why does wind power increase exponentially, not linearly, with increase of wind speed?
In: Physics
Think of the wind moving a wind turbine as lots of small discrete units of air. Each unit has a quanity if energy which depends on its speed. The faster the wind is, the more energy each unit of air has, and the more energy each unit can give to the wind turbine. Additionally, the faster the wind is, more units will pass through the wind turbine per second. The combination of wind speed increasing the energy of air and increasing how much air passes through the turbine means that wind power increases exponentially with speed.
It’s not exponential, it’s cubic. And you can think of it like this: if you double the wind speed, you get twice as much wind passing a given point. That’s 2x. But remember that kinetic energy is proportional to the square of the speed. So that’s 4x the kinetic energy.
Combine it and you get: a 2x increase in wind speed gives you an *8x* increase in energy, or a cubic relationship.
That hand wavy explanation won’t pass muster in physics class, but it’s good enough for here, I think.
There’s two things at work.
First; kinetic energy increases with the *square* of velocity, and not just velocity itself. That squaring is, by definition, not linear. On top of this, there’s also the fact that the mass of the air also contributes to the kinetic energy, so if the velocity is higher, you get an extra gain in the form of more mass being moved.
Second, and as a general rule in all power production; it gets easier to produce power as the increase in difference between the “hot” side and the “cold” side of your reaction, due to thermodynamic truisms that are at play in the background. This is seen most clearly in engines; in general, the hotter your engine runs, the more efficient it will be. For wind turbines though, the equivalent of your “hot” side is the velocity of the wind, and the “cold” side is the velocity of the wind turbine relative to the wind (in this case, it’s static, so zero).
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