Calculating MOA

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I'vebeenduped

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I recently shot a new Savage model 12 in .308. When I was unloading at the range, I found that I forgot my targets. Of course! I grouped this at 200 yards. This is a .308 case that I am holding to the so called target that I was zeroing in on. Can one of the many geniuses tell me what MOA I am shooting? Many thanks!
 

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take a ruler and measure the outside of the farthest bullets. Subtract .308 and that will give you the size of the shot group. Easier then trying to measure the center of the two farthest shot.

1 moa is 1.047, at 200 yards that would be 1.047 X 2 or 2.094

Now divide the measurement you got from your shot group by 2.094 and it will give you the percentage of MOA.

Convert the percentage into fractions.
 
Simple!

Measure from the inside edge to the opposite outside edge of the holes furthest apart. If you want to get picky stuff a bullet in the holes to get an "exact edge" of the fired rounds. No math needed just measure where the arrow shown is.

This is the group size in inches.
Convert to fractions.
At 100 Yds this is your MOA.

Divide by 2 to get a 200 Yd MOA, by 3 to get a 300 yd & so on.
groupsize_zpse179e67c.jpg
 
1 MOA is exactly 1 inch per hundred yards using the USA century old shooting standard as well as what SAAMI considers practical.

If you prefer the technical trigonometry one, it's 1.047197536428329.... inch per hundred yards of range for 1 MOA.

Use whatever makes you feel good. Divide the two widest shot hole centers by twice one of the above numbers for 200 yard targets.
 
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Well we know that the 308 case is 2.015, so taking a piece of paper and marking it at the center of the holes and comparing it to the case in the picture one could approximate the spread. My guess is 1" center to center or 1/2 MOA. Could have got it wrong but there it is.
 
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1 MOA is exactly 1 inch per hundred yards using the USA century old shooting standard as well as what SAAMI considers practical.
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Approximating 1 MOA as 1 inch @ 100 yards is exactly the same thing as approximating pi as 3.

That said, the error is only about 5% so if that level of error is acceptable, the approximation is fine. Still, it is a little amusing to think that many modern precision shooters are fine with an approximation of pi that "went out of style" around 2000BC.

For a fairly simple approximation that is a little closer to the actual value, one can divide the distance to the target (in yards) by 95.5 to get the approximate value of 1 MOA (in inches) at that distance. That approximation will provide a result that is pretty close--about 0.0074% smaller than the actual value.

The group looks like it measures about 0.46 MOA center-to-center, (about 0.963")
 
Using the On Target tool that was referenced above, and setting the reference measurement to the width of the .308 cartridge (0.469), the overall CTC groups size is 0.967 which makes the MOA 0.462.

If you want the image with the data on it, PM me with your e-mail address and I'll send you the jpg snip that I saved from the tool display.
 
Just enter this into your friendly EXCEL sheet:

Code: 
Group(in) Range(yds)	angle(min)	
0.967	    200	         0.46171 <-- " =DEGREES(A2/(B2*36))*60 "
 (A2)	    (B2)

Personally, I'm a fan of the New Math: 1 = 1
(and how do you feeeeel about that?)


.
 
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I wonder when high power and conventional smallbore targets will have their scoring rings changed to trigonometric MOA numbers instead of inches. The smallbore 100 yard target's X ring would then be a bit over 1.047" diameter. And all others the same relative amount

The next thing is to change the standard sight radius for so many existing rear sights with 40 tpi lead threads from exactly 30 inches to 28.647890160552565351356763198219 inches so 8 clicks on their knob would move bullet impact from dead centered on the X line at 3 o'clock 1.047197536428328546947470696664 inch left to dead center with the sight's lead screw tpi of 40 and 12 clicks per turn.

Then, for all those old but great target and varmint scopes made by El Monte, Fecker, Litchert, Lyman, Sidle and Unertl with bases 7.2" apart and the rear one's adjustment screws the same pitch but 50 clicks per turn for .0002" each giving 1/4 MOA in the old system, they have to be respaced to 6.875493638532615 inch so four clicks moves impact 1.047197536428328546947470696664 inch for every hundred yards of range.

If we want to be exact, we gotta do the above. Too bad there's not enough matter in the universe to make a pencil and sheet of paper big enough to write down all the digits to make what's in print exact.
 
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I wonder when high power and conventional smallbore targets will have their scoring rings changed to trigonometric MOA numbers instead of inches.
...
If we want to be exact, we gotta do the above.
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Not at all. There's nothing at all wrong or inexact about quoting group sizes in inches, creating scoring rings that are measured in inches or building sights and scopes that adjust in inch (or fraction of an inch) increments.

One can be just as exact by measuring in inches as when measuring in MOA. But whatever metric one choses, it's always preferable to use the correct value for the unit of measurement in question.

For example, if one were to measure a group in inches but wished to express the measurement in centimeters, it would be preferable to use the correct conversion value of 2.54cm/inch instead of approximating the conversion factor as 2.42 cm/inch or 2.66 cm/inch. Both the latter have a 4.7% error--equivalent to approximating 1MOA as 1" @ 100yds.

If one chooses to use MOA, then an approximation is necessary, of course, since the precise value is a non-terminating, non-repeating decimal. How close an approximation is reasonable? It all depends. As I mentioned in my previous post, if a person feels that an approximation error of about 5% is acceptable, then that person would certainly find it reasonable to approximate 1MOA as 1" at 100 yards.
 
Both benchrest shooting organizations (IBS and NBRSA) consider one minute of angle to be exactly 1 inch at 100 yards and even multiples for each 100 yards further. Scoring rings are in inch-based increments in size. Group measurements at ranges greater than 100 are often converted to MOA; a 1.000" group at 300 yards is considered to be .333 MOA. In countries using metric ranges but measure groups in inches, their sizes are multiplied by .914 to be realistically compared.

Then there's the connundrum of how many 36" yards are in a mile. There's at least five different amounts from 1650 to a bit over 2025.
 
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1 minute of angle = 1/60 degrees, hence "minute"

So 1" at 100 yards is:

60*arctan(1/100/36) = 0.954929634... MOA.

And 1 MOA at 100 yards is:

tan(1/60)*36*100 = 1.047197581... inches.




...at least mathematically speaking, as mentioned above different organizations might have their own rules.

Same thing with mils, a milliradian is supposed to be 1/1000 radians, there are 2*pi radians in a circle. So there should be:

2*pi*1000 = 6283.185307... mils in a circle.

But for some reason governments chose different a amount, the French said "6400" and the West copied them, so a military mil isn't really a milliradian...








Honestly better to state your group sizes in inches per 100 yards, then there's no confusion about whether you are using 1" or 1.047...". But if you're gonna need such mathematical precision you better measure the exact range down to a fraction of a yard too... :rolleyes:
 
Both benchrest shooting organizations (IBS and NBRSA) consider one minute of angle to be exactly 1 inch at 100 yards and even multiples for each 100 yards further.
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Well, in all fairness, the IBS calls it "approximate Minutes Of Angle"

See page 20 C, 2.
http://internationalbenchrest.com/downloads/IBS_Rule_Book_12b_Revised_2012.pdf
"...in approximate Minutes of Angle (1 inch = 1 MOA at 100 Yards)..."

NBRSA, as you say, isn't quite as precise and their rulebook does state that 1" @100 is 1 MOA.

Then there's the connundrum of how many 36" yards are in a mile. There's at least five different amounts from 1650 to a bit over 2025.
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That's a very different problem. In that case, the problem is that there have been multiple official definitions of the distance measurement "mile"--nautical miles, statute miles, imperial miles, etc. This situation arose, in part, because there were multiple standards organizations (in different countries) in times past and they didn't all agree on what constituted a mile. Also because some measurements (e.g. the nautical mile) are convenient for certain types of calculations (e.g. great circle navigation).

All of which means that there's no conundrum if one is specific about the particular type of mile in question, there's only a problem if one simply uses the term "mile" without qualifying it as being "imperial", or "U.S. statute", or "nautical".

There is not the same kind of problem with defining a minute of angle because it doesn't require a standards organization to create a definition in the same way that an arbitrary measurement of distance does. It is an angle measurement equal to 1/60th of a degree. That's been universally true for the last couple of thousand years, at least.

It's unfortunate that the IBS and NBRSA chose to muddy the water by ignoring the actual value of MOA and attempting to create their own--however convenient their preferred value is for them. That said, it's their game and therefore they get to set the standards that will be used in their game. Of course, their choice doesn't change the actual definition of "minute of angle" any more than you or I could change the definition of "degree of angle" by starting a competition and claiming in the official rulebook that there are actually 377 degrees in a circle instead of the correct value of 360. Which, by the way, is the same as approximating 1 MOA as 1" @ 100 yards.

All of which gets us back to the comment I made in my first post: it is a little amusing to think that many modern precision shooters are fine with an approximation of pi that "went out of style" around 2000BC.
But if you're gonna need such mathematical precision you better measure the exact range down to a fraction of a yard too...
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The approximation in question is only accurate to about 5%. As long as the distance measurement is more accurate than the approximation then the range measurement will contribute less to the error than the approximation will. So, for example, as long as the range measurement at 100 yards is correct to less than 4.7 yards (or less than 9.4 yards at 200 yards, 14.1 yards at 300 yards, etc.) then the approximation of MOA is a larger contributor than the error in the range measurement.

It's not hard to find laser rangefinders with accuracies better than a yard.
 
John, the original inch per hundred yards for MOA numbers was established a century ago by the NRA target scoring rings spaced in inches a target ranges in hundred yard increments. That was cause for sight makers to make them move in amounts for the common 30" sight radius; 40 tpi lead screws and 1/3rd turn on rear sights moved the aperture .00833333....." for one inch/MOA at 100. Rear sight moved 1/3600th the sight radius. Which is why the ones with 12 clicks per turn moved them 1/4 MOA per click. Commercial target rifles had scope base holes spaced for 7.2" scope mounts with .002" movement on 40 tpi screws making them move the LOS 1 MOA (inch per 1C yd.) the same as iron sights; 1/3600th the mount spacing.

As both NBRSA and IBS originally used scopes with those same mechanics in hundred yard increments on targets with rings in inch increments; they didn't change anything stating their disciplines decision to use inch per hundred yards as one MOA. That method was several decades old when they established it as theirs. In spite of the fact that all modern scopes have a small spread in how much one click moves the line of sight.
 
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John, the original inch per hundred yards for MOA numbers was established a century ago by the NRA target scoring rings spaced in inches a target ranges in hundred yard increments.
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LOL

You can continue to call it "MOA" but it's still inaccurate, no matter who "uses" it as a standard.

A true "MOA" is not 1" @ 100 yds
 
Whatever ......... Remember your internally adjusted scope doesn't move the line of sight per click exactly as claimed. Neither does any other. The same make and models don't all adjust the same, either.
 
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