Experimental Setup and Procedure
1. Test Setup
a. Equipment
i. DAQ: B&K LanXI 3052-A-3/0
1. Sampling Rate: 262k
ii. Microphones: B&K 4944-B
iii. Calibrator: B&K 4231
b. Microphone Locations: see Figure 1.
For 2024, we built a fixed firing fixture to remove the shooter's head and torso from being in the path from the sound sources to the mics. This fixture also made the weapon position more consistent shot to shot. See Figure 0A and 0B.
In 2024, we changed mic position around a little bit. We got rid of 225 and moved that one to milspec-right (MR). For shooter's ear (SE), we used a constant location located off of a fixed point on the firing fixture (but not connected to it) instead of being relative to the shooter's head.
FIGURE 0A. FIXTURE
FIGURE 0B. FIXTURE
FIGURE 1. MICROPHONE LOCATIONS
2. Test Location Properties
Data was obtained inside of the TBAC Barn with approximate setup and bullet trap location, see Figure 2.
FIGURE 2. BARN LAYOUT
3. Post Analysis Definitions
a. Peak – The maximum value in the curve, applies to Pa, dB and dBA
b. LEQ – Leq is a "sound energy metric" – Leq defines an equivalent constant sound energy for a fluctuating curve. It is calculated by averaging the SPL (sound pressure level) over the defined time frame and then converting that value to decibels. The LEQ curve becomes a time average sound level. In our case we are using Leq(10ms) dBA so the window for each Leq (dBA) value is a 10msec SPL average.
c. Impulse – Obtained using the Euler method where area under the curve is calculated by multiplying the value and the time interval, applies to Pa*ms and dB*ms
d. Pa-dB conversion – 20*log(Pa/Po) where Po=2e-5 Pa (Pascal equivalent of 1dB)
d. dB vs dBA – In this document, dB is used to refer to unweighted dB. dBA is used to refer to A-weighted dB.
4. Influence of Testing Indoors vs Outdoors
Testing was done indoors and outdoors to verify that peak, impulse, and Leq values representing the gunshots were not affected by the walls, ceiling, and bullet trap. In these plots, and all the plots in this data set, the triggering mic triggers at 50 ms (0.050 seconds), hence they all "start at .05" on the plots.
UNSUPPRESSED GUNSHOTS
FIGURE 3. BARE MUZZLE INDOOR VS. OUTDOOR: PRESSURE
In the instantaneous pressure plot above, the ground reflection can be seen in both the indoor and outdoor plots at approx 0.057 sec. Sound travels at approx 1100 ft/sec. The diagonal distance from the muzzle to the ground and back up to the microphone is 11'. The straight-line distance from the muzzle to the mic is 3.28'. By subtracting the straight-line distance from the diagonal distance and then dividing by the speed of sound, we get (11’-3.28’)/(1100 ft/sec) = 0.007 seconds (7 msec), which is consistent with the time the ground reflection shows up on the graph. The 0.007 seconds is the time it takes for the reflection to get to the triggering mic after the initial blast hits the triggering mic.
The intensity of the ground reflection is affected by the ground composition, i.e., concrete will reflect more energy than sand. In this case the compacted dirt outside reflected more of the pressure wave than the sand floor of the indoor testing.
The reflections from the walls show up just before 0.075 seconds in Figure 3 above. The wall reflections are also clearly visible in the Impulse and Leq figures below (Figures 4 and 5). On the impulse plot, there are oscillations similar to those in the pressure plot above. On the Leq plot, the reflections show up as a higher equivalent sound level (Leq) when they come back to the mic position.
FIGURE 4. BARE MUZZLE INDOOR VS. OUTDOOR: IMPULSE
FIGURE 5. BARE MUZZLE INDOOR VS. OUTDOOR: Leq(10ms) dBA
Note in the Leq plot, the ground reflection on the outdoor plot is a higher intensity than the ground reflection on the inside plot because the composition of the outdoor "ground" is more reflective (compacted dirt vs. sand).
In summary, for unsuppressed shots, from the above data, we can see that a window of approx 0 to 75 msec would be sufficient to accurately capture peak pressure, Impulse, and Leq(10ms) dBA in our barn, other than the varying influence of ground composition.
SUPPRESSED GUNSHOTS
FIGURE 6. SUPPRESSED INDOOR VS. OUTDOOR: PRESSURE
The various reflection events of the indoor and outdoor plots are harder to identify and differentiate when shooting suppressed. The suppressor extends the pressure-release time which causes the ground reflections to be lost in the noise of the event-- in other words, the time it takes for the muzzle report from the suppressor is long enough that the reflections from the ground also reach the mic while the initial pressure release at the muzzle is still happening (in many cases).
For peak pressure, the analysis is still simple: the entire waveform is evaluated in the search for the peak pressure. From the unsuppressed plots we know that the wall reflections occur at approx 75 msec. In Figure 6, the pressure has substantially decayed by this point and it's clear the peak pressure happens sometime before 0.065 sec. Thus, the reflections are coming back to the mic at least 10 msec after the pressure peak occurs. The 338 Ultra was chosen for this demonstration because it should represent a "worst case" in terms of retaining pressure longer (due to its volume and the gas volume and pressure of 338LM).
FIGURE 7. SUPPRESSED INDOOR VS. OUTDOOR: IMPULSE
FIGURE 8. SUPPRESSED INDOOR VS. OUTDOOR: Leq(10ms) dBA
In contrast to the somewhat chaotic looking pressure plots (Figure 6), the wall reflections are still easy to identify in the Impulse and Leq plots. Figures 7 and 8 show that an analysis window can be set to still find the maximum values of Impulse and Leq without those values being affected by wall reflections.
In Figure 7 (IMPULSE), the large negative curve and the second positive curve of the impulse calculation is due to noise in the base waveform being integrated. The analysis window for impulse only needs to be long enough to include the first positive portion and its return to zero (at approx 0.058 sec). Impulse plots used throughout various industries are typically truncated once they cross zero on the way down the first time. To achieve this for the impulse calculation, an initial window was set from 0 - 75 msec. The window was then dynamically adjusted for each waveform by finding the minimum value of impulse from 0 - 75 msec; this is known as the "trough." The end of the impulse analysis window was then adjusted to the trough before the maximum value was found.
For Leq, specifically Leq(10ms) dBA, the data analysis window was set at +0.025 sec after the shot, or 75 msec. This coincides with the time we have already determined that reflections come back. In Figure 9, it is clear that wall reflections start contributing to the Leq value at about 0.080 (80 msec), so we still capture the maximum Leq value of the gunshot with this window.
Also note that the Leq graph from approx 0.055 to 0.070 is higher for the outside plot primarily because of increased ground reflection.
Environmental Factors When Testing Outdoors
Testing indoors does have the advantage of reducing the influence of weather on the test data, primarily wind. Once wind velocities reach 5 mph data obtained outside can be affected. If you think of wading upstream vs downstream the current has a direct affect on how difficult or easy it is to walk. Wind has the same effect on pressure data i.e. wind blowing from the mic to the muzzle will cause the data to be arbitrarily lower and vice versa.
Influence of using a human shooter vs. a fixed firing fixture
FIGURE 9. FIXTURE vs. SHOOTER
The sound data when using the fixture is "cleaner" for the SE location as the reflections from the shooter's head are removed.
SUMMARY
By analyzing unsuppressed and suppressed gunshot data from indoors and outdoors, we determined that accurately finding peak pressure, Impulse, and Leq(10ms) dBA was possible by windowing the data to avoid the reflections by demonstrating that the peak or maximum value from the gunshot itself (and associated gun noise in the case of semi-autos) always occurred before the reflections returned to the mics.
