I helped a friend with a remote flash trigger to extend the range. The device operates at 433 MHz, and as-built has a 1.25" PCB stub serving as an antenna. Since the wavelength is 27.26", it's really poorly matched and the range petered out at under ten meters. We soldered a coiled insulated wire of length 12.4 in (lambda/2 minus the PCB trace length) to the end of the built-in antenna, and the range increased tremendously, by a factor of ten. The coiled wire fit in the original enclosure, so it worked out very well. However, after I thought about it I realized that I don't understand why this thing works.
My question is: what is the effective length of the antenna when it is coiled up? Since the E-M field extends outside of the antenna conductor, shouldn't the effective length be the actual length of the coil, rather than the length of the wire in the coil? Is there a simple, back-of-the-envelope argument on how the antenna length/configuration helps to couple the E-M radiation out?