The official formula for a half wave antenna in free space is 492/f where f is in Megahertz (MHz) and the length is in feet. For a practical 1/2 wavelength dipole length is feet use general formula of 468/f where f is in megahertz (MHz). A half wave antenna length (in inches) in free space is calculated by the official 5904/f where f is in megahertz (MHz) and the calculated length is in inches. If capacitive loading, end effects, etc. are taken into consideration this formula would then become 5616/f where f is in Megahertz (MHz). These formulas will work fairly well for a dipole mounted at least 1/4 wavelength above ground. Some tweaking might be in order due to capacitive loading from nearby objects. End effect may also change resonance requiring slight adjustment in length. It is best to cut a dipole a few percent longer then the calculated length then prune it for resonance. Starting longer is a LOT better then starting at the calculated length or shorter! It is easy to trim but a bit harder to stretch. Using the official free space formula is likely to be way to long. Proximity to ground, trees, homes, even the feedline greatly influence resonance so make sure you check it. The nominal feedpoint impedance of a dipole is generally 72 ohms but this can vary widely. The lower to ground it is, the lower the impenitence.
For a 1/4 wave vertical the above numbers would be half. Therefore, the height of a simple 1/4 wave vertical can be calculated by 234/f where f is in Megahertz (MHz). Since ground (including radials) act as the other half of the antenna a vertical is really a half wave antenna with a vertical polarization.
Let me add the following:
For composit or wood construction!
Half wave antennas do not need a grond plane, but they are LONG:
120 MHz which is a good place to start or tune your comm antenna to:
5616/120= 46.8 inches
Might start at the floor inside and work up the leading edge of the vertical stablizer? Could even stick out in the breeze.
C172Pilot
Mike
amature call sign: KB5UKT
KDTO