Correction:

Roy Lewallen wrote:
. . .
vf, if, vr, and ir, are the same everywhere on the line, so see the
previously calculated values. Likewise, the calculation of p(t) from the
forward and reverse traveling waves is the same as before, with the same
result.

This isn't true. The phase angles of these terms are different at
different places along the line, so the p(t) results are different. At
the load end of the line:

vf(t) = 0.5 * sin(wt - 180 deg.)
if(t) = 0.01 * sin(wt - 180 deg.)
vr(t) = 0.5 * sin(wt - 180 deg.)
ir(t) = -0.01 * sin(wt - 180 deg.)

At this point, the result for p(t) is still zero at all times because of
zero ir + if rather than vr + vf as at the center of the line. At other
points along the line, as I mentioned in the original posting, p(t) will
end up being non-zero -- it'll be a sinusoidal function with rotational
frequency 2wt. But it will have an average value of zero, indicating
movement of energy back and forth but no net energy flow over an
integral number of periods.

I apologize for the error.

May everyone have an enjoyable and peaceful holiday.

Roy Lewallen, W7EL