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

[Brian Whatcott <betwys1@sbcglobal.net>]

At 09:10 AM 4/25/2006, Mike, you wrote in part:

>  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.


Mike, I will take your numbers as read, and instead, examine
 the conclusions you draw.
In the case of a paper thin "hull" you find that a small bright spot
 is a winning configuration in view of peripheral  conduction losses.
 By contrast, I find it a losing configuration.

Let me explain. The surface thermal gradient at the edge of the
 bright spot  is (Thigh - T amb)/ representative distance across
the illuminated edge.  (And yes, THIS is where diffraction limits
might be considered, finally)

The surface thermal gradient at the edge of a similar sized spot
 on a hull illuminated by distant mirrors  is zero.
Because the whole surrounding area is also being heated.

I suppose you could say, that's a 20 times, a 200 times, a 2000,000
times more advantageous gradient for the mirrors?

But wait: if we are examining the practical aspect of burning enemy
ships, I suppose we should consider a representative timber?
Perhaps a 25 mm plank?

If we were to consider a glass of focal length 200 mm,
it is true it  becomes defocussed in passing through
 the depth of the 25 mm plank,  but more significantly, the surface
over which its several watts are spread grows quite rapidly.
We could model the isothermal contours  due to bright spot heating
 as growing hemispherically with depth to a diameter of twice the
timber thickness , or if the power density were great enough,
then the surface over which the energy is applied could grow as slowly
 as a cone of base diameter not much more than the bright spot diameter
and depth equal to the timber thickness?

You will easily see that the power density is rapidly diluted.
Shall we say by twenty times or more , possibly?   :-)

In contrast, the mirror approach  may possibly maintain its initial
 power density, and the isothermal contours are plane.

But this delightful argumentation avoids a fact of timber fire life,
and I am forced to mention it:

It is found that a heavy timber section maintains greater fire resistance
 than a steel joist of similar strength, due to the insulating effect of the
timber char.   I would be committing fraud not to at least nod in that
 direction.

Burning substantial wood sections is not easy.


Brian Whatcott    Altus OK    Eureka!