If I may just amplify (sorry) on the donut issue (one of my fav hobbies BTW, eating them that is....no I'm not a Constable On Patrol), actually a great deal of the efficiency of a vertical "ground-plane" type of antenna is the "radiation resistance" factor. By efficiency, I mean the relative amount of transmitted signal radiated by the antenna, in other words, it's effective radio signal output.

Look at it this way. A vertical antenna a quarter wavelength long at the operating frequency, when one ground wire (called a radial) is attached to the shield (ground side) of the coaxial transmission line and laid on the round going away from the antenna, will provide approximately a 50 ohm load (actually more like 38 ohms or so), which is what most solid-state radio transmitters these days like to operate into. Now this will certainly radiate a signal. However, the radiation resistance of this arrangement is relatively high, certainly higher than if a whole bunch of radials (say 10 or so) are used, in which case the effective radiated signal from the 10 radial antenna will be substantially higher than the 1 radial antenna system. Not only that, but the one radial antenna will tend to be somewhat directional in the direction that the one radial is pointing. If 10 radials are laid out spoke-wise around the antenna, this will help make the antenna more omnidirectional. So, bottom line, if you're going to use a vertical antenna, try to use as many radials as comfortably possible arranged more or less equally around the antenna. This provides a similar ground "plane" to that which might be achieved by placing a short roof-mount antenna smack in the middle of the top of a big van.

Sorry, I was going to say that radiation resistance is pretty much directly dependent on the quality of the ground plane, being higher in the case of just one radial, and much closer to ideal with 10 or more wire radials or a flat metal rooftop all around the vertical antenna. So, in a nutshell, adding more radials within reason tends to bring down the radiation resistance and increases the effective radiated signal output from the vertical antenna.

Sorry if this has already been mentioned.