Equivalent diameter of Rohn 25
This is where I found the reference to 5" (5.25" actually) as the equivalent
radius of Rohn 25 tower:
William F. Cummings (K6MYH), "Tower Equivalent Radius," Conference
Proceedings, 14th Annual Review of Progress in Applied Computational
Electromagnetics ("ACES" Conference), Monterey, CA 1998.
Information on ACES can be found at: http://aces.ee.olemiss.edu/
ACES papers can be hard to find, and the CD collections available on the web
site are $150, so I'll summarize key points of this paper.
__________
To begin, he notes these existing estimates of equivalent diameter:
Eq Dia = 0.4214a = 2.92"
where 'a' is the outscribed radius of the triangle [Jasik, Antenna
Engineering Handbook]
Eq Dia = 4.7" for a circular cross-section having equal enclosed area
Eq Dia = 5.73" for a circular cross-section having equal perimeter length
For the analysis, Cummings "constructed" a 44-foot high tower in NEC, with
all legs and braces included -- a large number of segments!
He then analyzed the power scattered from a vertically polarized plane wave
incident on the tower structure. Note that he did not compare feedpont
impedance; his comparison was for equal radiation (re-radiation, actually)
from the tower and an equivalent cylinder. His analysis used fields at both
1 MHz and 100 kHz, assuming that consistency over a 10:1 frequency range
would validate his method.
He compared the tower results to cylinders of the same length, with segments
of 16 inches to mimic the repetition of the 25G bracing pattern. Cylinder
diameters of 4.0, 4.5, 5.0 and 5.5 inches were used.
First, there was a small difference (a factor of 1.0049) in edge vs. face
illumination for the triangular tower, and the average of the values was
used. A plot of the scattered power at the various diameters was nicely
linear, simplifying interpolation. The resulting equivalent radii for the
two test frequencies were 5.24 and 5.25 inches.
My Notes:
This analysis does not consider feepdoint impedance, which varies roughly as
the log of height/radius. For my 100-ft. tower, the impedance with 5"
diameter would be 3.6% lower than 4", +/- effects of top loading and the
quality of the ground system.
Sometime in the past, I recall a discussion by a ham who constructed an 80M
or 160M vertical using 25G over an extensive radial system. He carefully
measured its height and its feedpoint impedance, and made modeling
comparisons similar to Cummings. My recollection is not 100% certain, but
his equivalent diameter was close enough to Cummings' that I adopted it for
my normal practice.
Hope some of you find this interesting!
73, Gary
K9AY
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