I've just come across this thread when googling looking for a replacement transmitter aeriel & it makes some some interesting reading.
those equations & maths Daniel quotes are correct "technicaly" speaking... but realistically it only applies to radio waves that are being transmitted... for recieving radio signals you could use a piece of wet string, a sheet of tin foil & a drawing pin, or simply tie a length of bared wire to an old biscuit tin. But basically the more aerial you have exposed or the more conductive to electricity the wire or aerial the better the signal will be recieved.
If you ever came through the CB revolution you may of remembered SWRing in which basically meant metering up the aerial wire & chopping bits off the end of the antenna to get the lowest rating possible - which basically meant 1/4 of the wave & you always measure the SWR on the transmit, not recieve. I know you may think that "what's CB got to do with RC" well quite a lot actually as CB runs on 27MHz so a lot of the stuff in the text books regarding transmitting / receiving radio waves is relevent to RC if running on 27MHz & SWR Or (standing wave ratio) is used on all types of transmitters & 2-way radio's. CB aerials are also about 1.5m tall & use a load (basically a coil of wire at the base of the antenna) to simulate the use of a longer aerial because when they legalised CB they also set a maximum height ruling & as was said the optimum height should be 2 metres. the SWR value also depends on the run of the cable & how long it is as that will affect the reading.
So to answer Pete's point i'm guessing that the likes of Futaba, Acom, Sanwa etc have worked out that the length they are using on that particular model of their receiever is probably the optimum minimum length for that design, so it probably is best to keep with the length of wire measurements it came from the factory with & probably explains why they say "don't cut the ariel down or shorten it" in their literature & of course they have probably taken into account that a lot of fiddling to make it fit into the car has to be done, so i'm also guessing they use the bare minimum they can & going too far below the magic 1/4 wave will start to have an effect!
It's also worth noting that some wire materials have different conductive properties & as i said in my previous statement, that can affect how good/bad the signals are being recieved. Personally if i change an aerial wire, i use model Railway wire - the thin stuff for wiring up 00 gauge model railway lines.. it's fairly strong (so it doesn't get cut so easily if going under timing bridges or if the car is sliding on it's roof a lot), the added benefit is it's also often sold in most model shops so easy to get hold of plus it's alluminium or low grade steel based wire so seems a better conductor than the more usual copper & also it helps with Skin effect - Skin effect is basically how good the wire absorbs & distributes AC signals & as we all should know radio waves work in much the same way as AC in an electrical circuit using sine waves. The railway wire is a bit more expensive than using regular copper wire from craplins & no doubt the model shop owner will sell it at a higher cost by the metre than if you bought a roll, but if your club has an overhead timing bridge that your antenna pipe/mast catches as you pass under it rather than using an under-floor loop it's probably worth the extra few pence.
Hope this helps