Audio Analysis Is Most Consistent Two Shooters At Trump Rally

cohler · August 14, 2024, 7:39pm

This is NEW analysis built on what I did in my previous post.

To refine and derive how close those first three shots were to Trump’s microphone:

v_s = speed of sound
v_b = average speed of bullet
d = distance from muzzle to microphone
d_c = distance from muzzle to bullet closest point
ε = distance from bullet to microphone at closest point
t_report = time of report arrival at mic
t_snik = time of snik arrival at mic
t₀ = time of shot
Δt = t_report - t_snik

d = v_s x (t_report - t₀) => t_report = ^d⁄_{v_s} + t₀

d_c = (d² + ε²)^0.5

t_snik = ^d_c⁄_{v_b} + ^ε⁄_{v_s} + t₀

So Δt = ^d⁄_{v_s} - (^d_c⁄_{v_b} + ^ε⁄_{v_s}) = ^{(d - ε)}⁄_{v_s} - ^d_c⁄_{v_b}

As ε increases, Δt decreases. I plotted this on Desmos for anyone who wants to look and play around with.

The assumptions all calculated accurately in my previous post are:

Distance shooter to mic d = 454 ft
Velocity of sound v_s = 1152 fps
Average bullet velocity v_b = 2644 fps (assuming a 77gr OTM bullet)

If you play around with the bullet velocity slider in the Desmos plot, you’ll see immediately that the ONLY average bullet velocities that make that first shot come close enough to the mic to have hit Trump, but not closer than he actually was, and still yield a 220ms snik-report (Δt) interval, are between roughly 2620 and 2644 fps.

The fact that the snik-report (Δt) time of the 1st shot was the largest is also clear proof that it was the CLOSEST shot to the microphone (and therefore to Donald Trump), which makes sense, because that is the only one that hit him.

The other shots produced snik-report intervals (Δt) that were 5 to 10ms SHORTER.

The measured snik-report (Δt) intervals of 220ms, 215ms, and 209ms for the first three shots imply that those three bullets passed at the following distances from Trump’s microphone:

2.75 ft
8 ft
15.25 ft

Does anyone have an accurate estimate of how far Trump’s ear was from the microphone???