I have seen a lot of commercial electronic shooting targets. Most of them seem to use microphones to "triangulate" the position of the projectile. If I wanted to do a diy version of this what kind of math would I need to determine the location of a projectile shot at a metal target?
closed as off topic by Kortuk♦ Jul 4 '12 at 20:54
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I haven't had an opportunity to look at any of them from a technical stand point. But my understanding of the ones used @ Blair Atholl (Scotland) when we visited last year for an invitational (going back as far as 1233yds) was that their target system used some sort of rubber membrane behind the target face, and a series of sensors attached to the membrane around the perimeter sensed the location of the shot to within a fairly accurate position (less than 1mm error).
I believe both this system and the ones utilizing microphones use some sort of triangulation to determine the location of the bullet as it passes through what ever sensor network is used.
(As for how they work, see memilanuk's answer)
For the math you need some sort of triangulation too see where several distances intersect.
Use several microphones, time the difference between when they heard the round hitting your target - by using the speed of sound you will get the distance between the microphone and the hit.
By having several distances you need to figure out where they intersect on the target; all mics will have heard the sound at different times (as the are placed on a line by the base of the target - in order to eliminate the possibility of them all reacting at the same time).
We are talking about the speed of sound and distances of about a meter (a few feet for you imperialists;) so use the same length of wire for all the microphones to rule that out as a variable and keep in mind that the accuracy of the sampling is crucially important for this sort of thing.
Another reason these sort of targets are so expensive is that they are made to be placed on a range, side by side (maybe as close as a feet in distance from each other) so they need to disregard if the target next to it was hit at the same time.
Also keep in mind that if you use metal (or any sort of "non healing" target) you might end up with a hole larger than the bullet - and if the bullet would pass it then no sound and thus nothing to hear.