Aftosmis, Michael J.

Spurlock, Wade M.

English

NASA Technical Reports Server

Michael J. Aftosmis
Computational Aerosciences Branch
NASA Ames Research Center 
Moﬀett Field,  CA 94035
michael.aftosmis@nasa.gov
Wade M. Spurlock
Science and Technology Corp.
Computational Aerosciences Branch
Moﬀett Field,  CA 94035
wade.m.spurlock@nasa.gov
sBOOM Propagation for the Third AIAA Sonic Boom 
Prediction Workshop
3rd AIAA Sonic Boom Prediction Workshop
4-5 Jan 2020, Orlando, FL, USA
1
2
Overview
• Preliminaries
– Conventions & propagation primer
– Mesh Convergence & oversampling
• Results for Cases 1 & 2
– Ground signals for Standard Atm. & Required Atm.
– Cutoﬀ angles
– Carpet noise metrics
– Ground Intercepts, boom carpets & raytubes
• Summary & observations
https://ntrs.nasa.gov/search.jsp?R=20200000443 2020-03-11T13:35:25+00:00Z
3x
y
β
β = 90°
0°
+y
+x
Left–handed
• sBOOM wind uses left handed coord. sys.
• β = heading
• β = 0° A/C pointed East, cw+
• sBOOM wind tables are in meters vs m/s
• x and y are wind components (“blows toward”)
  (x, y) = (1, 0) is tail wind if heading is East
  (x, y) = (0, 1) is tail wind if heading is South
  (x, y) = (1, 1) is tail wind if heading is SE
Wind Convention in sBOOM
• Workshop has aircraft flying E, 
– This is 0° heading in sBOOM
4
Propagation Primer
Ray that sound 
travels along
Sound 
generated
Sound heard•
µ
 π  – µ
2 this is the “ray path”
µ = sin 1
  1
M1
 
• Quasi-1D integration of Burger’s equations occurs in tube along the ray path
• Determines the ground intercept of sound emanating from given trajectory point & azimuth
• Ray path determines time required for signal propagation
• Only consider crossrange and downrange winds (no up/down drafts)
• Wind can alter path of raytube (ray at ϕ=0° shown)
• Paths are scaled by local raytube area Flight 
path (+x )
Al
tit
ud
e 
(ft
)
Down
range
 (ft)
Crossrange (ft)
5
Wind Effects
Raytube from SBPW2 axibody
6
Mesh Convergence
Sensitivity of noise output to discretization of near field signal
• Propagation code is solving augmented Burgers’ via finite diﬀerence
• Need to make sure loudness metrics are suﬃciently mesh converged
• Mesh convergence of propagation is case dependent ( on signal, azimuth & atm.)
• Mesh refinement study done for each near field signal (using Std. and Reqd. Atm.’s)
• Truncation error directly impacts accuracy, resolution requirements are driven by 
need to minimize error in propagation
• Initial signal typically has < 2000 points
• Propagation typically requires 40000-100000 points (oversampled by 20-50x)
• Discrete ASEL filter can be poorly behaved at high sampling frequencies ( > ~250kHz)
➛ this limits maximum allowable oversampling
• How much accuracy is needed?
• Atmospheric variability generally 2-5 dB, but may be ~10 dB in some cases
• Generally tried to keep propagation error under ±0.2 dB
7Mesh Convergence
Sensitivity of noise outputs to refinement of the propagation mesh
Ground Signature     
80 100 120 140 160 180 200
Time (ms)
48
50
52
54
56
58
60
62
64
66
68
SE
L[
a]
 (d
B)
  20k pts (81kHz)
  50k pts (204 kHz)
100k pts (409 kHz)
200k pts (818kHz)
300k pts (1.23MHz)
80 100 120 140 160 180 200
Time (ms)
-20
-10
0
10
20
30
Ov
erp
res
su
re 
(P
a)
  20k pts (81kHz)
  50k pts (204kHz)
100k pts (419kHz)
200k pts (818kHz)
300k pts (1.23Mhz)
Forward ASEL Buildup
Case1, C25P: ϕ = 0°
• C25P signals at ϕ = 0°, using from 20k 300k points (80-1230 kHz) for propagation
• Despite similarities in ground signal, mesh convergence of ASEL is quite slow
8
Mesh Convergence
Sensitivity of noise outputs to refinement of the propagation mesh
Ground Signature     
80 100 120 140 160 180 200
Time (ms)
48
50
52
54
56
58
60
62
64
66
68
SE
L[
a]
 (d
B)
  20k pts (81kHz)
  50k pts (204 kHz)
100k pts (409 kHz)
200k pts (818kHz)
300k pts (1.23MHz)
80 100 120 140 160 180 200
Time (ms)
-20
-10
0
10
20
30
Ov
erp
res
su
re 
(P
a)
  20k pts (81kHz)
  50k pts (204kHz)
100k pts (419kHz)
200k pts (818kHz)
300k pts (1.23Mhz)
Forward ASEL Buildup
• C25P signals at ϕ = 0°, using from 20k 300k points (80-1230 kHz) for propagation
• Despite similarities in ground signal, mesh convergence of ASEL is quite slow
156 158 160 162 164
-14
-12
-10
-8
160 165 170 175
Time (ms)
65
65.5
66
66.5
SE
L[
a]
 (d
B)
9Mesh Convergence
Convergence ASEL noise metric with sampling frequency
0 50000 100000 150000 200000 250000 300000
Number of Samples 
65.6
65.8
66
66.2
66.4
66.6
66.8
67
SE
L[
a] 
 (d
B) Discrete aSELFFT aSEL
• ASEL converges slowly
– Need ~600kHz (~150k pts) to 
converge ASEL to ±0.01dB
• However, discrete ASEL filter 
starts to have issues at ~250kHz, 
and blows up ~500kHz
• On this case (C25P) hard to 
guarantee ASEL error < ± 0.1dB
• Discrete BSEL and CSEL remain 
well behaved till ~1 & 10 MHz 
(respectively), so generally easier 
to mesh convergeCase1, C25P: ϕ = 0°
200 400 600 800 1000 1200kHz
10
Mesh Convergence
Convergence of BSEL, CSEL & PLdB noise metrics with sampling frequency
Case1, C25P: ϕ = 0°
0 50000 100000 150000 200000 250000 300000
Number of Samples 
78.6
78.8
79
79.2
79.4
SE
L[
B]
 L
ou
dn
ess
  (d
B)
0 50000 100000 150000 200000 250000 300000
Number of Samples 
79.8
80
80.2
80.4
80.6
Pe
rce
ive
d L
ou
dn
ess
 (P
Ld
B)
200 400 600 800 1000 1200
Sampling Frequency, kHz
200 400 600 800 1000 1200
Sampling Frequency, kHz
0 50000 100000 150000 200000 250000 300000
Number of Samples 
92
92.2
92.4
92.6
92.8
93
SE
L[
C]
 L
ou
dn
ess
 (d
B)
200 400 600 800 1000 1200
Sampling Frequency, kHz
BSEL convergence CSEL convergence PLdB convergence
• BSEL, CSEL and PLdB all show good mesh convergence (all on 1 dB scale)
• FFT used for all metrics except for BSEL, but appears to be well behaved
• C-weighting converges fastest (±0.02 dB @ 200kHz)
• PLdB converges slowest (approx. ±0.1 dB @ 200kHz) 
11
Mesh Convergence
Convergence of BSEL, CSEL & PLdB noise metrics with sampling frequency
• To avoid excessive discretization error in propagation used 500-800 kHz sampling 
frequencies for all workshop cases
• Computed noise metrics with FFT in LCASB (adloud) for ASEL, CSEL and PLdB noise 
metrics
• Used digital BSEL filter in sBOOM (well behaved at 500-800 kHz)
Case1, C25P: ϕ = 0°
0 50000 100000 150000 200000 250000 300000
Number of Samples 
78.6
78.8
79
79.2
79.4
SE
L[
B]
 L
ou
dn
ess
  (d
B)
0 50000 100000 150000 200000 250000 300000
Number of Samples 
79.8
80
80.2
80.4
80.6
Pe
rce
ive
d L
ou
dn
ess
 (P
Ld
B)
200 400 600 800 1000 1200
Sampling Frequency, kHz
200 400 600 800 1000 1200
Sampling Frequency, kHz
BSEL convergence PLdB convergence
0 50000 100000 150000 200000 250000 300000
Number of Samples 
92
92.2
92.4
92.6
92.8
93
SE
L[
C]
 L
ou
dn
ess
 (d
B)
200 400 600 800 1000 1200
Sampling Frequency, kHz
CSEL convergence
12
Powered version of the NASA Concept 25D
Case 1: C25P
Conditions: 
M∞ = 1.6
Altitude = 15.760 km (52k ft)
Ground height = 264.069m (866ft)
Lprop =  33.53m (110 ft)
r/L = 3.0 at signal extraction
Ground reflection factor = 1.9
Heading East (β = 0°)
Atmospheric Profiles:
1. Required Atm: with profiles for 
wind, temp, pressure & humidity
2. Standard Atmosphere
Case 1: C25P Standard Atmosphere
13
Near field and ground pressure signals
Near Field Signals
35 40 45 50 55 60 65 70 75 80
Distance along sensor (m)
-0.0100
-0.0075
-0.0050
-0.0025
0.0000
0.0025
0.0050
0.0075
Δ
p/
p ∞ Phi =-50Phi =-40
Phi =-30
Phi =-20
Phi =-10
Phi =   0
Phi = 10
Phi = 20
Phi = 30
Phi = 40
Phi = 50
r/L = 3
• Near field data provided for half-cylinder {-90°, 90°}, ({-50°, 50°} shown)
ϕ = +40° ϕ = - 40°
Prop. Alt =  15760m
Sign Convention for Azimuth, ϕ
Case 1: C25P Standard Atmosphere
14
Propagation altitude = 15760 m, ground height = 264 m
Ground Signature
Prop. Alt =  15760m
• Near field data provided for half-cylinder {-90°, 90°}, ({-50°, 50°} shown)
• Propagation shown used 500kHz sampling frequency (142k pts)
Near Field Signal
35 40 45 50 55 60 65 70 75 80
Distance along sensor (m)
-0.0100
-0.0075
-0.0050
-0.0025
0.0000
0.0025
0.0050
0.0075
Δ
p/
p ∞ Phi =-50Phi =-40
Phi =-30
Phi =-20
Phi =-10
Phi =   0
Phi = 10
Phi = 20
Phi = 30
Phi = 40
Phi = 50
r/L = 3
Case 1: C25P Ground Signatures
15
Standard Atmosphere
Prop. Alt =  15760m
• Reqired Atm. has profiles of crosswind, temperature, humidity and pressure
– Shows lots of asymmetry, and cutoﬀs are farther out on both sides
Required Atmosphere
Propagation altitude = 15760 m, ground height = 264 m
Case 1: C25P Ground Noise
16
Compare ground noise metrics across the carpet as a function of azimuth
Standard Atmosphere
• Azimuthal range of carpet with real atm. is much wider than Standard Atm.
• Real atm. (with wind) reduces peak loudness by ~1dBA, ~0.5dBB, ~0.4dBC & ~0.7PLdB
• Noise at carpet edge drops, but can still be significant
Required Atmosphere
-60 -40 -20 0 20 40 60
Azimuth Angle (deg)
50
55
60
65
70
75
80
85
90
No
ise
 M
et
ric
 (d
B)
PLdB
SEL[a]
SEL[b]
SEL[c]
-60 -40 -20 0 20 40 60
Azimuth Angle (deg)
50
55
60
65
70
75
80
85
90
No
ise
 M
et
ric
 (d
B)
PLdB
SEL[a]
SEL[b]
SEL[c]
0 10 20 30 40 50 60 70 80 90
Downrange (km)
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
20
30
40
50
60
70
Cr
os
sr
an
ge
 (k
m
)
Standard Atm.
Required Atm.
Case 1: C25P Ground Carpet
17
ϕ = -78.4°
t = 386 s
ϕ = -70°
t = 188 s
ϕ = 0°
t = 64.9 s
ϕ = 69.1°
t = 284 s
ϕ = 60°
t = 141 s
ϕ = 0°
t = 64.9 s
ϕ = 50°
t = 142 s
ϕ = 50.8°
t = 162 s
W E
N
S
• Boom carpet computed from the intercepts of raytubes on 
the ground-plane projection of the trajectory. Showing both 
standard and required atmospheres
• Crossrange wind profile makes the required atm. asymmetric
• Cutoﬀ angles: Std. Atm = [±50.8°], Req. Atm = [-78.4°,+69.1°]
• Long propagation distances near signal cutoﬀ imply that 
these raytubes take a long time to reach the ground 
– Raytube for ϕ = -78.4° takes over 6 mins in Required atm.
– Mesh convergence near signal cutoﬀ is not nearly as good as 
at low azimuth angles
– Higher discretization error due to much longer propagation
– Propagation for signal cutoﬀ used higher sampling frequency 
(800 kHz)
• Ground track for required atm is ~160 km, more than 2x as wide 
as standard atm. (~70 km)
Project raytube ground intercepts on aircraft ground track
15
6.
9 
km
69
.2
 k
m
Cros
sran
geDownrange
N
S E
W
Case 1: C25P Raytubes for Required Atmosphere
18
• 3D plot of raytubes 
for real atmosphere
• Shows extremely 
long propagation 
times & large raytube 
areas near edges of 
the carpet
Plot 3D raytubes colored by raytube area
Flight path (+x )
19
Conditions: 
M∞ = 1.4
Altitude = 16.4592 km (54k ft)
Ground height = 110.011 m (54k ft)
Lref =  27.43 m (90 ft)
r/L = 3 at signal extraction
Ground reflection factor = 1.9
Heading East (β = 0°)
Atmospheric Profiles:
1. Required Atm: with profiles for wind, 
temp, pressure & humidity
2. Standard Atmosphere
Preliminary design of X-59 Low Boom Flight Demonstrator
Case 2: C609
Case 2: C609 Near Field Signals
20
Sign Convention for Azimuth, ϕ
r/L = 3
Alt =  16459.2 m
Subset of Near Field Signals
ϕ = +40° ϕ = - 40°
20 30 40 50 60
Distance Along Sensor (m)
-0.0075
-0.005
-0.0025
0
0.0025
0.005
Δ
p/p
∞
Phi = 70°
Phi = 60°
Phi = 50°
Phi = 40°
Phi = 30°
Phi = 20°
Phi =   0°
• Near field signals provided for 23 azimuths from -70° to +70°
   ϕ = [0, ±10, ±20, ±30, ±40, ±50, ±60, ±62, ±64, ±66, ±68, ±70]
• Signals symmetric ±ϕ
Case 2: C609 Sampling Frequency
21
Metric convergence with sampling frequency (Std. Atm.)
• Using FFT for metric computation get reasonable mesh 
convergence of ASEL, CSEL and PLdB by 500kHz. 
• Discrete BSEL filter appears well behaved as well
• Similar mesh convergence behavior for other azimuths. 
Used 500kHz sampling frequency away from cutoﬀ.
0 200 400 600 800
Sampling Frequency (kHz)
60.5
60.6
60.7
60.8
60.9
61
61.1
61.2
61.3
61.4
61.5
No
ise
 M
et
ric
 (d
B)
SEL[a]
0 200 400 600 800
Sampling Frequency (kHz)
89.6
89.8
90
90.2
90.4
No
ise
 M
et
ric
 (d
B)
SEL[c]
ϕ = +20°
ϕ = +20°
ϕ = +20°
ASEL Convergence
CSEL Convergence
0 200 400 600 800
Sampling Frequency (kHz)
74.6
74.8
75
75.2
75.4
No
ise
 M
et
ric
 (d
B)
PLdB
PLdB Convergence
Case 2: C609 Ground Signals
22
• Reqired Atm. includes profiles of crosswind, temperature, humidity and pressure
– Very asymmetric, with much wider cutoﬀs on both sides
• Amplitude of ground signal in real atmosphere significantly reduced from Std. Atm.
Standard Atmosphere Required Atmosphere
Propagation altitude = 16460 m, ground elevation = 110 m
-60 -40 -20 0 20 40 60
Azimuth Angle (deg)
30
40
50
60
70
80
90
No
ise
 M
et
ric
 (d
B)
PLdB
SEL[a]
SEL[b]
SEL[c]
-60 -40 -20 0 20 40 60
Azimuth Angle (deg)
30
40
50
60
70
80
90
No
ise
 M
et
ric
 (d
B)
PLdB
SEL[a]
SEL[b]
SEL[c]
Case 2: C609 Ground Noise
23
Compare ground noise metrics across the carpet as a function of azimuth
Standard Atmosphere
• Azimuthal range of carpet with Required Atm. is much wider than Standard Atm.
• Despite wind & reduced ground amplitude, Real Atm. and Std. Atm. have similar loudness
• Noise at carpet edge drops significantly in Required Atm.
Required Atmosphere
0 20 40 60 80 100 120 140
Downrange (km)
-120
-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
20
30
40
50
60
Cr
os
sr
an
ge
 (k
m
)
Standard Atm.
Required Atm.
Case 2: C609 Ground Carpet
24
58
.4
 k
m
ϕ = -64.1°
t = 518 s
ϕ = -64°
t = 365 s
ϕ = 0°
t = 77 s
ϕ = 70.6°
t = 275 s
ϕ = 60°
t = 156 s
ϕ = 0°
t = 80.11 s
ϕ = 40°
t = 122 s
ϕ = 44.9°
t = 172 s
W E
N
S
Project raytube ground intercepts on aircraft ground track
• Boom carpet computed from the intercepts of raytubes on the 
ground-plane projection of the trajectory. Showing both 
standard and required atmospheres
• Crossrange wind profile makes the required atm. asymmetric
• Cutoﬀ angles Req. Atm = [-64.1°, 70.6°], Std. Atm = [±44.9°]
• Long propagation distances near signal cutoﬀ imply that 
these raytubes take a long time to reach the ground 
– Raytube for ϕ = -64.1° cutoﬀ takes over 8.5 mins in Reqd. atm.
– Mesh convergence near signal cutoﬀ is not nearly as good as 
at low azimuth angles
– Higher discretization error due to much longer propagation
– Propagation for signal cutoﬀ rays used higher sampling 
frequency (800 kHz)
• Ground track for required atm is ~160 km, more than 2.7x as wide 
as standard atm. (~60 km)
ϕ = -60°
t = 195 s
16
2.
0 
km
Flight path (+x )
N
S
E
W
Case 2: C609 Raytubes for Required Atmosphere
25
Cross
range
Downrange
• 3D plot of raytubes 
for real atmosphere
• Shows extremely 
long propagation 
times & large raytube 
areas near cutoﬀ
Plot 3D raytubes colored by raytube area
1
26
Summary
• Applied sBOOM v2.82 & LCASB to all required and optional steady propagation cases 
• Mesh convergence studies across the carpet to ensure accuracy of the ground signal and loudness 
metrics. Error in noise metrics can be 2-4x higher near signal cutoﬀ. 
• Mesh convergence is relatively slow on intricate non-smooth input signals
• Real atmosphere is usually quieter than Standard Atmosphere, (but not always - e.g. case 2) 
• Ground track of real atmosphere can be nearly 3x wider than Standard day. Crosswinds generally 
increase track width and can result in large cutoﬀ azimuths 
• On windy days, boom may not arrive oﬀ-track for over 5 mins after a/c passes (case 2 took 8 mins!)
• Raytube visualization shows potential for loud oﬀ-track azimuths to be blown back under-track
127
Acknowledgments
• Thanks to Sriram Rallabhandi for developing and supporting sBOOM, and to Marian Nemec and 
David Rodriguez for technical discussions on the various cases.
• SBPW3 organizers for their eﬀort in organizing and coordinating the workshop, particularly Melissa 
Carter, Sriram Rallabhandi & Mike Park
• ARMD Commercial Supersonic Technology Project for support of this work and advancing the state 
of the art in boom prediction over the last decade
• NASA Advanced Supercomputing Division for providing computing resources
• NASA Ames Research Center contract NNA16BD60 and Science & Technology Corp. for 
supporting Wade Spurlock’s involvement.  
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