This page is not a "How to Design Vertical Elements" manual. It is a review of the design path used for the elements in my 40 meter 4 Square array. The situation that governed how these elements were made is similar to what many amateurs face when taking on one of these projects. Often, we begin with a collection of materials that we would like to make work for the project and need to evaluate the situation, and make compromises to get things to work. The discussion that follows, may be a bit long and display more detail than most readers find useful, but it is a fairly thorough look at the things involved in a guyed vertical element design, and offered for those interested in finding out more about these things. This page addresses the use of the YagiStress software to perform a simple look at the problem. The next page addresses a more rigorous evaluation of the problem.
The elements were going to be made from existing sections of aluminum tubing from W7CY's 80M 4 Square (these used to be mounted on top of some Hy-Gain Hy-Towers), which would comprise the lower part of the elements and some KLM 20 meter beam elements, that would make up the top part. I had some long 1/2" x .058 wall sections that I used to replace the original KLM tips to make sure all of these elements would have enough length.
Because, I was working with existing material, the design effort was to try and make the existing material capable of surviving the highest wind speed practically possible, instead of developing a design from scratch for a specific wind speed.
Designing from "scratch" and designing around existing constraints are two different procedures. As it turned out, the existing material made a reasonable structure and was not very difficult to design. If I had designed the elements from "scratch", they would have been different from the elements that were built, and are now out back. It's always one compromise or another!
The tool used to initially design the elements was my YagiStress software. Although, YS was really developed to design Yagi beams, it can be used to design vertical elements, when the difference between analyzing a vertical and horizontal element are understood. The YS element analyses presented here can be done with a $12 calculator, or your favorite spreadsheet, but the dedicated software is so much easier, faster, and more fun to use.
Horizontal and Vertical Element Fundamentals
Before looking at the element design, understanding the difference between vertical and horizontal elements is helpful.
The horizontal yagi element is subjected to two fundamental loads in a static analysis. Usually, the most significant load is from the wind. The other load comes from the weight of the material in the element. In a simple analysis, the wind load is assumed to be purely horizontal, and the weight is a vertical load. Analyzing the horizontal element, we take the wind and weight loads and solve for a resultant load, and then calculate the stress caused by the resultant load. This is what YagiStress does. For elements that do not have ice accumulation, the magnitude of the loads caused by element weight is very small compared to the wind load. For a tapered 40 Meter element, capable of 80 Mph Basic wind speed survival, a very small percentage of the resultant load is caused by the element's weight.
This vertical load component (on the horizontally aligned yagi element) is not present on a vertical element. The vertical element has a "weight" induced load, that produces a very small order axial compression load on its cross-section.
Since, the element weight is a small factor in the yagi element's stress, one might wonder why it is even included. For antennas that are subject to ice accumulation, it is imperative to include the vertical loads on the element, as the ice loading can easily become the predominant load component. This has been empirically proven many times, where antennas have been destroyed by ice accumulation alone during very moderate wind conditions.
Now, when using the yagi design tool for a vertical element, if the vertical is not subject to ice accumulation, the error introduced by the vertical load component, is quite small and can simply be considered a small safety margin for the vertical design.
In fact, this error is most likely less that the inherent error bandwidth associated with trying to analyze this type of mechanical assembly, when things like the tolerances of the tubing sections, and their associated fits, and other mechanical assembly factors are taken into consideration.
Since, my location does not experience severe icing conditions, using the horizontal yagi element analytical tool is quite satisfactory for evaluating the vertical element.
Analyzing the Element With YagiStress
The first step in the process is to make a YS model of the existing material, and see what it looks like. The vertical has been modeled as 1/2 of a yagi element. The effective area and weight on the YS screen need to be halved to be correct for the vertical.
I made the model with the available sections extended far enough to be longer than needed for 40 meter cw. This can be seen in the lower left corner of the screen, where the element resonant frequency is well below what will be required to make the element work in the array. Shortening the element tips to obtain the desired
resonance inside the band will result in lower stress than this model produces, so it is a conservative approach.
The YS element display screen lists the section dimensions and other pertinent information, like the stress in each section. The Exposed Length shown is what one would be able to see, the difference between it and the Total Length, is how much of the section is inside the next larger one. The built in editor allows all section dimensions to be changed, sections can be added or removed.
This version of YS uses the EIA-222-C methodology for determining antenna loads. Information about wind loads can be found on this website's Mechanical Notebook - Wind Load page.
Initial Element Analysis
This was the first look at what the material on hand would do.
The 63 Mph safe wind speed does not satisfy the minimum 70 Mph basic wind speed zone, but we have to start somewhere....
The highest stress is in section #7. But sections #3 through #7 are all near limit, so to increase the element's survival speed, we have to reinforce all of those sections.
I did not have the right tubing on hand to do that. So I decided, the most sensible solution would be to use guys to support the elements.
Additionally, the "Sag" dimension indicates that the element is not very stiff, and would probably be moving around quite a bit in the wind. So, using guys would greatly increase the element's stability.
I had plenty of .875 Dia x .058 wall tube to reinforce section #3. So, I decided to try guying it at the bottom of that section. Section #9 is fully supported by the attachments to the wood post, so the unsupported span between the post and the guys would be 151" and the length cantilevered above the guy point would be 225" or just the original KLM 20 meter element.
I added another element to the antenna to look only at the cantilevered top sections and installed a reinforcing tube inside of section #3. The reinforced section is denoted "Dblr" (doubler) on the screen. It increases the wall thickness from .058" to .116" and sections #3 & #4 are the same exposed length as the original section #3.
Configuration #2 Analysis
The element top sections are adequate for an 80 mph zone and the modification is pretty simple.
I had most of the element sections assembled at this time, so I decided to try this configuration on one element and put it up and see how it behaved while I worked on the radial system. The test element also provided an opportunity for me to evaluate the "stealth" paint jobs.
After watching for a couple of weeks, I thought the tip was moving quite a bit in the wind and that the element deflections were making the lower sections, below the guy point, become a bit unstable.
I decided to have a look at what moving the guys up to the bottom of section #2 would be like.
Configuration #3 Analysis
The safe wind speed went up a little to 87 mph. The element behavior was greatly improved with this change, with low tip deflection and stable behavior of the column below the guys. So, I finished the rest of the elements in this configuration. Because the guys were moved up to section #2, the internal reinforcements were not used inside the 1" dia section. The tip lengths ended up quite a bit shorter after resonating them.
After the antenna was completed and working, I looked at how the finished tips were doing.........at 98 Mph, I was satisfied this part of the design would probably be ok.
Cheating a bit to finish the Job
With the top part of the element design resolved, I knew that, to do a proper job designing the guyed vertical, I needed to look at the buckling behavior of the sections below the guy attachment point. In this area, there is axial compression from the guy reactions and a bending moment from the cantilevered top portion.
There comes a time when ya have to put down your pencil, and go get it on the air, so you don't miss all the fun! It's also more fun, sleeping well at night, thinking you have it under control, and are not on the verge of a nasty surprise!
It is not a terribly simple analysis and I was running short on time. So, I went and looked at some other antenna designs where I had looked at this problem, and made an educated guess that this one would be ok. I made sure that I observed the elements, during wind events, to see if I could detect any column instability, below the guy point, that would indicate that there was an impending problem.
The 3/32" Dacron/polyester guy lines were anchored by 1/2" dia x 24" long rebar stakes. The stakes are placed in 3 equal places around the elements and are placed out at a distance of 100% of their connected height on the elements.
The elements saw several wind events over 70 mph in the first few months, and they seemed to behave quite well. I have seen no signs of buckling instability during these wind events.