Larry, N8KU wrote:
"I want to construct a 5/8 wave ground plane for 24 MHz.----Even the
ARRL antenna book hasn`t been much help."

At 1/2-wave, reactance nearly is zero and begins repeating as from
zero.. With a 5/8-wave, you have a 1/8-wave connected to the feedpoint
through a reactance repeating 1/2-wave line. A 5/8-wave antenna will
have nearly the same reactance as a 1/8-wave. Value of the reactance
depends on the characteristic impedance of the antenna and this depends
on length to diameter ratio.

Resistance of a vertical antenna increases with its length until it
reaches nearly 1/2-wavelength where it peaks and starts to fall.
Sharpness of this resonant peak depends on length to diameter ratio of
the antenna. You might expect a radiation resistance of between 50 and
150 ohms. Reactance may be between 200 and 1200 ohms. It depends on how
skinny the antenna is. Fat conductors have smaller impedance variations
(a lower Q).

My impedance numbers come from Capt. Paul H. Lee, USNR, K6TS`s "Vertical
Antenna Handbook".

5/8-wave vertical ground-planes were once popular on 27 MHz and often
used an autotransformer at the base to step up the impedance from the 50
ohms of the coax.

Best regards, Richard Harrison, KB5WZI