[marktwain]

I think your math is off.

The lag between bullet arrival and arrival of the sound wave would be very different.

Flight time for the bullet would be about .72 seconds for 400 yards. Time for sound arrival would be about 1.04 seconds. That would be a lag time of .32 seconds. Pretty close to the “shooter2” stated lag of .374. Speed of sound is approximate. It could be calculated much closer based on the current pressure and temperate in Las Vegas at the time of the shooting.

[DBG8489]

The lag time between arrival of the round and the arrival of the sound of the rifle firing is dependent on two things: The speed of sound, which is constant, and the speed of the projectile which starts at X and ends at Y (because a round slows down once it's fired). But this is known, and ballistics data can be generated for each type of round given a specific muzzle velocity and a chart can be made that shows for any given flight time, a resulting distance is traveled.

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.