Gene Fuller wrote:
You may believe it is obvious, but it is not quite clear what you are
trying to show in that figure.

Gene, I previously responded in words that I thought you would
understand, based on your previous understanding. It occurred
to me during my walk that not every reader is an engineer, not
every engineer is a EE, and not every EE also has a math degree.

Here it is in easier to understand terms. Given the 1/4WL conductor
and the web page at:

http://www.qsl.net/w5dxp/travstnd.GIF

The way to measure phase shift through a wire carrying the
traveling wave current is to put a current probe at location
A and location B, and measure the phase shift between those
two equal magnitude sine waves. If a coil exists in the circuit,
that would also be the way to get a rough measure of the phase
shift across the coil.

Example: The phase shift from 30% to 60% in the traveling wave
antenna is taken from the tabular data as 54.2-27.6 = 26.6 degrees.

The phase information is in the *phase* in a traveling wave.

For the standing wave current, the situation is completely
different. The phase measured between any two current probes
will always be zero. The phase of a standing wave current is
useless for measuring phase shift. The way to extract the
phase information is to measure the *amplitude* at two points
and then calculate the phase shift by taking the arc-cos of
the normalized amplitude.

Example: The phase shift from 30% to 60% in the standing wave
antenna is arc-cos(0.8843) - arc-cos(0.5840) = 26.5 degrees.

The phase information is in the *amplitude* in a standing wave.

Thus in both antennas, the phase shift in 30 percent of the
wire is about 27 degrees. (90*.3 = 27) If we had a coil installed
in that 30 degrees of the antenna instead of a wire, the same
concepts would apply.
--
73, Cecil http://www.qsl.net/w5dxp