Harry Veeder wrote:
On 28/10/2007 11:41 AM, Stephen A. Lawrence wrote:
Speed is not power. Power is speed times force.
Torque is not power. Power is rotational velocity times torque.
A simple lever can produce more _force_ than is applied to it, and a
simple chain and gear drive -- such as on my bicycle -- can produce far
more _speed_ at the output (the wheel) than the input (my feet on the
pedals).
What's more, a capacitor can produce far more _power_ out than _power_
in ... but only for a little while. The interesting question isn't
whether the machine can produce a lot of "speed" or "torque" or "force"
or even "power" -- the question is whether total /energy/ out is larger
than total /energy/ in.
Why is energy more important than power?
Well, it's not exactly more important. But "energy" is what you pay
for, literally and figuratively; power is the /rate/ at which energy is
delivered. This is, perhaps, a somewhat technical and nit-picky point.
From 1913 Webster:
Power (definition 8) (Mechanics)
The rate at which mechanical energy is exerted or
mechanical work performed, as by an engine or other
machine, or an animal, working continuously; as, an
engine of twenty horse power.
So, for instance, a lump of coal contains a particular, fixed amount of
chemical /energy/. The amount of /power/ delivered by burning the coal,
on the other hand, will depend on how fast it's burned. Similarly, gas
companies typically charge for the total number of (potential) BTU's
worth of gas they deliver during a month, which is a measure of energy,
rather than the rate at which you sucked the stuff up on particular days
during the month, which would be a measure of the peak power you used.
Many of us, myself included, tend to be sloppy about it and use the
terms almost interchangeably. Often, it doesn't matter. In a case like
Ron Stiffler's circuit, for example, it's not something worth worrying
about: Instant by instant, either his circuit is producing no more
/power/ than it's consuming, or something very interesting is happening.
But the reason there's no issue of energy versus power in his circuit
is because there are no components in the circuit which can store more
than miniscule amounts of energy. Energy going in immediately comes
back out, and all energy coming out would be expected to be energy which
went in mere microseconds before.
In the case of a large engine with a heavy flywheel, or anything which
contains batteries with large capacity, on the other hand, the
difference is vital. You can spin up the flywheel over a long period of
time, using little /power/ but a lot of energy (because the power is
applied for a long time), and then slow it down all at once, and get
back the same energy you put in far, far faster in a great burst of high
/power/ output. In the case of batteries -- the notorious lead-acid
batteries, in particular -- it's possible for the batteries to produce
power out, with no power in, for a long time. But, unless the total
/energy/ drawn from the batteries exceeds the total /energy/ which was
originally put into them, both in the form of chemical energy during
their assembly and in the form of electrical energy as they were
charged, there may be no indication of an over-unity process involved.
Consider this hypothetical system:
input power ---> gross output power out ---> net output power
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------<------------
If the net output power exceeds the input power doesn't this qualify as
"over unity"?
It may, or it may not. It depends on whether the system can keep it up
indefinitely -- and that, in turn, depends on whether there's any kind
of energy storage device within the system itself, and that depends on
where you "draw the line" around the system -- i.e., it depends on what
you include within the system.
As I said, if the system includes a flywheel, storage batteries, or
large capacitors, then the peak output power can easily exceed the peak
input power, and it's necessary to look at the total energy budget over
the course of the run (from zero charge back to zero charge) to see if
it was over unity.
Another example is an automobile. During normal operation, the
automobile, viewed as a single system, produces large amounts of power
out, with no power in. But eventually the gas tank empties out. At
that point it's necessary to stop the car and refill it; during the
refilling, there's a large amount of (chemical) energy being added to
the system, and nothing being produced. Power-out/power-in for the
automobile varies enormously and is often far larger than 1, but the
ratio of total energy out to total energy in is no larger than 1.
The automobile example also makes something else clear about this: It
depends on where you "draw the lines". If you can exclude all energy
storage devices from the system being tested, then you're back in a
situation where you can measure instantaneous power out and
instantaneous power in, and if the former is larger than the latter,
it's an OU situation. In particular, if you look just at the
automobile's _engine_, excluding both the gas tank and the battery, then
during constant-speed operation you would expect power-out to be no
larger than power-in, where power-in includes the rate at which chemical
energy is delivered from the gas tank through the fuel line.
Harry
