On Oct 23, 10:35*am, (Richard Harrison)
wrote:
Mike, N3LI wrote:

"I thought that the inductance tends donward as the diameter of the wire
increases. I can understand your calculation after the wavelength part,
but don`t quite get the increased inductance part."

Good observation.

Wire inductance decreases with the circumference increase as this
effectively places more parallel inductors in place along the surface of
the wire.

Wire capacitance increases proportionally with the square of the
circunference of the wire as it is proportional to the wire`s surface
area.

The fatter wire grows capacitance faster than it changes inductance.

Reactance along a wire antenna element varies quickly near resonant and
antiresonant points so is not uniformly distributed. This complicates
calculations and requires average values for some. Bailey says of surge
impedance: "Nevertheless, this variation in theoretical surge impedance
shall not deter us from setting uup practical "average" values of surge
impedance. *
Best regards, Richard Harrison, KB5WZI

I know we're talking about linear antennas here, but even in that
case, it's surely not true that capacitance increases as the square of
the wire diameter (or radius or circumference); nor inductance
proportional to 1/diameter. Consider that if both those were true,
doubling the wire diameter would quadruple the capacitance and halve
the inductance, and the propagation velocity along that wire would be
1/sqrt(4*0.5) or about .707 times as great as with the thinner wire.
Clearly things change much more gradually than that.

In the controlled environment of a coaxial capacitor, the capacitance
per unit length is proportional to 1/log(b/a), where a is the inner
conductor diameter and b is the inside diameter of the outer
conductor. If you change b/a from 10000 to 5000 (huge outer diameter,
like a thin wire well away from ground), the capacitance increases by
about 8 percent. Going from b/a = 100000 to 50000, the capacitance
increases by a little over 6 percent. Similarly, inductance in coax
is proportional to log(b/a), so in coax as you change the inner
conductor diameter, the capacitance change offsets the inductance
change exactly and the propagation velocity is unchanged. The
environment of an antenna wire is different than that, but not so
different that doubling the wire diameter has a drastic 30% effect on
the resonant frequency.

Cheers,
Tom