Artificial Biospheres In Space

--- In spacesettlers@yahoogroups.com, "victoriatangoman"
wrote:
> --- In spacesettlers@yahoogroups.com, Gturner6PPC@y... wrote:
>
> >> I just sketched out another simple concept that takes 3 or 4
> mirrors
> > to provide vertical illumination coming down from along the
axis.
> > I'm not sure if someone else has thought of it or not.
>
> Yep. Already been discussed in detail, but if it helps you get up
to
> speed, I'm sure we'd be happy to do the dance one more time.
>
> >It should be simple to make, though.
> >
> > I stuck it on my blog here.
> >
http://armor.typepad.com/bastardsword/2004/02/space_stations_.html
>
> I checked out your proposed design. You seem inclined to base your
> designs on mathematical and physical principles - that's good!
> Here's a hint that should yield some interesting results - look to
> the issue of solar concentration within that central light tube
that
> runs down the axis of the cylinder and then see what the resulting
> temperature would be and what materials could withstand such a
> temperature.
>
> If you want a shortcut to the answer then you can find it buried
> deep within the dungeons that are the archives of either this list
> or SSI-List.
>
I searched but couldn't find it! So I tried running some numbers.

Looking at the geometry of what I drew, it looks like the diameter
of the shaft of coming down the axis is 2 and the station diameter
is 8, and roughly 20 units long. So I'm trying to light an area of
around 502 (pi*8*20) with a incoming light bundle with an area of
pi, for a concentration factor of 160 to 1.

I want 1000 w/m^2 at the surface and if my final reflector is 92%
efficient, I'd need 1087W*160 = 173,920W/m^2 coming down the shaft
(1087W00W/.92%eff). My reflector reflects 92% and absorbs 8%, so
each square meter of reflector has 13,913.6 watts to dissipate.

This energy Q = emissivity*Stefan-Boltzmann constant (5.67e-
8W/m^2K^4)*area*(T^4 - To^4), where To^4 is the internal temp of the
station (I'm assuming an internal station temperature of 300K which
is 80F).

If I only radiate heat off the back side (polished metal is a very
poor emitter) of the reflector, I'd paint it black for an emissivity
of around 0.85. I'm completely ignoring convection since I'm lazy
and the worst case air current is no air current, though it
certainly would keep things running cooler than my numbers indicate.

The equilibrium temperature of my reflector comes to 924K (1204F)
(ignoring the fact that I'm emitting into a warmer environment,
instead of the cold of space), which excludes conventional Mylar as
a candidate material, since Mylar melts at 489F. A special 97%
reflective Mylar would still have a temperature of 912K (1182F) and
would likewise be out. Going with polished aluminum lowers my
reflectivity, and thus I have even more heat to dissipate.

If I went with the high durability X-1 silver coating (98%
reflectivity) http://www.dentonvacuum.com/coatings/metal.html on a
borosilicate substrate (painted black on the back) it should run at
910K or 1178F, which might just work for Pyrex which has a softening
point of 1094K.

If I was using 80% reflective straight aluminum I'd want to keep the
temperature down to around 770F, which would mean my maximum
concentration factor could only be 40, instead of 160, so my
aperature admiting the light would have to be twice as large,
roughly half the diameter of the station in the design I used.

However if I literally made the reflector as a long thing cone with
45 degree stair steps, then I get more radiative area, roughly a 9
to 1 ratio of emissive area to absorbtive in my illustration. Then
my 80% reflective aluminum (which requires upping my input watts by
25% to deliver 1000 watts to the ground) would still run at 553F for
the 160:1 concentration ratio. It looks like straight 97% Mylar,
just emitting from the back, is only good for a concentration ratio
of about 16 to 1 before it hilts melting temperature.

> Hint - There's a reason the central light tube concept hasn't
> supplanted the standard O'Neill Cylinder Solars.
>
> Compare to the *light corridors* under the mountains for the issue
> of light density. More room for dispersal down there. A large
> portion of the endcap is used to bring the light into the cylinder
> and then it is broken into three beams, each of which is directed
> under the mountain ridges.
>
> The light pipe has a very narrow point of entry along the axis and
> then must be contained within the pipe.
>
> Of course, we could just stick with the O'Neill solars and deal
with
> the inherent constraints.
>
> TangoMan

True. Or possibly I could have a slightly more diffuse outer beam
cylinder that gets redirected at 45 first, while part of the more
concentrated central beam in the same span starts making multiple
grazing reflections at a high efficiency to walk the beam outward.
The advantage of these multiple reflections is that the total
reflectivity is increased for aluminum (for very shallow angles),
the incident light per square meter is low, and the area to
dissipate this heat is very high. So while parts of the beam are
directed downward, on in toward the higher flux core of the beam the
grazing reflections are prepping the light by moving it outward
while dissipating almost none of it, till it's diffuse enough to tak
a final redirect to vertical.

It would be interesting to ray trace.