Knowing the range to the target is hugely important, if you want to shoot at it and hit it. This is less true if your target is a fulfilment centre warehouse for a major online shopping organisation, but for a normal sized battlefield target it matters.
So why does it matter? Well, because the gunner needs to elevate his gun by the right amount, to get the projectile to go to the correct distance.
If projectiles flew in straight lines, none of this would matter but because they are always under the influence of gravity, they don’t fly in straight lines, so it does matter. To hit a target at any distance a gun must be pointed up a little bit. The elevated gun fires the projectile upwards as well as forwards toward the target. Gravity slows down the upward movement of the projectile and reverses it, pulling it back to earth. The further we want the projectile to go, the more we must elevate the gun. We can mark up sights to account for this, to force the gunner to point the gun up by the right amount (which is what some parts of sight graticules are for). But “the right amount” varies with range. And in order to select “the right amount”, the gunner needs to know the range to the target. If you have not read about “Basic Gunnery and Gun Sights” yet, this might be a good time to have a look.
In a defensive battle, given time, gunners can measure ranges to landmarks they can see on the battlefield, or even place their own features at fixed ranges to help. But in a more mobile battle this isn’t possible, so some other means to estimate the range to the target is needed.
Clearly the gunner or his tank commander can guess. Not great, but it’s an approach.
Ranging Stadia in Gun Sights
Most tanks have some way of doing stadiametric range finding using a scale somewhere in the sight image, allowing the gunner to line up his target with the ranging stadia and estimate range with a bit of simple maths or a lookup table. The little sum below is a way of determining the range to a target, if you know how big the target is (width or height usually) and the angle subtended by the target, measured from the firing tank.
A 1 metre wide target subtends an angle of 1 milliradian (mrad) when at 1000m distance. So if your 1 metre wide target is at a different and unknown range, you can determine what that range is as long as you know the angle it now subtends, in mrad. A 3m wide target (like a tank head on, perhaps) subtends 3 milliradians at 1000m, but if it is subtending only 1.5 mrad, you can estimate that it is at 2000m, or 500m if it is subtending 6 mrad.
(Target Size x 1000) / Target Angle = Range
Target Size is in metres, Target Angle is in mrad and is the angle subtended by the target and Range is in metres.
A milliradian is 1000th of a radian, it is very a small angle. A mil is another small angle. There are 6400 mils in a circle, and if you do the sums, 1 mil is almost the same size as 1 mrad. Strictly they are not the same, but for most purposes they can be used interchangeably.
German sights from WWII are well known for having a rather interesting ranging graticule. This makes use of a series of triangles, of a fixed size and spacing (2 mils apart, 2 mils high, 2 mils wide). The triangles can be used to measure the target width as viewed. They can also be used to measure the height of the target, though there are significantly fewer points to measure with. This latter point matters, because if you can’t see all of the target (maybe the back is behind a bush), or if it is being viewed from a significant angle off head or side on then a better estimate can be got from the target height (though again, assuming the whole height of the target can be seen). If you can measure the target angle and you know how big the target is, you can determine the range.