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.

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Some guy’s comment on Reddit

Being both a Python zealot and an embedded systems zealot, I’ve been looking for an embedded system that I can program in Python. Most of the embedded code I write professionally I write in C. Having learned Python a few years ago, I’m finding C increasingly painful, approximately in proportion to my facility with Python.

Thus far, it seems that the Gumstix Verdex may be the answer I’ve been seeking. The Verdex is an embedded Linux board, about 1 inch by 3 inches, based around Marvell’s (previously, Intel’s) XScale PXA270, common in PDAs and cellphones. It uses around 1 W of power in its quiescent state (not suspended, but not at full processor load either).

I was able to compile a new binary image including the Linux kernel, various utilities, and Python 2.4.2 and upload it to the Verdex using the Gumstix’s console-vx serial interface board. (I seem to have hosed the ethernet interface at the same time, but I’ll worry about that later.)

The ultimate goal (well, for now) was to test on an embedded processor Pysolar, the Python sun-tracking code I’ve been writing. The Verdex I have, the XL6P, runs at 600 MHz. The Pysolar test suite executed in around 1.2 seconds. On my desktop Linux machine, the same test suite executes in 0.012 s. The fact that the times vary by a factor of precisely 100 makes me a little suspicious, but it doesn’t seem impossible that a desktop could beat an embedded computer by 100x.

As of the start of 2007, I am living in Cambridge, Massachusetts, and commuting 16 miles round trip by car at 35 mpg to GreenMountain Engineering in Waltham 250 days/year. That’s about 125 gallons of diesel per year, and I drive an additional 20% for other reasons. That’s around 150 gallons * 155 MJ/gallon = 25000 MJ/year = 25 GJ/year. Increase that by about a third to include the amortization of the energy used to build the car and transport the fuel before sale, according to the Institute for Lifecycle Environmental Assessment (summary of study by Maclean and Lave of Carnegie Mellon, 1988). That’s 33 GJ/year.

Additionally, I live in a house that consumes an average of 100 therms of natural gas and 400 kWh of electricity per month year-round. The total for the house is (100 therms * 105 MJ/therm) + (400 kWh * 3.6 MJ/kWh) = 10500 + 1440 MJ = 11940 MJ/year. I share the house with my girlfriend, so count this as 6 GJ/year. My office is similar in size to our house, but we have 4 employees, so add another 3 GJ/year. The total is now 42 GJ/year.

I eat about 2500 kilocalories of food per day, and that reflects 7500 kilocalories of energy used, once farming and transportation energy costs are included. I probably do slightly better than that buying local produce and eating mostly vegetarian. (The 3:1 ratio is from a 2002 paper by Leo Horrigan, et al., of the Johns Hopkins Bloomberg School of Public Health.) That’s the same as 7500 kilocalories * ~4 kJ/kcal = 30000 kJ = 30 MJ/day, which corresponds to 11 GJ/year. The total is 53 GJ/year. Virtually all of it comes from non-renewable resources (diesel, natural gas, and electricity from mostly coal).

This omits the amortized manufacture and transportation energy for the physical goods I buy–computers, books, furniture, clothes.

For reference, I’ve read of typical consumption rates for North America in the range of 200-300 GJ/year.

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.