MOA is not 1.000" at 100 yards

Discussion in 'Rifle Country' started by Catpop, Aug 22, 2016.

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  1. Jim Watson

    Jim Watson Member

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

    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.
     
  2. Warp

    Warp Member

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    One way or the other our current system of weights and measures is deplorable.
     
  3. 3212

    3212 Member

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    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.
     
  4. Blade First

    Blade First Member

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    "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.
     
  5. Arizona_Mike

    Arizona_Mike Member

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    When you drop the smiley face it almost looks mean.

    Mike
     
  6. JohnKSa

    JohnKSa Moderator Staff Member

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    Your original formula used ATAN, not TAN which accounts for the remaining discrepancy.
    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.
    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".
    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.
    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.
     
  7. Blade First

    Blade First Member

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    "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:
     
  8. JohnKSa

    JohnKSa Moderator Staff Member

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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
     
  9. Kendal Black

    Kendal Black Member

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    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.
     
  10. Dr T

    Dr T Member

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    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:
     
  11. denton

    denton Member

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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.
     
  12. JohnKSa

    JohnKSa Moderator Staff Member

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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.
    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.
     
  13. denton

    denton Member

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    But it was great fun, wasn't it?

    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.
     
  14. Kendal Black

    Kendal Black Member

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    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.
     
  15. JohnKSa

    JohnKSa Moderator Staff Member

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    I enjoyed it. But I don't claim to be normal...
    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.
     
    Last edited: Aug 29, 2016
  16. denton

    denton Member

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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.
     
  17. RX-79G

    RX-79G Member

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    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.
     
  18. JohnKSa

    JohnKSa Moderator Staff Member

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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
    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.
     
  19. Arizona_Mike

    Arizona_Mike Member

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    That was definitely wrong!
     
  20. RX-79G

    RX-79G Member

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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.
     
  21. 19-3Ben

    19-3Ben Member

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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.
     
  22. bushmaster1313

    bushmaster1313 Member

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    I bet some smart Alec is going to tell us that a United States Mint quarter is not an inch in diameter
     
  23. Bart B.

    Bart B. Member

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    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?”
     
  24. Double Naught Spy

    Double Naught Spy Sus Venator

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    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.
     
  25. lysanderxiii

    lysanderxiii Member

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    0.955" +/- .0025

    The gauntlet was thrown . . .
     
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