"High-altitude winds between 1,640 and 3,281 feet (500 and 10,000 meters) above the ground are stronger and steadier than surface winds. These winds are abundant, widely available, and carbon-free.
"The physics of wind power makes this resource extremely valuable. “When wind speed doubles, the energy it carries increases eightfold, triple the speed, and you have 27 times the energy,” explained Gong Zeqi "
Edit: I’m wrong, see edit below!
Huh? Kinetic energy increase is square, not cubic.
KE=1/2 m v^2
So every doubling of speed should increase the available kinetic energy by 4 times, not 8. 3 times the speed is 9 times the energy. Granted there are probably some efficiency gains in excess of this at the low end,
but as a rule that’s just wrong.Edit: Cool, I learned something new! I neglected to consider it in terms of power, just thought about kinetic energy.
So something like: KE = 1/2 m v^2
= 1/2 ( rho V) v^2
= 1/2 ( rho A d) (d/t)^2
= 1/2 rho A d^3 1/t^2
Where P = KE/t
Thus:
P = 1/2 rho A (d/t)^3
= 1/2 rho A v^3
Lots of other aspects I’m sure I have wrong, but I see how the cubic came to be.
Its cubic actually
https://thundersaidenergy.com/downloads/wind-power-impacts-of-larger-turbines/
I don’t understand the physics, but every model of power output from wind turbines uses V^3 for the formula
That’s a good link.
During the stampede scene in the Lion King, imagine the wildebeests were stampeding twice as fast. Then Simba’s dad Mufasa would not only have quadruple the amount of energy imparted by each wildebeest, but also be trampled by twice as many wildebeests per second, so the rate of energy imparted on Mufasa per second would be 4 x 2 = 8 times greater when velocity doubles.
Education via childhood trauma
Thanks for the correction! I got way ahead of myself.
thx for the link! just spent the last hr reading about windmills. and although I live in a country full of them I’ve often wondered, but never really paused to ponder about the intricacies that go into windmill design. fascinating stuff!
I work with statistics and joined a wind power forecast project, so I have been reading papers on wind power generation for the past month. There’s other more complex formulas that the one shared on the link, but that was the first I found not pay walled.
It has to do with type of turbine that uses “airfoil principle”. Your formula works for “cup”/Parachute design, but airfoils/upwind sails are “magic”
Increasing the speed increases both the kinetic energy of the wind hitting the turbines and the amount of wind that hits the turbines each second.
I’m out of practice with my physics so apologies if this is a n00b question, but:
I’m unclear what (rho V) is and how you converted to that from mass (m). Further unclear what (rho A d) refers to.
Can you explain / link to an explainer on this?
Rho is density
We don’t directly harvest the kinetic energy. That increase probably has to do with how the wind provides lift to the blades. Of course, you couldn’t keep increasing like that until the harvested energy is greater than the kinetic energy. But I’m sure at any wind speed we only get a tiny fraction.
Kinetic energy is exactly what’s harvested, which is why modern wind turbines are not far off the theoretical limit of the amount of energy that can be extracted. (Betz’s law)
By taking energy from wind, you slow it down. Slow it down too much, and it can’t get out of the way in time for new air.
I could have stated it better. What I meant was that the fraction of kinetic energy that is taken from the wind is so small that the total kinetic energy in the wind is probably not the important factor that changes with wind speed. The dynamics of how the lift depends on wind speed is probably much more important.
It is actually a notable fraction (~60%) and more importantly constant.
Meaning if your wind has 27x more energy, you can also capture 27x more energy.
This is the energy taken from the wind passing through the disk the turbine spins in, so turbines are placed in spaced out rows to let the wind mix with all the air that didn’t pass through a turbine and pick up speed again.
TIL thanks for bringing this up