Chart is from Wiki.
The general theory is that a single contact would only be a few Nm, but a convoy creates a larger volume of noise and it is possible to pick it up over the horizon, where the radar cannot see. Radar can of course pick up aircraft flying at higher levels, but then transmitting radio (or radar), as we know, is a dead give away of your position.
I'm not sure of the game modelling of the radar, but judging from SH3 and SH4 the hydrophone/sonar is not that bad. UBI 'professed' that the devs did a lot of research into all aspects of the game, which I can agree with. Not everything is accurate though as proven by the forum collective work done.
The range of sonar I think is probably difficult to model, as there are many variables, but I'd think for a good day, 10Nm (30Nm) would be ok for a single ship (convoy)
