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• 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  whileclimate changecan 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 sizethe 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 goSo 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 bladecatchesmore  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, whileslow-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 windgiving the air a reverse twist,

• and hence some rotational kinetic energywhich 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-intuitivebut 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 windthough 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 generationyou can find out more in the link below.

How did we get from this to this ?

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B1 windmill wind energy moving blade capture

# The Physics of Windmill Design

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Summer posted on 2021/03/02
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