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Old December 30, 2000, 06:55 PM   #1
Correia
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I know what Minute Of Angle means to most of us. But I'm not sure that I'm thinking of it correctly in a technical sense. Do any of you know where I can find a proper definition for MOA?
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Old December 30, 2000, 07:07 PM   #2
WalterGAII
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Am I nuts, or have you already initiated a thread like this before and had this explained to you in pretty good detail?
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Old December 30, 2000, 07:21 PM   #3
Steve Smith
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Rather than me typing an hour, go to this sight and read the page...the explanation of MOA is near the bottom.

http://www.swfa.com/mildot/index.html
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Old December 30, 2000, 07:29 PM   #4
James K
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Hi, Correia,

The question has been asked and answered before, but here it is in brief. A circle has 360 degrees, each of which is divided into 60 minutes and each minute into 60 seconds. Think of the protractor you had in grade school, with the little degree markings. If a rifle shooter is thought of as being at the center of the circle, the size of his group can be described in minutes of angle (MOA) or how big an arc the shots cover. By conicidence, one minute of angle equals about 1 inch at 100 yards, 2 inches at 200 yards, and so on.

So a rifle (and shooter) capable of placing a group of shots within a 1" circle at 100 yards is "shooting one minute of angle". Conventionally, groups are five shot unless otherwise specified, and group size is measured center to center of the farthest apart bullet holes. (If a center to center measurement is not feasible, the distance from the outside edges of the farthest apart holes can be measured, and the bullet diameter subtracted. This gives the same result.)

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Old December 30, 2000, 09:55 PM   #5
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Specifically, that would be a 1 inch radius circle at 100 yards.

See, since 100 yards equals 3600 inches and we're talking about a 1" radius circle at that range, we have an easy Trig problem: arcsin(1/3600) ~= .015915 degrees, which is sufficiently similar to one minute (1/60 degree) ~= .016667

Make sense now?
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Old December 30, 2000, 10:32 PM   #6
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Destructo6, Isn't it a 1" arc at 100 yards, not a circle with a 1" radius? Wouldn't a circle with a 1" radius equal a 2" diameter circle, and therefore a "1 MOA" rifle would shoot 2" groups?
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Old December 30, 2000, 10:56 PM   #7
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1 MOA = .0166666 degrees = total arc length of 1.0472 inches at 300 feet.

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Old December 30, 2000, 10:58 PM   #8
WalterGAII
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Destructo sound so cool, but he be wrong wid his math.
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Old December 31, 2000, 01:55 AM   #9
Bud Helms
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Search Results for the string <MOA>, Match All, Any Date, All Forums, Subject Only. There's only eleven threads on this subject besides this one. Did you do a search, Larry?
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Old December 31, 2000, 02:53 AM   #10
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I'm not sure why arc length is being brought into this, seeing as the relation of arc length to radius is: arc length = radius * angle (in radians). Sure enough that the arc length of a sector with a 3600" radius and angle of one minute is .523599", but why would we be messing with an arc when we're measuring distance on a flat surface?

Aren't we talking of an angular deviation of the bullet impact to the point of aim? If so, then one minute at 100yds will give a circle with a ~1" radius.
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Old December 31, 2000, 07:22 AM   #11
Ruben Nasser
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IT'S A 1" DIAMETER!!!!

Destructo, your math is right, but a MOA group is defined, as Jim Keenan put it: "...a group of shots within a 1"... Conventionally, groups are five shot unless otherwise specified,and group size is measured center to center of the farthest apart bullet holes."
So, we are not dealing with the deviation of the shots from the theoretical path (which, as you said,would lead to a 1" radius, and thus 2" grouping), but what we are doing is measuring the angle that subtends (covers) the entire group.
Then by definition, this arc (it's an arc, but due to the minute angle we can aproximate it to a line for the calculation you just did) it's the diameter of the group.
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Old December 31, 2000, 01:22 PM   #12
Patrick Graham
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This really covers it well

http://www.recguns.com/XIIC4.html

one inch group at 100 yards is really 0.95 MOA group
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Old December 31, 2000, 04:14 PM   #13
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Ah, I think I have it now...

We're measuring the small angle from of an isosceles triangle, whose legs are at the edge of the group, not a right triangle whose long leg is perpendicular to the target and centered in the group, having the hypotenuse at the edge of the group. That would explain why my calculation was exactly double the value given by the proper definition of MOA.

That's interesting.



[Edited by Destructo6 on 12-31-2000 at 11:08 PM]
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Old December 31, 2000, 10:40 PM   #14
Correia
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Thank you gentlemen.

Walter, I have never asked this before. (That I can remember).

sensop. I apologize, I was just reading along and thought of this question, and I did not bother to search. Of course, about fifteen minutes after I posted this I thought to myself: "You know I bet somebody else has asked this question and I just forgot." I'm going to feel really dumb when I look at your list and see something posted by me in one of the discussions.

And I will be honest, I wanted a technical definition because I am writing a small work of fiction that is very gun related and I just thought that Minute Of Angle sounded like a really cool title.
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Old January 1, 2001, 02:13 AM   #15
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Quote:
I wanted a technical definition because I am writing a small work of fiction that is very gun related and I just thought that Minute Of Angle sounded like a really cool title.
Naaaa, if there is going to be precision shooting in it title it "Second of Angle". Now that, IMO, would be a catchy title.

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Old January 1, 2001, 11:26 AM   #16
Bud Helms
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Jeez.

*********************
Larry, no problem. I have done that very thing. But you will be surprised when you read some of them.
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Old January 1, 2001, 03:29 PM   #17
Correia
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Yea, Schmit you might like the it when I'm done. It has a few Marines in it.
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Old January 2, 2001, 01:22 AM   #18
Schmit
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> Yea, Schmit you might like the it when I'm done.

Hehehe... why don't you send me your draft? I'll look it over and see if I can provide any assistance.
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Old January 13, 2001, 02:56 PM   #19
Michael Priddy
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You know fellows,it is really more of a solid geometry problem. If the tip of the cone is at the bore of the rifle and the base of the cone forms an imaginary circle on the target paper with a diameter on one inch, then every hole totally inside the circle would be within a moa. If you have to open up the circle to get all the holes in, it will open up the angle of the cone past a moa. BUT if you can cover them all with a dime, who cares about the math/geometry?
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Old January 29, 2001, 10:54 PM   #20
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For the metrically inclined, 3 cm @ 100m is a closer approximation (3% error) to 1 MOA than 1 inch @ 100 yards (4.7% error)
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Old January 30, 2001, 10:33 AM   #21
Correia
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Schmit. Actually when I get to that point, I probably will need some proof readers with solid real world experience. I'll e-mail you about it when I'm closer to being done. But I have a long way to go, I'm on page 106. So figure another 400 pages or so, probably sometime in 2002.
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Old January 30, 2001, 02:57 PM   #22
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Bear with me...

Somebody said this before, but we'll try again...

There are 360 degrees in a circle. Another more useful form of angular measure is the radian. There are 2*pi radians in a circle, or 180 degrees is pi (3.1416) radians. A minute of a degree is 1/60 of a degree. Or, if you're really nerdy, 1/60 degrees times 3.1416 radians/180 degrees gives .0002909 radians. "my rifle shoots .0002909 radians".

The fun thing about the radian is that one can get arclength simply by multiplying angle measure in radians times the radius of the arc. For example, everybody knows that the circumference of a circle is 2*pi*radius or pi*diameter. 360 degrees is 2*pi radians, or 6.2832 radians. multiply 6.2832 by the radius of the circle and you get the circumference (arclength of 360 degree angle).

Take a circle 600 feet in diameter (100 yard radius). 0.0002909 radians times 300 feet times 12 inches/foot gives 1.0472 inches for the arclength of 1/60 degree at 100 yards. Somebody also had a concern about this arc not being a straight-line measurement. Get yourself 100 yards of spectra fishing line, tie it to a post, go out 100 yards and tie a pencil to the string. use the pencil to draw a 1" long arc, and see how much it varies from a straight line.

Did this help?
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