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.

So 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.

This video was created in partnership  with Bill Gates, inspired by his new book  

“How to Avoid a Climate Disaster.” You can find  out more about how we can all work together to  

avoid a climate disaster - like how we need  huge development in energy/grid storage in  

addition to renewable energy generation -  you can find out more in the link below.