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

To: "Ham - Tower Talk" <towertalk@contesting.com>
Subject: [TowerTalk] Dipole length vs diameter -- a theory question
From: Larry Banks via TowerTalk <towertalk@contesting.com>
Reply-to: Larry Banks <larryb.w1dyj@verizon.net>
Date: Tue, 28 Jan 2020 13:19:27 -0500
List-post: <mailto:towertalk@contesting.com>
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

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