A problem with antennas on a fiberglass bodied car is - well - the fiberglass.
The typical car antenna uses the metal body of the car as it's "ground plane" and a fiberglass body doesn't work that way. A typical antenna has the center of the antenna connected to the center wire in the antenna cable. The shielding on the cable is connected to ground where the antenna is mounted to the metal body of the car.
In the case of the Elise, we don't have that grounding.
The cure is to install an antenna that doesn't need the ground plane - they make antennas specifically for boats that don't need one, and some of the "dipole" antennas (I suspect that what we have from the factory, although I've never checked into it) - an antenna that typically has two wires branching out in two directions (they make simple ones to attach to your radio at home).
When I installed a radio in my Elan, I had to come up with an antenna. The Elan has a metal rod that connects the top and bottom of the center of the windshield (holds things together). I ran the antenna wire to this rod. It didn't work very well, until I connected the shield to the sheet metal chassis (which provided the ground plane). I don't know what it would take on the Elise for a good antenna...
