5 ms·

As wind turbines get bigger, the loads on the blades, and therefore their weight, goes up exponentially. is that true? i would have expected it to be some fix

As wind turbines get bigger, the loads on the blades, and therefore their weight, goes up exponentially. is that true? i would have expected it to be some fixed power, like length^3. exponential means (technically) that it goes as k^length. maybe here it just means "quickly"?

ars 14y ago
I think it is actually exponential. The longer the blade the heavier it is, so the stronger it has to be, which means more material, which makes it heavier, so you need even more material for strength. A feedback loop like that means exponential. The volume goes up as length^3, but the strength has to go up faster than that, since the end of the blade must hold the entire weight plus the weight of the piece next to it, which also got heavier as it got longer.
- andrewcooke 14y ago
  good point; you could well be right. thanks.
- eric-hu 14y ago
  What other feedback loops like that have exponential growth?
  - dwiel 14y ago
    Amount of fuel in a rocket necessary to send a mass X into orbit? I dont know the math, but i've heard the exact same feedback explination used.
    - eric-hu 14y ago
      My mind went there too. I didn't mention that one because it doesn't seem to be exponential. I actually found a past entry on the xkcd what-if blog: http://what-if.xkcd.com/7/ http://what-if.xkcd.com/7/ For a given amount of ship mass, you need 20x that mass in fuel to get it into space. That seems to be multiplicative growth, unless I'm interpreting something wrong.
- sopooneo 14y ago
  I expect you're right, but I've found the popular press to use "exponential" to mean any upward curve.
- ScottBurson 14y ago
  Balderdash. It can't possibly be exponential. Exponential would mean that for every meter of length you added, the weight would be multiplied by a constant factor. I would expect it to be roughly cubic, as you suggest. I don't know if it's exactly cubic. Even if it's a little worse than cubic, there is a vast difference between any power law and an exponential. I have, of course, observed the tendency, which seems to have increased in recent years, for science journalists to characterize any superlinear progression as exponential, but as an MIT alum I am quite unhappy to see this repeated in Technology Review.

ars 14y ago

I think it is actually exponential. The longer the blade the heavier it is, so the stronger it has to be, which means more material, which makes it heavier, so you need even more material for strength. A feedback loop like that means exponential. The volume goes up as length^3, but the strength has to go up faster than that, since the end of the blade must hold the entire weight plus the weight of the piece next to it, which also got heavier as it got longer.

andrewcooke 14y ago
good point; you could well be right. thanks.
eric-hu 14y ago
What other feedback loops like that have exponential growth?
- dwiel 14y ago
  Amount of fuel in a rocket necessary to send a mass X into orbit? I dont know the math, but i've heard the exact same feedback explination used.
  - eric-hu 14y ago
    My mind went there too. I didn't mention that one because it doesn't seem to be exponential. I actually found a past entry on the xkcd what-if blog: http://what-if.xkcd.com/7/ http://what-if.xkcd.com/7/ For a given amount of ship mass, you need 20x that mass in fuel to get it into space. That seems to be multiplicative growth, unless I'm interpreting something wrong.
sopooneo 14y ago
I expect you're right, but I've found the popular press to use "exponential" to mean any upward curve.
ScottBurson 14y ago
Balderdash. It can't possibly be exponential. Exponential would mean that for every meter of length you added, the weight would be multiplied by a constant factor. I would expect it to be roughly cubic, as you suggest. I don't know if it's exactly cubic. Even if it's a little worse than cubic, there is a vast difference between any power law and an exponential. I have, of course, observed the tendency, which seems to have increased in recent years, for science journalists to characterize any superlinear progression as exponential, but as an MIT alum I am quite unhappy to see this repeated in Technology Review.