Math Riff: Hurricane Ike versus T. Boone Pickens… Fight!

Part of the fun with math is just playing with numbers, but the numbers have to actually mean something to make it interesting. I call these "Math Riffs" as in many respects they're just stream-of-consciousness runs of calculations, and while thought provoking, meant mostly for entertainment value. They're the kind of things that I hope provoke a "Wow!" response from my kids, but sometimes I'm sure they're thinking "Oh no... My Dad's a geek!" or something similar. Oh well. There’s a lot of numbers in my professional field, but they’re nothing like playing with big scary government sized numbers… the National Debt, the Federal Budget, the Gross Domestic Product, the Annual Energy Consumption… What? Last one didn’t ring a bell? Okay, fine… Let’s play! According to the Annual Energy Outlook, the United States used approximately 73 quadrillion BTU’s worth of energy in 2006. British Thermal Units aren’t exactly a familiar measurement, but if you know one BTU is 0.29307 watt hours, we can convert this to roughly 21 quadrillion watt hours. That’s the same as 21 petawatt/hours of electricity. Your electric bill is probably measured in kilowatt hours of energy, so still in rough terms, that’d be 21,000,000,000,000 kilowatt hours. Regardless of what electricity rates are like in your neighborhood, that’s not a bill I want to get. Those are all still mind numbing numbers, so the interesting part is putting it all into some context. If the whole country ran on electricity, how could you generate that much power? Texas oil magnate T. Boone Pickens is getting a lot of poking in the news over his advocacy of wind power (which is actually only one component of his energy plan), but it turns out we’ve got one Texas-sized wind generator in the news this week… Hurricane Ike. In the spirit of turning lemons into lemonade, let’s see what Mr. Pickens would do if he could really harness a bit of Mother Nature in his home state. Hurricane Ike made landfall as a category 2 storm near Galveston, Texas in the early hours of September 13th. Ike was a fairly wide storm and was over 400 miles across when it made landfall. With a radius of 200 miles, that means Ike had a total area of about 125,000 square miles. That’s a lot of potential wind generation capacity. Of course, Ike shrank as it came ashore, but let’s just assume we could tap a small chunk of that wind as it passed over Texas. If we cleverly planned ahead and covered 200 square miles with wind turbines, that would give us 200 x 5280 x 5280 = 5,575,680,000 square feet of space to work with. If we space our wind turbines on 200 foot centers (40,000 square feet per turbine… A wild guess on my part here), that gives us a wind farm with 139,392 turbines. And enough construction work to make the TVA projects look like building a Starbucks, but still, it’s Texas and everything’s bigger in Texas. Hurricane force winds start out at 74 MPH, and Ike made landfall with wind speed near its eye of over 110 MPH. If we figure average wind speed across the 400 mile diameter of the storm was in the mid-point, 90 miles per hour is a good estimate of the average wind speed over our wind farm. Current wind turbines are tuned to generate about 2 megawatts of electricity in a 15 mile per hour wind, but we’re not dealing with just any wind here. Wind energy increases with the cube of the wind speed, so if you double the wind speed there’s eight times as much energy present. If we can generate 2 MW in a 15 MPH wind, we can (in theory) generate 16MW in a 30 MPH wind, and 128MW in a 60MPH wind, and 1,024MW in a 120MPH wind. Our average wind speed at 90MPH is between the last two figures, so we’ll estimate 500MW of capacity for each of our new custom-designed, hurricane-proof wind turbines. Our wind farm has 139,392 turbines each capable of producing 500MW of electricity in a 90MPH wind. That means our generating capacity in Ike’s wind flow is roughly 69,696,000 megawatts (or, roughly 69,696 gigawatts, or 69 petawatts). That’s per hour… To get back to our actual generation capacity, we need to figure time into the equation. In one hour in the hurricane our hypothetical wind farm generates 69 petawatt hours of power. Now that we’re the electric company selling that power using turbines probably bought with enormous federal subsidies, I’m happy about those numbers! Take that, Hugo Chavez! Pfffpt! Just how much power is that? Well, 69 is more than three times larger than 21. That means we could generate three years of power at 2006 consumption rates in the span of one hour. Or, we could make our energy farm 3 times smaller (66 square miles with 46,464 turbines) and create all the energy we needed for year. We’ll leaving storing that energy with those battery experts somewhere. Along with figuring out how to make wind turbines that run in 100 MPH wind. Or building tens of thousands of them. Still, it’s fun to fantasize a bit, isn’t it? Regardless of how you look at it, the power present in a single hour’s worth of a single hurricane is amazing, especially when you realize we’re only considering a tiny fraction of surface winds. Or, you might conclude that our national energy usage is incredibly tiny compared to what’s going on in the environment around us. Either way, you’ve got to admit, weather is amazingly powerful… Wind power still needs a lot of development, but maybe we should stop picking so much on Mr. Pickens. Good luck and prayers to everyone in Texas! ReferencesAnnualEnergyOutlook.comWikipedia Watt Hour Reference