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The power generated by a wind turbine is given by:

$$\mathrm{Power} = \frac{1}{2}C\rho AV^3$$

Where:

  • $\rho = \text{Air density}$
  • $C = \text{Coefficient of performance}$
  • $A = \text{Frontal area}$
  • $V = \text{Velocity of the wind}$

In other words, the power is proportional to the square of the length of the blades and the cube of the velocity of the wind. As we know, the velocities of winds are high at high altitudes. So instead of building many smaller wind turbines, why can't we just build a giant wind turbine that is, say, 1000 m tall? That may be an engineering challenge at first, but won't that be more economical in the end? After all, the Burj Khalifa in Dubai has been 828 m tall.

Why can't we build three instead of one pillars to support such a structure? Why can't we build one at the sea?

The Vestas V164 has a rated capacity of 8.0 MW, has an overall height of 220 m (722 ft), a diameter of 164 m (538 ft), is for offshore use, and is the world's largest-capacity wind turbine since its introduction in 2014.

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    $\begingroup$ Cost vs benefit is usually the argument against scaling upward. $\endgroup$ – Paul Feb 23 '16 at 1:41
  • $\begingroup$ But then there is also the argument of innovation vs the resistance to change. I would love to see some mobile (wheel/caterpillar track) >1km-tall wind turbines supported by cross foundation mass-produced at a coast deployed all around the seas! $\endgroup$ – Chong Lip Phang Sep 18 '18 at 9:08
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Not everything scales linearly. In particular, the cross-sectional area of supports required scales faster than height of a structure, all else held constant. This explains why ants have tiny thin legs compared to elephants. An ant linearly scaled up to elephant size would not be able to stand, or would snap its legs trying.

The same thing happens to wind turbines. You get some advantages to making them bigger, as you mention, but you are also ignoring the disadvantages. Not only must the structural support for a large turbine be disproportionately larger than a smaller one, there is also more wind loading, and that loading is higher up. That puts disproportionately more torque on the mounting that has to be countered somehow.

Then there are manufacturing and maintenance issues. Building 500 m blades will be difficult, especially considering they would need to be assembled in the field where it will be more costly and more difficult to do well than in a controlled environment in a factory.

Wind turbines have gotten very large in recent years, for the reasons you mention. Material and manufacturing advances may allows them to get even larger and still make economic sense, but due to the non-linear nature of how various things scale, there will always be some finite sweet spot.

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  • $\begingroup$ The Square-Cube-Law strikes again! $\endgroup$ – Jörg W Mittag Feb 25 '16 at 4:40
  • $\begingroup$ Said the wing of the B-2 bomber is 172 feet and mathematically the best length for efficiency so maybe there is a sweat spot of the bade of a wind turbine. $\endgroup$ – user4139 Apr 17 '18 at 20:30
  • $\begingroup$ @Muze: The best length for efficiency is infinite. The optimum wing length for a particular design depends on many factors. These include efficiency, but also cost, structural capability, maneuverability, performance at various speeds, usable attack angles, etc, etc. $\endgroup$ – Olin Lathrop Apr 18 '18 at 9:54
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The cost of a wind turbine is not proportional to its size - like everything that needs to be manufactured, the cost exponentially increases as manufacturing becomes more complex, beyond what has been done. In terms of real estate on the ground, building a giant wind turbine may be more efficient (maybe not in fact, because stability issues may require the base to be much wider to the point two turbines could have fit), but it is by no means economical. Why build the highest skycraper ever built (if not for the fame) if you have the space for many houses? Not to mention the scary hazard of having a multiton generator plus hundreds of metres of rotating death threatening to kill anyone within a 1.5km radius if things go wrong. I also suspect the shaft will have too high an inertia to spin at a sensible rate when the wind is not constant: the voltage generated is proportional to the shaft speed. Finally, I nearly forgot: will you be the very lucky man climbing the 1km ladder to maintain the generator? Okay this is more of a joke rather than a real issue, since the wind turbine would be so big a lift could be built inside it, but that's one more thing that you do not need in reasonably sized wind turbines.

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  • $\begingroup$ Interesting. I suppose we can use an elevator. :) As to the safety and maintenance, won't you rather be looking after one 1000m wind turbine than hundreds of 100m wind turbines, assuming we go by that formula? $\endgroup$ – Chong Lip Phang Feb 23 '16 at 9:37
  • $\begingroup$ @ChongLipPhang, if you have many 100m turbines, you can do some today and some tomorrow. If you only have one 1000m turbine, you need to climb it all in one day, fix it, and climb back down. Unless you add a "room" half way up where you can sleep, but then you have a whole bunch of other problems (installations such as water and sewage). $\endgroup$ – Wasabi Feb 23 '16 at 10:32
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    $\begingroup$ There is also the effect of down time: if one of 100 wind turbines is out of service, it's no big deal. If it's the only one, then you've got issues. 100 might seem like a big number, but there are just too many things against building only one, in my opinion. But who knows, maybe no one was able to build such a wind turbine in the early days, and now that we can, conservationism wins! $\endgroup$ – Mister Mystère Feb 23 '16 at 10:55
  • $\begingroup$ Another advantage of the "little" 100m turbines is, paradoxically, you need more of them. Which brings you closer to the economic savings of mass production, rather than small quantity bespoke manufacturing. $\endgroup$ – Brian Drummond Sep 30 '16 at 20:15

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