On Mon, 08 Aug 2005 12:27:09 -0700, Roy Lewallen
wrote:

Unfortunately, the mathematical analysis in that paper was found to be
in error. A search of the literature shows that quite a number of people
worked on this problem well after publication of the BL&E paper. Some
notable work was done by J.R. Wait and W.A. Pope of the Radiation
Physics Laboratory, Defence Research Branch, in Canada. Two papers in
particular give equations for the impedance of radial systems which
appear to be valid -- "The Characteristics of a Vertical Antenna With a
Radial Conductor Ground System", Appl. Sci. Res. B, Vol. 4, 1954; and
"Input Resistance of L.F. Unipole Aerials With Radial Wire Earth
Systems", Wireless Engineer, May, 1955. The equations involve multiple
integral equations which can't be solved in closed form. In papers I've
read which do involve equations which can be solved in closed form, even
approximately, the results have deviated greatly from BL&E's measured
results, making the accuracy of the method doubtful. This holds true for
Reg's program, also, which apparently depends on some simplifying
assumptions which aren't valid.

snip

Roy Lewallen, W7EL

Roy, I don't have the Wait and Pope paper for review, but I'm
concerned over the validity of their equations that you say render
BL&E's measurements invalid. How can their measurements be invalid
when field-strength measurements of literally thousands of AM BC
antennas agree with BL&E's? Keep in mind that every BC station that
uses a directional array is required to prove the performance of the
array with field strength measurements that assure the measured values
agree with the calculated values.

It was only after verifying BL&E's measurements by comparing their
data with those obtained from many subsequent measurements of BC
antennas that the FCC used the BL&E data in standardizing the
requirements for radial systems for new BC stations.

Isn't it possible that Wait and Pope's equations relate to some other
aspects of BC antennas than those of BL&E? I simply cannot accept the
notion that BL&E's data is wrong.

Walt,W2DU