meaning of MOA?


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Charles W Webb
November 15, 2005, 01:42 AM
Well I am wanting to get into long range shooting and such and I have heard the term MOA alot but have never found out its meaning. Any info would be apreciated, thank you.

Charles

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Canuck-IL
November 15, 2005, 01:46 AM
Roughly an inch at 100 yards...see ref for details
http://riflestocks.tripod.com/moa.html
/B

Domino
November 15, 2005, 01:47 AM
If I am not mistaken MOA stands for "minuted of angle"

This refers to accuracy based on how many inches a gun shoots at the distance of 100 yards.

If a rifle shoots at 2 MOA it means that it groups 2" at 100 yards.

Charles W Webb
November 15, 2005, 01:55 AM
Thank you both for taking the time to answer my post.:cool:

rockstar.esq
November 15, 2005, 02:03 AM
Minute of angle.
Not so common vernacular.
A degree of angle is further divided into 60 minutes and further 60 seconds. Minute of angle refers to the tangent of the greatest group dispersion divided by the radius (linear distance to said target). By most accounts 1/60th of one degree is considered fine accuracy. The actual dispersion of 1 MOA at 100yds is .96 inches. Most folks assume one inch and tack on another every hundred yards. For example one minute of angle accuracy at 1000 yds would be 10 inches!

Hawken50
November 15, 2005, 08:36 AM
Most folks assume one inch and tack on another every hundred yards. For example one minute of angle accuracy at 1000 yds would be 10 inches!

dosen't it double with every hundred yards?

1moa @ 100yrds = 1 in
1moa @ 200yrds = 2 in
1moa @ 300yrds = 4 in
1moa @ 400yrds = 8 in
1moa @ 500yrds = 16 in

i have been wrong before...once.

USSR
November 15, 2005, 08:49 AM
MOA - Minute of Angle.

1MOA = 1.047" @ 100 yards
1MOA = 2.094" @ 200 yards
etc.

1MOA is typically rounded off to 1 inch. Long range competitors and snipers make scope adjustments/corrections in MOA - not clicks. If you have a typical scope with 1/4" adjustments and you are shooting 3" low at 100 yards, your spotter will tell you to come up 3MOA - not 12 clicks. Hope that helps.

Don

Swampy
November 15, 2005, 09:14 AM
The actual dispersion of 1 MOA at 100yds is .96 inches.

A true geometric "Minute of Angle" is 1.047" at 100 yds, 2.094" at 200 yds.... etc....

A SHOOTERS "Minute of Angle" is 1.00" at 100, 2.00 at 200..... and etc...

dosen't it double with every hundred yards?

1moa @ 100yrds = 1 in
1moa @ 200yrds = 2 in
1moa @ 300yrds = 4 in
1moa @ 400yrds = 8 in
1moa @ 500yrds = 16 in

i have been wrong before...once.

Now it's twice.....:p
The progression of MOA is geometric, not exponential.....

1moa @ 100yrds = 1 in
1moa @ 200yrds = 2 in
1moa @ 300yrds = 3 in
1moa @ 400yrds = 4 in
1moa @ 500yrds = 5 in

Best to all,
Swampy

Garands forever

GoRon
November 15, 2005, 09:55 AM
Here is a great post from TFL that I copied for future reference.

A circle is divided into 360 degrees.

Each degree is divided into 60 minutes.

If you pretend you are at the centerpoint of a circle and the target is on the circumference of the same circle then you can measure your accuracy in minutes of angle.

So, let's say you are 100 yards away from your target.

That makes the radius of the imaginary circle 100 yards. We can calculate the total circumference of the circle using 2 x pi x radius.

The total circumference of the circle is then 628.32 yards. Divide the circumference by 360 to get the distance on the circle defined by a single degree.

One degree of angle on a 100 yard radius circle is therefore 1.745 yards.

Now, divide that by 60 to get the distance on the circle defined by a single minute.

When we do that we find that one minute of angle on a 100 yard radius circle is 0.029 yards or 0.087 feet or 1.047 inches. That's pretty close to one inch and most folks just call 1 MOA and 1 inch the same thing at 100 yards.

You can calculate what 1MOA is at any distance using the following formula.

1MOA (inches) = distance (yards) / 95.49

At 50 yards, 1 MOA is 0.52 inches
At 75 yards, 1 MOA is 0.79 inches
At 150 yards, 1 MOA is 1.57 inches
At 250 yards, 1 MOA is 2.62 inches

Note that most people approximate these numbers by rounding them DOWN to the nearest quarter inch in practice. That makes it easy to calculate--simply divide the yardage number by 100 to get the APPROXIMATE value of 1 MOA in inches.
__________________

Rockstar
November 15, 2005, 10:03 AM
Well, rock, at least your name was on-the-money! :)

benEzra
November 15, 2005, 10:51 AM
One thing that's confusing is that in most technical fields, "minutes of angle" are usually called arcminutes. One arcminute (e.g., 1 MOA) is 1/60 of a degree. In astronomy, you'll also see arcseconds, 1 arcsecond being 1/60 of an arcminute.

An arcminute/MOA is a TINY angle. To put it in perspective, the earth rotates one arcminute/MOA every 4 seconds...

Hawken50
November 15, 2005, 11:00 AM
i have been wrong before...once.


Now it's twice.....


awww nuts, there goes my track record of near perfection.

Bwana John
November 15, 2005, 01:04 PM
Actually MOA measures the angle that the group subtends, it is NOT a linear measurment.:banghead:
This method of quantifying group size only "works" for very small angles.:cuss:
The math is actually much easier if radians, instead of degrees are used.:evil:

A more accurate method might be: 2 X arctan (1/2 group size / distance to target). This method would relate linear group size to the change in angle the barrel experances, without the problems of compairing radius to circumference.

AND just because a rifle shoots 1 inch groups at 100 meters does NOT mean you will shoot 10 inch groups with it at 1000 meters.:scrutiny:

USSR
November 15, 2005, 01:55 PM
...just because a rifle shoots 1 inch groups at 100 meters does NOT mean you will shoot 10 inch groups with it at 1000 meters.

Ahhh, you noticed that too.:D

Don

Zak Smith
November 15, 2005, 03:17 PM
Actually MOA measures the angle that the group subtends, it is NOT a linear measurment.:banghead:
This method of quantifying group size only "works" for very small angles.:cuss:
The math is actually much easier if radians, instead of degrees are used.:evil:

A more accurate method might be: 2 X arctan (1/2 group size / distance to target). This method would relate linear group size to the change in angle the barrel experances, without the problems of compairing radius to circumference.

For any rifle type accuracy measurements, the error between the linear distance and circumferential distance is about 7 / 1,000,000,000. In other words.. WAY past the number of significant figures you can measure in group size anyway. In summary, for rifle accuracy, use 1.047 or 1.0472" per 100 yards.

-z

Swampy
November 15, 2005, 03:40 PM
AND just because a rifle shoots 1 inch groups at 100 meters does NOT mean you will shoot 10 inch groups with it at 1000 meters.

Granted..... but up until this point I don't think that's what the issue was.... It WAS just about defining what a shooters MOA was, not what a rifle was capable of....

Now maybe's the time to switch tracks??? :p

Just my opinion,
Swampy

garands forever

ScopedOut
November 15, 2005, 04:41 PM
So a rifle capable of, say, 3/4 MOA at 100m is not necessarily capable of 3/4MOA at 900m? I'm guessing that factors both intrinsic to the rifle (bedding, spin rate, muzzle velocity, load consistency), and extrinsic (wind, humidity) play a role in widening the cone of precision?

Here's my chance to learn. Any takers?

Granted..... but up until this point I don't think that's what the issue was.... It WAS just about defining what a shooters MOA was, not what a rifle was capable of....

Now maybe's the time to switch tracks??? :p

Just my opinion,
Swampy

garands forever

Swampy
November 15, 2005, 04:55 PM
So a rifle capable of, say, 3/4 MOA at 100m is not necessarily capable of 3/4MOA at 900m?

True.....

Once the bullet leaves the muzzle it's "on it's own" so to speak and each bullets individual idosyncrasies and imperfections come into play with where it ends up at the terminal point of the trajectory..... i.e. dispersion from the ideal. :(

It's generally said of a bullet-load-rifle combo that, "If it's gonna' shoot 1 MOA at 600 yds (the size of the MR target X-ring is 6" diameter) it'd better shoot 1/2 MOA at 100 yards".

No hard rule that for certain... but just a common saying among Highpower shooters. There is some truth to it for sure.......

Best regards,
Swampy

Garands forever

30Cal
November 15, 2005, 05:10 PM
Velocity, drop and windage aren't a linear function of range (there's no straight line in a bullet's trajectory). Makes sense that accuracy isn't either.

Molon Labe
November 16, 2005, 12:43 PM
O.K., dumb question time:

If a firearms manufacturer says one of their rifles has an inherent accuracy of 1 MOA at 100 yards, what exactly does this mean?

I can think of two definitions:

1. The maximum error is 1 MOA. This means the point-of-impact (POI) will have a maximum error of 1.047" from the point-of-aim (POA) at 100 yards (error = POI - POA). If we use this definition, then a group of shots will have a maximum radius of 1.047", which means the maximum diameter of the group will be 2.094".

2. The maximum diameter of the group is 1.047". This means the worse error (error = POI - POA) is 0.5235".

So which is it? I assume it's #2.

Zak Smith
November 16, 2005, 12:57 PM
There is usually no concept of "error" of POA away from POI, the logic being that you can adjust the point of aim to the center of the group.

Group size is normally the maximum center to center distance for a 3, 5, 10, etc, shot group. In practice, it is easiest to measure by measuring the maximum outside to outside distance and subtacting one bullet diameter.

-z

USSR
November 16, 2005, 01:28 PM
O.K., dumb question time:

If a firearms manufacturer says one of their rifles has an inherent accuracy of 1 MOA at 100 yards, what exactly does this mean?

I can think of two definitions:

1. The maximum error is 1 MOA. This means the point-of-impact (POI) will have a maximum error of 1.047" from the point-of-aim (POA) at 100 yards (error = POI - POA). If we use this definition, then a group of shots will have a maximum radius of 1.047", which means the maximum diameter of the group will be 2.094".

2. The maximum diameter of the group is 1.047". This means the worse error (error = POI - POA) is 0.5235".

So which is it? I assume it's #2.

Molon,

First, manufacturers don't use the term "inherent accuracy". Only guys on website forums who believe certain cartridges possess mythical powers, and any rifle you chamber in that cartridge will be accurate use these terms.;) You are correct in your assumption that it is your #2 definition, although the .047" is usually dropped. The number of rounds fired to constitute a group are specified (usually 3 or 5), and although the type of ammo used is usually not specified, it is assumed to be match ammo such as Federal Gold Medal Match. The really top gunsmiths will guarantee the rifles they build to deliver 0.5" groups at 100 yards.

Don

Molon Labe
November 16, 2005, 01:42 PM
manufacturers don't use the term "inherent accuracy". Only guys on website forums who believe certain cartridges possess mythical powers, and any rifle you chamber in that cartridge will be accurate use these terms.;)I guess I was referring to the accuracy of a rifle that is mounted in a vice. In other words, the inherent, "mechanical" accuracy of a rifle + ammo combination.

USSR
November 16, 2005, 03:22 PM
Molon,

Nobody shoots their rifle in a "vise".

Don

Medusa
November 16, 2005, 04:22 PM
Well, the coefficient of friction is proportional to the speed, at high speed it's proportional to the velocity's square, at lower speed to the velocity itself. So the trajectory of flight has a shape of ballistic curve instead of perfect arc, besides, other factors that affect the projectile's flight are gyroscopic effect, then the lift created by the spin (total blackout on the effect's name :cuss: ), drag that depends on bullet's shape (whether the airflow is laminar or turbulent at the boattail), then of course the Coriolis effect, differences in air density (by pressure and temperature) over the flightpath, fluctuating gradient vectors of pressure and temperature. Hmm did I miss something? surely did :banghead: Did I mentioned wobbling hands and breathing at the wrong time?

benEzra
November 16, 2005, 04:26 PM
Molon,

Nobody shoots their rifle in a "vise".

Don

He's probably thinking of a machine rest.

Molon Labe
November 16, 2005, 04:53 PM
Molon,

Nobody shoots their rifle in a "vise".

Don"Machine rest." Whatever.

The point I was trying to make is that a rifle has an "inherent accuracy" independent of the skill of the shooter. To measure this, simply mount the rifle in a sturdy machine rest and actuate the trigger with a solenoid. The pattern after multiple shots will be a 2D Gaussian distribution.

MachIVshooter
November 16, 2005, 07:24 PM
So a rifle capable of, say, 3/4 MOA at 100m is not necessarily capable of 3/4MOA at 900m? I'm guessing that factors both intrinsic to the rifle (bedding, spin rate, muzzle velocity, load consistency), and extrinsic (wind, humidity) play a role in widening the cone of precision?

Here's my chance to learn. Any takers?

Not being a physicist, I will go out on a limb and say that reason for this is going to be external variables, as Medusa oulined. I would hypothesise that, under perfectly consistent atmospheric conditions, the MOA would not change. Meaning, if air density, barometric pressure, humidity, etc. remained the same from muzzle to 1000 yards, 1" @ 100 should be 10" at 1,000. But since no where on earth do such ideal conditions exist, we must go with the phrase Swampy used.

Zak Smith
November 16, 2005, 07:28 PM
Don't forget ammunition variances, which often manifest as elevation error.

USSR
November 16, 2005, 11:12 PM
Nobody mounts their rifle in a machine rest. A rifle that is tested by a gunsmith for it's accuracy is fired by a real live shooter firing off a bench rest. Someone who is a good marksman will have no trouble determining the accuracy, or lack thereof, of a rifle.

Don

Zak Smith
November 16, 2005, 11:20 PM
Nobody mounts their rifle in a machine rest.
Thesis: No person has ever mounted a rifle in a machine rest.

False.

Only one instance is needed to disprove the thesis, but I'm feeling spry-

http://www.researchpress.co.uk/targets/sandyhook.htm
Old Ordnance records show that when fired from a machine rest the .45 Springfield was expected to group all of its bullets inside a 4-inch circle at 100 yards, in a 11-inch bull's-eye at 300 yards, and inside a 27-inch circle at 500 yards.
(the ".45 Springfield" refers to a .45 caliber Springfield trap-door rifle, not the contemporary pistol)

http://www.gunsandammomag.com/reloads/match_0620/
Bo Clerke furnished the pressure barrel for these tests. That took care of the "good barrel" requirement. All the firing was done from a machine rest.

http://www.fulton-armory.com/M1NewRifle.htm
Each rifle manufactured is tested at the manufacturing establishment for functioning and for accuracy, the accuracy tests being made at a range of one hundred yards, using a machine rest

http://hornady.primediaoutdoors.com/HDstory4.html
The first step in my evaluation was to fire the ammunition in a pressure and velocity test barrel from my machine rest over the Oehler System 83.

weeklycigar
November 24, 2008, 12:22 PM
doesn't the projectile make a screw - type path through the air?

Swampy
November 24, 2008, 01:38 PM
doesn't the projectile make a screw - type path through the air?

Uh... no.

There is a certain amount of precession because of the high spin rate, but it is never so much (At least in any projectile to which the term "accurate" could even remotely be applied.) that the center of the precession moment and the cg of the bullet are more than a small fraction of the bullets diameter apart. IOW, the precession exists, as shown in ultra slo-mo video, but not in any truly measurable amount that shows up on a target.

Best to all,
Swampy

Garands forever

jbech123
November 24, 2008, 02:07 PM
So a rifle capable of, say, 3/4 MOA at 100m is not necessarily capable of 3/4MOA at 900m?

In pure theory it is, but since that ideal is never present in the real world, the question is by how much will all the factors that people have mentioned affect the end result. In my experience, wind (or my inability to read it properly out to 1000yards), is the main reason my 1/2 moa rifles do not shoot 5 inch groups at 1000.
To make things more confusing, I used to have a rem 700vs in .308 that would consistently shoot better from an MOA standpoint at 300 yards than 100. To make a long story short, It shot just under an inch at 100 and I could really never get it to do much better than that at 100, but would still be right at an inch at 200, and about 1.25" at 300. A few times when I did my part I had 300 yard groups under an inch. Made no sense to me. I posted around about it and some people mentioned the bullet "settling down" after the first 100 yards or so could be causing this. Not very scientific of an explanation for sure. It was however very repeatable, I even let a friend of mine test it out and he ended up with similar results. I was newer to shooting then, and I never shot it past 300 to see how far this would hold true for. I don't own the gun anymore. I know, why the hell would I sell a rifle that consistently groups ~1 inch at 300 yds with factory federal GMM.

hak
November 24, 2008, 02:37 PM
is that it's a 60th of a degree (or can be expressed in radians) as mentioned above. it's an angle, not a linear dimension.

does it come out to a bit over 1" at 100 yards? yes, but understand why and it makes plenty of sense.

it also gives you ideas on why mil-dot vs. moa, and why each school of thought has it's reasons. (mili-radian vs. minute of angle) 360 degrees x 60 minutes per degree = 21,600 'slices'. 6.2832 radians per circle, 'mili' = / 1000 or 6283 slices. sometimes more slices are desireable (in ranging, estimating, executing holdover or making adjustments), sometimes not (military DM ranges, speed of engagement, etc)

as someone who was researching if either is 'better' for their first 'good' scope, i came away with: a lot depends on what the shooter learned on and is most comfortable with. and that mil reticle and mil turrets weren't common on < $1000 scopes a few years ago. my only sure 'take away' was that i didn't want mil-reticle and moa knobs, b/c then i DO think of them difference as "'inches at XX yards". i'd rather stay in one camp, reticle + turrets.

i came across this a few weeks ago and found it helpful:

http://www.scribd.com/doc/4617008/Mils-and-Moa-Simplified

but on these forums, i find that IPHY (inches per hundred yards) is the more 'correct' way to express the linear "shooters MOA" mentioned above.

1858
November 24, 2008, 03:04 PM
It shot just under an inch at 100 and I could really never get it to do much better than that at 100, but would still be right at an inch at 200, and about 1.25" at 300. A few times when I did my part I had 300 yard groups under an inch. Made no sense to me. I posted around about it and some people mentioned the bullet "settling down" after the first 100 yards or so could be causing this. Not very scientific of an explanation for sure. It was however very repeatable

I suppose it's possible that a bullet could become more stable in flight at a given rpm and/or resonant frequency. However, I have a theory about this and I wonder if it's got more to do with your optics and how you shoot. Many shooters crank up the power on their variable scopes even at 100 yards where every tiny movement shows up. This has the effect of making it mentally hard to pull the trigger since the reticle appears to be moving around on the target. If you back off the power to where the smallest movements are undetectable or at least less noticeable, it's apparently easier to stay on target and thus it's easier to pull the trigger. So now I'm wondering what magnification you used at 100 yards and 300 yards. This is just a theory and certainly not a criticism of you or any other shooter that has a high powered variable scope. What do you think?

:)

1858
November 24, 2008, 03:09 PM
as someone who was researching if either is 'better' for their first 'good' scope,

I'm a bit confused ... as far as I'm aware there isn't a choice. Mil dot and TMR reticles are calibrated in miliradians whereas all adjustments are MOA.

:)

hak
November 24, 2008, 04:51 PM
"I'm a bit confused ... as far as I'm aware there isn't a choice. Mil dot and TMR reticles are calibrated in miliradians whereas all adjustments are MOA"


"TMR" = tactical milling Reticle? i'm not familiar with Leupold stuff. or a more general "tactical military reticle" ?

what i mean by a choice is: my choice #1: moa reticle with moa knobs (ie: 1/4 MOA clicks, or 1MOA clicks). vs. choice #2: a mil-dot reticle with 1/10th mil-dot knobs.

what i wanted to avoid is what you said (mil-dot scope and MOA clicks). i'm sure a lot of people dont mind it, but if i'm starting fresh, i wanted EITHER moa/moa or mil-dot/mildot, not a mildot reticle with moa knobs/adjustments.

(i chose: http://www.nightforceoptics.com/RETICLES_OVERVIEW/RETICLES_DETAIL/reticles_detail.html#npr1 an MOA reticle and the scope with Zero stop MOA knobs) instead of the mil-dot one with mildot knobs.

so: "Mil dot and TMR reticles are calibrated in miliradians whereas all adjustments are MOA" not on what i chose, by design.

jbech123
November 24, 2008, 05:04 PM
1858:So now I'm wondering what magnification you used at 100 yards and 300 yards. This is just a theory and certainly not a criticism of you or any other shooter that has a high powered variable scope. What do you think?

The scope was a 6.5-20x, and yes I did have it cranked up to 20 at all yardages. I read somewhere that unless there is a compelling reason like mirage, it is best to use a variable scope at the same setting(most likely highest) for the best consistency. I'd say your theory could definitely have some meat to it. I use a fixed 10x for eveything these days, which could be why I don't see this type thing any more.

1858
November 24, 2008, 05:28 PM
hak, hey thanks for the link ... I had no idea that MOA reticles were available and I can certainly see the benefit since windage and elevation adjustments are typically in MOA.

:)

jbech123, since you don't have the problem with the 10x maybe we're on to something. I was informed by an "experienced" shooter at the range that the 77 grain SMK HPBT bullet I shoot in .223 is "more accurate" at 200, 300 and 400 yards than it is at 100 yards ... for the supposed reason that you mentioned. I know enough to know that I don't know enough if you get my meaning so I have no idea if this is true. Intuitively it doesn't make sense but who knows?

:)

Lon371
September 20, 2009, 03:08 PM
While I know this is an ollldd post. I dont see where my pie plate is in any of the equations! :neener:

I knew that math teacher was crazy!

Thanks for the break down guys.

Dodahdude
September 20, 2009, 06:40 PM
"STOP", can't we all get along........:p

Zak Smith
September 20, 2009, 08:52 PM
No need for thread resurrection with no added information.

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