Friday, August 23, 2019

Stacking Scenarios for the New Tower: 15 and 20 M

As I grind my way towards completion of my stacks of 5 element yagis for 15 and 20 meters it is time to decide what goes where. The objective is to maximize performance, when used as a stack and when used individually. The major decisions on placement: height and separation.

There is also the matter of interactions with yagis for the other bands and with the guy wires. For the present exercise I will ignore those interactions since the way I broke up the guys to be non-resonant and with sufficient yagi separation the pattern impact will be small.

In addition to electrical considerations there are physical constraints:
  • The yagis atop the tower cannot be separated by more than 3 meters (10') to keep mast stress within reason. Similarly the smaller yagi for 15 meters will go at the top of the mast and the 20 meter yagi at the bottom of the mast.
  • Lower yagis must be above a guy set, but not too far above to avoid tangling with the guys further up. The constraint is tighter if those yagis are rotatable rather than fixed. At least t his year they will be fixed towards Europe.
When completed the tower for these antennas will stand approximately 133' tall (40.5 meters) and the mast will rise another 10' (43.5 meters). Guy stations are nominally at 30', 65', 100' and 135', however due to section overlap the heights are more like 28', 61', 93' and 128'.

To recap the yagi dimensions:
  • 15 meters: 5 elements on a 32' boom (10 meters). This antenna has low SWR across the full band and has been optimized for best gain while having a good match and F/B. Design details can be found in an earlier article.
  • 20 meters: 5 elements on a 40' boom (12 meters). This antenna is a minor optimization of the yagi having the same dimension in recent versions of the ARRL Antenna Book.
Modeling is done with EZNEC. I use dual sources for in-phase stacking rather than phasing harnesses to make the modelling exercise easier. This does not materially affect the pattern but does affect the impedance, and the latter is not the focus of this article. SDC (stepped diameter correction) is used for all elements per my tapering schedule. Construction detail will appear in a future article.

If you're new to stacking you may want to review my article on the basics of stacking. There are of course many other resources on the topic of stacking around the internet and in the amateur literature.
20 Meters

I'll look at 20 meters first since the stack is more constrained; that is, there are fewer viable options for placement of the yagis. The upper yagi is at the bottom of the mast, which I waffled on with regard to the precise height, as you can see in the plot traces. The 2' (0.6 m) different is negligible. The lower yagi is in the vicinity of guy stations, ideally slightly above as discussed earlier.

Height of the upper yagi is ~2λ. Height of the lower yagi is at either 1λ or 1.35λ. The modest difference in height of the lower yagi has a significant impact on the stack behaviour.

The respective separations are 41' (12.5 m or 0.6λ) and 67' (20.5 m or 1λ). The first is equal to the boom length, usually considered the minimum separation for good performance; this is discussed in more detail below. The second is well separated at the cost of placing the lower yagi relatively close to ground (1λ).

The lowest lobe of the upper yagi is 7°, and 11° or 15° for the lower yagi. Lowest lobe of the stack is 8° and 9°, respectively.

Gain of the stack and individual yagis varies by less than 0.4 db for the two scenarios. This is indicative of low interaction, and that is confirmed in the EZNEC model. Although not confirmed in this exercise the low interaction (mutual impedance) between yagis promises low pattern distortion when they are pointed in different directions.

Stacking gain over the individual yagis varies from 1.5 to 2.5 db, which is quite good for 20 meters at these heights. The nominal 3 db stacking gain is just that: nominal. There are many variables that determine this performance metric.

Notice that the patterns of the lower yagis differs quite a bit due to their different height, and this affects the pattern of their respective stacks.
  • Vertical radiation is higher for the lower yagi at 92' since that is the only position that is not a multiple of λ/2.
  • Inter-lobe nulls coincide more closely when the stack separation is smaller, as expected. Better elevation angle diversity is achieved with greater separation. That is desirable for paths with an elevation angle close to a null so that we can avoid dead spots. 
  • The major lobe of the lower yagi is significantly higher at the lower height. This, too, is desirable for path diversity. When fixed to Europe with its wide range of probable elevation angles the lower yagi becomes more useful.
  • High angle minor lobes are attenuated with the lower yagi at 1λ height.
The choice for 20 meters is quite easy. The lower yagi will go directly above the second guy station. When (if) the lower yagi becomes rotatable it will also perform well on paths to Africa, Caribbean and North America.

15 Meters

With the upper yagi at the top of the mast and the shorter wavelength it is easier to achieve low interaction between yagis on 15 meters in comparison to 20 meters. The shorter boom length is also helpful in this respect.

The maximum height possible for the lower yagi is below 120', otherwise the elements get dangerously close to the top guys. I therefore chose this height for the first test case since while not physically practical it highlights a too small stack height of 20' (6 m or 0.42λ), which is less than the boom length.

In the second case the lower yagi is at the more practical height of 100', a little above the second highest guy station. This maximizes the distance from the outermost elements to the upper guys. The stack height is 40' (12m or 0.85λ). This is much better spacing.

When modelled the difference in performance is readily apparent. As with the 20 meter stack the greater stack height there is better distribution of the elevation nulls, reduced high angle radiation and greater stack gain.

If I had a tower dedicated to each band I could exploit the height to add a third yagi to the stack. This is not practical in my case where 15 and 20 meter yagis present since optimum and equal spacing would have yagis tangling with the guys or parked too close to a yagi for the adjacent band. A friend of mine who does manage to have a 15 meter 3 stack shared with 20 meters uses a taller tower than mine.

My next test case was to move the lower yagi even lower, though not too close to the lower 20 meter yagi at approximately 68'. The chosen height of 80' is, like 120', risky since it places the outermost elements close to the next highest set of guys.

The result is a mixed bag. Rearward lobes are small but there is an increase in radiation at high angles. Differences in gain of the stack and individual yagis compared to 100' are negligible at less than 0.3 db.

My tentative choice is to place the lower yagi at 100' or a little lower to increase distance to the upper guys while not getting too cozy with the set of guys immediately below.

Other antennas on or near the tower

Interactions limit further use of the tower. I plan to use my TH6 and TH7, possibly stacked, at lower heights for short paths such as the US and Caribbean. There is no good place for these tri-band yagis on the tower that would not impact performance due to interactions with at least the lower 20 meter yagi in the stacks. The tri-band yagis will therefore go on the other big tower, well below the 40 meter and 10 meter yagis.

I would like to leave open the possibility of a wire 40 meter yagi pointed at Europe, strung on a catenary between the big towers. With 5 elements the wire yagi would be 30 meters longs, which is about half the distance between the towers. Interaction with 20 meter yagis should be managable. Impacts on the performance of the 15 meter yagis could be more severe. The same is true of the tri-band yagis which are, of course, resonant on 15 meters.

I am looking at alternative placements of the wire yagi to best advantage. There is modelling work to be done.

Vertical antennas for 160 meters are less concerning due to the polarization difference. However the T-top of my current 160 meter antenna will require a close look to confirm that it will not causing any problems with the yagis on both towers.

Yagi separation vs. boom length

There exists a rule of thumb that two yagis in a stack should not be closer together than the yagis' boom length (for identical yagis). This is good guidance even if it obscures the reason for why it is a useful rule. Without delving into excruciating detail we can dig a little deeper for some insight.

But first let's review how a stack develops gain. For two identical yagis fed in phase, in free space and far enough apart that the mutual impedance is negligible, the stacking gain is exactly 3 db. This fact alone is a curiosity since we are dividing the power so that each yagi get half of it and the yagis' far field patterns sum in the far field. Fortunately I wrote an article on how this is possible if it seems paradoxical.

In the real world the yagis interact with real ground and there will always be some mutual impedance between the yagis. The closer together the greater the mutual impedance since the various elements will have near field coupling to those in the other yagi.

It is possible to have stacking gain greater than 3 db with carefully engineered close spacing. However this is only advisable if the yagis always point in the same direction, whether fixed or rotatable. Otherwise when one of them is turned the high mutual impedance will distort the patterns of both yagis. In general it is a poor idea.

Ground reflections for the two yagis place their lobes and nulls at different elevation angles which affects stacking gain. By closely spacing the yagis the lobes, especially the lowest main lobes, will reinforce each other and give close to the theoretical but nominal 3 db gain. This is at the price of a reduced ability to sidestep elevation angle nulls since these, too, will coincide, as we saw in the discussion earlier in the article.

With the preliminaries out of the way let's return to yagi separation and coupling. Yagi gain increases with boom length. Gain comes from a narrowing of the main lobe. As the lobe narrows the mutual impedance to a vertically separated identical yagi decreases. This is due to field cancellation away from the main lobe, directions which would intersect elements of the other yagi. Note that for this purpose we are primarily concerned with the free space elevation pattern (shown on the right).

However the lobe narrowing happens in concert with a longer boom length. Therefore the angle of, say, the -6 db point is lower but will still interact with the outermost elements of the other yagi because they are further out. The relationship is not exactly proportional but close enough that the rule of thumb is justified: increase the separation as the boom length increases to achieve approximately the same amount of element coupling (interaction).

Keep in mind this is a minimum distance not an optimum distance. When you allow the yagis to point in different directions more separation reduces pattern distortion. This is usually a better choice than trying for maximum stack gain.


I have ample time before winter to refine the stacking arrangements. This can be done in parallel with the construction and tuning of the four yagis. Although I had hoped to be further along by now I am getting closer. It's been a learning experience, one with unexpected stumbling blocks.

You can see from the picture of aluminum shavings (the dark patches are steel) filling most of a 5 gallon pail that I have not been idle! Construction of the yagis is a story unto itself and will be covered in future articles.


  1. hello ,

    Seems both of us are on the same wave length , hi hi .
    I to am trying to build and erect a 4 element , 20 meter yagi .
    Acquired a good assortment of materials from metal scrap yards , mainly aluminum products .
    I came across a single piece of 2 1/2 aluminum tube at 20 feet long just laying on the ground at the scrap yard .
    Got a couple of really minor dings but straight end-2-end .
    The wall thickness is what I am most concerned about .
    My piece of tubing the wall thickness measures to be .065 thick .
    Tube seems hefty enough but for a 4 element 20 meter beam , I'm not sure .
    Question to you....
    What is the wall thickness of the booms you have ?
    Hard to tell from the pictures .

    I like the idea of joining sections together using pipe .
    I did exactly the same thing using aluminum lawn lantern posts from Lowes and turned down 2 7/8 diameter aluminum pipe to make 3 snug fit sleeves to join 4 posts together .
    Posts are 3 inch diameter by 80 inches long and will easily make a 20 foot boom .
    3 X 80 inches = 240 inches / 20 feet .
    Could add more post sections to make boom longer .
    4 X 80 inches = 26 1/2 foot boom ect....

    I need to know what material I should use for the boom since I have a choice between the single 2 1/2 inch piece or the coupled post section idea .
    Both are tough but who knows ?

    Elements will be heavy so proper boom size and type will be crucial .

    Thanks from one antenna builder to another , KC8GTR , Bill

  2. Hi Bill. Scrounging is good but be careful. You must ensure that all the pipe and tube you use is 6061-T6 or better with regard to tensile strength. Standard aluminum pipe should that alloy, however everything else is questionable and you should not use it if you cannot determine the alloy and strength. Here's a link to begin to learn about pipe sizes used in Canada and the US:

    Do a search on my blog for my many adventures in pipe and tube fitting for yagi booms and elements. With care you can find pipes that telescope well and others that require shims.

    With regard to what you should use, either you build to someone else's spec or you use software like Yagi Stress to do a full calculation based on your spec and wind/ice survival objectives. I can't advise you other than to point you to these resources.

    Also take care in how you join pipes and tubes so that they are strong and fasteners to not fail or come loose. There's a lot to learn! Good luck with your project.

    73 Ron VE3VN

  3. It would be great if you can provide the wall thicknesses of the booms you have in the pictures .
    That was my whole point .
    That info would be very helpful so I can compare what the major manufactures are using .

  4. Hi Bill. The reason I didn't get into specifics is that some will do the same but without doing the stress calculations. That's a common mistake and I didn't want to lead anyone astray. However...the upper 15m element has a 12' centre section of 2-3/8" OD schedule 40 pipe and 2"x1/8" wall end pieces. The upper 20m boom is 2-7/8" x 8' schedule 40 centre section, more of the 2-3/8" next and then again the 2"x1/8" tube. Some shimming required to make everything fit properly, which is typical of standard pipe sizes. Use of schedule 80 pipes, while stronger with a thicker wall is generally not recommended for booms since the extra weight when used horizontally.
    73 Ron VE3VN

  5. hello ,

    Ahh, news I can use !
    Thanks a bunch , that does help a lot and will be saved in my library of useful knowledge .

    The material I have here is quite similar but the outer boom sections are thinner .
    The basic design is laid out as follows for approximately a 32 foot boom ...
    the center section will be composed of 2 pieces of 2 inch aluminum pipe , threaded .
    Both pieces are about 78 inches long and threaded on one end only .
    Either I will use a humongous 2 inch electrical tee to screw everything into , mast included , OR use heavy duty threaded aluminum coupler and a mast plate .
    Overall center boom section will be around 13 feet depending which mounting method I select down the road .
    For the remaining 32 feet is where I have doubts about .
    I have in my possession 20 feet of 2 1/2 inch aluminum tube that has a wall thickness of .065 inches .
    The whole 20 foot tube seems flimsy if lifted and shaken a bit .
    Probably would work great for a 10 meter yagi but I already have one up in the air now .
    But how flimsy will it be if I was to cut in half ??
    The 2 halves will snugly fit over the 2 aluminum conduit / pipe .
    Tried it out and its a go .
    I'm curious if only about 9 to 9 1/2 feet of this thin wall tube hanging out from the center pipe sections would be strong enough to handle not just sagging forces and wind but ice and large birds !!
    I have a real serious huge bird problem , the whole flock like to sit on my beams and they are heavy . 20 meter beam will be 4 elements with the 2 inner elements clamped onto the pipe part of the boom .
    Only one element per outer boom sections .
    But they are at the extreme ends ...reflector and director 2 .
    I've seen elements do weird things in the wind like spinning as in propeller .
    If the elements twist enough back and forth per se , it will tear itself right off the end .
    All this is still in design and test phases so no serious commitments until next year when its warm and sunny and great antenna building weather .

    So I really do like the input from a experienced builder .
    It be a shame to chop this 20 foot aluminum tube in halves only to discover it is not strong enough .
    Got it real cheap , found it at a scrap metal yard and paid 60 cents a pound for it .
    Getting home from the scrap yard is another story .

  6. Hi Bill. I'll be brief, and I hate to have to dampen your enthusiasm. First, DO NOT use threaded couplers. The threads weaken the tensile load capacity of the pipes and the coupler couples too little of the pipe lengths to support structural loads, even just the static load of the pipe weight. That is not what they are designed for! Only nest pipes, perhaps 1' overlap, use shims or machined couplers for a snug fit to eliminate stress points and use through bolts of appropriate strength and weather durability.

    A 2" x 0.065" aluminum tube (do you know the alloy and tensile strength?) is not suitable for supporting elements for 15m and lower. But, again, you MUST use material of known alloy and tensile strength and do the calculation to determine wind and ice survival. Do it yourself or with software like YagiStress. A pretty antenna on the ground could be a disaster when up in the exposed to the elements and dynamic loads.

    Harsh words, I know, but I prefer to say it and avoid a preventable failure. I am concerned and I want you to feel the same concern. Be very careful with this project! Please don't take any undue risks with life and property.

    Here's the result of a tube of unknown alloy I used in an antenna that saw less load than an HF yagi boom:

    73 Ron VE3VN

  7. Hello ,

    No offense taken .
    Just one builder talking to another .

    I am concerned about the threaded portion of pipe breaking off .
    I was , and I repeat...was , a industrial journeyman electrician
    working in the machine tool industry .
    The biz I worked for designed and build the huge automated machinery
    that spot welded your cars , trucks and vans .
    I've seen thousands of robots over my 25 years and the never ending
    up-grading of machine control and software .
    My job among many others , was to locate boxes and run conduit to them
    and stuff wires .
    Bent hundreds if not thousands of feet of conduit , including 2 inch rigid .
    Cut and thread by hand or machine and assemble using hand tools .
    That is why my spine is wrecked and now I am completely and utterly disabled .
    Half of the crew watched while the other half struggled and destroyed
    their bodies .
    That is a another story for a different place .

    With that background , I think I've seen one or two pipe joint break
    off at the fittings .
    Only because for example... the dumb moron HiLo driver tried moving 5
    tons of machine by hooking onto a piece of 3/4 conduit and yanking on
    it .
    So I know they can be strong if not loading the joint too much .
    Only issue is they tend to unscrew and then they want to break off .
    So that is something to be aware of using either the TEE fitting or
    the coupling .
    The conduit coupling I was thinking of was to hold the two pipe halves
    together and use a 1/4 inch thick aluminum plate that is 6 X 16 inches
    for the mast mounting .
    Depending on if we will ever get out of this virus mess , I know two
    places that can do professional aluminum welding that could weld the
    pipe halves to the mast plate .
    OR , there is always the U-bolt method and drill a bunch of holes into
    the mast plate and bolt all the pipes to it that way .
    The TEE fitting on the other hand would eliminate a lot of
    those other steps and be a screw together affair .
    Might have to use set screws to stop pipe from unscrewing and coming apart .
    Can't weld aluminum to malleable iron conduit fittings .
    Don't know where I can buy [ locally ] 2 inch aluminum TEE fitting so
    I can have it welded .
    Kinda stuck with what I have on hand .
    The TEE fitting idea would force me to mount the beam at the top and
    if I ever wanted to added / stack more antennas , they would have to
    be mounted below .
    There is always trade offs and comprises .

    As to the quality of that 20 foot tube , I went out to the barn for a
    thorough look over and found nothing printed on it .
    It is a tough piece of aluminum tubing from what I can tell .
    Just a little thin in the wall thickness .

    I'll have to experiment with this some more when spring comes around again .
    See how much the tube deflects when weight ( i.e reflector element )
    is applied and so forth .

    I do have that other alternative boom idea on the table .
    Using those aluminum lawn lamp posts that were on sale at the big box
    hardware store last year .
    Already turned the inner coupling sleeves weeks ago before it got cold .
    Bought 4 feet of 2 7/8 inch O.D. aluminum tube , .188 wall , cut into
    12 inch sections and turned down .012 inches for that nice snugly fit
    Just for giggles I slipped 4 pieces of lamp post and 3 of the internal
    sleeves together just to see how heavy it would be .
    Not too bad , only obvious issue was the tiny bit of sagging due to
    the .002 +/- tolerance slop to allow the tubes and sleeves to slide
    together .
    Had not taken the steps of drilling, tapping and screwing everything
    together tight .
    It has gotten rather cold out thar in thee ol' barn .
    Boom would be a lot stiffer if it was screwed together and then see if
    it sags anymore .
    Meanwhile....still doing the antenna modeling work for my 40 meter
    vertical on the confuser .
    Hopefully next year will be better .

    Good luck and hope to hear ya on the air waves .
    Bill KC8GTR


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