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Author Topic: MILS & MOA The Math  (Read 1446 times)

Offline Dutch-Hunter

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MILS & MOA The Math
« on: February 02, 2016, 02:56:38 PM »
MILS and MOA (Get comfortable this is long (15 pages) and some would say boring.)                                                                                   Page 1

A Mathematical Guide to Understanding Range Estimation Equations
 
The equations for determining the range to a target using mils, and with some new scopes, moa, are: Has anyone ever wondered how they came up with these? Well I’ve assembled them here in the paper. I’ve read numerous accounts on the internet on “mils”, but none of them explained how to actually derive these equations. They just seem to pull them out of the air at some point in their explanation of “mils” without actually showing us how or where they came from. I searched the internet far and wide, but to no avail. I was starting to wonder if they were derived so long ago that nobody knew how to do it anymore. So I decided to derive them on my own.

The reason I wanted to do that is because I feel that if you know how or why something works, or where it came from, you get a better understanding and appreciation of it, as well as its uses and limitations. In this paper I will attempt to explain, in simple English and math, how they came up with these equations. I will try to keep it, to the best of my ability, simple, methodical (painfully in some cases), slow and easy to understand. So here it is.

First, a brief history of mils: A “mil” is a unit of angular measurement. The military use of mils was used to help direct artillery fire, goes back as far as the late 1800’s. Its modern form of use by the military for directing fire was developed in the 1950’s. The modern “mil” is short for milliradian, a trigonometric unit of angular measurement. It is finer in measurement than degrees, thus more precise. In shooting, we can use mils to find the distance to a target, which we need to know, to adjust our shot. It is also used to adjust shots for winds and the movement of a target. (The actual techniques of how to use mils for shot adjustments are beyond the scope of this paper since this paper only deals with the math behind the equations). That’s the short….very short….history of why we have and use mils.
I’m going to talk about and define another term; minute of angle, or moa. It is another unit of angular measurement and used quite a bit in shooting. It is even smaller than a “mil”. Usually, we range our targets in mils and adjust our scopes in “minutes of angle”, or we talk about our “groupings” in moa. For instance, “my rifle shoots 1 moa all the time” or something like that. Most new scopes have reticles etched in minutes of angle (moa) rather than in mils. Therefore we will also derive the moa distance equation.

Before we can derive the equations, we need to define a few things and establish a few relations. So just follow along, hang in there, and you will see why we will need these later.

Radians
What is a radian? (Warning: you might have to read this paragraph a few times). A radian is a unit of angular measurement. Officially, one radian subtends an arc equal in length to the radius of the circle, “r”. (Yeah that helps). How about this. What a radian is it associates an arc length, called a radian arc, which is equal in length to the radius of the circle, with an angle at the center of the circle. The angle the arc created is called a radian. Or, another way, it’s the angle created at the center of a circle by an arc on the circumference of the circle, and that arc length is equal in length to the radius of the circle. Think of it as a piece of apple pie, where the two sides of the pie (the radii) are each equal in length to the curvature part of the pie (the arc). The angle created by the three sides at the center of the circle equals 1 radian. (Refer to figure 1 below)

The rest of the article is attached in PDF format. It contains several diagrams.
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Offline russcat

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Re: MILS & MOA The Math
« Reply #1 on: February 02, 2016, 10:03:12 PM »
I started in on this and quickly realized my brain is too used up tonight.  I'll have to read this some morning over some coffee when the mind is sharp and hitting on all cylinders.  I'm looking forward to digging into to this one!
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Offline Madgomer

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Re: MILS & MOA The Math
« Reply #2 on: February 02, 2016, 10:19:57 PM »
Just when I thought I'd never need to remember any of that stuff from trigonometry class, here comes Dr Drip!  Good stuff there Dutch, I think you got it down.
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Offline BLUETOE

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Re: MILS & MOA The Math
« Reply #3 on: February 03, 2016, 06:23:58 PM »
Good stuff but you're burnin' my brain Dutch!!!  --099-780 --099-780 --099-780
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Offline Pure Instinct

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Re: MILS & MOA The Math
« Reply #4 on: February 04, 2016, 09:48:11 AM »
very good write up, thanks for the info!!

Offline Gutshot

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Re: MILS & MOA The Math
« Reply #5 on: February 04, 2016, 09:57:12 AM »
There you go again, destroying more brain cells, can't a person just go our there and shoot some paper  ()*$%RT

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Offline Dutch-Hunter

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Re: MILS & MOA The Math
« Reply #6 on: February 04, 2016, 05:48:55 PM »
There you go again, destroying more brain cells, can't a person just go our there and shoot some paper  ()*$%RT

 ##$%#115

Just print it off and place it by the "throne". It'll give you something else to think about.  Plus in case of a paper shortage you'll be armed.  ##$%#112
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Offline Foss1lHunter

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Re: MILS & MOA The Math
« Reply #7 on: February 09, 2016, 04:44:19 PM »
I've read it twice now. Not as bad of a headache the second read! I'll need to re-read often. Thanks for this important information Dutch!


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Offline BoBallistic

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Re: MILS & MOA The Math
« Reply #8 on: February 28, 2016, 11:41:01 PM »
Dutch - Thanks for the detail information. Everyone needs to down load it and then save it and read it over and over again until they sort of so how get it....

While you were trying to reach me on the phone today I was reading your article and had my phone off....I cannot obviously add anything to this...wonder what PA thought about this....

I agree with all your assessments. If you shoot/site in your rifle for a 1000 yards and you shoot with it at 100 yards then this article is for you...but folks who read this should go out and buy them a good rangefinder...

Folks just need to take a page at a time and read/understand it before moving on to the next...you can tell you had the training......

Sorry it took me a month to download it, I was on the road 6 days a week...but not anymore....thanks again, great article if you are a numbers person and can "see the shot" the bullet/pill will make...thanks for sharing your vast knowledge..... 
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Offline Two Tales

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Re: MILS & MOA The Math
« Reply #9 on: July 03, 2017, 07:19:47 PM »
Dutch,

I know this is an old thread...but very valuable to us "close just aint good 'nuff" guys...just thought I might refresh it for anyone new...thanks for posting the info...

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