What is the calculation used to figure the expansion of a minute of angle at any given yardage?

Ottomatic,

A minute of angle is a minute of angle (moa), regardless of yardage. There are 60 minutes in a degree, one moa is 1/60th of a degree. At 100 yards, this is approximately 1 inch (really 1.0472"), at 200 yards ~ 2 inches, 300 yards ~ 3 inches, etc.

A "mil", as in "mil-dot" scope, is one milliradian, or 1/1000th, so one "mil" is one yard at 1000 yards.

You're on the right track,

Bill

You want the big math or the easy math?

Here's both:

1MOA = 1.0472" @ 100 yards, so distance in yards times 0.0105 should give the expansion at that yardage for 1 MOA.

Example, @ 250 yards, 1 MOA is 2.62"

To get there, if you think of a long skinny cone whose angle at the point is 1/60th of a degree (at your rifle muzzle) you can find the diameter of the base of the cone (a circular shape) at any height of the cone by the formula:

Diameter of circle in inches=2*sin(1/120)*(distance in yards)*36

Hopefully if you're doing this you have a scientific calculator that figures sine, cosine, tangent, in terms of angle in degrees. Remember, there are 360 degrees in a full circle, so 1/60th of a degree is a pretty skinny angle.

If not, use the simplified formula above.

Tim

Pay no attention to that man behind the curtain!

[ 01-08-2003, 20:06: Message edited by: TimB99 ]

You guys have made my A-list today! Thanks for the info!

Simpler approach: For small angles, radius x theta = length of the chord, where radius is the distance to the target, theta is the angle in radians (6.28 radians = 360 degrees), and the chord is the distance from "right on" to where the angle intersects the target.

For small angles, theta = sin theta = tan theta.

One minute = .000291 radians.

1 MOA * 100 yards =

.000291 * 100 = .0291 yards = 1.04", to a very good approximation.