But seriously folks...

I was watching "Planet Mechanics" (a mildly interesting show that won't save the world but makes more sense than the silly "Discovery Project Earth" series). While reading Dr. Michael Tobis' latest post in his blog "Only In It For The Gold" during a commercial break, I heard, out of the corner of my ear, a commercial for Dr. Frank's Joint and Muscle Pain Relief." The anecdotal claims being made were impressive, so I listened a little more closely and heard the word "homeopathic." Quoting a famous line from the history of my beloved White Sox, "say it ain't so Joe!"



One of my constant sorrows is the susceptibility of the American public (the only public with which I'm familiar) to the most ludicrous pseudoscientific claptrap. But to see such a product advertised on a network representing itself as educational was shocking.



Delving into the website, I perused the producer's explanation of homeopathic cures and of so-called "homeopathic provings" which they take care to explain are "entirely different than the scientific double blind study methods most people are familiar with." I just bet they are. Allow me to quote further from the site: "Homeopathic "provings" are, in essence, the proof that homeopathic scientists and doctors use to demonstrate to themselves that specific homeopathic ingredients work for specific symptoms" (emphasis mine). Nope, I'm not kidding.



The idea, as I understand it, is that you expose healthy subjects to random substances and see what symptoms are caused. Then you take the substance, dilute and agitate the substance in a special procedure ritual called "succussing" to concentrations as low as one trillionth the original (or even lower). This is then used to cure the symptom caused by the substance in its original concentration. You just can't make this stuff up (though Samuel Hahnemann could).



Of course, the practitioners of this lunacy are immersed in conspiracy theories revolving around the iron grip of "big pharma" and "allopaths" (i.e., real doctors) controlling the media, the research institutions, etc. I haven't the patience to debunk this hooey, though such sites as Quackwatch do an excellent job of it. But it pains me to see people encouraged to send money to such charlatans on an educational channel.



Update: In my noodling around to find information on this bunkum, I happened upon this site. I may have to change my template.



Update 2: Looking at their "Our Formula" page, I note that they claim 10 "homeopathic ingredients." Though there seems to be a mathematical error wherein they think 10^-6 is one ten millionth and they claim that all ingredients are diluted "one trillion times or more," it appears as if five of the ingredients are diluted to one millionth of their original concentration and five were diluted to 1 part in 10^30. Hmmm... It looks like the container holds 40ml of "substance." Considering that Avogadro's number (the number of molecules in a mole of the substance) is about 6*10^23 and a mole of water is about 18 cm^3 (or 18ml) and this is mostly water at 1 g/cm^3, there are probably somewhere on the order of 2.2 moles or 1.2*10^24 molecules in a bottle. For the ingredients being diluted to 1 part in 10^30, this means there's about a chance in 800,000 that a molecule of any such ingredient will be found in a bottle. Seriously.

What's my house worth?

I live in Southern California, an area of the country where by almost universal agreement, housing prices are completely out of touch with reality. But what does this actually mean? What "should" a house be worth? Of course the first answer is that something is worth whatever a willing buyer will pay that a willing seller will accept. Thus, my house was "worth" what I paid for it when I bought it. But no willing buyer at that price could now be found and economists say that housing values are retreating to a "more normal" level. But what does this mean?



Let me start by saying that I'm no real estate expert, nor am I an economist. I'm merely a curious person who likes to read and analyze, particularly with numbers. Now I recall reading, many years ago, an expert's opinion that a house should ultimately be valued at the net present value of the cash flows that would be available by renting the house. I can use this as a starting point and see where it gets me.



So then, what "should" be the value of a house based on the rent assumption? As is usually the case in my blog posts, I have to make some assumptions and estimates Let's assume that a household has an income of $70,000/year and can devote 35% (as is often recommended) of the 65% left after taxes, or $15,925 per year to housing. Let's further assume that this household occupies a house of 1500 ft^2 (neither excessively small nor large). Further, let's assume that the house requires about 4% of its value in maintenance each year and 2% in taxes and insurance. I'll assume that a real rate of return (net of inflation) of 7% is the minimum requirement. Finally, I'll assume that, over the "period of interest," inflation as applicable to the home purchaser is at 4%.



All right, then what amount of money would allow the receipt of $15,925/year less the taxes, insurance and maintenance to result in a return of 11%? Simplistically, the equation is 15925-.06*x=.11*x. Solving yields a house value of $93,676.47, or $62.45/ft^2. I purchased my house for dramatically more than that so, by this criterion, I overpaid. Ah, but our household income exceeds $70,000/year so it's reasonable to assume I'll rent a nicer home with my income. Adjusting the rent by the income ratio (probably a pretty bad assumption) I can estimate that I overpaid by a factor of about 1.8.



Of course, I also purchased the property my house is on, the safety of the neighborhood in which I live, the school system my children attend, etc. It's hard to put a monetary value on these things, but I could rent them as well. This isn't making me feel good, so what about the replacement value? Well, evaluating building a home with the materials in my house, together with the landscaping, hardscaping, etc. might cost about 3/4 of what I paid for the house. Adding the land value gets me somewhat closer to the actual price paid.



So what can be concluded? Well, to start, the fact that the replacement value of my property isn't that far off of what I paid for it combined with the fact that using the rental value evaluation yields a much lower number shows that Southern California housing is out of the price range of "average" incomes even without regard to the "asset bubble" aspects of it. Duh. It also may portend a continuing secular downward trend in residential real estate values. $70,000/year is not poverty level income, even in California, so I think I'd best be prepared for lower valuations.

"18 Kids and Counting (19 now)", "Quiverfull", seriously?

Jim Bob and Michelle Duggar and their 18 children (now 19 with their newest indefinitely in neonatal intensive care) are the central focus of the TLC reality show 18 Kids and Counting. And there's an Evangelical Christian movement called "Quiverfull" whose primary tenet is to eschew any form of birth control and "joyfully accept children as a gift of God" in accordance with God's direction to "be fruitful and multiply." And, in fact, the Duggars are conservative Baptists. That said, two things need to be made very clear before going on: the Duggars claim no association with the Quiverfull movement; and, though covert white supremacy motivations are sometimes attributed to the Quiverfull movement, it appears to be a genuine philosophy of adherence to the joyful acceptance of what members believe to be God's divine direction.



But, motivations aside, what impact do such decisions have? While it's a certainty that the human population does not now and has never grown at a well-defined exponential rate, this is quibbling. The Earth's population has, for the past 100 years or so, exhibited a doubling rate on the order of 60 years. While the actual number is by no means beyond debate, surely we can all agree that there's some maximum number beyond which the Earth's resources cannot support us in a standard of living we'd accept, whether that number is nine billion, 12 billion, or two billion.



This makes the celebration of a bodily function that any gerbil can master not merely inane but harmful. We've seen an increasing number of amoral fame seekers doing "whatever it takes" to achieve a low brow fame by getting onto reality shows (e.g., the balloon boy Heenes, Tareq and Michaele Salahi and the White House party crash, the so-called octomom) It seems clearly destructive to grant celebrity to those who engage in an obviously non-sustainable practice.



Regardless of where you may stand on anthropogenic global warming, carbon footprint is a reflection of energy and resources used and these are indubitably strictly limited, classical economics notwithstanding. And nothing a person can do contributes more to carbon footprint and hence resource utilization (that is, depletion) than having children. And having them in the United States, where we each use energy at the rate of 11 kilowatts is as destructive as it gets.



I remember when "TLC" stood for "The Learning Channel," but a look at their program guide shows that they left that concept behind years ago. I'm sure they did so because the American appetite for actual learning is minimal and more advertising dollars can be gleaned with reality television. This is sad to such as I of course, but I see no likelihood of a reversal of this trend. And I'm by no means in favor of the imposition of top down rules on content. But is it really necessary to celebrate a lifestyle that can hardly be beat for the expediting of the destruction of civilization?

Push lawnmower?

Tim Garrett, an associate professor of atmospheric sciences at the University of Utah, makes the provocative claim that global warming is unstoppable. It's a very interesting argument and is reminiscent of Jevon's Paradox. I'll have to do more thinking before I post on the crux of Dr. Garrett's main argument, this post is about a minor point in the article linked above.



Garrett opines that conservation and efficiency are useless in the long term with respect to minimizing humanity's primary energy conversion but yet he bicycles to work, line dries his clothes, and uses a push lawnmower. Ah, there's something into which I can sink my meager teeth. Is using a push lawnmower more Earth friendly than an electric or gasoline mower? I'm going to make a guess and then see if I can confirm or refute the guess with numerical estimates. You'll have to trust that the guess is prior to the calculation. My guess is that the electric lawnmower is most Earth friendly, followed by the push mower with the gas mower bringing up the rear.



First, I'll have to state my definition of Earth friendly. I'm going to go with primary energy consumption for all inputs, i.e., for the electric mower it will be the electrical energy used by the mower plus the energy required to generate and transmit the electricity. The gasoline will be the gas used by the lawnmower plus all energy used in extracting, refining, and distributing the gasoline. I won't include gas for the car to go to the gas station since that trip will be added to a fuel trip for the car. For the push mower, it will be the energy used by the person pushing plus the energy used in planting, fertilizing, harvesting (or slaughtering, etc.), and distributing the food providing the energy. I won't include the embedded energy in the lawnmowers, though that may hurt the push mower. Needless to say, there's ample room for error in this analysis but damn the torpedoes, full speed ahead.



Let's set the lawn as follows: 1,500 meters^2 (a little over 16,000 feet^2 or about 0.37 acres). Starting with the gas mower, I'll look at the Honda HRX217K2HMA. It has a cutting width of 21" but I'll use 20", there must be some overlap. Its maximum self-propelled speed is 4 m.p.h., I'll go with 3 as an average. Cutting 1500 meters at 20" requires 1.84 miles of mowing, at 3 m.p.h., that will take 0.613 hours. Sounds about right. The mower uses the Honda GCV190 engine, which uses 1.21 quarts/hour of gasoline. Therefore, it will use about 0.742 quarts or about 0.186 gallons to mow the lawn.



Using the estimates from my previous post, the 0.186 gallons will require a total on the order of 2.84*10^7 joules of primary energy from an oil well. To this I must add the energy required to walk 1.84 miles and using other figures from the same post, this will require 181 kilocalories or 6.4*10^6 joules of primary energy to produce. This is yields a total of 3.48*10^7 joules (Big hat tip to Chris for pointing out the factor of 100 error in my original post).



For the electric mower, I'll use a rechargeable, the Earthwise 20 in Cordless Electric Lawn Mower. I'll reduce the cutting width by an inch as for the gas mower and find that I'll travel 1.93 miles. I'll figure that I'm going a little more slowly, say 2 m.p.h., since it's not self-propelled. Thus, I'll need 0.96 hours or 58 minutes. The specification says that a charge is good for 45 minutes (give or take) so I'll need 1.29 charges. This is for a 24 volt, 17.2 ampere-hour battery that I'll assume we recharge when it's 80% discharged. Thus, a charge uses 1.19*10^6 joules and the lawn takes 1.54*10^6 joules of electricity from the wall socket. Again using figures from my earlier post linked above and assuming some fossil fuel (coal, natural gas) is used, this quantity of energy will require about 5.27*10^6 joules of primary energy to provide the battery charge.



Since the electric isn't self-propelled, I'll be working harder to push it, so I'll estimate about half again the caloric input as for the gas mower, or 9.6*10^6 joules of fossil fuel input to push it for a total of 1.49*10^7 joules total. Note that, by my estimate, it takes more fossil fuel to have me push the lawn mower than to power the swirling blades.



Finally, let's look at the manual, reel, or push mower. I'll use the Brill Razorcut 38 Push Reel Lawn Mower. The cutting width of this mower is 15.2", I'll reduce it by an inch as above and find that I have to walk 2.58 miles. Since I'm doing all the work, I'll assume that I can move at about 1.75 m.p.h. and thus I'll mow for 1.47 hours. This handy page says that, at 180 pounds, I'll burn 447 kilocalories/hour for a total of 659 kilocalories. Again going back to the earlier post linked above, producing the food to power me through this walk will take about 2.34*10^7 joules of fossil fuel energy.



It would seem that my instinct was correct. In increasing order of energetic impact, it's the electric, followed by the manual, and finally, bringing up the rear, the gas powered mower. My original analysis was off by a factor of 100 with respect to the energy contained in the gas mower's fuel burn (blush) so it isn't as bad as I'd first calculated.



Finally, take a look at what is, in my opinion, the best solution. Here's the Epic Cordless Electric Solar Mower Model EP21H. It features 45 minutes on a charge, has a 21" wide cut, and the optional solar panel will recharge it in about three sunny days. This will leave the 9.6*10^6 joules of food energy as the only fossil fuel consumption to mow your lawn.

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."

Olduvai?

There's a cheery website called "Dieoff" that does a pretty good job of factually presenting the worst case interpretation of demographic, economic, and resource consumption data. A contributor to the site, Richard C. Duncan, Ph.D., is the nominal (he acknowledges the contributions of many others) originator of the so-called "Olduvai Theory" which posits that we're quickly headed for a "post-industrial stone age."



The metric used by Duncan is per capita energy use. It seems to be a reasonable idea - mankind's ability to convert energy at ever-increasing rates has gone hand in hand with increasing standards of living (at least in those societies able to capitalize on it). And ranking of countries by primary energy use looks pretty similar to a ranking by standard of living, though there are exceptions at the high end.



Duncan cites a variety of sources indicating that per capita energy use peaked somewhere in the 1973-1979 time period. It's estimated that peak per capita energy use was about 11.15 boe (barrels of oil equivalent) or 6.46*10^7 BTU. He predicted that per capita energy use would decline at a rate of about 0.33%/year after that. Such a decline would lead to a 2008 per capita use of 10.47 boe or 6.07*10^7 BTU. What's happened?



Using BP's incredible site, the historical data spreadsheet gives me the data I need (by the way, anyone interested in energy, oil, etc. should spend a lot of time on that site). In 2008, per capita consumption was about 6.68*10^7 BTU. This is actually down from a peak of 7.24*10^7 BTU. The drops in 2007 and 2008 were quite steep.



Since the U.S. uses about 25% of primary energy and about five times the average, our effect on such statistics is huge, and we entered a deep recession in 2007. It remains to be seen what trajectory our recovery, if it comes, will take. For this reason, I don't think the current data support the Olduvai theory, at least at the present time.



It's also opined that the developing nations' striving for increased standards of living will overwhelm the developed world's (and particularly the U.S.'s) efforts at efficiency and I think that this is where the constraint will manifest. Since we use about 32.7*10^7 BTU per capita per year, a little less than five times the average, it's not likely we can find a way to bring the rest of the world to our level of use. And this takes no account of any peak oil consideration.



I've included a graph showing world population, total energy use, and world per capita annual energy use from 1980 through 2008. Click on it to see a larger and clearer version. Note the precipitous drop in the latter two categories in 2007 and 2008.

Modeling

Many of the comments I've seen "debunking" the science behind climate change are based on criticism of "computer models." Such people need to stay off of bridges and out of buildings, cars, ships, and airplanes. All are now designed using computer models. So, just what is a computer model, what can one do, when is one useful, and how can one go wrong?



Let's start with "what is a model?" When a net force acts on an object, that object accelerates. We learn in high school (and I've used repeatedly in this blog) that "F=ma." This constitutes, in a broad sense, a model. After all, the universe is not a calculator and F=ma is a synthesis of the way people (starting before Newton) believe material objects behave. It's been found to be useful and successful but may need to be modified, for example, in situations where the general theory of relativity is applicable.



As it happens, simulations using this model can be run on pencil and paper, with slide rules, or with a calculator. Nevertheless, the equation takes our best understanding of the essentials of a physical principle and, given specific input, will provide predictions of the output. But here's the point: science is about modeling. The world is too complex to track and measure every degree of freedom.



The spreadsheet I used to analyze acceleration is also a model. Again, it involves assumptions, separation of what I believed to be essential vs. non-essential parameters, measurements, and estimates. Like all models, it's subject to error if I've made a mistake in any of these components.



How do I check? In such a simple model, it's fairly straightforward. Does it make sense? How do the orders of magnitude compare? Does it provide reasonable numbers in limiting cases? Does it make predictions that match measured results? In my case, I believe the answers to this question is "yes, to within the accuracy that I can measure."



So what about computer modeling of climate? The models are built by doing what I did for the acceleration of my car, i.e., culling non-essential (or non-measurable) parameters, applying basic physical principles (Newton's Laws, conservation laws, thermodynamic laws, transport and transfer laws, etc.) to initial conditions, and evaluating the output. Like my model, it's an iterative process - the model is tested with input conditions for which output conditions are known and a determination if adjustments are required is made.



Of course, the more assumptions included and the larger the input data set, the more complex (and potentially though not necessarily the more accurate) is the model. The so-called "global circulation models" (GCM's) are quite complex. But as with any model, confidence in their accuracy is gained by comparison with known initial and final conditions. Here is a summary of successes of the GCM's.



The point here is that naive criticism of the process of modeling is completely misguided. Such critics use the results of successful "computer modeling" every day. If one wishes to criticize the models, it must be based on the factors above: wrong choice of parameters; inaccurate measurement of initial conditions, etc. "How can we believe a computer model?" is a question indicative of blissful ignorance. As stated (and demonstrated) in the post cited above, there are improvements to be made, but the current state of the art appears to be very good. And when it comes to physics, models are all we have.

Is there a psychologist in the house?

Just kidding, my regard for the so-called "soft sciences" is pretty low, though my father was a psychologist. But I'm trying to understand a guy like Marc Morano. Amazingly, Mr. Morano has no Wikipedia entry, so I'm tempted to think he doesn't actually exist. But he's the driving force behind the Climate Depot web site, an aggregator of anthropogenic global warming ("AGW") denial (or skeptic, take your pick) stories modeled very much after the Drudge Report.



Morano was an early promulgator of the Swift Boat Veterans' attacks on John Kerry and has worked for Rush Limbaugh. I've watched Morano in several debates and he's a quick witted and intelligent man and he very clearly has his facts in hand. So what does this man believe? I know what he contends but what does he believe?



I see several possibilities: he's a true believer that AGW is false but thinks those who claim it to be true genuinely believe that it is; he believes it's false and that the professed believers know it's false and are using it as a trojan horse for control of the world's economy; he believes AGW is true but thinks those who pay him really think it's false and he wants to continue to get paid; he believes AGW is true and that his income comes from people who also know it's true but whose economic interests are more important or who think that the consequences of action against AGW are worse than the consequences of warming; and several more possibilities.



Suppose he really is a true believer. I came to the issue leaning toward acceptance of AGW and severe negative consequences but had doubts. Among other sites, my friend Michael Tobis' Only In It For The Gold web site and links and papers therefrom have led me to be fairly firmly in the "it's warming, it's us, it's bad" camp though reading the guys below and the comments on their blogs occasionally still causes doubt to creep in - this is just not my area of specialist expertise. Though I've taken a lot of physics courses I'm no physicist, and though my college major was math and I'm working on an M.S. in Applied Mathematics, I'm no mathematician. I doubt I'm smarter than Morano and I certainly don't have the time he does to devote to the issue. So how can it be that he's a true believer? Is it truly a matter of his being slavishly beholden to his philosophy?



I want to understand Morano, Anthony Watts of Watts Up with That?, Steve McIntyre of Climate Audit and others. I'm not sure it would help in the battle for the hearts and minds of the public and the politicians, but it certainly couldn't hurt to know what's really going on in the minds of these highly popular and influential bloggers.

And I thought my disdain for Bill Maher couldn't get any deeper

My comments about Maher tend to be so vituperative that they don't pass moderation even on blogs whose viewpoints I generally support and when Maher is espousing an opinion with which I agree (admittedly rare), e.g., my first comment at ClimateSight.

But here we find him telling pregnant women not to get the H1N1 ("swine flu") vaccine. And he not only repeats lame pseudoscientific claptrap ("Western Medicine misses a lot") but makes inane factual misstatements (i.e., "lies"). For example, he states that the injected vaccine is a live virus. It is not. If one pregnant woman sees his screed and consequently avoids the vaccine, contracts the disease, and dies, as far as I'm concerned it is depraved indifference tantamount to negligent homicide.

More on efficiency

The spreadsheet I created for my recent post on acceleration has enough data to enable me to make another estimate of the overall efficiency of my transportation system (the Land Rover LR3 HSE) during the acceleration phase. This is because I have a tenth of a second by tenth of a second tabulation of energy used to accelerate and to overcome external forces as well as a tabulation of the fuel used.



Summing the fuel and knowing the heat energy available in the amount burned and summing the energy expended to do useful work and dividing yields the answer: 21.0% using the 45 seconds to 55 m.p.h. regime and 22.7% using the 10 seconds regime. This is actually a little better than I would have imagined. I typically calculate cruise figures estimating 25%, but I'd have thought that accelerating from a dead stop would have a larger negative impact on efficiency. Admittedly, it's a long chain from the data I actually have obtained to the figures I've calculated and the weakest link is my use of a composite engine map adjusted with only a very few points from my specific car but as I've said repeatedly, I love it when multiple lines of data and/or reasoning converge.



If my car required half as much energy through weight and drag reductions and was twice as efficient, I'd use one fourth my current fuel. If we all did.....

Can we "go electric"?

I'm sure it's been covered elsewhere on the web, but since James Kunstler has declared that we won't be able to keep the transportation system he refers to as "happy motoring," I thought I'd point my brand of quick and dirty calculating at the situation.



I'll start at the Energy Information Administration page here. This site is a gold mine of information for sources and sinks of energy of all kinds, for not only the United States but for the world. We find that in 2008, 8,989,000 barrels of "finished motor gasoline" was supplied in the U.S. per day on average. This represents 4.72*10^16 joules of heat energy of which I'll assume that 22%, or 1.04*10^16 joules are translated to force applied to the earth by tires to do the work of moving a vehicle down the road.



Using estimates from this post of 85% efficiency of chargers and 60% efficiency of transmission, 50% of the energy developed at a power plant winds up in a battery. Electric motors are pretty efficient, Tesla claims 86%. I'm going to go with 85%.



Since this is very rough, I'm going to assume that the vehicles replacing the gasoline vehicles are equally efficient, thus enabling me to merely look at joules at the wheel. Therefore, I need 1.04*10^16/(0.6*0.85) or 2.04*10^16 joules/day. This is energy divided by time, or power and using google's calculator, it equates to 2.36*10^11 watts or 236,000 megawatts.



The current generating capacity of the U.S., according to the EIA, is about 1.05 million megawatts (a little over a terawatt). This is just a little bit below the so-called "generator nameplate capacity" of the generating facilities. In 2007, we used electrical energy at a rate equivalent to about 464,000 megawatts, so adding a need for another 236,000 megawatts (increasing utilization by over 50%) would seem to be problematic. The difference between the actual rate of use and total capacity represents down time for maintenance, peak capacity, etc. and thus is not simply idle generating capacity looking for a use.



To maintain the same ratio of actual usage rate to capacity we'd need to add over 500,000 megawatts of generating capacity. That's a whale of a lot of solar panels and windmills. Or, since an average nuclear generating facility has a nameplate capacity of about 1,000 megawatts, we'll need about 500 of those. Best we had get started.



And of course, this says nothing about the transmission of all this electrical energy via a grid that is currently limping along at best, nor does it address the resources required to set up the infrastructure for such an increase in capacity. While I certainly have my gripes with Kunstler, it's true that simply switching to electric cars is no magic bullet for our peak oil predicament.



Update: an ultra-quick "back of the envelope" calculation indicates that we'd have to cover about 7.4% of the state of Arizona with solar panels to supply this extra electrical energy. Of course, storage might be an issue and I'm not so sure that condemnation of the southern eighth of the state (the extra area needed for storage, switching, support, etc.) via eminent domain would be well received.

Acceleration - the final word?

In my efforts to drive in the most fuel efficient way possible, I've examined many factors. For most of these, it's easy to determine how the parameters involved affect fuel economy. The exception is rate of acceleration. I've posted on this before, here and here. And it's a topic of discussion at one of my most frequented sites, ecomodder. The developer of that site has another site, at which he posted the results of an experiment to determine this, at least for his vehicle. He concluded that quick acceleration was most efficient, but also believes that this gets him to "pulse and glide" mode more quickly and is most efficient for that reason. Pulse and glide techniques are not applicable to my LR3 with its automatic transmission.



The discussion at ecomodder revolves around engine maps, gearing, etc. and of course, these are a crucial factor in the analysis. One thing I don't see, though, is the discussion of kinetic energy addition I mentioned in my first post on the subject. The fact is, if I bring my Land Rover LR3 HSE from 0 joules of kinetic energy (i.e., standing still) to about 800,000 joules (the kinetic energy at 55 m.p.h.) at a given rate of acceleration, and at half that rate, I will travel twice as far in the latter case. Since addition of kinetic energy is a matter of converting the chemical potential energy of gasoline, I've used a given amount of fuel over a longer distance. Further, I've gone a greater distance at a lower level of aerodynamic drag.



On the other hand, I've spent a greater amount of time at a speed that is less efficient. It's less efficient for two reasons: low r.p.m. and low torque is a very inefficient part of the engine map, i.e., has a high brake specific fuel consumption; and I've spent a longer time down near 0 m.p.h., where all my fuel is going to turn the engine and not overcome external forces.



Another complicating factor is "torque converter lock up." For those who don't know, a car with an automatic transmission has a torque converter between the flywheel and the transmission. This fluid coupling enables the car to stop in gear without killing the engine and serves a purpose similar to the clutch in a vehicle with manual transmission. It consists (very basically) of a case containing a fluid, a pump attached to the casing that turns with the flywheel, and a turbine that is turned by the fluid forced onto it by the pump. There are losses in the fluid coupling for various reasons, so most vehicles have a solenoid that locks the pump and turbine together when they are turning at similar speeds. This prevents the losses in the fluid coupling but is only active at speed, thus increasing the likelihood that getting to speed faster (i.e., accelerating more quickly) will save fuel.



That must be all then, right? No, of course not. There's also the ECU, or engine control unit. If the throttle is pushed to the floor, most ECU's will operate in so-called "open loop mode." Here, the computer doesn't take feedback from the oxygen sensor and estimates how much fuel to inject based on outside conditions (temperature and pressure) and throttle position. It tends to supply a very rich mixture, thus hurting fuel economy and suggesting that slow acceleration is best.



So, does one method prevail, i.e., as slowly as possible or floor it? Or is there an optimal "Goldilocks" rate (not too quick, not too slow) of acceleration? I determined to find an analytical solution. Many estimates and assumptions are necessary since I don't have an engine map for my vehicle and I don't know the parameters of the ECU. Such considerations have never stopped me before though.



I'll start with a terrific document prepared by Sierra Research for Environment Canada entitled "Alternative and Future Technologies for Reducing Greenhouse Gas Emissions from Road Vehicles." It's linked and can be downloaded as a pdf file here. This document discusses (among a huge variety of other topics) "brake specific fuel consumption" and provides a generic engine map. This map shows engine load in brake mean effective pressure as a function of engine r.p.m. and the isopleth contours show lines of equal brake specific fuel consumption. It's a composite of 1995 normally aspirated, fuel injected, two valve per cylinder engines and thus is similar but not the same as my engine, but it's the closest I can find.



Now, it's well known that losses related to heating the engine block and throttling losses as the engine turns slowly at low r.p.m. and low demand, and heating oil due to friction at high r.p.m. lead to a an island of lowest specific fuel consumption at high engine demand and mid-range r.p.m. I don't have an engine map for my Land Rover LR3 HSE so I'll use the features of the map in the Sierra Research document adjusted for the few calculated points I have for my vehicle. This, together with the calculated force required to add kinetic energy and overcome external forces, will enable me to numerically calculate (estimate) the fuel used in going from 0 to, say, 55 m.p.h. at various acceleration rates.



I'll start with what I do now, which takes me from 0 to 55 m.p.h. in about 45 seconds and compare with a much brisker rate taking me to 55 m.p.h. in 10 seconds. The vehicle is rated to get to 60 m.p.h. in 8 seconds at wide open throttle. I've made a spreadsheet to analyze the energy required to add kinetic energy and to overcome external forces for each tenth of a second.



The result using slow acceleration is that I burn about 0.27 pounds of fuel in accelerating to 55 m.p.h. over a distance of 550 meters. Accelerating quickly, I burn about 0.19 pounds of fuel to get to 55 m.p.h. over 120 meters. To this I need to add the fuel used in going the additional 430 meters to get to where the slow acceleration regime took me. Using the figures from previous calculations on highway cruising fuel use, I'll use about 0.072 pounds to go 430 meters for a total of 0.262 pounds. This indicates that the quick regime is very VERY slightly more efficient. It's doubtful that my various estimates and interpolations are accurate enough to have much confidence in this result with respect to the specific numbers, but I do think it's safe to say that there isn't much difference.



Now, in gathering this data and calculating, it's clear that the poor economy is at the very low r.p.m.'s and speeds, and at r.p.m.'s above about 2600. So I believe the key is to accelerate briskly to second gear and then back off to a moderate rate to get to speed. I'll take the time to plug the numbers in for such a regime in the coming days, but I wanted to get something posted and the data gathering and calculations resulting in the conclusions above took about eight hours. So I guess the question mark in the title of this post is there for a reason, this isn't quite the final word.

Cooling

I made a post in which I estimated the total energy use in my family. It was disturbing, in that we use a LOT of energy and there aren't a lot of places where cuts are easy (hypermiling my 3 ton SUV notwithstanding). Over 18 months have gone by since I wrote that article, and I've learned a few things. None would change the overall thrust of the article though; the main modification would be in the energy content of purchased items (the so-called "embedded energy"). I estimated one third of the cost of the average purchased item went for the total energy used in producing it, I now think that's probably too high.



But the last couple of weeks have been quite hot (around 100 degrees F for a daytime peak) and I've had the air conditioner on quite a bit. Our air conditioning system was manufactured in 1995 by Goodman Manufacturing and is a model CK60-18. As best I can tell, this means it's rated at a little under 60,000 BTU/hour (about 56,000) cooling capability at a Seasonal Energy Efficiency Ratio ("SEER") of about 10.5. This is typically found by adjusting the Energy Efficiency Ratio ("EER") which is defined as the cooling capacity over a period (e.g., BTU/hour) divided by the power used during that period in kilowatts at a particular outdoor temperature. Thus, EER is a mixed unit, BTU/hour/kilowatt. In dimensional terms, it's unitless but it's expressing how much energy it takes to move any particular amount of heat from inside to outside in a particular amount of time. Residential central air conditioners installed in the United States after 2006 are required to have a SEER of at least 13.



Air conditioner cooling capacity can also be rated in "tons," equivalent to the ability to move 12,000 BTU/hour from inside to outside in an hour. This unit hearkens back to the days when ice was used for cooling and the melting of a (short) ton of ice removes about 288,000 BTU from the environment, so doing so in a day uses 12,000 BTU per hour. My air conditioner thus provides the equivalent cooling capacity of about 5 tons of melting ice and hence is a five ton unit. Furlongs per fortnight anyone?



Now interestingly, working it out, my air conditioner will move 56,000 BTU of thermal energy from the inside my house to the outdoors in an hour. 56,000 BTU/hour is energy divided by time or power and is equivalent to about 16,400 watts. But the EER is about 9.5 so, since EER=(btu/hour)/watts, the electrical energy input is (BTU/hour)/EER or 5,890 watts. That's nice, my air conditioner produces about 2.8 times as much heat output as electrical energy input. Has Goodman Manufacturing succeeded in defying the law of conservation of energy and the first and second laws of thermodynamics? And by specifying a SEER no less than 13 is the U.S. government requiring changing the laws of physics?



No. The electrical input is used to compress a fluid and pump it around a circuit (absorbing heat from room air by changing from a liquid to a gas in the evaporator coil, then releasing it by changing back to a liquid) and to power a fan to blow the air cooled by the coil into the rooms of the house. Thus, the work being done is the movement and compression of fluids. The entropy of the air inside the house is decreased, that of the air outside is increased more in strict accordance to the second law.



The functioning of an air conditioning system is the same as that of a refrigerator and the most wonderful television series of all time, "The Secret Life of Machines," covers the refrigerator (among many other fascinating topics), here. A series of three YouTube videos comprising that episode are embedded below, but all episodes can be downloaded in their entirety. I heartily recommend doing so.



If my air conditioner is operating at a SEER of 9 (it's 14 years old after all), and I replace it with a new one with an SEER of 14, what can be saved? Well, I'll use 9/14 as much electrical energy, and I estimate that I'm using 560 hours per air conditioning season at about 5 kilowatts costing about $0.125/kilowatt hour. This will cost me about $350. If I buy the new unit, I'll spend (9/14)*$350 or $225, saving $125. It will take a very, very long time to pay for the new unit at that rate.

A quick follow-up

My previous post dealt with the total energy required in using various means to go to the store for groceries. My conclusion was counter-intuitive, in that it appears that bicycling uses more energy than an electric scooter. Now clearly if I'm fulfilling another purpose, e.g., maintaining a level of physical activity for fitness, the energy issue may not be the deciding factor in my choice. And bicycles are cheaper than viable electric scooters.



But, speaking of price, let's focus on the cost analysis from an energy point of view. The energy used in my means of transportation should be reflected in the price I pay to use it so I'll see what each method costs. From the previous post, if I walk I'll have to buy 491 kilocalories of food to make the trip. Clearly, all kilocalories are not created equal, but I estimate that if I eat 2500 kilocalories/day and am doing so in a "not too unhealthy" way, I might spend about $7.00, or $0.0028/kilocalorie. Thus, my trip costs .0028*491=$1.37. An identical calculation for the bicycle, using the 162 kilocalories from my earlier post, results in a cost of $0.45.



For the electric scooter, I'll use 751,000 joules or 0.208 kilowatt hours (the 638,000 joules used by the trip divided by the 85% charger efficiency, i.e., this is what I pay for). This will cost me a little less than $0.03. Pretty darn cheap!



For the smart fortwo, I'll use $0.59 worth of gasoline (6 miles at 33 m.p.g. and premium fuel at $3.239/gallon) and for the Land Rover LR3 HSE, it will be $1.10.



So the cost results, surprisingly, do change the order. It's cheaper, in end user energy purchase price, to drive than to walk. This holds true even in my three ton Land Rover. Shocking indeed, but I don't see a huge error. Obviously, electricity and gasoline are commodities and food isn't so I can, to a certain extent, choose what to pay for a kilocalorie. One thing that quickly jumps out is that food is expensive! I bet no one reading was aware of this obscure fact.



Perhaps if I choose food for minimum kilocalories/dollar, I could cut the price by something like 70%. Doing that makes the trip $0.13 on the bicycle and $0.39 to walk. I think this is at least a reasonable view, the cost per kilocalorie above the minimum is for taste, convenience, "earth friendliness," etc. and not for energy. This adjustment changes the order back to a match for the total energy conversion analysis.



To recap (using minimal food cost):

Electric Scooter: $0.03

Bicycle: $0.13

Walking: $0.39

smart fortwo: $0.59

Land Rover LR3 HSE: $1.10



To recap (using food I typically buy):

Electric Scooter: $0.03

Bicycle: $0.45

smart fortwo: $0.59

Land Rover LR3 HSE: $1.10

Walking: $1.37

Going to the store

Hypothetical question (its hypothetical nature will be explained later): A grocery store is located 3 miles from my door with a level path. I need groceries that will fit in a single bag. How much fossil fuel is used, ALL INPUTS CONSIDERED, if I: walk; ride a bicycle; take an electric scooter; drive a smart fortwo; drive my LR3 HSE. I'll assume the two gasoline vehicles are warmed up.



As is typical, I'll be making estimates, but I doubt that the order will be wrong. Let's start with walking. Assuming I walk at 3 m.p.h., it will take 120 minutes to walk to the store and back. Using this calculator, I find that I'll convert 491 kilocalories of food energy to heat (the site calls them calories but this is incorrect). Now, it is said that 7 to 10 kilocalories of fossil fuel energy are required to produce a kilocalorie of food. I'll use 8.5, so 8.5*491=4170 kilocalories or 17.5*10^6 joules of fossil fuel energy to get me to the store and back.



How about a bicycle? Using the very nice calculator here and assuming I ride at 10 m.p.h. (faster on the way there, slower on the way back), I find I'll burn 162 kilocalories of food energy requiring 8.5*162=1377 kilocalories or 5.76*10^6 joules of fossil fuel energy.



Looking at the electric scooter, I'll use the Zapino (previously posted about here) as my representative. The optional 60 volt, 40 amp-hour Lithium battery supposedly gives it a range of "about 65 miles." Now, 60 volts at 40 amps for an hour is 8.64*10^6 joules but I would think the range would be based on, say, 80% discharge. So that means it uses 8.64*10^6*0.8/65=106,000 joules/mile and my 6 mile trip would use 638,000 joules. But wait. The charger would only be about 85% efficient and transmission of electricity is typically about 60% efficient. So I'll use 638,000/(0.85*0.6)=1.25*10^6 joules of electricity from the generating station. Are we done? No, this electricity is likely generated by a fossil fuel plant whose efficiency is on the order of 50%, so double that to 2.50*10^6 joules of primary fossil fuel energy. Finally, using an EROEI (energy return on energy invested) of 7.5:1, we multiply 2.50*10^6*8.5/7.5 to find that it requires 2.83*10^6 joules of primary fossil fuel energy in total to go to the store and back.



The smart fortwo about which I posted here? Certainly this will be city driving where the fortwo is listed by the EPA at 33 m.p.g. A nice little article singing the Tesla's praises gives me the "well to wheel" data I need. Without bothering my patient readers with the conversions and calculations, I find that the fortwo uses 28.9*10^6 joules of primary energy (including well to pump to wheel efficiency) to accomplish the mission. It should be noted that a "hypermiler" could likely do significantly better.



Finally, the LR3 HSE (with me driving it) will achieve about 17.6 m.p.g. in the city and thus uses 54.2*10^6 joules of primary energy to go to the store. So the electric scooter is the best, using about 5% of the energy of the LR3. Surprisingly, the bicycle uses twice as much energy (remember, all fuel inputs to food production are included and no distinction is made for vegetarian versus omnivorous diet, so your mileage may vary) as the scooter and walking even more. I may have to revisit the scooter yet again. And why is the question hypothetical? It's down a long and steep hill from my house to the store and, more importantly, up that long and steep hill to get back.



To recap:

Electric Scooter: 2.83*10^6 joules

Bicycle: 5.76*10^6 joules

Walking: 17.5*10^6 joules

smart fortwo: 28.9*10^6 joules

Land Rover LR3 HSE: 54.2*10^6 joules



Update: A very interesting analysis of the bicycle versus electric bicycle (scooter) energy requirements that includes life-cycle energy consideration done as a term paper is available here.

The CNW Research - Pacific Institute - Slate Magazine kerfuffle

Let me start by saying I've wanted for a long time to use "kerfuffle" in a blog post. The contretemps that's the subject of this post fits the word perfectly. You may remember a few years back that a meme went around stating that the "lifetime energy usage" of a Hummer was less than that of a Prius. As the rumblings had it, this was primarily because of the energy required to manufacture, carry, and dispose of the Prius' battery pack.



The origin of this meme was a report by an entity called CNW Research that is, as best I can tell, a marketing research firm. The report claims to use 3,000 data points to put a price tag on the "dust to dust" (inception of design to manufacture to use to disposal and recycling of the vehicle at its "end of life") energy of a wide variety of vehicles. It's stated that they even include the fuel used driving to work by the employees of the vehicle's manufacturer in their calculations.



They rank many vehicles in a tremendous variety of categories but the phrase that caught on was that the Prius uses more energy from dust to dust than a Hummer.This is despite the fact that the report itself puts these two vehicles in separate categories. CNW Research recommends that the report be used to compare vehicles within a category, not across categories.



On its face, this result seems ludicrous. And Pacific Institute (here) and Slate Magazine (here), among others have strongly criticized the results. CNW Research has defended their results at pages linked here.



Instinct often leads one astray in the field of energy, let's take a brief look. The actual report is available at CNW Research's site in pdf and Excel versions. The pdf is 458 pages and 3 MB so it's a chore.



That said, there are some telling indications to start with, among which are the misuse of units (watts, kilowatt hours, joules, etc.). In fact, they refer to "juelles." Not confidence-inspiring, to say the least. There are strange estimates of vehicle lifetime years of use (e.g., for the H1 34.96 years) with no indication of the source of the number. These numbers are critical because the ultimate number they give is energy cost per mile. The denominator, miles, is found by taking lifetime in years and multiplying by miles per year. There's no indication of the source of either number (other than "CNW Research").



It appears that they use several resales to secondary owners in their cost calculations, though this clearly has nothing whatsoever to do with energy expenditure - I doubt that the writing of a check, and a trip to DMV are significant energy expenditures in the final analysis. And cost is a telling indication. For example, the Prius is stated to have a "life-cycle energy cost" of $3.25/mile. Using the lifetime mileage of 109,000 miles, that means that, exclusive of the materials cost of the Prius, profit for the manufacturer and the various suppliers, distributors, etc., the energy from cradle to grave of a Prius costs over $350,000.



Now, suppose I buy a loaded Prius for $25,000 and drive it 109,000 miles. Using the IRS rate, a decent proxy for all costs of driving (including depreciation, maintence, etc.) and excessive if anything for the Prius, the total cost (not adjusted for time value of money) would be $84,950. Even assuming 100% of that is energy costs, who's paying the other $269,300?



I will acknowledge that "society" pays a significant amount in the form of road maintenance and other public goods. And CNW Research claims to account for these. But it's impossible that this would account for the enormous discrepancy.



All that said, it's clear that CNW Research has invested a lot of time and effort and gathered a spectacular amount of data. I'd like them to be open with it because the conclusions they've reached, correct or incorrect, are quite important. I don't accuse them of bias on the basis of funding, I don't see that kind of skew in their analysis and they claim to have funded it internally. Fair enough, I'll take them at their word.



If this information were to presented as a peer-reviewed publication and the data made available, it would be extremely valuable. I understand that CNW Research wants to profit from their efforts and I'm sympathetic to the profit motive. But the results, as presented, leave ample room for skepticism at best and dismissal at worst. To their credit, they have extensive appendices and answer many questions emailed by readers. Unfortunately, they don't clear up the points listed above.

Embarrassed to be conservative

I find myself going "off topic" more frequently on this blog as it becomes an avenue for me to express opinions on sociological and political matters. This may cause some dismay for those who've followed me to understand how it's possible to get 21 m.p.g. in a Land Rover or the effect on U.S. primary energy consumption should everyone switch to hypermiling. Sorry.



As I've intimated from time to time, I'm not a big government liberal. If anything, my political philosophy revolves around small-l libertarianism. That is, personal responsibility for outcomes and minimal government involvement in the day-to-day lives of the populace. I don't tend to support the attitude of "there's something we don't like, let's involve the government in the solution," and thus could be considered "conservative" in a sense. But what is it I'd like to conserve?



I'd like to conserve the natural resources necessary for both the advancement of civilization and the health of the entire ecology. I'd like to conserve our financial resources to enable us to invest in our future. I'd like to conserve our freedom to act in our own best interest so long as it can be done without the use of force, the threat of force, fraud, or coercion. In a nutshell, I believe that's what conservatism should mean.



I don't want to waste time and bytes on the truly wacko birthers and the like, though I'd point out that those who decry that conservatism leads to birther morons must then acknowledge that liberalism leads to truther fools (though I'll concede that there are nut cases of the black helicopter variety in the truther movement as well). In any case, my problem is with what has now become "mainstream" conservatism as represented by James Inhofe, Michelle Malkin, Rush Limbaugh, Glen Beck, Sarah Palin, George Will, etc.



These spokespersons and their ilk have turned the political discourse into a win at all costs war. Among the casualties of this war are civility, honesty, integrity, and reason. The "death panels" are one of the latest examples of the intellectual corruption of the conservative movement. As Mark Hoofnagle states in his Denialism blog post, there is a debate to be had on health care, but the idiotic shrieking and bald faced lies of the so-called conservatives are preventing us from having it.



Similarly, how to proceed to a world of lower energy conversion rates, given the extremely low rates and high populations of the developing world and their reasonable desire to increase those rates, is a complex topic requiring reasoned discussion and rational action. Whether one comes at the energy issue from the point of view of peak oil and resource depletion, climate change, or both, it's clear to any thinking person that we can't have nine billion people converting primary energy to heat at the U.S. rate of 11 kilowatts per capita. This would lead to a complete collapse of civilization, either through self-poisoning or complete resource depletion, or both, economic theory notwithstanding.



Yet the Moranos and the Inhofes continually propagate all manner of distortions implying that business as usual is the answer.



I'm not a big fan of categorizing my political philosophy with a single word, but if those I've mentioned are conservative, I most certainly would be embarrassed for the word to be applied to me.

The law of dimishing returns, the Chevy Volt, gas mileage, and hot air

The Chevy Volt, expected to hit the market in 2010 is claimed to achieve 230 m.p.g. in city driving. Is this possible? If so, how significant is it? Over at one of my favorite haunts, Ecomodder.com, Benjamin posted a blog entry about the Volt and the claims for it.



As is my nature, I was compelled to dig into the numbers. I commented there that it sounds suspicious. The claims for the Volt are that it will achieve "up to 40 miles" on electricity only and that it will achieve an efficiency on electricity only of 25 kilowatt hours per 100 miles on the EPA city cycle. This is stated to cost between $0.75 and $2.50 depending on electric rates. Interesting.



This is saying that, when using only electricity, the vehicle will have an energy cost of $.0075 and $.025 per mile. That is, between three quarters of a cent and 2 and a half cents per mile. Now, I'm currently getting 21 m.p.g. and spending about $0.15, i.e., fifteen cents per mile on energy. Comparing to the low end of the electrical cost, I'm spending 20 times as much on energy. At the high end, it's six times as much. So multiplying 21 m.p.g. by 6 and by 20, you'd infer that the Volt is achieving something from 126 m.p.g. to 420 m.p.g. just on a cost of energy basis. 230 m.p.g. is in this range, but this isn't very enlightening. Let's try something else.



We'll work with the 25 kilowatt hours (25 kWH) per 100 miles. A kilowatt hour of electricity is 3.6 megajoules, so 25 kWH is 90 megajoules. Since a gallon of gasoline will release about 125 megajoules of thermal energy upon oxidation, we can say that the Volt will go 100 miles on the energy contained in (90/125) or 0.72 gallons of gasoline, thus getting roughly the equivalent of 100/0.72 or about 139 m.p.g. (or, as Doug Pelmear would say, 139 MPGe).



So where did 230 m.p.g. come from? I'm not sure. One possibility is that they look at, say, a 50 mile trip, figure 40 miles on the electric motor and don't count that energy expenditure, then travel the remaining 10 miles on a gasoline engine that gets 46 m.p.g. while powering a generator to propel the car and recharge the battery. Conveniently, that would indicate travelling 50 miles on 10/46=0.217 gallons, or 230 m.p.g. At this point, I don't know.



In any case, suppose that we do have such a vehicle. What would it mean? In an earlier post I went into some detail on the fact that, the worse the gas mileage being achieved, that is, the lower the m.p.g. the more fuel is saved by relatively small improvements in that number. This result is surprising to some because miles per gallon is really not the best way to directly look at efficiency. The better way is gallons per mile, the inverse.* The Volt will illustrate the other end of the spectrum from that described in my previous post.



Let's say I trade a Toyota Yaris, where I was getting 30 m.p.g. driving mostly in the city for a Chevy Volt where I now get "the equivalent of" 230 m.p.g. Suppose I drive 10,000 miles per year. I'll go from burning 333 gallons of fuel to the equivalent of 43.5 gallons, saving 290 gallons.



Meanwhile, my Doppelgänger is driving his LR3 HSE, mostly in the city, and getting 15 m.p.g. He uses 667 gallons to drive 10,000 miles. He trades it in on a MINI Cooper and gets 30 m.p.g., using 333 gallons in the course of his 10,000 miles of driving. He saves 333 gallons, 43 more than I did by going from 30 m.p.g. to 230 m.p.g. This is the law of diminishing returns in action.



From a person who coasts to the cross street from his driveway before turning on the car to save a milliliter or two of fuel, it might seem odd to read something apparently dismissive of such extraordinarily good fuel economy. But I'm not dismissing it, only attempting to put it into perspective as to what's being achieved and where the big savings lie. In fact, my hat's off to Chevy for bringing this ultra-efficient vehicle to market but they need to be clear with their claims.



* In the Great White North, where civilized people use the SI ("metric") system, fuel economy is rated in liters per 100 kilometers (though "liter" isn't strictly a SI unit). My 21 m.p.g. rating turns to 11.2 liters per 100 kilometers. The Volt's stated 230 m.p.g. would be 1.02 liters per 100 kilometers.



Update: Rhett, over at DOT PHYSICS, has made a very thorough analysis of the Volt. Take a look!



Update 2: A better debunking than mine of the Chevy Volt m.p.g. claim is at Good Math, Bad Math. I've added this great blog to my blog roll. You're welcome.



By the way, I found Good Math, Bad Math by typing the conversion from 230 m.p.g. into the Google calculator. It made the conversion AND came up with the blog site. You have to love the Google folks. Even if you equate them to the Borg.



Update 3: Apparently, from reading the comments to the Good Math, Bad Math post linked above, Chevy is "just following orders," i.e., they're going by the tentative rules promulgated by the EPA for the fuel economy ratings of plug-in hybrids. I still think Chevy should be clear. As Rhett shows on his Dot Physics site (also linked above) if you pull out of your driveway and drive 230 miles, you'll use way more than a gallon of gas.

Time out

I am by nature a cynical and pessimistic person (not the same thing - it's said that an optimist is a father who will loan his teenager the car, a pessimist is one who won't, and a cynic is one who did). I don't say this to brag, I actually try to at least act as if I'm not. This blog covers topics that will, if major changes aren't forthcoming (and there's no reason to believe they will be), result in unprecedented trauma in our so-called social contract. Now, maybe we'll adapt and the result will be a stable and sustainable societal arrangement, albeit at a lower level of energy conversion. Maybe it will be a Mad Max world. I'd like to hope the former, but my makeup makes me dubious.



Thus, it's significant to me when I find something that makes me feel that it's not all bad. A few months ago, I was watching a youtube video of Leo Kottke, a guitarist I've admired for years and seen on multiple occasions. Youtube suggested I might want to see videos featuring Tommy Emmanuel, of whom I'd never heard. I didn't click on them for the first few times they came up next to Leo, but I finally did. Let me say that Tommy's talent, skill, and love of music have become one of the things that makes me believe there's good in the world and things worth preserving.



I drove four and a half hours to see Tommy Emmanuel perform in Exeter, CA and, though I anticipated that it would be a wonderful experience, I tremendously underestimated how moving it would be. His videos are all over youtube and, since this is a non-commercial blog, I've decided to put one here. It's called "Those Who Wait." I apologize in advance for no physics, vehicle, energy, or gasoline content but I feel compelled to share my wonder at this uniquely talented and genuinely beautiful musician and songwriter (the composition featured here is his). Click on it, you'll thank me. If you're wondering if he's capable of something a little more up-tempo, check out his Guitar Boogie. If your jaw doesn't hit the floor, you have more self-control than I.

Why "Hamiltonian Function"?

Physicists (of which I am most emphatically not one) will instantly recognize the "Hamiltonian." It's not about a horse race (though I stuck "function" on in the name to distinguish it from that) nor does it refer to a Founding Father. Rather, the Hamiltonian is a function that represents the total energy of a system utilizing a reformulation of Newtonian mechanics called, unsurprisingly, Hamiltonian mechanics. Since this blog is nominally about energy, how to minimize its expenditure, and take maximum advantage the energy I convert, the Hamiltonian Function as a title seems appropriate to me.



Though it typically doesn't make a particular problem easier to solve, it's considered that the Hamiltonian of a system is capable of providing deeper insight into the nature of the system under consideration than the second order differential equations of Newtonian mechanics. This is particularly true when the system involves quantum mechanical considerations, though it is completely general in its application. I'd be flattering myself to contend that my little blog is capable of providing deep insights, but I do hope that it can provide a different point of view and be thought provoking.

Playing with an iPhone

I dumped my forever locking up Samsung Omnia for an iPhone 3Gs. As most will know, one of the major selling points of the iPhone (and a good one at that, though some stridently disagree) is the availability of an ever-growing "app store." I've installed six apps so far, but this post is about the Wavefront Labs Accelerator Data Pro and Cross-Discipline Technology, LLC Gforce apps. These apps take the data from the three axis accelerometer in the iPhone and display it or log it. I thought it would be interesting to document exactly how slowly I accelerate, though I already had a pretty good idea from logging speed vs. time in five second intervals as mentioned in this post.



I've used the Gforce app more frequently because, well, I'm driving and the display is much more intuitive to understand at a glance (click on the photo for an enlarged view). It's capable of holding the peak in longitudinal and transverse axes for a user-set amount of time and of sounding an alarm when user-set limits are exceeded in either axis. The Acceleration Data Pro is capable of saving data to a file and exporting for subsequent analysis. I intend to so use it but have not done so yet.



As readers of this blog might imagine, my positive acceleration numbers are quite small, rarely exceeding 0.1 g (0.98 meters/sec^2), though the first movement from a stop is typically about 0.15 g. I estimate that the average acceleration up to speed is about 0.055 g. To get a feel for this, that means I'm gaining about 1.2 miles/hour in speed with each second. Using that acceleration, I get to 55 miles/hour in about 45.6 seconds. This is somewhat faster than the results I got from timing, referred to above. I don't know if I'm getting more rambunctious in my application of throttle (doubtful, judging from the reactions of those with whom I share the road) or I'm "guesstimating" the average acceleration from the iPhone inaccurately.



Probably of more interest, there's a curved ramp from the 605 freeway northbound to the 91 freeway eastbound that I take at a speed, v, of about 50 miles/hour (22.35 meters/second). The Gforce shows a centripetal acceleration, a, of about 0.38 g, or 3.724 meters/second^2. Now, since a=v^2/r, where r is the radius of the path described by my vehicle (for a very nice lesson on this topic, see Rhett Alain's Dot Physics entry), I can estimate that the radius of the ramp is about 134 meters. How can you not love the ability of the iPhone to measure the radius of curvature of a freeway on-ramp?



The ramp has a recommended maximum speed of 35 miles/hour (I maintain 50 m.p.h. because I don't want to apply brakes). Working backwards, this means that CalTrans has designed the ramp for a recommended centripetal acceleration of about 0.19 g. They should put that on the sign!



Starting early in my first high school physics class and reemphasized ever since, when looking at any physical situation, when in doubt, F=m*a. That is, force equals mass times acceleration, Newton's second law (well, sort of - Newton actually framed it as net force equals rate of change of momentum but it's the same thing). Let's apply it here. The mass of my Land Rover LR3 HSE is about 2,676 kilograms, and I take that curve at about 0.38 g or 3.72 meters/second^2. This means F is about 9966 Newtons, or about 2,240 pounds. Note that this is over 10 times the force required to move the LR3 down the road at 55 m.p.h. and it's applied by the road to the vehicle through the tires. No wonder they wear out!



Update: To really see what can be done with the iPhone and its acclerometer and GPS, see Michael Koppelman's exploits with an iPhone in a model rocket.



Update 2: I haven't done any programming since about 1989, and that was meager. My last (semi) serious bout with programming was in 1980. I wonder how hard it would be to write and install a program for the iPhone that would provide average acceleration in each axis from a start to a stop time, or average over user set intervals, say, every second?