That profile is not very well suited to having a windmill on top of it. The problem is that the nacelle is tilted backwards only a few degrees so you need a very slender tower (or you'll have tower strikes in high winds).

The cooling towers of a nuclear plant follow the same principle. The sides are formed from straight structural members angled in opposite directions (doubly ruled), and the gaps are filled with concrete.

The profile of a hyperbolic wind tower may be altered such that the cross section at maximum height minus blade radius is at a minimum. The largely conical profile of the existing Shukhov towers were used for power transmission lines and a radio broadcast antenna.

Check this out: http://www.pbs.org/wgbh/nova/next/tech/proposed-hyperboloid-...

Interesting! You'd think that the major wind power manufacturers would have looked at all possibilities. One major immediate concern is that these look quite ugly and fat compared to the relatively thin and slender supports that the latest generation of turbines uses. I'd love to see a side-by-side comparison of these towers and the various alternatives.

http://cache1.asset-cache.net/gc/78480146-crowley-ridge-wind...

Is one example of lattice towers in production that I know of (but not like the ones you describe and I have never seen those being used for windmills).

As mentioned in Jobs quote near the top of the article, you often find that people tend to do things in a certain way just because that is what has been done before. No one bothers to experiment because the old way has always been good enough.

This is why is is sometimes difficult to avoid premature optimization, because post-maturity optimization tends not to happen, even when it may be warranted. I know of no wind farm anywhere that is used for side-by-side comparisons of wind turbine technologies. It would very likely have to be owned by a university and supported by public funds.

I have never seen a hyperboloid lattice or diagrid structure in person, but they are not entirely unheard of for shapes that do not require a lot of space efficiency in the tower portion, such as for lighthouses, observation decks, water towers, radio towers, etc.:

https://en.wikipedia.org/wiki/Adziogol_Lighthouse

https://en.wikipedia.org/wiki/Kobe_Port_Tower

https://en.wikipedia.org/wiki/File:Ciechanow_water_tower.jpg

https://en.wikipedia.org/wiki/Corporation_Street_Bridge

https://en.wikipedia.org/wiki/Aspire_Tower

https://en.wikipedia.org/wiki/Canton_Tower

>No one bothers to experiment because the old way has always been good enough.

If you are a manufacturer though, you have all of the incentives to come up with something more efficient though. Wind turbines aren't controlled by a monopoly are they?