Let us consider for now, just only taut-wire LPAs designed for HF. Picture the typical phase harness as so frequently diagrammed for log-periodic dipole arrays. That criss-crossing feedline so very like the laces on shoes. Regarding those, certain questions occur to me.
Q1. Since criss-crossing adds length to the transmission line, how can it not be the case that, 𝜏-spacing for the elements gets ever more out of proportion to 𝜏-length of the transmission line wires themselves? The more so with each and every criss-cross. Such that criss-crossing feed harnesses must surely be, to some extent, not equivalent to fully parallel feed line harneses. Yet always they appear treated the same.
Q2. If choosing a high value for 𝜏 (or low for 1/𝜏) such that elements pairs are further apart apart, this while feed-harness transmission-line separation remains fixed, how can it not be that increased departure from a perfect right-angle crossing does not adversely perturb peformance? A solution to this would be to do as seen on commercial TV reception LPDAs where a right-angle mutual hop-overs are formed at time of manufacture from custom-bent, very stiff wire. Which solution brings us back to the question of accumulating excess length in the harness with regard to the 𝜏 factor.
Q3. This one's mechanical. In a construction all of taut-wire, a spreader (actually a 'spread-preventer') is surely required at every 𝜏-point where elemement pairs branch from the boom wire. This so as to resist whatever lateral tensions as there maybe from guying so that they not shift, unduely widening feed-harness separation. One solution would be a thin, diamond-shaped card with punched holes to serve as separator and guide. In the wind, however, these would each be little flags. Their flapping will induce bending stresses, creating stress risers where wires wend their way through the punched holes. Both copper and alumiumn have very poor resistance to fatigue, so how can life not be drastically shortened?
And does it not seem telling that for LPDAs they call it a phasing harness while on toothed arrays the term is transmission line? Almost as if a frank admission of all those criss-crossing making it not a proper transmission line? Certainly no one can call it a balanced transmission line. At the very first cross location where equal spacing is not maintained all balance is lost. Which could be solved if said phasing harness were contrived as a double helix.
Worth noting is that, a tooted array entirely does away with any such questions. This for requiring no twists at all in their element-to-element transmission-line harnesses. At VHF and above, many a commercial and home-brew LPDA designer likewise preferes the simplicity of a twist-free feed-line harneses.
Very strongly in their favor, LPDAs have the advantage of low cost for requiring not so much wire as a toothed array. And it is only taut-wire LPAs which occcupy my thoughts at present. An LPDA, for employing less total wire would prove advantageous also during an ice storm. That's on the one hand.
On the other hand, it is to be noted that radio astronomers, in designing ultra-wide band sensors for their million-dollar, multi-dish arrays always choose GHZ-range LPAs, and by preference sawtooth LPAs (the SETI project). Or, if on a budget, trapezoidal tooth LPAs (the SKA project). Never do they go with dipole LPAs (even though they'd surely be cheaper). So I likewise cannot help but entertain certain questions on that topic also. This despite certain findings by the venerable L. B. Cebik, W4RNL, in his published notes PDF which distinctly disparaged saw-tooth elements in favor of dipoles for LPAs. One question plagues me particularly.
Q. Would not a single saw-tooth element exhibit distinctly different characteristics than an equal-length dipole? Does a saw-tooth element not seem very like an inverted butterfly element. And, this beint the case, might not its bandwidth be greater? And also resonate differently? It is widely known that butterfly elements equal in length to a dipole resonate notably lower. So, just possibly, W4RNL's analysis shoot-out between an LPDA, an LPTA, and an LPSA may not have been all that equal?
I don't have the answer to that. Ponder the issue yourself, though. Segregate three elements from their respective arrays: a dipole, a trapezoid, and a saw tooth. True, they all have the same "length". Still they are hardly equivalent to one another. For one thing, all will resonate differently. All will exhibit different bandwidths, different radiation resistances, different resonances and impedances. Now put them back into their array models. Despite the three models all being equal-α and equal-𝜏, still they are not equivalent to one another. How could they be?
So perhaps the venerable W4RNL just possibly made an untrue assumption in this one case. And as a result, the reputation of LPSAs was unfairly tainted. Either it's that, or else a great host of radio-astronomers have all jointly made a series of very costly mistakes. It's something to ponder at the very least.
In no way whatever am I qualified to cast doubt upon any one of the esteemed W4RNL's exensive researches. It is not my intention to be doing that here. Especially as I, myself, am no less guilty of doing the very same thing as cited above. Take, for instance my LPA calculator written in LabVIEW.
Every presumption on the GUI's main tabe are as if for a dipole array. This despite its file-output tab presenting the user their choice of plural element types.
My excuses for that are all very simple. A lazy programmer am I. Also an impatient one. Guity as well of some little hubris. Putting aside that those qualities are considered virtues in certain progrmming circles, in my regular day job programming is merely a side line. It's a side line, as well, in my radio hobby. One which lately had got out of hand, this programming effort having kept me almost entirely off the air meanwhile.
My own calculator for LPAs is special only for its capacity to spit out file iterations by the dozen, stepping through any of several design parameters. Additionally, I have Perl scripts for calling Nec2Go, thus to facilitate plural-file analysis. A hodge-podge tool set, for certain. And all of them crafted mainly just so that I might have an interesting antenna up before the snow flies this coming winter. This because our varied antennas serve so well as topics of discussion during rag chews on CW.
The calculator's original purpose was for desiging taut-wire LPDAs whose elements on either side should all align so as to all guy as one to a single common point some distance away (most likely a tree). And it does serve for that. But then my attention got distracted elsewhere. I chanced upon a PDF describing the SETI Institue's multi-million dolloar upgrade to their 42-dish radio-telescope array. Particularly their choice of a saw tooth LPA for the cryogenically cooled sensor element. And the thought which then niggled, was maybe they a good reason for that. Plus, also, wouldn't it be cool to enjoy an uncommon antenna for chatting about during long rag chews?
So that's what I'm after. Something interesting to chat about. Something just a little bit different. Provided, of course, that it works well. Hence a newly-coded suite of math tools. All of which I'm happy to share. Those plus also the full results of my personal researches. Understand, however, that my own motivations may not be entirely above suspicion. The hope of an interesting outcome are guiding the thrust and direction of these researches.
No need to fear that I'll insert any deliberate bias. At least not beyond a clear and obvious tendency to seek data mainly on the type of antenna I plan to build. This while spending not as much effort to balance those data against potential competing designs. This because time is limited before the snow flies. Plenty of data can be got on dipole arrays from other sources. Or, if you like, generate your own by employing my calculator and your own NEC analyzer of choice.