[TowerTalk] Antenna element diameter \ length calculation (via Leeson)

[Dan Maguire via TowerTalk]

It's also possible to use one of the Leeson spreadsheets that John mentioned to calculate the resonant length for half-wave dipoles and quarter-wave grounded verticals, although not for other antenna types such as inverted vees, elevated verticals, or loops.  In the link that John gave, the appropriate file is "Element.wk1" which is in Lotus 1-2-3 format.  It can be opened with Excel although you may have to jump through some hoops to do so.  Also, you probably won't be able to make much sense of it unless you have the Leeson book.

I own both the book and the diskette.  Several years ago I created a copy of Element.wk1 and stripped out all the parts having to do with wind/ice loading and element to boom clamps, leaving only the "Equivalent Cylindrical Element" calculations.  Here's a screen grab.
 
http://ac6la.com/adhoc/VertFactor3.png

The Leeson algorithm is implemented in EZNEC as the Stepped Diameter Correction.  In the screen grab above, the section lengths and diameters correspond to the reflector of Yagi model 20M5ELYA.ez, one of the samples included with the EZNEC package.  If you open that model with EZNEC, show the "Wires" sub-window, and click Other > Show Stepped Dia Correction you'll see this.

http://ac6la.com/adhoc/VertFactor4.png

The inconsequential differences in overall element length and diameter are because EZNEC uses single precision for the calculations whereas Excel uses double precision.

The Leeson algorithm calculates the equivalent cylindrical element given a taper schedule.  It doesn't directly calculate a resonant length.  However, it does show the reactance for the equivalent element (cell J23) at the specified frequency so you can try different tip lengths until the reactance is zero.  For "mono-taper" elements like Gary's 4" 80m vertical just use section 1 and clear all the other sections.  (And remember, lengths are set in inches, not feet.)

Or, instead of manually trying different lengths, you can use the Excel "Goal Seek" tool.  Like this.

http://ac6la.com/adhoc/VertFactor5.png

When you click OK from the Goal Seek dialog Excel will adjust the length (cell G4, or B4 if only a single section is being used) such that the reactance (cell J23) is zero at the frequency specified (cell B1).  And it'll do it a heck of a lot faster than you can.

Here's the modified Leeson workbook.  It can be used with Excel or Excel clones like Open Office.

http://ac6la.com/adhoc/LeesonElementPartial.xls

I don't have explicit permission from the ARRL to distribute this workbook but as long as it's for personal use I don't think they'll mind.

Dan, AC6LA
http://ac6la.com