Students often ask the question “How many windmills would it take to power Marshfield?” So I answer. And then very quickly comes the followup question “Why don’t we do it?”
Today, students tried answer that first question for themselves. Wind is an example of kinetic energy (matter in motion). As such, it can be measured using the kinetic energy formula. However, because the mass of air is not easily measured, we typically use a specialized version of the formula:
Using that formula, we can fairly easily estimate the amount of energy produced by a windmill. And answering the rest of our question becomes rather simple. We just need to know (a) How much electricity does Marshfield need? (b) How big are the windmills? and (c) How fast is the wind blowing? After working through the problem the first time, students were discouraged. It would take 346 wind turbines to power our town? But wait a minute. Don’t we put wind turbines way up in the sky? And isn’t it much, much windier up there?
Students then worked through the problem a second time. But this time, they used a map that showed Marshfield’s average wind speeds at a height of 70 meters (close to the height of a typical windmill). This changed their answer significantly. Windmills generate much more energy at higher wind speeds; every time wind speed doubles, the energy produced increases by a factor of eight! It turns out that the town of Marshfield would only need…
If you’re looking for the answer, you won’t find it here. The answer, my friend, is blowing in the wind.