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.
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.