Wow, @vt1 . Thanks for doing those calculations. Just to be clear, you use the estimated speed of the bullet to determine the angle of the sonic cone. From what I’ve read, the internal angle of this cone decreases as the bullet’s speed increases past Mach 1.
Let me make sure I understand all the variables in Eq. 12
b = distance from shooter to the closest point of approach to the audio recorder
Vm = muzzle velocity
h = distance from the recorder to the bullet’s path of travel
Vc = speed of sound
If we go to Matthew Pearson’s Dropbox you’ll see an “audio” looking icon in the lower right that lets you select tracks.
We’re not sure where the mics are. They might be front cabin (we’re probably hearing air conditioning) and rear cabin (to record what suspects say) and something else, not sure.
Thanks, @brian60221. I downloaded the MP4 and can see that it has three tracks. The sounds at 5:27 when he is getting the rifle out from the rear compartment tell me that the tracks are:
As I have already stated several times, my analysis shows that if it is 55 or even 62gr, then the velocity is substantially higher for either 223 or 556 rounds. And then the snik-report difference would prove conclusively that the shots came from much closer (like 410 or 420ft). Which would mean TWO SHOOTERS.
The ONLY way that it could be ONE shooter is as I showed in my post with an average velocity of 2644 fps or less. That means 77gr round most likely.
WE NEED TO KNOW WHAT THE BULLETS WERE.
All the rest of this multi-mic nonsense is not useful.
Yes @greg_n your understanding is correct. The sound traveling in the air can be interpreted like waves of pressure differential. If the bullet travels at higher speed than the sound speed these waves are superimposed creating the shock wave. The angle formed define the proportion of the bullet speed and sound speed, that travels perpendicular to the shock wave. The sine of the angle is equal to that proportion, the inverse of that is the mach number. Tracing back from the reciver the shock wave that arrived there must have come perpendicular to that wave therefore it came from point 1, the distance 12 is the distance travelled at sound speed. At the same time the bullet travells from point 1 to point 3 at the bullet speed forming the rigth triangle 123. The shock wave total time is the time for the bullet to arrive at point 1 plus the time for the sound from point 1 to point 2. The report time is the time for the sound to go from the muzzle to point 2.
I plotted all the shot positions that have been proposed and found only Crooks position (and possible 2nd shooter in the building/ceiling below) aligned with the ear and puff of smoke at the top right rear bleacher.
I then looked at the alignment of two trajectories (from Crooks and from a second shooter ceiling position below Crooks) and compared them the famous photo of the bullet trail next to his head.
And found a perfect match. I see only two possible trajectories that work. Crooks and an above the ceiling position shooting out of a vent hole. The vents can be seen in photos.
It might be like you say. Yet stream 1 and 3 are always 10 ms apart, with stream 2 in between. There are numerous examples, beginning with undercarriage noise and further on with the firstly only intended door opening and various clicking sounds as well.
Overall, I now see that delay as a systematic error within the video/audio documentation system of that patrol car. Please see also my post here.
Your line of fire paralleling a vapor trace of the second projectile may do so only apparently, depending on how you correct for the perspective distortion. You may want to follow the discussion of my own approach here
In this post also concluded the same think from James Copenhaver footage.
If the line of sight from James Copenhaver footage is almost aligned with Trump ear and the Vent that means that a fire from the vent would pass at the height of the camera eyepiece. Therefore, if the bullet hit the rail it has come from an upper position.
I also explained that here to @roger-knight, where I did a model correcting Google Earth height using James Copenhaver footage.
In his opinion I cannot use the footage for the model, but I think that it still proves it did not come from the vent, but from an upper position.
@cohler No, the multi-mic approach is very useful. While it does not answer all of the questions, it does tell us that Shots 1-8 all came from the same location, within a 1 meter radius.
Without time-synced recording sources, TDOA cannot provide the absolute location, but if you believe that any of the 8 shots came from the crooks position, then all 8 of them came from that same spot.
I feel like listening to all the different audio sources that was pretty apparent, but at least we have data to back it up now since people’s ears don’t work.
Just to be clear, for this model to work I had to choose an initial condition to define the location of one of the shots. Without time-synched recording sources I had no other choice. So, I picked the crooks location and saw that the other 7 shots came from that same place. It doesn’t matter which of the 8 shots I choose to be the initial value, the results turn out the same.
A position directly overlooking Crooks, from I believe 3 meters higher, in the same trajectory, would also work would it not?
I see the image of the bullet is at a slight decline, suggesting either a bullet drop and/or a slightly higher position. Or it could simply be the camera angle.
Where would that shooter be? I already have a line of fire for a shooter on the top left of the other 2 story building. I did another trajectory from the center of that roof which puts is right over Crooks, but the higher start point means it hits the corner of the bleacher a few less than a foot above the top bleacher seat.
The photo is not that carefully aligned and corrected. It could be a few degrees off one way or the other.
It appears you have the potential other shooter (the professional, main shooter) aligned off center from Crooks. However if that person were masking his shots he’d have had the entire rooftop to align placing Crooks directly between himself and Trump.
This would be a near exact same trajectory left-to-right and a imperceptable vertical trajectory difference. Another member measured the heights and my memory says it was 3 meters difference (e.g. I think it was measured at 411 meters and 414 meters above sea level, for the lower and upper positions).
Different bullet types, speeds, weights, brands, etc. could easily mask those vertical and drop trajectories (e.g. a slower heavier round might drop sooner in the trajectory than a lighter faster round).
A shot from above the ceiling through a vent that hits Trumps ear, DOES hit the railing but 12" higher than a shot from Crooks.
I straightened the Copenhaver image and put a level line from the vent and a lighter line of a possible trajectory from the vent, which would be lower than the eyepiece.
He was standing the time of the footage and standing at the shooting time.
The video of him filming was between that and the shotting with 1 minute difference. Improbable.
Also, the margin of error of Goggle height is 1 foot. That error in Trumps position results in 6 feet error at Crooks position. The 3D models presented will put Crooks within that margin of error.
I’m do not have any certainty of this, I’m just looking at probabilities.
For other improbable cenarios to exist would need more evidence, like the vent origin for exemple.
I know conspiracy theories would appear even if everyone believed it came from Crooks position. Like a small hole in the roof near Crooks. But I’m going where the most probable scenario is.
