The Millieme (mil) is a unit of angular measurement used by the military, mainly the artillery. It is extremely versatile and is in many ways preferable to the degree. Everyone is familiar with the unit of measurement we call the degree and we all know that there are 360 degrees in one complete circle. The vast majority of hikers are happy with it and see no reason to change or even consider another system. For the purpose of navigation the degree is more than acceptable and serves us well. If we need to combine distances with angles however, the degree gets a little involved and the use of a calculator that has trigonometrical functions becomes necessary; a basic knowledge of sine, cosine and tangents will also be required. There are some circumstances when using subtended angles can be extremely useful to the navigator and almost indispensable for military personnel. An example may be to locate your position on the map when all-round visibility is limited and only reference points in one direction are available. As we know it makes little or no difference if our compass is graduated in mils or degrees as we very rarely use the graduations on the bezel for anything other than making a G.M.A. or magnetic declination adjustment although this is just as straight forward in either units.
We are still working with a complete circle but all we are doing is dividing it up into different sized segments. The mil is based on a milliradian or 1/1000 of a radian; a radian is expressed as the angle subtended at the centre of a circle by an arc that is equal in length to the radius of the circle. As we know the circumference of a circle is equal to π x the diameter (πd) or 2π x the radius (2πr), therefore in a complete circle there are 2π radians; as π is equal to 3.142, 2π is 6.284. We can now see that there are 6.284 radians in a complete circle (360 degrees), but we need to know how many milliradians there are in a complete circle; to find this we need only to multiply the figure by 1000. This gives us 6.284 x 1000 = 6284 milliradians in a circle.
The powers that be decided that this figure was unworkable and various figures of 6000, 6200, 6400 among others were tried; the standard that was settled upon was 6400 mils (not milliradians) in one complete circle. We must remember that there are 6284 milliradians in a complete circle and that figure cannot change so we can’t call the mil a milliradian, the mil is only based on the milliradian.
What We Have So Far
6400 mils = 360 degrees.
Therefore 17.777 mils = 1 degree.
We are still limited by how accurate we can position the graduated bezel on the compass, so how does having the bezel graduated in mils help us? The answer is … It doesn’t on a normal base-plate compass! You will need a sighting compass, preferably with a base-plate; there are a few to choose from, the Silva type 54 is only one. The rotating compass card on the type 54 is graduated in 1 degree increments and 20 mil (just over 1 degree) increments. It is generally regarded that the accuracy of any measuring instrument is its smallest division; however, Silva say that magnetic bearings can be taken to 0.5 of a degree or 10 mils (just over 0.5 of a degree). This is easily achieved as the width of the lubber line (the lubber line is a fixed line that indicates the direction of the bearing taken or the direction of travel) fits neatly inside the smallest divisions so that you can see the 1 degree or 20 mil graduations to either side.
The Simple Relationship Between the Millieme and Distance
A subtended Angle of 1 mil over a 1 kilometre line of sight distance gives a distance between features of 1 metre. A subtended angle of 3 mils over a 2 kilometre line of sight distance gives a distance between features of 6 metres. From this it is easy to see the relationship between the numbers and the ease in which they are calculated mentally.
The subtended angle (SA) is always in mils, the line of sight distance (LOSD) is always in kilometres and the distance between features (DBF) is always in metres.
LOSD = DBF ÷ SA
By transposing this formula we can satisfy all parts.
DBF = SA x LOSD SA = DBF ÷ LOSD
We are now able to take magnetic bearings accurately and we can use these to give our position on the map when having limited information. If, for example, we can see two distinctive peaks in the distance and can find them on the map we can plot our position easily. All we need to do is to take an accurate magnetic bearing in mils of each peak and take one from the other; this will give the subtended angle between the two peaks from your position. You can measure the linear distance that the two peaks are apart using the roamer on your base-plate along with the map and just apply the simple formula. In this case the answer will be a distance in kilometres. All we need to do now is to take the magnetic bearing from one of the peaks, turn it into a grid bearing and then plot this line from the peak onto the map. Now, using the roamer on the base-plate transfer the calculated distance along the line from the peak; this point is your position. I know this may sound obvious but always make sure that you measure the distance between the two features at ninety degrees to your line of sight, if you don’t you’ll dilute the accuracy of your position.
I can assure you that using and understanding the mil is a lot simpler than it is to explain! If you venture into wild areas that require good navigation the chances are that you will already own a base-plate sighting compass and probably know this method. It would be wrong of me to suggest that this information will be invaluable to the adventurer; look on it as just another tool in your ‘navigation toolbox’ along with all the others.
All the same, try it and see what you think!