Engineering with Geometry

Rachel WoodAffiliations: RET at The University of Tennessee, Knoxville,

Geometry, Bearden High School

Using Geometric Concepts to Optimize Wind Turbine Performance Objectives

•9th-10th Geometry•State Competencies: M1, M3, M5, G.MG.A.2•Students will collaborate in groups of 3 to construct and optimize a wind turbine using the engineering design process

•Students will establish the relevance of certain factors of wind turbine design based on their qualitative and quantitative data

•Students will discuss the success or failure of their wind turbine with supporting evidence from their data, how the engineering design process was applied in the lesson, and what limiting factors engineers might have to consider when designing full sized wind turbines in a one page reflection homework assignment

Essential Questions

“Is radius length related to efficiency?”

“Is symmetry related to efficiency?”

“Is angle of rotation (number of blades) related to efficiency?”

“How important is efficient wind turbine design to the green energy movement?”

• Cardboard or thin plastic• Masking tape• Wooden skewers• Voltage reader• Rulers/Meter • Sticks

Using Trigonometry to determine a Maximum Angle of Elevation of an Incline Objectives

•9th -10th Geometry•State Competencies: MP1, MP3, MP5, G.MG.A.2, G.SRT.B.8

•Students will collaborate in groups of 4 to optimize ramp construction (measured by their peer evaluations)

•Students will develop an understanding of the engineering design process, describe how trigonometry could be used in a real life situation similar to what they model during the lesson and discuss how voltage and mass are relevant to battery design for electric vehicles in a one page reflection

•Students will consider alternative energy methods of vehicle propulsion in a post lesson discussion

Materials• Meter Sticks• Pencils• Calculators • 7 battery powered

vehicles• Cardboard ramps• AA batteries

Essential Questions

“Does varying voltage affect the maximum angle of elevation achievable by a battery powered vehicle?”

“Will the mass of the vehicle affect the maximum angle of elevation achievable?”

“How do these concepts relate to life-sized electric vehicles?”

Materials

References: https://www.tva.gov/Energy/Our-Power-System/Coal/Bull-Run-Fossil-Planthttps://www.tva.gov/About-TVA/Power-out-of-Thin-Air https://www.energy.gov/sites/prod/files/wv_chapter2_wind_power_in_the_united_states.pdf

• 9V batteries• (Energizer Alkaline)• Scale• AA battery holders• (2, 4)

• 2 or more box fans• Foam spheres• adhesive or hot glue