Art wrote:
"Even better, let me know the TOA of a dipole in free space and how much
it varies to that of the same dipole over perfect ground."

If possible, look at Terman`s1955 opus page 882:
"Effect of Ground on the Directional Pattern of Ungrounded Antennas -
Image Antennas."

In free space, no reflecting surface is nearby to distort the pattern of
a radiator.

Terman gives the familiar radiation of a 1/2-wave dipole in space in
Fig. 23-4(a) on page 867.

Terman says on page 883:
"For purposes of calculation, it is convenient to consider that the
reflected wave is generated, not by reflection, but rather by an "image"
antenna located below the surface of the ground."

The summation of the direct and reflected waves from a horoizontal wire
above the earth often has serious consequences as Terman notes on page
885:
"Consequently, to obtain strong radiation in directions approaching the
horizontal using a horizontally polarized radiating system, it is
necessary that the height of the antenna above the earth be in the order
of one wavelength or more."

Terman shows the vertical radiation patterns for a horizontal wire at
various heights above the earth in Fig. 23-21 on page 884. Note that
half-wave elevation concentrates most energy into a good elevation angle
for sky wave reflection at some frequencies and distances.

Best regards, Richard Harrison, KB5WZI