Solar cells, fuel cells and RTGs. 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 8.886106 ANALYTICALLY INTRACTABLE!?!? Solve by plotting, vfinal versus mp Solar cells, fuel cells and RTGs. The Glast Satellite, source NASA/Sonoma State University (Aurore Simonnet) 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 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 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. 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. 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] 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). 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). 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 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] 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) 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! 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. Should now have an understanding of the different mechanisms available to power a spacecraft: ◦ Solar Panels ◦ Fuel Cells ◦ RTGs You should also understand the advantages and disadvantages of each. The power source you choose is dependent on the mission requirements.