Solar cells, fuel cells and RTGs.
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Payload mass, mp = 5 tons
ms1 = 140 tons
(given in table)
ms2 = 35 tons
“
ms3 = 10 tons
“
mf1 = 2160 tons
“
mf2 = 420 tons
“
mf3 = 100 tons
“
mo1
=ms1 + mf1 + ms2 + mf2 + ms3 + mf3 + mp
=2870 tons
mo2
=ms2 + mf2 + ms3 + mf3 + mp
=570 tons
mo3
=ms3 + mf3 + mp
=115 tons



Now calculate ‘R’ for each stage
Recall:
∴
moi
Ri 
moi  m fi
2870
R1 
 4.04
2870 2160
570
R2 
 3.80
570 420
115
R3 
 7.67
115 110

Now we have R1, R2, and R3 can calculate the
final rocket velocity, vfinal via:
v final  ve1 ln R1  ve 2 ln R2  ve3 ln R3
 2.32 ln 4.04  4.10 ln 3.80  4.25ln 7.67
 3.24  5.74  8.66
 17.3 km s -1
This wasn’t easy – my apologies. From definition of R we have:
R1 
2865 m p
705 m p
, R2 
565 m p
145 m p
, R3 
110 m p
10  m p
 v final  ve1 ln R1  ve 2 ln R2  ve3 ln R3  16.0
16  2.32 ln R1  4.10 ln R2  4.25ln R3
 2865 m p 
 565 m p 
 110 m p 
  4.10 ln
  4.25ln

16  2.32 ln
 705 m 
 145 m 
 10  m 
p 
p 
p 



2.32
4.10
 2865 m p 
 565 m p 
 110 m p 





16  ln
 ln
 ln
 705 m 
 145 m 
 10  m 
p 
p 
p 



 2865 m  2.32  565 m  4.10  110 m  4.25 
p
p
p
 
 
 
16  ln 
 705 m p   145 m p   10  m p  


 2865 m p 
16

e  
 705 m 
p 

2.32
 565 m p 


 145 m 
p 

4.10
 110 m p 


 10  m 
p 

4.25
4.25
 8.886106
ANALYTICALLY INTRACTABLE!?!?
Solve by plotting, vfinal versus mp
Solar cells, fuel cells and RTGs.
The Glast Satellite, source NASA/Sonoma State University
(Aurore Simonnet)
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These use solar radiant energy and convert it
directly into electricity, via the photovoltaic effect.
An array is made up of thousands of individual
cells (2 cm x 4 cm typically), connected in series to
provide DC power (28 V typical, 120 V can be
found today).
Power levels can be in range of a few Watts to
100’s of kW.
An individual cell is just a semiconductor p-n
junction.
Solar panels on ISS
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Silicon was typical, today (Gallium Arsenide) GaAs
has been used but is not universal.
Silicon is doped with boron to produce p-type
(electron deficient) material and phosphorous for
n-type (electron excess) material.
In dark conditions an equilibrium is reached where
no significant current flows. If illuminated, by
photons of sufficient energy, electron-hole pairs
are created, these flow creating a potential
difference across the device.
Schematic showing photoconduction of an electron
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To cause the hole-electron production the
photon energy has to exceed the band-gap
energy. If photons have excess energy this
can be deposited as heat.
We can define hf  Eg where h is Planck’s
constant, f is the frequency of the radiation
and Eg is the band gap in Joules.
You can characterise a solar cell by its I-V
curve. The best operating point is the
maximum power point, given by Vmp and Imp
Typical solar-cell
I-V characteristic

You can also define:
◦ Open circuit voltage (i.e. no current drawn) Voc
◦ Short circuit current Isc
◦ A fill factor (FF) which says how “square” the I-V
curve is. The “squarer” the better. FF is defined as:
FF = (Vmp  Imp)/(Voc  Isc)
The closer to 1 this is the “squarer” it is.
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For a silicon cell Voc is typically 0.5 to 0.6 V,
Isc depends on the illumination level, and FF
can be 0.7 to 0.85.
To find the peak power, you draw output
power vs. output voltage. A clear peak can be
found, which defines Vmp and hence Imp can
be determined.
If you heat a solar cell you will find its
performance changes. Its efficiency falls as its
temperature increases.
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There is a packing factor for a solar panel, which describes
how much of its surface area is really solar cells, 0.9 is good.
The rest is structure, edges, gaps etc. So the effective area is
less than the actual surface area of a solar panel.
Solar panels need to be face on to the Sun for maximum
efficiency. If they are tilted then a geometric correction has to
be applied to give the cross-section projected orthogonal to
the solar direction. If the angle between the normal to the
surface of the panel and the solar direction is θ, then there is
a factor cos θ that has to be applied when finding the
effective surface area illuminated and hence the power
output.
Typical bandgap energies for solar cell materials
nnn
Solar cells in orbit do suffer degradation with time. Due to:
◦ Accumulation of micrometeorite impact damage,
◦ Attack by atomic oxygen on the wiring
◦ Radiation damage to the semi-conductor.
 There is thus a factor for loss of efficiency with time – power
output falls slowly with time.
 Estimating this loss rate, and over-sizing the solar array at the
Beginning of Life (BOL) so it over-produces power but produces
the correct power at the End of Life (EOL). Solar panels at the
BOL in Earth orbit can produce 30 – 50 W/kg of mass.
 Current state-of-the-art Multi-Junction (MJ) solar cells have
efficiencies approaching 50%.

Fuels Cells [F & S Chapter 10, p. 337]
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The basic idea is to generate electricity from
chemical reactions.
They are used on the Shuttle, and were used in the
Mercury, Gemini and Apollo space missions.
An oxidation reaction is used. It has a high energy
density (typical o/p Gemini: 33W/kg, Apollo: 25
W/kg, STS: 275 W/kg). This is available on demand
and continuous when running (although the start
up time of early cells was long). But you need to
carry fuel (oxygen and hydrogen).
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A hydrogen/oxygen fuel cell is typical and
produces water (a useful output).
In an ideal cell the voltage (Er) produced is
given by:
 G
Er 
nF

Where ΔG is the Gibbs free energy in the
reaction, n is the number of electrons
transferred and F is the Faraday constant
(9.65× 104 C/mol).
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In the hydrogen/oxygen cell the reaction
transfers 2 electrons per molecule of water
formed and ΔG = -273.2 kJ/mol at 25 °C.
This gives 1.416 V. In reality this is the ideal
potential, as there are losses in the system.
Early cells could take 24 hrs to start and 17
hrs to stop (Apollo), but for the Shuttle start
up times is 15 min and shut down is
immediate.
v
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Radioisotope Thermal Generators (RTGs) are used
to generate power on space missions where solar
energy is at a low flux or not available for long
periods (mainly unmanned missions).
They generate heat. They then use the
thermoelectric effect whereby a voltage is
generated between two materials (semi-conductors
or conductors) if a temperature difference is
maintained between the two ends (think of a
thermocouple).
Here the cold end is achieved by exposure to
space. The hot end by waste heat from nuclear
decay.
A practical device is shown in F&S page 340
Gd Po
Decay
product
α
Power
τ½ (years)
density (W/g)
82
0.38
Plutonium 238
Pu O2
α
0.41
86.4
Curium 242
Cm2 O3
α
98
0.4
Strontium 90
SrO
β
0.24
28.0
Isotope
Fuel form
Polonium 210
Various radioactive materials for possible use in a RTG.
Pellet of glowing
238PuO
2
– generating 62 watts of heat
Cassini RTG – source, NASA
Cassini’s RTG? Doesn’t look like a clean room!
Much better…..New Horizons’ RTG (mission to Pluto)
[Cassini flight spare, using 11 kg of Plutonium pellets]
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When considering a design, care has to be made
to ensure that in the event of an accident during
launch, the radioactive material does not escape
into the environment. Clean-up costs would be
expensive in terms of money, and public support!
The power generated by a RTG is not constant
with time, the material decays so there is less as
time goes on and hence less power can be
generated.

You need:
  0.693 
Pt  Po exp
t 
  1/ 2 


Where Pt is power at time t, and P0 is the
initial power at t = 0.
τ½ (years) is given in the table above.

So you have to calculate what power you need
for the mission and start the mission
(Beginning Of Life - BOL) with too much
power. Then as the source decays, the RTG’s
output falls and you plan it so you have just
the right amount of power at the end of the
mission lifetime (End Of Life – EOL)
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Pros:
◦ You are not reliant on the spacecraft pointing at the
Sun or not being in eclipse.
◦ You are not dependent on radial distance from the
Sun
◦ Power levels can be sustained for periods of years
(depending on τ½). Voyager’s RTG has been running
for almost 30 years.
◦ Aside: Congress has just agreed to the start-up of
plutonium production to fulfil NASA’s requirement
for RTG material – at NASA’s expense it would
seem!
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Cons:
◦ Radiation is emitted and may affect instruments on the
spacecraft.
◦ The material is radioactive and often highly poisonous – it
needs careful handing during construction and spacecraft
integration at the launch.
◦ By definition the hotter the better, but this may not be good
for spacecraft components so may need to shield the heat
from the spacecraft interior.
◦ The public does not like the word radioactive and rockets
do fail during launch, so extra care has to be taken in
packaging the RTG to prevent disassembly during an
explosion or crash.
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Should now have an understanding of the
different mechanisms available to power a
spacecraft:
◦ Solar Panels
◦ Fuel Cells
◦ RTGs
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You should also understand the advantages
and disadvantages of each.
The power source you choose is dependent
on the mission requirements.