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Back of the Envelope Calculations: Renewable Energy

Laura Rademacher, University of the Pacific
University of the Pacific, Earth & Environmental Sciences
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Throughout an introductory level course highlighting sustainability themes, students do a number of Back of the Envelope Calculations to put the large numbers related to energy into perspective. In this calculation for the feasibility of applying wind energy to a new housing development, students are asked to determine the estimated payback time and assess the value of installing a wind turbine to provide electricity to the development. The students discuss the pros and cons of incorporating renewable energy installations into community planning in the context of previous lessons on fossil fuels and renewables.

Learning Goals

The goal of this activity is for students to determine whether wind energy is a viable alternative for communities in new housing developments. Through this Back of the Envelope Calculation (BOTEC), students will learn how much energy an average home uses, how much energy a typical wind turbine can provide, what the cost of installation of a wind turbine is, and what the payback period of a wind turbine is. Students will further develop their critical thinking and quantitative skills through this activity.

Context for Use

This activity was developed for an introductory level course with approximately 30 students, although it could be used in any size class with modifications to the follow up discussion. Approximately 15 minutes should be set aside for this activity. No special equipment is required, however, I ask my students to always have a calculator in class. This BOTEC follows a multi-lecture series on fossil fuels and energy usage and is embedded within lectures on renewable energy resources. This activity is situated as part of a semester-long series of back of the envelope calculations (approximately one BOTEC per topic).

Description and Teaching Materials

Question: Assume a new housing development is going up in town, which will consist of 150 homes. Our region is a good wind resource area. What is the payback period for a wind turbine if installed? Consider the following: approximately 500 kW are needed to sustain the neighborhood; the installed cost of a 500 kW wind turbine is approximately $500,000.

Students should estimate what an average monthly power bill is based on their experience (answers will vary by region and household).

Follow-up discussion questions (emphasizing environmental, social, economic implications):

1) What are the pros and cons of such a wind installation?

2) Where might be the best place to locate a wind turbine in a housing development?

3) How does the payback period change as the cost of electricity from the "grid" goes up and down?

4) Is your answer surprising? (and why)

5) Would you consider this in your neighborhood? (why/why not?)

Teaching Notes and Tips

This activity takes a minimum of 15 minutes, but it could be expanded to allow students to research average household energy usage and cost of wind turbines in advance, as well as to collect household energy bills to determine their electricity rates.

I always remind students to bring a calculator to class, but many of these calculations can be done without one.

These calculations usually generate good discussion, especially about why there isn't broader adoption of renewables in the US. Be prepared to guide these discussions.


Assessment is usually based on whether students participated in the discussion.

One alternative is to convert the back of the envelope exercises into clicker questions, which could be assessed in more detail.

References and Resources

SERC Back of the envelope page by Tewksbury:

US Energy Information Administration:

US Department of Energy:

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