Posted: 1/16/2017 9:11:03 PM EDT
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OK.
My math skills bottom out at estimating the number of beers left when 3 are taken from a 6-pack, so I need your help. So here's the problem. A group of 15 shots is fired at 100 METERS {109 yards for discussion} and extreme spread measures 4.563" center-to-center. What will that group measure at 100 YARDS? Would it be accurate to simply reduce it by 8% and call it 4.198"? |
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I get 4.563" * 100 / 109 = 4.186.
Or, a little more accurately, since you measured your group to the nearest thousandth of an inch, 4.563" * 100 / 109.361 = 4.172. You are very close. Don't make the problem hard. Just use the law of similar triangles. (Group size at R1) = (Group size at R2) * R1 / R2, where R1 and R2 are the 2 ranges. It is a very simple formula and there is no approximation. |
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Thought about typing the explanation about constant ratios using the tangent function of a right angle diagram but scotch and beer have sapped my determination.
Suffice to say if you draw your hypothetical as a right angle triangle using half your group size as the opposite side and 109 yards as the adjacent side, you can convert everything to inches and arrive at (2.2815/3924)=(x/3600) which tells you x=2.093119 which means your group at 100 yards would be equal to 4.186 inches. Edit, should have read replies, already answered. |
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I'm going to throw in a little twist.*
Bullets do not fly completely straight. They have a bit of spiraling, and this is why groups are shaped the way they are. Now, depending on the size and rate of spiral, the group you would have shot at 100 yards will not be perfectly proportional. It could be larger or smaller than calculated. It depends on where the bullets were at 100 yards in their precession. *Pun fully intended. |
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Quoted:
Alas, I'm beginning to think we have no mathematicians. The education system is worse than I thought... Just because you didn't think of it first, asshole. The answer is correct. The OP didn't specify units, so why not have some fun? BTW, I took 600-level math courses to fill in credits during my MSME. I mostly just showed up for exams, and aced the classes. |
Thanks for the actual help, and thanks for the comic relief otherwise. 
I approached it differently. I decided to simply calculate the MOA at the range shot. So.... Using 1.047 as "1 MOA" at 100 YARDS, the formula appears to be this: {1.047/100} X 109.361 which is the actual # of yards in 100 meters = 1.145. Then I simply take the group size minus bullet diameter / 1.145 to get the MOA. Thanks for all your help. 
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Don't forget the coriolis effect. |
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Quoted:
http://i.imgur.com/oHt7Cgn.png Keep in mind it's been nearly two decades since trig class and I'm half drunk. There are probably rounding errors (damned sig figs). It's not 109 yards though. 100m = 109.361y. That's enough to throw OP off by almost 0.02in. I'm just kidding around. AeroE and others have pointed out what's probably "close enough" There are several ways to solve it with triangles, but the simplest is with a couple conversion numbers to use as multipliers. If you want to pursue super ultra mega turbo precision just for making accurate estimates, use 0.9144 x your 100 meter group size in order to estimate what you should get at 100yds. Conversely, if you're trying to estimate your group size at 100 meters based on what you measure at 100yds, simply multiply by 1.093613 and you'll have numbers that are probably finer than you need to know (within a hundredth of an inch). |
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Quoted:
http://i.imgur.com/oHt7Cgn.png Keep in mind it's been nearly two decades since trig class and I'm half drunk. There are probably rounding errors (damned sig figs). I knew Trig would solve it. 
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Quoted:
Just because you didn't think of it first, asshole. The answer is correct. The OP didn't specify units, so why not have some fun? BTW, I took 600-level math courses to fill in credits during my MSME. I mostly just showed up for exams, and aced the classes. If you're so smart, can you calculate a $24 transaction from say a credit card to pay for a team membership? |
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Quoted:
If you're so smart, can you calculate a $24 transaction from say a credit card to pay for a team membership? Quoted:
Quoted:
Just because you didn't think of it first, asshole. The answer is correct. The OP didn't specify units, so why not have some fun? BTW, I took 600-level math courses to fill in credits during my MSME. I mostly just showed up for exams, and aced the classes. If you're so smart, can you calculate a $24 transaction from say a credit card to pay for a team membership? |