[OT] electricty calculations, was hand powered linux box

[D. Joe]

On Tue, Dec 14, 2004 at 12:52:47PM -0600, djgoku wrote:
> Reading on some solar panels that are out there I found these since my
> computer is using around 300 watts with monitor. I'm kinda confused on
> what Approx. Watt-Hrs / Day = 1200 - 1500. I know you just can't run
> your computer off these panels but you would need a battery of some
> sort for the panels to charge. But does that mean that it charges 1200
> -1500 watts/ a day so you would need a couple 700 watt batties or?
> Most car batteries are like 300-700 watts no? not crank just the
> storage part if that is what it is called.
> 
> http://www.icpsolar.com/ssfamille.php3?id_rubrique=56

>From my read of the "my laptop ate my TV" thread, I know there
are people on this list who have more experience doing these
kinds of calculations and can probably explain it better, but
here goes:

A watt is a unit of power.  Power is a measure of energy
transferred per unit time (electricity being just one way of
delivering power) watt-hours are a (common, but non-SI) measure
of energy.  Energy is something that gets stored, power isn't.

The SI unit of energy is the Joule (J).  A watt is a rate of
energy transfer equal to one Joule per second.  So, a watt-hour
is 3600 joules (1 joule/second * 60 seconds/minute * 60
minutes/hour * 1 hour).

When speaking of batteries, watts would be relevant in the sense
of how fast you could charge or discharge the battery, but not
so much in terms of what its storage capacity would be.  A
common (but again, non-SI) unit of battery capacity is
amp-hours.  Amps are similar to watts in that they are a unit
used to express the rate of transfer of something.  In this
case, though, instead of it being the transfer of energy, it's
the transfer of charge.  The SI unit of charge is the Coulomb,
which is the charge carried by one mole (~6.02E23, in other
words, a whole lot) of electrons.  The flow of one coulomb (C)
per second is an amp.  So, one amp-hour would be a charge of
3600 coulombs.

Now, the one missing piece here is how to tie the amount of
charge to the amount of energy.  This is where potential,
expressed in terms of volts, comes in.  One volt is one joule
per coulomb.  So, every amp from a 12 volt lead-acid (ie, car)
battery translates into:

1 amp = 1 C/s * 12 J/C = 12 J/s = 12 watts

A typical home circuit, let's say a 15 amp circuit at 120 volts,
provides:

15 amp = 15 C/s * 120 J/C = 1800 watts

and so on and so forth.

Aside from blue-skying about solar power possibilities and
trying to figure out battery capacities, getting a handle on the
arithmetic and factor-analysis involved is useful for sizing
power supplies, among other things.

I was just shopping at Radio Shack for some DC power supplies
for some hand-held consumer electronics devices we have (a TV
and a digital camera--there seems to be no substitute for
actually trying out all those little tips) and we ran through
some rough calculations to make sure that the 800mA power supply
I was looking at had a transformer big enough to supply the TV
(which, I figured, needed a bit over 500mA).  The specs given
for the two devices, the power supply and the TV, were not
expressed in the same terms, exactly, so we had to do this kind
of conversion.

Beyond this, there are other fun things you can do, like digging
up the factor for converting between British thermal units and
joules, and, with a couple of utility bills, figuring out just
how much more expensive it would be to heat your place with
electricity instead of gas.  (Or, to turn that on its head, you
can figure out how much your computer hardware habit is
contributing towards your heating needs in the winter, and what
kind of cooling burden they place on your AC in the summer,
since all the electricty consumed gets dissipated pretty much as
heat, all but for that bit of monitor and LED glow that escapes
the house through the windows).

One can also use this sort of thing to help understand the
appeal/practicality of heat+electricity co-generation, fuel
cells, hybrid vehicle powertrains, etc etc.

Good times for geek minds.

-- 
Joe

(SI is international system for expressing technical figures
like this, see http://en.wikipedia.org/wiki/SI)