As he says, Roy's resulta are very approximate. That's mainly because
he neglected proximity effect between the wires.

A better approximation is obtained by incorporating an approximate
expression for proximity effect. However, this makes differentiation
of the loss formula with respect to wire diameter ridiculously
tedious. So I found minimum loss by plotting a graph with a pocket
calculator and searching for it.

At HF when skin effect is fully effective, and neglecting dielectric
loss in comparison with conductor loss -

For a fixed wire spacing, as wire diameter increases, the wires get
closer together and proximity loss eventually increases faster than
ordinary loss decreases due to the increase in diameter.

Thus minimum loss occurs at a smaller diameter and a greater
Spacing/Diameter ratio. The Ro at which minimum loss occurs is
independent of both frequency and wire conductivity. Results are -

Ro = 177 ohms. Spacing between wire centres is 2.29 times wire
diameter.

Which demonstrates that mathematics is vastly superior and takes
priority over practical experiments and making measurements.

From an engineering point of view, K7ITM asked the wrong question. He
should have asked, for a given wire spacing, what wire diameter
minimises the cost of the copper. Or something like that.

Many years back a similar sort of calculation was done for coax. Coax
does not suffer from proximity effect. It's easier to work out. The
answer was 75 ohms. That's how 75 ohms became the standard
comunications Ro. There are many millions of miles of the stuff. The
Chinese are now making even more of it.
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Reg, G4FGQ