How did we get from this to this ?
In some ways the answer just boils down to “climate change” - we need way more renewable energy, so it makes sense that lots and lots of engineering and economic resources have gone into improving and enlarging windmills. But while “climate change” can explain why windmills have pushed towards really good design, it doesn’t explain what makes a design good.
I see three main features to explain: the size, the number of blades, and the shape of the blades.
Size is easiest: the bigger the area , the more wind you can use, and therefore the more wind energy you can capture . Plus, the higher up you go, the less the wind itself is impeded by stuff on the ground, the faster it blows, and therefore the more wind energy you can capture . So for a windmill to have access to air with a lot of energy , it should be giant and tall.However, a paradox of windmills is that they need to capture energy from the wind while also letting the wind past. If you extracted 100% of the kinetic energy from the wind, it would stop moving and there’d be nowhere for incoming wind to go.
So you have to let some wind through - calculation shows that a mathematically ideal windmill can only extract 59% of the wind’s kinetic energy .
Since windmills can’t block the wind too much, they’re faced with a tradeoff: either have fast-moving blades that cover a small amount of area, or slow-moving blades that cover a large amount of area. This is because, just as an airplane wing produces more lift the faster the plane is moving, a windmill blade “catches” more of the wind the faster it’s moving - so roughly speaking, a fast-moving windmill, like modern ones, needs correspondingly fewer, thinner blades in order to not slow the wind too much, while a slow-moving windmill can have more, wider blades.Obviously, modern windmills have gone with the narrow, fast approach. So why modern windmills are designed to spin more quickly than old windmills - I mean, if slower were better, there would be no reason modern windmills couldn’t look like giant high-tech sails!The answer comes from Newton’s third law: just as the wind pushes the blades sideways to turn them, so the blades push back on the wind, giving the air a reverse twist, and hence some rotational kinetic energy - which is energy the windmill doesn’t capture. So the most efficient windmill will give the wind the smallest twist possible.And, you guessed it, the faster a windmill blade moves, the less rotational energy it gives to the wind.
This might seem a little counter-intuitive, but a similar thing happens when a ball falls and bounces off an angled block - if the block isn’t moving, conservation of momentum and energy mean that the ball bounces to the left and the block gets pushed right. But if the block starts off moving to the right, it’s able to absorb more of the ball’s energy when it accelerates. The faster the block moves, the more energy it extracts from the ball! (You can see this because the ball moves less each time). Windmill blades are a bit more complicated, but it’s roughly the same idea - for decent efficiency, a windmill blade should be moving through the air at least five times faster than the incoming speed of the wind… though obviously different parts of the windmill blade are moving at different speeds and so the shape varies along the length of the blade.
In summary: an ideal power-generating windmill is big to capture a lot of wind, tall to capture strong winds, fast-moving to be most efficient, and narrow-bladed because a fast-moving windmill (needs to have a smaller blade area - aka, just a few, narrow blades) to not slow down the wind too much.
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