Milliradians: Definition
‘These are small. But the ones out there are far away.’
Give yourself a thumbs-up and hold it out at arm’s length. Congratulations! You’ve just measured two degrees of arc with the width of your thumb.
Now raise your hand and hold it out at arm’s length. Spread your fingers all the way. Brilliant! With the span between the tip of your thumb and pinky, you have measured 300 milliradians.
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Degrees of arc, the kind you use routinely from your compass, are relatively imprecise compared to milliradians, mrad or mils. Remember, the width of your thumb is already one or two degrees. You can’t easily go smaller without chopping your body to bits for MOA, minutes of arc.
The width of a finger in mrad is closer to 20 to 30.
More specifically, where a circle is 360°, it is also 6400 mrad. This gives us a conversion factor of 17.77, or close enough 18. You can be 18 times more precise using mrad than degrees! This is why we use them for marksmanship and artillery.
Your real-world hands are great tools for remarkably reliable rule-of-thumb estimations. In Arma, much more accurate (and immediately usable) tools to measure mils include your compass, binoculars, rifle optics and spotting scopes.
Milliradians: Apparent Size
The apparent size of an object changes with distance as we see daily. The width of your index finger may be a couple centimetres. Move it close to your eye and you can block your whole vision out of it. Move it further away and it occupies a small fraction of your field of view. All the while, the absolute width of your index finger has never changed.
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Because our field of view is described by an angle, the area we can see increases with distance. As an object moves farther away, its real-world size doesn't change, but its apparent proportion of our field of view becomes smaller and smaller. This proportion of an angle is also an angle: milliradians.
A metre is always a metre, but we can measure its apparent size to us in milliradians, so we can tell what a metre is at any distance.
If you know how far an object is and measure the milliradians between it and another point, you know the distance between them.
Similarly, if you know the real size of an object, you can use its apparent size to calculate or estimate the distance to it. We can do this with surprising accuracy and very little effort:
‘At 1000 metres, 1 mil is 1 metre.’
This relationship is the key to acquiring ranges quickly and accurately. Just like you know now how many milliradians are in different shapes of your hand, you can remember the real size of different objects and use milliradians to get ranges from them.
Let’s go through that step by step.
Remember our finger (known size) appeared bigger (milliradians) the closer we held it to our eye, but always the same moved side to side. Therefore:
One metre (known size) will always appear as 1 milliradian at a distance of 1000 metres.
That same metre will appear as 2 milliradians at a distance of 500 metres. Then again 4 mils at 250, 5 mils at 200, 10 mils at 100 metres.
So if you can remember different ‘metre sticks’ common to targets and terrain you encounter, you have a veritable arsenal of rangefinders using just your eyes and quick maths!
The specific formula is:
(object size in metres) * 1000 / mrad = (range in metres)
With this knowledge, you are also not limited to using objects that are exactly 1 metre. You can plug in any number for the (object size); 1 metre just makes it easier since you can divide 1000 by the number of mils you measured straight away, because 1 * 1000 is always 1000.
As a note, 1000 is a conversion factor. You could plug in the object size in millimetres without it and get the same effect.
