Reg, G4FGQ wrote:
"When the circumference of the antenna rod is one wavelength, Zo = 0."

Bailey adrees with Reg. I was remiss in not quoting Bailey`s caveat. The
formula does not hold for circumferences greater than one-quarter
wavelength.

Bailey notes that uniform cross section conductors don`t have ubiform
impedances throughout their lengths. Zo is inversely proportional to
capacitance per unit length. Zo is lower at the antenna feedpoint than
at its conductors` middles. At the tips or open ends of antennas, Zo is
low. This is explained by the concentration of electric force lines at
the open end.

Variation of Zo along an antenna need not deter one from finding a
workable average of surge impedance. Bailey has determined this to be:

276 log 1/P, where P=circumference of the conductor in wavelength, for
circumferences of less than 1/4-wavelength.

For practical lengths of center-fed dipoles, the feedpoint impedance is
determined by combination of incident and reflected waves. Bailey has
worked out these for resonant lengths between 1/2 and 5 wavelengths. I
posted these long ago. But, for infinite length, Zo must prevail, as no
reflection will ever return.

Best regards, Richard Harrison, KB5WZI