Richard Fry wrote:
. . .
A classic 1/4-wave vertical monopole working against a very good radial
ground system such as used in AM broadcast should produce a peak gain of
around 5 dBi. The theoretical max for such a system with perfect
conditions is 5.15 dBi.
. . .

Unfortunately, "perfect conditions" includes a perfectly conducting
ground far beyond the radial field, a luxury neither we nor the
broadcasters have. The maximum far field (sky wave) gain of a ground
mounted quarter wave vertical over average ground, with a completely
lossless ground system, is on the order of 0 dBi, and this occurs at
roughly 25 degrees above the horizon (both depending on frequency as
well as ground characteristics). See the EZNEC example file Vert1.ez as
an illustration. Its MININEC type ground simulates a lossless ground system.

Roy Lewallen, W7EL