August 2013

NASA/TP–2013-218035

Experimental Measurements of Sonic Boom 

Signatures Using a Continuous Data Acquisition 

Technique

Floyd J. Wilcox, Jr., and Alaa A. Elmiligui

Langley Research Center, Hampton, Virginia
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August 2013

NASA/TP–2013-218035

Experimental Measurements of Sonic Boom 

Signatures Using a Continuous Data Acquistion 

Technique

Floyd J. Wilcox, Jr., and Alaa A. Elmiligui

Langley Research Center, Hampton, Virginia
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Summary

A wind tunnel investigation was conducted in the Langley Unitary Plan Wind Tunnel (UPWT) to

determine the effectiveness of a technique to measure aircraft sonic boom signatures using a single

conical survey probe while continuously moving the model past the probe. Sonic boom signatures

were obtained using both move-pause and continuous data acquisition methods for comparison.

The test was conducted using an existing generic business jet model at a constant angle of attack

and a single model-to-survey-probe separation distance. The sonic boom signatures were obtained

at a Mach number of 2.0 and a free-stream unit Reynolds number of 2 million per foot. The test

results showed that it is possible to obtain sonic boom signatures while continuously moving the

model, and that the time required to acquire the signature is at least 10 times faster than the

move-pause method.

Introduction

Experimental research to measure sonic boom signatures of aircraft in wind tunnels has been

conducted since the 1950s using a variety of techniques (ref. 1–14). One common technique is to

use slender conical pressure probes to measure the sonic boom pressure signature of the aircraft

model (ref. 2–9). The basic test technique consists of mounting a reference probe and a survey

probe to the tunnel sidewall. The reference probe is mounted so that it remains in the free-stream

flow at all times during the test. The survey probe is located so that as the aircraft model is

moved longitudinally in the tunnel, the pressure field generated by the aircraft passes over the

survey probe. The pressure difference between the reference and survey probe is measured with

a differential pressure transducer that is sized for the small pressure differences to be measured.

A typical run begins with the model located so that the nose shock is downstream of the survey

probe. The model is then moved forward in small increments and paused as each point in the

sonic boom pressure signature is measured. The length of time required to measure the entire sonic

boom signature is dependent on the model size and can be significant if the model is large or the

number of data points acquired is large.

Another technique that has been employed to measure sonic boom pressure signatures is similar

to the slender probe technique described above except that the survey probe is replaced with a flat

plate that has static pressure orifices on the surface of the plate (ref. 1 and 2).

Recently, long rails with multiple static pressure orifices located along the surface have been

used to measure sonic boom signatures (ref. 10–14). With this technique, the entire sonic boom

pressure signature can be obtained in a single data point. Although this technique shows promise,

it is still being developed.

One of the advantages of the slender conical probe technique is that multiple survey probes

can be used concurrently to measure the sonic boom pressure signature directly under the aircraft

model (“on track”) and at locations to the side of the aircraft (“off track”). However, as mentioned

previously, the time required to measure a complete sonic boom pressure signature can be significant, and, consequently, the testing costs can be considerable. The purpose of this investigation

was to determine the effectiveness of a technique to measure sonic boom signatures using the slender conical probe technique while continuously moving the model past the probe rather than using

a move-pause technique. The continuous data technique was expected to significantly reduce the

time required to acquire an entire sonic boom pressure signature and, consequently, reduce wind

tunnel testing costs.

In the present study, a wind tunnel test was conducted to measure the sonic boom pressure

signature of an existing generic business jet model using a slender conical probe and acquiring

1
data using move-pause and continuous data acquisition techniques for comparison. The tests were

conducted in the Langley Unitary Plan Wind Tunnel (UPWT) at a Mach number of 2.0 and a

free-stream unit Reynolds number of 2 million per foot. The sonic boom signatures were obtained

with the model at a single angle of attack (≈ 2.3

◦

) and at a model nose to survey probe separation

distance of 13.5 in.

Nomenclature

Abbreviations and Acronyms

AOA angle of attack, deg

ID inside diameter

NF normal force, lbf

OD outside diameter

PM pitching moment, in·lbf

PRT platinum resistance thermometer

psfa pound-force per square foot absolute (lbf/ft2)

psfd pound-force per square foot differential (lbf/ft2)

SLSLE straight-line segmented leading edge

UPWT Unitary Plan Wind Tunnel

Symbols

favg number of continuous data frames averaged, frames

h distance from model nose to survey probe measured perpendicular to tunnel sidewall

(see figure 2b), in.

M Mach number

p free-stream static pressure, psfa

p0 free-stream stagnation pressure, psfa

pref reference probe pressure, psfa

q free-stream dynamic pressure, psfa

Re free-stream unit Reynolds number × 10−6, ft−1

td duration of a complete sonic boom pressure signature run, min.

T0 free-stream stagnation temperature, ◦F

v model longitudinal speed during continuous sweep runs, in/s

α angle of attack, deg

(∆p/pref )avg average sonic boom pressure signature parameter where ∆x ≤ 21.25 in.

(∆p/pref )cor corrected sonic boom pressure signature parameter (see equation 1)

(∆p/pref )unc uncorrected sonic boom pressure signature parameter

∆p measured differential pressure between survey probe and reference probe, psfd

∆x distance from model nose to survey probe orifices measured parallel to tunnel sidewall

(see figure 2b), in.

Apparatus and Experimental Methods

Wind Tunnel Description

The wind tunnel test was conducted in the Langley Unitary Plan Wind Tunnel, which is a continuous flow, variable pressure supersonic wind tunnel. The tunnel contains two test sections that

2
are approximately 4 ft by 4 ft square and 7 ft long. Each test section covers only part of the Mach

number range of the tunnel. The nozzle ahead of each test section consists of an asymmetric sliding

block that allows continuous Mach number variation during tunnel operations from 1.5 to 2.9 in

the low Mach number test section (#1) and 2.3 to 4.6 in the high Mach number test section (#2).

A complete description of the facility along with test section calibration information is contained

in reference 15.

The nominal free-stream conditions used during this investigation in test section #1 are shown

in table 1. Test section #2 was not used for this investigation.

Table 1. Nominal free-stream test conditions

M Re, ft−1 p0, psfa T0,

◦F q, psfa p, psfa

2.00 2.00 1253 125 448.5 160.2

The tunnel air dew point was maintained below −20◦F (at atmospheric pressure) to minimize

water vapor condensation effects.

General Test Description

Figure 1 shows a photograph and sketch of the wind tunnel test setup. One of the test section doors,

which normally contains schlieren windows, was replaced with a solid steel door so that some of the

sonic boom measurement hardware (free-stream reference probe, survey probe, and transducer box)

could be attached to the tunnel sidewall. The reference probe was mounted to the tunnel sidewall

above and slightly upstream of the survey probe using a fixed (non-movable) support bracket. The

tip of the reference probe was located 10.00 in. from the tunnel sidewall. The survey probe was

mounted to the sidewall near the tunnel centerline using a support that was part of a mechanism

that could move the probe longitudinally in the test section. However, during this test the survey

probe remained at a fixed longitudinal position for all runs. A transducer box was located above

and downstream of the survey probe location and was used to house pressure transducers that

measured the differential pressure between the reference and survey probes and a transducer that

measured just the reference probe pressure. Figure 2 shows the relative positions of the sonic boom

hardware. Figure 3 shows the overall dimensions of the reference probe mounting bracket, survey

probe mechanism, and the transducer box. The Instrumentation and Measurements section gives

details of the reference and survey probes.

The aircraft model used during this test had previously been tested in UPWT and was identified

as the straight-line segmented leading edge (SLSLE) model. Figure 4 shows a sketch and photograph

of the model. The SLSLE model was chosen for this test because it was available for the test and

because data from a previous test were accessible for comparison. The SLSLE model was tested

without boundary layer transition grit. The SLSLE configuration was designed using the following

criteria:

• Cruise Mach number . . . . . . . . . . . . . . . . . . . . . . 2.00

• Beginning cruise weight . . . . . . . . . . . . . 88,000 lbf

• Beginning cruise altitude . . . . . . . . . . . . . 53,000 ft

• Sonic boom ground overpressure . . . . . . . 0.5 psfd

3
References 8 and 16 contain additional details about the overall design of the model.

The SLSLE model and sting were pinned together and were designed not to be taken apart.

The sting was attached to the sonic boom angle of attack (AOA) mechanism, which was in turn

attached to the tunnel roll coupling and model support system. The SLSLE model was tested with

positive normal force in the horizontal plane, i.e., wings vertical for all of the sonic boom pressure

signature runs.

The tunnel angle of attack mechanism was not used to set the model angle of attack and remained at a fixed position during this test. Instead, the sonic boom AOA mechanism was used

to set the model angle of attack to approximately 2.3

◦

. The model angle of attack consisted of

both the pitch angle set by the sonic boom AOA mechanism and deflection caused by aerodynamic

loads. During this test, the AOA mechanism pitch angle was set to approximately 1.7

◦

to match

one of the settings used during the previous test of the SLSLE model in UPWT. Because data from

a previous test that used the sonic boom AOA mechanism showed that the mechanism contained

approximately 0.2

◦ of play (movement of the pitch mechanism that was not indicated by a linear

potentiometer located inside the mechanism), a jam nut was fabricated and installed in the mechanism to lock it at the required pitch angle. Figure 5 shows the jam nut installed in the sonic boom

AOA mechanism.

The tunnel model support system was used to position the SLSLE model laterally and longitudinally in the test section relative to the survey probe. During this test, the model nose was

positioned at h ≈ 13.5 in. (see fig. 2b), then the tunnel model support system was disabled in

the lateral direction to prevent h from varying during the test. The tunnel model support system

longitudinal movement capability was used to move the SLSLE model past the survey probe so

that the sonic boom signature could be measured. During each pressure signature run, the model

was moved longitudinally approximately 16.5 in.

During a typical run, the SLSLE model was initially positioned so that the nose shock was

located downstream of the survey probe. For the move-pause runs, the model was moved forward

in 0.125 in. increments while the model sonic boom pressure signature data were acquired. For

the continuous sweep runs, the model was again positioned so that the nose shock was located

downstream of the survey probe. The data acquisition system was started, and approximately 10 s

of data were acquired before the model movement began. After the model was moved forward the

required distance, the model movement was stopped and data were acquired for an additional 10 s.

Instrumentation and Measurements

Shown in figure 6 are sketches of the survey and reference probes. The probes were identical 4◦

included angle cones with two orifices drilled through the probe and into a central chamber. For

these tests, the reference probe orifices were oriented such that one orifice was on top of the probe

and the other on the bottom of the probe when viewing the probe from the side, i.e., looking into

the sidewall. The survey probe orifices should have been oriented the same as the reference probe;

however, because of an installation mistake, they were oriented such that one orifice was facing the

tunnel sidewall used to mount the probes, and the other was facing toward the model. Because

all of the sonic boom pressure signature data were acquired with the survey probe in the same

orientation, the installation mistake had no effect on the conclusions of this test. The lengths of

stainless steel tubing used to connect the reference and survey probes to the pressure transducers

located in the transducer box are noted in figure 6. The final pressure connections inside the

transducer box used flexible tubing (7/32 in. outside diameter, OD, by 3/32 in. inside diameter,

ID).

Figure 7 shows a schematic of the reference and survey probe connections to the pressure

4
transducers. A solenoid activated valve that could be remotely operated was used to equalize the

pressures across the differential pressure transducer to minimize the risk of over pressurizing the

transducer during tunnel start and stops. The differential pressure between the reference and survey

probes was measured with a ±13.006 psfd (±2.5 in. water column) pressure transducer, which had

a quoted accuracy of ±0.018 psfd in the manufacturer’s product literature. An in-situ calibration

of the differential pressure transducer was performed, and the uncertainty in the difference between

the applied and measured pressures, otherwise know as the regression uncertainty, was ±0.016 psfd

at a 95 % confidence level. In addition, the reference probe pressure was measured directly with

a 720 psfa absolute pressure transducer, which had a manufacturer’s quoted accuracy of ±0.72

psfa. An in-situ calibration of the absolute pressure transducer was performed, and the regression

uncertainty was ±0.172 psfa at a 95 % confidence level.

The transducer box was located on the tunnel sidewall above and downstream of the reference

and survey probes. The purpose of the transducer box was to house the differential and absolute

pressure transducers as close to the reference and survey probes as possible to minimize pressure

lag effects. The transducer box was sealed, and the inside was maintained at near atmospheric

conditions so that there would be no significant temperature or pressure effects on the pressure

transducers. The solenoid activated valve was also located inside the transducer box. Figure 8

shows the inside of the transducer box with the two pressure transducers and solenoid valve. The

transducer box was sized to house three differential pressure transducers so that in the future three

survey probes could measure on-track and off-track pressure signatures concurrently.

The transducer box was fabricated out of aluminum with a polycarbonate insulating cover,

which can be seen in figure 1a. The aluminum box was water cooled using 0.125 in. OD copper

tubing epoxied into grooves machined into the sides, top, and bottom of the box. There were

four separate cooling circuits for the left side, right side, top, and bottom of the transducer box.

Cooling water was supplied to each circuit, and the water flow was controlled with a small brass

needle valve. In addition to the water cooling, atmospheric air was circulated inside the box to

help maintain a constant temperature inside the box. Two 0.5 in. OD nylon tubes were routed to

the box and were used to supply cooling air to the box using a vacuum cleaner to pull atmospheric

air through one of the nylon tubes into the box and then out the second nylon tube. Six type

T (copper/copper-nickel) thermocouples were installed inside the transducer box to monitor the

differential pressure transducer, air, and transducer box wall temperatures.

Force and moment data on the SLSLE model were measured with a 2-component electrical

strain gage balance that was integral to the sting. The strain gages were located near the aft end of

the sting and were covered with auto body filler that was faired to the sting contour. Two platinum

resistance thermometers (PRT) were installed on the sting; one near the forward balance bridge and

the second near the aft balance bridge. The purpose of the PRTs was to monitor the temperature

gradient across the balance bridges and not to compensate for balance sensitivity changes caused

by temperature. Figure 9 shows the locations of the model and balance moment reference centers.

The full scale balance limits are shown in table 2.

Table 2. Range of balance components

Balance component Range

normal force ±5 lbf

pitching moment ±109.2 in·lbf

5
The tunnel stagnation pressure was measured with a 100 psia bourdon tube pressure transducer

that had a manufacturer’s quoted accuracy of ±0.003 psia at a 95 % confidence level. The tunnel

stagnation temperature was measured with a PRT.

The model support system lateral and longitudinal movement were measured by rotary encoders. The estimated accuracy of the model support system position based on calibration data

was ±0.005 in. for both the longitudinal and lateral positions.

The model support system angle of attack was measured with an accelerometer mounted to the

support system just downstream of the roll coupling. The model support system angle of attack

was adjusted so that the sonic boom angle of attack mechanism was level before the SLSLE model

was rolled to the wings vertical position. The tunnel model support angle of attack mechanism was

not adjusted after leveling the sonic boom angle of attack mechanism.

The sonic boom angle of attack mechanism pitch angle was measured with a linear potentiometer. As discussed earlier, a jam nut was used to lock the mechanism to a single pitch angle.

However, the jam nut could have locked in some unknown pitch error caused by the sonic boom

AOA mechanism play. Based on unpublished checks conducted during a previous test, the mechanism play (and, consequently, the unknown pitch error) was as large as 0.2

◦

. Because the sonic

boom AOA reading probably contained some fixed unknown error, the computed SLSLE model

nose separation distance, h, which was a function of the pitch angle, also probably contained some

error. However, since the pitch angle was fixed for the entire test, the small error in h would be

constant for the entire test and, therefore, would not affect the results or conclusions of the test.

Data were acquired in either a move-pause or continuous mode depending on the run. The data

acquisition system scan rate for the move-pause runs was 30 frames/s for two seconds; all of the

data acquired during the two second period were averaged. The data acquisition system scan rate

for the continuous runs varied from 60 frames/s to 480 frames/s. The data acquisition system had

a low pass filter (2-pole Butterworth) that was set to 1 Hz for most runs with a few runs set at

1000 Hz to determine the effect of filter setting on the continuous data acquisition.

Corrections

The data acquired during the test were not corrected for tunnel flow angularity. The model angle

of attack and the position of the model nose relative to the conical survey probe were corrected for

sting deflections caused by aerodynamic loads. Because the sonic boom angle of attack mechanism

was locked at one position, the SLSLE model angle of attack remained at approximately 2.3

◦

for

the entire test.

Because of static pressure variation within the tunnel test section, when the reference and

survey probes were in the free-stream flow, the measured differential pressure between the probes,

∆p, was not equal to zero. Consequently, the uncorrected sonic boom pressure signature parameter,

(∆p/pref )unc, was also not equal to zero when the model nose shock was located downstream of

the survey probe. Therefore, the sonic boom pressure signatures were adjusted by averaging all

(∆p/pref )unc values with ∆x ≤ 21.25 in. during a signature run (survey and reference probes in

the free-stream flow) and subtracting the average value from each (∆p/pref )unc value, i.e.,



∆p

pref 

cor

=



∆p

pref 

unc

−



∆p

pref 

avg

(1)

Figure 10 shows the corrected and uncorrected sonic boom pressure signatures as a function

of ∆x for a single run to illustrate the approximate magnitude of the correction. No additional

corrections or adjustments were performed to the sonic boom pressure signature data. Globally,

6
the variation of (∆p/pref )cor within a sonic boom pressure signature was significantly less than the

correction (∆p/pref )avg, which is typical for sonic boom testing in UPWT.

Results and Discussion

All of the plots in this section will show the corrected sonic boom pressure parameter (∆p/pref )cor

as a function of ∆x. As mentioned previously, the SLSLE model angle of attack remained approximately 2.3

◦

for the entire test.

Comparison Between Tests

The sonic boom pressure signatures obtained with the move/pause method are first compared to

data obtained in a previous test using the same method. The purpose of this comparison is to show

that the setup used in the current test was satisfactory. Figure 11 shows a comparison between

the sonic boom pressure signature data as a function ∆x for two sets of three back-to-back repeat

runs obtained during the current test and data acquired during the previous test of this model as

described in reference 8. The two sets of back-to-back repeat runs were obtained on two different

days. In general, the results show reasonable agreement between the six repeat runs of the current

test. Comparison with the previous test data shows a slight positive shift in ∆x for the previous

data. However, the magnitude and location of the signature peaks compare well between the tests

indicating that nothing significant had changed between the tests, which gave confidence that the

current test setup was satisfactory. The cause of the ∆x shift between the two tests is unknown.

One significant difference between the tests is shown near ∆x = 33 in. The previous test

data show a negative peak as the flow expands aft of the model wing, whereas the data for the

current test flattens and does not peak. The differential pressure transducer that measured ∆p

was overscaled in this region, and an internal mechanical stop inside the transducer prevented

over pressurization of the transducer. Although most details of the previous and current test were

identical, the reference and survey probes for the previous test were 2◦included angle cones while

the current test used probes with 4◦included angles. The larger angles on the reference and survey

probes resulted in a larger measured ∆p that caused the differential pressure transducer diaphragm

to hit the mechanical stop, resulting in a constant millivolt output from the transducer. Because

the purpose of this test was to compare move-pause and continuous data acquisition techniques, the

over pressurization of the differential pressure transducer in a small localized region of the pressure

signature did not affect the overall conclusions of this test.

Determining Model Movement Speed for Continuous Sweep Runs

The first step in conducting this wind tunnel test was to determine a reasonable speed to move

the model during the continuous sweep runs; however, optimizing the model movement speed was

not attempted during this test. Figure 12 shows a comparison between the first three back-to-back

repeat runs that were obtained in a move-pause mode of operation and the continuous data at five

longitudinal speeds that covered the range of speeds available. The speeds were set in the tunnel

model control system as a percentage of the maximum speed available, as shown table 3. The

continuous data were acquired in order from the fastest to the slowest speeds. The move-pause and

continuous data shown in figure 12 were acquired on the same day.

Figure 12a shows the results for the fastest longitudinal speed (v = 0.329 in/s). Overall, the

continuous data follows the move-pause data, and the magnitude of the signature peaks match

the move-pause data. However, there is a slight shift in the entire signature in the increasing ∆x

7
Table 3. Model longitudinal speed settings

Percentage v, in/s

100 0.329

50 0.170

25 0.088

12.5 0.048

6.25 0.025

direction that is caused by pressure lag in the tubing between the reference and survey probes and

the differential pressure transducer. The data also show slightly more unsteadiness compared to

the move-pause data, which is expected because each move-pause data point was an average of 60

frames of data while the continuous data were not averaged. Figures 12b–12e show the results as

the longitudinal speed is decreased. As the model longitudinal speed decreases, the shift in the

continuous data in the increasing ∆x direction is eliminated, and the continuous data essentially

fall on top of the move-pause data. With decreasing model longitudinal speed, the unsteadiness of

the continuous data basically forms a band that covers the move-pause data.

Based on the data in figure 12, it was decided to acquire the remaining continuous sweep data

at a longitudinal speed of 0.088 in/s for comparison with the move-pause data. The decision was

a compromise between how well the continuous data compared to the move-pause data and the

duration of the continuous data sweep (td in the plot key). Optimization of the time required for

a continuous data sweep was not considered during this test.

Move-pause and Continuous Data Repeatability

Figure 13 shows a comparison between two sets of three back-to-back repeat move-pause runs and

three back-to-back continuous sweep runs that were acquired on two separate days. In general,

these data indicate that the continuous data acquisition method does follow the trends and match

the peaks of the move-pause sonic boom signatures while significantly reducing the time required to

acquire a signature. The continuous sweep data does show more unsteadiness than the move-pause

data because the continuous data are not averaged.

The extent of the continuous data unsteadiness is shown in figure 14, which shows three backto-back move-pause repeat runs and two sets of continuous data acquired over approximately 30

seconds at ∆x = 23 in. and 29 in. while the model was stationary (v = 0 in/s). These data

show that the range of the sonic boom pressure signature parameter for the continuous data was

approximately 0.005. Figure 15 shows histograms for the two continuous runs presented in figure 14.

The histograms provide an overall view of the distribution of continuous data and an indication of

the central tendency and scatter of the data. These two plots indicate that the continuous data

obtained at a single ∆x location is roughly normally distributed with no significant skewing as

expected. The standard deviation of the data for ∆x = 23 in. and ∆x = 29 in. is 0.00075 and

0.00098, respectively.

8
Differential Pressure Transducer Variation

Because of the unsteadiness of the continuous data shown in figure 13, data were acquired to

determine if the differential pressure transducer caused any of the unsteadiness. Figure 16 shows

the variation of the reference and survey probe differential pressure transducer at a typical windon condition and a wind-off condition as a function of elapsed time. These continuous data were

acquired with the model stationary (v = 0 in/s). The shape of the curves for (∆p/pref )unc and ∆p

shown in figure 16a is essentially identical and illustrates that the unsteadiness of the sonic boom

pressure parameter obtained during wind-on continuous data acquisition is primarily caused by the

unsteadiness in the measured ∆p value. The variation in pref has little effect on the on the overall

shape of the (∆p/pref )unc curve. The stepped appearance of pref is caused by the least significant

bit fluctuations of the data acquisition system analog to digital converter. Figure 16b shows the

variation of ∆p and pref for a wind-off condition with the tunnel pressure at approximately 400 psfa.

The steady decrease in pref is caused by the inability to perfectly balance the removal of air from

the tunnel using vacuum pumps and the leaks in the tunnel circuit. The standard deviation of ∆p

with no flow is more than two orders of magnitude less than a typical wind-on condition as shown in

table 4. These results indicate that the variation seen in (∆p/pref )unc for wind-on continuous runs

is primarily caused by the unsteadiness of the measured differential pressure rather than transducer

unsteadiness.

Table 4. Differential pressure transducer standard deviation

Tunnel condition ∆p standard deviation

wind-on 0.1305 psfd

wind-off 0.0007 psfd

Smoothing Continuous Data

One method to reduce the unsteadiness of the continuous data is to perform a moving average

on the data. Figure 17 shows comparisons between continuous data with and without applying a

moving average. The number of data frames used in the moving averages varied from 61 to 481.

The moving average was centered, i.e., for a given ∆x value, the moving average with 61 frames

of data was computed by averaging 61 frames of data beginning 30 frames before the given ∆x

value to 30 frames after the ∆x value. The results show that as the number of frames used in

the moving average increases, the data variation is reduced; however, the peaks in the sonic boom

parameter distribution are also smoothed, thus reducing the magnitude of peaks. Therefore, a

trade-off between smoothing the data and reducing the peaks must be considered. For this test, a

moving average of 181 frames (fig. 17c) was chosen because it appeared to be the best compromise

between smoothing the data and not significantly reducing the peaks. All of the moving average

data shown in the remainder of this report use 181 frames of data for the moving average. Figure 18

compares the continuous data with a moving average applied with the move-pause data for both

sets of three back-to-back repeat runs. Comparison between figure 18 and figure 13 show that the

unsteadiness of the continuous data is significantly reduced by applying a moving average.

9
Comparison Between Move-pause and Continuous Data

Figure 19 shows the six repeat move-pause runs along with the mean of the six runs with confidence

and prediction intervals at a 95 % confidence level. The appendix shows the equations used to

compute the mean, confidence interval, and prediction interval. Because the ∆x values measured

in each run were different, the data were interpolated using a straight line fit between ∆x values to

obtain (∆p/pref )cor values at consistent ∆x values from 20 in. to 36 in. in steps of 0.125 in. These

interpolated (∆p/pref )cor values were then used to compute the mean, confidence intervals, and

prediction intervals at each ∆x.

Figure 20 shows the six repeat continuous data runs (no moving average applied) along with

the mean of the six runs with confidence and prediction intervals at a 95 % significance level. The

continuous data were interpolated with a straight line fit between the data points just as with the

move-pause data to obtain (∆p/pref )cor values at the same ∆x locations as used with the movepause runs. Finally, figure 21 shows the same continuous data results as figure 20 except that the

continuous data has a moving average applied.

In general, the confidence intervals for the move-pause (fig. 19) and continuous data (moving

average applied, fig. 21) are about the same magnitude as would be expected since the variation

between each set of six repeat runs is about the same. These confidence intervals are generally

smaller than the intervals for the continuous data (no moving average applied, fig. 20). The smaller

confidence intervals are a result of the smaller variation between the repeat runs of both the movepause and continuous data (moving average applied) compared to the variation between the repeat

runs for the continuous data (no moving average applied). The results for the prediction intervals

are similar.

Figure 22 shows a comparison between the mean values of the move-pause data and the continuous data with and without a moving average applied. The confidence interval on each set of mean

values at a 95 % significance level are also shown. At the bottom of the figure is the difference

between the means of the move-pause and continuous data along with the confidence interval at a

95 % significance level. The confidence interval on the difference in means was determined using

a pooled variance because an F-distribution test (ref. 17) showed that the variation from the two

sets of data were statistically equal.

Since the confidence interval on the difference in means in general encompasses 0 across the ∆x

range, there is no statistical difference between the move-pause data and the continuous data either

with or without applying a moving average. The confidence interval on the difference in means is

larger for the continuous data with no moving average applied than for the continuous data with a

moving average applied, as would be expected. The confidence intervals for the difference in means

where the nose shock begins (22.0 in. . ∆x . 22.5 in.) do not encompass 0 for the continuous data

with a moving average applied; however, the difference in means at the peaks of the signatures

shows no statistical difference across the entire signature. The difference in means plots indicate

that the mean value of the sonic boom signature acquired by continuously moving the model is

essentially equivalent to the mean value of a signature acquired with the move-pause technique.

The real benefit to acquiring sonic boom signatures continuously is that the time required to acquire

the signature is significantly less than for the move-pause technique as will be discussed in the next

section.

Data Acquisition Time Savings

The key in figures 19 and 20 shows the duration required to acquire the entire sonic boom signature (td) for the move-pause and continuous data, respectively. The results show that a typical

move-pause signature required approximately 52 minutes while the continuous data required ap10
proximately 3.5 minutes. The duration of the move-pause runs was longer than expected based on

other sonic boom tests conducted previously in UPWT. The cause of the longer duration for the

move-pause runs was a delay in the communication between the tunnel data acquisition system,

which had just been replaced and was being used for the first time in a production wind tunnel test,

and the tunnel model support control system. Because the duration of the move-pause runs was

adversely affected by the communication delay, a direct comparison between the duration of the

move-pause runs and the continuous runs was not attempted. Instead, the duration of move-pause

runs for previous sonic boom tests conducted in UPWT was used in the comparison.

Previous sonic boom tests in UPWT typically acquired data using a move-pause technique with

the distance between data points of 0.125 in., which is the same distance used in the current test.

The time required to acquire sonic boom data points for these previous tests ranged from 14 s/pt

to 24 s/pt. A 10 in. long signature would require 81 points and a duration of 18.9 min. to 32.4 min.

as shown below:

14 (s/pt) (81 pt) = 1134 s = 18.9 min.

and

24 (s/pt) (81 pt) = 1944 s = 32.4 min.

During this test, the majority of continuous data were acquired at v ≈ 0.09 in/s, which was

a compromise between how well the continuous data compared to the move-pause data and the

duration of the continuous data sweep. At this speed, a 10 in. long signature would require 1.85

min.

10 in. / (0.09 in/s) = 111.1 s = 1.85 min.

Therefore, the continuous data acquisition technique reduces the time required to acquire a sonic

boom pressure signature by 10 to 17 times compared to the move-pause technique. Consequently,

the total costs for a wind tunnel test would decrease because of the reduced tunnel occupancy costs

and electrical energy costs.

Effect of Filter Setting

Figure 23 shows comparisons between the move-pause data and continuous data obtained at data

acquisition low-pass filter setting of 1 Hz and 1000 Hz. The continuous data in these plots were

acquired at the maximum longitudinal speed (v = 0.329 in/s) that the model support system could

move the model. Typically, data in the UPWT are acquired with the data acquisition system filter

set to 1 Hz. The results of these runs show that at a filter setting of 1 Hz, the continuous data are

much smoother than the 1000 Hz data; however, at 1 Hz the data also show a slight time lag, i.e.,

∆x shift, compared to the move-pause data. The time lag is especially evident at the model nose

shock (22.0 in. . ∆x . 22.5 in.).

As discussed earlier, optimization of the time required for a continuous data run was not considered during this test. However, the low-pass filter setting data suggest that it might be possible to

adjust the data acquisition system filter setting and the model longitudinal speed setting to reduce

the time required to obtain a complete sonic boom signature and still acquire data that compares

favorably with the move-pause technique. The optimization of these factors would be a natural

extension of this test.

11
Concluding Remarks

A wind tunnel investigation was conducted in the Langley Unitary Plan Wind Tunnel to determine

the effectiveness of a technique to measure aircraft sonic boom signatures using a single conical

survey probe while continuously moving the model past the probe. Sonic boom signatures were

obtained using both move-pause and continuous data acquisition methods for comparison. The

test was conducted using an existing generic business jet model at a constant angle of attack and

a single model-to-survey-probe separation distance. The sonic boom signatures were obtained at a

Mach number of 2.0 and a free-stream unit Reynolds number of 2 million per foot.

The following is a summary of the significant findings:

1. The means of the move-pause and continuous sonic boom pressure signature data were statistically equivalent.

2. Performing a moving average on the continuous data smoothed the data but did not significantly improve the comparison with the move-pause data.

3. The time required to measure a sonic boom signature using the continuous data technique

was 10–17 times faster than the move-pause technique.

4. It might be possible to further decrease the time required to obtain a complete sonic boom

signature using the continuous data technique by optimizing the model longitudinal speed,

data acquisition rate, and data acquisition filter setting. Additional research would need to

be conducted.

References

1. Carlson, Harry W.: An Investigation of Some Aspects of the Sonic Boom by Means of WindTunnel Measurements of Pressures about Several Bodies at a Mach Number of 2.01.

NASA TN D–161, 1959.

2. Carlson, Harry W.: Correlation of Sonic-Boom Theory with Wind-Tunnel and Flight Measurements. NASA TR R–213, 1964.

3. Mendoza, Joel P.; and Hicks, Raymond M.: Further Studies of the Extrapolation of Near-Field

Overpressure Data. NASA TM X–2219, 1971.

4. Hunton, Lynn W.; Hicks, Raymond M.; and Mendoza, Joel P.: Some Effects of Wing Planform

on Sonic Boom. NASA TN D–7160, 1973.

5. Carlson, H. W.; and Morris, O. A.: Wind-Tunnel Sonic-Boom Testing Techniques. AIAA

Paper 66–765, 1966.

6. 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, 1965.

7. 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.

8. Mack, Robert J.; and Kuhn, Neil: Determination of Extrapolation Distance with Measured

Pressure Signatures from Two Low-Boom Models. NASA TM–2004–213264, 2004.

12
9. Wilcox, Floyd J., Jr.; Elmiligui, Alaa A.; Wayman, Thomas R.; Waithe, Kenrick A.; Howe,

Donald C.; and Bangert, Linda S.: Experimental Sonic Boom Measurements on a Mach 1.6

Cruise Low-Boom Configuration. NASA TM–2012–217598, 2012.

10. Makino, Yoshikazu; Suzuki, Ken0ichiro; Noguchi, Masayoshi; and Yoshida, Kenji: NonAxisymmetrical Fuselage Shape Modification for Drag Reduction of a Low Sonic-Boom Airplane. AIAA 2003–557, 2003.

11. Furukawa, Takeshi; Makino, Yoshikazu; Noguchi, Masayoshi; and Ito, Takeshi: Supporting

System Study of Wind-Tunnel Models for Validation of Aft-Sonic-Boom Shaping Design. AIAA

2008–6596, 2008.

12. 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 Configurations

Using Multiple Measurement Techniques at NASA Ames. AIAA 2011–3333, 2011.

13. Cliff, S.; Elmiligui, A.; Aftosmis, M.; Thomas, S.; Morgenstern, J.; Durston, D.: Design

and Evaluation of a Pressure Rail for Sonic Boom Measurements in Wind Tunnels. Seventh

International Conference on Computational Fluid Dynamics, ICCFD7–2006, 2012.

14. Morgenstern, John M.: How to Accurately Measure Low Sonic Boom or Model Surface Pressures in Supersonic Wind Tunnels. AIAA 2012–3215, 2012.

15. Jackson, Charlie M., Jr.; Corlett, William A.; and Monta, William J.: Description and Calibration of the Langley Unitary Plan Wind Tunnel. NASA TP–1905, 1981.

16. Mack, Robert J.; and Kuhn, Neil S.: Determination of Extrapolation Distance With Pressure

Signatures Measured at Two to Twenty Span Lengths From Two Low-Boom Models. NASA

TM–2006–214524, 2006.

17. Montgomery, Douglas C.; and Runger, George C.: Applied Statistics and Probability for Engineers. Fifth ed., John Wiley & Sons, Inc. 2011.

13
Solid steel door blank

Reference probe

Transducer box

Survey probe

Survey probe mechanism

SLSLE model and sting

Roll coupling

Sonic boom AOAmechanism

Instrumentation leads,cooling air, and coolingwater

2012–L–03809

Flow

Model support systemAOA mechanism

Model support system (a) Model mounted in wind tunnel. Figure 1. General experimental test setup.

14
Tunnel door

Roll coupling

Solid steel door blank

Model support system

(can move both laterally and longitudinally) Lateral

SLSLEmodel and sting Sonic boom

AOA mechansim Model support

system AOAmechansim

Referenceprobe

Flow

Longitudinal

Survey probe

Survey probe mechanism

(b) Top view (transducer box removed for clarity).

Figure 1. Concluded.

15
Reference probe

Transducerbox

16.06 22.63

36.97

42.01

Center 

of two

orifices

Center 

of two

orifices

Survey probe Survey probe

mechansim

28.25

Solid steel door blank

Test section doorleading edge Tunnel floor

51.19

Flow

Pressuretubing

Pressuretubing

(a) Side view.

Figure 2. Details of the experimental setup. All dimensions are in inches.

16
10.50

∆x

h42.00

Survey probeSurvey probe orifices

Referenceprobe

SLSLEmodel and sting

Solid steel door blank

Sonic boomAOA mechanism

10.00

Test section doorleading edge

Sonic boom

AOA mechanism

pivot

Flow

(b) Top view (transducer box removed for clarity).

Figure 2. Concluded.

17
10.00

0.50

5.00

0.75

17.06°

10.31

5.00

1.00 0.75

A

A

Section A-A

Referenceprobe

(a) Reference probe holder.

Figure 3. Various hardware sketches. All dimensions are in inches.

18
10.50

4.00

30.35

19.50

2.00

7.06

0.75

3.92

5.00

3.92

0.59

A

A

B

B

1.00

21.80°

17.06°

17.06°

Section A-A

Section B-B

Surveyprobe

(b) Survey probe mechanism.

Figure 3. Continued.

19
Fitting for 0.125 dia. pressure tubing

3.25

7.505.25

2.50

8.58

8.71

21.01

53.1°

(c) Transducer box.

Figure 3. Concluded.

20
0.568

7.590

4.500

56.516°

8.992

(a) Sketch with overall dimensions.

Figure 4. Straight-line segmented leading edge model description. All dimensions are in inches unless otherwise noted.

21
L–2003–01611

(b) Top view.

L–2003–01612

(c) Side view.

Figure 4. Concluded.

22
Jam nut

Figure 5. Jam nut used to lock the sonic boom angle of attack mechanism to one position.

23
0.035 dia. thru

0.050 dia.

To pressure transducers

4°

1.500

3.580

5.000

0.250

Tubing,

0.125 dia. OD

0.070 dia. ID

Tubing,0.094 dia. OD0.063 dia. ID

Tubing,0.125 dia. OD0.070 dia. ID

0.375 dia.0.188 dia.

9.925

0.075

A A

Section A-A

(sectioning excludes tubing) Tubing lengths (approximate)

Probe 0.094 dia. OD 0.0125 dia. OD

ReferenceSurvey

15

3

7

19

Figure 6. Reference and survey probe drawing. All dimensions are in inches unless otherwise noted.

24
± 13.006 psfd

pressuretransducer

Dashed line indicatestransducer box locatedinside of the tunnel

5 psiapressuretransducer

Reference probe

Solenoid operated bypass valve(used to equalize pressure across differential pressuretransducer during tunnel starting/stopping)

Survey probe

Figure 7. Reference and survey probe pressure hookup.

25
5 psia pressure

transducer

± 0.09 psid differentialpressure transducer

Instrumentation leadsand cooling air

Cooling water

Solenoid bypass valve

2012–L–03808

Figure 8. Transducer box (insulating plastic cover removed).

26
+PM

+NF

6.740

28.535

Model

moment

reference

center

reference area = 10.08 in2 = 0.07 ft2

reference length = 1.0 in.

Balance

moment

reference

center

Aft balancebridge location

Forward balancebridge location

4.50

8.992

Figure 9. Moment reference center locations. All dimensions are in inches.

27
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 

Δx, in.

-.01 -.02 -.03 -.04 -.05 -.06 -.07 -.08 

0 

.02 .01 

p/pΔ( ref)cor p/pΔ and ( ref)unc

uncorrected corrected 

run 

47 47 

M 

2.00 2.00 

Re, 1/ft 

2.00 2.00 

h, in.

13.60 13.60 

Figure 10. Comparison of uncorrected and corrected sonic boom pressure signatures.

28
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 

Δx, in.

-.005 -.010 -.015 -.020 -.025 

0 

.020 .015 .010 .005 

p/pΔ( ref)cor 

test 

1998 1998 1998 1998 1998 1998 1906 

run 

47 48 49 71 72 73 

8 

M 

2.00 2.00 2.00 2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.00 2.00 2.00 2.00 

h, in.

13.60 13.58 13.59 13.63 13.63 13.63 13.50 

probe 

4 ̊ cone 4 ̊ cone 4 ̊ cone 4 ̊ cone 4 ̊ cone 4 ̊ cone 2 ̊ cone 

current test current test current test current test current test current test previous test 

Figure 11. Sonic boom pressure signature comparison between tests.

29
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

47 48 49 52 

M 

2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.01 

h, in.

13.60 13.58 13.59 13.60 

v, in/s 

0.0 0.0 0.0 

0.329 

t

d, min. 

51.90 51.79 52.27 

1.25 

move-pause move-pause move-pause continuous 

(a) v = 0.329 in/s.

Figure 12. Comparison of sonic boom pressure signatures for move-pause and continuous data at various model longitudinal speeds.

30
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

47 48 49 53 

M 

2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.01 

h, in.

13.60 13.58 13.59 13.59 

v, in/s 

0.0 0.0 0.0 

0.170 

t

d, min. 

51.90 51.79 52.27 

1.92 

move-pause move-pause move-pause continuous 

(b) v = 0.170 in/s.

Figure 12. Continued.

31
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

47 48 49 54 

M 

2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.00 

h, in.

13.60 13.58 13.59 13.59 

v, in/s 

0.0 0.0 0.0 

0.088 

t

d, min. 

51.90 51.79 52.27 

3.51 

move-pause move-pause move-pause continuous 

(c) v = 0.088 in/s.

Figure 12. Continued.

32
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

47 48 49 55 

M 

2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.00 

h, in.

13.60 13.58 13.59 13.58 

v, in/s 

0.0 0.0 0.0 

0.048 

t

d, min. 

51.90 51.79 52.27 

6.21 

move-pause move-pause move-pause continuous 

(d) v = 0.048 in/s.

Figure 12. Continued.

33
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

47 48 49 56 

M 

2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.00 

h, in.

13.60 13.58 13.59 13.58 

v, in/s 

0.0 0.0 0.0 

0.025 

t

d, min. 

51.90 51.79 52.27 11.75 

move-pause move-pause move-pause continuous 

(e) v = 0.025 in/s.

Figure 12. Concluded.

34
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

64 65 66 47 48 49 

M 

2.00 2.00 2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.00 2.00 2.00 

h, in.

13.62 13.62 13.61 13.60 13.58 13.59 

v, in/s 

0.088 0.088 0.088 

0.0 0.0 0.0 

t

d, min. 

3.47 3.47 3.48 

51.90 51.79 52.27 

continuous continuous continuous move-pause move-pause move-pause (a) First set of repeats. Figure 13. Comparison of sonic boom pressure signatures for move-pause and continuous data for each set of back-to-back runs.

35
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

74 75 76 71 72 73 

M 

2.00 2.00 2.00 2.00 2.00 2.00 

Re, 1/ft 

2.01 2.01 2.00 2.00 2.00 2.00 

h, in.

13.63 13.63 13.63 13.63 13.63 13.63 

v, in/s 

0.088 0.088 0.088 

0.0 0.0 0.0 

t

d, min. 

3.48 3.57 3.82 

51.25 53.45 57.05 

continuous continuous continuous move-pause move-pause move-pause (b) Second set of repeats. Figure 13. Concluded.

36
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 

Δx, in.

-.040 -.045 -.050 -.055 -.060 -.065 -.070 -.075 -.080 

p/pΔ( ref)unc 

run 

47 48 49 60 61 

M 

2.00 2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.00 2.00 

h, in.

13.60 13.58 13.59 13.61 13.62 

v, in/s 

0.0 0.0 0.0 0.0 0.0 

td, min. 

51.90 51.79 52.27 

0.48 0.50 

move-pause move-pause move-pause continuous continuous 

Figure 14. Extent of continuous sonic boom pressure data unsteadiness at two ∆

x locations compared to move-pause pressure

signatures.

37
-.0528 -.0524 -.0520 -.0516 -.0512 -.0508 -.0504 -.0500 -.0496 -.0492 -.0488 -.0484 

(∆p/pref)unc 

0 

500 

1000 

1500 

2000 

2500 

3000 

Frequency of occurrence 

(a) ∆x = 23 in.

-.0544 -.0540 -.0536 -.0532 -.0528 -.0524 -.0520 -.0516 -.0512 -.0508 -.0504 -.0500 -.0496 -.0492 

(∆p/pref)unc 

0 

500 

1000 

1500 

2000 

2500 

3000 

Frequency of occurrence 

(b) ∆x = 29 in.

Figure 15. Histogram of continuous data (from figure 14) obtained at a single ∆x location over

approximately 30 s period.

38
0 4 8 12 16 20 24 28 32 

elapsed time, s 

170.4 

170.6 

170.8 

171.0 

171.2 

171.4 

pref, psfa 

run 

60 

M 

2.00 

Re, 1/ft 

2.00 

h, in.

13.61 

Δx, in.

23.00 

-9.2 

-9.0 

-8.8 

-8.6 

-8.4 

-8.2 

Δp, psfd 

-.053 

-.052 

-.051 

-.050 

-.049 

-.048 

(Δp/pref)unc 

(a) Wind-on.

Figure 16. Differential pressure transducer variation.

39
0 4 8 12 16 20 24 28 32 

elapsed time, s 

401.5 

402.0 

402.5 

403.0 

403.5 

404.0 

pref, psfa 

run 

69 

M 

0.00 

h, in.

13.43 

Δx, in.

19.52 

-.10 

-.09 

-.08 

-.07 

-.06 

-.05 

Δp, psfd 

(b) Wind-off.

Figure 16. Concluded.

40
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

64 64 

M 

2.00 2.00 

Re, 1/ft 

2.00 2.00 

h, in.

13.62 13.62 

v, in/s 

0.088 0.088 

t

d, min. 

3.47 3.47 

favg, frames 

0 

61 

no averaging moving averaged 

(a) Moving average using 61 frames.

Figure 17. Effect of applying a moving average to continuous sonic boom pressure signature data.

41
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

64 64 

M 

2.00 2.00 

Re, 1/ft 

2.00 2.00 

h, in.

13.62 13.62 

v, in/s 

0.088 0.088 

t

d, min. 

3.47 3.47 

favg, frames 

0 

121 

no averaging moving averaged 

(b) Moving average using 121 frames.

Figure 17. Continued.

42
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

64 64 

M 

2.00 2.00 

Re, 1/ft 

2.00 2.00 

h, in.

13.62 13.62 

v, in/s 

0.088 0.088 

t

d, min. 

3.47 3.47 

favg, frames 

0 

181 

no averaging moving averaged 

(c) Moving average using 181 frames.

Figure 17. Continued.

43
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

64 64 

M 

2.00 2.00 

Re, 1/ft 

2.00 2.00 

h, in.

13.62 13.62 

v, in/s 

0.088 0.088 

t

d, min. 

3.47 3.47 

favg, frames 

0 

241 

no averaging moving averaged 

(d) Moving average using 241 frames.

Figure 17. Continued.

44
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

64 64 

M 

2.00 2.00 

Re, 1/ft 

2.00 2.00 

h, in.

13.62 13.62 

v, in/s 

0.088 0.088 

t

d, min. 

3.47 3.47 

favg, frames 

0 

361 

no averaging moving averaged 

(e) Moving average using 361 frames.

Figure 17. Continued.

45
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

64 64 

M 

2.00 2.00 

Re, 1/ft 

2.00 2.00 

h, in.

13.62 13.62 

v, in/s 

0.088 0.088 

t

d, min. 

3.47 3.47 

favg, frames 

0 

481 

no averaging moving averaged 

(f) Moving average using 481 frames.

Figure 17. Concluded.

46
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

64 65 66 47 48 49 

M 

2.00 2.00 2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.00 2.00 2.00 

h, in.

13.62 13.62 13.61 13.60 13.58 13.59 

v, in/s 

0.088 0.088 0.088 

0.0 0.0 0.0 

t

d, min. 

3.47 3.47 3.48 

51.90 51.79 52.27 

continous (moving averaged) continous (moving averaged) continous (moving averaged) move-pause move-pause move-pause 

(a) First set of repeats.

Figure 18. Comparison of sonic boom pressure signatures for move-pause and continuous data (moving average applied) for each setof back-to-back runs.

47
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

74 75 76 71 72 73 

M 

2.00 2.00 2.00 2.00 2.00 2.00 

Re, 1/ft 

2.01 2.01 2.00 2.00 2.00 2.00 

h, in.

13.63 13.63 13.63 13.63 13.63 13.63 

v, in/s 

0.088 0.088 0.088 

0.0 0.0 0.0 

t

d, min. 

3.48 3.57 3.82 

51.25 53.45 57.05 

continous (moving averaged) continous (moving averaged) continous (moving averaged) move-pause move-pause move-pause (b) Second set of repeats. Figure 18. Concluded.

48
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

47 48 49 71 72 73 

M 

2.00 2.00 2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.00 2.00 2.00 

h, in.

13.60 13.58 13.59 13.63 13.63 13.63 

v, in/s 

0.0 0.0 0.0 0.0 0.0 0.0 

t

d, min. 

51.90 51.79 52.27 51.25 53.45 57.05 

move-pause move-pause move-pause move-pause move-pause move-pause 

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

mean of above 6 runs with 95 % confidence interval bars 

(a) Confidence interval.

Figure 19. Move-pause sonic boom pressure signature data with confidence and prediction intervals at a 95 % significance level.

49
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

47 48 49 71 72 73 

M 

2.00 2.00 2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.00 2.00 2.00 

h, in.

13.60 13.58 13.59 13.63 13.63 13.63 

v, in/s 

0.0 0.0 0.0 0.0 0.0 0.0 

t

d, min. 

51.90 51.79 52.27 51.25 53.45 57.05 

move-pause move-pause move-pause move-pause move-pause move-pause 

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

mean of above 6 runs with 95 % prediction interval bars 

(b) Prediction interval.

Figure 19. Concluded.

50
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

Plotting every 10th continuous data point 

run 

64 65 66 74 75 76 

M 

2.00 2.00 2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.01 2.01 2.00 

h, in.

13.62 13.62 13.61 13.63 13.63 13.63 

v, in/s 

0.088 0.088 0.088 0.088 0.088 0.088 

t

d, min. 

3.47 3.47 3.48 3.48 3.57 3.82 

continuous (no moving average applied) continuous (no moving average applied) continuous (no moving average applied) continuous (no moving average applied) continuous (no moving average applied) continuous (no moving average applied) 

mean of above 6 runs with 95 % confidence interval bars 

(a) Confidence interval.

Figure 20. Continuous sonic boom pressure signature data (no moving average applied) at specific ∆x locations with confidence and

prediction intervals at a 95 % significance level.

51
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

Plotting every 10th continuous data point 

run 

64 65 66 74 75 76 

M 

2.00 2.00 2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.01 2.01 2.00 

h, in.

13.62 13.62 13.61 13.63 13.63 13.63 

v, in/s 

0.088 0.088 0.088 0.088 0.088 0.088 

t

d, min. 

3.47 3.47 3.48 3.48 3.57 3.82 

continuous (no moving average applied) continuous (no moving average applied) continuous (no moving average applied) continuous (no moving average applied) continuous (no moving average applied) continuous (no moving average applied) 

mean of above 6 runs with 95 % prediction interval bars 

(b) Prediction interval.

Figure 20. Concluded.

52
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

Plotting every 10th continuous data point 

run 

64 65 66 74 75 76 

M 

2.00 2.00 2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.01 2.01 2.00 

h, in.

13.62 13.62 13.61 13.63 13.63 13.63 

v, in/s 

0.088 0.088 0.088 0.088 0.088 0.088 

t

d, min. 

3.47 3.47 3.48 3.48 3.57 3.82 

continuous (moving averaged) continuous (moving averaged) continuous (moving averaged) continuous (moving averaged) continuous (moving averaged) continuous (moving averaged) 

mean of above 6 runs with 95 % confidence interval bars 

(a) Confidence interval.

Figure 21. All six continuous data runs (moving average applied) and mean values at specific ∆x locations with confidence andprediction intervals at a 95 % level.

53
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

Plotting every 10th continuous data point 

run 

64 65 66 74 75 76 

M 

2.00 2.00 2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.01 2.01 2.00 

h, in.

13.62 13.62 13.61 13.63 13.63 13.63 

v, in/s 

0.088 0.088 0.088 0.088 0.088 0.088 

t

d, min. 

3.47 3.47 3.48 3.48 3.57 3.82 

continuous (moving averaged) continuous (moving averaged) continuous (moving averaged) continuous (moving averaged) continuous (moving averaged) continuous (moving averaged) 

mean of above 6 runs with 95 % prediction interval bars 

(b) Prediction interval.

Figure 21. Concluded.

54
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.0025 -.0050 

0 

.0050 .0025 

Difference in means 

M = 2.00 Re = 2.00 1/ft h ≅ 13.5 in. 

Bars are 95% confidence intervals. 

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

move-pause continuous (no moving average applied) 

(a) No moving average applied to continuous data.

Figure 22. Comparison of mean values of move-pause and continuous data along with the difference in means with confidence intervalsat a 95 % significance level.

55
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.0025 -.0050 

0 

.0050 .0025 

Difference in means 

M = 2.00 Re = 2.00 1/ft h ≅ 13.5 in. 

Bars are 95% confidence intervals. 

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

move-pause continuous (moving average applied) 

(b) Moving average applied to continuous data.

Figure 22. Concluded.

56
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

47 48 49 52 

M 

2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.01 

h, in.

13.60 13.58 13.59 13.60 

v, in/s 

0.0 0.0 0.0 

0.329 

t

d, min. 

51.90 51.79 52.27 

1.25 

filter, Hz 

1 1 1 1 

move-pause move-pause move-pause continuous 

(a) 1 Hz low-pass filter.

Figure 23. Comparison of sonic boom pressure signatures for move-pause and continuous data obtained at various data acquisitionsystem filter settings.

57
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Δx, in.

-.005 -.010 -.015 -.020 

0 

.020 .015 .010 .005 

p/p Δ( ref)cor 

run 

47 48 49 51 

M 

2.00 2.00 2.00 2.00 

Re, 1/ft 

2.00 2.00 2.00 2.01 

h, in.

13.60 13.58 13.59 13.58 

v, in/s 

0.0 0.0 0.0 

0.329 

t

d, min. 

51.90 51.79 52.27 

1.24 

filter, Hz 

1 1 1 

1000 

move-pause move-pause move-pause continuous 

(b) 1000 Hz low-pass filter.

Figure 23. Concluded.

58
Appendix

Equations for Calculation of Confidence and Prediction Intervals

The equations used to compute the confidence intervals for the mean of the six move-pause runs

and six continuous data runs were obtained from reference 17. The symbols used in the equations

presented below are defined in this appendix.

The sample mean was computed from:

sample mean =  ̄x =

Xn

i=1

xi

n

where,

xi = individual sample

n = number of samples

The sample standard deviation that is used in the calculation of the confidence and prediction

intervals was computed from:

sample standard deviation = s =

vuuuuuuut

Xn

i=1

x

2

i −

 Xn

i=1

xi

!2

n

n − 1

The confidence interval on the mean for the move-pause and continuous data runs was computed

from:

confidence interval =  ̄x ± (tα/2,n−1)

s

√

n

where,

tα/2,n−1 = two-tailed t distribution value at a 100(1 − α) % confidence level for

n − 1 degrees of freedom

α = level of significance (0.05 used in this paper)

Finally, the prediction interval on the mean for the move-pause and continuous data runs was

computed from:

prediction interval =  ̄x ± (tα/2,n−1)s

r

1 +

1

n

The equations used to compute the confidence intervals for the difference in means between the

move-pause and continuous data runs were obtained from reference 17 and are shown below:

pooled standard deviation = sp =

s

(n1 − 1)s

2

1 + (n2 − 1)s

2

2

n1 + n2 − 1

59
where,

n1 = number of samples from sample set 1

n2 = number of samples from sample set 2

s1 = sample standard deviation from sample set 1

s2 = sample standard deviation from sample set 2

confidence interval on difference in means = ( ̄x1 − x ̄2) ± (tα/2,n1+n2−2)sp

r

1

n1

+

1

n2

where,

tα/2,n1+n2−2 = two-tailed t distribution value at a 100(1−α) % significance level for

n1 + n2 − 2 degrees of freedom

x ̄1 = mean from sample set 1

x ̄2 = mean from sample set 2

60
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4. TITLE AND SUBTITLE

Experimental Measurement of Sonic Boom Signatures Using a

Continuous Data Acquisition Technique

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5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

122711.03.07.07.16.80

6. AUTHOR(S)

Wilcox, Floyd J., Jr.; Elmiligui, Alaa A.

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681–2199

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REPORT NUMBER

L-20226

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12. DISTRIBUTION/AVAILABILITY STATEMENT

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

A wind tunnel investigation was conducted in the Langley Unitary Plan Wind Tunnel to determine the

effectiveness of a technique to measure aircraft sonic boom signatures using a single conical survey probe while

continuously moving the model past the probe. Sonic boom signatures were obtained using both move-pause and

continuous data acquisition methods for comparison. The test was conducted using a generic business jet model

at a constant angle of attack and a single model-to-survey-probe separation distance. The sonic boom signatures

were obtained at a Mach number of 2.0 and a unit Reynolds number of 2 million per foot. The test results showed

that it is possible to obtain sonic boom signatures while continuously moving the model and that the time

required to acquire the signature is at least 10 times faster than the move-pause method. Data plots are

presented with a discussion of the results. No tabulated data or flow visualization photographs are included.

15. SUBJECT TERMS

Sonic boom; Aerodynamics; Supersonics; Wind tunnel test; Continuous data acquisition; Sonic boom pressure

signature

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