Gentleman:
For an interesting (albeit empirical) view of the non-exact harmonic
relationships in a dipole wire, I commend the following link from ON4AA. While
extolling the OCFD, the article does play into to non-exact harmonic
discussion currently on the board:
http://hamwaves.com/cl-ocfd/en/index.html
As to the notion of "end-effects", and the evolution of the number 468 vs 492
in the relationship of real-space vs free-space length, I have long been been
annoyed at the cavalier response as to "end effects," which if Googled even in
today's modern world, yields little mathematical justification for the "reduce
the loa by 3 to 5 %.
Back in the day at MIT, working for Lan Jen Chu, one of the more interesting
side trips was an assignment research the origins of the end-effect matter.
Believe it or not, starts with Lord Rayleigh and investigations to harmonics
and end effects from organ pipes, some open, some terminated. The next hundred
years or so saw incredible immersion in the math involved, and led to Max
Abramham researching the matter as extended from previous French academics
looking into the notion of vibrating metal rods; some open and some held fast.
Remember, this was in the day when EM radiation was evolving, albeit rapidly.
In fact, the time line is boggling when you think about it: Maxwell kicks if
off in 1855, Heaviside reduces notion to calculus in 1873, Hertz fires up his
rig in 1891, and Marconi's transatlantic experiment (some suggest they heard
Southern Hemisphere Atmospherics in Newfoundland and not the signal
transmitted, but what the hell, it was the guy with good marketing who got out
there first!)
The point is, all this took only 46 years!
But even then the math continued to be of interest, and continuing to advance
the principals to mathematics was de rigeur, frequently leading to academic
word-scuffles between sponsors of various theories (think battle of the
Matchbox, ARRL, SPC tuner overtaking the Ultimate TransMatch, etc.)
The essence of the mathematical analysis was a niggling term in a complex
calculus, relating to the accumulation of charge at the end of a radiating wire
that was terminated (read hooked to an insulator) rather than continuing into
free space.
This accumulation of charge (at the end the wire, or on the insulator) was a
capacitive event (accumulation of charge is what they do, right?) and as such
had the effect of shortening the physical length of a given wire for a given
frequency. We now assume this is reasonable at the high-voltage end of the
dipole, near the insulator.
Anyway, Old Max was caught up in the works of E/M radiation, with an
authoritative treatise in 1904/1905. Reviews from MIT and Yale follow at the
links below, as well as a link to the book.
http://www.ams.org/journals/bull/1908-14-05/S0002-9904-1908-01601-X/S0002-9904-1908-01601-X.pdf
http://www.ams.org/journals/bull/1905-11-07/S0002-9904-1905-01236-2/S0002-9904-1905-01236-2.pdf
https://ia601409.us.archive.org/32/items/theoriederelekt04fpgoog/theoriederelekt04fpgoog.pdf
Max was a big-time contributor to Annalen Physik back in the day, and stayed
involved with this world until he succumbed to the chase to define unified
field theory, and bumped into Einstein.
We don't hear much about Max these days, and clearly the modern math, has
eclipsed the need to mathematically explain the accumulation of charge at the
end of a radiating wire.
One of the then-hot topics of the day was published (pre-internet !) and
subject to Peer Review (duh-does it exist outside certain circles? Not even
much in Newington CT !):
Zur Theorie der Strahlung und des Strahlungsdruckes
AuthorsAnnalen Physik, Vol 319, Issue 7, 1904, pages 236-287.
http://onlinelibrary.wiley.com/doi/10.1002/andp.19043190703/abstract
While this is more than you cared to know about end effects, even to you
physicists, I thought it might go well with your morning coffee to expand a bit
on a topic that has not much of an interested audience left, since it's only a
matter of shortening the Antenna by three to five percent. What the hell.
PS-Nice to see topics like this pop up from time to time. Keep 'em coming.
73,
Ed McCann
AG6CX
Sent from my iPhone
> On Mar 28, 2017, at 7:18 PM, Richard (Rick) Karlquist <richard@karlquist.com>
> wrote:
>
>
>
>> On 3/28/2017 2:54 PM, jimlux wrote:
>>
>> because it's not "really" an end effect or capacitance. The actual
>> phenomenon is that X goes through zero at a frequency where the dipole
>> is not exactly a half wavelength long. There's a lot of ways you can
>> analyze around it or conceptualize it, but they're just mental models.
>>
>>
>> Another way to think about it is that the propagation velocity down the
>> wire is not c, but slightly slower (because the wire has inductance and
>> free space capacitance, and you can calculate the prop velocity as
>> sqrt(L/C))
>
> The trouble with this description is that it doesn't explain why the
> third harmonic resonance of a dipole is greater that 3X the fundamental
> (half wave) resonance. OTOH, the "end capacitance" concept neatly
> explains it. Three times as much wire, but no additional end effects.
>
> 73
> Rick N6RK
> _______________________________________________
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