Solar Energy Harvesting Preliminary Activity. Part 0: Strings, Stamps & Dice A check for understanding on measurement. 1. Measurement is counting

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1 Solar Energy Harvesting Preliminary Activity Name Part 0: Strings, Stamps & Dice A check for understanding on measurement. 1. Measurement is counting. 2. Length is counting. a. The units for length tell you b. Give three examples of length measurements and include reasonable units. i. ii. iii. 3. Area is counting. a. What makes a square a square? and. b. The units for area tell you c. How does measuring area depend on measuring length? d. Give three examples of area measurements and include reasonable units. i. ii. iii. Solar Energy Harvesting Student Pages Page 1 of 18

2 4. Volume is counting. a. The units for volume tell you b. Give three examples of volume measurements and include reasonable units. i. ii. iii. 5. Three versions of the perimeter formula for a rectangle are: P = = =, and all three versions are really just counting. a. Sketch and label a picture to illustrate how to count the correct number of one-inch string-lengths for the perimeter of a 3 inch by 5 inch rectangle. 6. The formula for area of a rectangle A =, which counts the number of it takes to cover the rectangle. It does this quickly by first counting in a, and then counting... a groups-of-groups counting method. a. Show your understanding by sketching and illustrating the groups-of-groups method to count the number of square-stamps it takes to cover a 3 x 5 rectangle. Solar Energy Harvesting Student Pages Page 2 of 18

3 7. The formula for volume of a rectangular-prism V =. a. Another way to find area is to use your understanding of area to count the number of dice it takes to cover the base(area of the base), and height (H) to count the groups of dice in each layer: V =. Show your understanding by labeling the pictures to show how to calculate volume by counting dice two different ways for a 3 x 4 x 5 rectangular prism. Solar Energy Harvesting Student Pages Page 3 of 18

4 Solar Energy Overview The sun produces solar radiation that travels about 8½ minutes to reach the earth. This solar power strikes the Earth s upper atmosphere with enough energy, that if one square meter of it were converted to electricity it could power about fourteen 100watt light bulbs. Unfortunately, not all of this energy reaches the ground because some is reflected and absorbed by the atmosphere, clouds, dust and pollution. By the time sunlight reaches the ground in North America, there is about 150 to 375 watts per square meter available in other words about enough for two to five 75watt bulbs (assuming all the energy is converted to electricity). The main advantage of solar energy is that it is free. The obvious disadvantage is that the sun sets in most places, taking away this free source of energy on a daily basis. To get through the night, most systems designed to harvest solar energy have two main components: Collectors that catch an area of sunlight (There are two main types): Solar thermal collectors collect it as heat. Photovoltaic cells collect and convert it directly to electricity, like on a solar-powered calculator. An energy-storage device to hold extra energy generated during the daytime that can be used up when solar energy is not available. Heat can be stored in any mass such as a tank of water or a slab of concrete. Electricity is generally stored in batteries. Block diagram of three main types of solar energy harvesting systems Typical thermal solar collectors Thermal Solar Collector Thermal Solar Collector Power Plant Thermal Storage (Water) Thermal Load (House, heat, hot water, industrial process) Photovoltaic Collector Electrical Storage (Batteries) Electrical Load (House, power grid) Solar Energy Harvesting Student Pages Page 4 of 18

5 Summary When collecting solar power the amount of energy available is directly proportional to area of sunlight collected. So if you double the patch of sunlight collected, you would have twice as much energy available to harvest. The energy to be stored is directly related to the area of the sunlight collected, and it is usually stored in a mass or volume of substance like a tank of water or a slab of concrete. Solar Heating System Design We will now explore one type of solar heating system: The active water-type solar system which transfers heat from a roof collector to a wellinsulated under-floor water storage tank. Warm water from the storage tank is pumped through pipes in the concrete floor of the building to heat the floor, which heats the building. Whenever the temperature difference between collector and storage is less than 10 o F, the water supply to the collector shuts off and it drains back to storage because the water is no longer being heated by the sun at an efficient rate. The water circuit for heating the animal area is a separate piping arrangement, with the pump taking water directly from the storage tank. A boiler is needed to provide supplemental heat when solar energy is insufficient. Cross-section of a typical Collection Requirements solar heating system. The energy requirements can be found in the following table that gives the required area of sunlight to harvest: Square Feet of collection per an animal unit **Area of Wall **Area of Roof Collector Collector Live Stock Type Air Type Air Type Water Type Sow & Litter Nursery Pig Dairy Calf Solar Energy Harvesting Student Pages Page 5 of 18

6 **Values shown are based on farmer experience and empirical calculations, and should be considered approximate. Storage Requirements Storage size is directly related to collector surface Storage needed for each square foot of collector surface Storage Medium Rock Concrete Water 1.5 Cubic feet 1.5 Cubic feet 4 Gallons **The energy storage requirements for 10 sq. ft of collector would be 15cu. ft. of rock or concrete or 40gal. of water. Solar Energy Harvesting Student Pages Page 6 of 18

7 Solar Energy Harvesting Overview Name Instructions: Read the Solar Energy Harvesting handout, and use the information to answer the questions below on solar Energy. 1. How long does it take for solar radiation to travel from the Sun to the Earth? 2. Label the diagram to indicate the amount of energy that reaches the upper atmosphere. x ( m 2 ) Patch of Sunlight s 100watt 3. How many watts of solar energy on average reaches the ground? watts per. a. Show how to determine the number of 15-watt compact-fluorescent light bulbs would this power. b. Give three reasons for why less energy reaches the ground. i. ii. iii. 4. What is the main advantage of solar energy? 5. What is the main disadvantage of solar energy? Solar Energy Harvesting Student Pages Page 7 of 18

8 6. Describe the two main components of solar energy harvesting a. The, which. There are two primary types: i. to collect ii. to collect b. The to be used later when. There are two primary types: i. Heat stored. ii. Electricity stored. 7. If one square meter of collected energy requires 150 liters of water for storage, then show how to determine the energy storage requirements for 8 square meters? 8. Sketch and label a diagram for a water based solar heating system. Include the four main components: a. Collectors b. Energy storage c. Heating units for the floor d. Backup heating Solar Energy Harvesting Student Pages Page 8 of 18

9 Solar Energy Harvesting Architect: Heating System Design Objective: Design an active water-type solar heating system for the floor of a sow farrowing house (a building for female pigs to build their nests and birth their litters of piglets). Part 1: Energy Requirements (You will need to reference the Solar Energy Overview handout for Sow & Litter collector requirements, and water storage requirements.) 1. Read the Solar Energy Overview, and use the information to help with Part Complete the table for solar collector and energy storage requirements Number of Sows with Litters Solar Collector requirements in square feet Energy Storage requirements in gallons of water 5 20 n 3. Explain your method to determine solar collector requirements. 4. Explain your method to determine energy storage requirements Solar Energy Harvesting Student Pages Page 9 of 18

10 5. There are approximately 7.5 gallons in a cubic foot. Show how to find the number of cubic feet: a. In one gallon of water. b. For energy storage using water for one sow with a litter? c. For energy storage using water for 20 sows with litters? 6. How many half-gallon milk cartons would it take to fill a cubic foot? Surprised? Part 2: Determine solar collector needs for a 18-sow farrowing house. Solar Collectors Thermal solar collector panels come in several sizes, but there are some standard modular sizes. The prices can vary depending on the manufacturing methods employed but usually fall in the $20 - $60 per square-foot range. 1. Assume you are buying panels that cost $30 per square-foot, to complete the table. Panel Style A Solar Panel Size 2ft x 4ft Number of Sq. Ft. Cost in Dollars B C D E F G 4ft x 4 ft 4ft x 8ft 6ft x 12ft 6ft x 20in 78in x 36in 19.5ft x 36in 2. How many times more area than panel A is: i. Panel C: ii. Panel D: 3. Sketch and label pictures showing why panel C costs four times more than panel A and is a scaled version of A. (Hint: Think Area.) Solar Energy Harvesting Student Pages Page 10 of 18

11 4. Sketch and label pictures showing why panel D costs nine times more than panel A and is a scaled version of A. 5. What would be the dimensions of a panel that was 4.5 times larger than panel A? 6. Panels C and D are scaled up versions of panel A, yet panel B is not. Explain why panel B is not a scaled up version of panel A. 7. Complete the table with help from the information from question #2. Scale Scale Perimeter Factor Factor Panel of Panel of Squared Style in Feet Panel A A = 1 C D X 4.5 Y 81 **Panels X and Y are new panels scaled up from Panel A 8. Find the areas and costs for the hypothetical panels X and Y if they are scaled versions of panel A. a. X: b. Y: Solar Energy Harvesting Student Pages Page 11 of 18

12 Summarize your understanding 9. Find a relationship between the scale factor of the perimeter and the costs of the panel compared to panel A. (Hint: How many times more area than panel A is each panel?) 10. Explain the relationship of perimeter to area when objects are scaled up. How many square inches are there in one square foot? (Hint: It s not 12 think about scaling up a square inch to a square foot.) 11. Find the cost in dollars per square inch for your solar collector panels. 12. If the side lengths of panel E were scaled up by a factor of 3.5 a. How many times larger would its perimeter be? b. How many times larger would its area be? 13. This relationship between linear dimensions and area only works for scaled objects. Show this is true by demonstrating it doesn t work for non-scaled objects. Sketch and label a picture of panel A and another panel with double the Area that doesn t follow the perimeter - area scaling rule. (Hint: Don t scale.) Solar Energy Harvesting Student Pages Page 12 of 18

13 14. This new relationship can also be used to go backwards. Practice this relationship by completing the table. Assume each object listed is a scale version of the others: Object # Dimensions in feet L x W Perimeter in feet Area in sq. ft x x x 12 4 x 25 5 x x 7 x 1 8 x x x Determine the cost and the number of collector panels needed for your design of a 18-sow farrowing house: a. Using panel style A. b. Using panel style E. Solar Energy Harvesting Student Pages Page 13 of 18

14 Part 3: Determine solar energy storage needs for a 18-sow farrowing house. Energy Storage The heated water from the solar collectors will be stored in a rectangular tank underneath the floor of the building. The water can be circulated through the floor later for heat when it is needed. The building s floor plan calls for the building to be 32 feet wide by 40 feet long. 1. Show how to determine the cubic feet of water storage required for your system s design of an 18-sow farrowing house. 2. Complete the table for tank designs, and give three other possible tank dimensions that would work for your storage requirements. Design Number Length in feet Width in feet Height in feet Area of Floor in square feet Volume in cubic feet ** **Note: Calculate to the nearest hundredth of a foot. 3. The tank with the least amount of surface area will lose the least amount of heat. Determine which tank design would be best for your project if you want to minimize heat loss due to surface area? 4. Which would be the worst? Explain your reasoning. Solar Energy Harvesting Student Pages Page 14 of 18

15 Part 4: Modifying designs. 1. Your client was impressed enough with your design that you have been asked to come up with different versions of a design scaled up in different ways. You are given an original tank that is 4 ft x 4 ft x 4 ft, and asked to make changes to it. 2. Modifications A: You are limited to a tank height of 4 feet due to rock underneath the building. So you can only change the length OR the width of the tank, OR both. Show your understanding by completing the table. Design Version Original Width doubled Length and Width doubled Length Tripled Length and Width Tripled Length 7 times longer Length and Width 7 times more Length Halved Length and Width halved Linear Scale factor used Floor dimensions In feet Floor Area in square feet Volume In cubic feet Area Scale factor Volume Scale factor 1 4 x x Solar Energy Harvesting Student Pages Page 15 of 18

16 3. What is the pattern for a 1-dimensional linear change on the tank s width, floor-area and volume? Make sure to indicate how the scale factor(s) help predict results. 4. What is the pattern for a 2-dimensional change? Make sure to indicate how the scale factor(s) help predict the results. 5. Optional Modifications B: Now assume there is not a 4 foot height restriction In other words it can be any height you need it to be. So, the design version has you change all three dimensions by the same factor. Show your understanding by completing the table built from the same original 4 ft x 4 ft x 4 ft tank. Design Version dimensions in feet Volume in cubic feet Surface Area Scale factor for ALL tank dimensions Scale factor for volume Scale factor for tank surface area Double the tank dimensions 2 Triple the tank dimensions Solar Energy Harvesting Student Pages Page 16 of 18

17 6. (Optional) What is the pattern that scaling all linear dimensions (length, width and height) have on the tank s dimensions, Surface area and tank volume? Make sure to indicate how the three different scale factors helps predict results. One of the reasons the client was asking about different scaled designs is because they know of a liquid mixture better than water for storing the thermal energy in. The mixture is called a glauber salt slurry. It uses a special kind of salt mixed in with water, and it effectively cuts the solar collecting requirements in half. 7. (Optional) Scale down a design that uses a cube-shaped storage tank of 1024 cubic feet of water to what the glauber salt slurry will allow. Be sure to indicate your methods. Your answer should include: The amount of solar collector area required. The amount of thermal storage required. The number of solar panel needed specified by type. The dimensions of the storage tank The surface area of the storage tank Scale factors linking all the dimensional changes between the old and new designs. Solar Energy Harvesting Student Pages Page 17 of 18

18 Solar Collector Manipulatives Panel A 2ft x 4ft Panel B 4ft x 4ft Panel C 4ft x 8ft Panel D 6ft x 12ft Solar Energy Harvesting Student Pages Page 18 of 18