A gentleman by the name of David Fisher has been getting some attention (examples: WSJ, New Yorker, Inhabitat) by describing his design for a new building in Dubai. It would be best for the world if bad ideas like these were ignored and forgotten, but without some knowledge of engineering, it’s not obvious that his ideas are bad.

Fisher’s tower is like a shish-kebab on a vertical skewer, where the skewer is an elevator shaft and the food are the apartments. Each apartment can rotate around the elevator shaft. This alone is perhaps impractical, or ugly, or dumb, but not impossible. If you could find a wealthy fool who wanted to build this, you could probably pull it off.

Where Fisher crosses the line into territory that I defend is with his claims about renewable energy. He says that there will be a wind turbine between each apartment, and solar panels on the roof of each apartment. According to his website, the building will “generate electricity for itself as well as other nearby buildings, making it the first skyscraper designed to be self powered.” As Walter says in The Big Lebowski, “OVER THE LINE!”

Before we even look at the available energy closely, we can be certain that it won’t work. One of the central problems of renewable energy is its low power density. According to the ever trusty Vaclav Smil, wind and solar typically yield 1-10 W/m^2; skyscrapers require in excess of 1000 W/m^2, (Energy in Nature and Society, pp. 311, 317). But perhaps Mr. Smil is wrong. Let’s take a closer look.

Judging by the drawings of Fisher’s tower (since removed), it would be about 300 x 50 m. Ignoring the narrowing of the tower as it rises, roughly 20% of the area is devoted to wind turbines. That’s around 15000 x 0.2 = 3000 m^2. (Fisher has described two versions of the tower, one at ~300 m with 60 floors, another at 420 m with 80 floors. Here, I analyze the shorter of the two.)

Fisher claims that the average wind speed in Dubai is 16 km/h, or 4.4 m/s.

Assuming a Rayleigh distribution for the wind speed, the average power available as kinetic energy in the wind is (6/pi) * 0.5 * (density of air) * area * (average velocity)^3.

The density of air is 1.2 kg/m^3.

That’s (6/3.14) * 0.5 * 1.2 * 3000 * (4.4^3) = 290 kW. If the wind turbines were 30% efficient, which would be pretty good for a vertical axis turbine stuck in a building, the yield would be 100 kW.

This ignores the narrowing of the building, the lack of wind near the ground, and obstruction from other buildings.

The building has around 50 m * 50 m * 60 floors = 150000 m^2 of floor space, so the areal power density is about 0.67 W/m^2. Say a room is 5 m in a side, so it has area of 25 m^2. That gives you 17 W per room.

But let’s not leave out the solar power! Fisher claims that 20% of each roof will be exposed to sunlight. On average, then, if photovoltaics yield around 1 W/m^2, we should expect a power density based on floor area of 0.2 W/m^2, which is another 5 W per room, 22 W total. That might be enough to light a single compact fluorescent light bulb in each room.

Oh, and the average temperature in Dubai is 27 C. I guess they can run the air conditioning when all the lights are off.

I should end by saying that I share Mr. Fisher’s enthusiasm for renewable energy. My concern is that his tower of epic fail gives the work that I spend all day on a bad name. We should be building wind turbines and installing solar panels as fast as we can, but we should do it in ways that optimize their performance. Put the solar panels where they will never be shaded by the floor above them, and put the wind turbines on ridgelines where the wind is strongest. Integrating turbines and panels into buildings with the expectation that they will produce energy to spare is moronic.

(And all you energy reporters should be ashamed of yourselves for repeating Fisher’s void claims without any skepticism. That means you, Paul Goldberger and Evelyn Lee!)

After a New York Times article this morning, Ben and I were hashing over the potential for successful tidal turbines (well, he was ranting; I was hashing).

Ben pointed out quite astutely that the requirements for a tidal turbine are actually surprisingly similar to a requirements for a wind turbine. The power density of both situations are similar. Wind velocity at a prime turbine location is in the low 10’s of mph, while tides are in the low single digits of mph. However, the power density scales with the cube of the velocity, to wind gains a factor of 1000 over water. This is roughly canceled by the ~800x difference in density between water and air.

Additionally, the Reynolds numbers for both situations are similar . The Reynolds number is Re = density * velocity * characteristic length / viscosity. Water is about 100 times more viscous than air, but that gets canceled by water’s ~800x higher density and 10x lower velocity.

This means that you want roughly the same blade geometry and tip speed ratio for a wind turbine as for a tidal turbine. The problem is that to get the same tip speed ratio in a medium that’s moving 10x slower, you have to reduce the angular velocity by a factor of 10 as well.

The folks at Verdant, featured in the New York Times article, have figured this out; they say that their turbines peak at 32 rpm. According to an interview with one of Verdant’s engineers, the turbines are about 5 m in diameter.

In the wind turbine world, Paul Gipe cites a 7 m wind turbine as having a peak speed of 310 rpm in his 2003 book Wind Power (p. 102), and Southwest Windpower’s new Skystream turbine, with a diameter of 3.7 m, nominally peaks at 325 rpm. So, Verdant has the right tip speed ratio– what’s the problem?

The problem is that the power density is the same, the size is the same, the angular velocity is 10x lower, and wind turbine blades are already made of composite materials to withstand high torques. Power is torque * angular velocity, so for a constant power, if the angular velocity drops by X, the torque goes up by X. It’s no wonder that Verdant’s turbines are getting ripped apart. Their plan now is to use cast aluminum, which has a yield strength around 150 MPa; composite materials are an order of magnitude higher (and remember, they need to beat wind turbines by 10x, not just match them).

The New York Times quotes the founder of Verdant: “‘The only way for us to learn is to get the turbines into the water and start breaking them,” said Trey Taylor, the habitually optimistic founder of Verdant Power.”

Just to be clear, while I do work in the renewable energy field, I’m not a friend or enemy of Verdant; I had not heard of them before today. I don’t have any investments in Verdant or any of their competitors.

Related links:
Some guy’s comment on Reddit

I’ve been arguing with my associate Ben about the relative costs of wind turbines. (We work at a GreenMountain, a renewable energy engineering firm near Boston, so this is what we do for fun.) We’re both puzzled over the continued growth in the size of wind turbines.

Aldo da Rosa writes in Fundamentals of Renewable Energy Processes, Elsevier Academic Press, 2005 (pp. 599-600):

“For a given wind regimen, the amount of energy that can be abstracted from the wind is proportional to the swept area of the turbine. . . . The mass of the plant (in a first-order scaling) varies with the cube of the diameter. . . . Hence for the same amount of energy produced, the total equipment mass varies inversely with the diameter. Since costs tend to grow with mass, many small turbines ought to be more economical than one large one.”

This is exactly the argument that Ben came up with last week. The flaw, as best as I can tell, appears to be that cost does not actually track mass. Historically, it appears that costs are dropping as mass increases.

(Chart removed because javascript was screwing up other scripts. It was just a falling line–just imagine looking at the right side of a silhouette of a mountain.)

The data above comes from Gil Masters’ Renewable and Efficient Electric Power Systems, Wiley-Interscience, 2004 p. 372, with the 1981 data point added from an American Wind Energy Association paper, “The Economics of Wind Energy.” Masters states that, “taller towers increase energy faster than costs increase,” (p. 372), but he does not directly address mass scaling relative to area scaling. Masters also cites data from the Canadian Ministry of Natural Resources that estimates the annual operating and maintenance costs (~$2m) of a 60 MW windfarm at 3% of the capital costs (~$60m).

Let me add here (because I can hear fellow wind energy enthusiast Keith gnashing his teeth over TCP/IP) that if I had the data, I would prefer to see wind turbine values expressed as $/(kWh/year), rather than $/kW, where the kW rating calculated can be achieved at some high windspeed found only in Stillwater, Minnesota.