Regarding your very long wire antenna.

Radiation pattern depends on the number of wavelengths that the wire is
long. When it is very long, also the propagations speed inside the wire
is going to count (some insulation, does slow down the propagation
speed of the traveling wave a bit, reducing the far field radiation).
Also the straightness of the line is important with very large
Le/lambda.

As propagation speed is equal to c, the radiation pattern will be a
cone (with side lobes), the longer the wire with respect to wavelength,
the narrower the cone will be (so a high directivity). But I believe it
is not a useful antenne, the radiation pattern of such a line is not
that good and maybe you don't want directivity. When you really want
to experiment with long wires at VHF/UHF, a non-linear expanding two
wire structure, fed from a balun would give better results. That gives
a better radiation pattern (with side lobes). If you would prefer a
V-structure, you have to adapt the angle between the wires depending on
frequency to get highest directivity (high frequency requires small
angle).

The impedance of the single wire antenna shown at the antenna terminal
depends on how you feed it. When you feed it from a gradually expanding
coaxial structure (launcher), you don't need a balun and get wide band
behavior. The "return" conductor is the coaxial structure. When you
insulate the wire it becomes a Goubau line (with less radiation).

The impedance of the wire itself is more difficult. The standard
formulas are only valid for cross sections much smaller than the
wavelength. In your case Mother Earth is not the return conductor.

Your wire is not terminated, so you may expect a reverse traveling wave
that cause a cone like radiation pattern in the opposite direction (and
of cause reflection into the transmitter).

When you search for traveling wave antenna or surface wave antenna you
will find useful information.

Best Regards,

Wim
PA3DJS