This is from the documentation in TWOS.
Range estimation
================
Binoculars and scopes have milliradian scales that allow to estimate/measure distances: "10" on the attack scope corresponds to "100" on the observation scope and represents roughly 100 milliradians (~5.73 degrees at low power magnification, at high power it's 4 times less: 25 milliradians or ~1.43 degrees).
One large mark on the binoculars represents roughly 10 milliradians (~0.573 degrees).
The markings are used as follows: given a target of height H that takes up M markings, its range R can be calculated:
R = H*k/M
where k is:
- 100 for attack scope low power and binoculars
- 400 for attack scope high power
- 1000 for observation scope low power
- 4000 for observation scope high power
Example:
Imagine you're observing a Liberty Cargo (mast height ~26m) through an observation scope at high power and ship's mast reaches "100" mark. Then the range will be:
26 * 4000 / 100 = 26 * 40 = 1040 meters
If you'd go up to conning tower and observe the ship through attack scope now (don't forget high power), its mast will reach "10" mark. Let's check the range:
26 * 400 / 10 = 26 * 40 = 1040 meters
RAOBF should give you something close to this value (between "10" and "11" on the range ring).
If you now surface and observe the target through your binoculars, it will take up 2.5 marks:
26 * 100 / 2.5 = 1040 meters
Mental rule for k:
"Normally x100, additional 0 for observation scope, additional x4 for high power magnification"
Take note that horizontal scale on the observation periscope is in degrees. I don't know for sure why that is, and the sources are scarce, but I believe this could be helpful for navigation and for estimating target's angular size i.e. to set salvo spread angle.
Les