I'm quoting from Jerry Sevick's (W2FMI) book "The Short Vertical Antenna and Ground Radial". A short antenna has been defined as one that is small compared to a wavelength.
He gives the following equation on p. 10:
Beta*h less than 0.5
where Beta equals 2*pi / wavelength and h is the height of a ground-mounted vertical.
BTW: the "less than" sign confused the HTML publishing process so had to remove it.
Solving for h gives us the following equation:
h less than 0.5 * wavelength / 6.283
For 40m antenna, the h is less than 3.2 m. If we use 130 feet for the wavelength, then h is less than 10.35 feet. The author uses 11 feet for his purposes.
He maintains that a 40m 1/4 wavelength ground-mounted antenna has a power gain of 1.62 when compared to the mythical isotropic radiator. This antenna is 33 feet high. The 11 foot vertical has a power gain of 1.513! Pretty impressive, don't you think? But HOW?
He further comments that "the very small value of its input resistance" is the important property that makes its capture cross-section nearly equivalent of a full 1/4 wave vertical. A ground mounted 1/4 wavelength vertical has a theoretical input resistance of 35 ohms and a 20 foot has an input resistance of about 8 ohms while the 10 foot antenna has about 2.5 ohms input resistance.
I'm not sure I understand all of this either, but it is very interesting (to me anyway). Well, I have some more to reading to do....AR
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