[ETR3(SS)]

From what I remember from my lookout training, it was 14k yds(7 nm) to the horizon but that also depends upon the observers height as well. As for the various circles, you're on the right track. The 1/2 circle is the coverage area of the units active sonar, the 3/4 circle is the passive sonar envelope. The next two full circles are for visual and radar, with radar having greater distance than visual.