VHF Comm/Nav Range
An interesting question for pilots is - what is the range of your VHF Comm radio?
Practically speaking, how high do you have to be, to talk to a remote ATC or FSS?
The thing to remember is that 118-137 Mhz VHF is (mostly) line-of-sight, so the higher you are, the more distant a radio on the ground that you can talk to.
Think of the aircraft as a very high antenna. You can calculate it's range with the following simple formula:
Range (nm) = 1.23 x square_root(height in feet)
This is actually slightly further than the visual horizon, and takes into account the fact that VHF will "bend" ever so slightly.
For example, my small airport is 25nm from a big airport where the antennas for ATC Terminal are physically located. I think I can take off VFR to circuit altitude. Can I talk to Terminal on downwind, to pick up an IFR clearance?
Range (nm) = 1.23 x sqrt(1000 feet) = 39 nm
So the answer is - yes.
A few examples:
1000 feet: 39 nm
5000 feet: 87 nm
10000 feet: 123 nm
20000 feet: 174 nm
30000 feet: 213 nm
Note that the above calculations also apply to your VHF VOR reception altitude, if you were to ever turn it on for your amusement.
Also note that as you climb up, you may start to "see" more than one VOR using the same frequency - there are only so many VOR freqs to go around.
See VOR MAA.