Your VHF radio and your AIS receiver or transceiver operate in the marine VHF band which is 156 to 163Mhz. VHF transmissions are almost entirely restricted to ‘line-of-sight’ which means that from the antenna of a boat at sea the radio waves can travel as far as the horizon. In practice radio waves can see a little further than the horizon, about 20% beyond it. The higher the antenna is located the further away is its horizon and, therefore, the longer the range of transmission.
Communication range is actually the combination of how far your antenna can see and how far the antenna with which you are communicating can see. Imagine that you’re boat is surrounded by a huge circle whose diameter is determined by the height above sea level of your antenna. The higher the antenna is located, the larger will be the diameter of this circle, this radio horizon. Other boats and ships, as well as coastguard land stations, have their own radio horizon depending on the height of their antennae. When your horizon meets another horizon you can communicate, and the distance at which you’re communicating is the combined horizon distance of the two antennas.
I’m going to get a bit nerdy now, just skip to the end if your eyes start to glaze over.
You can calculate your horizon distance with the formula: Horizon in nautical miles is 1.4 x √H1 where H1 is the height of the antenna in feet.
Range is, therefore, 1.4√H1 + 1.4√H2 where H2 is the other fellow’s antenna height in feet. (By the way, that constant, 1.4, takes into account that extra distance the antenna can see over the horizon due to the bending of radio waves).