Considering it as a conductive sheet, from Jaggard the equivalent radius
for a triangular tower shape comes out about 42% of the face width
(equivalent diameter is 84%).
There are formulas for two parallel conductors, and it's a more complex
problem to find the exact equivalent of just the legs and cross braces
of a triangular tower. For the calculation for three parallel
conductors, see "Equivalent radius of parallel-three-conductors,"
Section 3.3.3 in S. Uda and U. Mushiake, "Yagi-Uda Antenna," Sendai,
1954, pg. 20. Their formula for the equivalent radius is a = cube
root(r*d^2), where r is the radius of the conductor and d is the
spacing. This yields a different estimate of equivalent radius,
depending on the radius of the legs. For a tower with leg radius 0.625"
and leg spacing of 16.75" (Rohn 45G), the equivalent radius from the
Uda-Mushiake formula is 5.6" or 33% of the leg spacing.
Of course, a numerical way to determine the equivalent radius of a
lattice tower is to model it with an electromagnetic software. But these
simple estimates should do to get an idea of the effect of a tower on a
mounted Yagi.
Dave
On 6/25/24 9:56 AM, Leeson wrote:
From "Physical Design of Yagi Antennas," ARRL 1992, pg. 9-2:
"This problem is resolved in a short paper by Jaggard [D. Jaggard, "On
Bounding the Equivalent Radius," IEEE Trans AP, Vol. AP-28, May 1980,
pp. 384-388, https://ieeexplore.ieee.org/document/1142336] Jaggard shows
that the equivalent radius ae of a noncircular shape must lie between
the radii ai and ac of the inscribed and circumscribed circles which
geometrically bound the noncircular conductor. Further, he shows that
these bounds can be narrowed by the use of radii ain and aout which are
the radii of circles of the area A and perimeter P of the cross-section
shape of the conductor, ain = sqrt(A/pi) and aout = P/2pi. A
satisfactory estimate for the equivalent radius is the mean of the two
bounding radii."
A freely downloadable scan of my 1992 book with more details about the
equivalent radius of irregular shapes, "Physical Design of Yagi
Antennas," is at
https://www.dropbox.com/s/hmhkeofz0igrg1e/Physical%20Design%20Of%20Yagi%20Antennas%20D%20B%20Leeson%20V2.pdf?dl=0
73 de Dave, W6NL/HC8L
On 6/25/24 5:40 AM, john@kk9a.com wrote:
To check for interaction, I have done the easy model method of using
a very thick wire for the tower. Since the tower is triangular and a
wire model is round, I took a wild guess at the wire diameter. I
never thought of matching the surface area.
John KK9A
Jim Lux wrote:
There's two ways to approach the modeling. The easiest is to model a
"very thick" wire - match the surface area of the tower with the
surface area of the wire.
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