If I was to mount it hanging off the bed towards edge of the road, how does that change the signal radiation and how the antenna sees the ground plane?
Have you figured it out yet?
Easiest way to work it out is like this.
First of all remember we're dealing with electrical fields, electrons and the like. Remember that electricity and electrons and everything to do with electricity like to take the path of least resistance.
Now imagine a flat circle on the ground, your antenna sticking up vertically out of the middle of it. Any part of that circle which is metal is going to have electrickeries flowing in it much better than any part of it that isn't. And any direction those electrickeries are flowing well is going to have a stronger signal than one that isn't.
So if you have half of that circle in metal and half of it as bare ground those electrickeries are going to flow much better in the metal half than the ground because the bare ground is more lossy. So in this case you will transmit and receive signals stronger in the 180 degrees where there is metal under the antenna.
So lets cut that half circle of metal to a quarter circle. Again still the electrickeries want to flow more in the direction of the bit that's metal so you end up with much stronger signals in the direction of the quarter of the circle covered by metal than the 3/4 covered by earth.
And so it is with your vehicle. The disc still effectively exists even though there's nothing physically in one direction or the other if you mount the antenna on a side or in a corner. So in the case of sticking it in one corner of the vehicle as far as the antenna fields are concerned you've got that disc that only has 1/4 of it metal and 3/4 of it bare lossy ground, even though that ground is a few feet below it. And as we said the electrickeries prefer to flow in the direction there's metal. So if you've put it in the rear left corner you will transmit and receive signals much stronger towards the front right of the vehicle.
And thanks to studies done on RF grounding we know the difference in signal strengths between the direction where there's ground wires at least a 1/4 wavelength long of this disc and just the lossy earth. That difference is 6dB or 2 S points on a CB S-meter.
So now you know how to figure out which direction your antenna is going to favour depending on where you place it on the vehicle, it's going to be in the direction there's more vehicle.
So how does this work putting it in the middle of the roof I hear you cry because obviously the vehicle is narrower than its length so the "groundplane disc" isn't round. And you'd be right that signals towards the back and front will be stronger than to the side but the signals towards the sides are still going to be stronger than if there was no metal under the antenna at all in those directions so it's more omnidirectional than any other option.
