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National Aeronautics and Space Administration
Alexandra Loubeau, NASA Langley Research Center
Sriram K. Rallabhandi, National Institute of Aerospace
Comparison of sonic boom propagation and
loudness level calculations
AIAA Aviation 2014
Sonic Boom Activities III
June 17, 2014 High Speed Project
Acknowledgments
• David Richwine, Lori Ozoroski, Edward Haering, Larry Cliatt, Jacob Klos (NASA)
• Partners who participated in the comparison study
– Hao Shen (Boeing)
– Joseph Salamone (Gulfstream)
– Yoshikazu Makino and Yusuke Naka (JAXA)
– John Morgenstern (Lockheed Martin)
– Victor Sparrow and Joshua Palmer (Penn State)
– Kenneth Plotkin (Wyle)
2
Introduction
• Elements of sonic boom propagation
• Sonic boom propagation prediction and metrics calculation tools are used to
evaluate supersonic aircraft designs
• Desire to compare predictions from different developers
3
Atmospheric
Propagation
Human Response
Near-field Signature
Previous Study
• Comparison of sonic boom propagation codes conducted by Cleveland et al.
– Three codes compared favorably
4 Cleveland et al. Comparison of computer codes for the propagation of sonic boom waveforms through isothermal atmospheres. J. Acoust. Soc. Am.
100(5): 3017-3027, 1996.
• Reasons to conduct a new comparison
– Codes have been modified over last 20 years
– New codes have been developed
– Boom waveforms of interest have changed
– Cleveland analysis did not consider any noise metrics
Sonic Boom Propagation and PL Comparison
• Objective
– To achieve more consistent results across partners and to facilitate understanding of
possible differences in computer codes used in sonic boom research
• Approach
– Conducted a new baseline comparison of sonic boom atmospheric propagation and
noise metric calculation tools
• Developed a set of input cases for propagation and Perceived Level (PL)
calculation
• Participating organizations used their tools to run these cases and returned their
results to NASA
• All provided results were reviewed and compared with baseline results from
NASA’s tool suite
5
Summary of Perceived Level (PL)
• Metric for perceived level of loudness developed by Stevens
– Developed to predict behavior of human auditory system in response to sound
• Adapted for use with sonic booms by Shepherd and Sullivan
• PL has been shown to correlate well with human perception of sonic booms
heard outdoors
– PL is used today to evaluate supersonic aircraft designs
• Uses signal spectrum in one-third-octave bands
• Uses a set of frequency weighting contours that vary with level
– (By contrast, A-weighting contour does not vary with level)
– Based on equal loudness contours for bands of noise
– Extends down to 1 Hz, but this is an approximation
• Band of highest weighted level is the most important to overall level
6 S. S. Stevens. Perceived level of noise by Mark VII and decibels (E). J. Acoust. Soc. Am., 51(2):575–601, 1972.
K. P. Shepherd and B. M. Sullivan. A loudness calculation procedure applied to shaped sonic booms. NASA Technical Report TP-3134, 1991.
Calculation Steps for Perceived Level (PL)
1. Calculate Sound Pressure Level of signal
in 1/3-octave bands
2. Apply frequency weighting for loudness of
individual bands
• where loudness of 1 sone is referenced to
1/3-oct band of noise at 3150 Hz at 32 dB
3. Apply summation rule for total loudness
4. Convert to PL in dB
St = Sm + F(SS - Sm)
where
St = total loudness
Sm = loudness of loudest band
SS = sum of loudnesses of all the bands
F = fractional factor based on Sm
PL = 32 + 9 log2(St)
7 S. S. Stevens. Perceived level of noise by Mark VII and decibels (E). J. Acoust. Soc. Am., 51(2):575–601, 1972.
Sound P
ressure
Level
Equal
Loudness
(sones)
Boom
spectrum
PL Test Cases of Ground Booms
8
0 0.05 0.1 0.15
-20
-10
0
10
20
Time (s)
Pre
ssur
e (P
a)
boom1, PL = 91.82 dB
0 0.05 0.1 0.15-15
-10
-5
0
5
10
15
Time (s)
Pre
ssur
e (P
a)
boom2, PL = 75.79 dB
• Included to test that PL algorithms are implemented correctly
• Synthesized N-waves with different rise times, peak pressures, and durations
• Adequately sampled at 48 kHz with ample zero-padding
• Initial results indicated some codes needed to be modified to be in compliance
with NASA’s baseline method
• Majority of updated results within 0.1 dB of baseline (all within 0.45 dB of
baseline)
PL Test Cases of Ground Booms
• Included to highlight
difficulties in processing
measured booms and
predicted booms
• Results more varied
than for simpler cases
• Windowing,
zeropadding, and
resampling methods
varied
• All calculations agree
within 1 dB of baseline
9
0 0.5 1 1.5 2-20
-10
0
10
20
30
Time (s)
Pre
ssur
e (P
a)
Original Boom3
Windowed Boom
Window
0 0.5 1 1.5-20
-10
0
10
20
30
Time (s)
PL = 85.38 dB
0 0.1 0.2 0.3 0.4 0.5
-20
0
20
40
Time (s)
Pre
ssur
e (P
a)
Resampled Boom4
Windowed Boom
Window
0 0.2 0.4
-20
0
20
40
Time (s)
PL = 76.11 dB
Sonic Boom Propagation Prediction Overview
• Input is the overpressure signature predicted at several body lengths away from
the aircraft
• Geometrical acoustics method (ray tracing)
– Determines propagation path from altitude to ground
– Accounts for variations in speed of sound and wind speed
• Nonlinear, lossy propagation based on extended generalized Burgers equation
– Predict evolution of sonic boom as it propagates along rays
– Second-order nonlinearity and the formation of shocks
– Atmospheric absorption due to thermoviscous and molecular relaxation effects
• Varies according to input of atmospheric conditions (stratified atmosphere)
– Geometrical spreading loss
– Solved numerically with a finite-difference method
• Numerical implementation varies
10
Inputs to Propagation Codes
• Overpressure signature predicted at several body lengths away from the aircraft
– F-function
– Overpressure distribution on a cylindrical surface from CFD flow predictions
– Wind tunnel test measurement
– In-flight near-field probing measurement
• Flight altitude and Mach number
• Flight trajectory
• Atmospheric conditions
– Atmospheric pressure, temperature, relative humidity, winds
• Ground impedance or reflection factor
11
Propagation Test Cases
• Near-field signature, Mach number, altitude, and atmospheric conditions
provided as input to sonic boom propagation codes
• Ground waveforms (undertrack) requested as output
• PL calculated with NASA baseline tool
• Boom 5: multi-shock low-boom configuration
• Boom 6: strong front shock
12
0 50 100 150 200-4
-3
-2
-1
0
1
2
3
4x 10
-3
X (ft)
dp/
p
0 50 100 150 200 250 300 350-4
-2
0
2
4
6
8x 10
-3
X (ft)
dp/
p
Boom 5 Boom 6
Mach 1.6
13,700 m
Mach 1.6
14,630 m
Atmospheric Conditions
• No winds included
• Temperature and relative humidity provided
– Boom 5 conditions are similar to U.S. Standard Atmosphere (1976) and ANSI S1.26-
1995 App. C (2009)
– Boom 6 conditions are non-standard and include unrealistic relative humidity values
13
-100 0 1000
10
20
30
40
50
Temperature (oF)
Alt
itud
e (k
m)
0 20 40 60 800
10
20
30
40
50
Relative Humidity (%)
Standard
Boom 5
Boom 6
Initial Results for Propagation Test Cases
• Boom 5 results within 0.7 dB of baseline
• Boom 6 results varied by up to 10 dB from baseline
• Main variation across partners due to differences in mid-frequency content
• In addition to method differences, differences in PL may be due to assumptions
and input settings of
– Vehicle length
– Atmospheric pressure
– Sampling frequency
– Step size 14
-0.05 0 0.05 0.1 0.15 0.2-40
-20
0
20
40
60
80
100
Time (s)
Pre
ssur
e (P
a)
NASA Baseline Boom 5
NASA Baseline Boom 6
100
101
102
103
104
105
0
50
100
One-Third-Octave Band Center Frequency (Hz)
SP
L (
dB
re
20
Pa)
NASA Baseline Boom 5 PL = 75.52 dB
NASA Baseline Boom 6 PL = 94.61 dB
Examined using NASA baseline tool sBOOM
S. K. Rallabhandi. Advanced sonic boom prediction using augmented Burgers equation. AIAA-2011-1278, 2011.
Effect of Sampling Frequency (sBOOM)
• Variations observed of 0.4-0.7 dB
• Convergence
– Boom 5 sampling frequency = 697 kHz
– Boom 6 sampling frequency = 462 kHz
• Sampling frequency/number of points needed depends on input waveform
– Higher sampling frequency needed to resolve fine shock structure
15
0 100 200 300 400 500 60097.8
98
98.2
98.4
98.6
98.8
Sampling Frequency (kHz)
PL
(dB
)
0 200 400 600 80075.2
75.4
75.6
75.8
76
76.2
Sampling Frequency (kHz)
PL
(dB
)
Boom 5 Boom 6
Effect of Step Size (sBOOM)
• Variations observed of ~ 0.5 dB
• Boom 5 and 6 convergence at 10-5 step size
• Step size needed depends on input waveform
• Computation time varies from 10-20 s for 10-3 to ~22 hours for 10-6
16
10-6
10-5
10-4
10-3
10-2
98
98.2
98.4
98.6
98.8
99
Step Size
PL
(dB
)
10-6
10-5
10-4
10-3
10-2
75.4
75.6
75.8
76
76.2
76.4
Step Size
PL
(dB
)
Boom 5 Boom 6
2nd Round: Revised Atmospheric Conditions
• Revised atmospheric conditions for Boom 6
– More resolution in relative humidity definition
– Specified atmospheric pressure due to suspected differences in built-in calculation of
pressure in different codes
• Updated Boom 6 results are within 3.5 dB of baseline
17
0 20 40 60 800
5
10
15
20
Relative Humidity (%)
Alt
itud
e (k
m)
Standard
Boom 5
Boom 6
0 50 1000
5
10
15
20
Atmospheric Pressure (kPa)
Revised Results for Propagation Test Cases
18
100
101
102
103
104
-20
0
20
40
60
80
100
One-Third-Octave Band Center Frequency (Hz)
SP
L (
dB
re
20
Pa)
NASA Baseline PL = 75.95 dB
A. PL = 75.86 dB
B. PL = 75.81 dB
C. PL = 75.47 dB
D. PL = 75.50 dB
E. PL = 75.28 dB
F. PL = 75.78 dB-0.05 0 0.05 0.1-15
-10
-5
0
5
10
15
Time (s)
Pre
ssur
e (P
a)
Boom 5
100
101
102
103
104
0
50
100
One-Third-Octave Band Center Frequency (Hz)
SP
L (
dB
re
20
Pa)
NASA Baseline PL = 98.86 dB
A. PL = 98.72 dB
B. PL = 98.29 dB
C. PL = 98.30 dB
D. PL = 100.78 dB
E. PL = 95.37 dB-0.05 0 0.05 0.1 0.15 0.2 0.25
-50
0
50
100
Time (s)
Pre
ssur
e (P
a)
Boom 6
Loudness for Propagation Test Cases
19
100
101
102
103
104
-20
0
20
40
60
80
100
One-Third-Octave Band Center Frequency (Hz)
SP
L (
dB
re
20
Pa)
NASA Baseline PL = 75.95 dB
A. PL = 75.86 dB
B. PL = 75.81 dB
C. PL = 75.47 dB
D. PL = 75.50 dB
E. PL = 75.28 dB
F. PL = 75.78 dB
100
101
102
103
104
0
50
100
One-Third-Octave Band Center Frequency (Hz)
SP
L (
dB
re
20
Pa)
NASA Baseline PL = 98.86 dB
A. PL = 98.72 dB
B. PL = 98.29 dB
C. PL = 98.30 dB
D. PL = 100.78 dB
E. PL = 95.37 dB
100
101
102
103
104
0
2
4
6
8
10
12
14
One-Third-Octave Band Center Frequency (Hz)
Lou
dne
ss (
sones
)
Boom 5
100
101
102
103
104
0
10
20
30
40
50
60
70
One-Third-Octave Band Center Frequency (Hz)
Lou
dne
ss (
sones
)
Boom 6
Summary
• Comparison of PL calculations and boom propagation predictions for 6 test
cases resulted in
– Some modifications of codes for consistent implementation
– Awareness of factors contributing to differences
• Observed up to 3.5 dB variation due to propagation codes
• Observed less than 1 dB variation due to sampling frequency and step size
• Observed up to 1 dB variation due to ground signal processing
• Majority of submissions in very good agreement with baseline
– Differences at high frequencies generally occur at very low levels that are not
significant to PL or human response
• Based on these results, baseline calculation recommendations have been
drafted for ease of evaluation of supersonic aircraft designs
• Future
– Could be useful to consider the effect of winds in different codes
– Include more participants 20
Backup Slides
22
Baseline Boom Propagation Prediction Method
• Sonic boom propagation prediction
– sBOOM is the preferred tool, and it is available from NASA
– A standard atmosphere should be used (U.S. Standard Atmosphere, 1976):
• Pressure, temperature, and humidity
• No winds should be included
• sBOOM should be used for all boom predictions, with the exception of focus
boom predictions. Since sBOOM does not include calculation of focus booms,
other methods may be used.
• The step size should be set to 0.001
• The sampling frequency should be set to ≥ 40 kHz i.e. do NOT use resamp.dat
from sBOOM output to calculate loudness metrics
• Propagation should start at a distance from the aircraft that gives a converged
ground signature
• The ground reflection factor should be set to 1.9
• Sufficient zeropadding should be applied to the input waveform to avoid clipping
the shocks during propagation
23
Baseline PL Calculation Method
• LCASB is the preferred tool, and it is available from NASA
• PL should be calculated according to Shepherd and Sullivan (1991)
• PL should be calculated on the waveform with a sampling frequency ≥ 40 kHz
• A Hanning-type window should be applied to the beginning and ending of the
waveform to ensure a smooth transition to zero acoustic pressure. This window
should be applied so as not to affect the main boom event to be analyzed.
• Adequate zeropadding should be applied to allow for resolution of low
frequencies (total signal length ≥ 0.5 s)
• PL values should be rounded to the nearest 0.1 dB
24
