[TowerTalk] Modeling a self supporting tower interaction

[Leeson]

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 at 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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