Quarter size groups at 25 yards!! MOA vs U.S. Coin Diameters

[Texdance]

This is similar to a recent post which I could not fully view because my Excel is too ancient. I could not upload an xls file so could not include the various formulas, but included a jpg for those not wanting to download anything. The attached .doc file can be transformed into Excel without much fuss.

In 2013 I began testing the accuracy of several .22 rounds, all fired from various firearms using a steady rest and a good scope. I chose 1 inch at 100 yards for my definition of 1 MOA accuracy, later using 1.047 inches for calculation purposes.

I had become tired of seeing claims like "my rifle shoots quarter size groups at 25 yards!! Hoo rah!!".
I knew that was less than stellar accuracy.

I developed a simple formula of "Coin Diameter in Inches / 1.047 = MOA" to plug into Excel, got the coin sizes off the internet, and voila, a list showing MOA per US Coin Sizes. My friends north of Buffalo can do their own coin sizes, I don't have a loony or a toony to my name...

Details:
*I use 1.047 inches at 100 yards as the definition of MOA; since Excel is doing the math I didn't settle for the easier "1 inch at 100 yards."
*My definition simply says a five shot group will fit inside a circle of the coin's size, with no part of the bullet hole extending outside the circle. This makes for a simple test - can all the bullet holes be covered by the coin, or not?
*There is no allowance for c-to-c, or for actual-bullet-holes-being-smaller-than-bullet-diameter, or anything else. Just one test - does the 3 or 5 shot holes made by the .22 LR ammo fit inside the coin circle diameter, or not.

My spreadsheet, my terms.

As you can see, a dime at 50 yards is the only US coin size that is anywhere near 1 MOA at less than 100 yards, but almost all US coins make a circle of better-than-MOA accuracy at 100 yards.

So if you see a claim of a quarter or a nickel or a dime sized group shot at much less than 100 yards, you can assume the firearm was shooting a little (or a lot) less than 1 MOA in accuracy.


Distances & MOA
U.S. COINS 10m 50 ft. 25 yd. 50 yd. 100 yd.
Penny 5.83 3.85 2.57 1.28 0.64
Nickel 6.50 4.29 2.86 1.43 0.71
Dime 5.49 3.62 2.41 1.21 0.60
Quarter 1965- 7.43 4.90 3.27 1.63 0.82
Half 1971- 9.38 6.19 4.13 2.06 1.03
SB Anthony Dollar 1979- 8.12 5.36 3.57 1.79 0.89
Ike Dollar 1971-78 11.67 7.70 5.13 2.57 1.28


Inches COIN
0.67 Penny
0.75 Nickel
0.63 Dime
0.86 Quarter 1965-
1.08 Half 1971-
0.93 SB Anthony Dollar 1979-
1.34 Ike Dollar 1971-78

[Chris__Colorado]

Thanks for sharing. That was a bit interesting and along the same vein when I calculated 10m pistol scores for US coins
http://www.targettalk.org/viewtopic.php?f=4&t=56467

If you email me the file, I can post a link and host it in the electronic Airgun Reference Library.
http://www.targettalk.org/viewtopic.php?f=2&t=56517

Since you have the spreadsheet working, would you mind posting the answer to the following question?

At what distance would a US quarter have to cover all the shots, as you described it, to equal 1MOA?
I'm guessing a dime at 63? yards and a nickel at 75? yards.

Chris

[Texdance]

[quote="Chris__Colorado"]7

If you email me the file, I can post a link and host it in the electronic Airgun Reference Library.
http://www.targettalk.org/viewtopic.php?f=2&t=56517

I'd prefer just to have the jpg file linked, Pilk won't allow xls or doc files, says they are risky.
Download the larger jpg below for better visibility.

At what distance would a US quarter have to cover all the shots, as you described it, to equal 1MOA?
I'm guessing a dime at 63? yards and a nickel at 75? yards.

Your guesses are correct if you choose the less accurate figure of 1” at 100 yds. for 1 MOA. It should be 1.047”, not 1.000”

Coin Diameter in inches / 1.047 * 100 yards = yds. at which the coin covers 1 MOA.
Or, less exact, Coin Dia. * 100 = yds. at which the coin covers 1 MOA.

Nickel coin size .75 inch / 1.047 = .715, then .715 x 100 = 71.5 yds.
Nickel coin size .75 inch x 100 = 75 yds.

Coin Dia. Yds. to 1 MOA
Penny 0.67 64.2
Nickel 0.75 71.5
Dime 0.63 60.3
Quarter 1965- 0.86 81.7
Half 1971- 1.08 103.1
SB Anthony 1979- .93 89.3
Ike Dollar 1971-8 1.34 128.4

There is an MOA Calculator at
http://www.indecorous.com/bullseye/moacalc.html
It is confusing at first but makes sense after inputting some known data like .5 inch at 50 yards is about 1 MOA. Then change numbers around to get the hang of it.

I looked at your linked data, but can’t quite get my head around the whole ‘tenths’ idea when scoring manually. Since we only shoot .22LR in one match per season, and don’t have electronic scoring, our hand scoring excludes ‘tenths’ and is fairly easy.

[marky-d]

I don't want to criticize the work you've done, but note that I think this can only be assumed 100% true if you only have two shots in the group. In that case, the outer edges of the two holes define the diameter of circle/coin that can cover them, but if you have more than two holes, it can become more complicated.

Take, for example, two 0.22" diameter holes aligned horizontally, with their outer 'edges' exactly 1.000" apart (for round numbers). Now add a third hole above the first two, so the three holes form an equilateral triangle. Any TWO are still 1.000" apart, but to cover all three, you need a circle/coin that is 1.087" in diameter.

Does that make sense, or am I over-thinking it? Or are you measuring groups, by definition, by the circle that can cover them, rather than by the maximum distance between any two shots?

marky-d

[Texdance]

There's lots of ways to define and measure accuracy, some of them quite complex. I could use three or five or more shots per group. I could use actual or average Center-to-Center bullet hole distance. Or I could measure and calculate Average-To-Center. I have used the 'ON TARGET' program to calculate Offset Width, Offset Height, Group Width, Group Height, Center-to-Center, Average to Center (ATC), MAX MOA (Minute of Angle), ATC MOA , MAX MOA AVG, or ATC MOA AVG. But to me those extensive details are for special projects. For example, when going through extensive ammo tests, I take a group of fired targets, calculate the Standard Deviation, then used the Std Dev to throw out the outliers and re-calculate. This makes for an average free of true flyers, without just throwing out shots that I guess might be flyers.

Back to simplicity: For this exercise I only wanted to know if, when someone says "I shot a Quarter Size Group at X yards", was that a statement of good or bad or indifferent accuracy, using the industry standard of 1 MOA as my own accuracy standard.

The guys measuring with coins usually mean all the bullet or pellet holes can be covered by the coin in question, so that is exactly the definition I used. It is simple and requires no calculation at all. All it requires is a coin, a firearm, some bullets, and a target. You probably would want to mention a measured distance to the target. You can shoot offhand, prone, kneeling, sitting, from a one-piece or two-piece or sandbag rest, or looking through a mirror a la Annie Oakley.

Edit: The defining feature is NO MEASUREMENT IS REQUIRED except to put a coin over the group and see if all the bullet holes fit under the coin.

No calculation is required unless you want to convert the coin measure to something easier to compare, like MOA. Then all you need to know is the diameter of the coin, or the diameter of a circle that will cover all the bullet holes.

If a Quarter covers all the holes with no overlap, it's a Quarter size group, though in fact it could be a much better Penny or even Dime size group, so carry lots of coins if this is your way to measure accuracy. At 25 yards, that Quarter calculates to 3.27 MOA; at the 4H Youth Shooting Sports distance of 50 feet, it is 4.90 MOA. If, like me, you want a firearm and bullet combo that shoots sub-MOA, neither of those quarter size groups would indicate very good accuracy, but the shots might indeed score well on an official NRA or USA Shooting target. At 100 yards, a Quarter size group is very good, certainly better than average.

The beauty is if you don't like the results, just grab a bigger coin... most people won't know the difference in MOA.

U.S. Coin Diameters in inches.:
Dime 0.63, Penny 0.67, Nickel 0.75, Quarter 1965- 0.86, SB Anthony Dollar 1979- 0.93, Half 1971- 1.08, Ike Dollar 1971-78 1.34


U. S. Coin Sizes and Composition
https://en.wikipedia.org/wiki/United_St ... coin_sizes

[marky-d]

Again, I'm not trying to ruffle any feathers, and I understand you say you are just making rough generalizations, but at the same time you are being very specific by using 1.047" for 1 MOA, and giving equivalent MOA values to two decimal places -- implying much more precision than "rough generalizations".

I have no problem using rough rules of thumb for various coin sizes -- I was just pointing out that once you take the 'extra' step to convert to quantifiable MOA values and have more than two shots, then the calculation becomes more complex and involves the position of the shots as well.

Using my example of three shots in a triangle, a quarter would no longer cover the three holes if they are equally spaced at 0.86" (to the outside edges of the holes) -- they would have to be closer together than that. As such, using your method, if you shoot two shots JUST covered by a quarter at 25yd, they are 3.27 MOA. However, if you shoot three or more shots that can be JUST covered by the same quarter, you may actually be shooting somewhat less than 3.27 MOA (depending on the arrangement of the holes). I don't have the geometry in front of me right now, but it could be as low as ~3 MOA or so.

marky-d

[marky-d]

To illustrate my point, I have attached a picture below.

All three examples have a 0.86" diameter 'quarter' and three 0.22" diameter shots on target.
On the left, we have a 0.860" group (3.29 MOA at 25yd) that can be covered by a quarter.
In the middle, we have a 0.860" group (3.29 MOA at 25yd) that CANNOT be covered by a quarter.
On the right, we have a 0.794" group (3.03 MOA at 25yd) that CAN be covered by a quarter.

So if your goal is to say a group that can be covered by a quarter is 3.29 MOA OR BETTER at 25yd, than yes, you are absolutely, 100% correct. But just because you CAN'T cover the group does not mean it's NOT 3.29 MOA or better.

BTW, I came across this statistical look at measuring group sizes that is kind of an interesting read:
http://the-long-family.com/group_size_analysis.htm

It suggests, among other things, that using a group size of four will give you the best approximation for a firearm's statistical repeatability (without having to convert numbers).

marky-d

[Texdance]

Marky-d
No feathers ruffled here, appreciate the different ways to look at things. I can't write 'simple' without a whole lot of effort, and I was in a hurry for these comments, so no doubt it looked like I was in a blather.

You have a fine diagram. It is not what I was trying to illustrate initially, but you pose an interesting and valid point.

The answer is simple, but I have to go feed the cats now. If no one has figured it out by later today I'll post again.

Or maybe I'm the one who is herding cats here, dunno til I get a chance to plug in some figures. Alfred Einstein I ain't; maybe Alfred E Neuman...