Thanks for the information and explanation, Roy.

I do agree that the error introduced by using an SWR minimum as a proxy
for zero reactance would not alone account for Ken's results. I also
agree that resonance is important here only insofar as it is a
definitional element in the nnn/f = L formula. I understand the formula
is an approximation. At issue was whether the approximation held
constant over a frequency excursion of approximately 5%, not an
unreasonable expectation. Ken offered measurements purportedly showing
that the approximation did not hold over that range. I will try to show
that the uncertainty in the reported measurements does not provide
confidence in the conclusion that the "constant" has changed. Whether
the "constant" actually changed, and if so why, does not concern me here.

Ken initially reported a change to the "constant" (i.e., 234) of 2.32 in
going from 9.5665 to 10.1955 MHz by trimming the length of a dipole. He
based this on his measurements of SWR used to determine resonant
frequency and on his measurements of wire length.

What is the required precision in SWR measurement needed to determine
resonant frequency?

An error in measuring the resonant frequency that would produce a
"constant" error of 2.32, is roughly 0.097 MHz. For a 30 meter half-wave
dipole, the feed-point SWR ranges from 1.35 at 9.97 MHz to 1.35 at 10.02
MHz, with 1.34 being the minimum at 10.0 MHz (from Reg Edwards'
swr_freq.exe program). This SWR range corresponds to a frequency
difference of 0.06 MHz. More directly, an SWR measurement error of 0.01
at the antenna could produce an error in computed resonant frequency of
0.06 MHz. Measuring at the end of a transmission line is not likely to
improve this relationship.

So how likely is it that SWRs were actually read with precisions on the
order of 0.01, when the measurements were taken hours or days apart? I
can't do that on my Bird. I think only a digital SWR meter can provide
that kind of precision. On a calm day. With no inherent lsd jitter. And
would it be repeatable after hours or days between measurements? Try it
on your antennas. In any case, to achieve the 500 Hz precision reported
would require something like five significant digits of SWR measurement.
Maybe in a lab with a cutting-edge network analyzer. The issue is not
accuracy, of course, but whether SWR measurements of the required
precision are feasible. Please, no lectures, folks, on how unimportant
such SWR measurements are in normal practice. This is a very unusual
application of SWR measurement.

What is the effect of errors in length measurement on calculated
frequency using the formula?

For the length measurement, Ken reports a precision of 0.001 foot. That
is 0.012 inches, less than 1/64 inch. I don't believe this kind of
precision was achieved either. An inch in a 24 foot length of wire is
actually pretty good, considering the difficulty in holding it taut
without stretching it, etc. But a one inch difference will produce an
equivalent frequency error of 0.03 MHz (by the formula).

Simply adding the 0.06 Mhz and 0.03 MHz errors gives a total uncertainty
of 0.09 MHz, an amount roughly equal to that required to generate an
error of 2.32 in calculating the "constant". I know, I know. These are
not rms errors. But they're what we have.

In other words, no cigar for for showing that the "constant" changes by
2.32 when the frequency changes by five percent.

Perhaps someone can provide a more sophisticated analysis of the
measurement uncertainty involved. Perhaps with a better analysis, we
will find that we can all go out and measure SWR to within 0.01 so we
can calculate resonant frequency to within 500 Hz. Yeah, I know all that
precision is imaginary, thanks to umpteen digit calculators.

And sure, changing the height of the antenna ends could also
explain a change in the "constant". At least the change would be in the
reported direction.

So there it is! I looked at the problem and tried to understand where
the data came from and how they were measured and how much confidence I
should give them. Meanwhile, I missed the whole point of the exercise,
which seemed to be hypothetical: if one were to do such and such and
found that the "constant" changed, what might have caused it. That's
what's great about this group. The rest of you pretty much thought about
the question and went to what is probably the correct answer. Do the
data Ken reported really support that answer? Who knows.

Gotta love this stuff.

73 to all and thanks for your patience on this tediously long post.

Chuck
NT3G