LHA of a Sawtooth Array
A more easily visualized hybrid measure of log-periodic antennas than sigma (Greek 'σ'). One not referred to elsewhere, since I may just have coined it myself. As to that, I'm not really sure. Anyhow, the concept kind of jumped out at me while diagraming saw-tooth arrays in pencil on paper prior to coding the geometry into my calculator.
Consider the saw-tooth element type. How I calculate them varies slightly from the 1966 patent. Aside, that is, from just adding a boom up the middle the better to reduce ohmic losses. My saw teeth do not form perfect isoscelese triangles either side of the boom. My saw teeth further employ two measures governed by 𝜏, rather than one, for defining a single saw tooth.
I ended up defining single saw teeth as mirror-pairs of not-quite-equal right triangles. The variance between those and a single isosceles triangle is trifling. Barely a fraction of one degree. But done that way entirely for my own programming convenience rather than real-world advantage. How I came to make that decision may be read about on its own separate page, should any so wish: XML
LHA of a Sawtooth Array
Thus does LHA present itself (at least to my way of thinking) as a potential substitute for sigma. Especially as it may very well be pretty much the same exact thing, simply expressed as an angle instead of a ratio. And in the case of perfect isosceles triangles, the leading and trialing half-angles would be identical. Employ it or not, just as you please. But it did need explaining, since I make use of the term frequently on my own pages.
Once discovered in saw-tooth elements, LHA can likewise be seen in relation to trapezoidal teeth, thus.
LHA of a Trapezoidal Array
And similarly also in relation to dipoles as well, as shown below.
LHA of a Dipole Array
I was hoping that LHA might reveal a magic value. But that's not proved the case. Hopes rose briefly when a string of ten high-gain arrays were all achieved with an LHA of 10°. I wish I had saved them out of the RAM drive before Windows 10 had got a chance to force a reboot while I happend to be AFK.
Much in the same way as σ (and possibly exactly so), LHA is thus proven significant only in combination with another factor. And what now I expect to discover, is that the sought-after ideal value will reveal itself as an all-too-familiar squiggly line marking the intersection of LHA with either α or 𝜏.
Nevertheless, LHA is still a more visual concept, is it not?