Homemade AQT...check my math

[hillbilly]

I took a shot at making my own "AQT" targets this morning.

I'm not a math major, and have never been that friendly with math, but here's what I came up with.

Check my math and let me know if I'm completely wrong here.

The standard "iron maiden" target, representing a human torso is 36 inches tall by 20 inches wide (yeah, yeah, some are 40 inches high, but I'm going with the 36 inchers here).

At 100 yards, an actual iron maiden would be 36 MOA tall by 20 MOA wide.

So, at 1/4 of that distance (25 yards) I would need to divide 36 and 20 both by 4 to get a target 1/4 that size, or 9 inches high by 5 inches wide.

Okay.

At the same 25 yard distance ( or 1/4 of 100) I could simulate the same target at twice 100, or 200 yards by dividing both 9 and 5 by two.

Three times the distance, by dividing by 3, four times by four, etc.

Here's what I've created quickly with a calculator, sheets of printer paper, and a magic marker.

I've drawn rough tombstone shapes in the following dimensions, to shoot from 25 yards.

Again, "life sized" at 100 yards would be 36 inches high by 20 inches wide.

At 25 yards, "life sized" at a simulated 100 yards would be 9 inches high by 5 inches wide.

Shooting from 25 yards, "life sized" for a simulated 200 yards would be 4.5 iches high by 2.5 inches wide.

Simulated 300 yards would mean 3 inches high by 1.6 inches wide.

Simulated 400 would be 2.25 inches high by 1.25 inches wide.

Simulated 500 would be 1.8 inches high by 1 inch wide.

Does this sound right?

hillbilly

 

[Bwana John]

Looks good.

 

[hillbilly]

My digital camera needs a new battery, so no pics yet.

But here are my results.

I got the number of rounds and time limits off Fred's site.

I used a stock Ruger 10/22 with stock iron sights, and Winchester white box cheapo value pack from Wal-Mart.

I did draw one small circle and confirm my sights from 25 yards before starting the run. Turns out I had to hold about 1/2 inch low at 25 yards to hit what I aimed at with my current sight settings. I didn't want to get a screwdriver out to adjust the rear site, so I just held a bit low.


Simulated 100 yards (5 inches wide X 9 inches tall):

10 for 10 in about 40 seconds standing.

Simulated 200 (4.5 inches tall by 2.5 inches wide) going down into a sitting position, shooting two rounds, changing mags and shooting eight more in only 50 seconds:

9 for 10, with one pulled right. I was done in 34 seconds.

Simulated 300 (3 inches tall by 1.6 inches wide) using same procedure for 200, only with a full 60 seconds allowed:

9 for 10, with one flier right. Two of the hits were "Scratch hits" on the
right and bottom edge, but hey, scratch hits is hits. I was done in 48
seconds.

Simulated 400 ( 2.25 by 1.25). Fred's procedure calls for 20 shots in 20 minutes, prone slow fire. I shot only 10, as I was going to use another 10 at a simulated 500, and I found only directions for out to 400 on Fred's website.

10 for 10. And I was done in 4 minutes and change.

Simulated 500 (1.8 X 1) 10 rounds in prone:

6 for 10. Four minutes and change.

And just for giggles, I did the math and came up with a simulated 1000 yard target. It was only .9 inches tall by one-half inch wide.

Slow fire prone resulted in four hits. Another four went into a tight
cloverleaf about 1/2 inch right. I think my 35 year old eyes couldnt tell the
diference between the target, and a couple of bullet holes, so I shot at
the bullet holes a few times. Again, a little more than four mintues.

Yee-haw, indeed.

hillbilly

 

[JohnKSa]

A straight scaling will be close enough for reducing from 100 to 25 yards.

If you reduce the distance a LOT, you also need to compensate for the bullet size as well. The bullet size stays the same regardless of the distance. If you scale the target WAY down, the bullet is now much larger than it used to be--compared to the target.

Say, for example, you wanted to reduce a 500 yard target to 10 yards for shooting in your backyard with an airgun. You do your divide by 50 to get the target sized down, but now you have to consider projectile size.

If you were originally shooting the 500 yard target with a .30 cal, then you could have the center of your bullet hole be .15" from the black and still get a hit. Now, you're shooting a .177 pellet at 10 yards. You can have the center of your pellet hole be 0.089" from the black and still get a hit.

But that 0.089" works out to be over 4.4 inches if you scale it back up by multiplying by 50 to see what it would be on the original 500 yard target. Obviously, you can miss the smaller target by a much larger relative amount and still get a hit--like shooting at the original target at the original distance with an 8.8" diameter projectile. You need to scale the target down a little further to take the bullet size into account.

The formula for the scaled down target size is:

( Original target size - PSF) x new distance / original distance

PSF = Projectile scaling factor is:

NPD x (original distance / new distance) - OPD

NPD = New projectile diameter
OPD = Old projectile diameter

So, in the example above, if the 500 yard .30 cal target was originally 30" then the 10 yard target .177 cal target would be 0.34" If we hadn't taken the projectile size into account, it would have been 0.6"

If we look at the 20"x36" target going from 100 to 25 yards without taking projectile size into account, you end up with a 5"x9" target.

If you take projectile size into account and assume you're using a .223 at both distances, you get a 4.83"x8.83" target.

The same calculation but with the assumption that a .30 cal is being used at both distances gives 4.55"x8.55" for the 25 yard target size.

BUT, now what about going from 500 to 25 yards? Assume the use of a .30 cal at 500 yards and a .22LR (.224?) at 25 yards.

A straight scaling yields a 1"x1.8" target as you calculated. Taking the projectile size into account changes that to a 0.79"x1.59" target. That's a reduction of over 20% in one dimension and about 12% in the other dimension.

BUT, now we have another problem. You can end up with a target that LOOKS much smaller than the original target did. In extreme cases, you can end up with targets that are virtually invisible--or at least very tiny--which is what will happen if you do the proper scaling for your 1000yard scaledown. (0.28"x0.68"--.30 at 1000yards, .224 at 25yards) When I make targets like this for my airgun shooting, I make the target so that the black portion is determined by the straight scaling factor so that the target LOOKS the same relative size. Then I put a white scoring line inside the black at a distance determined by the projectile size compensation. That gives me a target that LOOKS the same size as the original did, but will score properly.

P.S. I have no idea if Fred's targets take projectile size into account.

 

[444]

Fred's targets do scale down two 600 yard targets to be shot at 25 meters.
The biggest target on Fred's AQT is scaled down from 200 meters.

But, the important thing is that you are out shooting your rifle. And, you are trying to attain real accuracy and not just shooting beer cans.

Good Job.