[Antennaware] Equivalent Diameter of Triangular Tower

[K9AY]

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