Using Solar Panels to Teach Integration -...

Using Solar Panels to Teach Integration

Victor Donnay

Department of Mathematics Bryn Mawr College

vdonnay@brynmawr.edu

January 18, 2014 !

Solar Panels on Campus

How much total energy did the solar panels produce today?

Home Electrical Bill

Home Electrical Bill

Units are kWh = Kilowatt hours

Power and Energy

Three light bulbs use 3 x 100 watts of power = 300 watts

= 300 joules/sec = rate

Bulb is on for 10 hours Total Energy used

= 300 watts x 10 hours = power x times = 3000 watt-hrs = 3 kWh

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Power (W) vs Time (hours)

Question: How to determine total energy produced by solar panels?

Graph of Power vs Time

Question: How to determine total energy produced by solar panels?

Graph of Power vs Time

Answer: Area under the curve!

How to estimate area under the curve?

How to estimate area under the curve?

Lots of ways beyond the standard Riemann sum. For pre-calculus students, use triangles and other shapes. Cut out paper and weigh it.

How to estimate area under the curve?

Riemann sums. Can get solar panel data in spreadsheet form.

Raw data: date, time (5 min intervals) power (watts)

Clean up the time data to make it easier for students to use. Time now in hours written in decimals. 5 min = 1/ 12 hour = .08 hour

Can plot data from spreadsheet to make graph of power vs time. Graph is data points joined by lines. It is not given by a formula. Math students are used to thinking that graphs are always given by formulas. Can also display just individual points.

Calculate energy produced over each 5 min = .08 hr interval Energy = power x length of time. Then sum up amount of energy

In each interval to get total energy produced during the day.

Materials include: Essays describing how math gets used in various fields of sustainability Sustainability Counts! Educational Initiative with range of lesson plans including this Solar panel lesson. Resources page with links to additional materials.

www.mathaware.org/mam/2013/

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Additional References: How People Learn: Brain, Mind, Experience, and School, National Academies Press, http://www.nap.edu/openbook.php?isbn=0309070368 Sustainable Energy – Without the Hot Air, David JC MacKay, http://www.withouthotair.com/ Great book that does all types of interesting calculations to model the potential for scaling up renewable energy use to a national scale. Only requires high school math. The materials from Mathematics Awareness Month 2013 – Mathematics and Sustainable are archieved and available at: http://www.mathaware.org/mam/2013/ Essays at: http://www.mathaware.org/mam/2013/essays/ Sustainability Counts! Educational materials: http://www.mathaware.org/mam/2013/sustainability/ Other Resources: http://www.mathaware.org/mam/2013/related/