Sniper Math

[TaintedArt]

Hey All,

To preface this, I know the calculations on how to figure out size at a distance and things of that nature. I am pretty confident on how to use my mil-dot for calculations.

And Granted there are huge factors that play a role when you increase distance but this would be a pure exercise in target size in the scope. And getting comfortable with it.

However, And I may be biting off more than I can chew here, but I have a pretty big math question for you. I have heard rumors about elite units shooting the tops off of match sticks at a very close distance and that representing a head shot at a very lengthy distance.

I want to know how to make smaller targets to shoot at closer distances that represent normal targets at further distances.

How do I do that?

Example:
Lets say my intended target is 11". At 100 yards that 11" will appear as (A) big. At 10 yards I can make my target (B) to appear as (A) which will duplicate those 11" at 100 yards.

I hope I am getting my point across and that somebody may have some type of math for that?




A buddy of mine came up with this. What do you guys think?


<span style="font-style: italic">Ok, so quick response because we've been discussing this for the last 20 minutes or so, but I wanted this posted so that someone could check my math.

Using the formula:

For distance in yards: (27.77 X Target Dimension) ÷ Mil Reading = Range

we found here, I solved for mil for a 11" x 8" target @ 100 yards = 3 x 2.2

Using those mil numbers, I solved for target dimension based on 10 yard range, and came up with 1" by .8" to "fill" the same mil readings as the original 11" x 8" target @ 100 yards.

Can someone spot check my math and/or confirm I'm even using a correct forumla?
</span>

 

[Exo]

Re: Sniper Math

tag

 

[ArmsB]

Re: Sniper Math

so to get range you take :
(target in in.x25.4)/target size in mils=range in meters

and the equation youre wanting
range in meters x target size in mils/25.4=target size in inches

an 11 in. target at 100m appears to be 2.794 mils (im only going to the thousands to balance the equation, i know you cant read mils that accurately)

so to make the target at 10m appear to be 2.794 mils it should be 1.1 inches

I know you wanted it in yards, but i didnt know the conversions off the top of my head. The same reverse algebra should give you it for yards if you sub the yard conversion for the meter conversion(25.4)

god help me if im wrong ha.

 

[gstaylorg]

Re: Sniper Math

Remember that you're dealing with an <span style="font-style: italic">angular</span> measurement. The angle doesn't change with distance, regardless of whether you're using MOA, mil, or even quatloos for that matter. What changes is the arclength that is subtended by that angle as distance (ie. the radius of the circle) changes. In the cartoon below, you can see that a for a specific angular measurement, the only thing that changes as the distance (radius of the circle) increases, is the arclength. More importantly, it increases proportionally to the increase in the radius.

So one MOA subtends an arclength of 1.0472" at a distance (radius) of 100 yd. At 1000 yd, one MOA subtends an arclength of 10.472", or ten times greater that that subtended by the same angle at 100 yd. The angular measure itself (one MOA) did not change.

Using the above example, you can then calculate A) the specific distance where an object of given dimensions will appear to be the same size as an object of different dimensions at a different distance; or B) the dimensions an object must be at a specific range to appear to be the same size as an object of different dimensions at a different distance:

Object 1 = 10.472" square (Dimension 1) at 1000 yd (Range 1)

Object 2 = 1.0472" square (Dimension 2) at 100 yd (Range 2)

Note that both Dimensions 1 and 2 are the arclengths subtended by <span style="font-style: italic">one MOA</span> at Ranges 1 and 2, respectively. The mathematical relationship between D1, D2 and R1, R2 is as follows:

D1/R1 = D2/R2 [or R1/D1 = R2/D2, it doesn't matter which]

You need any three of these numbers to solve for the 4th. To use your example of an 11" target at 100 yd, it's pretty intuitive that it will need to be 1.1" at 1/10th the distance (10 yd) in order to satisfy the equation above. However, let's say you wanted to determine how big a target needed to be at 17 yd to appear the same as an 11" target at 100 yd.

So, D1 = 11" and R1 = 100 yd, and you know that R2 = 17 yd. Plug in the numbers and solve for D2 and you'll see that D2 (Target 2 dimensions) will need to be 1.87" to appear the same size at 17 yd as an 11" would at 100 yd. Alternatively, if you want a 2" target to appear the same size as your 11" target at some distance, again just plug in the three numbers you have and solve for the unknown distance (18.18 yds).

It's simple proportionality, so there are only a couple things you need to know for this to work. As I mentioned, you need three of the four numbers (ie. two different ranges and one target dimension or two different target dimensions and one range) . You also need the units to be the same for either the two ranges, or the two target dimensions. The output units will be the same as your 3rd known variable. The beauty is that it doesn't matter whether you're using mil or MOA, yards or meters. As long as you keep the units the same, it will work, and you don't have to memorize any conversion factors. The other consideration for what you're trying to do will be how close can you actually focus your scope and on what magnification. The above is true for a constant mag setting on the scope. But you'll likely have to back way off on the mag to see an object in clear focus only 10 yds away. Chuck's IOTA (Indoor Optical Training Aid listed in the Equipment forum was designed for this very reason). Anyhow, if you have to decrease the mag to see an object up close, whatever the proportional change in mag is will also have to be taken into account with respect to the object size.

 

[Enough Said]

Re: Sniper Math

:vomit:

 

[DP425]

Re: Sniper Math

I'm not totally sure I understand what you are trying to do. On the face of it, it appears you want to scale your targets down. Why the fuck are we talking mils, mil-relation formula and what not if that is the goal?

You want a target to appear as though it is at 100 yards? What does the 100 yard target measure? What distance do you want it to appear the same as at 100 yards?


Let me make this so very simple:
make a 20x20 target at 100 yards appear the same at 10 yards.
100/10=10
20/10=2
target size at 10 yards=2x2

20x20 target at 100 yards appear the same at 500 yards
500/100=5
20*5=100
target size at 500 yards=100x100

20x20 target at 1000 yards appear the same at 50 yards
1000/50=20
20/20=1
target size at 50 yards=1x1



If I'm not following your intended goal here, I apologize- but if this is, in a nut shell, what you are trying to do... stop making it complicated.

 

[DP425]

Re: Sniper Math

One more thing- if you have to reduce mag, multiply your scale adjusted size by precent mag used at your close range:

50x50 target at 1000 yards, same appearance at 10 yards
1000/10=100
50/100=0.5

shooting 15x at 1000 yards and 3x at 10 yards
3/15= 0.2 (this is, 20% of the 15x magnification)

Take your reduced size target dimensions, multiply by precent of magnification you are going to use:
0.5*0.2= 0.1



So here we have completed ALL steps required to do the following:
-Target measuring 50"x50" actual size at 1000 yards, engaged using a scope on 15x...
WILL APPEAR THE SAME AS
-Target measuring 0.1"x0.1" actual size at 10 yards, engaged using a scope on 3x.

 

[Augustus]

Re: Sniper Math

Divide the dimensions of the 100 yd target by 10. Presto it is to scale at 10 yds. Mils has nothing to do with it. Your 11 by 8 100 yd target should be 1.1 by .8

Don't believe a scaled down target at 100 yds will prepare you to shoot at 1000 yds. There are a lot of gremlins tugging at your projectile over that extra 900 yds.

 

[Sterling Shooter]

Re: Sniper Math

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Augustus</div><div class="ubbcode-body">Divide the dimensions of the 100 yd target by 10. Presto it is to scale at 10 yds. Mils has nothing to do with it. Your 11 by 8 100 yd target should be 1.1 by .8

Don't believe a scaled down target at 100 yds will prepare you to shoot at 1000 yds. There are a lot of gremlins tugging at your projectile over that extra 900 yds.</div></div>

The gremlins are related mostly to not countering for wind correctly and not mustering a position which gets consistent recoil resistance. These errors are masked at SR. Nevertheless, I use a 4.5 inch bull for 1000 yard practice at 100 yards and attempt to shoot zero dispersion for 20 round strings of fire by concentrating on making my position perfect. Some of my rounds will indeed go though previous bullet holes but with irons and sling support I feel real good if I can hold to a 1/2 minute. This translates for me to about 2 MOA at 1000 yards in actual match conditions (NRA LR Service Rifle Division).

 

[TaintedArt]

Re: Sniper Math

I completely understand the gremlins and know not to get water on them or feed them after midnight...

On a serious note, I do know they exist and know what to do to correct them.

But, Like stated above, It is more an exercise in scope visuals and basics. If you can get used to a 1/2 mil or less target you wont get flustered when you see that at 1000 yards. Once you dial in your winds, surroundings and bullet type you will essentually feel right at home. And to be quite frank sometimes I just do not have 1000 yards to play with.

Thanks for all the input guys. I feel good about this and will start getting some targets made up.

 

[Sterling Shooter]

Re: Sniper Math

Interestingly, I don't see, when using a scope, how anyone could be intimidated by the 1000 yard NRA LR bulls-eye. But, for a Service Rifle shooter, relying on picture memory to hit the target using irons, it can be a challenge, especially, if the shooter has not practiced on some sort of equivalent reduced course target to develop picture memory.