Yesterday I posted a review of a riflescope that had MIL dot markings on the reticle. In the comments there was some confusion about the purpose MIL dots have in range estimation, and so I wanted to break the answer out into a more complete article. It involves some math and a slight chance of high school flashbacks, but I swear it’s not that complicated. Let’s begin at the beginning, then…
Range estimation is useful in shooting when you’re not on a flat “known distance” range and need to hit something with a well aimed shot. Known distance ranges typically have markers you can use to determine how far away they are (MCB Quantico’s 1,000 meter known distance ranges have berms every 100-200 meters) but when those aides are absent you need to rely on other clues to know how far the bullet will drop before it hits the target and adjust your aim accordingly. One method of range estimation (preferred by most shooters) is by using MIL dots.
The theory behind MIL range estimation is basic trigonometry. If we assume that the target makes a right angle with the ground (standing up straight, angle “C”) and we estimate the height of the target (the average American male is 5 feet 9.5 inches, leg “a”) then the angle between the bottom of the target and the top of the target (from our viewpoint, angle “A”) can tell us how far away they are (leg “b”). The ratio of leg “a” to leg “b” is the tangent of angle “A” (SOH – CAH – TOA), and once we know the ratio it’s simple math to figure out the approximate number for leg “b”.
MIL dots provide a fixed reference on the scope that enables us to determine the angle between the top and bottom of the target. Fixed, that is, if they’re in the “first focal plane” of the scope. I talk about focal planes in another Ask Foghorn post but the basics are that first focal plane reticles will remain a constant size relative to a fixed target no matter the magnification. If the reticle is in the second focal plane the ratio between the target and reticle will change and make the markings basically useless. Second focal plane scopes typically let you know at what magnification the dots will be the “proper” size compared to the target but that’s one more thing you need to remember and one more thing to go wrong.
Thanks to the wonders of physics we know that an object appears to be “bigger” when we are closer to it and “smaller” when we are farther away from it. Objects appear to grow and shrink linearly, so a target twice as far away will be half as big. So if we assume that the badly drawn green man in the crosshairs above remains a constant size then the one on the left would be “closer” than the one on the right assuming the crosshairs are the same size (first focal plane or optics without variable zoom). If the reticle was in the second focal plane then this could be a target at the same distance but just with a different zoom setting. But for now let’s continue with the first case.
MIL dots allow us to dispense with the complicated mathematics of trigonometry, as the “simple” formula has been derived for us thanks to the standard distance between MIL dots. Here it is:
This equation (simplified from the Wikipedia equation for distance in imperial units) gives us the distance in yards to a target whose actual size (in inches) we know and whose apparent size (in MILs) we can measure through our scope, where “H” is the height in inches, “M” is the apparent height in MILs, and “D” is the distance to the target in yards.
For our example poorly drawn human in the left hand reticle, assuming they are a standard American male (69.5 inches) and measuring them at about 3 MILs high in the scope they would appear to be 643.57 yards downrange. For the right hand reticle (smaller poorly drawn man) they would calculate out to be 965.36 yards downrange — the target is 1/3 smaller and therefore 1/3 further away from us.
And that’s how range estimation using MIL dots works. If any of this is unclear let me know and I’ll do my best to make it easier to understand.
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