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When spelled with one "L", it doesn't mean millimetres, but milliradians.

Before I dig deep into the depths of my failing memory for the maths, as far as the British Army is concerned, there are 6,400 mils in a circle, meaning one degree = 17.77 recurring mils.

The direction of North is thus at "zero mils" or "6,400 mils", South at "3,200 mils", East at "1,600 mils" and West at "4,800 mils".

The mils system is used instead of degrees because one mil subtends one metre at 1,000 metres (1 kilometre).

Sounds great. What does it mean?

If you have some means of measuring the angle between, or bearing to, two objects and you know how far away they are, you can work out the distance between them.

Objects A and B are measured at 20 mils apart, and are known to be 1,000 metres from the observer. This means they are 20 metres apart.

Objects C and D are measured to be 20 mils apart and are known to be 2,000 metres from the observer. This means they are 40 metres apart (20 x 2).

This is obviously useful to an observer who needs to adjust artillery fire onto a target.

How does the maths work?

You'll doubtless remember from school that the circumference of a circle is related to its radius by the constant "Pi". Pi approximates to 3.141592654ish.

The formula used to calculate the circumference of a circle is 2 x Pi x R, where R is the radius.

If the radius is 1,000 metres (bear with me ....), then the circumference of the circle would be 2 x Pi, which would be 6.284, all times by 1,000 which equals 6,284 metres.

If you were to draw this circle on the ground and stick a pole every metre along the circumference, you could measure the angle between two posts and it would be one mil as close as makes no difference. Thus the distance one metre is subtended by one mil at 1,000 metres.

There are therefore 6,284 true mils in a circle.

Edited by Dragstrip on 15 Nov 08:

Hmm, the treatment given to mils theory above, although quite correct, neglects their application for military purposes. Note that the circumference theory above relates to arcs of a circle, whereas mils are not for measuring circles. As the 'angle that subtends from..' definition suggests, mils are used to approximate straight-line distance between 2 distant points. The difference then is that 2 points on the circle referred to will be further apart than the same 2 points measured in a straight line (because they're parts of a curve). So, a shape with a radius of 1 km and made up of 6399 corners (i.e. a mils circle) will in fact have a 'perimeter' (not circumference) of 6400 metres.

Note also that the Russian version is also entirely appropriate as a shape with 5999 corners will also provide the accuracy and standardisation required.

Furthermore, the word milli refers to any system of units denoting a factor of 1/1000th. So, the term milliradian is inappropriate unless the perimeter was to divided by 1000 (ie, equating to 360degrees/1000mils as 1 mil per 3.6 degrees. Not very useful for our purposes.

In short, you could split a perimeter down into as many parts as you like to serve a particular purpose, eg navigation or fire control, and give them whatever name you want (mils, degrees, coconuts, etc. it matters not much). The greater the number of parts in a perimeter, the greater the potential for accuracy. However, the device becomes cumbersome at high figures. We, the British military use a the system of 6400 mils to a perimeter for standardisation and simplicity purposes. It matters not if it is actually out by a few cms here or there, we use it for navigation and fire control (both of which have natural tolerances built in in any case).

So why 6,400 mils and not 6,284

We use 6,400 mils as it's easily divisible into half, quarter, eighths, sixteenths etc.

Other countries use 6,000 mils to the circle, or 6,200. Beware the Soviet compass!

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