This is quite likely overly pedantic, but “velocity factor” is a characteristic 
of transmission lines. Interestingly, it is independent of frequency (up to the 
limit of the dielectric). It depends on the geometry of the line and the 
dielectric material.

Antennas don’t have a velocity factor. The shortened elements are caused by 
capacitive loading against (RF) ground. There is a percentage of the free-space 
electrical length due to capacitive loading, but it is not a velocity factor. I 
don’t think this has a snappy shorthand other than “electrical lengthening due 
to capacitive loading”.

For example, dipoles with capacity caps on the ends, like the N6BT designs, 
don’t change the velocity of propagation along the elements. They use massive 
capacity loading on the ends (the high-voltage part of the dipole) to shorten 
the elements.

http://www.force12inc.com/products/sigma-20-hd-20-meter-heavy-duty-vertical-dipole.html
 
<http://www.force12inc.com/products/sigma-20-hd-20-meter-heavy-duty-vertical-dipole.html>

OK, overly pedantic mode off, plus I’ve nearly hit the limit of what I remember 
from my fields and waves class decades ago. I was pretty happy to get a B- in 
that class.

wunder
K6WRU
Walter Underwood
CM87wj
http://observer.wunderwood.org/ (my blog)

> On Dec 29, 2016, at 2:08 PM, Jim Brown <[email protected]> wrote:
> 
> On Thu,12/29/2016 1:53 PM, Bill Frantz wrote:
>> If this is really what is going on, then a bit longer than 1/8 wave should 
>> be about right for radials on/under the ground.
> 
> I did an NEC study several years ago placing a half wave dipole at heights 
> above ground from several feet down to an inch, and varied the length of the 
> dipole so that it remained resonant at each height. From that I plotted VF. 
> As close to the earth as I could model it, VF was about 0.7. At heights of 3 
> ft or more, VF on 160M was close to 1.
> 
> N6LF published a detailed study of radial lengths and recommended an optimum 
> length for elevated radials slightly less than a quarter wave. His basis was 
> that making them slightly shorter caused current distribution between them to 
> be more equal, which reduces ground losses. Rudy's website is a wealth of 
> great info about radials.
> 
> 73, Jim K9YC
> 
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