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!)

I am periodically accosted at parties when someone mentions to a friend that I work on renewable energy.

“You there, always talking about renewable energy and solar cells and all that! Why haven’t you solved this greenhouse problem yet?”

The problem is one of scale. To explain what I mean, I have to talk about a sculpture.

Arthur Ganson has a sculpture at the MIT museum consisting of a 12-stage geartrain, where each stage reduces the speed of rotation by a factor of 50. The left end is spinning furiously at around 200 rpm; the right end is embedded in a concrete block. The end in the concrete makes one revolution every 2 trillion years or so.

(You can see a video of the sculpture at the 8:30 mark in this video from the 2004 TED conference, but finish reading this first.)

I can see that the gear at the left end of the sculpture is spinning. After three or four 50:1 reductions, I can only see the gears moving if I watch for a while. When I think about gear reductions in the abstract, I think, “Sure, if you reduced the speed enough, it wouldn’t break the concrete,” but when I look at the real thing, it’s baffling. I stand there looking at the sculpture, knowing that I should expect to see what I’m seeing, but my weak human mind can’t adjust its expectations.

In the same way that when I look at Ganson’s sculpture, I can’t understand what I’m seeing, it’s hard for us to grasp on a visceral level the difference between the 1000 watts Americans use in their homes, the 1,000,000,000 watts we generate in a large power plant, and the 15,000,000,000,000 watts that we use globally.

We hear news of advances in renewable energy. The amount of installed wind power has been growing at around 30% for the last two years. Investment in renewable energy startups is through the roof in the last 2 or 3 years. The news we hear of huge investments, the technological breakthroughs, and Prius drivers loading up with compact fluorescent bulbs at Costco are the first gear spinning wildly (well, maybe not the people loading up the bulbs– they’re just excitable).

Yet on the global scale, the vast majority of our energy comes from fossil fuels. Even after 30 years of work on photovoltaics, the global installed capacity is around 8 GW, or roughly 1/2000th of the energy we use globally. Windpower is about ten times larger, but still only approaching 1% of global energy usage. (I’m ignoring the differences between installed capacity and actual production here, but that correction just makes the fraction of renewables even more slight.)

What’s more, the concrete block end of the spectrum is not reported in the news (rightly so, as it’s not interesting). The massive juggernaut of fossil fuel infrastructure continues to expand. Installation of large natural gas turbines is proceeding in China at more than 1 GW per week, which is enough to match the entire history of photovoltaics installed worldwide in 2 months.

What’s the result? We think we see progress–the gear spinning wildly–but if a global switch to renewables actually happens, it will take a lot longer than our scale-limited minds expect.

In a comment to my last post, Ben Harris suggests that I read Cape Wind by Williams and Whitcomb. I haven’t read the book yet, but I did read up on Cape Wind.

The outcry against Cape Wind is a travesty. It comes down to an unpleasant choice of how we get the energy we need. We have to satisfy our rising energy needs somehow. If you’re opposed to using local energy sources to fulfill our energy needs, you have to be in favor of either reduction of our energy needs (which have been strictly increasing for all of recorded history) or getting the energy from somewhere else.

The first choice, reducing energy consumption, requires either widespread, voluntary efficiency gains among the populace, forced efficiency gains via government intervention, or the arrival of the hard times. I think it would be imprudent to plan on any of those events occurring. Our understanding of efficiency improvements falls vastly short of what we need. Even the NPR-listening Prius drivers among us are making decisions around the level of 20% improvements by 10% of the population, while the population continues to increase. We’re excited about skyscrapers with green roofs, which collect water for irrigation of the plants in the lobby, and building-integrated solar, which can supply maybe 1% of the heating and cooling requirements of the building. We’re not thinking about changes on the level of, “You don’t get to heat your house in the winter any more.”

Forced efficiency gains via government intervention seems equally unlikely to me. The current US administration argues about whether we should mandate minor increases in fuel efficiency, while allowing exemptions for vehicles over 6000 pounds. The most recent increase was from 21.6 mpg to 24 mpg, and it doesn’t take effect until 2011. 10% decrease mandated in 4 years, while our vehicle usage continues to increase? This will not solve the problem.

The arrival of the hard times may well solve the problem, but I would strongly prefer to avoid having to affiliate myself with a local warlord in order to get bread, watery gruel, and a burlap sack to keep me warm in the winter. I don’t think that constraining energy usage by simply failing to build more power plants, be they clean or dirty, is likely to be an optimal solution.

If we won’t reduce our energy consumption, we need to get more energy somewhere. There’s a temptation to think that we don’t need to get energy locally, but everywhere is local to someone. If we had an uninhabited Oil Planet, we would need only design a sturdy pipeline to connect the two planets (akin to the Moon Bomb). The location of the Oil Planet is currently unknown, and nobody wants a coal plant in their backyard any more than I do. At some level, we need to collect energy locally.

It’s reasonable to debate the resolution of “local.” Do I need to get all my energy from my state? My town? My house? My desk?

Right now, eastern Massachusetts imports the vast majority of its energy. In Boston, the major electricity source is the Mystic Generating Station in Everett (you know, the pixelated section on Google maps, just north of the river). According to the Energy Information Administration, the 2600 MW Everett plant currently runs off of natural gas from the Gulf Coast, Canada, and the Appalachian Basin. Additional natural gas in liquid form is brought from foreign sources to the LNG terminal in Everett. According to the EIA, we also burn coal from West Virginia and Colorado. Coal is burned in the Brayton Point plant in Somerset, Massachusetts.

The limited availability of fossil fuels, the pollutants released by their combustion, and my assumption that if I don’t want my tap water tainted with mercury runoff from strip-mining coal, the residents of West Virginia probably don’t either, lead me to believe that we need to look for local alternatives for energy.If you’re going to satisfy your energy needs locally, what’s the best choice?

In Massachusetts, we get about 40% of our electricity from natural gas, 50% from coal and petroleum-fired power plants, and 5% from nuclear power. The remaining 5% is from hydro, solar, and wind. Nationally, the percentages are similar, but more hydro and nuclear, less natural gas.

The non-renewable options aren’t pleasant. We don’t have coal, oil or gas– you have to go at least as far as western Pennsylvania to find it. Robert Milici of the USGS says of the areas east and north of the Appalachians that, “these provinces do not produce oil or gas and are not currently viewed as prospective for oil and gas.” The USGS only studies 5 major coal beds; nobody is digging up coal in Massachusetts.

Nuclear power is waning in New England. Since the 1991 shutdown of the 540 MW Rowe nuclear plant in western Massachusetts, there is only one nuclear power plant in the state (Pilgrim, nominally 690 MW, in Plymouth), and one just over the state line in Seabrook, New Hampshire. The Seabrook plant is larger, nominally 1150 MW. Another New England nuclear plant, the 900 MW Maine Yankee plant in Wiscasset, was shut down in 1997 due to lack of economic viability. The spent fuel rods are still there under armed guard, as they will likely remain until at least 2017. There are two plants, totaling around 2000 MW, operating in Connecticut and one 650 MW plant in southwestern Vermont. There are currently no new nuclear plants planned [PDF] for New England.

There’s not much opportunity for large hydropower in Massachusetts– we’re a mostly flat state, especially toward the eastern end. The Idaho National Laboratory puts its total estimate of hydropower potential in Massachusetts at 132 MW, which is about a third the size of Cape Wind. Furthermore, the estimate include sites like Moody Street in Waltham, that face worse public acceptance problems than Cape Wind.

That leaves solar and wind. Solar power is great, but New England is not particularly sunny, compared to, say, Arizona or New Mexico. Cape Wind is proposing a wind farm that peaks at 420 MW. According to the Prometheus Institute in Cambridge, total US installations of solar this year are around 120 MW, with the bulk of them in California and New Jersey. (Sorry, Keith, for using peak numbers– I know you find it galling. Post better comparisons in the comments or, better yet, start your own blog.) The point is that on the scale of renewable energy projects, the Cape Wind installation would be massive. (On the scale of coal fired power plants, which currently top out around 1500 MW, it would not be that big.)

In eastern Massachusetts, wind power is a good choice. From a power density perspective, the site chosen by Cape Wind is in a zone characterized as “excellent” by the Massachusetts Technology Collaborative (MTC, hereafter) and verified by the National Renewable Energy Lab. (Disclosure: the company for which I work has recently worked on a technology assessment for the MTC, and we may do more for them. However, I have not been personally involved in any of the work, it hasn’t involved wind, and I didn’t know that MTC had done this study until a few minutes ago.)

While I do agree with Robert Kennedy, Jr.’s assertion in the New York Times that the project ought not to be enabled by government subsidies of $241 million dollars, his characterization of Nantucket Sound as a pristine region is ridiculous. I’ve been there; what I recall was a bunch of champions from the Buzzards Bay Power Squadron running two-stroke engines at full throttle. Maybe if I had a compound in Hyannis like that of Mr. Kennedy, I would feel differently, but I’m in the same boat as the roughly 6.4 million non-Kennedy residents of Massachusetts.

Currently, opposing wind power in eastern Massachusetts is extremely likely to result in the construction of new fossil fuel power plants like the plant in Everett. The cost of wind power incurred on the neighborhood is different from the cost incurred by a coal plant. If your kid breathes enough crap out of a smokestack for long enough, your kid will die. I won’t say that the visual damage done by wind turbines is nothing, but if forced to make the choice, as we are, I think choosing your view at the price of the lungs of some kid growing up across the street from the Brayton Point plant in Somerset is unconscionable.

The state approved the Cape Wind project in March of 2007, though the project is in federal waters, so state review is less significant than federal review. The Boston Globe predicts federal review to be complete in mid-2008. I would be proud to live in the state that supported the first offshore wind farm in the nation.

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.