Angela's Tools · Chapter 19 · Earth's Natural Resources
Worksheet 9 of 10
Power for Cinder Ridge: Choosing an Energy Source With Criteria and Constraints
Learning target: I can define the criteria and constraints of a design problem, evaluate competing energy solutions against them with a systematic process, and justify a choice that depends on which resources the region actually has.
Transfer and designAbout 50 minPairs
MS-ETS1-2 · assessesMS-ETS1-1 · practiceMS-ESS3-1 · supports
engineering designdata analysiswritingdiscussion
NameDatePeriod
Directions
Work in pairs. Cinder Ridge is an invented town and all the numbers are teaching data, but the four kinds of power plant and their strengths and weaknesses are real. Read the brief and the option cards. In Part A, write the criteria and constraints with numbers. In Part B, calculate the 30-year cost of each option and fill in the decision matrix. In Part C, make your recommendation and defend it. You may disagree with your partner in Part C; if you do, each of you writes your own justification.
You will need: This worksheet, Pencil, Calculator
The brief from the Cinder Ridge town council — Cinder Ridge has 8,000 people and sits in a mountain valley on the slopes of a dormant volcano, 150 km from the nearest city. The town's old power line failed and will not be rebuilt. The council must choose one way to generate the town's electricity for the next 30 years. The town uses about 40 million kilowatt-hours (40 GWh) a year, and it must have power every hour of every day, including winter nights and dry summers. The council can spend at most $130 million in total over the 30 years, counting construction, fuel and running costs. Cinder Creek, which runs through the valley, has a protected salmon run that must be able to pass upstream. The valley's farmland is the town's main income, so no option may take more than 1 square kilometer of it. The council also wants the option with the least air pollution that meets everything else.
Geology report (teaching data): A drilling survey found rock at 2 km depth under the town's north edge at 240 °C, with groundwater in cracked volcanic rock, because magma sits a few kilometers below the dormant volcano. Cinder Creek's flow drops to one-third of its spring value in late summer and in drought years. The valley gets about 2,100 hours of sunshine a year, but December and January together receive only about a fifth of the sunshine that June and July receive.
Four competing designs (teaching data)
1 Option A: Flash-steam geothermal plantTwo production wells and one injection well into the 240 °C rock. Output: 45 GWh a year, steady day and night in every season. Construction: $60 million. Running cost: $1.5 million a year. Land: 0.1 km² on rocky ground outside the farmland. Air pollution: very low. Risks: the first well might miss the hottest rock (a test well would cost $4 million extra); if the plant pumps faster than the rock reheats the water, output falls over the years unless the injection well returns all the water.
2 Option B: Diesel generatorsFour generators burning diesel fuel trucked 300 km from the coast. Output: up to 50 GWh a year, any hour, as long as fuel arrives. Construction: $15 million. Fuel and running cost: $5 million a year at today's prices. Land: 0.05 km². Air pollution: high; also the largest carbon dioxide release of the four. Risks: fuel prices can double; the mountain road closes for several days each winter, so the town must store fuel.
3 Option C: Hydroelectric dam on Cinder CreekA 30 m concrete dam and reservoir 4 km upstream of town. Output: 32 GWh in an average year, but only 18 GWh in a dry year and much less in late summer. Construction: $75 million. Running cost: $1 million a year. Land: the reservoir floods 2 km² of the upper valley, of which 0.6 km² is farmland. Air pollution: very low. Risks: the dam blocks the salmon run unless a fish ladder is added ($8 million, and ladders work only partly); the reservoir traps sediment that used to reach downstream fields.
4 Option D: Solar farm with batteriesSolar panels on the valley floor with a battery bank that stores power for the night. Output: 42 GWh in an average year, but December and January together produce only about 3 GWh, and the batteries hold enough for one night, not a week of winter storms. Construction: $90 million. Running cost and battery replacement: $1.2 million a year. Land: 1.2 km² of farmland (there is no flat rocky ground large enough). Air pollution: very low. Risks: a cloudy winter week would leave the town without power unless a backup is added.
Part A: Define the problem precisely
1.Turn each of the council's wishes into a precise, testable statement. A criterion is a goal the design is judged on; a constraint is a limit it must not break. Write at least one number or a clear yes/no test in every row.
| Criterion or constraint? | Measurable version (with a number or a yes/no test) | Where in the brief it comes from |
|---|
| Enough electricity | | |
| Reliable every hour | | |
| Affordable | | |
| Salmon can pass | | |
| Farmland protected | | |
| Least air pollution | | |
2.'Reliable' is the hardest wish to measure. Explain why 'produces at least 40 GWh a year' is not enough by itself, and write the extra test that catches Option C's and Option D's weaknesses.
Part B: Evaluate the four designs systematically
3.Calculate the 30-year total cost of each option: construction + (running cost per year × 30). For Option A include the $4 million test well. For Option C include the $8 million fish ladder. Show all four calculations and state which options stay within $130 million.
4.Fill in the decision matrix with yes, no, or the pollution level, using the cards, the geology report and your q3 costs. In the last column write yes only if the option passes every constraint and meets the supply criterion in every season and every kind of year.
| Enough and reliable all year? | Within $130 million? | Salmon pass? | Farmland ≤ 1 km²? | Air pollution (low / high) | Passes every constraint? |
|---|
| A: Geothermal | | | | | |
| B: Diesel | | | | | |
| C: Hydro dam | | | | | |
| D: Solar + batteries | | | | | |
5.For each option that fails, name the single most serious failure and the card sentence that proves it.
Part C: Recommend and justify
6.Write your recommendation to the council. State the option, show that it meets every criterion and constraint with numbers from your matrix, name its main risk and how the town should reduce that risk, and explain what the town gives up by not choosing the runner-up.
7.Explain, using the geology report and what you know about how geothermal energy is distributed, why your recommended option is available to Cinder Ridge at all. Then say whether the same recommendation would work for a town on flat farmland 1,000 km from any plate boundary, and what that town's best option might be.
8.Option A uses a renewable resource, but the card says output can fall over the years. Explain how the town could run the plant unsustainably, and what one rule in the plant's operating contract would prevent it.
Fail fast, then compare
Engineers check constraints first, because a design that breaks a constraint is out no matter how good it is otherwise. Go down the matrix column by column: cost, salmon, farmland. Cross out any option that fails a constraint. Only then compare the survivors on the criteria (supply in the worst season and the worst year; pollution). For the cost column, write the multiplication on one line and the addition on the next: for example, $15 million + ($5 million × 30) = $15 million + $150 million = $165 million.
Design the hybrid
Real towns rarely choose only one source. Design a two-source system for Cinder Ridge that costs no more than $130 million over 30 years, meets the supply criterion in every season, and respects every constraint. Scale the options as you wish (for example, half-size solar at half the cost and land, with a small geothermal plant), show the cost arithmetic, and explain which weakness of each source the other one covers. Then write one sentence on what the Hoover Dam team would recognize in your process.