbulent conditions (i.e., surface conditions were hot 

with no sustained winds and few minimal wind gusts) or mechanically turbulent conditions (i.e., mild surface 

conditions with sustained winds and gusts) (ref. 9.23).

In summary, the Bauer-Bagley (ref. 9.22) ballistic range tests to replicate the full-scale Àight measurements 

showing the atmospheric turbulence inÀuences on boom signatures showed that signature distortions that were 

seen on the bow shock are repeated at the tail shock of the N-wave and are in agreement with the Crow theory 

(ref. 9.24) of frozen turbulence. For the model signatures to be geometrically similar to full-scale Àight results, the 

ratio of N-wave rise time to signature period needed to be preserved. The full-scale value of this ratio for a large 

supersonic transport is about 250. In these tests, this ratio was 450 for one series of tests and 270 for another. It 

is stated that the main problem using this particular size ballistic range and projectiles for these studies was the 

limitation in frequency response of the microphones and scaling of the turbulence. A larger ballistic range and 

larger projectiles would ease microphone requirements and make the task of providing the proper turbulent scales 

more achievable.

It is believed that there are even more advantages of the ballistic range projectile experimental setup. Unlike 

experiments where the N-wave signature is provided via a spark device or shock tube, projectiles can be modeled 

so as to generate cylindrical and non-N-waves (i.e., shaped signatures). Such shaping has been predicted by Hague 

and Jones (ref. 9.25) and is illustrated in ¿gure 9.43 (ref. 9.25). The shaped projectile could be gun launched using 

sabots. A projectile ¿red down a ballistic range generates cylindrical waves, like an actual aircraft, rather than 

the spherical waves of a spark source or the plane wave of a shock tube. A signi¿cant, quantitative, and needed 

database could be established well before any low-boom shaped vehicles are Àown and would play an important 

role in the development of computer codes designed to compute the alteration of the boom signatures that pass 

through various turbulence models.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

421

Spark Discharge and Gas-Filled Bubble

About a year or so after the Bauer-Bagley experiments (ref. 9.22), Davy and Blackstock (ref. 9.26) conducted a 

set of model experiments to test Pierce’s (ref. 9.27) explanation that sonic boom signature peaking and rounding 

are due to atmospheric non-homogeneities that act as converging and diverging lenses. They set out to observe 

the distortion of boom signatures resulting from speed of sound gradients in the atmosphere. Their experimental 

setup consisted of a gas-¿lled soap bubble to refract and diffract N-waves produced by an electric spark discharge. 

Figure 9.44 (ref. 9.26) illustrates the experimental setup, which consists of three main elements, a spark source, 

bubble, and microphones mounted on an optical bench. A gas laser (not shown in ¿gure) was used for alignment. 

Each bubble was held by a ring of thin wire and surface tension caused the bubble to stick in the ring. Two 

different size rings were used to hold large (6.95 cm) and small bubbles, which permitted a variation in the 

propagation time of the N-wave through the two mediums. An example of measured signatures for the spark 

generated N-wave passing through a large argon and helium bubble along with the no bubble control shot is 

provided in ¿gure 9.45 (ref. 9.26).

(a) Single arc power bodies with a ¿xed length and 

base radius.

(b) Selected signatures for single arc power bodies with 

base and length constrained, Mach 1.414, and h/l = 10.

Figure 9.43. ([DPSOHVRISRVVLEOHSURMHFWLOHVKDSHVDQGUHVXOWLQJVLJQDWXUHVUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

422

The top trace in each oscillograph trace is the control shot (no bubble) and it is seen that the signature is 

predominantly N-wave in shape. The experiment produced N-wave shapes with overpressures of about 34 lbs/

ft2

 and a period of 20 ȝsec at a distance of 10 cm. At 60 cm, these values were about 4 lbs/ft2 and a period of 26 

ȝsec, respectively. Refraction and diffraction inÀuences on the signature are noted by the authors – the argon 

¿lled bubble, acting as a converging lens, caused considerable peaking of the N-wave resulting in a three-fold 

increase in the overpressure. On the other hand, the helium ¿lled bubble, acting as a diverging lens, resulted 

in considerable rounding of the N-wave and a reduced overpressure to about 70 percent of the control shot. In 

these experiments, they also stated that no rounded signatures were ever observed with the argon-¿lled bubbles. 

Notice also that the shock rise times are increased in both cases and that the signature distortions that occurred 

on the leading shock is repeated on the tail shock, as is found in all full-scale Àight measurements. However, as 

the bubble is moved away from the microphone, the waveforms trend towards N-waves, as shown in ¿gure 9.46. 

Figure 9.44. 6NHWFKRIDSSDUDWXV/LVOXFLWHPRXQWLQJEUDFNHW6LVVSDUN%LVEXEEOHDQG0LVEDIÀHGPLFURSKRQHDQG

SUHDPSOL¿HUUHI

Figure 9.45. :DYHIRUPVUHFHLYHGE\PLFURSKRQHVIRUODUJHFPGLDPHWHUEXEEOHV8SSHUWUDFHLQERWK$DQG%LVFRQWURO

shot (no bubble in the wire ring). Bubble-microphone distance was 30 cm (ref. 9.26).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

423

Figure 9.46 (ref. 9.26) shows four signatures that passed through small helium-¿lled bubbles. Measurements were 

made at 10 cm, 20 cm, 30 cm, and 40 cm from the bubble. Examination of these four signatures shows that they 

are trending towards an N-wave shorter rise time as the ring and bubble are moved further from the microphone. 

Traces for small argon bubbles showed similar features.

Shock Tube Horn and Air Jet

Ribner, Morris, and Chu (ref. 9.28) held the opinion that the peaking and rounding of sonic boom signatures due 

to disturbed atmospheric conditions was associated with turbulent eddies, somewhat jet-like, resulting from the 

speed-of-sound (temperature) or velocity gradients. The authors were aware of the work of Davy and Blackstock 

(ref. 9.26) who looked at the speed-of-sound effects in a laboratory using gas bubbles and, thus, focused their 

efforts on demonstrating the velocity gradient effect using air jets. 

Their experimental setup, shown in ¿gure 9.47 (ref. 9.28), utilized a horn-type sonic boom generator 80-feet long 

with a 10- by 10-foot opening at the end.

Figure 9.46. :DYHIRUPVREVHUYHGIRUVPDOOFPGLDPHWHUKHOLXP¿OOHGEXEEOHIRUYDULRXVGLVWDQFHVEHWZHHQ

microphone and bubble. The spark-microphone distance was held constant at 60 cm (adapted from ref. 9.26).

Figure 9.47. 8QLYHUVLW\RI7RURQWR,QVWLWXWHIRU$HURVSDFH6WXGLHV87,$6KRUQW\SHVRQLFERRPJHQHUDWRUVKRZLQJ

SRVLWLRQRIMHWUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

424

In reference 9.28 (p. 927), the authors state that:

A 1⁄2-inch nozzle air jet with a settling chamber was installed near the large end of the horn, pointing towards 

the small driver end (¿g. 9.47). Several shock-tube drivers were used to produce quasi N-waves of 2 to 10 

msec duration, roughly 2 to 10 feet in length. Thus, the length-scale factor of the experiments was about 1/50, 

and an effective zone of jet Àow some 4-feet long would simulate a 200-foot atmospheric eddy.

These tests involved propagating the quasi N-wave signatures down the horn against, and with, the jet Àow of 

varying velocities, thus producing turbulence at the far end of the conical horn. They also obtained measurements 

without the jet turbulence. Some results of their experiments are given in ¿gure 9.48 (ref. 9.28) for the no-Àow 

and a jet Àow where the shock N-waves are traveling down the shock tube and against the jet Àow of 340 ft/sec 

(see sketch at bottom of the ¿gure).

The top trace, ¿gure 9.48(a), represents the boom signature produced by the shock tube propagating down the 

tube having no jet Àow. As can be seen, the signature closely resembles an N-wave except for slight asymmetry 

at the tail shock portion of the time history. Propagating this N-wave signature against the jet Àow of 340 ft/sec 

is illustrated in ¿gure 9.48(b). It can be seen that refraction, due to the mean Àow pattern of the jet, caused the 

signature to become peaked, or focused, the bow and tail shocks showing similarity to what happens in supersonic 

Àight-test measurements, and that the same peaking characteristics on the bow-shock show up at the rear shock. 

Note that the maximum overpressures for the no-Àow case is about 5 lbs/ft2

 and for the turbulent spiked signatures 

it is about 12 lbs/ft2

.

Figure 9.48. 6SLNHGVXSHUERRPVSURGXFHGE\DLUMHWLQKRUQVLPXODWRUMHWIDFLQJGULYHU±DMHWRII

DQGEMHWYHORFLW\DWIWVHFDGDSWHGIURPUHI

(c) Sketch of shock and air Àow direction.

(b) Jet velocity at 340 ft/sec.

(a) Jet off.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

425

When the air jet was turned around so that the jet Àow was traveling in the same direction that the shock was 

traveling (see ¿g. 9.48(c)), rounded signatures were observed, as shown in ¿gure 9.49 (ref. 9.28). Once again, 

the shock signature in the no Àow condition (¿g. 9.49(a)) is mostly N-wave in character with about 5.0 lb/ft2

overpressure. At a jet Àow velocity of 240 mph (¿g. 9.49(b)) the boom signature is rounded and the bow and tail 

shocks have large rise times. Measurements of this sort were acquired at jet-Àow velocities of 240, 340, and 420 

ft/sec. Results show that as the jet Àow velocity increases, so too does the peaking and rounding of the signature. 

From these initial experiments, the authors concluded that jets in the atmosphere can cause peaking and rounding 

of N-wave type sonic boom signatures. It should be noted that no details are given in reference 9.28 as to the 

turbulence scale or structure of the jet Àow. 

Shock Tube and Grid Turbulence

Tubbs (ref. 9.29) undertook an experiment aimed at explaining why sonic boom shock thickness measured 

from full-scale Àight tests were some 100 to 1000 times the theoretical (Taylor’s) values. He conducted a series 

of laboratory experiments using a shock tube to generate the shock wave that passed through grid-generated 

turbulence. A shock tube is a device used to generate and direct a shock wave on to a test device. The shock 

wave inside the tube can be produced by developing a high pressure behind a diaphragm that is ruptured to 

allow the shock wave to propagate down the tube. A view of the test setup is given in ¿gure 9.50 (ref. 9.29).

Figure 9.49. 5RXQGHGERRPVLJQDWXUHVSURGXFHGE\DLUMHWLQKRUQVLPXODWRUMHWIDFLQJRSHQHQG±DMHW

RIIDQGEMHWYHORFLW\DWIWVHFUHI

(a) Jet off.

(b) Jet velocity at 340 ft/sec.

(c) Sketch of shock and air Àow direction.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

426

A weak shock, produced by a shock tube was passed at right angles through turbulent Àow generated by placing 

obstructions at the exit of a wind-tunnel duct having an opening of 8 inches by 12 inches. Mean Àow velocities of 

about 100 ft/sec were produced and turbulent velocities in the planetary boundary were the order of about 10 ft/

sec. The turbulent path length was about one foot. Six turbulence generators were designed and used in the tests, 

two of which are shown in ¿gure 9.50(b) representing the extremes in the designs.

Small rise times, the order of 10 ȝsec or less, and low overpressures about 2 to 3 lbs/ft2

 were of paramount 

importance to the author. The authors decided to ¿re the boom across the turbulence in order to eliminate the 

spiking and rounding that Ribner, Morris, and Chu (ref. 9.28) observed when a jet was blowing against, and with, 

the shock. Two diaphragm materials were used – carbon paper and red zip (a cellophane about 4 ȝm thick). Some 

82 shocks through turbulence were made with the carbon paper diaphragms and 134 with the red zip. There was 

dif¿culty with the carbon paper not rupturing properly resulting in considerable scatter in the measured rise times. 

The red zip diaphragm ruptured well and produced consistent rise times. Samples of oscillograph traces for shock 

produced by the red zip diaphragms measured with microphone 1 and 2 are shown on ¿gure 9.51 (ref. 9.29).

(a) Overall test arrangement.

(a) Still air. (b) Still air. (c) Turbulence.

(b) Turbulence generators.

Figure 9.50. Schematic of experimental setup and two of six turbulence generators (adapted from ref. 9.29).

Figure 9.51. Typical oscillograph for shocks produced using red zip diaphragms. (a) and (b) 

reference shock (still air) and (c) shocks after passing through turbulence (adapted from ref. 9.29). 
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

427

Figures 9.51(a) and 9.51(b) show the measured reference shock (still air with no turbulence) and ¿gure 9.51(c) 

is the waveform after passing through turbulence (note the change in the pressure and time scales). It can be seen 

that signature rise times on the order of 10 ȝsec are observed for the still air with no turbulence case was achieved 

and overpressures of around 3 lbs/ft2

. Large increases in rise time on the order of 15-20 ȝsec are observed for the 

turbulent case.

A plot of frequency of occurrence against shock rise time is shown in ¿gure 9.52 (ref. 9.29) for the red zip 

diaphragms. It was noted that these results are clearer than the carbon paper diaphragms – both showed that rise 

times with turbulent Àow are higher. Also, this ¿gure presents a statistical treatment of all the data, without regard 

to turbulence generators used.

Examination of ¿gure 9.52 shows that a consistent reference rise time, IJr , of about 7 ȝsec is altered by the 

turbulence, IJt,indicating shock thickening. It is noted also that the frequency of occurrence, of the thinnest shock, 

decreases with turbulent Àow and there was no instance of a shock thinner than the thinnest of the reference shocks 

observed. It further states that this would seem to indicate that turbulence is a shock thickening mechanism, but 

not a shock thinning mechanism.

Since Tubb’s (ref. 9.29) work was directed towards explaining why sonic boom shocks had thicknesses 100 to 

1000 times the Taylor shock thickness, he concluded his experiments were not successful in showing such large 

shock thickening by turbulence.

Projectiles into Atmospheric Turbulence

Bass et al. (ref. 9.30) conducted a model experiment to investigate the inÀuence of real atmospheric turbulence on 

an N-wave sonic boom signature generated by supersonic projectiles. As will be shown, they were to experience 

the results of a mismatch in scaling between the projectile shock thickness and period, and the atmospheric 

turbulence. Recall that in the Bauer-Bagley ballistic range experiments (ref. 9.22), discussed earlier in this Chapter, 

it was found that as projectile size increased relative to the model turbulence scale, a rather low sensitivity to the 

turbulence was observed.

The Bass et al. experimental range is illustrated by ¿gure 9.53 (ref. 9.30) and consists of a target into which 

the projectile was ¿red and microphone arrangement where the alignment of the microphone face to the Mach 

cone was considered to be very important for these experiments. Three outdoor ranges were used, range 1 on 

Figure 9.52. Distribution of reference rise time (IJr࣠DQGULVHWLPHDIWHUSDVVDJHWKURXJK

WXUEXOHQFHIJt ) for shocks produced using red zip diaphragms (adapted from ref. 9.29).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

428

which the projectiles were 30-06-caliber bullets with muzzle velocities of 1000 and 720 m/sec. The projectiles 

at range 2 were from a military tank ¿ring projectiles in a sabot with muzzle velocities of 1460 m/sec. At range 

3, the projectile source was a tank ¿ring sabot and HEAT-T rounds at muzzle velocities of 1539 and 1173 m/sec. 

Although not stated, it is believed that these tank rounds were 105 mm in diameter. A fourth range was an indoor 

range with no air circulation or other sources of turbulence. The projectile used at range 4 (indoor) was 0.22 

caliber with an average muzzle velocity of 1260 m/sec.

For each shot, two microphones at two locations recorded the waveforms simultaneously – one was near the 

projectile path, was not moved, and acted as the reference and trigger for the second microphone that was moved. 

A typical waveform, from the 30-06-caliber projectile at range 1 is presented in ¿gure 9.54 (ref. 9.30). The 

signature is N-wave in character with an overpressure of 0.28 kPa, a period of 147 ȝsec and rise time of about 12 

ȝsec. The range of N-wave values included in these tests ranged from 0.04 kPa to 2.8 kPa in overpressure, from 

about 76 ȝsec to 3.4 msec in period and from about 2 ȝsec to 18 ȝsec for the rise times. It was stated that the 

general form of the wave was reproducible, but not the ¿ne structure. Propagation distance ranged from about 0.2 

m to 92 m and a total of 43 rounds were ¿red during the tests.

The major results from the experiments are presented in ¿gure 9.55 (ref. 9.30), which shows rise times as a 

function of N-wave overpressure. All of the rise time results acquired from the various projectiles, including 

the 22-caliber bullets, 30-06-caliber bullets, and 105-mm tank guns plotted on the ¿gure. The associated scale 

of turbulence and turbulence strength of the real atmosphere ranged from about 1 m to 6 m and about 4 x 10-6 to 

about 24 x 10-6, respectively. One major feature of this ¿gure should be noted – as stated by the authors (ref. 9.30, 

p. 308), “...Speci¿cally the measured rise times do not change in any speci¿c way with turbulence strength, ȝ2

. 

This observation suggests that turbulence plays a minor role, if any, in determining the rise time.”

Figure 9.53. 7\SLFDOH[SHULPHQWDOFRQ¿JXUDWLRQ7KHDQJOH ת is the Mach angle (adapted from ref. 9.30).

Figure 9.54. 7\SLFDOUHFRUGHGZDYHIRUPDWUDQJHIURPWKHFDOLEHUSURMHFWLOHUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

429

A second feature of ¿gure 9.55 noted by the authors (ref. 9.30, p. 308) is: “The experimental rise time appears to 

reach a lower limit of about 2 ȝsec. This limit is most probably a result of experimental constraints, speci¿cally, 

microphone alignment and bandwidth.”

In reference 9.30 (p. 306), the authors observed that “No correlation between measured rise times and the 

atmospheric turbulence was observed. This is in contrast to the ¿ndings of full-scale Àight results and could have 

been expected because of the small scale of the projectiles used to generate the sonic boom.”

Spark Discharge and Fan Duct Turbulence

Lipkins and Blackstock (ref. 9.31) also performed a model experiment dealing with sonic boom propagation 

through turbulence by using an electrical spark to provide the N-wave signature and model turbulence generated 

by a plane jet. The authors took particular care to make the downscaling of the turbulence the same as that for the 

model N-waves – with a scale factor of about 10-4. An illustration of the arrangement of the experimental setup is 

given in ¿gure 9.56 (ref. 9.31).

Figure 9.55. Experimental and computed rise times (ref. 9.30).

Figure 9.56. $UUDQJHPHQWRIWKHH[SHULPHQW±SODQHMHWVRXUFHVSDUNVRXUFHZLWKRXWWKHSDUDEROLFUHÀHFWRUDQG

receiver. The dimensions shown are in meters (adapted from ref. 9.31).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

430

The spark source and receiving systems were mounted on the optical bench. Both spherical and plane N-waves 

were used in the tests, the latter being generated by placing the spark gap at the focus of the parabolic reÀector. 

The model turbulent velocity ¿eld was generated by a fan, plenum chamber, and rectangular nozzle to provide 

the plane jet. Flow exited a slot nozzle with a height of 0.25 m and a width that could be varied with the use of 

a sliding door, typically 25.4 mm for the experiments. Increasing the slot width increases the thickness of the 

turbulent Àow. As such, the shocks are being inÀuenced by the turbulence over a longer period of time. This 

situation is analogous to Àight through the lower level of turbulence at a low or high Mach number, as was 

illustrated in ¿gure 2.39 of Chapter 2. Measured boom signature variability was found to be increased for Àights 

at Mach 1.3, as compared to Àights at Mach 1.6 where the shock ray paths spent less time propagating through 

the turbulent lower layer. Reynolds numbers of about 53,000 were achieved at this open width and the N-wave 

propagation path was 0.7 m downstream where the jet velocity was about 30 m/sec. 

An example of the signature of the spherical N-wave measured 400 mm from the spark is shown in ¿gure 9.57 

(ref. 9.31). It is seen that a nearly symmetrical N-wave is produced except that the tail shock is not as well formed 

as the bow shock. Overpressures of from 2 lbs/ft2

 to 4 lbs/ft2 were produced from spherical N-waves and up 

to about 13 lbs/ft2

 from plane N-waves. The period and rise time of the N-wave signatures was about 15 ȝsec 

and 0.5 ȝsec, respectively. Such values place severe demands on the microphone receiving system. The authors 

used a system having a frequency response that was Àat from 10 Hz to 2.25 MHz. Table 9.2 lists the nominal 

overpressure, period, and rise times for full-scale Àight sonic booms and the experiment spark N-waves.

Table 9.2. Typical Values of Rise Time IJ3HDN3UHVVXUHǻSDQG'XUDWLRQ7IRU6RQLF%RRPVDQG6SDUN3URGXFHG

1:DYHVUHI

Parameter Sonic Boom Spark Produced N-wave

ǻp 30-200 Pa 100-500 Pa

T 100-300 msec 10-30 ȝsec

IJ 2-10 msec 0.4-2 ȝsec

For both the signature period and rise time, the ratio between full-scale and model experimental values is on the 

order of 5,000 to 10,000. Table 9.3 gives three characteristics of atmospheric turbulence, the design scale model 

values, and the actual measured values.

Figure 9.57. ([DPSOHVLJQDWXUHRIDVSKHULFDO1ZDYHPHDVXUHGPPIURPWKHVSDUNVRXUFHUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

431

7DEOH7XUEXOHQFH3DUDPHWHUV7\SLFDO$WPRVSKHUHDQG'HVLJQDQG$FKLHYHG9DOXHV

IRUWKH0RGHO([SHULPHQWUHI

Characteristic 

Lengths for 

Atmospheric 

Turbulence

Atmospheric 

Turbulence

Model Exp. Turbulence 

Scaled Down

Model Exp. Turbulence 

Measured

Turbulent Boundary

Layer Thickness 1000 m 0.1-0.2 m 0.05-0.3 m

Outer Length Scale

(Large Eddies) 100-200 m 0.01-0.02 m 0.01-0.08 m

Inner Length Scale

(Smallest Eddies) 10 mm 0.001 mm 0.1-0.01 mm

The author’s note that except for the Kolmogorov inner length scale (small eddies), which is not important to these 

experiments, the measured valves agree very well with the design values and thus conclude that the turbulence 

of the plane jet has about the right scale to mimic the role of the atmosphere where model N-waves are simulated 

sonic booms (ref. 9.31, p. 154).

Sets of 100 to 200 pressure waveforms were recorded, mostly using plane N-waves. Fewer measurements were 

recorded for spherical N-waves. However, the ¿ndings were qualitatively the same. The test procedure was to 

¿re 100 spark-generated N-waves into quiet air, then turn the jet on and ¿re a second set of 200 N-waves. Several 

examples of waveforms of plane N-waves passing through the model turbulence to one with no turbulence are 

shown on ¿gure 9.58 (ref. 9.31). The signature in the upper left of ¿gure 9.58 is for the no-turbulence case. All the 

others are inÀuenced by turbulence and vary from peaked and spiking to smoothing and rounding of the signature. 

Also, similar distortions are associated with the bow and tail shocks, as observed during supersonic Àight in the 

atmosphere.

Figure 9.58. :DYHIRUPVRISODQH1ZDYHV±WKHXSSHUOHIWWUDFHLVDUHIHUHQFH1ZDYHUHFRUGHGLQWKHDEVHQFHRI

WXUEXOHQFHDOORWKHUVUHFRUGHGDIWHUSURSDJDWLRQWKURXJKWXUEXOHQFHUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

432

An illustrative display of recorded results of the distribution of overpressure and rise time also from reference 

9.31 is provided in ¿gures 9.59 and 9.60. Figure 9.59 shows the variability of the peak overpressure for 100 plane 

N-waves in still air and 100 plane N-waves into model turbulence. The dashed horizontal lines represent the 

average measurements with turbulence.

For the no turbulence case, little variation is noted from the 600 Pa nominal plane N-wave overpressure throughout 

all 100 N-waves. A signi¿cant scatter is seen to result in the overpressure of N-waves passing through turbulence 

with a majority of the data points lying below the dashed line representing the difference between the average and 

median overpressure with turbulence.

Similar observations can be seen in the case of the plane N-wave rise times, as shown in ¿gure 9.60 (ref. 9.31).

Here, little variability in rise time is displayed for the no turbulence cases and considerable scatter in the data is 

seen for the turbulence runs. Most of the data points fall below the dashed line representing the average rise time 

measurement with turbulence.

Figure 9.60. 9DOXHVRIULVHWLPHIRUSODQH1ZDYHVPHDVXUHGZLWKDQGZLWKRXWWXUEXOHQFH7KHGDVKHGOLQHVKRZV

the average for the measurements with turbulence (ref. 9.31).

Figure 9.59. 9DOXHVRISHDNSUHVVXUHIRUSODQH1ZDYHVPHDVXUHGZLWKDQGZLWKRXWWXUEXOHQFH7KHGDVKHGOLQHVKRZV

the average for the measurements with turbulence (ref. 9.31).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

433

From the measured results of overpressure variation due to turbulence, a cumulative probability plot of equaling 

or exceeding the no turbulence plane N-wave overpressure is presented in ¿gure 9.61 (ref. 9.31). The authors 

note that the fact that these data ¿t a straight line on the log-normal scale illustrates that these results are similar 

to those for sonic boom in the atmosphere.

Regarding signature rise time, two interesting plots are presented by the authors of reference 9.31 and are shown 

in ¿gure 9.62. They plotted the rise time cumulative probability function on an (a) linear and (b) log-normal scale.

The linear curve (¿g. 9.62(a)) con¿rms that for plane N-waves, turbulence almost always increases signature 

rise time. The log-normal curve, ¿gure 9.62(b) indicates a two-part behavior in that one can draw a straight line 

for rise time values greater than the no-turbulence average value and a second line for values smaller than the 

average.

As a result of this experiment, the authors concluded among other ¿ndings that they have successfully simulated 

sonic boom propagation through the atmosphere and that they reproduced waveform distortions both in scale and 

in character in this laboratory. Once again, the reduced scale of these experiments placed serious demands in the 

response of the measurement system with particular attention to the scaling of the spark N-wave and turbulence 

to a real atmosphere.

Figure 9.62. &XPXODWLYHSUREDELOLW\FXUYHRIULVHWLPHSODQH1ZDYHVDIWHUSURSDJDWLRQWKURXJKWXUEXOHQFHIJno is the average 

rise time measured in the absence of turbulence (ref. 9.31).

Figure 9.61. &XPXODWLYHSUREDELOLW\FXUYHRISHDNSUHVVXUHRISODQH1ZDYHVDIWHUSURSDJDWLRQWKURXJKWXUEXOHQFH7KHFXUYHLV

plotted on a log-normal scale and ǻpno is the average peak pressure measured in the absence of turbulence (ref. 9.31).

(a) Linear. (b) Log-normal.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

434

Quantifying Focus Boom Intensities

Sonic boom focusing is associated with certain Àight conditions of an aircraft including steady level Àight 

at cutoff Mach numbers (MCO), transition Àight from subsonic to supersonic speeds and maneuvering Àight 

including supersonic turns, pull-ups, pushovers, and dives. Although acoustic theory provides for the location 

of the focus, it is not able to predict the intensity in that as the ray tube area approaches zero, the overpressure 

goes to in¿nity. Recent work by Auger and Coulouvrat (ref. 9.32) and Kandil and Zheng (ref. 9.33, Appendix 

D) now allows one to calculate the magnitude of the transition focus boom for a variety of in-coming boom 

signatures. However, the predicted levels from these computer codes require experimental validation.

Over the years, a substantial Àight database has been established for each of these Àight maneuvers (see 

Chapters 3 and 5). Acquiring boom signatures at the maximum focus during Àight tests for any of these 

types of maneuvers is dif¿cult and costly, requiring numerous microphone systems, knowledge of the aircraft 

operating conditions, careful execution of the particular Àight maneuver, and detail information on the expected 

atmospheric conditions at the test site.

In response to the need for quantifying the boom intensity at a focus, several simulation techniques were 

developed and included ballistic ranges, a supersonic sled track, shock tubes, and spark discharges onto mirrors/

refractors. A brief review of the application of each of these techniques to focusing conditions associated 

with steady-level Àights at MCO, transition Àight from subsonic to supersonic speeds, and maneuvering Àight 

involving accelerations and changes in Àight path angle will be presented.

Mach Cutoff Focus Using Ballistic Range-Mixed Gases

It has been shown that steady-level Àight at Mach cutoff (MCO), where the aircraft speed over the ground 

is equal to the sound speed at the ground, will result in a focus at the shock extremity due to atmospheric 

refraction (see ¿gs. 5.5, 5.6, and 5.7 in Chapter 5). In 1971, Peter et al. (ref. 9.34) conducted an experiment 

using a ballistic range and ¿red a projectile into a strati¿ed medium of air and carbon dioxide. These results 

are brieÀy discussed by Wanner in reference 9.35. A focus factor of 1.7 was observed on the front shock that

resulted in a focus factor of about 3.3 after a position correction, which compares to Àight-test focus factors 

of about 3 (refs. 9.36 and 9.37). In 1974, Sanai, Toong, and Pierce (ref. 9.38) conducted a similar experiment 

to create refraction focus booms in a ballistic range ¿ring projectiles at low supersonic speeds into a strati¿ed 

medium of varying sound speed consisting of a homogeneous mixture of CO2

 and air. A schematic of this setup 

along with some measured results are presented in ¿gure 9.63 (ref. 9.38). Pressure signatures were recorded by 

a fast response transducer inserted in the Àow ¿eld. Dual Schlieren pictures were taken simultaneously during 

each run. A graphic summary of their ¿ndings is provided in ¿gure 9.64 (from ref. 9.38). It can be seen from 

the ¿gure that they too obtained a focus factor of 1.7 on the front shock, duplicating the values presented by 

Wanner et al. (ref. 9.35). It should be mentioned that experiments such as the one described herein where the 

shock signature is small and the range facility con¿ned, one must contend with the dif¿culties associated with 

transducer size regarding response, shock diffraction, shock waves, and shock reÀections.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

435

Transition Focus Utilizing a Rocket Sled Track

The focus boom resulting from an aircraft accelerating from subsonic to supersonic speeds cannot be eliminated 

or avoided. One can only inÀuence the point at which the focus reaches the ground. In Chapter 3 of this 

publication, it is shown that transition focus booms can be placed to within 1000 feet of the desired location 

(see, for example, ¿g. 3.11) if the vehicle’s performance and atmospheric conditions are known. As in the 

case of MCO, focusing acoustic theory does not quantify the maximum overpressure experienced at the focus. 

However, as shown in Chapter 3, a computer code developed by Auger and Coulouvrat (ref. 9.32) and replicated 

by Kandil and Zheng (ref. 9.33, Appendix D) permits a prediction of the maximum focus value for a transition 

maneuver. Prior to this code development, an extensive Àight database was generated in order to establish 

these maximum focus overpressure values and corresponding focus factors. Focus factors on the order of 2.5 

to 5.0 have been experienced from N-waves (see ¿gures 3.11–3.12 and 3.14 of Chapter 3). As noted earlier, 

obtaining focus boom measurements via Àight tests is costly, dif¿cult, and complex and requires great care and 

experience in their execution (see, for example, the work of Wanner et al. reported in ref. 9.35).

(b) Schlieren photographs of comparable runs in 

homogeneous (left) and strati¿ed (right) media.

(a) Schematic of ballistic range test setup.

Figure 9.63. Schematic diagram and test results of experimental apparatus to measure sonic boom 

focusing due to atmospheric refraction (adapted from ref. 9.38).

Figure 9.64. 5DGLDOYDULDWLRQRIWKHIRFXVIDFWRUIRUOHDGLQJVKRFNDGDSWHGIURPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

436

It is obvious that simulation techniques involving ballistic ranges, shock tubes, or spark discharge arrangements 

would not be suitable for addressing the transition focus concern, since the initial starting condition on each is 

already supersonic. A rocket sled track was believed to have applications and tests were made to determine its 

suitability. In 1974, Reed (ref. 9.39) conducted a series of tests using the Sandia 5000-foot long rocket sled track. 

Photographs of the sled track and carriage are shown in ¿gure 9.65 (ref. 9.39).

The sled track has suf¿cient track length and supersonic capability to provide the necessary simulated conditions 

and also is of a size to allow for adaptation of fairly large-scale vehicles designed to produce N-wave type 

signatures and also shaped signatures. Some results of these tests obtained during a transition run are shown in 

¿gure 9.66 (ref. 9.39). The location of the 12-microphone array with respect to the predicted caustic (focus line) 

about 3000 feet lateral to the sled track is shown in ¿gure 9.66(a). The overpressure scale is essentially the same 

for all signatures (¿g. 9.66(b)).

The observed sonic boom signatures are typical of those measured in Àight tests, that is, rumble type signatures 

are observed in the pre-focus region upstream of the focus line, a single N-wave within a focus region, and the 

N-wave carpet signature followed by the refracted (U-shaped) signature in the post focus region. A focus factor 

of about 2.2 is realized in ¿gure 9.66(b). The maximum focus factor measured during these tests was about 3.3.

One of the major drawbacks of using the supersonic sled track for sonic boom simulation is the presence of 

the ground surface, which does not allow the boom signature to develop in three dimensions. In addition, the 

(b) Utility sled with 25 High Velocity Air-to-Ground 

Rockets (HVAR), 425-m/s maximum speed (1394 ft/sec).

(a) Sled test. 

Figure 9.65. 3KRWRJUDSKVRI6DQGLDIRRWVXSHUVRQLFVOHGWUDFNUHI

(a) Location of microphone array to caustic. (b) Microphone signatures.

Figure 9.66. Measured sonic boom signatures during transition of sled track from subsonic to 

supersonic speeds (adapted from 9.39).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

437

atmosphere in which the boom is to be measured is horizontally strati¿ed and inÀuenced by the ground cover 

between the point of generation and measurement locations.

Maneuver Focus

In the two focus boom situations just presented – that of Mach cutoff (MCO) and transition (the acceleration 

from subsonic to supersonic speeds) – the focus is associated with a single focus line or caustic. During aircraft 

Àights involving both acceleration and geometric changes such as turns, dives, and pushover maneuvers, multiple 

focus lines (caustics) may be produced. At the point at which these focus lines merge, there is a superfocus. An 

excellent example of a superfocus resulting from turn-entry maneuver is presented by Wanner et al. (¿gs. 5, 15, 

and 17 of ref. 9.35 and also ¿g. 3.8 of this publication). A focus factor of 9 was observed. Simulation techniques, 

including spark discharges and parabolic and ellipsoidal reÀectors, a shock tube, and a ballistic range, were 

utilized in laboratory experiments conducted with the objective of de¿ning the maximum overpressures that could 

be experienced due to focusing of a sonic boom N-wave. A discussion of each of these techniques follows.

6SDUN0LUURU5HÀHFWRU

In 1969, Beasley, Brooks, and Barger (ref. 9.40) conducted a laboratory investigation of N-wave focusing using a 

spark to generate the N-wave and parabolic mirror as a reÀector. Figure 9.67 depicts the lab test setup showing the 

arrangement of the spark, mirrors, and microphone. A comparison of the calculated and measured signatures 

of the initial N-wave, showing their shape at the focus and in the post focus region, is presented in 

figure 9.68. Although the summary presented in figure 9.69 shows the variation of peak overpressure 

with distance from the focus, it also indicates a maximum focus factor of about 3.0. The authors 

caution whether any conclusions concerning the maximum value could be drawn from such data. They 

further noted that although the data indicate significant amplitude in the vicinity of the focus, the very 

large amplitudes predicted by strict ray-tube theory were not obtained and that these large amplitudes 

are influenced by wave length, microphone response, mirror astigmatism, and mirror dimensions.

Figure 9.67. 6FKHPDWLFGLDJUDPRIWHVWDSSDUDWXVIRUVSDUNPLUURUIRFXVERRPH[SHULPHQW

7RSYLHZ$OOGLPHQVLRQVDUHLQFHQWLPHWHUVUHI

Figure 9.68. &DOFXODWHGDQGPHDVXUHGVKDSHVRIWKHSUHVVXUHVLJQDWXUHDVWKHZDYHSDVVHVWKURXJKWKH

focus. The arrow indicates the direction of wave propagation (adapted from ref. 9.40).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

438

Laboratory tests similar to those just discussed were performed in 1972 by Cornet (ref. 9.41) utilizing the 

spark technique and a spherical mirror. Later on, Wright and Blackstock (ref. 9.42) conducted an experimental 

laboratory investigation of the focusing of intense, airborne pressure pulses (N-waves) by an ellipsoidal mirror. 

Three ellipsoidal reÀectors (large, mid-size, and small) were used during these tests. All had the same major and 

minor axis and eccentricity as seen in ¿gure 9.70(a). A schematic representation of the reÀected (B) and edgediffracted (C) wave fronts from the reÀector are shown in ¿gure 9.70(b). To the right of the exterior focus (F2

) is 

the pre-focus region and to the left is the post-focus region. The observed waveforms from one of the experiments 

is presented in ¿gure 9.70(c) (ref. 9.42). Seven signatures are shown that represent measurements in the prefocus (+12 cm), focus, and post-focus (-12 cm) regions. Each position corresponds to the arrival of the direct 

N-wave from the spark (A), reÀected (B), and edge-diffracted (C) signals. For the case of the large reÀector, a 

focus factor of over 10 is experienced. Reduced values of focus factor for the mid-sized and small reÀectors were 

observed. Once again, the small scale of this experiment required considerable care and attention to maintain 

shock strength and consistency, and microphone size and frequency response. Since the spark-discharge method 

will always produce N-waves, an additional constraint is that focusing associated with shaped such as Àattop or 

ramp signatures is not possible with this technique.

Figure 9.69. /DERUDWRU\WHVWVHWXSDQGUHVXOWVIURPVSDUNZLWKSDUDEROLFPLUURUIRFXVERRPH[SHULPHQWUHI

Figure 9.70. /DERUDWRU\WHVWVHWXSDQGUHVXOWVIURPVSDUNDQGHOOLSVRLGDOPLUURUIRFXVERRPH[SHULPHQWUHI

(a) Geometry of ellipsoid, showing interior (F1) and exterior (F2) 

foci and three reÀector with differing depths but common axes 

(2a=28 cm, 2b=14 cm) and eccentricity İ = 0.866.

(b) Schematic representation of reÀected and edge diffracted. 

(C) wave fronts from hemi-ellipsoidal reÀector.

(c) Waveforms observed along the axis of the large hemiellipsoidal reÀector.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

439

6KRFN7XEH5HÀHFWRU

Distortion or wrinkling of the shock fronts, as illustrated in ¿gure 9.71(a), by atmospheric anomalies or from 

non-steady Àights were thought to cause boom focusing. Whitham (ref. 9.43) suggested that as the shock waves 

strengthen near the focus of, say, a concave curvature in the shock front, the converging rays bend away from 

each other and the concave front becomes convex and focusing would not occur. In 1973, Sturtevant (ref. 9.44) 

conducted an experiment to study shock waves focused from concave reÀectors in a 17-inch diameter shock tube. 

In ¿gure 9.71 (ref. 9.44) are shown the test arrangement and results from the shock tube experiment. It can be 

seen that as shock strength decreases, as a result of decreasing Mach number, the focus factor increases, varying 

from about 3 to 9. 

%DOOLVWLF5DQJH0L[HG*DVHV

In an attempt to address superbooms generated as a result of acceleration maneuvers, Sanai, Toong, and Pierce 

(ref. 9.45) made use of a dual Schlieren system and several fast response pressure transducers on the same small 

ballistic range that was utilized in the previous tests described in ¿gure 9.63. The major difference was that 

the leak-proof gate, containing the gases of higher and lower sound speeds, was mounted vertically rather than 

horizontally, as shown in ¿gure 9.72 (ref. 9.45).

(a) Schematic diagram of wrinkled 

wave front.

(b) ReÀected wave fronts according to geometrical acoustics. 

Solid lines reÀected shock. Dashed lines – diffracted waves.

(c) Ampli¿cation factor on tube axis versus distance from reÀector.

Figure 9.71. $UUDQJHPHQWDQGUHVXOWVIURPVKRFNWXEHH[SHULPHQWRQIRFXVLQJRIZULQNOHGZDYHIURQWDGDSWHGIURPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

440

Prior to the ¿ring of the projectile, the gate is removed and the gases mix, creating a transition region of variable 

sound speed in the vicinity of the gate (black region at left of Schlieren picture). The projectile, passing through 

this medium, experiences increasing Mach number similar to an accelerating supersonic aircraft. Shown in the 

¿gure is a Schlieren photograph and simultaneous pressure signatures obtained from the shocks emanating from 

the bullet traveling 1235 m/sec from a helium-argon mixture into nitrogen causing the wavefronts to be concave. 

Comparison of the two pressure signatures show the magni¿cation of the bow and tail shocks caused by the shock 

front concavity for the inhomogeneous case, as compared to the near N-wave shape in the homogeneous case.

The largest focus factor obtained in these experiments was 2.0. The authors point out that this focus factor value 

of 2.0, with appropriate theoretical scaling to account for differences in shock overpressure ratios suggests that 

peak magni¿cation of atmospheric sonic booms due to accelerated aircraft Àight should be in the range of 6 to 13. 

These values bracket the results of ¿eld tests. Although the small ballistic range technique confronts dif¿culties 

associated with signatures of small size and response and shock waves and reÀections, it does have an advantage 

over the spark-mirror systems in that signature shapes other than N-waves can be generated by proper shaping of 

the projectile. Focus factors other than these attributed to N-waves can be examined.

Underwater Studies

An analytical and experimental database has been generated since the late 1960s time period regarding the 

penetration of sonic booms into water and their impact on marine life in the oceans and seas of the world (see

Chapter 8). A portion of the experimental database was generated by full-scale Àight vehicles. As was noted in 

the discussion regarding the effect of sonic booms on marine life in Chapter 8, there is a large mismatch of sound 

speeds in air (1116 ft/sec) and water (4800 ft/sec). As a result of this large difference, the effect of sonic booms 

from vehicles in level Àight at supersonic speeds over lakes and oceans was expected to be minimal since about 

99 percent of the impinging energy would be reÀected.

It is of interest to note that in the early years, only two documented experimental model studies regarding this 

subject were performed and they will be presented. The ¿rst was the scaled experiment by Waters and Glass (ref. 

9.46) in 1970 using dynamite caps and a Àooded quarry. In 1972, Intrieri and Malcolm (ref. 9.47) conducted 

scaled measurements using gun-launched projectiles over a water tank. Waters and Glass focused mainly on 

booms associated with supersonic Àight and Intrieri and Malcolm investigated both supersonic and hypersonic 

speeds.

Figure 9.72. 5HVXOWVIURPEDOOLVWLFUDQJHH[SHULPHQWWRPHDVXUHVXSHUERRPVIURP

aircraft acceleration maneuvers(adapted from ref. 9.45).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

441

Blasting Caps/Flooded Quarry

The Waters and Glass (ref. 9.46) experiment was the earliest effort to investigate underwater sonic boom 

propagation. To accomplish this, they used an explosive charge detonated in the air over a small body of water. A 

schematic of their test setup is presented in ¿gure 9.73 (ref. 9.46). The small body of water was a Àooded quarry 

about 300 feet wide and 80 feet deep. The explosive charges, 6-grain dynamite blasting caps, were suspended 

from a high horizontal cable about 30 feet above the water. Two arrays of sensors were suspended in the area from 

a low horizontal cable and consisted of a microphone and hydrophone for the local array, directly under explosive 

charge, and a movable array consisting of a microphone and three hydrophones. All of the experiments were 

made with a Àat water surface. No measurements were made to investigate effects of water roughness.

The explosive charges that produced a spherical spreading shock wave simulated the sonic boom upon the water 

surface, as shown in ¿gure 9.74 (ref. 9.46). The indicated region of the spherical wave front was used to simulate 

the corresponding position of a conical wave front that a supersonic aircraft would generate. About 20 shots 

were made with the remote array positioned between 15 feet and 145 feet away from the local array, which was 

directly under the explosive charge. It was found that the optimum location, free from interference due to other 

transmitted signals, was from 2 to 60 feet from the local array. The location of the sensors is shown in ¿gure 9.75 

(ref. 9.46), which depicts the rays of sound within the critical angle that were transmitted across the air-water 

interface into the water. These rays were plotted in 5° increments in the water using Snell’s law. The curves are 

wave fronts at successive intervals of time.

Figure 9.73. *HRPHWU\RIVRQLFERRPVLPXODWLRQH[SHULPHQWUHI

Figure 9.74. Simulation of region and shock cone using portion of spherical shock wave (ref. 9.46).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

442

Figure 9.75 shows that the hydrophone directly below the explosive charge will be experiencing the shock 

penetrating the surface at speeds greater than the speed of sound in water (4800 ft/sec) and the remote hydrophone 

array positions will see shocks at Mach angles greater than 13.4° with effective velocities in the 1000 ft/sec to 

2000 ft/sec range depending upon the location of the remote array from the overhead position. In an attempt to 

increase the width of the penetration measurement windows, a 16-foot square plywood reÀector-absorber was 

suspended over the water directly under the explosive charge about 6 feet above the water surface to block out 

the shock wavefronts within the 13.4° cone. However, diffraction effects at the edge of the reÀector-absorber 

resulted in its abandonment. In the initial stages of these experiments, inÀated auto inner-tubes were used as 

Àoats to hold up the local and remote arrays rather than the overhead cables. However, it was found that the 

Àoats above the remote array were being excited by the incident airborne shock wave and were reradiating 

sound back into the water. This introduced signals that interfered with the desired measurements. Thus, all 

subsequent experiments were done without Àoats. A typical shock waveform measured 3.8 feet above the water 

by the local array microphones and is shown in ¿gure 9.76 (ref. 9.46).

Both the incident and reÀected signatures of the airborne shock are shown. The dynamite cap pressure signature 

is a good approximation of an aircraft N-wave, except for the 10 lbs/ft2 bow shock and a reduced level of the 

recompression tail shock (7 lbs/ft2). However, although the dynamite cap simulated the order of magnitude of a 

sonic boom of 2.0 lbs/ft2

, its signature duration of 1.8 msec was considerably shorter than the 100 to 300 msec 

measured from an aircraft. Since the dynamite cap shock signature duration is about 1 percent of that of a real 

Figure 9.75. /RFDWLRQVRIVHQVRUVIRUPHDVXUHPHQWVRISHQHWUDWLRQRIVKRFNZDYHHQHUJ\LQWRZDWHUUHI

Figure 9.76. $LUERUQHSUHVVXUH1ZDYHGXHWRJUDLQG\QDPLWHFDSH[SORGHGDWIHHWDERYHZDWHUVXUIDFHUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

443

boom, the authors stated that the predicted water penetration for the experiment would only be 1 percent of that 

which would actually occur. In reference 9.46 (pp. 3-5), the authors went on to state:

But this amount of penetration, of the order of one foot in the experiment, did prove to be measurable. 

In retrospect, it is clear that if N-waves having durations of 100 msec to 300 msec had been used in the 

experiment, no meaningful measurements could have been made because of reverberations in the small 

body of water that was used. It would have been necessary to conduct the experiment in the deep ocean, 

which would have been a much more ambitious undertaking.

Placement of the hydrophones of the movable remote array was based on Sawyer’s (ref. 9.48) theoretical 

expression for the penetration of an N-wave into the water and was found to be a few feet for the 1.5 msec 

duration of the dynamite cap explosive charge. The four hydrophones were set at 1, 1.5, 2.5, and 4.5 feet, the 

actual depth being somewhat greater than intended due to the catenary of the overhead cable suspension. The 

hydrophones and microphones had good frequency response, the hydrophones down to about 10 Hz and the 

microphones from about 1.0 Hz to about 10 KHz. The results of a measurement, including both transmission 

and penetration effects, are presented in ¿gure 9.77 (ref. 9.46) for the local array directly below the explosive 

charge and the remote array, which was about 35 feet from the local array.

The measured results are quite interesting. Note that the signature measured by the local array of hydrophones 

directly below the explosive charge (see ¿g. 9.75) one foot below the water surface has the same characteristics 

as the airborne shock and is only slightly lower in overpressure. This was expected since the shock arrival angle 

to the water surface was within the critical angle (13.4°) resulting in a shock wave penetration speed greater 

than the sound speed in water. In contrast, for the remote location some 35 feet from the local array, the shock 

arrival angle to the water surface was well outside of and greater than the critical angle of 13.4°, which resulted 

in the shock front moving across the water surface at only 1600 ft/sec. The hydrophone measured signatures 

become more rounded and are an order of magnitude less than the airborne signature value, measured 2.4 feet 

above the water surface at the 35-foot remote array location, and decrease with increasing depth.

Figure 9.77. $LUERUQHDQGXQGHUZDWHUPHDVXUHPHQWVRIVKRFNVLJQDWXUHWUDQVPLVVLRQDQGSHQHWUDWLRQDW

remote array 35 feet from local array (ref. 9.46).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

444

A detailed comparison between the theoretical prediction provided in reference 9.46 for the test shot results 

shown in ¿gure 9.77 is presented in ¿gure 9.78 (ref. 9.46). The agreement between the predicted and measured 

signature is quite good, within a factor of two on both amplitude and signature duration. At the time of these 

experiments, during the early 1970s, the authors were satis¿ed that the experiment resulted in veri¿cation of 

predictions based on existing theory of N-wave penetration into a Àat body of water. This simulation experiment, 

like others discussed in this chapter, had to address scaling concerns such as the explosive N-wave signature 

overpressures of about 10 lbs/ft2

 and periods of 1.5 msec and the water depth of 80 feet. 

Ballistic Range Water Tank

Intrieri and Malcolm (ref. 9.47) conducted a unique experiment in investigating the penetration of sonic boom 

signatures moving over the water at speeds less than and greater than the speed of sound in water using the 10-

foot diameter 300-foot-long NASA ARC Pressurized Ballistic Range and a gun-launched projectile over a large 

Plexiglas tank containing water. A sketch of the setup is shown in ¿gure 9.79 (ref. 9.47). 

Two tanks were utilized in this experiment, the large tank in which pressure measurements were made and a 

smaller tank that was used for obtaining shadowgraphs of the shock behavior in air and water. These were placed 

directly under the Àight path of the projectile. Details of the makeup of the large tank are given in ¿gure 9.80 (ref. 

9.47). The tank was a 24-inch by 24-inch by 12-inch open top container. The tank and the Àat plate shown with 

the pressure cell could be moved vertically to vary the distance from the projectile Àight path and the water level 

was also adjusted to vary the depth of the pressure cell beneath the water surface.

Figure 9.78. &RPSDULVRQEHWZHHQWKHRUHWLFDOSUHGLFWLRQDQGH[SHULPHQWDOPHDVXUHPHQWRISHQHWUDWLRQRIVKRFNZDYH

energy into water (adapted from ref. 9.46).

Figure 9.79. Sketch of test setup in ballistic range (ref. 9.47).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

445

A description of the projectile and resulting shock pressure signature is presented in ¿gure 9.81 (ref. 9.47). A 

powder gas gun was used to launch the 45o

 half cone projectile, about 0.5 in., or 1.25 cm in diameter (¿g. 9.81(a)) 

at Mach numbers of 2.7 and 5.7, corresponding to Mach numbers of 0.6 and 1.3 in water. The measured signature 

(¿g. 9.81(b)) is N-wave in character with the tail recompression being signi¿cantly less in amplitude than the bow 

shock as a result of the large trailing wake on the projectile. Peak overpressures in air of from about 270 lbs/ft2

 to 

1375 lbs/ft2

 were experienced at distances of about 34 inches to 8 inches, respectively. The signature period was 

1.5 msec in duration.

The shadowgraph of the projectile traveling over the water tank at Mach 2.7 is shown in ¿gure 9.82 (ref. 9.47).

Since the speed of the shock in air (i.e., Mach 2.7) is less in air than the speed of sound in water, which is about 

Mach 4.4, the bow and tail shocks are reÀected off the surface of the water, as can be seen in ¿gure 9.82. However, 

when the projectile is launched at Mach 5.7, the results are entirely different because airborne shocks do, in fact, 

penetrate below the water surface. These results are presented in ¿gure 9.83 (ref. 9.47).

Figure 9.80. 'LPHQVLRQDOVNHWFKRIODUJH3OH[LJODVWDQNZLWKSUHVVXUHWUDQVGXFHUUHI

Figure 9.81. 'HVFULSWLRQRISURMHFWLOHDQGVKRFNSUHVVXUHVLJQDWXUHDGDSWHGIURPUHI

(a) Sketch of steel projectile. (b) Oscilloscope record of 

measured pressure signature.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

446

The underwater shock resulting from the impingement of the projectile bow shock on the water surface is barely 

seen in the shadowgraph. Since the penetration of the projectile tail, or trailing shock, was signi¿cantly lower in 

overpressure than the bow shock, it is less visible in the shadowgraph, but still exists at shallow depths and will be 

shown in ¿gure 9.84. The researchers found that when the aluminum plate was replaced with a Plexiglas plate, the 

shock wave propagating in water was not reÀected by the plexiglass tank and bottom and passed through almost 

undisturbed. The authors stated that this occurred because the acoustic impedance (product of density and sound 

speed) of water and Plexiglas are nearly identical. Pressure signatures of the measurements obtained in air and 

underwater for the two cases shown on the above shadowgraphs (¿gs. 9.82 and 9.83) are presented in ¿gure 9.84 

(ref. 9.47).

Figure 9.82. 6KDGRZJUDSKSLFWXUHRIPRGHOÀ\LQJRYHU3OH[LJODVZDWHU¿OOHGWDQNDW0DFKLQDLU0water UHI

Figure 9.83. 6KDGRZJUDSKSLFWXUHVRIPRGHOÀ\LQJRYHU3OH[LJODVZDWHU¿OOHGWDQNDW0DFKLQDLU0water UHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

447

A signi¿cant difference is apparent in the pressure signatures measured underwater between the subsonic and 

supersonic cases (Mach 2.7 and 5.7 in air, respectively). For the Mach 2.7 Àights (subsonic case in water), there 

is a rapid decay in strength and a rounding of the signature with increasing water depth. For the Mach 5.7 Àights 

(supersonic case in water), there is little loss in pressure amplitude and the signatures remain N-wave in shape, 

similar to the in-air case. Note too that the trailing shock, which was not too evident in the shadowgraph picture 

(¿g. 9.83), is clearly evident in the measured pressure signature. 

For the Mach 2.7 in-air case, the authors calculated the pressure signatures at various depths covering the 

range measurements of figure 9.84 using Sawyers’ theory (ref. 9.48), and these are shown in figure 9.85 

(ref. 9.47). The symbol į is defined as the decay parameter for a sinusoidal plane wave underwater. In 

figure 9.86, the calculated maximum pressure variation with į is shown. The reduction in peak pressure 

with water depth predicted by Sawyers is shown along with the measured results and the comparison is 

good. In fact, the authors state that these results (Intrieri and Malcolm) and those of Waters and Glass (see 

fig. 9.78) both support the theory even though they were conducted with completely different techniques 

and greatly differing time scales. The N-wave durations of 0.15 msec for the present tests and 1.5 msec 

for the Waters and Glass tests are an order of magnitude different and the shock overpressures are of 

about two orders of magnitude different for the Intrieri and Malcolm experiment than Waters and Glass.

Figure 9.84. Oscilloscope records of pressure measurements in air and underwater (ref. 9.47).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

448

Recall that for the Mach 5.7 in-air case, shown in ¿gure 9.84, the underwater pressure signatures changed little 

from the one measured in air at the water surface. The variation of the signature bow shock as a function of water 

depth for a constant distance of the projectile Àight path above the water surface is shown in ¿gure 9.87 (ref. 9.47).

It can be seen that the maximum shock overpressure remains fairly constant with increasing water depth and is 

of the same level as the pressure at the water surface indicating essentially no loss in peak pressure due to water 

depth. This is further illustrated in ¿gure 9.88 (ref. 9.47), which presents a variation of peak overpressure in air 

and underwater as a function of distance from the projectile Àight path. Note that the variation in-air faired line, 

shown in ¿gure 9.88(b), passes through data sets at all three depths at which measurements were obtained.

Figure 9.85. &DOFXODWHGSUHVVXUHVLJQDWXUHVDWYDULRXVGHSWKVLQZDWHUXVLQJWKHRU\RIUHIHUHQFH0 LQDLUFDVHUHI

Figure 9.86. Variation of peak pressure from underwater sound waves with normalized depth parameter (ref. 9.47).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

449

The simulation technique utilized by Intrieri and Malcolm also had to address the scaling concern of shock 

signature characteristics, water depth, transducer response, and measurement techniques. They did conduct an 

experiment to address the concern for the reÀection and refraction of the shocks that may result with the pressure 

cell Àush-mounted in a Àat plate. The use of a ballistic range-projectile setup has great potential for examining 

the overwater sonic boom that will be associated with future vehicles designed to produce low-boom shaped 

signatures. Projectiles can be shaped to produce a variety of signature shapes, such as the bodies of revolution 

examined by Hague and Jones (ref. 9.25) and shown in ¿gure 9.43.

Figure 9.87. 9DULDWLRQRISHDNSUHVVXUHZLWKZDWHUGHSWKXVLQJSUHVVXUHFHOOPRXQWHGLQÀDWDOXPLQXPSODWHUHI

(a) In air. (b) Underwater.

Figure 9.88. 9DULDWLRQRISHDNSUHVVXUHZLWKGLVWDQFHIURPÀLJKWSDWKUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

450

Diffraction and Refraction of Sonic Boom Due to Buildings and Topography

Of the numerous environmental concerns contained within the sonic boom arena, the interaction between the 

sonic boom and topographical features such as buildings, mountains, rolling terrain, and canyons is one of the 

most interesting. Attention was brought to reÀection and refraction concerns by Dini and Lazzeretti in their 

1969 paper (ref. 9.49), which showed incident boom overpressure could be enhanced from two to eight times 

depending upon the ground con¿guration, a few of which are illustrated in ¿gure 9.89 (ref. 9.49). 

A substantial database has been established regarding this subject, but most relate to sonic boom loadings on 

commercial and residential structures (refs. 9.50 and 9.51) including the more recent work by Klos (ref. 9.52) and 

Cho and Sparrow (ref. 9.53). In each, however, these studies address various types of individual structures. No 

cluster of residential homes or multiple skyscraper arrangements have, as yet, been addressed. Several analytical 

efforts have been performed, i.e., Ting and Pan (ref. 9.54) and Ting and Kung (ref. 9.55), but these also deal with 

single structures.

In their earlier study, Ting and Pan (ref. 9.54) looked at obtaining a near-¿eld solution for the diffraction of a plane 

wave by a three-dimensional body and found one was not yet available. However, some partial information at the 

corners could be obtained using the averaging principle (ref. 9.56, p. 96), which states that “The intensi¿cation 

factor at the vertex of a cone with a solid angle Ȝ is equal to the ratio of the solid angle of the Àow ¿eld at the 

vertex without and with the cone, i.e., 4ʌ/(4ʌ-IJ).” Results from their study concerning a dimensional calculation 

for a V-shaped building shown in ¿gure 9.90 (ref. 9.54) were obtained.

Figure 9.89. 6FKHPDWLFVRILQFLGHQWDQGUHÀHFWHGVKRFNSDWWHUQVUHI

Figure 9.90. Three-dimensional diffraction of incident wave (ref. 9.54).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

451

Three Àight path approaches are indicated on the ¿gure – direction I approaches the concave side of the V-shaped 

building, direction II is parallel to one leg of the V (which is, in effect, equivalent to a face-on boom to a single 

building), and direction III is opposite to I. The intensi¿cation factor (I.F.), calculated at the base of the V at 

position A for Àight paths I and II and at position Aƍ for Àight path III, is provided in table 9.4 (ref. 9.54).

7DEOH,QWHQVL¿FDWLRQ)DFWRUVIRUD96KDSHG%XLOGLQJ$UUDQJHPHQW5HVXOWLQJIURP

Supersonic Flight in Three Directions (ref. 9.54)

,QWHQVL¿FDWLRQ)DFWRUV,)

Flight Path

Corners I II III

I.F. Ȝ=ʌ/2 I.F. Ȝ=ʌ/2 I.F. Ȝ=ʌ/2

A 4ʌ/Ȝ 8 4ʌ(2Ȝ) 4 (a) (a)

B 4ʌ(2ʌ+Ȝ) 8/5 4ʌ(2ʌ+Ȝ) 8/5 4ʌ(2ʌ+Ȝ) 8/5

 Aƍ (a) (a) 2ʌ(2ʌ-Ȝ) 4/3 4ʌ(2ʌ-Ȝ) 8/3

 Bƍ 4ʌ(4ʌ-Ȝ) 8/7 4ʌ/(4ʌ-Ȝ) 8/7 4ʌ/(4ʌ-Ȝ) 8/7

(a) Reached by diffracted waves from adjacent corners and edges.

Spark Discharge – Parabolic Mirror

In 1970, two laboratory simulations addressing boom refraction and diffraction were conducted. 

The first by Brooks, Beasley, and Barger (ref. 9.57), who used a spark discharge system and parabolic 

mirror to generate the sonic boom signatures and the second by Bauer and Bagley (ref. 9.22), who 

used a ballistic range and projectiles fired from a gun to produce the boom signatures. Brooks, 

Beasley, and Barger (ref. 9.57) describe a technique for simulating the fundamental phenomenon that 

occurs when a weak shock wave passes over a building and they present some representative data 

obtained using this technique. A schematic drawing of the apparatus is shown in ¿gure 9.91 (ref. 9.57).

The test setup consists of a spark device placed at the focus of a parabolic mirror so as to produce the sonic 

boom N-wave, which is then reÀected from the mirror to the smooth ground surface plates, the latter made of 

6.35-mm thick aluminum 41-cm wide by 51-cm long. Various building models were placed on this surface. 

The angle-of-incidence at which the shock impacts the model structure is varied by changing the ground 

plane angle with respect to the projectile trajectory. The distance between the mirror and model was 4.216 

Figure 9.91. 'LDJUDPRIWHVWDSSDUDWXVVKRZLQJVSDUNPLUURUJURXQGVXUIDFHDQGEXLOGLQJPRGHOUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

452

meters. A conventional off-axis Schlieren system (not shown) was used to photograph the shock waves.

The author stated that the diffraction phenomenon resulting from an obstacle in the path of a sound wave depends 

primarily on the size of the obstacle to the wavelength of the sound pulse. As such, the models were scaled in 

accordance with the length of the N-wave. Various sizes of buildings were tested. They varied in height from 1/8 

wavelength to 5 wavelengths and in width from 1/2 wavelength to a width greater than the mirror size.

They also chose to use ground shock angle (Į in ¿gure 9.90) rather than Àight Mach angle ( = sin-1(1/M)) mainly 

due to the atmospheric effects. Shock tubes and projectile ranges were considered in the selection of a source to 

generate the N-wave but were discarded for the electric spark method. This latter method, which produces a plane 

wave rather than a conical wave, was found to be very consistent in both overpressures and wavelengths (period) 

and repeatable. The small size of the spark generated N-wave did present a limitation on the tests in that the 

microphone size relative to the signature period was large (microphone diameter is 3.22 mm or 1/8 wave length). 

The system had a Àat response of 2 dB to 140 KHz.

A typical signature of the N-wave produced by the spark and measured with a microphone Àush-mounted in a 

ground plane is shown in ¿gure 9.92 (ref. 9.57). The N-wave is quite representative of a sonic boom N-wave with 

the exception of the tail shock having somewhat greater amplitude than the initial bow shock. Boom overpressure 

of the bow shock is the order of 10 lbs/ft2

 and the signature period is about 100 ȝsec (wavelength of 2.5 cm).

In ¿gure 9.93 (ref. 9.57), the general features of the wave pattern formed when the bow shock of the sonic boom 

N-wave passes over a two-dimensional building is shown. Shock wave passage is from left to right. Seven regions 

(see ¿g. 9.93) are identi¿ed and include: region 1 is the direct wave; region 2 is the wave reÀected from the 

ground; region 3 is the wave reÀected from the front face of the building; region 4 is a part of the direct wave that 

is diffracted around the upper rear corner of the building; region 5 consists of the compression wave diffracted 

from the upper front corner; region 6 is the expansion wave diffracted from the upper rear corner; and Region 7 

is the wave refracted from the top of the building. The authors state that the wave pattern for a building of ¿nite 

width is even more complex. Further examination of ¿gure 9.93 (ref. 9.57) indicates that on the ground ahead of 

the building, the overpressure should be that of the direct wave with the ground reÀection factor of 2.0. Near the 

top of the building front face, the overpressure should be the direct wave overpressure multiplied by the reÀection 

factor for the building (also a factor of 2.0). As one approaches the base of the building, the wave reÀected from 

the building overlaps the direct wave measured at the ground and at the base juncture, they are superimposed such 

that the overpressure is increased by a factor of 4.0.

Figure 9.92. 7\SLFDOVLJQDWXUHRI1ZDYHZKHQPLFURSKRQHLVPRXQWHGÀXVKZLWKJURXQGVXUIDFH

2VFLOORVFRSHVZHHSVSHHGȝVHFFPDGDSWHGIURPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

453

Test results from such an experiment is given in ¿gure 9.94 (refs. 9.57). The overpressure measured on the 

ground at the base of a two-dimensional building of various heights is plotted as a ratio to the ground pressure pg

. 

It is noted that there is a small difference in the pressure ratio at the building base apex with the shock ground 

angle (i.e., simulated aircraft Mach number). In addition, the base apex overpressures are about 1.7 times those 

of the measured ground pressure rather than the factor of 2 for a perfect reÀection case. This is due to diffraction 

effects and microphone size. The intensi¿cation ahead of and behind the intersection corners of an V-shaped 

building due to sonic booms at 30° and 60° incident angles is shown in ¿gure 9.95 (ref. 9.57).

Figure 9.93. 5HÀHFWLRQDQGGLIIUDFWLRQRIVKRFNZDYHSDVVLQJRYHUDEXLOGLQJ$UURZVLQGLFDWHGLUHFWLRQRIVKRFN

wave (ref. 9.57).

Figure 9.94. 0D[LPXPSUHVVXUHWRIURQWEDVHFRUQHURIEXLOGLQJRIYDULRXVKHLJKWVDQGLQ¿QLWHZLGWKGXHWRVRQLFERRPV

DUULYLQJDWLQFLGHQWDQJOHVRIDQGUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

454

The experiments also examined whether unusual building shapes are better or worse than rectangular block 

shapes in regards to boom shielding or magni¿cation. Results are presented for a V-shaped building in ¿gure 9.95 

(ref. 9.57). It can be seen that when the V-shaped building faces the incoming wave so that reÀections from both 

sides and from the ground coincide at the base vertex, the amplitude, as expected, is magni¿ed. When the wave 

is incident from the other direction, the pressure at the forward building base is lower and there is a signi¿cant 

amount of shielding on the inside of the L shape.

The inÀuence of building cross-section, whether Àat-faced or circular, is shown to have an effect on the pressure 

ratio that is realized on the front and behind the building. Some results for cylindrical buildings are shown in 

¿gure 9.96 (ref. 9.57).

It is shown in ¿gure 9.96(a) that as the cylindrical building’s diameter decreases, the pressures also decrease from 

those measured for a rectangular building. This is a result of the bene¿cial effects of diffraction as the incoming 

Figure 9.95. *URXQGSUHVVXUHLQIURQWRIDQGEHKLQGWKHLQWHUVHFWLQJFRUQHURID9VKDSHGEXLOGLQJZDYHOHQJWKKLJKDQG

wavelength on each side due to sonic booms at angles of 30°and 60° (ref. 9.57).

(a) In front of building. (b) Behind building.

Figure 9.96. 3UHVVXUHUDWLRRQWKHJURXQGLQIURQWRIDQGEHKLQGF\OLQGULFDOEXLOGLQJGXHWRVRQLFERRPVDWDQDQJOHRI

30° to the building and 60° to the ground (ref. 9.57).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

455

shock impacts and moves across the cylindrical building. As the building diameter increases from 1⁄2 wavelength 

to 11⁄2 wavelengths, the bene¿cial effects of diffraction are reduced to the point where the shock front begins to 

see the cylindrical building as a rectangular Àat surface. Behind the building (¿g. 9.96(b)), the pressures depend 

on the phase relationships of waves coming over and around the cylindrical building.

In summary, this method of simulation proved to be of signi¿cant value giving results that are consistent with 

the previous analytical studies and suggest extending the scope to include clusters of building and some terrain 

topography. However, producing the sonic boom signatures using the spark discharge techniques, which results 

in an N-wave, does not allow for investigating the inÀuence of low-amplitude shaped signatures.

Ballistic Range – Projectiles

The second of two experimental simulations regarding sonic boom reÀection and diffraction on building structures 

and other topography was performed by Bauer and Bagley (ref. 9.22) using the same ballistic range and projectiles 

employed in their investigation of the inÀuence of atmospheric turbulence on sonic boom signature distortions 

discussed early on in this chapter. The arrangement of the test setup is shown in ¿gure 9.97 (ref. 9.22), which is the 

same arrangement as presented in ¿gure 9.36 with the exception that the Àow-duct is disabled and topographical 

models are placed on the ground plane. A sketch of one of these has been inserted to illustrate the arrangement.

Their experimental setup shown in ¿gure 9.97 (ref. 9.22) utilized an existing ballistic range enclosed within a 

barricade wall with inside dimensions of 25 feet by 22 feet with a 20-foot height.

Sonic boom signatures were generated by ¿ring projectiles at Mach numbers of from about 1.5 to 3.0. Pressure 

signature measurements of the projectile baseline signatures were made at three positions at around 6-inch spacing 

along a ground plane 15 feet below the projectile trajectory. The same series of bullets and projectiles used in the 

experiments on the inÀuence of atmospheric turbulence on boom signature distortion discussed early on in this 

chapter were also used in the present experiment and are shown in ¿gure 9.98 (ref. 9.22) and included 22-, 30-, 

and 46-caliber bullets and three machined projectiles of 0.22-, 0.457-, and 1.5-inch diameters.

Figure 9.97. 3ODQYLHZRIEDUULFDGHDGDSWHGIURPUHIVHHDOVR¿J
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

456

Projectile A was launched from a ballistic range light gas gun and the other projectiles and bullets were launched 

by riÀe. Mach number was controlled during the experiment by varying the powder charges. For the 15-foot 

distance at which measurements were taken, the ground plane reÀected overpressures ranged from about 17 to 72 

lbs/ft2

. Signature lengths were on the order of 160 msec to 800 ȝsec. Six topographical models having dimensions 

from 3 inches to 24 inches are shown in ¿gure 9.99 (ref. 9.22). Included is a step model, parallel wall model, 

and overhang models shown in ¿gure 9.99(a), a two-corner model (shaped) with apex angles of 45° and 90° 

(¿g. 9.90(b)) and a canyon model (¿g. 9.90(c)). For each model, the microphone locations are designated as IV 

through XII and are indicated on each sketch.

Shadowgraphs were taken and played an important role in these tests, especially in positioning the models on the 

ground plane such that overpressure measurements from the incoming shock are made at the various microphone 

locations shown on ¿gure 9.99. For the purpose of discussions, three models were chosen and include the step 

model, 2-inch overhang model, and the parallel wall model. Shadowgraphs of the N-wave shocks passing over 

each of the three models are presented in ¿gure 9.100 (ref. 9.22).

Figure 9.98. %XOOHWDQGSURMHFWLOHVKDSHVXVHGLQH[SHULPHQWUHIVHHDOVR¿J

(a) Two-dimensional topographical models. (b) Corner topographical. (c) Canyon model.

Figure 9.99. 'HWDLOVRIWRSRJUDSKLFDOPRGHOVXVHGLQWKHWHVWVQRWHGLPHQVLRQVDUHLQLQFKHVUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

457

The two basic N-wave signatures generated by projectile B at Mach numbers 1.4 and 2.56, and measured at 

the ground board surface are shown in ¿gure 9.101 (ref. 9.22). At Mach 1.4, the N-wave overpressure was 21.5 

lbs/ft2

 and period was 300 msec, and at Mach 2.56, the overpressure was 25.0 lbs/ft2 and period was 260 msec.

Boom signatures measured on the step model at position IV (ground plane), V (apex of ground plane and step), 

and VI (on the step face at 2/3 the step height) for projectile B at Mach 1.4 are shown in ¿gure 9.102 (ref. 9.22).

As expected, an enhancement of the overpressure is realized at microphone V. Ting and Pan (ref. 9.54) predict a 

peak intensi¿cation factor (IF) of 4.0. Using 1/2 of the measured overpressure (i.e., the incident pressure) of 12.6 

lbs/ft2

 and the 46.7 lbs/ft2 of microphone V, the IF is about 3.7. At the 2/3 height location, microphone VI, three 

shocks are observed with the largest overpressure of 39.6 lbs/ft2

. Note also that the mid-shock of signature IV is 

at a different location than the location in ¿gure 9.101(a) (which is near the trailing shock). In addition, there is a 

slight variation in the ground board signature overpressures between the two bow shocks at Mach 1.4 (i.e., 21.5

versus 25.3 lbs/ft2).

(b) Two-inch overhang model – 

projectile B at Mach 2.55. 

(c) Parallel model – projectile B at 

Mach 2.55.

Figure 9.100. 6KDGRZJUDSKVRIWKUHHPRGHOVDQGVKRFNVIURP1ZDYHVSURGXFHGE\3URMHFWLOH%UHI

(a) Step model – projectile B at Mach 1.4. 

Figure 9.101. %DVLFVLJQDWXUHVIURPSURMHFWLOH%DGDSWHGIURPUHI

(a) Mach 1.4. (b) Mach 2.56.

Figure 9.102. 6LJQDWXUHVDWORFDWLRQ,99DQG9,IURPSURMHFWLOH%DW0DFKDQGWKHVWHSPRGHODGDSWHGIURPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

458

A quite complicated sonic boom signature is observed for the 2-inch overhang model shown in ¿gure 9.103 (ref. 

9.22). Note also the change in horizontal time scale on this plot. Multiple signatures were observed at all three 

microphone locations with the largest overpressure occurring at microphone V at the intersection of the ground 

plane and wall base with a value of 34.5 lbs/ft2

. The resulting IF is 2.62. Signatures associated with the parallel 

wall model, shown in ¿gure 9.104 (ref. 9.22), are not too different than those measured on the step model (¿g. 

9.102). The signature measured at location IV with an overpressure of 15.7 lbs/ft2

 with the parallel wall model 

does not represent the direct ground pressure of 25 lbs/ft2

 for the step model seen in ¿gure 9.101 due to the 

presence of the second simulated building. Thus, using the value of ground overpressure for the step model yields 

an IF of 3.9 associated with microphone V located at the intersection of the ground plane and the base of the 

second simulated building of the parallel wall model.

Figure 9.104. 6LJQDWXUHVDWORFDWLRQV,99DQG9,IURPSURMHFWLOH%DW0DFKDQGSDUDOOHOZDOOPRGHODGDSWHGIURPUHI

Figure 9.103. 6LJQDWXUHVDWORFDWLRQ,99DQG9,IURPSURMHFWLOH%DW0DFKDQGWKHVWHSPRGHODGDSWHGIURPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

459

A summary of the IFs for all of the topographical models tested along with a canyon model is provided in tables 

9.5 and 9.6 (ref. 9.22).

7DEOH%RRP,QWHQVL¿FDWLRQ)DFWRUV3URGXFHGE\7RSRJUDSKLFDO0RGHOVUHI

Shot Intensi¿cation Factors Measured at Station

Task No. Model Projectile M IV V VI

III 1-3 Step D 2.5 - - 3.70 1.72

III 3-3 Step D 1.4 - - 3.04 1.56(-1.66)

III 7-3 Step B 2.6 - - 3.22 1.78

III 4A-3 90° Cor. D 2.5 - - 4.14 2.80

III 5-3 90° Cor. D 1.4 - - 4.78 2.76

III 6B-3 90° Cor. B 2.6 - - 3.18 3.00

IV 104 Step B 2.56 1.78 3.78 2.00

IV 111 Step B 1.40 1.86 3.68 1.70

IV 133 90° Cor. B 2.57 1.80(-2.40) 4.24 4.16

IV 137 90° Cor. B 1.46 2.84(-3.06) 7.54 3.48

IV 138 45° Cor. B 2.57 2.56(-2.74) 5.62 5.24

IV 142 45° Cor. B 1.40 3.60(-3.94) 10.52 8.08

IV 122 1 in. O.H. B 2.56 1.94 2.86 1.48(-1.80)

IV 121 2 in. O.H. B 2.56 1.86 2.62 1.24(-1.58)

IV 127 3 in. O.H. B 2.56 1.41 2.75 1.44

IV 124 4 in. O.H. B 2.57 1.32 1.80(-1.92) 1.02(-1.04)

IV 123 1 in. O.H. B 1.39 1.80 3.78 1.36(-2.42)

IV 116 2 in. O.H. B 1.40 1.86 3.28 1.02(-1.51)

IV 126 3 in. O.H. B 1.40 1.86 2.34 2.22(-2.34)

IV 125 4 in. O.H. B 1.36 2.06 1.86(-1.88) 1.96

IV 128 Parallel B 2.56 1.10(-1.16) 3.88 1.90

IV 131 Parallel B 1.47 1.18 2.42 1.82

( ) for tail shock
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

460

7DEOH%RRP,QWHQVL¿FDWLRQ)DFWRUV3URGXFHGE\&DQ\RQ0RGHOUHI

Shot ĮC

Intensi¿cation Factors Measured at Station

Numbers M (Degrees) VII VIII IX X XI XII

144, 146, 2.57 0 2.68 3.70 2.14 1.04 1.04 1.14

149, 150

145, 147, 1.40 0 3.32 3.18 1.96(-2.42) 1.10 1.14 1.18

148, 151

152, 154 2.56 66 2.28(-2.98) 3.48(-3.82) 13.8

156 1.40 45 2.58(-3.18) 3.08(-3.88) 12.8

Note that the largest value associated with the step, corner, overhang or parallel wall model was 10.52 and this 

was for the 45° corner. An even larger IF of 13.8 was measured on the canyon model from the B projectile at 

Mach 2.56 and at an angle of 66° from horizontal.

In summary, the simulation technique of using a ballistic range and firing projectiles is uniquely suited to 

experiments with clusters of model buildings and other topographical models. Further, as pointed out in the 

turbulence studies using this same simulation device, non N-wave boom signatures can be designed and 

launched via sabots. This would allow for examining the reflecting and diffraction of low-boom shaped 

signatures to establish the IF level.

,QGRRU2XWGRRU6XEMHFWLYH5HVSRQVH

Research into the adverse environmental effects of sonic booms produced by aircraft goes back to the early 1960s. 

Laboratory and Àight research has been performed (see Chapter 8) to de¿ne and understand how sonic booms 

affect structures, people, and animals. While Àight experiments are the most realistic, they are also restricted 

in that they only apply to the particular aircraft used and the Àight conditions Àown. They are also expensive. 

Consequently, a variety of ground simulation devices have been developed and employed that yield realistic sonic 

booms to people, animals, and structures. They fall into four categories – (1) headphones, (2) loudspeakers inside 

closed booths, (3) piston systems, and (4) explosive charges. In subsequent paragraphs, short summaries of some 

of these systems and a sample of the research carried out using some of them will be discussed. The parameters of 

interest in the early days of developing sonic boom simulators are shown in ¿gure 9.105 relative to the classical 

N-wave boom signatures.

Figure 9.105. ,OOXVWUDWLRQRIVRQLFERRPVLJQDWXUHSDUDPHWHUVWKDWPD\EHRILQWHUHVWIRUVLPXODWLRQ:DYHVKDSH

overpressure (ǻpGXUDWLRQǻtDQGULVHWLPHIJ) are depicted.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

461

They include the magnitude of the leading-edge shock, the time it takes for the leading-edge shock to reach 

its maximum value (rise time), and the duration of the pressure signature. Since the mid-1960s, when the 

minimization of sonic booms became of prime interest to researchers, several new sonic boom signature shapes 

have become subjects of interest and three are illustrated in ¿gure 9.106 along with the N-wave signature. One 

is termed a Àat top or plateau, another called a ¿nite rise time, and a third called minimum boom, or initial shock 

ramp signature. With the maximum shock magnitude and rise time added to the basic shapes there is almost 

an unlimited number of signatures that can be investigated. However, the three most investigated signature 

variables are initial and maximum shock strength, rise time, and signature duration.

Most of the laboratory sonic boom testing has been devoted to determining the reaction of people to sonic 

booms. The major issues of concern are:

 • How loud is the boom"

 • How annoyed are the subjects"

 • How startled are the subjects"

 • What is the difference between indoor and outdoor reactions"

 • What is the effect of rise time, boom intensity, and signature shape on the above variables"

 • What simulator provides the most realistic sonic boom simulation"

 • What metric best represents the subjects’ opinions"

Headphones

One of the ¿rst simulation schemes (refs. 9.58 and 9.59) utilized custom headsets and electronic circuitry, as shown 

in ¿gure 9.107. In their study of the subjective loudness of an N-wave, Zepler and Harel (ref. 9.60) set requirements 

for the headsets to be used in these tests. The headset included customized speakers (Àat frequency responses in a 

range from a few Hertz to about 1500 Hz) and close attention to the ¿t of the headsets to keep out extraneous noises.

The earphone cavities were 8 cm3

 and the maximum pressure obtainable was 1 lb/ft2. The relatively large earphone 

cavity was chosen to minimize the effect of different sizes of people’s ears and also to reduce the effect of air leakage. 

Figure 9.106. $LUSODQHGHVLJQIRUVRQLFERRPPLQLPL]DWLRQ
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

462

The sonic boom variables investigated using the customized headsets were the same as those described 

earlier. The effect of these variables on loudness was determined. Figure 9.108 (ref. 9.60) shows both the 

pressure wave measured with an artificial ear in the headset and two sets of measurements (indicated 

by ż and Ƒ) where the loudness measurements in dB were obtained as a function of rise time with a 

constant maximum pressure. The pressure wave measured with an artificial ear is shown in figure 

9.108(a). The slight deviation of the expansion portion of the signature from that of an N-wave, due to 

the headsets’ lack of low frequency response, is not significant in regards to the loudness of the boom.

Test subjects evaluated N-waves having fixed overpressure and a range of rise times. Each N-wave was 

compared to a 400 Hz tone, the amplitude of which was adjusted to be equal to the loudness of the N-wave. 

The experimental results for two series of tests are shown by the symbols in figure 9.108(b), and illustrate a 

decrease in loudness by increasing rise time. The solid lines represent predictions based on acoustic energy 

in the boom, frequency-weighted according to three different assumptions regarding loudness of impulsive 

sounds.

Figure 9.107. ,OOXVWUDWLRQVRIWKHDSSOLFDWLRQRIHDUSKRQHKHDGVHWV\VWHPVIRUVLPXODWLQJVRQLFERRPVDGDSWHGIURPUHI

Figure 9.108. 5HVXOWVRI1ZDYHORXGQHVVXVLQJKHDGSKRQHVDGDSWHGIURPUHI

(a) Measured pressure produced by

headphone in arti¿cial ear.

(b) Loudness versus rise time with constant maximum

pressure. Experimental results – ¿rst series of experiments.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

463

Loudspeaker Chambers

Some lack of realism is lost when only the ears are exposed to the simulated sonic boom. Whole body exposure 

to the transient sonic boom pressure ¿eld is clearly a more realistic simulation, especially for outdoors. To 

overcome this shortcoming, small closed chambers or booths equipped with loudspeakers were constructed by 

several organizations. Closed chambers or booths equipped with loudspeakers at the following locations will be 

subsequently discussed:

 • Bolt, Beranek, and Newman (BBN) Chamber at Cambridge, Massachusetts (ref. 9.61)

 • Bioacoustics Laboratory at Lockheed (Rye Canyon), California (ref. 9.62)

 • University of Toronto, Canada (refs. 9.63, 9.64, and 9.65)

 • NASA LaRC in Hampton, Virginia (ref. 9.66)

 • Lockheed Martin in Palmdale, California (ref. 9.67)

 • Gulfstream Aerospace Corporation in Savannah, Georgia (ref. 9.68)

 • Laboratory of Mechanics and Acoustics in Marseilles, France (ref. 9.69)

%%1&KDPEHU

Pearsons and Kryter (ref. 9.61) experimented with a 100 cubic-foot chamber to produce N-wave type pressure 

stimuli, as shown in ¿gure 9.109. The room, constructed of 8-inch solid concrete block shown in ¿gure 9.109, had 

inside dimensions of 3.5 feet deep by 3.5 feet wide by 7.9 feet high. The curtains shown in the ¿gure were closed 

to cover the loudspeakers during the test. The door was 4 inches thick, with adequate sealing to provide a nearly 

airtight enclosure. Five 18-inch loudspeakers with center-tapped voice coils mounted in the walls and ceiling were 

used to produce the peak pressure associated with a sonic boom. The loudspeakers were driven by either a 75-watt 

McIntosh ampli¿er or a specially built power ampli¿er with push-pull output that used the loudspeaker center tap. 

A simulated outdoor sonic boom was generated by the speakers using a waveform generator called a photoformer. 

This device generated an electrical waveform by following a silhouette placed in the photoformer. The simulated 

indoor sonic boom, because of its complexity, was simulated from FM tape recordings made inside a house under 

the Àight path of a jet aircraft Àying at a supersonic speed.

Figure 9.109. %%16RQLF%RRP7HVW&KDPEHUZLWKFXUWDLQVGUDZQWRVKRZORZIUHTXHQF\VSHDNHUVUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

464

Using this chamber, the investigators studied the subjective acceptability of simulated sonic booms that would 

be heard outdoors and indoors and made comparisons with sounds of subsonic jet aircraft and bands of ¿ltered 

white noise. The subjective acceptability of the booms was expressed in terms of equivalent perceived noise level 

in PNdB. When heard indoors, a sonic boom having an outdoor overpressure of 2.3 lbs/ft2

 was judged to be as 

acceptable as the sound of a subsonic jet heard indoors and having an outdoor level of 113 PNdB – the same boom 

heard outdoors was judged to be less noisy by an equivalent of 17 PNdB than the sound of a subsonic jet at 113 

PNdB (ref. 9.61). The BBN Chamber is no longer in existence.

/RFNKHHG&KDPEHU

In the summer of 1965, the Bioacoustic Lab at Lockheed built a chamber similar to that of Pearsons and Kryter 

(see ¿g. 9.109). It was built to accommodate a single person, as shown in ¿gure 9.110, and was later expanded 

to hold two people. The Lockheed system (ref. 9.62) used direct current ampli¿ers and servo system techniques 

to produce the low-frequency responses. Overpressures in the range of 0.5 to 5.0 lbs/ft2

, durations in the range of 

100 to 500 msec, rise times from 1 to 50 msec, and a variety of ¿ne-structure detail were capable of simulation. 

Sonic boom signature variables that were studied included those enumerated earlier for several other wave-shape 

changes.

Several results are provided in reference 9.62 that show the effects of rise times, N-wave duration, and shock 

magnitude on loudness. The relative loudness of 1/2 N-wave with several types of bow wave modi¿cations are 

provided in ¿gures 9.111 and 9.112. Figure 9.111 shows the effect on relative loudness of increasing the magnitude 

of the initial pressure rise of a 1/2 N-wave with a duration of 180 msec and a peak pressure of 1.6 lbs/ft2

. Note that 

the effect is substantial and the relative loudness increases almost linearly with the peak overpressure. For the two 

types of sawtooths (1/2 N-waves), ¿gure 9.112 shows that the type 2 Àat saw-tooth arrangement was not sensitive 

to inter-peak duration (i.e., the spacing between the sawtooth shocks) while the ramp-arrangement curve shows 

that for small spacings of less than 16 msec, there was a substantial reduction in relative loudness with respect to 

the standard 1/2 N-wave signature. The reference signature for ¿gure 9.112 had a 150-msec duration with a peak 

pressure of 1.6 lbs/ft2

. This Lockheed Chamber is no longer in existence.

Figure 9.110. /RFNKHHG6RQLF%RRP6LPXODWLRQ&KDPEHU±QRWHKLQJHGZDOODFFHVVUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

465

8QLYHUVLW\RI7RURQWR,QVWLWXWHIRU$HURVSDFH6WXGLHV87,$6&KDPEHU

The University of Toronto’s acoustic research concerning sonic booms began in the early 1970s and is documented 

in references 9.63, 9.64, 9.65, 9.70, and 9.71. This research was conducted in an airtight chamber with a volume 

of 2.1 m3

 (74 ft3). The chambers had a double wall, plywood construction, and the inside was lined with soundabsorbing ¿berglass. The chamber operating features are excerpted from reference 9.65 (pp. 1617-1618) and 

described below:

Six 15-inch low frequency loudspeakers and six 8-inch medium-frequency loudspeakers are used with a 

crossover network at 500 Hz. The electronic system consists of four d.c.-20,000 Hz 100 W ampli¿ers plus 

an equalizing network to compensate for speaker and booth coloration of the frequency response. The 

main element of the equalizing network is an Altec Lansing Model 729A “Acousta-Voiced” containing 

twenty-four one-third octave ¿lters centered at frequencies from 12,000 Hz down to 63 Hz; each ¿lter 

is adjustable over a range 12 dB. Additional ¿lters utilizing summation circuitry are used to control the 

response of the system in the frequency range 0.1-60Hz. Careful adjustment of these ¿lters compensates 

for the major part of the non-uniform frequency response of the basic system, eliminating much of the 

waveform distortion.

Figure 9.111. 5HODWLYHORXGQHVVRI1ZDYHVZLWKERZZDYHPRGL¿FDWLRQUHI

Figure 9.112. 5HODWLYHORXGQHVVRI1ZDYHVW\SHVDQGZLWKGLIIHUHQWVDZWRRWKVSDFLQJUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

466

The basic scheme of this sonic boom simulation system is shown in ¿gure 9.113. Initially, the pressure signatures 

produced in the booth for the results of reference 9.64 had an unwanted oscillation just after the initial shock, 

as seen in ¿gure 9.114. This is attributed to faults in the compensating ¿lters. As noted by other investigators, 

the pressure signal has to be distorted in a very speci¿c way to achieve the desired signal. Figure 9.115 shows 

examples of pressure signals recorded by microphones in the booth, both with (bottom) and without (top) the 

required distortion. Niedzwiecki and Ribner (ref. 9.65) investigated the effects of rise time and signature duration. 

A sample result is shown in ¿gure 9.116 where an equal loudness curve is plotted as a function of rise time for 200 

msec duration N-waves. It is clear from ¿gure 9.116 that as rise time decreases, the overpressure (ǻ3test) can be 

increased and still maintain the same loudness. A similar curve for signature duration is also provided in reference 

9.65.

Figure 9.113. 6FKHPDWLFDUUDQJHPHQWRI87,$6ORXGVSHDNHUGULYHQVRQLFERRPVLPXODWLRQERRWKUHI

Figure 9.114. 5HSURGXFWLRQRI1ZDYHVRQLFERRPVLJQDWXUHVLQ87,$6VLPXODWLRQERRWKUHI

Figure 9.115. ([DPSOHVRISUHVVXUHVLJQDOVUHFRUGHGE\PLFURSKRQHLQ87,$6VLPXODWLRQERRWKZLWKRXWWRSDQG

 with (bottom) pre-distortion of input signal (ref. 9.65).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

467

Another paper by Niedzwiecki and Ribner (ref. 9.70) detailed the results of an investigation into the effect of the 

low-frequency portion of the sonic boom spectrum on subjective loudness by using a high-pass ¿lter. Two cut-off 

frequencies (25 and 50 Hz) were used and the resulting signatures are shown in ¿gure 9.117.

As a result of this investigation, they concluded in reference 9.70 (p. 706):

The subjective tests reported herein permit the conclusion that the low-frequency content of the N-wave 

signature spectrum at typical levels has no signi¿cant inÀuence on the subjective loudness. This is 

further supported by the observation that the changes in N-wave duration (which dominates the lowfrequency content) have negligible inÀuence upon the loudness. One practical inference follows: it may 

be unnecessarily rigorous to conduct subjective loudness tests on sonic-boom-like impulses in expensive 

Figure 9.116. (TXDOORXGQHVVFXUYH7UDGHRIIEHWZHHQRYHUSUHVVXUHOHYHOUDWLRORJ10 ǻ3test /ǻ3ref ) and rise time for 

PVHFGXUDWLRQ1ZDYHV ǻ3ref OEIW23Dtref PVHFUHI

Figure 9.117. (IIHFWRIKLJKSDVV¿OWHULQJRQVRQLFERRPVLJQDOSUHVVXUHZDYHIRUPVUHFRUGHGLQ87,$6VLPXODWLRQ

ERRWK1ZDYHVLJQDWXUHVIJ PVHF' PVHFǻS 3DUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

468

and complex simulation facilities like ours, facilities with extended low frequency response down to 1 

Hz. A very high quality hi-¿ system (preferable with both low phase and low amplitude distortion versus 

frequency) may be suf¿cient.

The UTIAS Chamber is no longer in existence.

1$6$/DQJOH\&KDPEHU

NASA LaRC’s sonic boom simulator (ref. 9.66) came on line in 1991. Because this simulator is air tight, it can 

create low-frequency waveforms on the order of tenths of a Hertz. Thus, it has the capability to generate userspeci¿ed N-wave and other boom shapes having rise times as low as 0.5 milliseconds and peak overpressures 

up to 191 Pa (4 lbs/ft2

). The design of the LaRC simulator was based upon the pre-distortion schemes described 

earlier and documented in references 9.64 and 9.71. However, several design enhancements were made to 

overcome some of the previous de¿ciencies through application of recent advances in electronic and computer 

technology (i.e., digital ¿lters rather than analog ¿lters). It has walls of 20 cm thick concrete block and a concrete 

ceiling and Àoor of thicknesses 13 cm and 10 cm, respectively (see ¿g. 9.118). The acoustical door is of foam-

¿lled construction and has edge seals to maintain the booth as airtight as possible. The internal dimensions of 

the booth are 1.52 m high, 0.96 m deep, and 1.07 m wide, yielding a volume of 1.6 m3

 (56.5 ft3). To reduce the 

effects of acoustic resonances the Àoor is carpeted and interior walls and ceiling are covered with 10 cm thick 

acoustical foam. This reduced the volume to about 1.1 m3

. One wall contains a small window made of 2.5 cm 

thick Plexiglass. The window edges and the electrical wiring access holes were sealed with caulking material to 

maintain an airtight booth. The simulator door contains eight loudspeakers, four 38 cm low-frequency units and 

four 18-cm mid-range units. The speakers are protected from possible damage by a perforated metal screen.

The major elements of the sound generation and monitoring system are shown in ¿gure 9.119. The input signal 

originates from a computer-driven, 24-bit digital to analog converter and is then low-pass ¿ltered to remove 

the digitizing frequency from the signal. A cross-over network (cross-over frequency set at 420 Hz) separates 

the high- and low-frequency components of the signal for input into the high- and low-frequency loudspeaker 

systems. Each set of four loudspeakers, connected in parallel, is powered by a DC-coupled ampli¿er rated at 200 

watts when driving an 8 ohm load. For the reduced load of this loudspeaker arrangement, and for a low-duty cycle 

as required for sonic boom testing, the ampli¿ers are capable of generating more than 1000 watts.

Since human subjects are required in subjective response testing, a peak sound pressure level of 140 dB and an 

A-weighted limit of 95 dB(A) were enforced. Two microphones were located in the chamber (see ¿g. 9.119) 

Figure 9.118. 1$6$/D5&6RQLF%RRP6LPXODWRUUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

469

and two sound level meters are used to monitor the levels. As noted earlier, a pre-distorted sonic boom signature 

was input to the chamber in order to achieve the desired signature shape (ref. 9.66). Pre-distorted and measured 

shapes for the different desired shapes are shown in ¿gure 9.120. Clearly, the digital broadband equalization ¿lter, 

designed for the application (ref. 9.72), worked quite well.

One of the ¿rst tests of the LaRC simulator was to do an equal loudness test and compare the results to those of 

reference 9.65 (see ¿g. 9.116). In order to do this, adjustments had to be made to the data of reference 9.65 since 

the LaRC standard N-wave signature had a rise time of 3 msec and a peak overpressure of 49 Pa (1.03 lbs/ft2

) and 

the reference 9.65 standard test had a rise time of 1 msec and a peak overpressure of 48 Pa (1.0 lb/ft2

). As stated 

in reference 9.66 (p. 9):

Based on this, the increment in overpressure required to maintain constant loudness between a rise time 

of 1 msec (ref. 9.65, standard boom) and a rise time of 3 msec (standard boom in current study) was 

determined. This increment in overpressure was then subtracted from the reference 9.65 curve. This 

effectively resulted in a new equal loudness curve having loudness equal to that of the standard boom 

signature used in the present investigation.

Figure 9.119. Sonic boom generation and monitoring system (ref. 9.66).

Figure 9.120. ([DPSOHVRIGHVLUHGSUHGLVWRUWHGDQGPHDVXUHGVRQLFERRPVLJQDWXUHVUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

470

Figure 9.121 shows the comparison, which is obviously quite good therefore lending credibility to both results.

Test results for other signatures are provided in reference 9.66 using various metrics including C-weighted (SLC) 

A-weighted (SLA), and Perceived Level (PL(dB)).

/RFNKHHG0DUWLQ&KDPEHU

This simulator was similar in design to the previously described NASA chamber in that it is an air-tight booth 

driven by loudspeakers located on the door surface of the enclosure (ref. 9.67).

*XOIVWUHDP3RUWDEOH&KDPEHU

The Gulfstream sonic boom simulator is different in many respects from the small airtight booths that have 

speakers in the doors (ref. 9.68). A major difference is that it is in a mobile trailer for demonstration purposes and 

is 32-feet long, 8.5-feet wide, and approximately 11.5-feet high. The trailer is divided into two sections, as seen in 

¿gure 9.122 – one for the operator and one for the test subjects. The speakers are located between the two sections.

Figure 9.121. &RPSDULVRQRIHTXDOORXGQHVVFXUYHVUHI

Figure 9.122. 9LHZDQGLQWHULRUOD\RXWRIWKH*XOIVWUHDPVRQLFERRPVLPXODWRUDGDSWHGIURPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

471

The overall setup and acoustics system, described in reference 9.68 (p. 668), was as follows:

The operator area contains the computing and audio hardware that produce the simulation. A laptop 

contains discrete-time data sampled at 24kHz that is output to the audio system via a data acquisition 

system. That hardware then sends an analog signal to the digital audio equalizer that is pre-programmed 

with the gains, ¿ltering, and delays necessary for each power ampli¿er. Two power ampli¿ers supply 

signals to the four drivers in the wave-guided subwoofer and two power ampli¿ers supply signals to the 

four drivers in the mid/high frequency speaker. The full performance bandwidth of the system is 8 Hz to 

18 kHz, but for sonic boom simulations the upper end of the system is reduced to 5 kHz.

The listening section in the simulator has interior dimensions of 6 feet wide, 7 feet high, and approximately 

12 feet long. One to four people can stand in the designated listener area, which is roughly 5 feet wide and 

2 feet deep. The sound travels from the speakers in the middle of the trailer, passes through the listener 

area, and into the anechoic termination at the front of the trailer The anechoic termination, ¿lled from Àoor 

to ceiling with ¿berglass insulation, was constructed to absorb sound down to nearly 50 Hz. The walls and 

ceiling are thermally and acoustically treated with ¿berglass insulation and absorptive open-cell foam. A 

thin sheet of perforated aluminum separates the foam and ¿berglass. The foam has a thin, acoustically 

transparent cloth glued to its surface for aesthetics.

As with the other simulators, it was necessary to establish a transfer function between the input to the system and 

its output at several locations in the listener area. A multi-point equalization using time-domain Wiener ¿ltering 

was computed that addresses the above mentioned problem. Additional details were provided in reference 9.68.

The Gulfstream simulator has a frequency bandwidth constraint, thus the target acoustic output is a band-pass 

¿ltered version of the full-¿delity waveform. The concern then is how well the system can match the target 

waveform in the time domain. Figure 9.123 compares the pressure versus time data for the full-¿delity waveform 

(dashed line), the band-pass ¿ltered waveform (dotted line), and the simulator output (solid line) at listener 

position B for the measured N-wave. The simulator acoustic output closely matches the ¿ltered version of the 

full-¿delity waveform.

Sullivan et al. (ref. 9.67) made comparative tests of the NASA, Lockheed, and Gulfstream simulators. Aside from 

the usual rise-time, peak-pressure, and pulse-duration studies, the effect of post-boom engine noise was studied in 

comparative tests of the Lockheed and Gulfstream simulators. Sullivan et al. (ref. 9.67, p. 156) note that:

Post boom noise (the “rumble” occurring after the boom) is essential for realistic simulation of sonic 

booms. The duration of the post boom noise should be at least about 1.5 sec. Longer duration does not 

improve realism ratings greatly, but shorter duration causes a rapid decrease in perceived realism.

Figure 9.123. Time-domain comparison of the simulator acoustic output at listener position to the desired output and 

IXOO¿GHOLW\ZDYHIRUPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

472

Finally, Sullivan et al. (ref. 9.67, p. 156) conclude that:

Of the three simulators studies, the Gulfstream SASSII simulator was rated as somewhat more realistic 

than either the NASA or the Lockheed booths. The superior performance of the Gulfstream simulator 

could be due to its fundamentally different design or to subtle differences in the equalization ¿lters.

6RXQG5HVWLWXWLRQ&DELQ

The last simulation chamber to be described is the Laboratoire de Mecanique et d’Acoustique in Marseille, France 

(ref. 9.69, p. 664):

The simulation cabin has been built inside a room with concrete walls ensuring a very good insulation 

from outside noise. Its dimensions have been kept to a minimum, thus reducing the requirement on the 

sources, and shifting modal resonance toward higher frequencies. Cabin dimensions of 3 x 2 x 2 m have 

been considered adequate, and leave enough room for ¿tting 16 subwoofers at appropriate locations on 

the walls.

At very low frequencies, monopole subwoofers radiating inside an almost sealed room (pressure chamber) 

create a spatially uniform pressure. For increasing frequencies, the structure of the ¿eld is more complex, 

involving several degrees of freedom, but it may also be almost uniform with a suitable repartition and 

control of speakers. Conversely, at higher frequencies, a suitable lining on the walls allows one to consider 

the room as close to semi-anechoic. The whole frequency range is therefore driven by a triple control 

system, with different constraints for each frequency band.

More details about the cabin and loudspeaker design can be found in reference 9.73.

When reference 9.69 was being written, additional improvements were being undertaken to the simulator using 

active noise control techniques. As stated in reference 9.69 (p. 665):

A sound ¿eld reproduction strategy called Boundary Pressure Control (BPC) has been proposed (ref. 

9.74), which is based on active noise control techniques. BPC intends to reproduce the required sound 

¿eld inside a given volume via the active control of the acoustic pressure measured at some microphones 

placed over the whole boundary surface of the volume. Unlike other sound reproduction strategies, BPC 

is able to compensate ef¿ciently for the room reÀections, using adaptive ¿ltering methods.

The results (¿g. 9.124), were presented in reference 9.69 and show the effects of rise time, inter-peak durations 

(roughly signature length in milliseconds), and peak overpressure of synthesized N-waves. The results show, as 

have other investigations, that rise time and peak overpressures are the important quantities.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

473

The chambers previously discussed are best used for outdoor sonic boom responses. Indoor responses to 

booms are different due to the effects of the impedance of the walls, roofs, doors, and especially windows 

since the construction features of the windows and their window panel(s) are the most responsive features 

of a house. Also, the interiors of the house (including the room geometries, furniture, rugs, etc.) have 

an effect on what a person actually senses. Added to the above variables is what a person is doing at 

the time of exposure, e.g., he/she is watching the television, working on computers or asleep, etc. and 

secondary noises such as a “rattle”. Shepherd and Sullivan (ref. 9.75) described in detail a procedure that 

can be used to calculate the loudness of sonic booms. The procedure is applied to a wide range of sonic 

boom shapes. Of particular interest here is that estimates are made of the loudness of sonic booms, as they 

would be heard indoors, based on the measured noise reduction provided by typical dwellings. Indeed, 

calculations are presented with windows open and closed for a range of shaped booms. The difference 

in loudness between indoors and outdoors for a flat-top boom is about 8 dB. The noise reduction for 

typical residential structures as a function of frequency for these calculations is shown in figure 9.125.

Figure 9.124. 5HVXOWVRIWKHSHUFHSWXDODVVHVVPHQWRI1ZDYHVLJQDOVV\QWKHVL]HGLQWKHVLPXODWLRQURRPDGDSWHGIURPUHI

(a) Estimated loudness as a function of rise 

 time (rt) for various values of the inter- 

 peak over-pressure of 110 dB SPL.

(b) Estimated loudness as a function of the

 inter-peak duration for various values

 of the rise time, with a peak overpress-

 ure of 110 dB SPL.

(c) Loudness function for various values

 of the inter-peak duration with a rise

 time of 2 msec.

Figure 9.125. 1RLVHUHGXFWLRQIRUW\SLFDOUHVLGHQWLDOVWUXFWXUHVUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

474

Figure 9.126 illustrates the dif¿culty associated with the measurement and prediction of sonic booms indoors. 

This type of input (i.e., indoor sound levels, annoyance level, and activities affected) for each speci¿c house 

of different shapes and construction features will be different. Added to these, the differences in the interior 

environment and the codi¿cation of the responses of people in different houses will clearly lead to average 

numbers for human responses with the large error bands.

,Q+RPH6RQLF%RRP6LPXODWLRQ

The previously discussed simulators allow for the study of loudness and annoyance of a single sonic boom 

of a given amplitude, period, and shape. However, these ¿ndings reveal little about the reaction of people in 

communities exposed to multiple booms of a given amplitude, period, and shape over a period of time on a regular 

basis in their homes. In order to gain more insight to this question, McCurdy, Brown, and Hilliard (ref. 9.76, p. 

1574) developed a computer-based system for studying the subjective response of people to the occurrence of 

multiple simulated sonic booms in their homes:

The apparatus developed for the present study, the in-home noise generation/response system (HONORS), 

is a computer-controlled audio system that generates simulated sonic booms, measures their levels, and 

records the test subject’s ratings. Eight of the systems were rotated through 33 homes for 8 weeks in each 

home, providing a total of 1848 days of sonic boom exposures.

The system consisted of a computer and compact disc player that played the simulated sonic booms 

at randomly selected pre-programmed times through a preampli¿er and ampli¿er into three or four 

loudspeakers located in different rooms of the house. No warning was given as to when the booms would 

occur. The two indoor microphones and sound level meters measured the levels of the booms as they 

occurred and also continuously measured the ambient noise levels in the home. The measurements were 

then transferred to the computer and stored on its hard disk. At the end of the day, the test subjects used 

the trackball to answer a series of questions about his/her activities during the day and his/her overall 

subjective response to the total sonic boom exposure for the day.

The arrangement of the test components in a subject’s home is shown in ¿gure 9.127. Only single family detacheddwelling homes were selected and covered the economic range from lower middle to upper middle class homes. 

The system components were located so as to minimize their disruption of the family’s normal routines.

Figure 9.126. ,QKRPHQRLVHJHQHUDWLRQUHVSRQVHV\VWHPGLDJUDPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

475

Three pressure signatures were used in the McCurdy, Brown, and Hilliard study (ref. 9.76). Two were outdoor 

signatures (an N-wave and a shaped wave) and the third was an indoor signature developed from an outdoor 

N-wave based on the noise reduction curves provided by typical dwellings (see ¿g. 9.125). All three wave shapes 

had an initial rise time of 4 msec. Three A-weighted noise levels were employed – 66, 70, and 74 dB. There were 

seven boom occurrence rates employed – 4, 10, 13, 25, 33, 44, and 63 per day. 

Several result ¿gures are presented in reference 9.76, two are shown here. The ¿rst, ¿gure 9.128, shows the 

subjective annoyance rating versus the A-weighted sound exposure level of the individual sonic booms. Plots are 

provided for ¿ve exposure levels. Over the sound exposure levels from 63 to 77 dB, the annoyance ratings range 

from roughly 1 to 5, respectively. As one would expect, the annoyance rating goes down as the exposure level 

goes down and the annoyance level goes up with an increase in the number of occurrences.

Figure 9.127. ,QKRPHQRLVHJHQHUDWLRQUHVSRQVHV\VWHPUHI

Figure 9.128. (IIHFWRIQXPEHURIVRQLFERRPRFFXUUHQFHVRQDQQR\DQFHYHUVXV$ZHLJKWHGVRXQGH[SRVXUH

level of individual sonic booms (ref. 9.76).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

476

Figure 9.129 shows the effect of sonic boom waveforms on annoyance for day-night average sound level based 

on perceived level. The ¿gure shows the regression line of subjective annoyance rating DNL(PL) for each of the 

three waveforms used in the study. No signi¿cant difference in slope or intercept is evident. Results for other 

annoyance effects, such as startle, ambient noise level, subject activity, and subject adaptation to the booms are 

presented in reference 9.76. These experiments con¿rmed that the increase in annoyance resulting from multiple 

occurrences is commonly modeled by the addition of the term “10
log (number of occurrences)” to the sonic 

boom level, as is commonly used for airport community noise assessment.

*HRUJLD7HFK6LPXODWRU

In the early 1990s, Ahuja, et al. of Georgia Tech (ref. 9.77) set out to construct a facility so that human response 

to sonic booms and aircraft noise could be studied both indoors and outdoors. The facility consisted of unique 

low-frequency, high-power drivers and several more conventional loud speakers. This is an arrangement, when 

attached to a residential building, that allows for a range of from about 3 Hz to 4 KHz. Figure 9.130 shows 

a drawing of the test house and speaker complex, locations of indoor and outdoor subjects, and microphone 

measurement locations. As noted in reference 9.77, the suggested system is well suited to simulate realistic sounds 

of helicopters, tilt-rotors, trucks, trains, aircraft, and sonic booms of various shapes and durations. It can thus be 

used for human response, building response, sound propagation, and noise control studies. It was used to study 

the effect of sonic boom shaping on human response and reported in reference 9.78.

Figure 9.129. Effect of sonic boom waveform shape on annoyance versus day-night average sound level based on the 

perceived level noise metric (ref. 9.76).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

477

1$6$/D5&,QGRRU6RQLF%RRP6LPXODWRU

As previously shown, a signi¿cant database has already been established regarding low-amplitude booms using 

loudspeaker booths. This test environment represents outdoor conditions since indoor phenomena such as 

vibration, rattle, and reverberation are absent. In 2008, NASA LaRC began construction of a facility that would 

allow researchers to systematically expose test subjects to realistic indoor soundscape representative of indoor 

sonic boom exposure. Klos, Sullivan, and Shepherd (ref. 9.79) described the design of this indoor simulator that 

allows independent control of the boom signature overpressure, duration, rise time, and spectral shape as well as 

the level of rattle, squeak, the source of rattle and squeak, and the level and source of vibration. The con¿guration 

of the indoor sonic boom simulator, shown in ¿gure 9.131, has a 12-foot by 14-foot rectangular Àoor and ceiling 

height of 8 feet.

Figure 9.130. /D\RXWRI*HRUJLD7HFKVLPXODWRUUHI

Figure 9.131. 9LHZRIWKHVWUXFWXUHRIWKHVLPXODWRUFHLOLQJKDVEHHQUHPRYHGIRUFODULW\UHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

478

The simulator was set atop a raised platform and located in a large laboratory space at LaRC. The authors stated 

that the soundscape inside a house exposed to booms is primarily a result of two vibroacoustic phenomena, 

transmission of the boom through the structure and contact induced vibration sources such as window rattle. Both 

sources are simulated and independently controlled in this simulator. To simulate the transmission of a boom 

through the structure, the room is surrounded on two sides by 15-inch diameter subwoofer speaker arrays, 24 on 

the shorter wall, and 28 in the longer wall. Figure 9.132 illustrates this arrangement and also shows the support 

structure to hold the speakers.

The secondary sources that resulted from contact-induced vibration, such as rattle, squeak, and creak can be 

simulated with small speakers placed inside the room. Photographs of the completed facility showing an exterior 

and interior view are presented in ¿gure 9.133. It is important to point out that simulating sonic booms using 

earphones or loudspeakers do not generate shock waves (i.e., no propagating acoustic wave, only a pressure 

change). However, the two pressure disturbances, when experienced in a small volume such as headphones or 

loudspeaker chambers, look the same as a sonic boom to a microphone or the human ear.

Figure 9.132. $UUDQJHPHQWRIVSHDNHUVDQGVXSSRUWV\VWHPRQ1$6$/D5&¶VLQGRRUVLPXODWRUUHI

(a) Speaker array butted up to the Àange, 

creating an air cavity between the 

speakers and the wall surface.

(b) Frame attached to the panel holding 

the speakers to add stiffness and mass to 

the speaker support. 

Figure 9.133. ([WHULRUDQGLQWHULRUYLHZVRI1$6$/D5& indoor sonic boom simulator.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

479

Piston Systems

While acoustic booths are the most popular way of testing human response to sonic boom, there were several 

other devices that have been used for this purpose. A piston-driven facility (see ¿g. 9.134), developed at the 

Wright Patterson Air Force Base (ref. 9.80) and no longer in existence, had a chamber volume of 1.2 m3

 and 

was developed speci¿cally for testing human response to very low frequency noise (0.8 Hz to 10 Hz). A unique 

feature of the facility was that the position of the test chamber could be changed from vertical to horizontal 

so that the subject could be sitting, standing, or lying down during a test. Another piston-driven simulator (no 

longer in existence) was developed by the Stanford Research Institute (ref. 9.81) for the purpose of conducting 

sleep-awakening and startle-response studies on humans. This simulator consisted of a bedroom structure 

mock-up with a pressure chamber along one wall (see ¿g. 9.135). An electromechanical driver actuated a piston 

in the outside wall of the pressure chamber that provided a pressure load on the wall of the bedroom and thereby 

generated the desired acoustical and structural vibration environments within the room.

Figure 9.134. 3HUVSHFWLYHYLHZVNHWFKRIWKH$HURPHGLFDO5HVHDUFK/DERUDWRU\G\QDPLFSUHVVXUHFKDPEHUUHI

Figure 9.135. 3ODQYLHZVNHWFKRI6WDQIRUG5HVHDUFK,QVWLWXWHVHWXSIRUVLPXODWLQJLQGRRUVRQLFERRPHQYLURQPHQWIRU

sleep awakening studies (ref. 9.1).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

480

The boom simulator was intended to replicate the type of booms heard indoors, i.e., those that transmitted 

through building structures and windows. Further details of this facility and some illustrative results can be 

found in references 9.81 and 9.82.

Explosive Charges

Another method of simulating sonic booms is through the use of explosive charges, two of equal amplitude 

that could be detonated in series at a time interval equivalent to the duration of the sonic boom signature to be 

replicated. Although the boom signature overpressures and duration can be simulated using explosive charges, 

the spectra of the boom signature and explosive signatures are quite different, the latter lacking the lowfrequency contribution associated with the expansion portion of the N-wave signature. This spectral difference 

means that although outdoors, booms and explosive charge simulations may not be observed as being different. 

Indoors, the observer would not realize the full extent of the vibratory and visual effects, only the acoustic aspects. 

Over the years, several experiments were performed that compared observer responses to booms from aircraft to 

those using explosive charge simulations. The ¿ndings of three such experiments are subsequently given.

([HUFLVH&UDFNHUMDFN

In July 1961, a series of tests were conducted by the Ministry of Aviation of the Royal Aircraft Establishment to 

provide bangs of nominal 1 lb/ft2

 and 2 lbs/ft2 overpressures using the aforementioned explosive charges as well as 

using an English Electric Lightning F-3 aircraft (¿g. 9.136). This program, called Exercise Crackerjack, exposed 

a group of listeners to the bangs created by these two disturbance sources. Researchers could then determine how 

tolerable the bangs were with ratings of 100 percent being completely tolerable (ref. 9.83). The exercise extended 

over 4 days with the listeners positioned in an open ¿eld and in a modern, one-story Àat top laboratory building.

The outdoor and indoor signatures generated by the Lightning aircraft Àying at Mach 1.4 at 43,000 feet are 

presented in ¿gure 9.137 (ref. 9.83). These Àight conditions were to generate a sonic boom with an initial shock 

strength of 1.0 lb/ft2

 on the ground out of doors. In this case, it only achieved a signature of about 0.8 lb/ft2. The 

indoor leading-shock magnitude was only about 0.15 lb/ft2

. Other outdoor initial-shock values generated by the 

Lightning aircraft, intended to be a nominal 1.0 lb/ft2

, varied from 0.7 lb/ft2 to 1.3 lb/ft2. Similarly, the 2.0 lbs/

ft2

 nominal signatures varied from 1.6 lbs/ft2 to 2.7 lbs/ft2. Some of the scatter from the nominal values can be 

attributed to adverse weather conditions in the form of wind and rain on 2 days of testing. Similar scatter was seen 

in the explosive charge bangs.

Figure 9.136. (QJOLVK(OHFWULF/LJKWQLQJ)

SKRWRFRXUWHV\RI$GULDQ3LQJVWRQH
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

481

A time variation of the overpressure caused by a single explosive charge, both outside and inside, is shown in 

¿gure 9.138. The left side plot of the ¿gure shows a peak initial shock pressure similar to that of ¿gure 9.137(a), 

except the pressure recovery is much faster. The indoor signature in the plot at the right side of the ¿gure shows 

an oscillatory behavior much like that of ¿gure 9.137(b). Double explosive-charge signatures for open air, and 

inside a large room, are shown in ¿gure 9.139.

Figure 9.137. 6RQLFEDQJIURP/LJKWQLQJÀ\LQJDW0DFKDQGDQDOWLWXGHRIIHHWUHI

(b) Recorded simultaneously in large

room 30ft x 15ft with windows and

doors closed.

(a) Recorded outside.

Figure 9.138. Explosive bang from single 11-ounce charge (ref. 9.83).

(a) Recorded outside. (b) Recorded simultaneously in large

room 30ft x 15ft with windows and

doors closed.

Figure 9.139. Explosive bang from double 3-pound charge (ref. 9.83).

(a) Recorded outside. (b) Recorded simultaneously in large

room 30ft x 15ft with windows and

doors closed.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

482

Note that ¿gure 9.139(a) represents an attempt to simulate a 2 lbs/ft2 outside initial and trailing shock signature. 

Thus, the oscillations of pressure of the indoor signature, ¿gure 9.139(b), achieve a magnitude of very roughly 

twice that of the ¿gure 9.138(b), which simulated a 1.0 lb/ft2

 sonic boom. The degree to which humans tolerated 

the Lightning aircraft booms and explosive booms is shown in ¿gure 9.140. The solid symbols are the explosivecharge data and the open symbols are the Lightning aircraft data.

The alphabetical key for the various shock simulations from ¿gure 9.140 is given in tables 9.7 and 9.8 below.

7DEOH0RUQLQJ/LVWHQHUVRQWKH0RXQGUHI

Identifying 

Letter

Disturbance 

Vehicle

Nominal 

Intensity, lb/ft2 Actual Intensity, lb/ft2

A F-3 Lightning 1.0 0.7

W Explosive 1.0 1.1

B F-3 Lightning 2.0 1.6

X Explosive 2.0 2.5

Figure 9.140. 3HUFHQWDJHVRIWKRVHZKRZRXOGWROHUDWHEDQJVRIYDULRXVSUHVVXUHMXPSVDWGLIIHUHQWIUHTXHQFLHVGXULQJ

GD\WLPHDQGQLJKWWLPHDGDSWHGUHIVHHWDEOHVDQGIRUEDQJRUERRPGH¿QLWLRQV
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

483

7DEOH$IWHUQRRQ/LVWHQHUVLQ%XLOGLQJLQ'LIIHUHQW5RRPV

6RPHZLWKWKH:LQGRZV2SHQUHI

Identifying 

Letter

Disturbance 

Vehicle

Nominal 

Intensity, lb/ft2

Actual Intensity, 

lb/ft2

C F-3 Lightning 1.0 1.3

Y Explosive 1.0 0.8

D F-3 Lightning 2.0 2.7

Z Explosive 2.0 1.8

V Explosive
 2.0 2.0

U Explosive

 2.0 2.0


Surprise explosive - double 3 lbs



Surprise explosive - single 3 lbs

As noted in reference 9.83 (p. 6):

Great caution should be exercised in drawing conclusions from ¿gure 9.140. We must remember that the 

percentages given are the percentages of people who consider they would tolerate bangs of the intensities 

and frequencies indicated. One wonders, for example, what percentage of people would have considered 

that they would have tolerated a network of railways being built all over Britain on witnessing the ¿rst 

journey of the Rocket from Stockton to Darlington in 1828: We must remember also that the sample of 

people was far from being representative of the community at large. Because of these reservations, it is not 

proposed to draw any conclusions of an absolute, quantitative, nature, but rather to make some relative, 

qualitative, observations.

Nevertheless, there are some aspects of the tests that are noteworthy. From ¿gure 9.141 it is evident that there 

is not a signi¿cant difference between the Lightning aircraft’s sonic bangs and the explosive bangs. As revealed 

in reference 9.83 (p. 6), answers to a questionnaire gave the impression that explosive bangs were not very 

different from the sonic bangs, particularly when heard indoors, and most particularly if made double. In fact, an 

appreciable percentage of those present thought that the unannounced bang V (see table 9.8) was a sonic bang, 

and several “did not know.”

Exercise Westminster

A second test utilizing aircraft and explosives was conducted by the RAE and reported in 1965 (ref. 9.84). It 

was called Exercise Westminster since it was staged primarily for several members of Parliament. As with 

Exercise Crackerjack, both Lightning supersonic Àyovers and explosive charges were used to provide the 

required disturbances. There were four supersonic Àyovers, ¿ve explosion events and two subsonic Àyovers by 

a DeHavilland Comet jetliner. The four supersonic Àyovers were Àown on successive days. Measurements were 

taken at 10 instrument stations.

There were listeners or juries involved in the tests, one jury group was assembled inside a tent and a second jury 

group was assembled inside of a Barrack Block building. The jury consisted of 61 voluntary listeners that were 

divided into two groups – one party (Group A) consisting of 31 outdoor listeners and another party (Group B) 

consisting of 30 indoor listeners during the morning session, with vice versa after lunch. The outdoor party was 

situated in a relatively unobstructed position on the air¿eld at Upwood. The indoor party occupied a room on the 

¿rst Àoor of a barrack block adjoining that used for the afternoon demonstration of Exercise Westminster.

A wide-band white noise signal was chosen as an acoustic calibrating signal for the subjective judgements and, 

in order to have the level under close control, it was reproduced through loudspeakers. At the indoor location, in 

the barrack block, four loudspeakers were disposed at the corners of the room – at the outdoor location a ring of 

loudspeakers was arranged to surround the jury who were in a tightly packed group. As described in reference 
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

484

9.85 (p. 243), the tests were conducted in the following way:

The ¿rst sound heard by the juries was a white noise event, presented at a level expected to lie within 

the range of annoyance of the other events. Subjects were instructed to consider the annoyance of this 

sound to be worth 10 units, and then to award every succeeding noise in the sequence, a numerical score 

indicating how annoying it appeared to be, in relation to this initial sound.

Following the subjective tests using white noise, the authors (ref. 9.85, p. 242) went on to describe the testing as 

follows:

The Àying programme consisted of a series of four sonic bangs with nominal peak over-pressures ranging 

from 0.75 mb to 1.12 mb (1.6 lbs/ft2

 to 2.33 lb/ft2) and two low altitude full-power runs by a Comet jet 

aircraft planned to give a peak level of around 110 PNdB, the latter being included to provide a more 

familiar type of noise for purposes of comparison. These events followed one another about every ¿ve 

minutes and during the intervals a series of high explosive charges was detonated. The explosions were 

¿red in pairs with a time delay between the detonations of about 100 msec, corresponding to the bow 

and stern shocks of the sonic bangs. The ground zero for the explosions was located so that the wave 

fronts arrived from the same direction as the sonic bangs.

Typical oscillograms of the pressure signatures measured outdoors at 1.2 m above the ground and indoors of 

the sonic bang and double explosion are presented in ¿gure 9.141 (ref. 9.85). The outdoor boom signature 

overpressures varied from about 0.5 mb to 0.65 mb (1.04 lbs/ft2 to 1.36 lbs/ft2

) and the duration are the order of 

100 msec with the double explosive signatures having overpressures of about 0.9 mb – 1.2 mb and a period of 82 

msec.

While outdoors, the observers would experience a double bang from the passage of the sonic boom signature 

since the ear would respond to the rapid change in pressure at the bow and tail shock and would not respond to 

the slowly changing pressure associated with the expansion portion of the signature. Likewise, for the double 

explosive, the ear again would hear the bangs from both charges. The inÀuence of the low-frequency portion of 

the boom signature associated with the expansion portion of the waveform is quite apparent in the indoor situation 

as compared to the double explosive signature. Results of the test are summarized in ¿gure 9.142, which displays 

the relative annoyance as a function of loudness level in phons for both outdoor and indoor subjects for all four 

stimuli.

Figure 9.141. The waveforms of typical sonic bangs and explosions as measured outdoors and indoors 

(adapted from ref. 9.85).

(a) Typical oscillograms of sonic bangs, Event B in p.m.

(b) Typical oscillograms of the double explosions, Event C in p.m.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

485

It is apparent that as loudness increases, so too does annoyance. Another feature is that when the loudness level is 

equal both outdoors and indoors, the annoyance level indoors is greater than that of outdoor exposure. In reference 

9.85 (p. 257), the authors state:

For this experiment we did not adopt either the criterion of “loudness” or “noisiness”, but rather 

“annoyance” in order to preserve continuity with the previous laboratory experiment. No recognized 

evaluation procedure exists for deriving “annoyance” from physical measurements, but our results accord 

well with loudness and perceived noisiness calculated by the recognized methods. This suggests that the 

annoyance scores given by our subjects were a measure of subjective magnitude largely related to the 

element of intensity. In the case of bangs, it is reasonable to assume that other factors such as the degree 

of startle would in general contribute to the annoyance, unless they were completely dominated by the 

intensive element. Whether startle was absent because of the voluntary nature of our test, or whether it is 

a secondary effect at realistic levels cannot be inferred from our results.

A summary of the group scores relative to the annoyance of the jet aircraft outdoors is given in table 9.9 (ref. 

9.85).

7DEOH*URXS6FRUHV5HODWLYHWRWKH$QQR\DQFHRIWKH-HW$LUFUDIW2XWGRRUVUHI

Outdoors Indoors Outdoor/Indoor 

Difference

Source

Relative 

Annoyance

50

%

Loudness

Level

Phon OD

Perceived

Noise 

Level 

PNdB

Relative 

Annoyance

5i

%

Loudness 

Level

Phon OD

Perceived 

Noise 

Level

PNdB

Physical 

Reduction

Phon OD

Subjective


Reduction

Jet Aircraft

 (Comet)

Sonic Bangs

Explosive Bangs

Door Slams

100

102

199

-

100.5

98.2

111.3

-

103.0

99.2

111.9

-

49

41

91

53

84.6

81.6

93.7

-

86.7

83.0

94.9

-

15.9

16.6

17.6

-

10.3

13.2

11.3

-


 Derived from the relative annoyance values by the formula 10 log2

 (50/5i).

Figure 9.142. Summary of results of outdoor-indoor tests (ref. 9.85).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

486

The results are presented in the form of percentages relative to the annoyance of the jet Àyover noise as heard 

outdoors. This comparison stems from previous efforts to relate sonic booms to the airport noise role or landing 

approach noise limit of 110 PNdB. Thus, from the table, it is seen that the outdoor sonic bangs were judged to be 

1.02 times more annoying than the Comet aircraft at an average level of 103 PNdB. The authors translated that a 

N-wave type sonic bang of peak overpressure 1.4 mb would be equal in annoyance to a jet aircraft Àyover noise 

of 110 PNdB.

86$UP\&RQVWUXFWLRQ(QJLQHHULQJ5HVHDUFK/DERUDWRULHV86$&(5/7HVWV

Schomer, Sias, and Maglieri (ref. 9.86) documented the results of a substantial study to validate a new method 

for the assessment of high-energy impulsive sounds based primarily on blast noise research (ref. 9.87, p. 169):

A key factor in the design of this study was the presentation of real blasts and booms to subjects situated 

in real structures in the ¿eld. The study was performed as a paired-comparison test with the same control 

sound being used in this study as had been used in all the previous blast research that formed the basis for 

the assessment method. In this new study, 232 subjects each judged 20 booms and 30 blast sounds.

Additional data concerning the subjects is provided in reference 9.86 (p. 170):

The study was performed during August 1995 at the Naval Air Station (NAS) Fallon, Nevada. The study 

site was located in the Nevada desert almost centrally within a 15,000-sq. km supersonic Àying area. Three 

differing test structures were located at the test site. One structure was a rehabilitated heavy brick house 

with a large Àat timber-beam, wooden-decked roof covered with about 350 mm of small gravel stones. 

The main room in this house was approximately 5.5- by 7-m living room. The second structure was a 

rather small, single-room, 3- by 6-m wood frame building. The third structure was a large mobile of¿ce 

trailer that was divided into two 3.5- by 8.5-m living rooms. Each test room was furnished as a normal 

living room, including couches and chairs, carpets or rugs, coffee and end tables, window treatments, etc. 

The booms and blasts came from about the same direction and each room had windows that faced the blast 

site and the direction of arrival of the sonic booms. All windows in each test room were closed.

A schematic of the test site is shown in ¿gure 9.143. Further details of the arrangement can be obtained from 

reference 9.86.

Figure 9.143. 7KLV¿JXUHQRWWRVFDOHVKRZVWKHOD\RXWRIWKHLPPHGLDWHWHVWVLWHLQFOXGLQJWKHWHVWVWUXFWXUHV

and instrumentation (ref. 9.86).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

487

The sonic booms were produced by a Navy F-5 jet ¿ghter Àying at approximately Mach 1.2 and at altitudes 

ranging from 6400 to 9800 m (21,000 to 32,000 ft). Flight tracks were aimed directly at the test site or offset 

laterally to produce lower boom levels. Blasts were generated by C-4 explosives set off at a height of ~ 0.9 m 

(3 ft) and at a distance of 900 m from the test houses. Three sizes of the charges were used – 2.26 Kg of C-4 

explosives for the large blast, 0.55 Kg for the small blast, and the double blast was two 1.13 Kg charges set off 

simultaneously but were separated by about 30 feet to achieve the 100 msec delay at the test houses. The double 

blast was created to mimic a sonic boom as revealed in reference 9.86 (p. 174):

The metrics used were the test sound C-weighted sound exposure level (CSEL) and the control sound 

A-weighted sound exposure level (ASEL). The control sound was adjusted such that at low sound levels 

nearly all of the subjects would ¿nd the test sound more annoying and at high control sound levels nearly 

all of the subjects would ¿nd the test sound less annoying. In between the point where 50 percent of the 

subjects found the test sound to be more annoying and 50 percent found the control sound to be more 

annoying was the equivalency point, the point where the annoyance generated by the test sound (blast or 

boom) was equivalent to the annoyance generated by the control sound.

The actual determination of the equivalency point is quite complex and is described in reference 9.86.

Equivalency point data is plotted in ¿gures 9.144 and 9.145. Figure 9.144 shows the data where the blast and 

booms were measured indoors, as was the control sound. Data obtained during this study as well as previous blast 

data are plotted. A regression line ¿t is shown for the older blast data. The ¿gure shows that the previous blast 

noise data and the new Fallon data are generally similar but there is quite a bit of scatter. Figure 9.145 is similar to 

¿gure 9.144 except that outdoor CSEL measurements are plotted as a function of indoor measured, equivalently 

annoying white noise control sound ASELs. 

Figure 9.144. &6(/RIEODVWRUERRPVRXQGVYHUVXV$6(/RIHTXLYDOHQWO\DQQR\LQJFRQWUROVRXQG%ODVWDQG

booms measured indoors (ref. 9.86).

Figure 9.145. &6(/RIEODVWRUERRPVRXQGVYHUVXV$6(/RIHTXLYDOHQWO\DQQR\LQJFRQWUROVRXQG%ODVWDQG

booms measured outdoors (ref. 9.86).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

488

Like ¿gure 9.144, ¿gure 9.145 includes the previous blast data and a regression line that has been ¿t to these data. 

Figure 9.145 also includes the outdoor measured NAS Fallon data. One can compare the ¿t of the Fallon data to 

the respective regression lines in ¿gures 9.144 and 9.145. From observation, it is clear that the new data in ¿gure 

9.145 better ¿t the regression line than is the case for the data represented by ¿gure 9.144. To quantitatively aid 

in this comparison, the 95 percent prediction intervals for the previous blast data are shown in ¿gures 9.144 and 

9.145. In ¿gure 9.144, three of the new data points (25 percent) lie outside the 95 percent prediction interval 

for the previous blast data, while in ¿gure 9.145 none of the new data points lie outside the indicated prediction 

interval. This result, that the outdoor-measured data form a better prediction of response, tends to reinforce the 

concept that C-weighting is a useful outdoor measure for assessing the indoor community response to high-energy 

impulsive sounds. It should only be used outdoors – not indoors since one reason for choosing C-weighting was 

to include those acoustical energies that induce building vibration and rattles. 

In summary, a multitude of sonic boom simulators, designed to investigate indoor-outdoor subjective response 

to sonic booms, have been built. They include the use of headphones, loudspeaker enclosures, piston-driven 

systems, and use of explosive charges. Details of some of the facilities are given, along with some examples of 

the results of the research. Many of the facilities no longer exist (ref. 9.2), so the referenced papers are the only 

places where additional information can be obtained.

Building Response Simulations

The simulation of sonic booms on buildings and their components gained traction in the 1960s when it became 

increasingly clear that the use of an airplane and a single dwelling did not produce the kind of generalized or 

parametric results needed for different dwellings and locations subjected to different boom signatures. In any 

case, the expense associated with experiments requiring several airplane Àights and a variety of buildings was too 

expensive. As noted by Hawkins and Hicks in their 1966 paper (ref. 9.88, p. 1244), “A simulation technique has 

the advantages of cheapness, localization of effects, and the potential ability to produce bangs characteristic of 

future aircraft types, for example Concorde.”

In this section, several simulation techniques and devices used to generate sonic boom signatures in the study of 

building and human responses, especially those indoors of structures will be discussed. Included in this review are 

the use of linear charges, air modulation devices, piston-driven generators, and loud speakers.

Linear Charges

The explosive line charge technique was explored in reference 9.88. A single line charge produces a pressure 

waveform like that shown in ¿gure 9.146 along an extension of its line of sight. The superposition of several 

line charges of different strengths, as shown in ¿gure 9.147, can be used to simulate N-waves, or tailored boom 

shaping of varying strength. Figure 9.148 shows the simulation of an N-wave of 200 msec duration. It was noted 

in reference 9.88 (p. 1245) that the straightforward application of the line-charge technique yielded frequency 

Figure 9.146. Experimental pressure waveform from straight linear charge of uniform explosive linear 

GHQVLW\OHQJWKLQUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

489

contents suitable for structural studies but “in the higher frequency range divergencies appear between the spectra 

owing partly to the higher inherent noise level of the simulant and partly to the different pressure rise rates in its 

shock fronts.”

With the critical roles that rise time and peak pressure play in the noise spectra and magnitude, the authors of 

reference 9.88 (p. 1245) were led to develop a second type of line charge distribution:

This type of simulant is composed of two identical linear charges arranged side by side and detonated 

consecutively with an appropriate time delay. It is designed to reproduce in amplitude and rise rate the 

bow and stern shocks of the sonic bang waveform--the acoustically insigni¿cant slow linear fall in the 

middle of the wave is replaced in the simulant by an equally acoustically insigni¿cant slow asymptotic 

return to ambient pressure; this is not possible with point source explosive charges.

Figure 9.149, from reference 9.88, shows the signature generated by the new technique where the emphasis 

appears to have been on rise time.

Figure 9.147. 3ULQFLSOHRI1ZDYHV\QWKHVLVIURPXQLIRUPOLQHDUFKDUJHVUHI

Figure 9.148. ([SHULPHQWDOSUHVVXUHZDYHIRUPIURPPVHF1ZDYHVLPXODQW0DUN,UHI

Figure 9.149. ([SHULPHQWDOSUHVVXUHZDYHIRUPIURPRQHKDOIRI0DUN,,VRQLFEDQJVLPXODQWUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

490

Another explosive device invented in the late 1960s and documented in a publication in 1971 (ref. 9.89) is the gas-

¿lled balloon with a line charge through the center. The line charge was ignited by a conventional detonator at the 

end of the balloon nearest to the observation point such that the detonation propagated away from the observation 

point. The resulting N-type signatures have less ¿ne-structure distortion than those from the multiple line charges, 

probably because of the more uniform ignition characteristics of the gas.

Experiments were carried out, documented in reference 9.89, to determine the effects of shapes, length, diameter, 

and ignition placement. Empirical relationships were derived that permit the design of a balloon similar to that in 

¿gure 9.150. Figure 9.150 shows the shape and dimensions of a balloon used in this reference to obtain an N-wave 

pressure signature. The balloon is tapered on either end with a cylindrical section in the middle. An illustration of 

type N-wave obtained using the balloon con¿guration and how the boom signature develops with distance along 

the ground is given in ¿gure 9.151 (ref. 9.89).

Signature overpressures vary from about 10 lbs/ft2 at 200 feet from the explosion sources to about 1.5 lbs/ft2 at 

a range of 728 feet and the signatures become more N-wave in shape with a period of about 35 msec. For the 

30-foot long balloon considered here, this ultimate shape is obtained at a range of less than 800 feet. Pressure 

pro¿les for the other three N-wave balloons tested show similar pro¿les. The duration of the pulses, i.e., peakto-peak, is approximately proportional to the length of the balloon.

Figure 9.150. %DOORRQFRQ¿JXUDWLRQWRREWDLQ1ZDYHUHI

Figure 9.151. 3UHVVXUHWLPHKLVWRULHVDWYDULRXVUDQJHVIRU1ZDYHEDOORRQ6%6,OOXVWUDWLQJ

GHYHORSPHQWRI1ZDYHDGDSWHGIURPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

491

Figure 9.152 from reference 9.89 gives results obtained from tests that employed a range of balloon sizes. Peak 

overpressure is plotted on a logarithmic scale versus range showing that the peak overpressure decays as

The negative peak overpressure, Pn

, is described by

5, /, D1

 and D2 denote the range from the end of the balloon, the length of the balloon, the diameter of the balloon 

at the microphone end, and the diameter of the balloon at the other end. The end product of the research, described 

in reference 9.89, was the design chart (see ¿g. 9.153) that enables one to pick the length of a balloon that will 

yield a required ǻp and duration of pulse. Since 60 feet was the maximum balloon length tested, much of the plot 

is based on a reasonable extrapolation. Clearly by proper design of the balloon and controlling the constituents 

of the detonable gas mixture, or the relative proportion of each gas in the mixture, almost any wave shape can 

be generated. The equipment can be moved to almost any location, it appears to be safe to operate, and is cheap.

Figure 9.152. 3HDNRYHUSUHVVXUHYHUVXVUHGXFHGUDQJH1ZDYHHQYHORSHV±6HULHV,9UHI

Figure 9.153. 5HTXLUHGUDQJHIRUVRQLFERRPVLPXODWLRQVJLYHQUHTXLUHGSHDNSUHVVXUHDQGGXUDWLRQH[WUDSRODWHGUHI

lbs/ft2

lbs/ft2
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

492

A paper by Haac et al. in 2009 (ref. 9.90) documented the initial phases of a study aimed at developing a computercode package capable of predicting the vibro-acoustic response of residential buildings exposed to sonic booms. 

The booms were produced using linear explosion charges consisting of multiple detonating chord strands. The 

predictions from this code will eventually be used in the study of indoor subjective human response to sonic 

booms. In carrying out this study, a small building was fabricated using standard construction materials and 

techniques. It has dimensions of 4.86 x 2.82 x 3.05 m (16 x 9.25 x 10 ft) and a photograph is given as ¿gure 9.154. 

Two double-panel glass windows (0.7 m x 0.90 m) were installed on the front wall of the test structure shown in 

the ¿gure. A hollow core masonite door, 0.69 m x 2.01 m, was installed on one of the walls adjacent to that with 

the windows, as shown in ¿gure 9.154. 

The sonic boom was generated by an explosive technique, following the work reported by Hawkins and Hicks 

(ref. 9.88). The test site was at the rural Kentland Farm setting of Virginia Tech. A schematic of the test setup 

along with the exterior microphone locations is provided in ¿gure 9.155. 

Figure 9.154. $VVHPEOHGWHVWVWUXFWXUHUHI

Figure 9.155. 6FKHPDWLFVKRZLQJVWUXFWXUHOLQHDUFKDUJHGLVWULEXWLRQVDQGSODFHPHQWRI microphones along the boom 

propagation path (ref. 9.90).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

493

The charge consisted of multiple detonating chord strands positioned to create a linear charge distribution as 

shown in ¿gure 9.156. This charge distribution was located at the height of 10.7 m (35 ft), parallel to the ground, 

and aimed at the basic structure so that the surface of the wall with windows was perpendicular to the axial 

propagation direction of the blast.

The pressure loading on the structure was recorded by a total of 84 microphones mounted to the outside surface 

of the structure and inside the room. To monitor the boom propagation generated by the linear charge, an array 

of microphones was also used. These microphones, which have a Àat frequency response function down to 0.07 

Hz, were placed on plywood on the ground and distributed over the test site. To measure the structural response, 

an array of accelerometers was mounted to the interior and exterior of the structure. The frequency responses of a 

sample of representative accelerometers were measured Àat over a range from 5 to 2200 Hz.

In support of the structural and acoustical response to sonic booms, an extensive modal characterization of the 

structure was performed. These data were useful in the interpretation of the sonic boom measurements and in 

the numerical modeling of the structure. Modal testing of the structure used impulse hammers to excite the 

accelerometers placed on various structural components and the windows. Frequency response functions (FRFs) 

were then computed and selected for each structural component with a combination of suf¿cient levels and wellseparated peaks. These were then analyzed to obtain the resonances. To this end, a mode indicator function was 

obtained by adding each of the FRFs together (ref. 9.91). The ¿rst 10 modes of the resonant frequencies associated 

with the entire test structure, the windows and the doors, are presented in tables 9.10 and 9.11.

Figure 9.156. /LQHDUFKDUJHGLVWULEXWLRQXVHGWRSURGXFHDW\SLFDOVRQLFERRPUHI

7DEOH:LQGRZDQG'RRU5HVRQDQFHV

from a Simple Mode Indicator Function 

(Adapted from ref. 9.91)

Table 9.10. Building or Global Resonances 

Determined from a Simple Mode Indicator 

Function (Adapted from ref. 9.91) 
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

494

An acoustic characterization of the room was also performed using a speaker placed in a corner of the room on the 

Àoor. Acoustic data with an array of microphones were recorded in time blocks of 32 sec at a sampling frequency 

of 12.8 kHz. The input disturbance was white noise low-pass ¿ltered at 400 Hz. The Natural Excitation Technique 

(NEXT) was used to calculate modal parameters (ref. 9.92). The modal results (¿rst 10) are presented in table 

9.12. As reference 9.90 points out, it is evident that some of the measured natural frequencies are related to the 

structural components, e.g., the window fundamental frequency at 15.1 Hz. Due to the simplicity of the room 

geometry, it was possible to calculate the room’s natural frequencies tabulated in table 9.12.

Table 9.12. Room Cavity Natural Frequencies Measured Using the Natural Excitation Technique (NEXT)

 Compared to Theoretical Natural Frequencies (Adapted from ref. 9.90)

Experimental Theoretical

Mode

1DWXUDO)UHTXHQF\

+]

'DPSLQJ5DWLR

%

1DWXUDO

)UHTXHQF\+]

1 15.1 3.7 -

2 22.3 0.1 -

3 29.5 8.4 -

4 37.4 2.7 37.0

5 41.7 3.2 -

6 44.7 4.7 -

7 50.1 4.7 -

8 55.2 5.4 -

9 59.4 6.3 -

10 63.1 6.6 61.1

Measurements were made of the structural response of the various building components and the acoustic response 

in the room to the sonic boom simulated by the linear live charge. Figure 9.157(a) shows the actual time history 

of the sonic boom, which has a duration of approximately 100 msec and a maximum overpressure of close to 100 

Pa (2 lbs/ft2

). There is considerable high frequency content, as seen in the spectrum in ¿gure 9.157(b), particularly 

beyond 100 Hz.

Figure 9.157. 7KHVRQLFERRPH[FLWLQJWKHVWUXFWXUHWLPHKLVWRU\DQGIUHTXHQF\VSHFWUXPUHI

(a) Time history. (b) Frequency spectrum. 
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

495

Figure 9.158 shows four acceleration time histories that were measured near the center of the interior surfaces of 

the structure at the locations given in the ¿gure. As expected, the largest accelerations were experienced by the 

front wall and the least by the sidewall without a door. The acceleration spectra for the same components are given 

in ¿gure 9.159. Similar acceleration and spectra plots for a window and the door are given in the paper.

(a) Front wall. (b) Back wall.

(c) Side wall (without door). (d) Floor.

Figure 9.158. $FFHOHUDWLRQWLPHKLVWRULHVQHDUWKHFHQWHURIWKHLQWHULRUVXUIDFHVRIWKHVWUXFWXUHDGDSWHGIURPUHI

(c) Side wall (without door).

(a) Front wall. 

(d) Floor.

(b) Back wall.

Figure 9.159. $FFHOHUDWLRQVSHFWUDRIWKHLQWHULRUVXUIDFHVRIWKHVWUXFWXUHDGDSWHGIURPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

496

The interior acoustic response is depicted by the microphone measurements made near the middle of the room. 

The pressure time history and frequency spectrum at this location are provided in ¿gures 9.160(a) and 9.160(b), 

and show that the basic character of the sonic boom is maintained, but with the maximum pressure level reduced 

by about a third. As noted in reference 9.90 (p. 15), “The reason the boom shape is relatively preserved while 

transmitted inside the room is that (i) the boom is tuned to the fundamental frequency of the structure and (ii) that 

the interior acoustic response is due to the bulk compressibility of the cavity...” Spectral data of ¿gure 9.160(b) 

shows that the main free responder is the window (see table 9.10). Similar data is observed for a microphone near 

the window (see table 9.10). 

In summary, reference 9.90 contains the results of detailed structural and acoustic modal testing of the test building 

that enables a better understanding of the response of the building to a sonic boom disturbance. The latter was 

provided by a line charge that had an overpressure of about 100 Pa (2 lbs/ft2

) and duration of 100 msec. While the 

test building is a single-room building with two windows and a door, it is instrumented to give the most detailed 

measurements of all of the other known simulators. This highly detailed data set, both in terms of detail and 

vibroacoustic response, is intended to enable the assessment of prediction models that can be applied to a wide 

range of building structures.

Air Modulation Devices

There are several air modulators or horn-type simulators that differ in the way the pressure pulse is generated 

and in the way test specimens are exposed to the sonic booms generated.

5R\DO$LUFUDIW(VWDEOLVKPHQW5$(%OXQGHUEXVV

The Blunderbuss, developed at the British RAE, was one of the ¿rst air modulation devices conceived. The 

Blunderbuss was a conical cannon that ¿red a slug of air, the pressure distribution of which was N-wave shaped 

(see ¿g. 9.161). The horn was terminated by an acoustic absorber. As noted by Edge and Hubbard in reference 

9.1 (p. 726):

Such devices can generate N-type signatures for a range of overpressures up to at least 20 lbs/ft2

 by varying 

the stagnation pressure in the driver section and by changing the rupture diaphragm con¿guration. The 

duration of the signatures can be varied over a range by changing the length dimension of the driver 

section (a 5-ft dimension corresponds to a 40 msec duration).

Test specimens were located near the downstream end of the horn or exposed at the surface of the horn.

(a) Time history. (b) Frequency spectrum.

Figure 9.160. ,QWHULRUPLFURSKRQHUHVSRQVHSRVLWLRQHGQHDUPLGGOHRIURRPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

497

/797ZLQ6KRFN7XEH

A device similar to that of reference 9.93 was the acoustic horn of LTV (ref. 9.94). It employed a twin-driver 

section and two diaphragms and was intended for testing of structures outside the horn. As seen in ¿gure 9.162, 

the simulator was 26-feet long with a horn exit of 13-feet in diameter. An electronic time-delay circuit provided 

a controllable period between the rupture of the two diaphragms, thus providing a wide range of time intervals 

between the two-shock-wave pressure pulses. The pressure time history diagram on the right side of ¿gure 

9.162 illustrates that the device does not produce an N-wave signature due to lack of low frequencies. Two 

short duration pressure pulses occur at predetermined time intervals to represent any given value of duration. 

Because of its dimensions, there was very little radiation at frequencies below 50 Hz. This simulator was used 

in outdoor studies of the effects of sonic booms on small animals. The acoustic horn (4 m) presently resides at 

NASA Goddard and all other components no longer exist.

*HQHUDO$SSOLHG6FLHQFH/DERUDWRULHV*$6/

GASL produced another air modulation device (refs. 9.95 and 9.96) schematically depicted in ¿gure 9.163. 

As with other air modulation or horn simulators, the primary control and innovative component was the driver 

section and the valves or diaphragms used to modulate the Àow into the horn.

Figure 9.161. Sketch of the Blunderbuss shock-tube simulator (adapted from ref. 9.1).

Figure 9.162. 3ODQYLHZVNHWFKRIWKH/79WZLQVKRFNWXEHVLPXODWRUDGDSWHGIURPUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

498

In the GASL facility, a plug valve similar to that of ¿gure 9.164 (ref. 9.95) was used to control the mass 

Àow. The shape of this plug, on the end of the driving piston, controlled the rate of change of mass Àow. 

ReÀections back into the conical duct were reduced substantially by means of a unique porous-piston absorber. 

This absorber consisted of a ¿berglass blanket held in a frame mounted on rollers that rode on a pair of rails. 

The overall length of the conical duct was 100 feet. The GASL facility was capable of testing a variety of 

articles and recording a broad array of measurements. Figure 9.165 shows the installation of a test panel (e.g. 

a window) and window exposed to the passing shock for use in a psychoacoustic study.

Figure 9.163. 3ODQYLHZVNHWFKRIWKH*$6/DLUPRGXODWRUVLPXODWRUDVXVHGLQSDQHOUHVSRQVHWHVWVUHI

Figure 9.164. Schematic of plug valve (adapted from ref. 9.95).

)LJXUH3V\FKRDFRXVWLFVWXGLHVUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

499

Another application of the facility was for measuring the dynamic response of large structural models, as shown 

in ¿gure 9.166 (ref. 9.95). A major advantage of the air-modulation facility, as with other similar devices, was 

that it could be operated with only a short interval between runs, thus repeated load testing could be performed, 

such as required for fatigue and crack growth investigations. The GASL facility is no longer in existence.

:\OH/DERUDWRULHV

An air modulator device that does not use a horn but a specialized test chamber (see ¿g. 9.167) is described in 

reference 9.97. It is 7-feet in diameter and 9-feet long, and divided into two separate compartments by glass 

or window test specimens. As with the horn device, compressed air was admitted at one end through an airmodulator valve. Unlike the horn devices, the compressed air was exhausted at the other end through a second 

air modulator valve. The valves were customized by Wyle Laboratories and controlled electrically to provide 

the desired operational sequences.

Piston-Driven Devices

Piston-driven sonic boom generators have been built by several organizations, each having a different purpose. 

The Aeromedical Research Laboratory Dynamic Pressure Chamber at Wright Patterson Air Force Base was 

designed for testing humans and was discussed earlier (see ¿g. 9.134). The Stanford Research Institute device was 

designed to conduct sleep awakening and startle response studies on humans and was also discussed earlier (see 

¿g. 9.135). However, the device built at NASA LaRC in the mid-1960s was designed to test structural models.The 

Langley piston-driven simulator is shown in ¿gure 9.168 (ref. 9.1).

Figure 9.166. Measurement of dynamic response of large structural models (ref. 9.95).

Figure 9.167. 6FKHPDWLFGLDJUDPRIWKH:\OH/DERUDWRULHVDLUPRGXODWRUGHYLFHXVHGLQVWXGLHVRIJODVV

breakage (ref. 9.97).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

500

As noted in reference 9.1 (p. 725):

The main features of this facility are a cylindrical test chamber, a 14-foot diameter piston, and a movable 

wall that can be positioned to close the opposite end of the test chamber. The facility is of suf¿cient size (24 

feet in diameter by 21-feet long) to accommodate a small building structure or a building component for 

environmental testing. By means of proper control of the piston motions, N-wave type pressure transient 

can be generated in the range of overpressures from 0.5 to 20 lbs/ft2

, and for durations of 100 to 500 msec.

This facility is no longer in existence.

Loudspeakers

It has been demonstrated that loudspeakers can be used in rooms or booths to simulate outdoor and indoor sonic 

booms to determine their effect on humans. However, the use of a loudspeaker in the design of a simulator for use 

in determining the response of buildings and building components to sonic booms becomes a more dif¿cult task 

due to size, intensity, and low-frequency requirements. In this section, descriptions and results will be presented on 

two devices – the Wyle Laboratories Acoustic Drivers used in the study of window rattle and the Acta Simulator 

used in the study of plaster damage.

:\OH/DERUDWRULHV$FRXVWLF'ULYHUV

A study focusing primarily on window rattle was documented in reference 9.98 and was similar to the study 

described in reference 9.77, but was more restricted in nature. Instead of exposing a house with its outside wall 

and interior rooms to a simulated sonic boom, only a window was exposed. Window rattle is a common indoor 

noise in houses exposed to low-frequency noise from such sources as railroads, blast noise, and sonic boom. 

Human response to rattle can be a negative in the tolerance of the aforementioned noise and thus a barrier to its 

acceptance. The dimensions of the simulator used in the study were 1.4 m x 1.2 m x 0.5 m and the simulator had 

two 15-inch full range speakers (¿g. 9.169, ref. 9.98). The inner part of the simulator containing the speakers had 

dimensions of 0.9 x 0.3 x 0.6 m. The simulator was placed outside of the house (covering the tested window) and 

was pressed ¿rmly against the wall. When in position, it formed an enclosed acoustic cavity between the speakers 

and the exterior surface of the window. It was lined with poly-foam to dampen the acoustic resonances of the air 

cavity and increase the spatial uniformity of the sound ¿eld acting on the window. The simulator was capable of 

Figure 9.168. 6HFWLRQDOYLHZVNHWFKRIWKH/DQJOH\ORZIUHTXHQF\QRLVHIDFLOLW\DVXVHGLQVWXGLHVRIEXLOGLQJ

component responses to simulated sonic booms (ref. 9.1).
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

501

generating a sound level above 140 dB (4 lbs/ft2). Transient and steady state excitation were studied and results 

for sinusoidal excitations were presented in the paper. Displacement and vibration were sensed using several 

accelerometers attached to the window and window frame, as depicted in ¿gure 9.170. This picture is for window 

W6 in the house designated as house 226.

A database of responses from more than 40 windows was collected. Some windows had storm windows and 

some had screens. The presence of those components affected the measured vibration response. It was found that 

when a window has a storm window or screen its rattle threshold is higher. The rattle threshold of the windows 

was determined by exciting them acoustically using amplitude swept sinusoidal signals at discrete frequencies 

ranging from 10 to 500 Hz. The excitation was produced using a signal generator, the output of which was passed 

through an ampli¿er to drive the speakers of the simulator. To create the amplitude sweep, the signal generator’s 

output voltage was gradually increased. Figure 9.171 shows the envelope of the sound pressure measured inside 

the simulator for a manual amplitude sweep of 50 Hz tone. As the test was performed, the sound pressure level 

measured by a microphone placed inside the simulator varied from low level to a maximum level of 189 Pa (140 

dB, or 4 lbs/ft2

), then back to a low level.

Figure 9.169. Sonic boom simulator (ref. 9.98). )LJXUH$FFHOHURPHWHUSRVLWLRQLQVLGHWKHKRXVH

KRXVHZLQGRZ:UHI

Figure 9.171. 2XWVLGHSUHVVXUHDPSOLWXGH+]FKDQQHOKRXVHZLQGRZ:UHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

502

The total elapsed time of the test shown in ¿gure 9.171 was 40.4 sec. The data was for the same window pictured 

in ¿gure 9.170. Accelerometer data for the same window and 50 Hz sweep, as in ¿gure 9.171, is shown in ¿gures 

9.172, 9.173, and 9.174. The data was for channel 8, which was located at the center of the upper horizontal 

sash of the lower windowpane. Rattle onset occurred at 3.4 seconds, at an acceleration level of ~ 1.5 m/sec2

, and 

pointed out by the arrows in ¿gure 9.172. Figure 9.173 shows the acceleration time history for the maximum 

acceleration experienced and ¿gure 9.174 the acceleration variation at the time where rattle ceased.

These three ¿gures show that there is a great variability in the response at the various locations around the window 

and for various window types as well. Some data are provided in reference 9.98 for the rattle threshold for various 

locations in W6 of house 226. Window screens and storm windows also had a big effect on window response to 

rattle. No sonic booms were simulated in this program, however, window responses similar to those measured in 

this program could be simulated. The authors noted in reference 9.98 (p. D-685) that “Results of this study will 

be used in further investigation of rattle mechanisms and the development of tools for predicting rattle response 

of windows exposed to sonic booms.”

Figure 9.172. 7LPHKLVWRU\RIDFFHOHUDWLRQUDWWOH+]FKDQQHO

KRXVHZLQGRZ:DGDSWHGIURPUHI

)LJXUH$FFHOHUDWLRQWLPHKLVWRU\DWDPD[LPXP

H[FLWDWLRQ+]FKDQQHOKRXVHZLQGRZ:

(adapted from ref. 9.99).

)LJXUH7LPHKLVWRU\RIDFFHOHUDWLRQUDWWOHFHVVDWLRQ

+]FKDQQHOKRXVHZLQGRZ:UHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

503

References 9.77 and 9.98 describe simulations that are positioned outside of real houses and simulate boom or 

noise inputs to their walls and windows or, in the case of reference 9.98, just windows. 

$FWD6LPXODWRU([SHULPHQW

In 1993, Haber (ref. 9.99) investigated the potential for cumulative damage to plaster walls from sonic booms, 

including ¿xtures by simulating the plaster ceiling and room sidewalls, and exposed them to some 10,000 

simulated sonic booms at overpressures that varied from about 1.8 lbs/ft2

 to 20 lbs/ft2. A view of the Acta (BBN 

Systems and Technologies) Sonic Boom Simulator is shown in ¿gure 9.175 (ref. 9.99). It was designed to expose 

a test article surface, ceiling, or walls measuring 8 feet by 10 feet.

Simulated booms were generated by a three-by-four array of specially designed speaker modules, each containing 

a pair of loudspeakers (not visible) as shown in ¿gure 9.175. Signatures produced are shown in the upper part of 

¿gure 9.176 (ref. 9.99). An algorithm was written to compensate for the distortions in the signatures resulting from 

the speaker-driven motors and deformation of the test article. The compensated signature closely approximated 

the target N-wave. Overpressures of up to 20 lbs/ft2

 were obtained and signature periods were not identi¿ed.

The test articles were full-scale walls and included window framing, exterior plywood, and interior plaster. 

Particular care was taken to design and install those test articles to respond like walls of residential structures 

having resonance frequencies in the range of 11 Hz to 25 Hz. The measured resonance of the test walls was 14 Hz.

As described in reference 9.99 (p. 2), “A test sequence involved three types of activities: (1) recording the surface 

Figure 9.175. Sonic boom simulator (ref. 9.99).

Figure 9.176. (IIHFWRIFRPSHQVDWLRQRQ1ZDYHUHI
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

504

plaster cracks, (2) subjecting the test article to a sequence of simulated booms at a speci¿ed overpressure, and (3) 

recording the number of cracks on the specimen following the sequence of booms.” A view of a test article and 

test ¿xture is shown in ¿gure 9.177 (ref. 9.99).

Framing of the test articles used two-by-three studs instead of two-by-four studs to obtain more realistic response 

characteristics. The base of the test article was bolted to the Àoor of the sonic boom simulator and the top and 

edges were free to move under the boom loads. The interior ¿nish of the wall consisted of a 3/8-inch thick rock 

lath (board with a 1⁄2-inch thick base coat of plaster and a 1/8-inch thick plaster ¿nish coat). Simulated sonic 

booms were imposed on three types of walls – two walls were strong plaster (i.e., tensile strength of 160 lbs/

in2

) and the third a weak plaster (i.e., a base coat of 80 lbs/in2). The strong plaster article was subjected to 5000 

simulated booms of 20 lbs/ft2

 followed by 5000 more at 1.8 lbs/ft2. The weak plaster article experienced three 

sequences of 5000 booms at 20 lbs/ft2

. It was stated that damage to all three walls was remarkably similar.

Figure 9.178 (ref. 9.99) presents the results of the strong plaster wall to simulated sonic booms in terms of the total 

crack length. This ¿gure was also used earlier (¿g. 8.12) in discussing the factors involved in structural response. 

Recall that this strong plaster article was subjected to two sequences of simulated booms, 5000 at 20 lbs/ft2

 and 

5000 at 1.8 lbs/ft2

. A few observations can be made – (1) on the curve representing major cracks above window 

(solid points), a breakpoint occurs at 1000 booms – from then on, as boom exposures increase, the curve shows 

a constant damage rate and (2) the damage rate at this point is less than for the balance of the wall (open points).

Figure 9.177. 7HVWDUWLFOHDQGWHVW¿[WXUHUHI

Figure 9.178. 6WURQJSODVWHUZDOO±WRWDOFUDFNOHQJWKYHUVXVQXPEHURIERRPVUHIDOVRVKRZQDV¿J
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

505

This particular laboratory simulation was aimed at better de¿ning how sonic booms contribute to plaster damage 

is an excellent example of the gathering of a substantial database under more controlled conditions at lower cost 

and in a relatively short time period compared to Àight tests. This BBN simulator facility no longer exists.

Several simulation techniques and the many devices used to generate sonic boom signatures in the study of 

buildings and human response have been discussed in this section. Included are the use of linear charges, air 

modulation devices, piston-driven generators, and loudspeakers. Most no longer are in use or no longer exist.

Chapter 9 Summary Remarks

Sonic boom simulation devices have ful¿lled a wide variety of sonic boom research needs that have led to a 

more complete understanding of sonic boom generation, propagation, prediction and responses.

Sonic boom simulation devices and test techniques are a necessary alternative to full-scale Àight testing. In 

addition to providing insight and guidance, simulation devices can provide an early assessment of the viability 

of low-boom shaped signatures.

Sonic boom simulation experiments are shown to be less expensive and complex than Àight tests and allow for 

more control of the physical environment and test parameters.

Issues addressed via simulators include validation of sonic boom design and prediction codes, the inÀuence of 

atmospheric variability on boom signature distortions, quantifying focus boom intensities, boom penetration 

into water, boom reÀection/refraction by building and topography, indoor-outdoor subjective response, and 

building response.

Controlled sonic boom disturbances can be generated using models in supersonic wind tunnels, projectiles 

in ballistic ranges, spark discharges, shock tubes, explosive and linear charges, piston systems, air modulator 

valves, and loudspeaker systems.

Chapter 9 References

9.1 Edge, Phillip M., Jr. and Hubbard, Harvey H.: Review of Sonic-Boom Simulation Devices and 

Techniques. J. Acoust. Soc. Am. 51, 722–728 (1972).

9.2 Shepherd, Kevin P. and Powell, Clemans A.: Status and Capabilities of Sonic Boom Simulators. NASA 

TM 87664, Jan. 1986.

9.3 Carlson, Harry W.: An Investigation of Some Aspects of the Sonic Boom by Means of Wind-Tunnel 

Measurements of Pressures About Several Bodies of Revolution at a Mach Number of 2.01, NASA TN 

D-161, Dec. 1959.

9.4 Carlson, Harry W. and Morris, Odell A.: Wind-Tunnel Sonic-Boom Testing Techniques. AIAA J. Aircraft 

4, 245, pp. 245–249, 1967.

9.5 Jackson, Charlie M., Jr.; Corlett, William A.; and Monta, William J.: Description and Calibration of the 

Langley Unitary Plan Wind Tunnel. NASA TP 1905, Nov. 1981.

9.6 Mack, Robert J. and Kuhn, Neil S.: Determination of an Extrapolation Distance with Pressure Signatures 

Measured at Two to Twenty Span Lengths from Two Low-Boom Models. NASA TM-2006-214524, Nov. 

2006.

9.7 Graham, David H.; Dahlin, John A.; Page, Juliet A.; Plotkin, Kenneth J.; and Coen, Peter G.: Wind-Tunnel 

Validation of Shaped Sonic Boom Demonstration Aircraft Design. AIAA Paper 2005-0007, Jan. 2005.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

506

9.8 Carlson, Harry W.:An Investigation of the InÀuence of Lift on Sonic Boom Intensity by Means of WindTunnel Measurements of the Pressure Fields of Several Wing-Body Combinations at a Mach Number of 

2.01. NASA TN D-881, July 1961.

9.9 Bobbitt, Percy J. and Darden, Christine M.: A Wedge-Shaped Supersonic Flow Field Probe. NASA CP10133, Vol. II, May 1993, pp. 379–398.

9.10 Carlson, Harry W.; Mack, Robert J.; and Morris, Odell A.: A Wind-Tunnel Investigation of the Effect of 

Body Shape on Sonic-Boom Pressure Distributions. NASA TN D-3106, Nov. 1965.

9.11 Shrout, Barrett L.; Mack, Robert J.; and Dollyhigh, Samuel M.: A Wind-Tunnel Investigation of Sonic 

Boom Pressure Distributions of Bodies of Revolution at Mach 2.96, 3.83, and 4.63. NASA TN D-6195, 

April 1971.

9.12 Carlson, Harry W.: Measurements of the Flow Properties in the Vicinity of Three Wing-Fuselage 

Combinations at Mach Numbers of 1.61 and 2.01. NASA TM X-64, Oct. 1959.

9.13 Putnam, Lawrence E. and Capone, Francis J.: Experimental Determination of Equivalent Solid Bodies to 

Represent Jets Exhausting into a Mach 2.24 External Stream. NASA TN D-5553, Dec. 1969.

9.14 Bobbitt, Percy J.; Maglieri, Domenic J.; Banks, Daniel W.; Frederick, Michael A.; and Fuchs, Aaron W.: 

Wind-Tunnel and Flight-Test Results for the Measurements of Flow Variables at Supersonic Speeds Using 

Improved Wedge and Conical Probes. NASA TM-2012-216004, December 2012.

9.15 Durston, Donald A.; Cliff, Susan E.; Wayman, Thomas R.; Merret, Jason M.; Elmiligui, Alaa A.; and 

Bangert, Linda S.: Near Field Sonic Boom Test on Two Low-Boom Con¿gurations Using Multiple 

Measurement Techniques at NASA Ames. AIAA-2011-3333, June 2011. 

9.16 Cliff, Susan E.; Elmiligui, Alaa A.; Campbell, Richard L.; and Thomas, Scott D.: Evaluation of Re¿ned 

Tetrahedral Mesh with Projected, Stretched, and Sheared Prism Layers for Sonic Boom Analysis. AIAA2011-3338, June 2011.

9.17 Ferri, Antonio and Wang, Huai-Chu: Observations of Problems Related to Experimental Determination of 

Sonic Boom. NASA SP-255, Oct. 29–30, 1970, pp. 272–284.

9.18 Hicks, Raymond M.; Mendoza, Joel P.; and Thomas, Charles L.: Pressure Signatures for the Apollo 

Command Module and the Saturn V Launch Vehicle with a Discussion of the Strong Shock Extrapolation 

Procedures. NASA TM X-62, 117, April 6, 1972.

9.19 Hicks, Raymond M. and Mendoza, Joel P.: A Brief Study of the Space Shuttle Sonic Boom during Ascent. 

NASA TM X-62,050, July 23, 1971.

9.20 Wayman, Thomas R.; Waithe, Kenrick A.; Howe, Donald C.; Bangert, Linda S.; and Wilcox, Floyd J.: 

Near Field Acoustic Test on a Low Boom Con¿guration in Langley’s 4x4 Wind Tunnel. AIAA-2011-3331, 

June 2011. 

9.21 Callaghan, J. G.: A Feasibility Investigation Concerning the Simulation of Sonic Boom by Ballistic 

Models. NASA CR-603, 1966.

9.22 Bauer, A. B. and Bagley, C. J.: Sonic Boom Modeling Investigation of Topographical and Atmospheric 

Effects. Report No. FAA NO-70-10, July 1970.

9.23 Downing, Micah; Zamot, Noel; Moss, Chris; Morin, Daniel; Wolski, Ed; Chung, Sukhwan; Plotkin, 

Kenneth; and Maglieri, Domenic: Controlled Focus Booms from Maneuvering Aircraft. J. Acoust. Soc. 

Am. 104(1), July 1998, pp. 112–121.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

507

9.24 Crow, S. C.: Distortion of Sonic Bangs by Atmospheric Turbulence. J. Fluid Mech. (1969), Vol. 37, Part 

3, pp. 529–563.

9.25 Hague, D. W. and Jones, R. T.: Application of Multivariate Search Techniques to a Design of Low Sonic 

Boom Overpressure Body Shapes. NASA SP-255, Oct. 1970, pp. 307–323. 

9.26 Davy, Bruce A. and Blackstock, David T.: Measurements of the Refraction and Diffraction of a Short 

N-Wave by a Gas-Filled Soap Bubble. J. Acoust. Soc. Am., Vol. 49, No. 3 (Pt. 2), March 1971, pp. 732–

737.

9.27 Pierce, A. D.: Spikes on Sonic Boom Pressure Waveforms. J. Acoust. Soc. Am., 44, 1052–1061 (1968).

9.28 Ribner, H. S.; Morris, P. J.; and Chu, W. H.: Laboratory Simulation of Development of Superbooms by 

Atmospheric Turbulence. J. Acoust. Soc. Am., Vol. 53, No. 3, 1973, pp. 926–928.

9.29 Tubbs, P. E.: Measured Effects of Turbulence on the Rise Time of a Weak Shock. AIAA Paper 75-453 

(1975).

9.30 Bass, H. E.; Layton, B. A.; Bolen, L. N.; and Raspet, R.: Propagation of Medium Strength Shock Waves 

through the Atmosphere. J. Acoust. Soc. Am., 82, 306–310 (1987).

9.31 Lipkens, Bart and Blackstock, David T.: Model Experiment to Study Sonic Boom Propagation through 

Turbulence, Part 1: General Results. J. Acoust. Soc. Am., 103(1), June 1998, pp. 148–158.

9.32 Auger, T. and Coulouvrat, F.: Numerical Simulation of Sonic Boom Focusing. AIAA Jour., Vol. 40, No. 9, 

Sept. 2002, pp. 1726–1734.

9.33 Maglieri, D. J.; Bobbitt, P. J.; Massey, S. J.; Plotkin, K. J.; Kandil, O. A.; and Zheng, X.: Focused and 

Steady-State Characteristics of Shaped Sonic Boom Signatures: Prediction and Analysis. NASA CR2011-217156, June 2011.

9.34 Peter, A.; P¿ster, N.; StimpÀing, A.; and Devaud, M.: Edute Experimentale de la Refraction d’une 

Detonation Balistique Dans Une Atmosphere Strati¿pe. Institut Franco - Allemand de Recherches de 

Saint-Louis, France, Rep. No. 17/71 (1971).

9.35 Wanner, F. C.; Vallee, J.; Viver, C.; and Thery, C.: Theoretical and Experimental Studies of Focus of Sonic 

Booms. J. Acoust. Soc. Am. 52, pp. 13–32 (1972).

9.36 Maglieri, D. J.; Hilton, D. A.; Huckel, V.; Henderson, H. R.; and McLeod, N. J.: Measurements of Sonic 

Boom Signatures from Flights at Cutoff Mach Number. NASA SP-255, Oct. 1970, pp. 243–254.

9.37 Haglund, George T. and Kane, Edward J.: Flight Test Measurements and Analysis of Sonic Boom 

Phenomena Near Shock Wave Extremity. NASA CR-2167, Feb. 1973.

9.38 Sanai, M.; Toong, T. Y.; and Pierce, A. D.: Ballistic Range Experiments on Superbooms Generated by 

Refraction. J. Acoust. Soc. Am., Vol. 59, No.3, March 1976, pp. 512–519.

9.39 Reed, J. W.: Sonic Boom Measurements from Accelerating Supersonic Tracked Sleds. NASA CR-132388, 

Jan. 1974.

9.40 Beasley, W. D.; Brooks, J. D.; and Barger, R. L.: A Laboratory Investigation of N-Wave Focusing. NASA 

TN D-5306, July 1969.

9.41 Cornet, E. P.: Focusing of an N-wave by a Spherical Mirror. Tech. Rept. ARL-TR-72-40, Applied Research 

Laboratories. The Univ. of Texas at Austin, Sept. 1972.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

508

9.42 Wright, Wayne M. and Blackstock, David T.: Focusing of N-Waves in Air by an Ellipsoidal ReÀector. J. 

Acoust. Soc. Am., 102(2), Pt. 1, Aug. 1997, pp. 741–746.

9.43 Whitham, G. B.: A New Approach to Problems of Shock Dynamics, Part 1, Two-Dimensional Problems. 

J. Fld. Mech. 2, 1957, pp. 145–171.

9.44 Sturtevant, Bradford: Studies of Shock Focusing and Nonlinear Resonance in Shock Tubes, “Recent 

Developments in Shock Tube Research,” Eds. D. Bershader and W. Grif¿th, Stanford Univ. Press, 

Stanford, CA, 1973, pp. 23–34.

9.45 Sanai, M.; Toong, T. Y.; and Pierce, A. D.: Ballistic Range Experiments on the Superboom Generated at 

Increasing Flight Mach Numbers. J. Acoust. Soc. Am., Vol. 59, No. 3, March 1976, pp. 520–524.

9.46 Waters, J. and Glass, R. E.: Penetration of Sonic Boom Energy Into the Ocean. An Experimental 

Simulation. Hydrospace Research Corp., Final Report. on Contract FA-70-WAI-185 HRC TR 288, June 

1970, available from NTIS-/DTIC as AD 711 963.

9.47 Intrieri, P. and Malcolm, G.: Ballistic Range Investigation of Sonic-Boom Overpressures in Water. AIAA 

Jour., Vol. II, No. 4, 510-516, April 1973 (also AIAA paper 72-654, 1972).

9.48 Sawyers, K. N.: Underwater Sound Pressure from Sonic Booms. J. Acoust. Soc. Am., 523-24, 1968.

9.49 Dini, Dino and Lazzeretti, Renzo: Ground Con¿guration Effects on Sonic Boom. Aircraft Engine Noise 

and Sonic Boom. FDP-PEP, CP12, AGARD, 1969, pp. 25–1 to 25–29.

9.50 National Sonic Boom Evaluation Of¿ce: Sonic Boom Experiments at Edwards Air Force Base. NSBEO 

1-67 (Contract AF 49(638) – 1758), Stanford Res. Inst., July 28, 1967.

9.51 Blume, John A. and Associates: Structural Reaction Program. National Sonic Boom Study Project, FAA 

Rept. SST-65-15, Vol. I, Apr. 1965.

9.52 Klos, J.: Vibro-Acoustic Response of Buildings Due to Sonic Boom Exposure: July 2007 Field Test. 

NASA TM-2008-215349, Sept. 2008.

9.53 Cho, Sang I. and Sparrow, Victor W.: Sonic Boom Diffraction around Buildings using a Finite Difference 

Time Domain Approach. Noise-Con 2008, July 2008, pp. 650–657.

9.54 Ting, L. and Pan, Y. S.: Part II - Incidence of N-Waves on Structures. NASA SP-180, May 1968, pp. 

89–98, May 1968.

9.55 Ting, Lu and Kung, Fanny: Studies in the Diffraction of a Pulse by a Three-Dimensional Corner. NASA 

SP-255, Oct. 1970, pp. 161–180.

9.56 Ting, L.: On the Diffraction of an Arbitrary Pulse by a Wedge on a Cone. Quart. Appl. Math., Vol. 18, No. 

1, April 1960, pp. 89–92.

9.57 Brooks, J. D.; Beasley, W. D.; and Barger, R. L.: Laboratory Investigation of Diffraction and ReÀection of 

Sonic Boom by Buildings. NASA TN-D-5830, June 1970.

9.58 Turner, M.: A Sonic Boom Simulator for Subjective Testing. Master’s Thesis, Univ. Southampton. 1963.

9.59 Ellis, R. M.: Subjective Reaction to Simulated N Waves. Master’s Thesis, Univ. South Hampton, March 

1964.

9.60 Zepler, E. E. and Harel, J. R. P.: The Loudness of Sonic Booms and Other Impulsive Sounds. J. Sound 

Vibration 1965 2(3), 249–256. 

9.61 Pearsons, K. S. and Kryter, K. D.: Laboratory Tests of Subjective Reactions to Sonic Boom. NASA CR 

187, Mar. 1965.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

509

9.62 Shepherd, L. J. and Sutherland, W. W.: Relative Annoyance and Loudness Judgments of Various Simulated 

Sonic Boom Wave Forms. NASA CR-1192, Sept. 1968.

9.63 Falkiewicz, A.: Development of Loudspeaker-Drive Simulator for Sonic Booms and Other Transient 

Sounds. M.A. Sc. Thesis. Inst. for Aerospace Studies. U. of Toronto, 1972.

9.64 Glass, I. I.; Ribner, H. S.; and Gottlieb, J. J.: Canadian Sonic Boom Simulation Facilities. Can. Aeronau. 

Space J. 18(8), 1972, pp. 235–246. Also AIAA paper No. 72-26, Sept. 1972.

9.65 Niedzwiecki, A. and Ribner, H. S.: Subjective Loudness of N-wave Sonic Booms. J. Acoust. Soc. Am., 

64(6), Dec. 1978, pp. 1617–1621.

9.66 Leatherwood, Jack D.; Shepherd, K. P.; and Sullivan, Brenda M.: A New Simulator for Assessing 

Subjective Effects of Sonic Booms. NASA TM 104150, Sept. 1991.

9.67 Sullivan, Brenda M.; Davies, Patricia; Hodgdon, Kathleen K.; Salamone, Joseph A.; and Pilon, Anthony: 

Realism Assessment of Sonic Boom Simulators. Noise Control Eng. J56(2), Mar.–Apr. 2008, pp. 141–

157.

9.68 Salamone, Joe: Portable Sonic Boom Simulation. CP838, Innovations in Nonlinear Acoustics: 17th Int. 

Symp. on Nonlinear Acous. Edited by A. A. Atchley, V. W. Sparrow and R. M.; Keolian. Melville, NY, 

2006, pp. 667–670.

9.69 Epain, N.; Herzog, P.; Rabau, G.; and Friot, E.: Preliminary Work about the Reproduction of Sonic Boom 

Signals for Perception Studies. CP838, Innov. in Nonlinear Acous. 17th Int. Symp. on Nonlinear Acous. 

Edited by A. A. Atchley, V. W. Sparrow and R. M. Keolian, Melville, N. Y. 2006, pp. 663–665.

9.70 Niedzwiecki, A. and Ribner, H. S.: Subjective Loudness and Annoyance of Filtered N-Wave Sonic Booms. 

J. Acoust. Soc. Am. 65(3), March 1979, pp. 705–707.

9.71 Niedzwiecki, A. and Ribner, H. S.: Subjective Loudness of “Minimized” Sonic Boom Waveforms. J. 

Acoust. Soc. Am., 64, 1978, pp. 1622–1626.

9.72 Brown, D. E. and Sullivan, B. M.: Adaptive Equalization of the Acoustic Response in the NASA Langley 

Sonic Boom Chamber. Proc. of Conf. on Recent Adv. in Active Control of Sound and Vibration, VPI	SU, 

Blacksburg, VA, April 15–17, 1991.

9.73 Rabau, G. and Herzog, P.: A Speci¿c Cabin for Restitution of Sonic Boom; Application for Perceptive 

Tests. Proc. of Joint Cong. CFA/DAGA μ04(2004) on CD ROM (2 pages).

9.74 Takane, S.; Suzuki, Y.; and Sone, T.: A New Method for Global Sound Field Reproduction Based on 

Kirchoff’s Integral Equation. ACUSTICA - Acta Acustica 85 (1999), pp. 250–257.

9.75 Shepherd, Kevin P. and Sullivan, Brenda M.: A Loudness Calculation Procedure Applied to Shaped Sonic 

Booms. NASA TP 3134, Nov. 1991.

9.76 McCurdy, David A.; Brown, Sherilyn A.; and Hilliard, R. David.: Subjective Response of People to 

Simulated Sonic Booms in Their Homes. J. Acoust. Soc. Am., 116(3), Sept. 2004, pp. 1573–1584.

9.77 Ahuja, K. K.; Stevens, J. D.; and Walterick, R. E.: A Giant Simulator of Sonic Boom and Aircraft Noise. 

AIAA Paper 93-4430, Oct. 1993.

9.78 Pearsons, K. S.; Tabachnick, B.; Howe, R.; Ahuja, K. K.; and Stevens, J. C.: A Study of the Effects 

of Sonic Boom Waveform Modi¿cation on Annoyance. NASA LaRC Contract No. NAS1-19061, Final 

Report, March 1993.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

510

9.79 Klos, Jacob; Sullivan, Brenda M.; and Shepherd, Kevin P.: Design of an Indoor Simulator at NASA 

Langley Research Center. Noise-Conf. 2008, July 28–30, 2008, pp. D-638-649.

9.80 Johnson, Daniel J.: Auditory and Physiological Effects of Infra-sound. Inter-Noise 75, Aug. 27–29, pp. 

475–482.

9.81 Lukas, J. S. and Kryter, K. D.: A Preliminary Study of the Awakening and Startle Effects of Simulated 

Sonic Booms. NASA CR-1193, Sept. 1968.

9.82 Lukas, J. S. and Kryter, K. D.: Awakening Effects of Simulated Sonic Booms and Subsonic Aircraft Noise 

on Six Subjects to 72 Years of Age. NASA CR-1599, May 1970.

9.83 Warren, C. H. E.: A Preliminary Analysis of the Results of Exercise Crackerjack and Their Relevance to 

Supersonic Transport Noise. RAE, TN No. Aero. 2789, Sept. 1961.

9.84 Webb, D. R. B. and Warren, C. H. E.: Physical Characteristics of the Sonic Bangs and Other Events at 

Exercise Westminster. RAE TR NO. 65248, Nov. 1965.

9.85 Johnson, D. R. and Robinson, D. W.: The Subjective Evaluation of Sonic Bangs, ACUSTICA, Vol. 18, 

No. 5, 1967, pp. 241–258.

9.86 Schomer, P. D.; Sias, J. W.; and Maglieri, D. J.: A Comparative Study of Human Response Indoors to Blast 

Noise and Sonic Booms, Noise Control Eng. J. 45(4), 1997, July–Aug. 1997, pp. 169–182.

9.87 Schomer, Paul D.: New Descriptor for High-Energy Impulsive Sounds. Noise Control. Eng. J. 42(5), 

1994, pp. 179–191. 

9.88 Hawkins, S. J. and Hicks, J. A.: Sonic Bang Simulation by a New Explosives Technique, Nature 211, No. 

5055, 1966, pp. 1244–1245.

9.89 Strugielski, R. T.; Fugelso, L. E.; and Byrne, W. J.: Sonic Boom Simulation with Detonable Gasses. AIAA 

paper No. 71-186, January 1971.

9.90 Haac, T. Ryan; Corcoran, Joe M.; Ramillieux, Marcel C.; Reichard, Georg; and Burdisso, Ricardo A.: 

Experimental Characterization of the Vibro-Acoustic response of a Simple Residential Structure to a 

Simulated Sonic Boom. AIAA Paper 2009-3386, May 2009.

9.91 Ewins, D. J.: Modal Testing: Practice and Application, Philadelphia Research Studies Press, Ltd. 2000.

9.92 James, G. H., III; Carne, T. G.; and Lauffer, J. P.: The Natural Excitation Technique (NExT) for Modal 

Parameter from Operating Wind Turbines. Albuquerque, NM, Sandia Nat. Labs., 1993.

9.93 Webb, D. R. B. and Pallant, R. J.: A Device for Simulating the Sonic Bang. Presented at the Symp. on 

Aero. Acoust., Toulouse, France, March 1968. 

9.94 Bablke, H. E.; Kantarges, G. T.; Siddon, T. E.; and Van Houten, J. J.: The Shock Expansion Tube and Its 

Application as a Sonic Boom Simulator. NASA CR-1053, June 1968.

9.95 Tomboulian, R.: Research and Development of a Sonic Boom Simulation Device. NASA CR-1378, July 

1969.

9.96 Tomboulian, R. and Peschke, W.: Description and Capabilities of a Traveling Wave Sonic Boom Simulator. 

NASA CR-1696, 1970.

9.97 Kao, G. C.: An Experimental Study to Determine the Effects of Repetitive Sonic Booms on Glass Breakage. 

FAA-70-13, June, 1970.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques

511

9.98 Sizov, Natalia; Schultz, Troy; Hobbs, Christopher; and Klos, Jacob: Measured Rattle Threshold of 

Residential House Windows. Noise Con. 2008, pp. D-677-685, July 2008.

9.99 Haber, J.: Cumulative Sonic Boom Damage to Plaster. AIAA 93-4446, Oct. 1993.
Chapter 9 Sonic Boom Simulation Devices and Test Techniques 

512
Chapter 10 Outlook for Civilian Supersonic Overland Flight 

513

CHAPTER 10 OUTLOOK FOR CIVILIAN SUPERSONIC OVERLAND FLIGHT

This concluding chapter presents the authors’ outlook for civilian supersonic overland Àight based upon their 

assessment of the nearly 6 decades of sonic boom research developments described in this publication. The 

authors are of the opinion that the technical community is currently capable of designing a SSBJ-sized aircraft 

similar to the supersonic airliner concepts (refs. 10.1 and 10.2) shown in ¿gure 10.1. These aircraft would have 

a low-boom shaped cruise signature of maximum overpressure in the 0.3 lb/ft2

 to 0.5 lb/ft2 range combined with 

signature rise times greater than 5 msec. Acceptable performance, economic feasibility, and operational safety 

would also be required. To enable these class of civilian supersonic aircraft and enable regulatory change, the 

technical community is also prepared to design a low-boom demonstration vehicle similar to the vehicle depicted 

in ¿gure 10.2.

The desire to Ày supersonically overland has presented the technical community with a plethora of complex 

technical challenges with regard to research efforts aimed at mitigating the sonic boom phenomenon over the past 

(Courtesy of NASA)

(Courtesy of Lockheed Martin, ref. 10.1)

Figure 10.1. Potential supersonic airliner concepts.

(Courtesy of The Boeing Company)

Figure 10.2. NASA low-boom demonstration vehicle concept.
Chapter 10 Outlook for Civilian Supersonic Overland Flight

514

six decades. Most of these technical challenges have been overcome. However, four signi¿cant questions require 

more comprehensive resolution before civilian supersonic overland Àight operations can be realized:

(1) Will overÀown communities ¿nd the magnitude of low-boom shaped cruise signatures acceptable"

(2) Can the magnitude and extent of the transition focus boom footprint be minimized to allow supersonic 

overland operations"

(3) Are low-boom shaped signatures less inÀuenced by the atmosphere"

(4) Can low-boom shaped cruise signatures possibly damage ground structures or create undesired building 

 vibration or rattle"

Each of these four questions will be addressed in this chapter, which concludes with a citing of continuing research 

needs. Although considerable insight is gained through the use of simulation devices and techniques, the ¿nal 

answer to the four questions must be acquired via Àight validation of a low-boom demonstration vehicle and 

associated ground measurements and community response surveys.

In 1988, approximately 60 representatives of industry, academia, government, and the military gathered at 

NASA LaRC for a 2-day Sonic Boom Workshop on the state of the art of sonic boom physics, methodology, and 

understanding (ref. 10.3). Attendees included many internationally recognized sonic boom experts who were very 

active in the Supersonic Transport (SST) and Supersonic Cruise Aircraft Research (SCAR) programs of the 1960s 

and 1970s. The purpose of the workshop was to assess the state of the art in sonic boom knowledge and prediction 

capability and to prioritize research efforts needed in the immediate future.

Participants in the workshop agreed that efforts should begin immediately on the three primary challenges shown 

in ¿gure 10.3 in order to achieve civilian supersonic overland Àight operations. The 1988 workshop participants 

(ref. 10.3, p. 21) concluded that “Answers to whether an acceptable waveform exists, whether an aircraft can be 

designed to that waveform, and whether the atmosphere will destroy the bene¿ts of that waveform will be needed 

very early in any studies to develop overland high-speed civil transports.” During this time period, the question 

arose as to whether a shaped boom signature from a full-scale aircraft would persist through a real atmosphere 

to the ground. Theory and wind-tunnel tests had established that would be the case. The necessity to demonstrate 

that this persistence would be realized was identi¿ed by Maglieri, Sothcott, and Keefer (ref. 10.4). This Àight 

demonstration was eventually accomplished by the Shaped Sonic Boom Demonstrator (SSBD) Àight-test program 

on August 22, 2003 (ref. 10.5). The shaped signature was produced by modifying the Northrop Grumman F-5E 

aircraft (see Chapter 5, ¿gs. 5.17 and 5.18) using existing analytical design codes to alter its nominal N-wave 

signature into a Àat-top boom signature for the forward section of the aircraft.

Figure 10.3. 3ULPDU\FKDOOHQJHVWRFLYLOLDQVXSHUVRQLFRYHUODQGÀLJKWRSHUDWLRQV
Chapter 10 Outlook for Civilian Supersonic Overland Flight 

515

The 1988 workshop was also the waypoint leading to the NASA High Speed Research (HSR) program of the 

1990s, in which minimization of the sonic boom, airport noise, and vehicle emissions were the primary challenges 

for the civilian supersonic transports under consideration. In early 2000, the Defense Advanced Research Projects 

Agency (DARPA) funded the Quiet Supersonic Platform (QSP) program that focused on a smaller supersonic 

vehicle. The single goal set forth was that the vehicle shall have an initial sonic boom overpressure of 0.3 lb/ft2 

(ref. 10.6). The same year, NASA commissioned the National Research Council (NRC) to identify breakthrough 

technologies for overcoming key barriers to the development of environmentally acceptable and economically 

viable commercial supersonic aircraft (ref. 10.7). Low-boom shaped signatures with overpressures less than 1.0 

lb/ft2

 were cited along with the need to ascertain the limits on overpressure and rise time that would ¿nd public 

acceptance of overland sonic booms.

The desire and need for establishing supersonic overland operations was recognized as a necessity by the 2003 

Partnership for AiR Transportation Noise and Emissions Reduction (PARTNER), established between the FAA/

NASA/Transport Canada Center of Excellence (CoE) (ref. 10.8) consortium. The Center sponsored several 

projects aimed at determining the acceptability of low-boom signatures to the general population (i.e., what 

signatures will be acceptable to the public for overland supersonic Àight). There were three tasks that were 

initially funded: (1) analytical incorporation of atmospheric turbulence onto shaped waveforms, (2) determining 

the annoyance of low-boom shaped waveforms, and (3) the development of the proper noise metrics. In 2004, 

a consortium of 10 companies was formed to pursue a supersonic cruise technology demonstrator that included 

Boeing, Lockheed, Northrop Grumman, Gulfstream, Cessna, Raytheon, Rolls-Royce Allison, General Electric, 

Pratt and Whitney, and NetJets. In July 2004, the Supersonic Cruise Industry Alliance (SCIA) charter was formed 

with the stated objective of conducting a Àight-test program to “obtain scienti¿c data necessary to document and 

establish a publicly acceptable supersonic cruise acoustic signature, thereby allowing unrestricted supersonic 

Àight overland.” Note that the objective states an acoustic signature and did not specify a particular vehicle. 

The low-boom demonstration vehicle would, in fact, be a “low-boom simulator” and not be associated with any 

speci¿c type of civil supersonic vehicle. It is also of interest to note that the SCIA objective was essentially the 

same as the ¿rst of the three research priorities identi¿ed by the 2003 PARTNER (ref. 10.8) and sonic boom 

experts who gathered at NASA LaRC in 1988 (ref. 10.3).

Given the recommendations of the 1988 workshop members, along with the positions taken by the NRC, PARTNER 

and SCIA consortiums, continued advancement and of low-boom design tools, and improved understanding of 

community response metrics, the authors of this publication now feel that the supersonics community has reached 

an appropriate juncture to provide an optimistic outlook for civil overland supersonic Àight.

Predicted Annoyance to Cruise Boom Levels

An enormous amount of effort has been directed toward the establishment of acceptable low-boom shaped 

signatures using simulator chambers (see Chapter 8) resulting in a large creditable database. In addition, recent 

NASA low-boom Àights (see Chapter 8, ¿gs. 8.23-8.25), where subjects outdoors and inside instrumented houses 

were exposed to low overpressure N-waves of less than 0.6 lb/ft2

 and with increased rise times, have added to the 

existing human response database to booms of less than 1.0 lb/ft2

.

Revisiting the data previously shown in Chapter 8, ¿gure 8.36, the percentage of the population highly annoyed 

by N-wave type sonic booms of various levels is presented using two metrics: (1) the overpressure (ǻp) in lbs/ft2 

together with number of booms per day and (2) day-night average C-weighted Sound Exposure Level (CSEL). 

The day-night average was an aggregation based on the equal energy hypothesis, accounting for the number 

of events as well as their level. Also plotted on the ¿gure was the Committee on Hearing, Bioacoustics, and 

Biomechanics (CHABA) curve (ref. 10.9) adopted by the American National Standards Institute (ANSI) (ref. 

10.10) that provided an assessment of high-energy impulsive sounds, with respect to residential communities. 

Examination of the data showed that the early US-SST cruise boom level design target of 1.5 lbs/ft2

 was predicted 
Chapter 10 Outlook for Civilian Supersonic Overland Flight

516

to result in 10 to 35 percent of the population being highly annoyed by 1 to 8 booms/day, respectively. However, 

at boom levels of 0.3 lb/ft2

 to 0.5 lb/ft2, the annoyance numbers are reduced to about 1 to 5 percent for the one to 

eight booms/day.

The impulsive sounds previously mentioned included explosions, quarry blasts, artillery and gun¿re, as well 

as sonic booms. The CSEL metric is quite insensitive to rise time and is mostly controlled by overpressure and 

signature duration. As a result, the CSEL does not recognize the reduced loudness of a shaped signature of the 

same overpressure and period but with a larger shock rise time (see Chapter 8, ¿g. 8.37). 

A shaped signature with longer rise times (e.g., o > 5 msec) will always be more acceptable than an N-wave 

signature of zero rise time with the same overpressure and duration. Studies using sonic boom simulators have 

shown that Perceived Level (PL(dB), or also referred to as PLdB, is a better metric for assessing the loudness of 

N-wave and shaped signature booms. Sonic boom simulator studies indicate that a civilian supersonic business jet 

design with a low-boom shaped cruise signature (with a rise time greater than 5 msec) of less than 80 PLdB would 

¿nd outdoor and indoor community acceptance since its shaped signature has been shown to be more acceptable 

than an N-wave signature of the same overpressure and duration. 

Transition Focus Boom

In Chapter 3, it was shown that a creditable database has been acquired regarding the nature, measurement, and 

generation of transition focus booms for N-wave design aircraft. These focus booms from transition Àight, which 

can be anywhere from two to ¿ve times as intense as the steady level carpet booms, can not be avoided and only 

minimized. However, they impact relatively small regions on the ground, are a singular occurrence, and are not 

dragged along with the aircraft as is the case of carpet booms.

The beginning of every supersonic Àight must contend with this challenging phase of supersonic Àight. Transition 

focus booms were not of concern during Concorde operations since they took place over the ocean. However, 

for civilian overland supersonic operations, transition Àight will be the most critical phase of the entire overland 

Àight pro¿le. 

Recent analytical studies (see Chapter 3, ¿g. 3.18) have shown that aircraft designed to generate certain shaped 

sonic boom signatures will result in lower transition focus booms as compared to aircraft that generate N-wave 

signatures. A comparison of the focus boom overpressures along the ground track for an N-wave design aircraft, 

such as the 105-foot long SR-71, and a similar sized low-boom shaped vehicle such as a SSBJ during transition 

Àight from Mach 0.9 to 1.2 at a constant altitude of 30,000 feet is given in ¿gure 10.4.

Figure 10.4. 3UHGLFWHGIRFXVERRPRYHUSUHVVXUHVDORQJWKHJURXQGWUDFNGXULQJWUDQVLWLRQÀLJKW
Chapter 10 Outlook for Civilian Supersonic Overland Flight 

517

In the case of the SR-71, it can be seen that a focus overpressure of about 8.0 lbs/ft2 is predicted, which is about 

three times as intense as the 2.5 lbs/ft2

 carpet boom that follows. For a low-boom shaped signature from a SSBJ, 

using the focus factor based on ¿gure 3.19, the focus level is predicted to be the order of 1.0 lb/ft2

 or less, which 

is about two times the assumed 0.45 lb/ft2

 carpet boom at 30,000 feet. Based on the ¿ndings from references 

10.11 and 10.12, one can assume that the low-boom shaped signature at cruise also retains its character during the 

transition phase of Àight at a lower altitude and Mach number. Performing this transition at higher altitudes and 

incorporating an optimum climb-acceleration schedule with a robust low-boom design would likely minimize the 

focus boom level and footprint to the point of community acceptance.

Atmospheric Distortion of Sonic Boom Signatures

In Chapter 2, it was shown that N-wave boom signatures can become signi¿cantly distorted by turbulent activity, 

especially in the lower layers of the atmosphere, which cause them to become peaked or rounded. This peaking 

and rounding of sonic boom signatures is statistical in nature and occurs as a function of time and distance. An 

indication of what these statistics are for N-wave design aircraft and what they are projected to be for low-boom 

shaped signatures is provided in ¿gure 10.5. A summary of the variations of the on-track N-wave signature 

overpressures resulting from atmospheric distortion for steady level Àight (see Chapter 2, ¿g. 2.38) is shown 

again by the solid line in ¿gure 10.5. This statistical analysis comprises most of the sonic boom experiments that 

have been conducted in the United States over the past 50 years. Data are included from a wide range of N-wave 

designed aircraft for the Mach number range of 1.2 to 3.0 and altitude range of about 10,000 to 80,000 feet. A total 

of 12,406 data samples have resulted from 1,625 supersonic Àights. 

Figure 10.5. Measured and predicted statistical variation of sonic boom signatures resulting from atmospheric distortion. 
Chapter 10 Outlook for Civilian Supersonic Overland Flight

518

The relative cumulative frequency distribution for on-track measurements showing the probability of equaling 

or exceeding the ratio of the measured N-wave overpressure to the design value for an N-wave designed aircraft 

in steady level Àights, in standard atmosphere with no winds, is plotted in ¿gure 10.5. Rounded signatures of the 

waveform sketched in the chart are usually associated with overpressure ratios less than 1.0. Nominal N-wave 

signatures are observed on the average and peaked signatures of overpressures are observed at ratios greater than 

1.0. The data indicate the variations in the sonic boom signatures, resulting from the effects of the atmosphere, 

can be expected during routine operations. For example, one N-wave boom in a thousand is expected to exceed 

the design value by a factor of about 3.0. Signature variability is also known to increase with increasing distance 

laterally from the aircraft ground track (See Chapter 2, ¿g. 2.40). 

Whether or not these exact statistics for N-wave booms apply to shaped signatures remains to be demonstrated. 

There is a reasonable expectation that the probability distribution for a low-boom shaped signature, which has 

low initial shock overpressure and increased shock rise time, will show less variation and thus a lesser slope, as 

illustrated by the dashed red line shown in ¿gure 10.5. Since it is known that the atmospheric distortions of boom 

signatures take place at the bow and tail shocks, which are made up of the high frequencies, it is reasonable to 

expect that shaped signatures, which have less energy at high frequencies due to the increased rise times (see 

Chapter 8, ¿g. 8.7), will be less inÀuenced by the atmosphere. As a result, the boom signatures observed at the 

ground during routine supersonic cruise Àight operations are expected to be more closely associated with the 

design cruise boom signatures.

Another bene¿t of low-boom shaped signatures is the additional increase in shock rise time with decreasing 

overpressure. This increase in signature rise time is a result of atmospheric absorption due to molecular relaxation 

(see Chapter 2, ¿g. 2.45) and further reduces the inÀuence of the atmosphere in bringing about signature distortions. 

The establishment of a statistical database on the variability of low-boom shaped signatures due to atmospheric 

variability and turbulence can be best achieved with a low-boom demonstration vehicle combined with Àight and 

ground research instrumentation. 

Sonic Boom Induced Structural Damage, Vibration, and Rattle

To appreciate the substantial, cumulative bene¿ts that result from designing a vehicle to have a low-boom shaped 

signature during cruise Àight, it is necessary to look back upon previous community observations to sonic boom 

overÀights conducted during the mid-1960s, where N-wave signatures on the order of 1.0 lb/ft2

 to 3.0 lbs/ft2 were 

experienced. In each of these community overÀight experiments, three aspects of sonic booms were found to be 

most disturbing – (1) people being startled, (2) structural component vibrations and rattles, and (3) rising concerns 

over the possibility of sonic boom induced structural damage (see Chapter 8, ¿gs. 8.34 and 8.35).

The nature of the sonic boom-induced damage problem as it relates to the current N-wave database wherein 

nominal cruise boom design levels of about ǻp ~ 1.5 lbs/ft2

 are experienced during routine steady-level supersonic 

Àight operations was discussed in Chapter 8 (¿g. 8.22). The nature of the problem is revisited here in order to 

make a comparison of a likely scenario for aircraft designed with low-boom shaped signatures during cruise on 

the order of 0.3 lb/ft2

. This comparison is further illustrated in ¿gure 10.6.

The number of damage incidents (shown by the dashed curve) for a given type of structural component increases 

as the overpressure increases. This is particularly evident at the higher overpressure values. Also shown is a 

schematic illustration of the amplitude distribution of sonic boom overpressures from current and future lowboom supersonic vehicles (the two solid line bell-shaped curves). The current N-wave database as it related to 

sonic boom induced damage is addressed in the ¿gure as well. At a designed cruise overpressure of about 1.5 lbs/

ft2

, illustrated by the vertical short-dashed line, the design boom level of 1.5 lbs/ft2 is generally lower than that at 

which building damage might be expected for structures in good repair. However, as previously noted in ¿gure 

10.5, there is a distribution of boom overpressure amplitudes such that a small percentage of the total amplitude 

values occur in the relatively high overpressure range. 
Chapter 10 Outlook for Civilian Supersonic Overland Flight 

519

These high values, which occur occasionally because of either atmospheric effects or focus booms due to 

maneuvers, may be suf¿cient to trigger incipient damage in existing structures. In order to reduce the probability 

of building damage, future supersonic vehicles must have much lower design cruise overpressures, as shown in 

¿gure 10.6, and shaped signatures that are less likely to be altered by the atmosphere.

The distribution of sonic boom pressure loads associated with the design of future aircraft having a low-boom 

shaped cruise signature of about 0.3 lb/ft2

 is shown in the lower left-hand side of ¿gure 10.6. The ǻp distribution 

of pressure loads curve shows considerably less variability (narrower bell shape distribution) because of the lowboom shaped signature experiencing less distortion by the atmosphere. It has also been noted that boom signatures 

with low overpressures realize increased rise times resulting from molecular relaxation and absorption. These 

features, along with the shaping (e.g., ramp-type signature) aspects provide a signature spectrum with even less 

high frequency energy and further assure that the boom signature experienced at the ground during supersonic 

overland Àight will experience less variability and thus be much nearer the design cruise low-boom signature. 

Thus, a low-boom shaped cruise signature will be unlikely to damage ground structures or create undesired 

building vibration or rattle.

Research Needs

At the end of each of the chapters of this publication, summary remarks have been provided that capture the 

key concepts discussed in each Chapter. Therefore, it is appropriate to conclude with a similar, but expanded 

summary that also includes future research needs and the rationale for a low-boom Àight demonstration. Below 

is a listing of research needs that should be met prior to gaining of¿cial approval for routine civil supersonic 

overland Àight operations:

• Continue laboratory and Àight activities to support the development of appropriate low-boom signatures 

and metrics for community acceptability.

• Continue to re¿ne integrated aircraft design and optimization tools to achieve viable aircraft designs with 

optimum low-boom signatures.

• Understand and minimize the transition focus boom magnitude and footprint.

• Continue to improve our understanding of turbulence and other atmospheric effects on low-boom shaped 

signatures.

• Develop a low-boom demonstration vehicle that enables Àight validation of low-boom technologies and 

the study of atmospheric effects on and community acceptability of low-boom shaped signatures.

Figure 10.6. Nature of sonic boom induced damage. 
Chapter 10 Outlook for Civilian Supersonic Overland Flight

520

Low-Boom Flight Demonstration

The completion of research efforts cited above combined with the nearly 60 years of fundamental research on all 

aspects of sonic boom will signi¿cantly advance our knowledge and understanding of this highly fascinating and 

complex phenomenon of the science of supersonic Àight. Moreover, this level of knowledge and understanding 

will be advanced to the point where transition to systems level research is necessary. Further progress can be best 

achieved through a low-boom Àight demonstration. 

The need for such a vehicle was highlighted in early 2000 with the DARPA Quiet Supersonic Program (QSP) (ref. 

10.6) along with the National Research Council (ref. 10.7). In 2005, NASA announced that the Vehicle Systems 

Program (VSP) was working on developing a low-boom Àight demonstrator with the goal of providing a Àight 

demonstration of sonic boom signatures that delineate acceptable human response. In addition to the speci¿c 

vehicle designs (~100 feet in length, ~ 30,000 pounds in takeoff gross weight, Mach range 1.4-1.8 at  55,000 

feet), considerable effort was directed towards assuring that the low-boom shaped signatures of less than 0.5 lb/

ft2

 was relevant to future larger SSBJs. During the low-boom demonstrator planning, the NASA Aeronautics 

Program was restructured and the project did not proceed beyond the planning phase.

In recent years, NASA’s Aeronautics Program has continued research to overcome the sonic boom barrier and 

has produced key breakthroughs in sonic boom noise reduction through the advancement of design tools, sonic 

boom simulators and ¿eld studies, and advanced concept studies of civilian supersonic aircraft. In 2012, NASA 

began concept formulation and design studies of a new low-boom Àight demonstrator taking advantage of these 

key breakthroughs.

A low-boom Àight demonstration would enable the validation of the design tools and methods for achieving a 

low-boom shaped signature, enable the establishment of a database on the inÀuence of the atmosphere on lowboom shaped signatures, and demonstrate that transition focus boom footprints can be minimized to the point 

of community acceptance. Such a vehicle will allow for the type of broad community experiments that will 

be required to fully demonstrate and garner the acceptability of low booms, generate vast sets of data that will 

be critical to supporting changes to the present rules that limit civil supersonic overland Àight (ref. 10.8) and 

ultimately play a key role in the development of sonic boom standards for civilian supersonic overland Àight.

Chapter 10 Summary Remarks

The authors have presented their assessment of the potential for civilian supersonic overland Àight of a SSBJ 

type and eventually larger transport aircraft having a low-boom shaped signature during cruise Àight. However, 

before civilian supersonic overland Àight can be realized, the issues of community acceptance, transition focus 

minimization, impact of atmospheric distortion, and the possibility of vibration or rattle of ground structures 

remain for more comprehensive resolution.

This assessment shows that supersonic vehicles having low-boom shaped signatures of less than 0.5 lb/ft2

 would 

¿nd community acceptance. Transition focus booms are shown to be on the order of 1.0 lb/ft2

 or less and the 

atmosphere is expected to have much less inÀuence on bringing about boom signature distortions as compared 

to N-wave signatures. A low-boom shaped signature would signi¿cantly reduce the sonic boom startle factor, 

building vibrations, and thus minimize the rattle factor and greatly reduce the probability of sonic boom induced 

damage.

Sonic boom simulator studies indicate that a civilian SSBJ design with a low-boom shaped cruise signature (with 

a rise time greater than 5 msec) of less than 80 PLdB should ¿nd outdoor and indoor community acceptance since 

its shaped signature has been shown to be more acceptable than an N-wave signature of the same overpressure 

and duration. 

Although considerable insight into designing an acceptable low-boom shaped signature is gained through the use 

of ground-based simulator signatures, conclusive data showing that civilian supersonic overland Àight operations 
Chapter 10 Outlook for Civilian Supersonic Overland Flight 

521

will be acceptable can only come from the Àight validation of a low-boom demonstration vehicle and associated 

ground measurements and community response surveys that will enable the determination of future low-boom 

design and community response metrics. 

Chapter 10 References

10.1 Morgenstern, John; Norstrud, Nicole; Sokhey, Jack; Martens, Steve; and Alonso, Juan J.: Advanced 

Concept Studies for Supersonic Commercial Transports Entering Service in the 2018 to 2020 Period – 

Phase I Final Report, NASA CR-2013-217820, Feb. 2013.

10.2 Magee, Todd E.; Wilcox, Peter A.; Fugal, Spencer R.; Acheson, Kurt E.; Adamson, Eric E.; Bidwell, Alicia 

L.; and Shaw, Stephen G.: System-Level Experimental Validations for Supersonic Commercial Transport 

Aircraft Entering Service in the 2018-2020 Time Period – Phase I Final Report, NASA/CR-2013-217797, 

Feb. 2013.

10.3 Darden, Christine M.; Powell, Clemans A.; Hayes, Wallace D.; George, Albert R.; and Pierce, Allan D.: 

Status of the Sonic Boom Methodology and Understanding. NASA CP 3027, Jan. 19–20, 1988.

10.4 Maglieri, D. J.; Sothcott, V. E.; and Keefer, T. N., Jr.: Feasibility Study in Conducting OverÀight 

Measurements of Shaped Sonic Boom Signatures Using the Firebee BQM 34E, RPV. NASA CR-189715, 

Feb. 1992.

10.5 Pawlowski, J. W.; Graham, D. H.; Boccadoro, C. F.; Coen, P. G.; and Maglieri, D. J.: Origins and Overview 

of the Shaped Sonic Boom Demonstration Program. AIAA 2005-0005, Jan. 2005.

10.6 Wlezien, R. and Veitch, L.: Quiet Supersonic Platform. AIAA Paper 2002-0143, Jan. 2002. 

10.7 National Research Council, “Commercial Supersonic Technology: The Way Ahead”, National Academy 

Press, Washington, D.C., 2001.

10.8 Sparrow, Victor W.: Lowering the Boom, Acoustics Today, Vol. 2, Issue 1, Jan. 2006, pp. 20–28.

10.9 Anonymous: “Community Response to High-Energy Impulsive Sounds: An Assessment of the Field since 

1981”, Committee on Hearing, Bioacoustics, and Biomechanics (CHABA). National Research Council, 

National Academy of Science, Washington, D.C., 1996 (NTISPB97-124044).

10.10 Anonymous: American Standard Method for Assessment of High Energy Impulsive Sounds with Respect 

to Residential Communities. ANSI S12.9, part 4, 2005.

10.11 Maglieri, Domenic J.; Bobbitt, Percy J.; Massey, Steven J.; Plotkin, Kenneth J.; Kandil, Osama A.; and 

Zheng, Xudong: Focused and Steady-State Characteristics of Shaped Sonic Boom Signatures: Prediction 

and Analysis, NASA/CR-2011-217156, June 2011.

10.12 Elmer, K.; Welge, H.; Salamone, J.; and Cowart, R.: SCAMP: Supersonic Passenger Transport Transonic 

Acceleration Flight Pro¿les with Consideration of Focused Boom, AIAA-2013-1065, Jan. 2013.



NASA/SP-2014-622