Placeholder Image

Subtitles section Play video

  • The paradox of windmills is this: extract kinetic  energy from the wind while still letting the  

  • wind past. Unlike a dam, where you extract the  potential energy from the height of the water  

  • and so you can lower the water as much as you  want without slowing the flow, with a windmill,  

  • you extract kinetic energy from the *motion* of  the wind, which causes the wind to slow down.

  • So how much wind should a windmill mill?

  • Well, the maximum possible amount  of energy you can extract from the  

  • wind is simply the difference between  its initial and final kinetic energy.  

  • Kinetic energy depends on speed squaredso if the outgoing wind speed is, say,  

  • half of the incoming speed, then the final wind  energy will be a quarter of the initial energy,  

  • meaning that three quarters of the energy of the  wind was extracted when it passed the windmill.

  • But then there's the question of how much  of the wind you can actually extract energy  

  • from. It turns out that the speed of the  wind at a windmill is halfway between the  

  • incoming and outgoing wind speeds. So forfinal wind speed of half the incoming speed,  

  • the speed at the windmill will be  three fourths the incoming speed,  

  • which means only three fourths as much wind  can actually pass the windmill every second.

  • Combining these two facts means thatwindmill that slows the wind to half its  

  • initial speed allows three fourths as much  wind to pass and extracts three fourths of  

  • the energy from that wind, for a total efficiency  of three fourths times three fourths, or 56.25%.

  • Doing the same math for other  possible wind speed reductions,  

  • you find that the most efficient windmill possible  slows the wind to a third of its incoming speed.  

  • Reducing to 1/3 speed achieves a kinetic energy  "efficiency" of v^2-(v/3)^2 equals 88.88% of  

  • the energy of wind passing the windmill  is extracted. And reducing the wind to  

  • 1/3 speed after the windmill means the wind  passing the windmill is going at 2/3 speed,  

  • so 2/3 as much wind passes through the  windmill. And 88.88% energy extraction  

  • from 2/3 of the wind results in an overall  efficiency of 88.88*2/3 = 59.259 percent.

  • A windmill that slows the wind down  below 1/3 speed will get a higher  

  • percentage of the energy but from even less wind,  

  • for a lower overall efficiency. And a windmill  that slows the wind down less will get a lower  

  • percentage of the energy from somewhat more  wind, again for a lower overall efficiency.

  • So how much wind should a windmill mill? 2/3 of  it, for 59% efficiency in extracting the energy.

  • Obviously, real world windmills are  far more complicated and have way  

  • more engineering considerations, so  the 59% number may not apply exactly.

  • Ok, Henry here, I've put a bonus video  on Nebula that covers some details I had  

  • to leave out of the main video. Nebula is the  Streamy-award-nominated independent streaming  

  • service that's the co-sponsor of this videobuilt by and for a collection of educational video  

  • creators including Real Engineering, Mike BoydUp and Atom, Jordan Harrod - and me. And Nebula  

  • has partnered with CuriosityStream, which offers  thousands of documentaries and nonfiction titles,  

  • to give you access to both platforms in one go...  for just a few dollars a month! I really enjoyed  

  • watching the European Inventor Award episode about  Henrik Stiesdal, who has been intimately involved  

  • in the invention and development of modern wind  turbines, building the first offshore wind farm,  

  • and more. Sign up for CuriosityStream using the  link in the description and you'll also get access  

  • to Nebula, including the bonus video that goes  with this one, as well as an ad-free viewing  

  • experience across the site. And you'll also get  26% off an annual subscription to CuriosityStream.

The paradox of windmills is this: extract kinetic  energy from the wind while still letting the  

Subtitles and vocabulary

Operation of videos Adjust the video here to display the subtitles

B1 wind windmill speed energy kinetic energy kinetic

How Much Wind Should A Windmill Mill?

  • 4 1
    Summer posted on 2021/04/01
Video vocabulary