Re: [TenTec] NEC, ground, grounds, and radials

[Jack Mandelman <modelman@ieee.org>]

Jerry,
The point that I'm making is that the formulas discussed are applicable 
only for very specific geometries.  The validity of formulas breaks down 
at the extremes of the underlying physical assumptions.  Formulas are 
not predictive beyond their ranges of applicability.  A case in point is 
conductor cross-sectional geometry that departs from circular.  General 
inhomogeneous dielectric distributions in the vicinity of the conductors 
is another difficult case.  How would you handle these cases?  These are 
only a couple of examples where the classic formulas may result in 
inaccuracies.  By not limiting ourselves to the strict geometries on 
which the formulas are based, we open a world of opportunities for 
innovation improving upon the state of the art.  The point that I'm 
making is that finite-element analysis is state of the art, which frees 
us of the constraints imposed by formulas.
Certainly, Harold Wheeler's work is widely recognized.  However, he 
relied on geometry mapping techniques for deriving his formulas.  As 
such his formulas have limited applicability if one wishes to depart 
from his geometric assumptions.  Because of computational limitations, 
finite-element analyses were not a practical option in his day.  But it 
is a valuable tool available today, even for hams, and we should take 
full advantage of it for going beyond what formulas predict.
No need to get defensive about Wheeler's work.  I have the highest 
respect for his achievements.  So please lighten up a bit.
Jack K1VT

> Harold Wheeler was a transmission line guru of the highest class with 
> many
> papers to his credit, but when interviewed later in life he was most
> proud of the inverse hyperbolic cosh formula for capacitance of closely
> spaced parallel wires. His career ran another 30 or 40 years after that
> paper and he had plenty of time to revisit it but didn't change the
> results while investigating many other transmission line shapes and
> publishing curves and formulas for their parameters.