[TowerTalk] Dipole length vs diameter -- a theory question

[Larry Banks]

Hi TTers,

A friend of mine asked me what first appeared to be a simple question.  Paraphrasing:

          “How do I calculate the length of my HB 2M halo, based on
            the diameter of the aluminum rod.  Is it like propagation
            velocity with coax?”

My quick answer was: “No, propagation velocity only relates to transmission lines.  Use the graph in the literature for your design to start.  Modeling will help.  But let me do some research.”  

I had realized that I really didn’t know the answer.  I have looked in my two usual places: the ARRL Antenna Book and Wikipedia and found lots of hand-waving and the usual references to the “K-factor” graph, which appears to be derived experimentally.  BUT NO THEORY, other than vague references to the capacitance and inductance of the rod changing with dimensional changes which, in fact, is similar to transmission lines.

Do any of you have a reference to some real theory and an equation that allows me to calculate this based on length, diameter, and material characteristics?  (Ignoring environment effects of course.  This would be for free space.) 

73 -- Larry -- W1DYJ