Unless I goofed up the math (a distinct possibility), the answer is that
you want a Z0 of about 144 ohms, which is a spacing/diameter ratio of
about 1.81.

This was pretty easy to solve via differentiation using the
approximation Z0 ~ 120 * ln(2S/d) where S = the center-to-center wire
spacing and d is the wire diameter. The answer I got was 120 ohms, or d
= 2S/e, or S/d ~ 1.36. Unfortunately, this spacing is too close for the
approximation to be accurate, so the answer wasn't good. When I used the
full inverse hyperbolic cosine formula for Z0 and took the necessary
derivative, I found the resulting equation too messy to solve in closed
form. So I went brute force and used a simple program to iterate and
spot the maximum. It looks to me like you need to maximize d * Z0 in
order to minimize the loss (see below).

Don't trust my answer without some checking -- I did it pretty quickly
so there's lots of room for error.

It's good to have an opportunity to dust off the neurons once in a
while. Thanks.

------

Loss per unit length = attenuation constant alpha = 1/2 * (R/R0 + G/G0)
nepers/m. With air dielectric, G ~ 0, so alpha = R/(2*R0), where R = AC
resistance per meter (both wires) and R0 = (assumed purely real) Z0.
Assuming skin effect is fully developed, R ~ k / d where d = wire
diameter and k depends on frequency, resistivity, and permeability of
the wire but not on d, S, or Z0. So alpha = k / (2 * d * R0). This shows
that minimizing alpha (loss) requires maximizing d * R0, which appears
to occur when R0 ~ 144 ohms (S/d ~ 1.81).

-----

Roy Lewallen, W7EL

K7ITM wrote:
More for the fun of pondering it than for any immediate practical
reason...

If I make a balanced two-wire transmission line from round wires, and
I'm constrained to have the wire center-to-center spacing some
particular value (say one inch, or five centimeters, or whatever), what
wire diameter should I use to get the lowest matched-line loss? What
impedance line does that give (assuming air dielectric)?

Clearly for a given wire diameter, the wider the spacing the lower the
loss up to the point where radiation plus dielectric loss becomes
significant, but I can imagine situations where you want to limit the
wire spacing and get low loss.

Cheers,
Tom