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Re: [Phys-l] fire starter from the sun - revisited



Responding to Brian Whatcott...

(1)(3) I was not suggesting that ancients
might-have/could-have/should-have used lenses. I was just pointing out
that it shouldn't be too surprising that one gross of 1-ft^2 flat
mirrors did not produce a very hot spot. I was comparing the 144
mirrors to the common activity of using a magnifying glass to burn paper
or burn your initials in a block of wood. We know a 100-mm f/2 lens
easily chars paper and wood. How does the power per unit area compare
between a 100-mm f/2 lens (that we know quickly chars wood) and 144 flat
mirrors that reportedly didn't fair very well in an attempt to char
wood?

Brian rounded the area of one gross of a 1-ft^2 mirror to 13 m^2. I
agree with that. He rounded the area of a 100-mm lens to 0.008 m^2. I
agree with that. He used the sun's power as 700 W/m^2. I think that's
a bit high for sea level, but let's use it. That means the mirrors are
collecting about 9kW and the lens is collecting 5.6 W. I think we can
agree up to that point.

If the mirrors are able to aim all that energy into a 1-ft^2 area, the
power density is 9 kW/ft^2. For the 100-mm f/2 lens the spot has an
area of 2.72 mm^2 = 3E-5 ft^2. 5.6 watts into 3e-5 ft^2 is roughly 2E5
W/ft^2 or 200 kW/ft^2

So the mirrors are producing a power density of 9 kW/ft^2 and the lens
is producing a power density of 200 kW/ft^2. The lens is producing a
power density about 20 times more than the mirrors, which is what I said
in my original post. I am not sure how Brian calculated a 2-fold
advantage for the lens. It seems to me the advantage is 20-fold.
Perhaps he made a decimal error.

I'm not totally convinced of the quenching argument, although I haven't
thought about it much. If the material being heated is thin (like
paper) energy distributed by conduction would exit from the spot with
circular symmetry, that is, proportional to the circumference of the
spot. If you decrease the spot diameter by two, you increase the power
density by four, and you decrease the conductive path by a factor of
two. That seems like a win-win. If the material is thicker so that the
conduction is into "2pi", then decreasing the spot diameter by two
increases the power by four and decreases the conductive path by four.
That seems like win-biggerwin.

It would appear to me that if conductive losses are bigger for smaller
spots, it would have to be driven by the temperature difference
(delta-T), not by geometry factors. The geometry factors appear to
favor the small spot.

Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu