Originally Posted by
_Agrajag_
Just had a poke around on the web. No idea how far out of the water a periscope pokes, but if it was 10ft then the horizon limit is about 4 miles. If it's 20ft the horizon limit is about 6 miles. If it was 30ft the horizon limit is just over 7 miles. Less than I thought. May be periscopes poke a lot higher out of the water though. A 50ft high one could see out to a bit over 9 miles. 50ft seems high to me, could well be wrong though.
Those figures are for waterline visibility. If you add in the height of the ship, then they look more realistic (e.g. a periscope at a height of 20ft can see a 70ft warship out to 13Nm.
On the wider point, target-motion analysis as a method for estimating range from passive sensors has been around in crude form since before the 2nd world war. On modern submarine with automated analysis it is much more sophisticated.