Energy Systems. Sub Module 2

Transcription

1 Energy Systems Sub Module 2

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3 Mars Challenge: Energy Systems CONTENTS Student assessment exercises: Part 1 Energy Systems: Reflective Journal Part 2 Solar Cells in Space: Reflective Journal Solar Cells in Space: Investigation A Electrical Energy: Investigation B Part 3 SoIar Cells in Space - ISS Energy Model: Investigation C It is not intended that all the parts of these modules are required to be investigated in order for students to undertake the Mars Challenge. Rather, the sections are provided to give flexibility learning options to teachers and students. Students that specifically chose to design a product that is actively rather than hypothetically utilising power, may for instance be directed to undertake additional parts of the investigations above to assist in their understandings and applications. 89

4 Mars Challenge: Energy Systems Module 3: Energy Systems Overview With current technology on the market, space exploration requires electrical power and an efficient means of storing energy. This energy must provide a wide range of functions and have the ability to be stored safely, under a wide range of environmental conditions for extended periods of time. A trip to the Moon will take astronauts approximately 3 days, however a trip to Mars has been estimated to take up to 6 months and will require much research to close the significant gaps that exists in advanced power capabilities to date. This may include harnessing free energy that does not require storage, however, much more research into these potential energy sources is required. With current knowledge, research into advanced power technologies will aim to improve overall power management efficiencies during missions, including reducing the mass and size of deployed systems. Teacher Preparation Print and distribute Energy Systems Overview and Factsheet to students Provide computers for students to research potential energy sources available to power a range of space exploration equipment (large and small) with a wide array of functions Print and distribute Student Worksheet for Reflective Journal entry During the Energy Systems module Part 1, students will investigate a broad range of power technologies required to enable the various activities for living and working in space. Part 2 and 3 of this module, Solar Cells in Space, provides specific experimental design procedures and investigations to assist students in testing the effectiveness of the power source chosen to operate each product designed for a mission on Mars. 90

5 Mars Challenge: Energy Systems Energy Systems FACT SHEET To consider energy production requirements and energy systems options for any mission is a difficult challenge. Power requirements can range from milliwatts for some robotic exploration components, to watts for human-portable energy storage devices, to kilowatts for surface mobility, to hundreds of kilowatts for surface habitats and operations, and up to multi-megawatts. Within the 10s of watts up to a few kilowatts to support initial human visits to Mars, scientists are currently considering radioisotope power systems to be used for robotic applications as they offer a mass and development cost advantage relative to fission systems in this power range. However, to support higher energy requirements for permanent Mars bases, fission power systems are advised. Nuclear power is the preferred option for surface power needs based on its high power capability at reduced mass and volume, fewer deployment issues and its insensitivity to changes in operating environment, i.e., latitude, atmospheric sunlight attenuation, and seasonal variation of day/night ratio. The selection of nuclear power for any mission poses concerns due to its inherent nature, and therefore, safety to public, crew, and equipment are considered paramount in the design requirements. Figure 1: Regenerative Fuel Cells 91

6 Mars Challenge: Energy Systems The ability to store energy, is an essential consideration during extended missions It is paramount for scientists to also investigate stored energy systems particularly important during the night time when solar energy is not available or during eclipse or periods of shadow when solar energy is blocked from reaching the solar arrays. Portable utility pallet houses regenerative fuel cells to provide power during eclipse periods on planetary surfaces. Several types of advanced energy storage devices, such as primary batteries, rechargeable batteries, fuel cells, regenerative fuel cells, capacitors, and flywheels, are potentially available to enable future robotic and human exploration missions. Lithium Ion Batteries Figure2: Lithium-Ion Battery used in Extravechicular Suit Demonstration Advanced batteries deliver moderate to highspecific energies (200 to 500 Wh/kg), can operate over a temperature range of 40 to 60 C and have proven lifetimes up to 10 years. With high specific energy and long cycle life can extend the range of planetary robots and mobility systems and reduce the mass of landing systems (increasing available payload mass) while adding functionality by providing more power. For crew excursions, compact spacesuit batteries with even greater specific energy are critical for extending mission durations and therefore scientific return 92

7 Mars Challenge: Energy Systems Shuttle Flight Unit Fuel cells are enabling technologies for many aspects of Martian surface operations. In applications where electrical power is needed for an extended period of time, fuel cells are a viable option. The total amount of energy available from a fuel cell is dependent on the size of the hydrogen and oxygen reactant tanks. The reactants feed into a fuel cell to produce electricity with drinkable water as a by-product. Figure 3: Orbiter Fuel Cell Regenerative Fuel Cell (RFC) System. There are two types of fuel cells. Primary fuel cells convert oxygen and hydrogen into electrical energy and water, but stop producing electricity once the reactant supply is depleted. Regenerative fuel cells produce electrical energy in the same way as primary fuel cells. However, they are also capable of recovering the reactants by using electricity to split the product water molecules into hydrogen and oxygen in a process called electrolysis. For this process, electricity could be provided by solar arrays or a fission power system. 93 Figure 4: Regenerative Fuel Cell System

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9 Mars Challenge: Energy Systems Energy Systems - Design Challenge Inquiry There are many other options for energy systems considered by the space industry for supplying reliable and efficient power to facilitate the various operations and functions performed during a mission. With some further investigation into current mission technologies, including those used on the ISS (International Space Station), and for studying lunar and Martian environments, innovative and creative energy solutions can be suggested to power the Mission Team products.. The accuracy of the energy solutions suggested for the specific product chosen by teams is not important, rather the creative thinking behind current technologies and imagination used in designing future energy systems that could perhaps become the next great invention, is a key objectives of the design challenge. The following weblinks provide additional energy systems and creative solutions: Alternative energy Biofuel Antimatter and nuclear power 95

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11 Mars Challenge: Energy Systems STUDENT WORKSHEET Energy Systems: Reflective Journal Assignment A broad research investigation across a range of power technologies is required to enable the various functions during a mission. Energy is necessary to power rovers, tugs, habitats, experiments, beacons, astronaut tools, and in-situ resource utilization equipment, which is used to obtain material resources from lunar and Martian regolith (soil). Energy is needed to run equipment inside the space suits including liquid cooling and ventilation systems, communications equipment, bio-instrumentation and other life support systems. Answer the following question in your journal as completely as you can. Your entry will be evaluated on the thoughtfulness of your answer and the reasoning you give in support of your answer: What energy source/s would you recommend for operating a hand-held power tool for working in a space habitat and during field expeditions? What do you believe are the 3 most reliable energy sources available for powering a rover/buggy on Mars and why? Bonus question: If you were to invent an energy source from your imagination to operate any power device of choice, what would it be AND OR where would the energy come from? 97

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13 Solar Cells in Space

14 SOLAR CELLS in Space Introduction For space exploration close to the sun near the inner planets (Earth, Mars, Mercury and Venus), solar power with battery backup is often an optimal option, although it is can be used in conjunction with alternative power sources. Solar cell technology is improving rapidly. The solar cells used on the ISS are about 12 percent efficient. Those developed for the Mars Rovers are about 26 percent efficient. The students will have to do their own research to determine the efficiency of the solar cells and in the process, will learn core concepts relating to energy, energy transformation, electricity and circuits. The same procedure applies when NASA engineers plan a mission, they have to know all of the specifications for all of the components, and the components have to be space tested. Sizes, electrical characteristics, masses, and connections must be known at the beginning of the planning. Since a mission might take 10 years to plan and construct, equipment might be 10 or more years outdated. Your students will have to work with the same restrictions. Note that the material presented has direct extracts from the NASA Solar Energy for Space Exploration Teacher s and Student s Guide designed for grade levels The entire Teacher and Student guides are not relevant for the purpose of incorporating solar cells into the design of a product for Mars, however the extracts used are an excellent resource for the overall objectives of this Space Exploration Challenge. 100

15 CONTENTS Part 1 Solar Cells in Space: Journal Solar Cells in Space: Investigation A Electrical Energy in Space: Investigation B Part 2 ISS Energy in Space: Investigation C It is not intended that all the parts of these modules are required to be investigated in order for students to undertake the Mars Challenge. Rather, the sections are provided to give flexibility learning options to teachers and students. Students that specifically chose to design a product that is actively rather than hypothetically utilising power, may for instance be directed to undertake additional parts of the investigations above to assist in their understandings and applications. 101

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17 Solar Energy Investigation A Solar Cells in Space OBJECTIVES 1. Given solar cells or panels kit with motor, students list variables that affect the operation of solar panels and explain how these variables affect the power production of solar cells 2. Through laboratory investigations with electricity, students can create parallel and series circuits, calculate power, and apply this knowledge to solve at a minimum, theoretical power requirements needed to operate the product designed by each Mission Team. 3. By analysing the power requirements of their model-sized prototype students can apply calculations to achieve a more realistic estimate of power required to operate their product on Mars. Students are to assume energy requirements for the ISS (international space station) will be the same as the requirements for Mars habitation. 103

18 Teacher Preparation The experimental design provides a direct connection between energy and work. The solar energy is converted into electrical energy. The electrical energy is transformed into mechanical energy in the motor. As the axle in the motor turns, it turns a disk attached to the axle. The mechanical energy of the motor is transformed into kinetic energy (rotational) of the disk. Students will need to have studied work and kinetic energy and able to understand that the greater the speed of the disk, the greater the kinetic energy the disk will have. To undertake Solar Cells in Space, teachers will need to buy the Solar Kit and multimeter for this module that are easy to source in companies such as Jaycar, Dick Smith Electronics etc. Ask C2C for wholesaler distributor contact details for bulk orders of solar kits at $8 to $12 each. Some of this equipment to undertake this module may already be available in the school. It is recommended that you source motors that have low rpm (revolutions per minute). If the motor turns too fast, students won t be able to count the revolutions. If the only motors you can find turn too fast for students to count the revolutions per minute, you can add a 5 kω (kilo-ohm) potentiometer in series in the circuit and use the potentiometer as a rheostat (like the rheostats used as light dimmers). Instructions for making this modification can be found at All About Circuits : Another alternative exercise for students is to use the motor to lift a mass against the force due to gravity. Attach a small pulley wheel 104

19 to the axle and wind a length of string around the wheel. Attach the other end of the string to a known weight. The motor should pull the weight upward at a constant rate of about 0.5 meters per second. Power is defined as work/time. Work can be calculated using the simplified formula W = force x distance. In this case, the force is the weight of the mass (in N [Newton s]), and the distance is the vertical distance the mass is raised. You will have to experiment with your solar cells and motor to determine the best weight and distance. You could also measure the power output from the solar cell directly. Power for an electrical circuit is equal to the voltage times the current (P=V x I). The Teacher resource Solar Cells in Space Fact Sheet, provides an experimental procedure. This is a more difficult idea for students to understand and it is suggested that students may test power output simply by using an electrical multimeter. Have students think carefully about the experimental procedure in this investigation. The transparent films also decrease the intensity of light. Does each film decrease the intensity by the same amount? Also, the red film blocks green and blue light very well. Most green films block blue light well, but do not block red light completely. Blue films usually allow some green and red light to pass. ***Procedures and questions shown next are provided in the STUDENT WORKSHEET. Note that the SOLAR CELLS in Space: Journal exercise can be used as a homework exercise prior to undertaking the other units in this module. *** 105

20 Equipment and Materials per Mission Team Solar Cell kit: 1. solar cell 2. small electric motor inch pie round (25.4 cm stiff cardboard disk 4. plastic wheel that will fit over axle of motor 5. glue 6. black marking pen 7. stopwatch 8. black construction paper 9. red, green, and blue transparency film 10. electrical wire to connect solar cell and motor Additional Materials 1-2 electrical multimeters per class Print and distribute SOLAR CELLS in Space: Journal SOLAR CELLS in Space: Investigation A 106

21 TEACHER RESOURCE: SOLAR CELLS in Space FACT SHEET The following background information will help you to guide students more effectively. The critical variables that affect solar cell performance other than the efficiency of the cell itself is the affect of the intensity of light on the solar cell. There are several factors that affect intensity: Blocking : Natural conditions can block solar radiation from reaching the solar cells. Earth s atmosphere can partially block incoming solar radiation. The amount of light reaching Earth above the atmosphere is about 1366 Watts per square meter. When the Sun is directly overhead at the Equator, the intensity of solar radiation reaching Earth s surface is between 800 and 1,000 Watts per square meter. On the Moon and on Mars, solar panels can be blocked by dust. It was expected that the solar panels on the NASA Mars Rovers would become covered with dust and cease to provide energy for the systems. A chance dust devil swept the panels clean. Dust devils occur frequently enough on Mars that Rover panels are kept relatively clean. 107

22 Angle: The angle between the Sun and the solar panel is critical. The intensity of light is measured in the Watts (power) per square meter. You can experimentally quantify how the angle changes the intensity. Hold a flashlight directly above a sheet of graph paper. The light source is at 90 to the paper. Count the number of squares illuminated. Keep the flashlight at the same distance from the paper, but tilt the flashlight so that it is at an angle to the paper. This represents a lower Sun angle. Count the squares illuminated again. More squares will be illuminated at the lower angle. The power of the light stays the same, but the area lit increases as the angle gets lower. When the same amount of power is spread over a larger area, the intensity decreases. The 23.5 tilt of the Earth s axis determines the angle of sunlight. The Sun is overhead in June in the Northern Hemisphere at the Tropic of Cancer at 23.5 N. latitude. The Sun is overhead in January in the Southern Hemisphere at the Tropic of Capricorn at 23.5 S. The GEMS (Great Explorations in Math and Science) Guide, The Real Reasons for the Seasons, could be used during this lesson to help students to understand how the tilt of the Earth s axis affects the light intensity and the seasons. The axis of Mars is tilted at 25, so very similar conditions prevail on Mars except the year is longer and each season is longer than Earth s. During the winter on Mars, the Rovers are parked on the slope of a hill to point the solar panels more directly at the Sun. As the International Space Station orbits Earth, the solar panels can be rotated to point more directly at the Sun. At times, the entire space station is pointed in a different direction to improve the angle of the panels and the Sun. For more information see What are ISS Attitudes? html. 108

23 Distance from the Sun As you know, the further you are from a light source, the dimmer (less intense) the light is. Students can confirm this experimentally and discover that the intensity (I) of light is inversely proportional to the square of the distance (r) from the light source (I 1/ r2). You will need a light bulb, a meter tape measure, and a light intensity probe. In a dark room, measure the intensity of light at 10 cm, 20 cm, 40 cm, and 80 cm from the light. Plot Intensity versus distance. If you plot this curve on a graphing calculator, you can also obtain the equation for the curve. The intensity decreases because the light spreads out farther away from the source. The Sun emits light energy in all directions. The light of the Sun is spread out over the surface of an imaginary (hollow) sphere with its centre at the Sun. The farther the sphere is from the Sun, the bigger the sphere is and the more surface it has (surface area of a sphere = 4πr2). So, the power (energy per second) emitted by the Sun as light spreads over the surface of this imaginary sphere. Close to the Sun, the sphere is small. There is a lot of power per square meter (Intensity). Farther away, the sphere is big. There is less power per square meter. There is an equation that lets us calculate the intensity of light at a distance from a light source. The equation is: Intensity = Power/(4πr2) But how can you measure the power of the Sun at its source? You can t. However, scientists have measured the intensity of light at Earth, and we know the distance from the Sun to Earth. The intensity of sunlight outside the Earth s atmosphere is 1366 Watts/m2 (It varies from slightly with solar output). 109

24 The distance (r) from the Sun to Earth is 150,000,000 km (kilometres). If you substitute these values into the equation above and solve for Power, the value for the power of light from the Sun is x 1024 Watts (Joules/second). Now we can use this value for Power in the equation above and calculate the intensity of light at Mars. The average distance from the Sun to Mars is 227,900,000 km. You can calculate that the intensity of light at Mars is W/m2. That is less than half of the intensity at Earth! But wait! The orbit of Mars is less circular than Earth s orbit. It is more elliptical. At perihelion (closest to the Sun), Mars is 206,600,000 km away from the Sun, and the intensity is calculated to be W/m2. At aphelion (farthest from the Sun), Mars is 249,200,000 km away from the Sun, and the intensity drops to W/m2. These differences could be significant to the design of a solar energy system. You will have to assess whether your students will be able to understand the maths involved. The Planetary Fact Sheet ( nasa.gov/planetary/planetfact.html) will provide additional information. Resource information from Solar Energy for Space Exploration Teacher Guide, NASA 110

25 STUDENT WORKSHEET Investigating Solar Cells SOLAR CELLS in Space: Journal Assignment The Sun radiates, or sends out as light, an enormous amount of energy. The Sun radiates more energy in one second than people have ever used. Only a small part of the radiant energy produced by the Sun strikes the Earth. Yet, every day enough solar energy strikes Australia to supply the energy needs of the Australia for about one and a half years. Much of the energy is reflected back into space, evaporates water, or is absorbed by plants, land and water. This still leaves enough to supply our energy needs. Some solar energy is used to heat water, homes, or other buildings. Solar cells can change solar energy into electrical energy. Answer the following question in your journal as completely as you can. Your entry will be evaluated on the thoughtfulness of your answers and the reasoning you give in support of your answer: What factors (variables) might affect how much electrical energy a solar cell could produce? 111

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27 STUDENT WORKSHEET Investigating Solar Cells: Investigation A Page 1 Will different colours of light affect how much electrical energy a solar cell will produce? Purpose This investigation will allow you to explore one of the variables that might affect how much energy a solar cell can produce. A solar cell will provide energy for a small electric motor to do work. The motor will turn a disk. More energy will make the motor and the disk turn faster. By covering the solar cell with different coloured transparent films, you can test whether one colour of light provides more energy to the solar cell. Materials per Group of Students 1. solar cell 2. small electric motor inch pie round (25.4 cm stiff cardboard disk 4. plastic wheel that will fit over axle of motor 5. glue 6. black marking pen 7. stopwatch 8. black construction paper 9. red, green, and blue transparency film 10.electrical wire to connect solar cell and motor 113

28 STUDENT WORKSHEET Investigating Solar Cells: Investigation A Page 2 Procedure 1. Attach the plastic wheel to the shaft of the motor. 2. Make a small dot on the edge of the cardboard disk. 3. Glue the cardboard circle to the wheel so that it will rotate when the motor is turning. 4. Attach the solar cell to the motor. Follow the teacher s instructions. 5. Place the solar cell and motor in bright sunlight. The motor should cause the cardboard disk to spin. If no spinning occurs, check the connections. 6. Watch the dot on the cardboard disk. Start the stopwatch as the dot gets to the top. Count the number of times the cardboard disk spins in 15 seconds. Multiply this number by four to get the number of revolutions per minute. Record this information. 7. Using the piece of black construction paper, cover half of the solar cell. Repeat Step Cover approximately one-fourth of the solar cell with the construction paper. Repeat Step Cover the solar cell with one piece of the red transparency film. Repeat Step 6, and record the data. 10. Repeat Step 9 with each of the different colours of transparency film. 114

29 STUDENT WORKSHEET Investigating Solar Cells: Investigation A Page 3 Questions 1. What happened when you covered part of the solar cell with black paper? Why? 2. What is the relationship between the amount of solar cell that is covered and the speed at which the disk turned? Explain 3. How is the speed of the disk related to the energy provided by the solar cell? 4. How did the coloured transparencies affect the solar cells ability to function? 115

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31 ELECTRICAL ENERGY SOLAR CELLS in Space: Investigation B This section of the Solar Cells in Space module, students discover: o o What variables affect how much electrical energy a solar cell will produce. How to design your own experiments to investigate different variables. Purpose These experiments will help you to understand how design the most effective solar panel system. Procedure 1. Create a list of three to five variables that might affect how much electrical energy a solar cell will produce. 2. Design an experimental procedure to test each variable. If you have three variables, you will have three different procedures. 3. Perform each experiment and use the multimeter to record the solar cell voltage (V) and record the data in your journal notebook. 4. Graph the relationship of 2 variables examined e.g. light intensity over time 5. Make a conclusion about what variables affect solar cells and if these variables will be the same on Mars and why? 117

32 Teacher Preparation Have a variety of materials on hand. You can keep this simple by only using the Solar Kit and multimeter, including a few general items that may already be available in the classroom such as protractors, metric rulers and graph paper. Alternatively, to provide a unique experiment, you can for instance provide fine sand or finely ground volcanic rocks used for landscaping as Mars or Moon soil simulant. Refer to the link below and research on soil stimulants listed in the reference section of this guide. Glossary provides definition of soil stimulant. The discussion following the journal assignment will also alert you to the types of materials you may need The NASA Science News follows the journey of the Mars Exploration Rovers, Spirit and Opportunity that is an excellent introduction to teachers and students to examine reports on the Martian environmental factors as they occur that have impacted on their operation. Below are examples: Refer to Investigation A and the SOLAR ENERGY Fact Sheet for further background reading

33 STUDENT WORKSHEET SOLAR CELLS in Space: Investigation B Page 1 Within your Mission Teams, work together to discover how different variables and procedures can affect how much electrical energy a solar cell will produce? Design your own experiments to investigate as many variables as you can. Purpose These experiments will help you to understand how to design the most effective solar panel system for a Mission to Mars. The product that you design for this mission will need to take into consideration that it will be required to rely on a power source of your choice that is suitable for long-term operation on Mars under extreme environmental conditions. Solar cells used on the ISS (International Space Station) that currently orbits around Earth at this very moment are working at about 12 percent efficiency. Those developed for the Mars Rovers are about 26 percent efficient. It is therefore important to study and learn about what factors may limit their ability to produce electrical power, as the product that you design for a mission to Mars may be usable for periods of time, affecting Mission objectives. 119

34 Background information Electrical Energy Investigation B: Page 2 Before you undertake this solar cell investigation, you should be familiar with the environmental conditions on Mars and the planets relationship to the Sun that may affect solar panel operation. You are then ready to come up with creative and effective solutions by listing variables and then testing them on the solar cells like teams of NASA engineers are doing right now. Procedure o o o o o Create a list of three to five variables that might affect how much electrical energy a solar cell will produce. Design an experimental procedure to test each variable. If you have three variables, you will have three different procedures. Perform each experiment and use the multimeter to record the solar cell voltage (V) and record the data in your journal notebook. Graph the relationship of 2 variables examined e.g. light intensity over time Make a conclusion about what variables affect solar cells and if these variables will be the same on Mars and why? Equipment and materials per group See previous list and include: oprotractors ometric rulers ograph paper 120

35 ISS Energy Investigation C Energy In Space Objectives: Examine the solar array energy requirements for the ISS Perform calculations involved in converting solar energy into electrical energy Give students a living and working model for the types of powered equipment, materials and general energy requirements needed for habitation and further exploration missions to Mars. Teacher Preparation To provide stimulation to the students in preparation for this ISS investigation, utilise the following resources: Download Virtual tour of ISS to show class features of Living and Working Download ISS Station SpaceWalk game on student classroom computers for a 3D spacewalk game 121

36 Workshop investigation Download the link below for the student investigation: Print, and distribute Interview with a PHALCON Print, and distribute Solar Arrays for the International Space Station and Model Space Station Power Loads and Assembly Sequence Additional resources o o o The Inconstant Sun The Mars Student Imaging Project allows students to discovermars. Marsbound is a great game that engages students in developing a mission to explore Mars that can enrich their exploration of Solar Energy for Space Exploration. Note that teacher answers to solar energy Math Connection questions at the end of Solar Arrays for the International Space Station are provided at the end of this module. Designing Energy Solutions for Mars Challenge Once the students have completed investigating the energy requirements for the ISS, that includes the living and working life of an astronaut, and aware of energy systems available to utilise on Mars, students will be ready to apply their knowledge to their product. 122

37 Designing a solar energy system for Mars with backup power sources requires creative solution inquiry skills. There are no definite procedures for students investigating design energy requirements for their product they choose, however the following questions and suggestions may assist in this process. 1. What are the power requirements for ISS? 2. Are the power requirements constant or do they vary during the day and during the year? 3. How much solar energy is available where your research habitat on Mars will be located? 4. Does the amount of available solar energy change during the day and during the year? 5. What can you do if your solar panels produce more energy than your research habitat or product requires? 6. What happens if your solar panels don t provide enough energy for short periods? 7. How does the answers to the above questions relate to the product that yor teams designs for a Mission to Mars? Explain To design an energy system for the MARS Exploration Design Challenge, the group will have to agree on some assumptions. Make certain that their assumptions are clearly stated and reasonable considering what they know. The emphasis should be on careful creative and innovate thinking and not a correct solution. Even scientists and engineers struggle finding solutions. The group should clearly be required to support the products energy requirements with evidence. The students will need to consider factors such as the decrease in solar energy that reaches Mars because it is farther from the Sun than Earth is and investigate alternatives. The instructions for the product design process and assessment criteria incorporating energy systems are clearly outlined in module 1: MARS Exploration Design Challenge. 123

38 TEACHER ANSWERS to SOLAR ENERGY QUESTIONS Mars Challenge: Solar Cells in Space Answers to math questions at the end of Solar Arrays for the International Space Station, are provided below. Download Solar Energy for Space Exploration Student Resources for questions and student. Math Connections - Solutions 1. How much power does each solar cell produce? Information: Scientists have measured the intensity of solar radiation at the space station as about 1366 W/m2. Each solar cell is about 12 percent efficient. This means each cell can convert about 12 percent of the energy from the Sun that falls on the cell into electric power. What is the area of each solar cell? Solution Intensity of solar radiation x area of solar cell x efficiency = 1.05 W 2. Using the amount of power from each cell, how much power should two arrays produce? How does this answer compare with the information in this article? 124

39 Information: Each array contains 32,800 solar cells. Solution Number of cells per array x number of arrays x 1.05 W (answer from #1) = 68,880 W. The value in the text is 64 kilowatts (64,000 W) from two arrays. Some values have been rounded and some efficiency is lost. 3. What is the efficiency of two arrays? Why might this be different from the efficiency of a solar cell? Information you need to know: What is the intensity of solar radiation at the space station? What is the area of an array? What is the power output from two arrays? Solution Intensity of solar radiation x area of array x two arrays = 1,023,000W Efficiency = power output from two arrays (64,000W) divided by 1,023,000W = about 6 percent The difference arises because a significant part of the array is structural, holding the cells together and giving strength to the whole array. One must always be careful about given information. In this case, students need the total area of the solar cells. The area of a solar panel will include structural material. This really isn t a trick question. Students will often assume that the total surface of their habitat can be covered by solar cells, but some of the area must be dedicated to the structure of the solar panel 125

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