Sorry it’s taken a while for me to reply - I work weird hours.
And you’re correct - the lag time isn’t the flight time. It can be used to get the flight time - but it isn’t the flight time itself. I apologize for the confusion - I’m old, tired, and don’t always think when I’m typing.
Here is a link to a study about using acoustic data (from a cell phone or other recording device) to reconstruct a shooting. It covers determining distance if the mic is either close to the rifle, or close to the victim - or somewhere in between. It even covers using multiple recordings from different places to “triangulate” the exact location(s) of a shooter or shooters.
http://www.btgresearch.org/AcousticReconstruction02042012.pdf
It appears to use a differential equation modeled after the “crack-thump” method of determining range on the battlefield but using actual impact instead of the “crack”.
There are other scientific papers about this but all of them are behind paywalls - and it’s not worth $40 for me to get access when this one lays it out plainly.
I’m not peer-reviewing their data, just posting it. BTG Research appears to have done a lot of studies on a lot of subjects, and the two individuals who make up the team seem to have decent bona fides; so I don’t think they’re any fly-by-night operation. Although I could be wrong as I don’t know them personally.
The point of the paper is that using a decent recording - which nearly all cell phones made today are capable of, an audio engineer can easily examine the wave-forms and pull the impact time (or sonic boom “crack”) and the “thump” of the weapon from any extraneous data like echoes. And if you know the location of the recording device, and it doesn’t move, then you can determine the distance to the shooter within a few meters for a given round, in a given set of atmospheric circumstances - it even works with automatic rifle fire...
In fact, this is part of how the gunfire sensors they’re installing in cities now operate. Their algorithms and methods are proprietary and they won’t share, but they can use acoustic data to determine shooter locations to within meters in some cases depending on distance from the differnt sensors.
In any case, even if I discard the science and math, and instead use the battlefield method on the lag time recorded, I’m still left with the following:
For the 7.62x39 123 grain:
LAG DISTANCE
.559 - 550 meters/600 yards
.374 - 280 meters/300 yards
For the 5.56x45 55 grain:
LAG DISTANCE
.559 - 350 meters/400 yards
.374 - 160 meters/175 yards
And interestingly enough I happened to find a video that deals with exactly this subject and even has spreadsheets and charts for both the 5.56 55 grain and the 7.62x39 123 grain.
https://www.youtube.com/watch?v=Rb4BP7lZnk0
The charts in the video use the exact weapons we are discussing and show pretty much those exact ranges.
Battlefield use of “crack-thump” isn’t scientific - and it’s dependent on knowing the caliber and weight of the round you’re facing, but in this case we aren’t on a battlefield - we’re dealing with recordings where we can easily use the wave-forms to pull the data and get an accurate lag time in milliseconds. We also know the atmospheric conditions on the night of the shooting. And we know the location of the recording device and that it didn’t move between recording sample A and sample B. And finally - we know - at least we can surmise from the photos released (if they’re real) that the hotel room had .223 and .308 rifles. We don’t know exactly what ammo he was using however - nor do we know the caliber and weight of the rounds found on the ground and in the pavement. They may not ever release that info.
However, using what we *do* know we can do the calculations for a ton of variants of caliber and weight and using the results my opinion is that it’s unlikely one shooter from that hotel room was able to create two totally different lag times even if he switched between weapons and calibers.
And he certainly wasn’t able to fire both of them at the same time using bump-fire stocks. They require the use of both hands. And there are several places in the recordings where there are two weapons overlapping.
I don’t claim to know why - or who did it. Just because I am calling out law enforcement for what I consider to be shoddy investigative work doesn’t mean that I think the shooting was a government sponsored conspiracy. Incompetence is rampant in the ranks of government employees and that includes law enforcement.
Thanks for getting back.
The crux of the matter is how accurately we can identify the various sounds recorded on the cell phones.
I suspect that is quite difficult. Some cell phones are better than others, and it would be very helpful to have the original recording device to find out the mike response to frequencies.
Maybe enough resolution is there, maybe not. There are a lot of recording devices out there.
There are experts in this exact field. It would be nice if they would spend a couple of hundred hours, free, and weigh in.
I think the overlapping strings of fire is likely to be the most fruitful. The recordings give fairly precise timing. So the exact timing of a string of shot is very likely to positively and uniquely identify that string. That would allow identification of echoes, which are a problem because of all the hard, flat surfaces available in the city.
Once we have positively identified all the strings of shots recorded, we can do further analysis. I do not think there are more than a couple of dozen strings, but even 50 or a hundred shot strings would not be excessively burdensome.
There is considerable motivation to find evidence of a second shooter. Anyome who does so will have made their reputation.
A second shooter, of course complicates the picture enormously.
We also know that theories of multiple shooters, and mis-characterizations of multiple shooters have been common in just about every mass shooting, at least in early reports.
That should keep us skeptical.
Know any good acoustic people who are willing to devote a couple of hundred hours to carefully identify shot strings?