ESTIMATING RANGE

Coup d'Oeil -- A Quick Glance

The aspect of war that has always attracted the greatest attention is the engagement. Because time and space are important elements of the engagement, and were particularly significant in the days when the cavalry attack was the decisive factor, the idea of a rapid and accurate decision was first based on an evaluation of time and space, and consequently received a name which refers to the visual estimates only. Many theorists of war have employed the term in that limited sense. But soon it was also used of any sound decision taken in the midst of action -- such as recognizing the right point to attack, etc. Coup d'oeil therefore refers not alone to the physical but more commonly, to the inward eye.

On War, Book One, Chapter Three "On Military Genius"

Having a good eye has always been important. For a commander of horse cavalry, being able to, with a quick glance or coup d'oeil, judge distances and estimate the time it would take for horsemen to cover a piece of ground was necessary when trying to co-ordinate movement with the other arms of a battle formation. The coup d'oeil was such a familiar term at his time, that Clausewitz used it to describe the 'genius' of great military commanders.

But, being able to make sound judgments of distances and timing isn't something that's just beneficial for military geniuses and horse cavalry commanders. It's also beneficial for the humble rifleman and even the virtual tanker.

The way the US Army trains rifle marksmanship changed significantly after the Second World War. This change was primarily due to the influence of S.L.A. Marshall's work, Men Against Fire. Marshall, as an official Army historian during the war, routinely interviewed soldiers immediately after engagements, and when Men Against Fire was published in 1947, he claimed that only about fifteen percent of the men involved in an engagement would regularly fire at the enemy. This claim, of course, troubled all interested parties -- those who believed it and those who didn't.

In any case, the Army doesn't train marksmanship by shooting at bullseye targets anymore. Marksmanship is now taught on ranges with silhouettes that are vaguely human in outline, that fall down when hit, and performance is rewarded with skill badges that are worn on dress uniforms. Qualification on such ranges is required to be performed regularly. The shape of the silhouettes is designed to condition against the natural aversion to killing other people, the falling of the silhouettes provides immediate feedback on performance, and the skill badges provide positive reinforcement. Important to the discussion here though, is the fact that those silhouettes are man-sized and are placed at known distances.

Repeated exposure to targets of uniform size at known distances trains marksmen to accurately judge distances by the apparent sizes of the targets relative to their rifles' front sight posts. As long as you fight and train with the same type of rifle, and you know how big a man-sized target is at a range of 200, 300, or 400 meters compared to your front sight post, you're, hopefully, going to be able to estimate the range to an enemy combatant with just a quick glance.

The same is true with tank sight reticles. While tanks don't have front sight posts, they do have mil circles at the centers of their reticles. A mil is a unit of angular measurement that can easily be explained with resort to some simple trigonometry.

As you can see from the figure to the left, as the distance from the apex of a triangle increases, the length of its opposite leg increases. These increases are proportional, so that when the distance doubles, the length of the far leg doubles as well.  In the figure, the angle that 'pinches' the sides of the tank at 1000 meters will pinch two similar tanks at 2000 meters.

A mil is a unit of angular measurement such that when the angle of a triangle like the one to the left is one mil, the length of the opposite leg is one unit when it is 1000 units distant from the angle.  So, if a tank sight has a circle with a one mil diameter, that circle will cover one meter at a distance of one kilometer, two meters at a distance of two kilometers, and so on.

This relation gives rise to a three variable formula that is helpful when trying to compute distances:   Width divided by mils equals Range.

From the front, a T-72 is about 3.6 meters wide and a T-80 is about 3.4 meters wide.  From the flank, a T-72 is about 7 meters and a T-80 is about 7.4 meters.  So a good rule of thumb for remembering the dimensions of Soviet tanks is 3.5 by 7.

The value for the mils in the formula should be derived from comparing the target to the circle and lines in the reticle.  The circle has a one mil diameter, the tick marks directly horizontal from the circle are 2 mils long and the other horizontal tick marks are 2.5 mils long.  Note well: The reticles for the M2/M3 and for the Leopards have slightly different dimensions.

 M1 reticle

T-80 1000 metersNow for some math:  If you click on and enlarge the first thumbnail image, you'll see a T-80 from its front.  Comparing it to the reticle, it overlaps the full circle and one of the first horizontal tick marks.  Adding up the overlap on each side looks to be about a half of the circle.  The mils then would be, 1 for the circle, 2 for the horizontal tick mark, and about .5 for the overlap.  That comes to a total of about 3.5 mils.  Using the 3.5 by 7 rule of thumb, We get a width of 3.5 divided by mils of 3.5 for a result of 1 kilometer or 1000 meters.  The image includes a laser return of 1000, so the formula checks out.

T-80 2000 meters This next thumbnail shows about the same thing. The difference is that there are two T-80s, side by side, at a range of 2000 meters. Because they are at a range double that of the first image, two of them take up the same amount of space relative to the reticle as the first T-80 did.

Certainly solving math formulas does not increase the speed of tank engagements.  However, understanding a bit of what the function of the reticle's pattern is will improve gunnery skills.  By being aware of the function of the reticle pattern, a gunner can deliberately make a quick mental comparison of the size of a target relative to the reticle and its range.  Over time, those quick mental comparisons will give the gunner a good eye and he'll be able to estimate range with just a quick glance.

You can download a short practice scenario with an M1 engaging targets at known distances here.

mil angle
World Wide view of meters and range
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