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Are Wind Farms The Solution? Do the Math!

It’s Agreed: Teachers Should Teach Environmental Responsibility

Teachers around the world are expected to teacher their students to be responsible citizens, to reduce their impact on the environment and to support sustainability. For one example, see the new Australian Curriculum’s Cross-Curriculum Priority: Sustainability.

Great, good stuff. In fact, it would be difficult to imagine a teacher anywhere who did not believe in protecting the environment for future generations, and teaching today’s students to be responsible adults in the future.

But does mean that we should agree to promote every green cause or environmental suggestion, “just because”. Some ideas are really dumb, including those with a green label applied. How can we tell them apart? Do we just let others decide for us, or do we think for ourselves? I reckon we should use math to check out the facts – and teach our students to do the same.

Will Wind Farms Fix the Energy Crisis?

A lot of environmental activists and politicians are currently promoting wind energy as the solution to global warming and the world’s reliance on dirty fossil-fuel-generated energy. Are they correct?

The answers aren’t all in yet, but it is important to do some basic research, rather than just believing the promoters. There are some great sites out there with lots of information on outputs, days of output, daily averages, hourly averages, etc.,  which give a much better idea of what is actually happening.

Will wind energy on its own replace other forms of electricity generation?

Other considerations for developing an informed basis for developing an opinion could be factors that are unique to wind farming. Such as:

This is the final podcast episode that was recorded on our trip in Europe. Future episodes will be videoed in the classroom.

Podcast Location:

South Lanarkshire wind farm. You’ll notice that the Google maps photo doesn’t show the wind turbines; the photo must have been taken before they were constructed. If you check the Street View, you will see them.
View Lochhead (Wind) Farm, South Lanarkshire in a larger map

So Where’s the Math?

Teaching about environmental issues is a great opportunity to promote socially responsible outcomes in your students’ lives. It is also a wonderful opportunity to put those mathematics skills to really practical use. Environmental projects always produce controversy, because they always involve costs to someone or other, along with the benefits. In order to reach sensible, informed conclusions, we should return to the data, and ask “What are the facts?”. Your students are ready to answer questions of concern to them, that are matched to their level of maturity. Use math to help them decide!

With your class you could do some activities such as actually planning a family’s daily needs based on the output from turbines on different days. How is industry affected? What is the daily consumption, or even the hourly consumption of power of a city? Are its needs steady or fluctuating? How does this affect the power industry? With these ideas it would be possible to follow through on an idea and make a great math project where the application of math is almost limitless.

The Wind Farm Performance site has lots of real-time stats and graphs on Wind Farms:

What do you teach in environmental studies that could use some reality in the form of data? I’d love to hear your ideas – please leave a comment below.

Related Videos

Explanation of the components of a wind turbine:

Turning the Weather Into Power (article + Flash animation) – click image for link:

Danish wind turbine fails in storm:

Wind energy in west Texas, Wind Turbines:

Wind Farms in the Media This Week:

Photo Credit

Children Recycling: © iStockphoto.com/Randy Plett

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Math and International Travel

If you’ve followed previous episodes of this blog, you will know that earlier this year in the northern spring my wife and I were blessed to travel in Europe.

Traveling between countries got me thinking about the types of mathematics you do when traveling. In addition to the usual math of budgeting, cooking, scheduling events, and so on, when you travel into a foreign country you have the extra challenges of conversions.

There are two main types of conversion an international traveler will likely have to do:

  • Converting currency from one country’s currency to another’s
  • Depending on the two countries, converting units of measurement between metric (SI) units and British/Imperial/American Conventional units

The video was shot in a studio in front of a ‘green screen’, to allow me to overlay videos. The background shows shots I took on the ferry between the UK and France on our trip, to set the scene for traveling between countries. I thought of doing the video live on the ferry, but it was too windy and noisy.

Converting Currency

Unless money was truly unlimited (certainly not the case for me), when buying food, gasoline and souvenirs a traveler will want to work out just how much he or she is paying for an item, in a familiar unit of currency. This is done using a currency conversion factor,  a number which changes continually. As explained in the video, there will be a pair of currency conversion factors for any two currencies, which are numerical inverses of each other. For example, the pair of conversion factors for Australian dollars (AUD) and British Pounds (GBP) at the time of writing is:

  • 1.52875
  • 0.65413

[source: XE.com on October 16, 2011]

This means that £1 British, the more valuable of the two currencies, is equivalent to A$1.52875; conversely, A$1 is equal to £0.65413.

The neat thing is that one can use either of these factors to derive the other by inverting it, and one factor can be used to convert the two currencies in either direction. Thus:

  • 1 ÷ 1.52875 = 0.65413
  • 1 ÷ 0.65413 = 1.52875

Using these data in everyday transactions, when traveling in the UK I could convert prices to Aussie dollars pretty easily and accurately by adding a half. So a burger for £4.99 would be worth around $7.50 in our money. Going the other way, I could take around two thirds of an Australian price to get the rough equivalent in British currency.

Of course, a calculator will do this more easily, and a travel calculator is designed to simply convert in either direction by the touch of a couple of buttons.

Converting Units of Measurement

Depending on where you travel, you may be faced with different units of measurement from those you are familiar with. Europe, Australia and much of the rest of the world use Metric units, whereas the US and the UK are largely still using British Imperial units. Traveling on UK roads I changed the settings on my GPS device to use miles rather than kilometers, but in France I changed back to kilometers. That way road signs indicating how far a town was would match what the GPS indicated.
Manual or calculator conversions of measurement units are done in much the same way as converting between currencies, and again each type of conversion will have a pair of inverted factors. One example:

  • 1 inch = 25.44 mm (millimeters)
  • 1 mm = 0.3931 inch
  • 1 ÷ 25.44 = 0.3931
  • 1 ÷ 0.3931 = 25.44

International travel is not the only context for conversions like these. Other uses for these processes are international trade, which might be the subject of investigation in a geography or economics class; and international commerce, such as purchasing goods over the internet. Given the growth in trade and the opening up of secure, simple ways to buy goods on the internet, these are relevant topics for students and a straight-forward context for multiplication and division, including discussion of the best method for these calculations.