Calculating MOA

RC20 said:
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Calcs are easier, actually hitting something at distance is a different story
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BING-GO!

It's easy to send a bullet from most any rifle a mile (and some to 5+ miles). Predicting where it's going to land *accurately* is the hard part. Doing that when there are high velocity kinetic events with your name on them is the separator between a cool professional and the rest of the world.

I can tell you first hand walking a bullet at a mile 10 yards left or right is way more difficult than you can imagine if you haven't tried it.
 
RC20 said:
Agreed, but the reality is that Canadian sniper at (x range) took 3 shots.
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I'm not sure what this has to do with my disagreement that mil-dot scopes are mostly marketing.

As far as stoopid MOA/MIL scopes are concerned, at one time, that was all we had. They were indeed VERY stoopid. And the elevation knob was 1 MOA per click. Not 1/4, not even 1/2 MOA per click. A whole MOA. With a mil-dot reticle. With targets at unknown distances. On the clock. And no laser range finder. I'm very glad that time is behind me.

I much prefer a MIL/MIL scope, and measure distance in meters.

Regarding an MOA being 1" @ 100 yds vs 1.047" @ 100 yds, some ballistic calculators allow you to choose between "shooter's MOA" (1" @ 100), and "true MOA" (1.047" @ 100).... The difference is less than half an inch at 1000 yds.
 
Regarding an MOA being 1" @ 100 yds vs 1.047" @ 100 yds, some ballistic calculators allow you to choose between "shooter's MOA" (1" @ 100), and "true MOA" (1.047" @ 100).... The difference is less than half an inch at 1000 yds.
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Yup, not much practical difference, is there?

...and yet, one runs into people who somehow seem to be pretty heavily invested in which approximation folks choose to use. At least nobody actually gets irate when it's pointed out that MOA has a mathematical definition that differs from the common convention. :D
 
1.04719753642832854694747069666400334739860873986429830552235157457471965151538005004775737357536725837... inches per 100 yards never came to any popularity level until the 1960's when people used the new tangled hand held scientific calculator's trig functions "calculating" MOA values at target ranges. Too bad they were limited to only a few decimal places.

A few of them used high school level optical lens formulas to learn internally adjusted scope LOS values are not exactly what maker's specs are and they change a few percent across range focus points. Such math is often detailed patents and library books available to the public. While the angular change on a scope's inside erector tube per LOS angle click is fixed and the same for a given make/model, the first focal plane target image size is not constant across all target ranges; gets bigger as range decreases. Then value per click gets less. Optical tolerances cause up to a few percent spread.
 
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Once upon a time, it was fairly common to epoxy the internal adjustments on a Leupold and put it in external adjustment mounts. One of the small deluxe scope companies had an external adjustment scope, but I cannot find it now.
Are external adjustments no longer considered necessary because internals have gotten better?
 
Jim Watson said:
Are external adjustments no longer considered necessary because internals have gotten better?
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One needs the focal length tolerances for objective lenses to know for sure. But that doesn't correct the first image plane from changing size with target range.
 
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Jim Watson said:
Or just watch what the good shooters use. Outside adjustments seem to have faded away... again.
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Those great Lyman, Unertl and DiSimone target scope's front base on the barrel changed its vibration frequency enough to impair accuracy. Both bases on the receiver were better.

Wasn't as bad as putting a bedding pad or angled screws at the fore end tip under the barrel.
 
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1.04719753642832854694747069666400334739860873986429
830552235157457471965151538005004775737357536725837... inches per 100 yards never came to any popularity level until the 1960's when people used the new tangled hand held scientific calculator's trig functions "calculating" MOA values at target ranges. Too bad they were limited to only a few decimal places.
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Which, of course, means that "1.04719753642832854694747069666400334739860873986429830552235157457471965151538005004775737357536725837..." has really never come into any popularity. Calculators probably did make it more likely that folks would use a better approximation than 1", but even today, trying to run it out past 9 or 10 digits would not only be ridiculous but would task most readily available calculators or software packages. But yes, calculators have made it easy to be more accurate when more precision makes sense.

When I was in grade school, it was, for example, still common to use 22/7 as an approximation for pi. Now that almost never happens although there are probably some folks out there somewhere complaining about how people now use "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798" for pi and how no one ever did crazy stuff like that until those newfangled calculators came along. :D
 
I was reading this article and thought it was interesting/amusing in the context of this thread.

https://www.gunsamerica.com/digest/benchrest-shooter-1000-yard-group/

"Wilson’s world record-setting 5-shot group measured 1.068 inches or, in angular terms, a stunning 0.102 minutes of angle (MOA)."​

Not only did they quote the group size out to 3 places past the decimal (Why not just say it's 1"--they might as well have used 102 digits if they're going to go all the way out to 3 decimal places!), if you do the math, it's also apparent that they used 10.47" as the approximation for 1MOA at 1000 yards instead of approximating it as 10".

What were they thinking? Kids these days! :D
The compromises we make when "exact' ain't worth the effort getting there
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Nobody ever gets to exact in the real world. Everything is an approximation or an estimate, or a measurement that includes some amount of error. A big part of practical mathematics is understanding what level of accuracy you really need (and have) in your answer.

Of course, in this case we're really talking more about a "convention" than about a compromise or an error. It's certainly true that many people follow the convention of 1 MOA being exactly an inch at 100 yards and there's really nothing wrong with that as long as everyone understands how the numbers being quoted should be interpreted.
 
"Wilson’s world record-setting 5-shot group measured 1.068 inches or, in angular terms, a stunning 0.102 minutes of angle (MOA)."
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The IBS and NBRSA benchrest rules in so many words:

Aggregates for group shooting at 100, 200 and 300 yards are calculated in approximate Minutes of Angle (1 inch = 1 MOA at 100 Yards). Grand Aggregates are figured as an average of the MOA at each distance.

The IBS and NBRSA websites lists their single and aggregate group records in inches for their disciplines. Their measuring devices are graduated in inches. People can convert them to whatever they want. Microseconds of time on a clock face, if they wish.
 
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Yup, not much practical difference, is there?
Well lets look at this. So I am at 110 yards, hmmm, 1 inch.

Or we can break it down and 110 yards is really 1/6 of an inch.

That is an 1/8 inch in real terms.

Yea, I calculate it out that fine.

You really don't know how well you are shooting unless you do.

As I recall Indiana in a fit of stupidity decided to round Psi off (50s?)

Yep, its important and they ignored it.
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We aren't just limited to 'angle' when it comes to MOA. Sure, you have to replace that "A" with something else that can equally describe the shooters skillset.

Minute of Pieplate?

Minute of Torso?

:D
 
The National Shooting Sports Foundation established one MOA is 1 inch per hundred yards of range back in 1961. It was based on NRA competition and other commercial target scoring rings being spaced in inches as required by NRA rules.

That said, their web site gave the wrong formula to convert to trigonometry angle MOA for those insisting trig's better. They didn't suggest making metallic sights radius 28.648096334.. inches for trig numbers, either, so their 40 tpi lead screw clicking 12 per turn would work.
 
You guys are going crazy with these digits.

Many laser range finders are only accurate to the nearest yard. Since 100 yards is equal to 3600 inches, and one yard is greater than 10 inches, that means that only the first three digits of that 3600 number are going to be significant, most of the time.

So keeping more than four significant digits for Pi, or the length of the arc minute subtended by one minute of angle is an exercise in futility.
 
pblanc said:
You guys are going crazy with these digits.

Many laser range finders are only accurate to the nearest yard. Since 100 yards is equal to 3600 inches, and one yard is greater than 10 inches, that means that only the first three digits of that 3600 number are going to be significant, most of the time.

So keeping more than four significant digits for Pi, or the length of the arc minute subtended by one minute of angle is an exercise in futility.
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I agree because zero digits worked very well for a century or more.

Reminds me of the centuries old issues of the length of a nautical mile that span about 7 to 8 percent growth across the last several hundred years.
 
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Or, ... don't be that Fuddley and run a MOA/Mil scope on your once-a-year deer rifle. :rolleyes:

Just use the iron sights for shots inside 100yds and call it good. Point-n-shoot. You won't miss.
 
The National Shooting Sports Foundation established one MOA is 1 inch per hundred yards of range back in 1961.
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They agreed on a convention for the approximation of 1 MOA for use in shooting sports that they governed. And, for what it's worth, their information now explicitly notes that 1 MOA is not exactly 1" at 100 yards and provides the correct definition of 1/60th of a degree.

https://www.nssf.org/shooting/minute-angle-moa/

"A MOA is 1/60th of a degree.

1 MOA spreads about 1″ per 100 yards. (actually 1.047″)"​
Nobody can "establish" what 1 MOA is--there's a mathematical definition that predates the shooting sports by centuries. One might as well try to "establish" what pi is, or what '3' is or what 5 x 25 is--it makes no sense because they already have established values.
Reminds me of the centuries old issues of the length of a nautical mile that span about 7 to 8 percent growth across the last several hundred years.
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Not remotely the same thing. Measurements that are not pure mathematical units are defined by standards organizations and those definitions can change over time--or they can be defined in different ways by different organizations. So a country that uses one standards organization might measure a mile differently than another country using a different standard.

Degrees, minutes and seconds are pure mathematical units that do not need a standards organization to define them. They have a mathematical definition, and they have had for centuries. Long before the shooting sports existed. There has never been any confusion about what a minute of angle was or about the official definition and there still isn't. The fact that some organizations and people choose to abide by a convention that says 1 MOA is 1" at 100 yards doesn't change the value of 1 MOA, it just establishes a convention for the organizations that choose to use it. If they are honest about it (as the NSSF is) they will point out the real value but make it clear that the convention is done for simplicity of use.

Here are some approximations that are virtually identical to approximating 1MOA as 1" at 100 yards.

360 degrees = 377 degrees.
pi = 3
1047 = 1000
 
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