MOA is not 1.000" at 100 yards

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Catpop

Catpop

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I was reading my newest edition of Shooting Times when I came across a statement that MOA is actually 1. 047 inches at 100 yards and not what I had always taken for granted being 1.000".
I was ready to fire off a letter of error when I decided to dig out my old trig book from days gone by (way way by for that matter) at Moo U in Raleigh NC. Back in the days when Roman Gabriel played football for the pack and won the Liberty Bowl. When David Thompson and Monty Towe ruled the basketball court. When the Vietnam war was winding down. When Moo U was not U but the Cow College. That's enough Catpop!!!!!
Sure nuff, it computed out to not be 1.000" but rather 1.047 inches or there bouts.
Geez, I learn something new everyday! Of what difference 0.047 makes is moot, but it's nice to know anyway.
Correct me if I'm wrong as I usually am!!!!!
 
As much as I hate to embarrass you, most shooters already know this.

Don't worry, at least you are not engaging in an angry argument about how to convert 1 MOA at 100yd to 300yd :evil:

Mike
 
Most of us can't measure group size accurately enough to tell the difference. Close enough.
 
It's approximate. One minute of angle ~= 1" at 100 yds.
I measure groups with a ruler, not a micrometer, and trying to find center-to-center on ragged bullet holes, that 0.047" gets lost
 
The exact value of 1MOA at 100 yards is pi divided by 3.

Approximating 1MOA at 100 yards as 1" is less than a 5% error. 5% error may sound like a lot, but when taking real world measurements, it is actually very reasonable.

For practical purposes, the approximation works very well and is easy to remember. There's no practical use in carrying out the value to three places past the decimal point except in unusual circumstances.
 
And one minute of angle subtends almost 10 1/2 inches at 1000 yards instead of only 10.
What a difference.
If you are an astronomer, sure. If you are a shooter or even a ballistician, nope.

If it still troubles you, work in the French System with milliradians. That way a mil is 10cm at 100 metres.
 
Inch per hundred yards was first used over a century ago because smallbore and high power rifle targets had rings spaced in even inches apart. It's still the standard for the National Shooting Sports Foundation and National rifle teams.

That couldn't be good enough for those few who bought the new fangled hand calculators in the 1960's and used trig functions to see it's 1.0472........ inch per hundred yards.

But they didn't mind the 7.2 inch spacing for externally adjusted target scopes having .0005" movement per click which move impact exactly 1 inch per hundred yards. And they never moved 100-yard targets back to about 95 yards so the rings would be spaced trigonometrically.

Same for the standard 30 inch sight radius for metallic sights with the rear sight's 40 tpi threads with 1/3 turn moving bullet impact exactly 1 inch at a hundred.

This issue's the same thing as folks adjusting parallax on scopes. Used to be "focusing" but that was not well understood by most. So they glommed onto "adjusting parallax" in spite of the fact that parallax is only exactly eliminated by adjusting their head position so their aiming eye's on the optical axis of the scope.

There's four standards for the "mil" angular measurement; just for comparison.

And a 4.72% spread in internally adjusted scope's movements across all of a given make and model can happen because the magnification is not exact for some specified amount. The image size varies that much at the mechanically adjusted reticle plane because of tolerances in each lens' focal lengths.
 
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I promise not to be overly upset if my rifle and I only managed to consistenly shoot within 10.47 inches at 1000 yards instead of 10 inches. We should all convert to metric anyway to really drive us crazy.

And yes, I knew that 1 MOA is not a perfect inch at 100 yards.
 
Thanks guys! Now I feel right at home ------ last to know the latest town gossip! Haha
I'll try really hard to come up with some more words of wisdom as they are presented to me.
 
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Most people are happy with the inch, the gap of a spark plug is insignificant in most worlds.
 
There are actually 6283 mils in a circle. This was rounded off to 6400. Artillery has done well all over the world using 6400 for some time now.
 
JohnKSa said:
The exact value of 1MOA at 100 yards is pi divided by 3.
Click to expand...
No pi/3 is a better approximation, an excellent approximation in fact (good to 6 decimal places) but still an approximation. It is based on the curved length of a segment of a circle being approximately equal to its secant (straight line) [as well as the secant being ~ perpendicular to the line of fire] for very small angles (and also some of the yd, degree, inch conversion conveniently cancelling out).

1 MOA at 100 YD is exactly 100[yd] * ATAN(1/60 deg) / (36in/[yd]). pi/3 deviates from this starting in the 7th decimal place.

Mike
 
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JohnKSa said:
The exact value of 1MOA at 100 yards is pi divided by 3.

Approximating 1MOA at 100 yards as 1" is less than a 5% error. 5% error may sound like a lot, but when taking real world measurements, it is actually very reasonable.

For practical purposes, the approximation works very well and is easy to remember. There's no practical use in carrying out the value to three places past the decimal point except in unusual circumstances.
Click to expand...


It isn't 1.047" either. It's 1.047197551" :neener:
 
You guys amaze me.
I never did figure out what calculus was or what it was good for.
I did grasp trig, but it slipped out of my hands very quickly-- like an Ole river eel.
Algebra was a donkey on the little rascals in the 50s. I got that one cuz i was good with horses as a kid.
Logarithms were something I cut in our family sawmill.
But because I had a use for geometry and it was touchie-feelie, I held onto it longer. I used a=btanA from my surveying book to solve my moa problem. Hey it worked!
Thanks for all the great info.
Catpop the 65 yo student- always learning!
 
JohnKSa said:
The exact value of 1MOA at 100 yards is pi divided by 3.

Approximating 1MOA at 100 yards as 1" is less than a 5% error. 5% error may sound like a lot, but when taking real world measurements, it is actually very reasonable.

For practical purposes, the approximation works very well and is easy to remember. There's no practical use in carrying out the value to three places past the decimal point except in unusual circumstances.
Click to expand...
Strictly speaking, Pi/3 is a very close approximation, but not exact. Pi/3 is the arc length of an angle of one minute for a radius of 3600 inches. What you are measuring on the target is the Tangent of one minute times 3600 inches. The difference is negiigibly small, About 3 e-8 inches. Sorry to be a math crank, but I'm an engineer, I can't help it!
 
No dummies, it's an inch no matter what the range is.
Click to expand...

I've seen THAT on the Internet, too.

The geometric mil is 6283... 2000 x pi in a circle.
At one time the infantry mil was very close, 6280 while the artillery used 6400 which broke down neatly into right angles. The infantry surrendered and now the US and NATO use 6400 with the mil being exactly 3.375 MOA.
But the Russians, ah, the Russians. 6000 even.
I once saw a chart of different countries' rounded off mils, but cannot find it now.
 
Christopher B said:
Strictly speaking, Pi/3 is a very close approximation, but not exact. Pi/3 is the arc length of an angle of one minute for a radius of 3600 inches. What you are measuring on the target is the Tangent of one minute times 3600 inches. The difference is negiigibly small, About 3 e-8 inches. Sorry to be a math crank, but I'm an engineer, I can't help it!
Click to expand...
If my hunting rifles are minute-of-2-liter-bottle at any distance at which I'll be shooting, that's good enough for me.

And welcome to THR! (from another math crank who's bought more than his share of old math books at thrift stores and garage sales. :) )

Matt
 
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