Just find the capacitance for a wire of length L and diameter D.

A wire of length L and diameter D is a cylinder.

I vaguely remember seeing, in Terman, in graphical or tabular form,
the capacitance to its surroundings of a vertical wire of length L,
the bottom end of which is at a height H above a ground plane.

If you can't find an equation for capacitance then use the equation
for inductance. The velocity factor for an antenna wire is 1.00 or
0.99. From inductance per unit length you can calculate what the
capacitance per unit length must be to give a velocity factor of 1.00
That's the perfectly natural way I sort things out. My education must
be altogether different to yours.

The equation for capacitance in terms of length and diameter must be
of the same form as inductance with a just a reciprocal involved.

I'm even more certain you will find an equation for inductance of an
isolated wire of length L and diameter D somewhere in the bibles.
From which the equation for capacitance can be deduced.
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Reg.