i spend an hour or so today with a physics professor trying to determine the length and it turns out to be an nasty calculus problem and our answer was nowhere near reasonable. w=1/(LC)^.5 had to do some guess work on the capacitance and inductance which didnt help. So it is guess and check time!
Physics professors *tsk tsk*
Tell him that the formula is:Wave length, λ [m]= Speed of light [m/s] / frequency [Hz]
So that he won't torture another student for an hour
The Speed of Light is 299,792,458m/s
A wave length at 72MHz (M means Mega and Hz means Hertz) is thus
299,792,458/72,000,000 = 4.164m
If you round up SoL to 300,000,000 and slice off 6 zeroes each side of the division sign, it gets easier to handle:
300/72 = 4.167m (an error of less than 0.1%)
For peak reception you'd use (a half or) a quarter of a wave length (not going into other possible fractions here), which makes it (2.08m) 1.04m.
(Now 2.4GHz looks really appealing, right?
This calculation is only needed for a ball park figure in your app., as there's nothing critical. The transmitter antenna might be more so, but I think most R/C equipment is fairly sturdy these days - just don't transmit completely without an antenna, as you may burn the power stage of the transmitter due to standing waves.
Nothing critical, as mentioned, so you can get by with less than optimum length and a length of 1/8λ should even do for this purpose, so just make it 52 cm if the connecting wire is short (otherwise, subtract its length from the 52cm).
If going for optimum range, it's quite another story, involving trimming the antenna length by nibbling off 1mm at a time until you just passed the point of max (no, you don't glue back 1mm then
). But this is more for comms radios and such - close to electrical motors, it would be a challenge anyway.