Roger wrote:

Hmmm, Like Roy, I thought there was still a traveling wave in this
situation. The voltage at the far end of the line must reverse polarity
as time passes, so the waves must continue to travel, or so I would think.

In the case of an open circuited line, the voltage traveling wave
maintains the same polarity upon reflection from the end of the line.
Mathematically, the voltage reflection coefficient is +1. The voltage
and current traveling waves continue to travel after reflection, which
results in the interference pattern known as a standing wave.

Maybe it could be said better, but I thought Roy was trying to say that
although power could not be detected at the center or ends, it was
flowing as a result of the initial impetus charged into the system.

It's easy to confuse power and energy, and I've been careful to use
those terms correctly. Power is the rate of energy flow, and I said
nothing about power flowing. (That's Cecil's concept, and careless
application of it leads to irreconcilable problems.)

I
would understand that this power would be the power needed to charge the
impedance and capacity of the line as it continually reversed polarity.

Capacitance is charged by charge, which is the integral of current, so
you can if you want track the charging and discharging of the line's
capacitance by integrating the current. Impedance is the ratio of V to I
and isn't something that's charged.

This would be real power from energy stored (but constantly moving) on
the 1/2 wavelength line so long as the system is active. We know we
have power present because we find energy distributed as V and I on the
time plot (viewed as a "standing wave" on the time plot).

The existence of both voltage and current at any point along the line
tells us that there is instantaneous power at that point, which means
that energy is flowing past that point. At any point along the open
circuited line except the ends and middle (where the power is always
zero), we can see that the power is in the form of a sine wave having
twice the period of v(t) or i(t) and no offset. This means that at any
point, energy flows first one direction, then back, equal amounts and
for equal amounts of time, twice during each v(t) or i(t) cycle. The
result is no net energy flow in either direction.

Roy Lewallen, W7EL