For Edinburgh Airport we use 2 different "drop off" methods, usually for our son and his g/f. We either take them to a tram stop and they get to the airport by tram, or we take them to the free drop off at the airport which gives you (I think) 30 minutes free and is about a 10 minut walk to the terminal. The problem with the tram is that while a tram single is £2, a trip from any tram stop to the airport costs £7.50 which IMO is a bit steep and makes the tram relatively unattractive. The airport bus is also £5.50. Mrs Salt and Vinegar and my good self get the tram because free tram travel is included in our bus pass.
If the powers that be really want to get folk out of their cars, cheaper public transport is a no brainer but the cost puts some people off.