On Sat, 17 Nov 2007 21:46:30 -0500, "Stefan Wolfe"
wrote:


"Richard Clark" wrote in message
.. .
On Sat, 17 Nov 2007 20:30:54 -0500, "Stefan Wolfe"
wrote:

Well, for one powers do not add, just energies.

Well, power is a vector quanity subject to the rules of vector math.
But
look at it in terms of the energy domain:

The total energy in the system over any time interval is equal to the
sum
of
the each power integrated over each segment of the transmission line
during
the same time interval.

This isn't getting any better.

Since Energy is the integral of power over time,

Now from bad to worse.

You are going to have to unwind a lot of your own problems before you
can get to Cecil's tricks of subterfuge.

What are the units you use to express the integral of watts over time?

Watt-Hours?

OK, fine. I prefer joules. Stay calm, Richard.

Joules is the integral of watts over time? Beyond superlatives!

Now consider the equation

Ptotal = P1 + P2 + 2*SQRT(P1*P2)cos(A)

For energy, integrate Ptotal for 1 second:

= (50 - 0) + (50 - 0) - 2SQRT P1*P2 sine(A)
= 100 - 2*SQRT*P1*P2(sine(0 - n*2*pi)) = 100- 0 = 100

The integral of one full sine or cosine cycle totals zero assuming zero
reference.
It isn't in integral form.

No ENERGY lost, even though at certain times the power was greater than 100W
while at other times it was less.
that's not the meaning of integration

Let's rewind up that list of charades to revisit:
Well, power is a vector quanity subject to the rules of vector math.
and ponder the implication of a negative power, for simplicity:
P1 = 50W @ 90deg
P2 = 50W @ 270deg
what does the math reveal?

73's
Richard Clark, KB7QHC