As it happens, you've caught me right in the midst of trying to program
just that calculation. But it turns out to be a toughie. It involves a
couple of Bessel functions -- which aren't a problem in themselves, but
the problem is that when the tube diameter is the skin depth, the
formulas I've come across so far require subtracting two huge numbers of
limited accuracy (even if the wall itself isn't particularly thick in
terms of skin depth). So the results I've gotten so far, even with
double precision math, are garbage. I've been working at reducing and
rearranging the equations, and using asymptotic approximations, but so
far no joy.

Anyway, I believe the phenomenon you mention. I've come across it a
couple of places. A similar thing happens with the plating of wires,
where a relatively poorly conductive plating of the right thickness
actually improves the RF conductivity of the wire. The effect,
unfortunately, is quite small, as for the case of wall thickness.

Roy Lewallen, W7EL

Reg Edwards wrote:
Take an ordinary round solid conductor. For well known reasons at
alternating currents it will have a higher resistance per unit length that
at DC.

Now, if a round hole is drilled down the centre of the conductor, ie., its
highly-conductive center is removed, the AC resistance will be REDUCED.
There are, of course, better ways of producing tubes.

The effect is at a maximum when the wall thickness of the tube is about 1.6
times skin depth in the material, ie., when an appreciable fraction of the
current flows on the internal surface. The reduction in resistance is only a
few percent and for a conductor of given dimensions it affects only the
lower frequencies.

It has something to do with internal inductance and the relative phases of
the inside and outside surface currents.

It is likely the effect is considered only when transmission line efficiency
is of overriding importance, perhaps at power frequencies, the 'hole' in the
conductor's center being occupied by a steel tensile strength member.

My one and only reference book is Robert Chipman's "Theory and Problems of
Transmission Lines", 1968, McGraw Hill, where the effect is described in a
little more graphical detail than above. But the likelihood of obtaining a
copy of this book is remote
----
Reg, G4FGQ