Calculation of 1 MOA at 100 yds

[Shoobee]

I recall from one of the posts that someone wanted to determine the width of 1 minute of angle (MOA) at various distances.

The geometry on this is:

Circumference / 360 degrees per circumference / 60 minutes per degree

At 100 yds this comes to 2 x pi x R / 360 / 60

= 2 x 3.14159 x 100 yds x 36 inches per yd / 360 / 60

= 1.05 inches

The algegra is linear, so 200 yds would equal 2.10"

300 yds would equal 3.15"

400 yds would equal 4.2"

500 yds would equal 5.25"

etc.

1000 yds would equal 10.5"

With good ammo and a good scope, 1 MOA groups should be possible.

With really good ammo and a good scope and really good technique, 1/2 MOA should be possible.

[freonr22]

About the markings on the knob and the reticle.
There are two common measurement systems in use on scope knobs as well as some uncommon ones which I will ignore for now.
The most common system is Minutes of Angle, also known as MOA.
The other common system is Milradians, also known as MILS.
Both of these are angular measurments.
One minute of angle is 1/60th of a degree.
Of course there are 360 degrees in a full circle.
So there are 21,600 MOA in a full circle.
One milradian is 1/1000th of a radian and there are 6.283 radians in a full circle.
There are 6,283 MILS in a full circle.
What's important to know is that 1 MOA equates to 1.047" per 100yds and this is commonly rounded to 1" per 100yds.
So, if you are shooting at 100yds, a 1 MOA change is basically 1" on target.
What's important to know about MILS is that 1 MIL is equal to 1/1000th of your distance to target.
So, if you are shooting at 100yds (3600 inches), a 1 mil change is 3.6" on target.
You can convert back and forth between MOA and MILS using the factor of 3.437.
1 MOA = 0.291 MILS or 1 MIL = 3.437 MOA.
I commonly round the factor to 3.5 for easy math in your head.
The following diagram will give you an idea what the angle looks like.



You can see that MILS are much larger units of angle than MOA.
There is another whole thread here that you can read on MOA vs. MILS as it relates to reticles:
http://www.calguns.net/calgunforum/s...d.php?t=154758

here

[brando]

It's even easier with milradians

[dieselpower]

optics forum...

[CSACANNONEER]

I recall from one of the posts that someone wanted to determine the width of 1 minute of angle (MOA) at various distances.

The geometry on this is:

Circumference / 360 degrees per circumference / 60 minutes per degree

At 100 yds this comes to 2 x pi x R / 360 / 60

= 2 x 3.14159 x 100 yds x 36 inches per yd / 360 / 60

= 1.05 inches

The algegra is linear, so 200 yds would equal 2.10"

300 yds would equal 3.15"

400 yds would equal 4.2"

500 yds would equal 5.25"

etc.

1000 yds would equal 10.5"

With good ammo and a good scope, 1 MOA groups should be possible.

With really good ammo and a good scope and really good technique, 1/2 MOA should be possible.

But I thought that an out of the box factory rifle with any cheap ammo and a laser scope could automatically shoot 1/4moa for any shooter???? Isn't that what you posted just a few days ago? It looks like you're actually starting to learn that precision shooting takes a lot more than just an out of the box rifle and a laser scope. That's a good start. Keep learning.

[buffybuster]

1000 yds would equal 10.5"

With good ammo and a good scope, 1 MOA groups should be possible.

With really good ammo and a good scope and really good technique, 1/2 MOA should be possible.

At long range beyond 800yds, in real application, it is no longer a straight linear relationship, as the wind plays a MAJOR factor.

[john doe]

good thread i like this information as i am just getting into all this long range shooting and understanding moa

[CSACANNONEER]

At long range beyond 800yds, in real application, it is no longer a straight linear relationship, as the wind plays a MAJOR factor.

A minute of angle is a minute of angle. It is linear no matter how far you go from the radius. Now, where the bullets may hit is another story but, even that has been tested in real life applications. I know that Randy Dierks, Skip Talbot and a few others conducted a test by putting a bunch of targets in a line at different distances and shooting one group that went through all of them. The results were that the groups (at various distances up to 1000 yards) all measured the same angular difference. I agree that wind plays a factor in accuracy but, if conditions are identical for all shots, wind does not affect precision.

[captbilly]

not sure what younare getting at.

A minute of angle is a minute of angle. It is linear no matter how far you go from the radius. Now, where the bullets may hit is another story but, even that has been tested in real life applications. I know that Randy Dierks, Skip Talbot and a few others conducted a test by putting a bunch of targets in a line at different distances and shooting one group that went through all of them. The results were that the groups (at various distances up to 1000 yards) all measured the same angular difference. I agree that wind plays a factor in accuracy but, if conditions are identical for all shots, wind does not affect precision.

Wind deflection is not a linear relationship to distance to target, just as bullet drop does not vary linearly with distance to target. So it is true that the angular error due to wind increases non-linearly with distance. If the bullet didn't slow down as it moved through the air the angular from wind would vary with the square of the distance to target, but since the bullet is slowing the actual wind error/drift will be larger. Only in zero wind conditions will the bullet pass though a group of targets in a straight line, and even then the targets would have to be aligned along a downward curving line to accomodate for bullet drop.

If you are suggesting that the groups size will not vary with distance from the rifle, that is closer to reality but still not quite. The angular error of a bullet on a target is caused by a number of factors beyond the angular variation with thich the bullet leaves the barrel. An obvious additional factor is the variation of muzzle velocity from one cartridge to the next. At 100 yards the bullet drop variation due to a muzzle velocity variation of 100fps is s only a few hundredths of moa, but at 1000 yards this error grows to about 4 moa since bullet drop is a nonlinear function with distance. This is why long range match ammo needs to be incredible consistent in muzzle velocity, not just accurate at 100 yards.

[Shoobee]

Nice chart, Freonr22.

Most scopes (that I know of) have 4 clicks per MOA.

So that's where your 1/4 MOA illustration comes in handy.

I always do the math in my head, remembering 1 MOA is very close to 1 inch per 100 yds, and one click on the rifle scope is 1/4 inch adjustment per 100 yds.

This all comes into play when boresighting a scope, or calibrating a scope, or fine tuning a scope, or whatever you want to call it.

It also comes into play when adjusting for windage and distance, windage being lateral MOA adjustment and elevation being vertical MOA adjustment.

The wind has to be constant not gusty, for a windage adjustment to be valid. As for me, I am not good at windage adjustments. My general rule is that I only shoot on calm days, otherwise I simply don't take the shot. After all, a man has got to know his limitations.

Elevation adjustments due to range can be put on a range card. There are websites that make these charts for you, where you type-in ballistic coefficient, muzzle velocity, atmospheric temperature and pressure (or topographic elevation), and it cranks out a range card for you. My range card for the California Sierra looks like this:

100 yds = 0.0 (sighted-in for 100 yds)
200 yds = 1.4 moa
300 yds = 3.5 moa
400 yds = 6.0 moa
500 yds = 8.9 moa
600 yds = 12.1 moa
700 yds = 15.9 moa
800 yds = 20.2 moa
900 yds = 25.1 moa
1000 yds = 30.8 moa

It is interesting to note the non-linear progression of these vertical adjustments over these long distances. On an archery target, the non-linear relationship is similar, but you notice it much more quickly, over shorter distances, with either a recurve or a compound bow.

[Shoobee]

good thread i like this information as i am just getting into all this long range shooting and understanding moa

Playing with archery and studying arrow-drop is a good way to understand rifle ballistics and bullet-drop.

[Droppin Deuces]

optics forum...

That'll be the day.

[Shoobee]

It's even easier with milradians

I remember that the US Army, and Navy, and Marine Corps love to use mils in their artillery and naval gunfire adjustments.

And that there are 6400 mils in the circumference of a circle, equivalent to 360 degrees.

http://en.wikipedia.org/wiki/Angular_mil

The wiki tells us that the French artillery invented this.

Once I got used to it, I was used to it. Now I have long since forgotten it.

And now I am back to degrees and MOAs.

Way prior to the French and their mils, the ancient Greeks and Babylonians before them used degrees.

Here is the wiki on where degrees came from.

http://en.wikipedia.org/wiki/Degree_(angle)

[cfusionpm]

But I thought that an out of the box factory rifle with any cheap ammo and a laser scope could automatically shoot 1/4moa for any shooter???? Isn't that what you posted just a few days ago? It looks like you're actually starting to learn that precision shooting takes a lot more than just an out of the box rifle and a laser scope. That's a good start. Keep learning.

My factory, out of the box 700 SPS Tactical shot 1/2MOA just yesterday:



Using American Eagle "7.62 M1A" ammo:



And all I did was watch Magpul's precision rifle DVD a couple times.

[CSACANNONEER]

Wind deflection is not a linear relationship to distance to target, just as bullet drop does not vary linearly with distance to target. So it is true that the angular error due to wind increases non-linearly with distance. If the bullet didn't slow down as it moved through the air the angular from wind would vary with the square of the distance to target, but since the bullet is slowing the actual wind error/drift will be larger. Only in zero wind conditions will the bullet pass though a group of targets in a straight line, and even then the targets would have to be aligned along a downward curving line to accomodate for bullet drop.

If you are suggesting that the groups size will not vary with distance from the rifle, that is closer to reality but still not quite. The angular error of a bullet on a target is caused by a number of factors beyond the angular variation with thich the bullet leaves the barrel. An obvious additional factor is the variation of muzzle velocity from one cartridge to the next. At 100 yards the bullet drop variation due to a muzzle velocity variation of 100fps is s only a few hundredths of moa, but at 1000 yards this error grows to about 4 moa since bullet drop is a nonlinear function with distance. This is why long range match ammo needs to be incredible consistent in muzzle velocity, not just accurate at 100 yards.

I'm getting at the fact that well respected bench rest shooters have lined up targets (yea, in an arc along the flight path of the projectiles) and shot 5 shot groups through all the targets at once. In the end, the largest deflection angle of each group (in layman's terms "the moa of each group") was the same. Sure, these shooters load some of the best ammo in the world. Sure, this was only one test. Sure, wind does effect POI but consistant wind consistantly affects the POI and a very consistant wind does not affect precision at all. In the end, a 1000 yard 2moa group would have been a 100 yard 2 moa group. Nothing more and nothing less. Now, that does not mean that every 100 yard 2 moa group will be a 2 moa group at 1000. There are factors like ammo going subsonic and different conditions which may appear over the 600 yard berm but, given consistant conditions, even consistant wind, group sizes (measured by angular deflection in MOAs) will stay constant. There is not some magical wind troll that starts making bullets fly differently when they pass get 800 yards from the muzzle. There can be varying conditions anywhere along the bullet's flight path and these conditions will always take their toll. But, I was not refering to varying conditions. I was talking about real world testing which indicated that the bullet spread stays consistant as long as the ammo and everything else is consistant too. Wind only plays a factor on precision if it is inconsistant. Wind will alway play a factor in accuracy though.