Good question. And… yep, that would be it… for the Crooks scenario, we need the velocity of the bullet at 150ish yards.
One thing: to be honest, I’m not sure how manufacturers come up with the 0-100-200-300 data… on the muzzle I know they have a chronograph in front of the test barrel or the weapon, but I’m not sure if they get the 100-200-300 from formula or a chrono down range. Some manufacturers do a better job than others. Hornady, for instance, uses real rifles, instead of test barrels. Some don’t even have the data, just slap a muzzle velocity there after chrono and call it a day apparently. But I’m getting the feeling that Crooks was inserted in a place where he would choose better ammo. The range he went to apparently is where top shooters of that area go to, the store where he bought that ammo appears to be owned by a very good gunsmith, kind of the go-to guy, you know…? His shooting environment has all the traces of making one go for that top shelf ammo, learning how to tell the difference between ammo, etc.
As for the velocities, online ballistic calculators could calculate the velocity at 150 yards for all of those, but it’s very time consuming (and not fun enough, just boring to do lol).
I imagine we have to start like this: for a given range of crack-thump sounds… say 213 to 222 milliseconds, a distance of x, sound speed of y, what would the average speed have to be for those durations? This would give us 2 average velocities as an interval. Then, part 2, we calculate the velocity of each cartridge at the 150ish ft, like you said.
I defaulted to AI on approaches to estimate the velocities from the available data, it came back with two:
Approach 1: Linear Interpolation Between Data Points
Since you have velocities at 0 yards (muzzle), 100 yards, 200 yards, and 300 yards, you can perform linear interpolation between the closest values (100 yards and 200 yards) to estimate the velocity at 154.11 yards.
Interpolated Velocity=V100+[(154.11-100) / (200-100)]×(V200−V100)
### Approach 2: Estimate Average Deceleration
If you want a broader approach that doesn’t rely on interpolation, you can estimate an average deceleration based on the muzzle and 100-yard velocity. Then, project what speed the bullet would have at 154.11 yards and filter bullets accordingly.
Is there another way we could estimate the distance at 150ish?
Then we get the average for each cartrige, from muzzle to the velocity at 150ish feet. Then whatever’s not inside our previous interval, we can filter out. Then we can make qualitative eliminations also, say, filter out training ammo or some hard to find brands, etc… follow a trust-the-reporting-scenario and leave only 5.56 in boxes of 50, or follow the trust-noone and leave .223 and 5.56 as candidates.
At this point, just from filtering higher velocities and using qualitative assumptions, my top 5 candidates were these (let’s see if they change after the math)
1- Hornady 5.56 75 gr BTHP T2 TAP PRECISION (id 16)
2- Magtech 5.56 HPBT 77GR CANNELURED (id 124)
3- Hornady 5.56 62 gr TAP® BARRIER™ (id 13)
4- BackHills .223 Heavy Match HP 68gr (id 151)
5- CorBon .223 Urban Response JHP (id 55)
BTW, what exact distances are we looking at, @vt1 ? From Crooks, HighRoof, Vent, 2ndFloorWindow (which window, actually?) Do you have these distances in metric centimeters or imperial with decimals? I remember seeing these somewhere…
The durations of crack-thumps (or snicks-reports) from @greg_n are on this post here.
1-0.221
2-0.217
3-0.212
4-0.212
5-0.212
6-?
7-?
8-0.218
shorter: 0.212
longer: 0.221
On determining the average speed from the snick-report, Greg and @sonjax6 were writing about accounting or not for the distance from bullet to microphone here on this post
And @vt1 also wrote about it here
And @cohler wrote about it here
Do we already have the calculated average velocities from these snick-report durations?