So if you know the flight time, you can look at the ballistics chart and get a (rough) distance the round traveled. In other words, you know how far the recording source was from the rifle.
We *know* the flight times because we can look at the waveforms in an audio program and see how many msecs there are between impacts and reports - on each sample.
I admitted that my original calculations were "back of the napkin" type stuff. And you wanted me to check the math, so I went back and re-did it using ballistics calculations for each round along with accurate climate data. And it did change some of the values although it didn't wipe away the discrepancy.
The constants are:
Two samples, taken from a single recording device in a single location.
Temp - 60F
Rel H - 20%
Alt - 2030ft
Barometric Pressure - 29.98inHg
In those conditions, the speed of sound is about: 1130 fps; 345 meters/sec; 377 yards/sec
For each projectile given, the muzzle velocity is:
| TYPE | WEIGHT | VELOCITY |
| M193 5.56x45mm | 55gr | 3250 fps |
|
M855 5.56x45mm
|
62gr | 3025 fps |
| M80 7.62x51mm | 149gr | 2750 fps |
| M2 7.62x51mm | 152gr | 2740 fps |
| M852 7.62x51mm | 168gr | 2550 fps |
| M118 7.62x51mm | 173gr | 2640 fps |
| *M43 7.62x39mm | 162gr | 2350 fps |
Time lags between impact and report (flight time) for each is:
Sample 1 - 0.559s
Sample 2 - 0.374s
Using those figures, and the ballistcs data for each round, we can calculate that for each lag time (flight time) given, each of the rounds listed will travel the following distances:
| Projectile | Weight | Yards in .559 secs |
Yards in .374 secs |
| M193 5.56x45mm | 55 gr | 425 | 320 |
| M855 5.56x45mm | 62 gr | 425 | 320 |
| M80 7.62x51mm | 149 gr | 425 | 320 |
| M2 7.62x51mm | 152 gr | 425 | 320 |
| M852 7.62x51mm | 168 gr | 400 | 280 |
| M118 7.62x51mm | 173 gr | 420 | 290 |
| M43 7.62x39mm | 162 gr | 380 | 270 |
In the case of your round, with a flight time of .56 seconds the round will travel around 380 yards. With a flight time of .38 seconds, it will travel around 270 yards.
If you don't believe it, I don't care. You can do the calculations yourself.
My guess is that if they ever release the data on the rounds found at the scene, you will see pretty much nothing but 5.56 in either 55 or 62 grain. It doesn't matter which because both travel about the same distance in the given times.
And given those different flight times, there's no way there was only one shooter 425 or so yards away in the Mandalay Bay hotel. There was at least one other shooter about 100 yards closer.
I appreciate your efforts. You did some good work. Thanks for finding the speed of sound and the meteorological data. The temperature in Las Vegas at 10:56 p.m. was 77 degrees. The pressure was 29.50 mm of HG. according to a weather site I checked. The difference in temperature is not significant.
Unfortunately, I believe you are making a simple logical error.
Lag time is not flight time.
Lag time is the difference between flight time and the time for the report to reach the point of impact. (actually, as you point out, the time between the report of the bullet strike and the report of the shot to reach the recorder)
A slower bullet results in a smaller lag time for the same range, because it is closer to the speed of sound.
You have to know the bullet ballistics to get the flight time, and know the speed of sound to get the time between report and arrival of the report. The difference between the two is the lag time. It varies with the ballistics of the round and the distance. The acoustic path can also be significantly different than the flight path of the bullet, though that is more of a problem at longer ranges. Given a lag time and knowledge of the ballistics, you can approximate the range.
A simple way to look at this is to compare the lag time for a known distance between types of rounds. Lets use speed of sound data and a known distance, say 400 yards, or 1200 feet.
The sound of the report takes 1200/1130, or 1.06 seconds to move 1200 feet, assuming a line of sight acoustic path. A 7.62x39 bullet (123 grain at 2,350 fps) takes about .72 seconds to travel the same distance. A 7.62X51 (150 grain at 2,820) takes about .51 seconds to travel the distance. A .223 (55 grain at 3,239 fps) takes about .53 seconds to cover the 400 yards. The lag times are .34 seconds for the 7.62x39 (1.06-.72), .55 seconds for the 7.62x51 (1.06-.51), and .51 seconds for the .223 (1.06-.55).
Of course, the exact round lag time will vary with the exact cartridge, the length of the barrel and the atmospheric conditions, which can be put into a good ballistic calculator, once they are known.
But this ignores other important problems with using cell phones recordings.
Can we reliably differentiate between bullet strikes and echoes of reports? Maybe. Echos should reach us later, and strike sooner. I suspect they can be differentiated with a sophisticated analysis.
How about the geometry of where the recorder is in relation to the shooter and the bullet strikes? If the phone is 50 yards closer to the shooter than to the strikes, the lag time will appear to be about 100 yards less, because the acoustic path time from the bullet strike is added to the time of the bullet strike recording while the acoustic path from the shooter is shortened because the recorder is closer to the shooter. This reduces the lag time considerably.
That should not make a difference in determining the relative difference in lag times, because that would cancel out when using the same recording device. It does make a difference in absolute range.
I would like to see some evidence of what rounds were fired by the shooter, how many, and of what type. We should also be able to get a count of the total number of rounds fired, the sequence, and the timing.
There are lots of recordings out there, so that sequence and timing should not be too difficult. Echoes complicate things quite a bit, because they can give false readings of multiple strings of shots. A good analysis could sort them out, as the time string of shots would nearly duplicate other time strings.
The lag time analysis seems inconclusive to me, at least for now.