A full wave antenna wound not be what you normally want. A 1/4 wave antenna
gives you a good omnidirectional pattern, with limited nulls off the end.
If you installed a full wave vertical ground plane on an aircraft, it would
have a bit of gain - up.

Remember that gain is not free. It is realized taking the energy from one
direction and increasing it in another. Which direction are you going to
take it from? Easy when you are at a fixed location. Not so easy when you
are flying around in an aircraft.

What you hope to accomplish in a good installation is th make sure all the
connectors are installed properly, the coax is good and the antenna is tuned
for the proper frequency.

Regarding the ground plane, sometimes you have to do the best you can. If
there is not enough vertical room for a dipole or a ground plane, you could
install a 24" wire vertically in the vertical tail and then install a single
24" wire in the horizontal axis, also in the vertical tail. That will not
be perfect, but sometimes you have to live with less. You could also have
one vertical wire and three horizontal wires, serving as the ground plane,
with one in the vertical tail and two in the horizontal tail.

Colin