Re: Power!

[T.L.G.vanderLinden@student.utwente.nl (Timothy van der Linden)]

To: Brian Mansur . . . still there and thinking

>I ran some calculations over Christmas and found that to produce 1E18 W, 
>which is what Kevin, and the rest of the solar system would like, requires 
>billions of square kilometers of solar arrays.  The exact number depends on 
>collection/transmission efficiencies and, of course, the distance of the 
>collectors from the Sol.  Since the total circular area of say Mercury is on 
>the order of mere millions of kilometers, even covering the planet with 
>solar panels is not going to produce close to 1E18 W.

Indeed just use:
Area needed for 1E18 watt solar power = (4 pi r^2)/4E10   r=distance to the Sun
(This assumes 100% efficiency)

For Mecury this means r=5.8E10 --> Area=1E12 m^2
The radius of Mercury is 2.433E6 metres thus its surface is 4*Pi*r^2 this
gives a surface of 7.44E13 m^2. So the total surface of Mercury is 70 times
bigger. Of course only one half can be illuminated at once so then the area
is 35 times bigger than needed by 100% efficiency.

>Since launching and recovering these arrays at the rates needed to keep up 
>E9's of panels at any given time seem to cost more power and resources than 
>we'd like, I suggest that we tether the panels to Mercury's poles.
>
>What?!  Can't be done, you say?  Well, probably, but we're grasping for 
>ideas here.
>
>Think about it.  It would be like flying a kite on the solar wind.  Since 
>Mercury does have some rotation relative to its revolution (it is not faced 
>locked with the sun like the moon is with Earth) we build superduper strong 
>suspension cables/towers/ whatever at the poles where we could perhaps 
>counter-rotate the cable anchors on a merrygoround  to prevent them from 
>winding up as Mercury spins.  That or we could put down many, many 
>individual connections to the surface that can be unlinked and reset to keep 
>(torquing is it?) to a minimum.

I wonder what will be a bigger force, Mercuries gravity or the solar
radiation pressure, this of course depends on the distance from Mercury.
The cables you are talking about should indeed be very strong:

m=mass of the cable
g=Mercury gravity (3.58 m/s^2)
F=force
rho=density of the material of the cable (using Aluminium 2.6E3 kg/m^3)
l=length of the cable
A=Area of a cut through surface of the cable (depends on the tickness)
T=Pull strength (in Pascal=N/m^2)

F=m*g  m=rho*l*A  T=F/A --> T=rho*l*g

So now we know the minimum pull strength needed for a cable of length l and
a density rho in having a gravitional acceleration g.

So assuming that gravity doesn't change much the first 1E6 metres:

T=2.6E3*1E6*3.58=9.3E9 Pa

The pull strength of aluminium is about 3E8 Pa thus such a long line will
snap under its own weight. Of course I used a line that had the same
thickness all along the line. It would be better if the line was thick at
the bottom and thin high in the "air".

So in these cases the weight of the cable is an important factor assuming
that it is pulled upward enough (In the worst case the cable is so heavy
that it will drag the whole solar-array down to Mercury.)

Now that I think about it, I wonder if cables are needed. You could just
keep the whole array floating in at a place where solar radiation pressure
and the pull of Mercury are equal, then add some small engines to keep it there.

I thought of this before but then not using Mercury but using the Sun itself
to pull the array back, the problem thereby was that it probably had to be
to close to the Sun, unless ofcourse it rotates around the Sun at just the
right distance. The porblem that I see though is that any rotating
solar-array is difficult to use, since the angles of incoming and outgoing
radiation constantly change and don't equal each other, which causes an
instable orbit.

>As I said, I don't know if this will work because I realize that, even with 
>a lot of cables dividing the load of the pull by a collector the size of a 
>face of Jupiter, the tension will be incredible.  Also there is Mercury's 
>gravitational attractions for the array and the cables to consider.  I hope 
>someone can give some hope to this idea because I don't have the time or 
>skills to try to figure out the dynamics.  An advantage to this idea, 
>however, would be that we could keep the array very close to a planet sized 
>solar panel service station.  Oh, and another problem to consider is how the 
>mercury rises as one nears the orbit of Mercury.

Radiation levels at Mercury are about 7 times higher, so it may be able to
overcome the increase of temperature.

Timothy