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# Angular mil

This article describes "mil" as a unit of angle. For alternative meanings, see Mil (disambiguation).

The mil (in full, angular mil) is a unit of angular measure common in the military of many countries. There are three different specifications for the unit, each roughly 1000th of a radian.

The name of the mil comes from the its definition as (approximately) a thousandth of a radian, or milliradian. Its relationship to the radian gives rise to the handy property that object of size S that subtends an angle A mils is at a distance D = 1000·S/A. Alternatively, if the distance is known, we can determine the size of an object by S = A·D/1000. The practical form of this that is easy to remember is: 1 mil at 1 km is about 1 metre. Another example: 100 mils at 2 km is about 200 metres. (No conversion to Imperial units is worthwhile here, for all armies use metric maps, even the U.S. Army.)

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 men, 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.

Mathematically, recall that the arc that subtends one radian is one radius in length. Thus, one thousandth of this distance subtends a milliradian. The multiplication factor is introduced to avoid fractional measurements for common sizes of observed objects such as men, buildings and vehicles.

## The three definitions of the mil

• In NATO countries, including Canada, a mil is defined as 1/6,400 of a full circle. There are 1600 mils in 90 degrees, 17.8 mils in one degree. This mil is usually used in artillery discussion. It is also used in long-range precision rifle shooting, where the crosshairs on riflescopes are often calibrated in mils. This type of riflescope is usually referred to as a mil-dot scope.
• The army of the Soviet Union used a mil that was 1/6000 of a full circle, which means that there were 1,500 of its mils in a right angle, which would be less accurate though easier to remember.
• The military of Sweden during the Cold War desired to demonstrate its independence from both NATO and the Warsaw Pact, so they chose a size of greater accuracy. Because a right angle is more nearly 1.5708 radians than 1.600, their mil (which is called streck, literally "line") was 1/6,300 of a circle, so that there were 1,575 streck in a right angle.
Last updated: 05-25-2005 19:36:23
03-10-2013 05:06:04