Richard Fry wrote:

...
Then how do you account for the measured performance and commercial
success of antenna systems that for the last 60+ years have implemented
the antenna engineering principles originating from sources you have
ridiculed in your post?

RF

I said what I meant and meant what I said.

Our present formulas/equations leave much to be desired and apply only
within narrow constraints of construction and design. However, when
dealing with these antennas of strictly limited proportions and design
(long wire, dipole, 1/4-1/2 monopole, etc.) these "approximations" are
usually adequate ... stray too far from "conventional" and you find they
begin to fall apart around the edges.

JS