The silliness of the "Discovery Project Earth" series

I watched "Infinite Winds" on Planet Green. This is one of a series of programs in the "Project Earth" series purporting to use technology to save the Earth. Some of them are related to energy generation, others to geoengineering. They have a team, consisting of an entrepreneur, an engineer, and a scientist to assist people with ideas. This episode features the idea of helium filled airships equipped with turbine blades and generators to capture winds above the level of interference from trees and buildings and transmit it to the ground.



The link above will take you to the so-called "lab book" for the episode. It's divided into three preliminary tests and a "Final Test." The first preliminary test is apparently meant to determine the winds at altitude. In order to determine this, Dr. Basil Singer, a "quantum physicist," uses a powered parachute and a gps system to check winds at various altitudes (though, as a pilot, I must say that I was not clear on how their system measured airspeed, a necessity when using gps ground speed to determine wind speed and direction). Unless a series of tests over a period of time is taken, this is worthless. There's ample data and well-established theory available regarding the general variation of wind with increasing elevation. Such a one-time flight is completely useless with respect to the gathering of useful data.



The next preliminary test was of the cable to connect the airship to the ground and conduct electrical energy. Dr. Jennifer L. Languell, "the Engineer," concocted a scheme to use a crane and a series of cars, lifting them with the cable. They needed to lift five cars and keep the headlights on. Now, as it happens, I'm a partner in a firm that has (get ready) test equipment for exactly this sort of thing. We can perform tensile testing ranging to 600,000 pounds force. I estimate that we could have tested five samples (when gathering data, more than one sample is nice) and given actual numerical results for the maximum tensile load, complete with load vs. displacement data while continuously monitoring electrical continuity for, oh, say... $2,500.



Wind data gathered during Dr. Singer's flight were used in a wind tunnel to model the performance of the proposed airship and turbine. Modifications were made to the prototype model to eliminate uncontrollable spinning. No detail was given with respect to how scaling laws were implemented during this testing so I'll give them the benefit of the doubt and assume the appropriate dimensionless variables were utilized.



Finally, the team went to the field (where, exactly, is a subject of dispute) with a 21 meter prototype. The first effort was a failure, mainly because the generators (mounted at each end) deformed the airship to such an extent that it failed to rotate. Two weeks later, the team reconvened, having changed the configuration of the turbine blades and added internal bracing. The airship turbine was able to finally deliver about 200 watts and was deemed a success, with hugs all around.



Now, the prototype flown is on the order of .059 times the "flat plate area" of the proposed product, so we can expect that airship to intercept about 17 times the wind of the prototype. Let's assume that the wind is, on average, 3 times as fast at the proposed height at which the airship will be flown. This yields 3^3 or 27 times the available power. Let's also generously assume they are able to triple the efficiency of the system. Then we can expect 200*17*27*3=276,000 watts or about 280 kilowatts. We read here that a megawatt is anticipated (though the show itself states that it will be 1.5 megawatts).



It should be noted that the forces on the tether will scale with the wind-facing area of the airship and the square of wind speed. The airship, in turn, must lift this cable, though the helium volume and hence the buoyant lift scales with the cube of length. And, of course, the tether itself will be subject to wind loads. I haven't run any numbers because I have insufficient data but this may be problematic. Be that as it may, Fred Ferguson, the Canadian airship engineer responsible for the concept, envisions nine million full-sized airships providing for the the majority of the Earth's electrical requirments.



To Discovery Network's credit, they include a page listing some objections to the idea that such turbine airships will replace fossil fuels. However, the show itself reminded me very much of a high school science fair project, but with more money. It's a shame that the public is given the impression that this actually constitutes science. The problems facing us with respect to energy sources and climate change are too serious for this sort of cavalier approach. I won't waste my readers' time with the other episodes in the "Project Earth" series, suffice it to say that they are no better. My advice? Stick with Bill Nye the Science Guy.

More on adoption of electric cars

In my previous post on going electric I looked at the total generating capacity in the United States as compared to average usage and the electrical requirements of replacing the U.S. personal transportation fleet with electric vehicles. Of course, this is the most cursory look possible. Among other things, as Geoffrey Styles of the blog "Energy Outlook" pointed out, efficient management of the grid via utilization of available capacity at times of low baseline consumption would be required and might even be sufficient.



It's also clear that it wouldn't be the case that on, say December 31, 2011 there would be almost no electric cars on the road (as today) and on January 1, 2012 all personal vehicles would be electric. Mathematicians have developed several methods that purport to model the adoption and spread of technology. Among these are the logistic function and the Gompertz function. So what might the adoption and market penetration of electric vehicles look like, and how quickly, if at all, would generating capacity need to be added?



In reply to President Obama's call for one million plug in hybrids and electric vehicles, Nissan CEO Carlos Ghosn has stated that this number could be easily surpassed.



Based on a paper concluding that the logistic function best represented the adoption of cellular phones in Taiwan, I'm going look at the logistic function and adjust the coefficients so that the ultimate adoption is 235,000,000 vehicles and 2,000,000 are on the road in 2015. I'll estimate an annual growth rate of 20%. The resulting logistic equation is N = ((235x10^6) 2000000)/(2000000+233000000 e^(-0.2 t)) where N is the total number of electric vehicles and t is the time in years. Using Wolfram Alpha (if you click this link, the equation will already be input, you can change the parameters at will) the plot looks like this:







Given that it's said that readership in a blog is reduced by half for every equation posted I'm reluctant to say it but, using calculus, we can determine the rate of change of the population of electric vehicles (that is, how many electric vehicles will be added each year) and determine, at any given time, approximately how much additional demand on the grid will accrue. If we differentiate the equation above (this is kind of backwards in that the logistic equation stems from a differential equation representing the rate of change) we get: d/dt(((235x10^6) 2000000)/(2000000+233000000 e^(-0.2 t))) = (2.1902*^22 e^(-0.2 t))/(233000000 e^(-0.2 t)+2000000)^2. The plot looks like:







At the risk of completely alienating every reader, we can find the maximum rate of addition by taking the second derivative, setting it equal to 0 and solving for t. Plugging this t back into the first derivative and evaluating will give us the maximum rate of addition. But this is such a cascade of estimates that I'll spare the details and just look at the graph. It appears that the maximum rate is about 12,000,000 electric vehicles per year in 2039. That's a long way out and such predictions are obviously fraught with possibilities for error. But I don't know how to do any better.



How much capacity will these 12,000,000 added vehicles per year demand? Let's assume that each vehicle travels 12,000 miles per year and uses 0.2 kilowatt-hours/mile. Further, similarly to the previous post on electric cars linked above, I'm going to assume that the overall efficiency of the transmission and charging systems, we'll need to generate twice what the vehicle uses, or 0.4 kilowatt-hours/mile. So, we'll need to generate 12,000,000 cars*12,000 miles/car/year*0.4 kilowatt-hours/mile=57.6*10^9 kilowatt hours/year. Google's calculator conveniently converts this to 6,570 megawatts or about 6.6 gigawatts of added capacity per year required at the peak. A modern large generating facility will have a nameplate capacity of about a gigawatt so this seems eminently achievable using nuclear power or with the invention of, as my friend Michael likes to say, the boron guy.

Energy use and standard of living

I mentioned in my post on the Olduvai theory that, to a large extent, a high standard of living is correlated with a high level of per capita energy use. Using the spreadsheet for Human Development Index from the United Nations here and the spreadsheet for International Primary Energy Consumption from the Energy Information Agency here, I've put together a graphic to show this.



Here's the display (click to enlarge), with a logarithmic scale of per capita annual energy use in btu on the horizontal axis and the U.N. Human Development Index on the vertical axis. This index attempts to measure human development by life expectancy at birth, knowledge and education measured by adult literacy rate and gross enrollment rates, and economic standard of living as represented by natural logarithm of gross domestic product per capita at purchasing power parity. In the graph, each red square indicates the data from a specific country.



The so-called "coefficient of determination," R^2, of the the scatter plot is about 0.82. This can be interpreted as meaning that per capita energy use explains about 82% of the variation in the Human Development Index (though statisticians will cringe).



This is truly very bad news though. The vast majority of the world's population is concentrated in countries with relatively low measures of human development and low energy consumption. These people justifiably would like to increase their standard of living and their ability to do so will either be constrained by lack of primary energy resources or will cause an enormous increase in "self-poisoning" of the human race.



I'll have more to say about this graph in future posts.

Mass and energy

You might have heard of Einstein's famous equation E=mc^2. I would imagine if there is a single equation of any kind, let alone of physics, that a random American could quote, that would be the one. Many who can quote it don't have a grasp of what it means (much as I appreciate E=mc^2, I'd go for F=ma). Of course, it doesn't take much algebra to change E=mc^2 into m=E/c^2.



In the U.S., each year we use about 100 quadrillion btu (100 "quads") of primary energy. This is electricity, fuel for transportation, manufacturing, etc.; that is, for everything. With the handy Google calculator we can determine the mass whose total conversion to energy would supply this amount of energy by simply typing "(100 quadrillion btu)/((3*10^8 meters/second)^2) in kilograms" into a Google search bar (3*10^8 meters/second is the speed of light or "c"). Be careful with the parentheses and groupings or the units won't work out correctly. Google handles all of the unit conversions and returns "(100 quadrillion btu) / ((3 * (10^8) (meters / second))^2) = 1 172.28428 kilograms." That is, conversion of the mass of a small car completely into energy would supply our U.S. energy needs for a year.



Of course, many teams are pursuing the goal of reliable direct conversion of mass into energy using the fusion process. It's said that "fusion is the energy source of the future and always will be."