MOA is not 1.000" at 100 yards

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Degrees were good enough for the Babylonians, they are good enough for me.

Shooters are one of the very few subgroups in the world that still measure shotgun shells in dram equivalents, and measure powder in grains.
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I don't think so. Most foreign load data is given in grammes for the convenience of foreigners using the French System. You can also, if you wish, the metric system has been legal for trade in the USA since 1866. Not required, as some would like, though.
I think we missed the boat not using the Jefferson decimal system of weights and measures like we use his money.
 
One way or the other our current system of weights and measures is deplorable.
 
Wow! Alot of technical information I never considered here.I'm just interested in minute of deer.In my case,with my skill level and my rifle thats 3 shots in less than 2 inches at 100 yds.My longest kill was 270 yds uphill through the heart while holding high on the shoulder.A 100 grain Rem. corelokt,.243 Win and 5 power scope setting.
 
"1.047197522 smart-ass"

How many digits should we append due to the 'smart-ass' designation? Might challenge the true experts. [no, not really]

Dry humor...at the opposite end of the comic scale from puns, thank goodness.
 
Still don't know how you got 2 something, you should have gotten something really small with the typo. Did you use radians by accident?
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Your original formula used ATAN, not TAN which accounts for the remaining discrepancy.
So I gave some thought to the double tangent of the half angles and decided against it. It might be more legitimate if you are measuring the spread of a group around a point of aim however, I tend to think of it as the deviation from point of aim for most applications (like scope adjustments).
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I was thinking of it as a spread around the point of aim, i.e. a measure of precision. I suppose looking at it as a deviation from the point of aim is also a valid approach.
So to be super correct, perhaps we should say +/- 0.5 MOA.
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Or one could say "1MOA converted to a linear measurement and centered on the point of aim on a target that is perpendicular to the shooter".
Not that it matters, 1 inch at 100 yards is close enough for government work.
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Yup.

The fact that the two approaches provide differing values points out an interesting, and perhaps counterintuitive, consequence of turning the angular value into a linear measurement. The exact value of 1 MOA (linear) differs based on where on the target, relative to the perpendicular point/aimpoint, that it is evaluated. Not a practical issue, of course.
Wow! Alot of technical information I never considered here.I'm just interested in minute of deer.In my case,with my skill level and my rifle thats 3 shots in less than 2 inches at 100 yds.My longest kill was 270 yds uphill through the heart while holding high on the shoulder.A 100 grain Rem. corelokt,.243 Win and 5 power scope setting.
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Most of this thread could reasonably be characterized as minutia or perhaps trivia. 1" @ 100yds is accurate enough for any practical applications involving small arms that I can think of.
 
"One way or the other our current system of weights and measures is deplorable."

No,sir...intellectually challenging and sometimes a major source of scientific angst? Assuredly.

Deplorable? No, and you should know it has worked very well for a very long time and still works for the majority of us.

What the heck, blame the bureaucrats!

Are you familiar with engine displacement in liters or cubic inches? Soft drinks in liquid ounces or liters? Still have acquaintances who refer to buying a 'fifth' of liquor? Have your medical office take your height measurement in 'feet' or 'meters'?

The 'net has free conversion tables...and what the heck, we're 'Muricans!

Pi, for instance, would be measured by you as what [exact] number?! Is 3.14 close enough...or should it be 3.1415926535?

We've established that for some of us, estimation is more than adequate, and for others of us, lots of decimal places are a way of life.

It's in my nature to be in the latter class [and lots of friends make their living in the Secret City], but my groups at distances approximating 100 yards/100 meters are certainly more practical by accepting the very small variance given my location here in Tennessee...a long shot here in our terrain is 75-100 yards.

We don't have to pay megabucks to shoot really tiny critters at really astounding distances, but some of us do. Our need to adjust to different terrain is far from deplorable...we revel in it. :cool:
 
Pi, for instance, would be measured by you as what [exact] number?! Is 3.14 close enough...or should it be 3.1415926535?
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No weights and measurement system is going to change the representation of pi as long as it uses a base ten numbering system.

Pi's value and representation isn't a consequence of the weights and measure system in use, it's a consequence of the definition of a circle, its diameter and the base ten numbering system, none of which will change between differing weights and measuring systems.

Of course, anyone is free to approximate pi as 3.14 (or even as 3) if that approximation provides acceptable accuracy for their application. But that doesn't change the actual value of pi and neither does changing to a different weights & measurement system.

By the way, did you know that pi is equal to the square root of 10 for large values of pi and/or small values of 10? :D
 
It's actually true. A mill is not quite an inch. Call me when you can hold a rifle close enough, or point a cannon straight enough, that it trumps easy arithmetic. An inch at a hundred is easy.
 
Perfect is the enemy of good enough. And, 1" at 100 yds is good enough for me.

When I was working on my doctorate in pure mathematics (probability theory, see the poem about Hiawatha the Statistician at http://www.math.utah.edu/~cherk/hiawatha.html that is related to this very topic), I came across something that has stayed with me: There is much in mathematics that will neither help you if you do know it or hurt you if you don't.


I spent 38 years of working closely with engineers and physicists as a professional mathematician in industry (never taught after the PhD). During that time (actually about 2 years in), I became a firm believer in the value of rules of thumb. In some cases (1" at 100 yds is about 1 MOA) they are close enough be reasonable substitutes in real world conditions (like shots under 300 yards). In other cases, they are valuable checks on calculations done by more complex systems. And, they are quite useful for quick, easy to remember performance estimates.

So, if my pocket tape measure gives me a measurement of extreme center to center spread of a group as 1", I am likely to think of it as 1 MOA.

And, since I am from West Texas, not the DFW area (though I worked east of Dallas for 18 years), I know that pi*r^2 has nothing to do with circles, since every one knows that pies are round and cornbread are square. :evil:
 
Most foreign load data is given in grammes for the convenience of foreigners using the French System
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You're right, of course. I should have specified the US attachment to quaint units of measure. I'm half surprised that we don't express muzzle velocity in some form of furlongs per fortnight.

And to Dr. T's point, one of my bedrock principles is to never spend the time to get a number more precise than I need to make a good decision.

With that in mind, for small angles, there is nothing to be gained by worrying about whether the triangle is right or isosceles, and whether we're measuring the arc or the chord at the end of the angle. The simple r*theta is abundantly adequate for the case at hand.
 
one of my bedrock principles is to never spend the time to get a number more precise than I need to make a good decision.
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Yup. And when one thinks about all the real-world work done with slide rules (3 or maybe 4 digits of precision) one gains a certain appreciation for how little precision is really required to get a useful answer.
With that in mind, for small angles, there is nothing to be gained by worrying about whether the triangle is right or isosceles, and whether we're measuring the arc or the chord at the end of the angle. The simple r*theta is abundantly adequate for the case at hand.
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The discussion in question was purely about getting an exact value--and it was, by admission of all participants, not about anything practical.

The only thing to be gained is a different ways of thinking about a geometry problem. If you want a practical number divide the range in yards by 100 and that's the value of 1 MOA at that distance.
 
The discussion in question was purely about getting an exact value--and it was, by admission of all participants, not about anything practical.
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But it was great fun, wasn't it?

real-world work done with slide rules
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Yup. Got us to the moon. I usually assumed that you could get an honest 2 significant digits, and occasionally 3. I think you were being generous.
 
The arshin (one step forward) is a better unit for military use than either meters or yards. If Sarge said to go about two hundred arshins to the east and set up there, you knew when you arrived.

I find it more accurate to estimate distance in arshins. It is because my mind's eye can readily imagine how may steps it would take to get there.
 
But it was great fun, wasn't it?
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I enjoyed it. But I don't claim to be normal...
I usually assumed that you could get an honest 2 significant digits, and occasionally 3.
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Unless you end up on the far right end of the rule, a full-sized rule should generally get you decent results in the third digit. If you end up on the far left, you can get a pretty good estimate of the fourth digit for some results. I just checked and was able to get 1.225 (admittedly the last digit was an estimate) for the square root of 1.5 on a 12" P&E N-500-ES.

Before you ask, I never actually used a slide rule for work or school. I got interested in them awhile back and found one for sale cheap online. Kind of fun to mess with.
 
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Kind of fun to mess with.
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Ahhhh.... there was a time I could make mine tap dance. And on a Burroughs mechanical calculator, I could extract square roots by subtracting every other odd number... or something. Long lost skills, replaced by better methods.
 
Technically, you should hang your target with a slight curve to match a circle with a 100 yard radius - otherwise it isn't going to be an accurate group.
 
I could extract square roots by subtracting every other odd number... or something.
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Subtract the odd numbers starting with 1 and keep track of the number of subtractions. When you get your last non-negative result, the integer portion of the square root is the number of subtractions performed. Or, said another way, the integer portion of the square root is one less than the number of subtractions required to return a negative result.

Find the approximate square root of 17.
1st Subtraction: 17-1=16
2nd Subtraction: 16-3=13
3rd Subtraction: 13-5=8
4th Subtraction: 8-7=1
5th Subtraction: 1-9=-8

Since the last non-negative result was obtained on the 4th subtraction, the integer portion of the square root of 17 is 4 which is obviously correct.

If you know some logs or have a slide rule, you can get a better answer faster. I get 4.125 off my P&E and 4.12 working it in my head with logs. The calculator says: 4.1231056256176605498214098559741
Technically, you should hang your target with a slight curve to match a circle with a 100 yard radius - otherwise it isn't going to be an accurate group.
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It won't change the accuracy, but it will mean that 1 MOA is the exactly same as 1MOA measured as a line on the target.
 
It won't change the accuracy, but it will mean that 1 MOA is the exactly same as 1MOA measured as a line on the target.
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Just kidding around. :)

You'd have to curve the paper into a section of a sphere, not a circle! Then you'd have to form it into a Mercator projection when you're done.
 
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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No worries, i had no idea either. Fortunately, for me it makes absolutely no difference. If I possessed the skills to a) be able to shoot to within .047 at 100" and b) measure that accurately, you can be sure I wouldn't be an average Joe Schmoe cruising a gun forum. You'd be reading about me in the newest gun rags.
 
Marvelous Modern Math

Three old friends were finishing lunch at a local restaurant. They hailed the server to bring the bill. She arrived then said she sometimes had problems adding numbers up so the bill was correct. So she asked “How much is 2 plus 2?”

The building contractor piped up quickly saying “4.”

The computer scientist engineer said: “I don’t think so; let me calculate it on my laptop.” After crunching numbers he says “3.999999999999999999999999999999999999999999999.......” until the third person politely interrupted.

The certified public account said to the waitress: “Come here young lady; I’m a professional doing math for money management. How much do you want it to be?”
 
You know, if I could see that <5% inch/moa difference in my scope at 100 yards, it might matter to me. I know I can't see it across my desk. To be honest, I have trouble seeing it at arm's length.
 
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