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Mils / MOA and the Range Equations and the math behind them. 2019-03-03

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These two papers. one a more detailed version and the other a simplified version (very little math) explain mathematically what a Mil is, what a MOA is, what a Shooters MOA is and how they came up with the Range Estimation Equations. You don't need to read these to use your Mil/MOA scope, but for the curious mind, it gives you an understanding of how they came to be. It's a great understanding of your scope, uses very basic math, and also might help put you to sleep on those nights when you are having trouble getting to bed.
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  1. Mils / MOA and the Range Equations and the math behind them.

    Newer version with minor edits.

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I read the short version and learned/realized something new about mils.
However it focused mostly on converting target in inches to distance in yards.
I will continue to the deeper article.

As I use metrics, I use this way to calculate distance to target:

Target is known to be 25cm tall.
Measure the target in mils (2 mils)
Now lets divide the target height with the mils:
And then multiply it by only 10 to get meters
12.5 -> 125.
Near miss, thank you for your review. To keep the papers as short as I could, I did most of the examples in inches because that is what most American shooters are familiar with. The concepts are the same for cm though, and I do give examples in cm and have equations for cm at the end of both papers. Remember, mils are a "natural" way to to measure angles, based on the properties of a circle, and any unit can be used as the properties of mils are the same for all units. Big guns (Navy and artillery) use yards and meters. Thinking in inches or cm for rifle shooters are equal. It's just that most Americans use inches and almost all europeans use cm. Bob