"Reg Edwards" wrote
Just the same 'formula', in fact, as any other tuned circuit or
transmission line. Resonant rise in voltage and current,
and bandwidth, etc., all follow.
______________

The impedance bandwidth of a fat dipole can be so large that an acceptable
input match is possible at frequencies where the dipole is no longer very
near a resonant 1/2 wavelength. In those cases and at a constant input
power, there is a redistribution of the current in the radiators, resulting
in a relatively modest change in the peak gain of the radiation pattern.

It is true that the Q of a fat radiator is less than a thin one, but that in
itself does not produce a change in gain. A gain change results from a
change in the radiation pattern of the antenna -- which is related only to
the length of the dipole elements with respect to the operating frequency;
independent of Q.

For example, a "short" dipole (fat or thin) has a gain of 1.50X and a 3dB
beamwidth of ~90°. A standard 1/2-wave dipole (fat or thin) has a gain of
1.64X and a 3dB beamwidth of ~78° [Kraus, 3rd Ed, Table 6-2].

Another example is that of the vertical radiators used in MW AM
broadcasting. There is no term for Q in the equations for their radiation
patterns. For a given set of installation conditions, a thin tower produces
the same elevation pattern/peak gain at the carrier frequency as a fat one.

RF