I agree with Roy on this, that an accurate understanding will take some
fairly serious analysis. For example, the top hat in my example had
_less_ shortening effect than simply using a wire with radius only 1/4
as large as the length of the top hat radials. Also, calculations of
the capacitance of a spherical capacitor, compared with capacitance per
unit length of the antenna wire, don't give me any confidence that the
end capacitance fully explains the shortening effect.

Cheers,
Tom