An angular mil, also mil, is a unit of angle.
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Origin of the name
All versions of the angular mil are approximately the same size as a milliradian.
Use
The angular mil is commonly used by military organizations. Its relationship to the radian gives rise to the handy property of subtension - that "One mil subtends one metre at a distance of one thousand metres". More formally it means that object of size s that subtends an angle θ angular mils is at a distance d = 1000s/θ. Alternatively, if the distance is known, we can determine the size of an object by s = θd/1000.
The practical form of this that is easy to remember is: 1 mil at 1 km = 1 metre (2π/6.4 ≈ 0.98 m in NATO countries where mil is defined to be 1/6400 of a circle) or 1 mil at 100 yds = approximately 3.6 inches. Another example: 100 mils at 2 km = 200 metres.
In the general case, where neither the distance nor the object size is known, the formulae may be of little use. In practice, sizes of observed objects are known with reasonable accuracy since they are often people, buildings and vehicles. Using the formulae, distances of the objects can be readily calculated without a calculator. In military terms, distances are of course essential for artillery bombardments and estimations of journey times.
Artillery forward observers are usually trained to estimate the number of mils using their fingers, fist or hand, or combinations thereof, held at arm's length.
Note: Do not confuse the angular mil with the MOA (minute of angle). 1 mil = 3.43775 MOA
History
The milliradian was first identified in the mid 19th Century. Degrees and minutes were the usual units of angular measurement but others were being proposed, with 'grads' (circle/400) under various names having considerable popularity in much of northern Europe, the grad was based on dividing a right angle into 100 units. However, Imperial Russia used a different approach, dividing a circle into equilateral triangles and hence 600 units to a circle.
Around the time of the start of World War 1 France was experimenting with the use of millemes (circle/6400) for use with artillery sights instead of decigrades (circle/4000). UK was also trialling them to replace degrees and minutes. They were adopted by France although decigrades also remained in use throughout World War 1. Other nations also used decigrades. The United States, which copied many French artillery practices, adopted mils (circle/6400). After the Bolshevik Revolution and the adoption of the metric system of measurement(eg artillery replaced 'units of base' with metres) the Red Army expanded the 600 unit circle into a 6000 mil one, hence the Russian mil has nothing to do with milliradians as its origin.
In the 1950s NATO adopted metric units of measurement for land and general use. Mils, metres and kilograms became standard, although degrees remained in use for naval and air purposes, reflecting civil practices.
Markings on gunsights
Artillery uses angular measurement in gun laying, the azimuth between the gun and its target many kilometres away and the elevation angle of the barrel. This means that artillery indirect fire azimuth sights (called dial sights or panoramic telescopes) and their associated instruments (directors or aiming circles) and their elevation sights (clinometers or quadrants), together with ther manual plotting devices, firing tables and fire control computers, are graduated in mils.
in Many telescopic sights used on rifles have reticles that are marked in angular mils, and these are generally called mil dot scopes. The mil dots serve two purposes, range estimation and trajectory correction. By determining how many angular mils an object of known size subtends, the distance to that object can be estimated with a fair degree of accuracy. Once the distance is known, the drop of the bullet at that range (see external ballistics), converted back into angular mils, can be used to adjust the aiming point. Generally mil dot scopes have both horizontal and vertical crosshairs marked; the horizontal and vertical marks are used for range estimation and the vertical marks for bullet drop compensation. Skilled shooters, however, can also use the horizontal dots to compensate for bullet drift due to wind. Mil dot scopes are most suited for long shots under uncertain conditions, such as those encountered by military snipers and varmint hunters. In both of those cases, the range to the target is not fixed and shots are taken at extreme ranges, so accurate compensation for bullet drop is required.
To determine the distance to a target of known size: (Distance in yards) = 1000 / 36 x (Object size in inches) / Mils
To determine the size of a target at a known distance: (Object size in inches) = 36 / 1000 x (Distance in yards) x Mils
Knowing these relationships, you can set up a target range by drawing a vertical or horizontal line onto our target that is 3.6 inches long then backing up until the line is exactly one mil long in your scope for a 100 yard range, 7.2 inches for 200 yards, 10.8 inches for 300 yards, etc.
Known Target Size (8 inch) Ranging:
| Target, inches | Mils | Distance, yards |
|---|---|---|
| 8 | 0.1 | 2222 |
| 8 | 0.2 | 1111 |
| 8 | 0.3 | 741 |
| 8 | 0.4 | 556 |
| 8 | 0.5 | 444 |
| 8 | 0.6 | 370 |
| 8 | 0.7 | 317 |
| 8 | 0.8 | 278 |
| 8 | 0.9 | 247 |
| 8 | 1.0 | 222 |
| 8 | 1.1 | 202 |
| 8 | 1.2 | 185 |
| 8 | 1.3 | 171 |
| 8 | 1.4 | 159 |
| 8 | 1.5 | 148 |
| 8 | 2.0 | 111 |
| 8 | 2.2 | 101 |
| 8 | 3.0 | 74 |
| 8 | 4.0 | 56 |
| 8 | 5.0 | 44 |
| 8 | 6.0 | 37 |
| 8 | 7.0 | 32 |
| 8 | 8.0 | 28 |
| 8 | 9.0 | 25 |
| 8 | 10.0 | 22 |
The four definitions of the angular mil
There are 2000π milliradians (≈ 6283.185 mrad) in a circle. So a milliradian is just over 1⁄6283 of a circle. Each of the definitions of the angular mil are similar to that value but are easier to divide into many parts.
- 1⁄6400 of a circle in NATO countries.
- 1⁄6283 The “real” trigonometric unit of angular measurement of a circle in use by telescopic sight manufacturers using (stadiametric) rangefinding in reticles.
- 1⁄6000 of a circle in the former Soviet Union and Finland (Finland phasing out the standard in favour of the NATO standard).
- 1⁄6300 of a circle in Sweden. The Swedish term for this is streck, literally "line". Sweden has not been part of NATO nor the Warsaw Pact. Note however that Sweden is changing its map grid systems and angular measurement to those used by NATO, so the "streck" measurement is about to become obsolete.
External links
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