MATH - how do I convert click-moa/mil value when sight radius changes?

[sb_pete]

Hello all,
I am sure there is a previous thread somewhere that covers this, but I cannot find it. I'm probably just using the wrong keywords. If that's the case, sorry, please just point me in the right direction and I'll shut up and move along...

In any case, my specific situation is that I want to figure out the click to moa/mil value of a 1/4MOA and 1/2 MOA A2 sight designed for use on a rifle length (M16A2) weapon when placed onto a carbine length weapon. I am trying to figure out what the click values of a detachable carry handle (looking at pinned NM 1/4MOA & 1/2 MOA - WOA, CLE or Keystone Accuracy) which is designed and calibrated for use on 20" bbl A2 Rifles will be when used on a std military M4 (14.5" bbl with std FSB).

Additional questions:
1. I don't actually know what the spec'd sight radius is for either configuration. Does anyone know the actual spec of the sight radius for rifle and carbine length ARs (using FSB)?

2. How do you go about calculating the conversion based on a known click value for one sight radius to a different sight radius? EG: sight radius 1 (SR1), Sight Radius 1 Click Value (SR1-CV) and Sight Radius 2 (SR2) are known, but Sight Radius 2 Click Value (SR2-CV) is unknown.

3. What about the formula for moa/mil per click when you know the sight radius length and the value of the vertical movement each click represents?

Thanks in advance guys,
-Pete

[FMJBT]

Based just on sight radius, I'd calculate the difference using the shorter carbine length as a percentage of the rifle length the sight was designed for. I don't have the specific dimensions, but figure the carbine length would be roughly 70% of the length of the rifle sight radius. The shorter sight radius will result on greater angular movement for a given adjustment, so you'd need to divide the moa/mil values by that 70% (just guessing on that) figure to get your larger corrected value.

[Unretarded]

This could be a case of lots of hours of speculative math or a few hours shooting to see exactly what happens.........which will be the case anyway after all the math. You will need to shoot and confirm........take the shortcut , shoot and document, then compare.

There are a lot of variables to get right for the math to be even close.

[Fjold]

The math is actually pretty easy. The formula is:

0.25" at 100 yards / Rifle sight measurement = X at 100 yards / Carbine sight measurement


Change that to:

(Carbine sight measurement * 0.25 at 100 yards) / Rifle sight measurement = The amount of X at 100 yards


Let's say the rifle measurement is 20" and the carbine sight distance 16" That would be (16" * 0.25") / 20" which would equal 0.20" per click at 100 yards.




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[sb_pete]

This could be a case of lots of hours of speculative math or a few hours shooting to see exactly what happens...

While you are right, Unretarded, the larger problem here is that that is not always possible or plausible in an institutional setting. Arms room weapons and gov't ranges do NOT lend themselves well to testing and experimenting. While, I can figure out my specific usage question on my own time with my own weapons at private ranges now, when the question came up, doing so was out of the question. Stupid, but that's how things roll in .mil

The math is actually pretty easy. The formula is:

0.25" at 100 yards / Rifle sight measurement = X at 100 yards / Carbine sight measuremen...

BAM! That's what I needed. Thanks Fjold!

[sb_pete]

Well, now that I think about it, the formula you give is almost what I am looking for. The only issue is that the formula is not done in angular units of measure (MOA/MILS), but rather based on extrapolation.

It is formulated as a given POI shift at a given range for a given sight radius. When calculated in inches for sight radius and inches for POI shift @ 100 yds, this basically gives you MOA, but it is not readily adaptable to other units of measure or ranges...

[Fjold]

The units don't matter.

If one click is 1/4 MOA then just change the .25" to .25 MOA, So the formula is:

(Carbine sight measurement * 0.25 MOA at 100 yards) / Rifle sight measurement = The amount of MOA at 100 yards

Rifle site radius = 20" and carbine sight radius 16", the formula be (16" * 0.25 MOA) / 20" which would equal 0.20 MOA per click at 100 yards.



If you are talking mils and one click is 1/10 Mil then the formula is:

(Carbine sight measurement * 0.1 Mil at 100 yards) / Rifle sight measurement = The amount of Mil at 100 yards

Rifle site radius = 20" and carbine sight radius 16", the formula be (16" * 0.1 Mil) / 20" which would equal 0.08 Mil per click at 100 yards.



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[sb_pete]

The units don't matter.

I just did a whole bunch of math. It seems you're right. I don't know why it strikes me that it would matter, but it sure doesn't seem to.


For my specific purpose
(0.25 * 20.25) / 14.25 = X
5.0625 / 14.25 = 0.355
So call it 1/3 MOA Clicks when a 1/4moa A2 sight is mounted on an M4

[sb_pete]

a bunch of calculations to prove the formula
I went down the rabbit hole and did it all in MOA instead of the quick approximation. It seems to make no difference. I'm assuming because the conversion factor in and out is the same.
It looks like this:
0.25MOA * 1.047 = .26175" @ 100 yds
(0.26175 * 20.25) / 14.25 = 0.3719605263
0.3719605263 / 1.047 = .3552631579 = 0.355 = No measurable difference when using something as small as 1/4 MOA clicks @ 100 yds - the quick math works fine for that.
Even taking it out to 1000 yds and using the Front Sight (1.25 MOA / click) we don't get enough variation to matter - Actually, I don't get any. Maybe I'm doing it wrong...
1.047*1.25*10 *20.25= 265.021875 / 14.25 = 18.598026316 / 10 = 1.8598026316 / 1.047 = 1.7763157895 = 1.78
vs
1.25*10*20.25 == 253.125 / 14.25 = 17.763157895 / 10 = 1.7763157895 = 1.78

Seems that the units really don't matter.

[sb_pete]

FORMULA RESTATED

to convert the click value of iron sight adjustments from the original sight radius to a new one

(SR1-CV * SR1) / SR2 = SR2-CV

where:
SR1 & SR2 = Sight Radius #1 & #2
SR1-CV & SR2-CV = the POI shift click value at a given range of the sighting system using SR1 or SR2

for my 1/2 MOA & 1/4 MOA A2 Carry handle sights, when mounted on an M4:
(0.25 * 20.25) / 14.25 = .355 = ~1/3 MOA for 1/4MOA sight
(0.5 * 20.25) / 14.25 = .71 = ~2/3 MOA for 1/2MOA sight

Thanks Fjold!