One Resource a (Week)Day #16: Math in Wind Turbines

I got off on a tangent today looking at ways to build a simple electric generator and an electric motor (both operate on the same concepts, but one converts mechanical energy to electrical energy, and the other does the opposite). I think it would be awesome to do some RPM math associated with motors after building them in class, but the electric motor math turns out to be pretty physics-heavy. (I could see us building a simple DC motor with a variable resistor attached to it to allow adjustment of the rotational speed of the resulting electromagnet, but the math from there is just basic formula manipulations.) So, I dug around a bit and found, instead, some accessible mathematics related to wind turbines.

If you think about it, wind turbines tie nicely to simple geometry. This website from the Minnesota Municipal Power Agency has a nice set of fairly basic math activities related to wind turbine analysis. In particular, I was intrigued to learn that it's not always the more turbine rotational speed, the merrier! In fact, the ratio between the "tip blade speed" (how fast the tip travels) and the actual linear wind speed needs to maintain a healthy ratio (which differs based on the number of blades in the turbine design), in order for the drag to be minimized and the maximal amount of wind to be propelling the turbine. So, modern turbines have the ability to control their orientation and pitch in order to tweak the tip speed within a range of wind conditions. (Pictures below taken from the modern turbines link above, entitled "Wind Turbine Control Methods.")

Neat, eh? (A far more thorough explanation of the wind turbine power calculation is available here, but that's firmly in the realm of mechanical engineering, I think, and not appropriate for secondary students.)