Is this trigonometry?

09 January 2003, 03:55

<OTTO>

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

09 January 2003, 05:02

Bill M

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

09 January 2003, 05:03

<TimB99>

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 ]

09 January 2003, 10:37

XWind

quote:
Originally posted by OTTO:
What is the calculation used to figure the expansion of a minute of angle at any given yardage?

Otto,
I ran through this a few posts back and have cut/pasted here for you:

Ready for 'too much information'

I found the 'easiest way to calculate this is with the following formula:

inches X (tangent of 1) / 60

This is based on the basic trigonometric function:
T=O/A
Where T = Tangent of Angle at the shooting position created by a straight line to the target for one shot (Adjacent) and the angle created from the shooting position to the second shot. This second line is technically the hypotenuse but it is not solved for here. You can get that value if you need it.
" A = Adjacent side of triangle (range in inches)
" O = Opposite side of triangle (spread in inches of two target holes...the moa we're solving for)
O is, as mentioned, what we are solving for so the equation becomes: O = T x A / 60

So for 100 yds you get:
3600" x (.01745506492822) / 60 = 1.04730389569306"

There's more than one way to do this but you get the idea...right [Wink]

You can just as easily use O = T x (1/60). One is used because we're interested in the minute(s) of a 1 degree angle. We divide it by 60 to get into the realm of 'minutes'

Here it is out to 1000 yds in 100yd increments
1 MOA=

100 yds = 1.04730389569306"
200 yds = 2.09460779138611"
300 yds = 3.14191168707917"
400 yds = 4.18921558277222"
500 yds = 5.23651947846527"
600 yds = 6.28382337415833"
700 yds = 7.33112726985139"
800 yds = 8.37843116554444"
900 yds = 9.42573506123750"
1000 yds= 10.4730389569305"

Accuracy is +/- .00000000001" or better

It is linear so you can just take the 100 yd number and multiply it by whatever yardage you want/100. So for 375 yds take the 100 yd figure and multiply by 3.75

In practical use if you remember 1.05" / 100 yds the accuracy will be within about .003" (three thousandths) at 100 yds and .030" (thirty thousandths at 1000 yds. Probably close enough I would think.. [Big Grin]

Hey you asked... [Roll Eyes]

So to answer your question, yes this is trigonometry and if you need more detail, just let us know.

XWind

p.s. I've added just a little more explanation of the terms in this post compared to the original...Hopefully to add clarity [Razz]

[ 01-09-2003, 02:35: Message edited by: XWind ]

09 January 2003, 16:54

<OTTO>

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

09 January 2003, 17:25

denton

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.