Environmental Engineering Reference
In-Depth Information
These are generous assumptions and we use them to judge the feasibility of a
power satellite to deliver 1 GW to earth. The solar array will have to be enlarged to
provide 1.5GW on the satellite, and if we assume the cells are 40% ef
cient
(at present possible only with advanced cells using mirrors for light concentration),
the cells will need to intercept 1.5GW/0.4
3.75 GW. At 1.366 kW/m
2
the area of the
¼
10
6
m
2
, or a square area whose side
L
is 1656m (about
1 mile). This large solar array could be assembled in orbit along the lines of the
International Space Station, as suggested by Figure 5.7. If the cells are in thin-
lm
form, they might conceivably be unrolled once in orbit, making use of weightless-
ness. The weightlessness in orbit means that the supporting structure for the arrays
of solar cells and antenna elements need not be strong, and thus they need not add a
lot of mass. But the overall mass of the cells, antenna elements, and the transmitter
and cabling will still be large andmake it expensive to put the system into orbit. Let us
make minimal estimates of the masses that would be required.
The working part of a thin-film solar cell needs only to be a few micrometers in
thickness. A common commercial thin
lm is
1
/
2
mil mylar, aluminized to form a
space blanket that re
ects heat back to keep the person warm. If our solar cells are
10
solar collector is 2.745
mil thick of semiconductor and conducting metal, plus
1
/
2
mil of mylar, then
the overall thickness is 10
5
m
m
10
5
m. If
þ
0.5 (2.54 cm/1000)
0.01m
¼
2.27
we assume this thin-
lm solar cell to have an average density of aluminum, 2700 kg/
m
3
, then the solar panel as modeled, to deliver 1.5GW, will have mass
M ¼
2700
2
:
27
10
5
m2
:
745
106 m
2
¼
168 000 kg
:
At 907 kg per U.S. ton, this is 185 tons of solar collector. The International Space
Station mass is 417 289 kg, is only about 2.5 times bigger. This mass is unavoidable
and cannot be reduced, to intercept 3.75GW of sunlight.
The antenna mass of Radarsat is given as 750 kg, and is 1.5m wide. The power
satellite antenna width will be much larger, although it may not need a larger number
of elements, for two reasons. The altitude ratio is 14.8 as noted above, and the desired
resolution on the ground is to be reduced to 139m from 45 km, this is a ratio 323, so
the total width enlargement factor is 323
4791, and the new width of the
transmitting antenna is 7186 km. This is extraordinarily large, but could be thought
of as an array of widely spaced dipole elements: the overall size, not the density or
weight, is the determining factor. As the second estimate, we extrapolate from 500m
antenna for GEO (Figure 5.7) at 36 000 km altitude by 1/3 for altitude 12 000 km, and
multiply by 7.5 km/139m (since we require the rectenna to occupy only two football
fields, versus 7.5 km), we get an estimate for antenna dimension
14.8
¼
¼
(500/3) (7500/
139)
8992m, fairly close to the earlier estimate of 7186 km. These two estimates
are quite close, and impractically large.
To
finish our projection of the Radarsat to make a 1GWpower satellite, let us take
the new dimension as 8000m, compared to the 1.5m antenna width on Radarsat.
If we were to linearly scale the mass of the antenna (750 kg on Radarsat), we get an
antenna mass estimate 4
¼
10
6
kg, or 10 times the mass of the International Space
Station. It seems likely that the transmitter mass is more likely the right quantity to
