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Real World Math

This informative guide dives into the algebra behind wind turbines, focusing on a site in Prescott, Idaho, famously featured in a box office sleeper. You'll learn how to build a wind turbine through a step-by-step approach, applying algebraic concepts to calculate cement volume, costs, and turbine performance. Interactive algebra problems challenge you to compute the tip speed of turbine blades and understand the relationship between wind speed and power output. Engage with real-world math while contributing to sustainable energy solutions.

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Real World Math

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  1. Real World Math The Algebra of Wind Turbines

  2. Idaho Trivia Question: What box office sleeper was filmed in Prescott, Idaho? Wind Turbine Site Prescott

  3. How to Build a Wind Turbine

  4. Step 1: Build Some Roads

  5. Step 2: Dig Some Holes Baylor Grad

  6. Step 3: Put Some Steel in the Holes

  7. Step 4: Pour Some Concrete in the Holes

  8. Step 5: Stack the tower with a crane

  9. Step 5: Stack the tower with a crane

  10. Step 6: Build and raise the rotor

  11. Step 7: String the wire and plug them in

  12. Algebra Problems 1.) • Calculate volume of cement in cubic yards for the octagonal base • Multiply by the projected number of turbines • Estimate cost for cement required for footings ($100 per cubic yard)

  13. Wind Turbine Foundation Wind Turbine Tower – 80 meters tall Ground Level when complete 3’ 6” Pedestal Side View 2’ Base 2’ 16’ Base Top View Pedestal 14’ 20’ 14’ 48’

  14. Algebra Problems 2.) • Calculate the tip speed of the blade in miles per hour. • Calculate the distance in feet that the blade travels in one hour.

  15. Nacelle Blade Tower Top Tower Mid Tower Base

  16. 125 feet 250 feet Blade Speed = 17 rpm

  17. Power output as a function of wind speed The independent x variable is: Wind speed in meters per second The dependent y variable is: Power output in kiloWatts Here’s the basic equation: w = ½ r A v 3 w is power r is air density A is the rotor area v is the wind speed Problem: Solve the equation for r (section 1-3 in Alg II)

  18. a cubic function A: 40% Capacity Factor = 40% of theoretical annual energy output Q: What polynomial function does the graph look like? Capacity Factor Wind Turbine Power Curve Power Output in kW Wind Speed at Hub Height in meters/second

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