The "smart" car

I've put "smart" in quotation marks for a reason. Is it smart? Here we have a very small vehicle in which storage space and room for more than two occupants are sacrificed in return for a promise of great economy. Is the trade off worth it?



Let's assume that economy is the only consideration for the purchaser of the smart. The purchaser will then select the smart fortwo Pure, with a base price of $11,990. I'll add A/C, the "Silver metallic tridion safety cell" (though I don't know exactly what it is, since it has the word "safety" in it and everyone I've spoken with is concerned about the smart fortwo's safety, I'll add it), the alarm system and the premium radio. I'll leave out the heated seats, power steering, and metallic paint. The options bring the total to $13,420. We should note that most people don't tend to get the base model, but this will put the best face on the purchase of a Pure.



So what do I get for my $13,420? This is not a car review blog, so I'll only look at the fuel economy aspect of the purchase. The EPA estimates the car to provide 33 m.p.g. in the city, 41 m.p.g. on the highway, and 36 m.p.g. combined. For comparison, the Volkswagen Jetta Diesel gives 30 m.p.g. in the city and 41 m.p.g. on the highway. Admittedly, some won't purchase a diesel. For those, how about the Mini Cooper at 28 m.p.g. city and 37 m.p.g. highway or the Toyota Yaris at 29 m.p.g. city and 36 m.p.g highway? Of course, going the hybrid route will up the mileage ante, but also the price, so we'll ignore those for this post. The low end base price of the Jetta Diesel is $21,990, the Mini Cooper is $18,550, and the Yaris $13,005. The Jetta and the Mini are significantly more costly than the Pure, so we'll go with the Yaris. The base cars in this range are all pretty bare, so we'll figure a similar amount in options and compare the Yaris at about $14,450 and the Pure at $13,420.



The Yaris offers seating for five (nominally) and storage area with a 1.5 liter four cylinder engine. The smart fortwo offers seating (ready now) for two, storage for a few grocery bags, and a 1.0 liter three cylinder engine. Clearly, the Yaris offers significantly more utility at a price that's not dramatically higher. Thus, the big incentive for the purchase of a Pure, other than kitsch, would have to be the fuel economy.



It's recommended that the Pure, whose US engine configuration has a relatively high compression ratio of 10:1, be fueled with premium. Thus, purely from a cost point of view, the Pure is handicapped by about 8% (depending, of course, on actual prices) compared to the Yaris which uses regular grade fuel despite its 10.5:1 compression ratio. Assuming that regular is selling for $2.45/gallon and premium for $2.65/gallon, the Pure will burn $0.0646 worth of premium fuel per highway mile while the Yaris burns $0.0681 worth of regular. In the city, the Pure burns $0.0803 worth as the Yaris burns $0.0845 worth. Because the Pure is fundamentally designed as a city commuter car (though I see them on the freeway) let's analyze a 10,000 mile year (lower than the mean but reasonable for a city car) consisting of 90% city miles. The Pure would burn $723 worth of premium while the Yaris burns $829 worth of regular. The Pure saves $106 in the year, not enough to make a car payment but I would certainly bend over to pick up an envelope with that amount in it.



In terms of carbon dioxide, the Pure would emit something like 5,490 pounds during this "typical" year while the Yaris was emitting about 6,250 pounds, a difference of 760 pounds. The average US family emits something like 22,880 tons of carbon dioxide per year (though I question the accuracy of that figure) so the 0.38 tons saved by the Pure compared to the Yaris seems rather small. In comparison to replacing an incandescent bulb with a compact fluorescent though, it's a big deal.



Is the smart fortwo Pure (or the other higher priced models) worth the sacrifice? For someone who must spend lots of time (and miles) alone or with another person in a car and doesn't anticipate a lot of highway driving, or as a second car in a two car family, it may be a good choice economically. Is its 33 m.p.g. city and 41 m.p.g. highway mileage as good as I'd expect from such a diminutive vehicle? My initial gut reaction was "no" but I'll take a look analytically in another post.

The Obama High Speed Rail Initiative

President Obama has proposed a $13 billion dollar high speed rail initiative. Based on the statements accompanying his announcement, it would appear that Obama's primary motivation for this program is economic stimulus, although he did state that "we must start developing clean, energy-efficient transportation that will define our regions for centuries to come."



So, how efficient is rail transportation? Surprisingly, not particularly. While the famous CSX claim that railroads can transport a ton of freight 436 miles on a gallon of fuel is factually correct, this outstanding efficiency would not seem to carry over to our passenger rail system. In 2005, Amtrak reported an energy intensity of 2,935 BTU/passenger mile. Using 129,500 BTU/gallon for diesel #2, this is about 44.1 passenger miles/gallon. If I'm on the freeway in my Land Rover LR3 with a passenger in my car, I do as well or better (net of the conversion from the energy equivalent of diesel fuel in automobile gasoline).



On the other hand, very high figures for passenger miles per gallon can be found. For example, on the French TGV Duplex on the Paris-Lyon route with two intermediate stops, the train consumes 17.65 kilowatt hours/train-kilometer over a distance of 427 kilometers, or a total consumption of 7536.55 kilowatt hours. This is 2.7132x10^10 J (joules). This train has 545 passenger seats and if we assume an occupancy factor of 0.8, we see that the train converts 0.0404817 kilowatt hours/passenger kilometer.



Finding an equivalent passenger miles/gallon figure is fraught with difficulty, but let's proceed undaunted. I'll assume a diesel generator with efficiency of 50%, we find that the generator would use 276.26 btu/passenger kilometer or 444.6 btu/passenger mile. This is the fuel in 3.4332*10^(-3) gallons of diesel fuel. This is 291 passenger miles per gallon of diesel fuel. Wow, big difference!



What explains this huge difference? Part of it is the load factor. In fiscal year 2007, Amtrak's load factor was 48.9%, so increasing this to 80% (though this article states that a load factor of 65% technically makes a long distance train sold out, because allowances have to be made for entraining/detraining passengers at intermediate station stops) would effectively increase the passenger miles/gallon to (80/48.9)*44.1 or 72.1 passenger m.p.g. This is still a sad comparison to the TGV Duplex and not much better than airline service. I haven't been able to explain the remaining discrepancy.







The geographical areas contemplated by the Obama plan would seem to make sense for the types of route on which the TGV, for example, excels. That would be routes of intermediate length connecting the center portions of relatively large concentrations of population. There are further advantages of new rail over new road. Most importantly, for a given capacity, the amount of land required for rail is much smaller. This assumes, of course, that that capacity is actually used but the same can be said for passenger cars.



On the other hand, evaluating only from an energy efficiency point of view, it would seem that intercity bus service with a high occupancy factor is easily the best option. And to the extent that people could be induced to leave their cars for buses, the need to build new infrastructure could be avoided. This may be one of the reasons why it doesn't happen.

Clean Tech

Last Saturday morning I hopped in my Piper Saratoga and flew it from Long Beach, CA to Houston, TX to attend a conference called "Clean Tech." This was, of course, ironic at best and hypocritical at worst, given that the theme of the conference was renewable energy, clean technologies, etc. But it was a nice flight. In any case, I got plenty of material for multiple posts, which is a good thing, since the well had run a bit dry.



Today, the keynote address was given by James Woolsey, former head of the CIA and currently a Senior Vice President at Booz Allen Hamilton and a venture partner at VantagePoint Venture Partners. I found him to be entertaining, well-versed, and engaging. He's a long-time advocate of strong steps to ween ourselves from our security threatening dependence on oil and is quite aware of the issues surrounding peak oil.



I had a chance to speak with Mr. Woolsey for a few minutes after the session. He had advocated taking a series of steps that would result in drastically reducing the role of oil in our society. He drew an analogy with salt in the pre-refrigeration days, when it was the only method of preserving meat. Wars were fought over salt, over trade in salt, etc. He pointed out that technology enabled us to move past the point where salt was anything but a commodity, and outlined his vision for doing the same with oil.



I don't think it will be so easy, but my question related to the effect such a development would have on the political stability in Saudi Arabia, who has already warned us not to be hasty about moving to reduce our dependence on their oil. His position is "better now than later, when they are a nuclear power," certainly a point well taken.



We also spoke briefly about what it takes to get things done in the United States. I suggested that we have developed and refined a nearly flawless system for preventing significant programs from being implemented. Mr. Woolsey pointed out that World War 2 was a counterexample, recalling how the Detroit auto industry turned on a dime to the manufacture of war materials. My regular readers (are you there dear?) will remember that I've pointed out on multiple occasions that the single-minded, goal oriented, "we're all in this together" environment of that time is exactly what is needed and what is missing as we suffocate in our current miasma.



I suggested that the incredible accomplishments of that period couldn't have been made had the political and social environment then been similar to what it is now. He conceded that it will be difficult but stressed that that makes it even more important that we do whatever it takes to achieve consensus around a demand for action.



All in all, I found Mr. Woolsey to be optimistic and determined. It could be argued that he has a dog in the fight financially (several dogs, actually) but I play a lot of poker, and I don't think he's bluffing. It's heartening that people with knowledge, access to capital, and political connections are moving in the right direction.


Credit to Brian at The Goleta Air and Space Museum, an online aeronautical photo and video collection, for the picture of my Saratoga.

I've stopped reading James Kunstler

Yes, I've done it. James Howard Kunstler, for those who don't know, is a journalist who's written for Rolling Stone Magazine, among others. As always, the most authoritative source of information about him can be found at Wikipedia, the source of all truth (or truthiness), here.

Kunstler's schtick, and I use the word quite intentionally, is that we're headed to hell in a hand basket. He covers so much ground that a small post such as this really can't do it justice, but fundamentally suburbia is a waste of resources, he doesn't care for fried foods, strip malls are appalling, big box stores worse, the automobile is doomed, airlines will be history, stocks worthless, the U.S. dollar not worth the paper upon which it's printed, "big agriculture" is doomed, NASCAR fans have low IQ's, nearly everybody is shallow and self-indulgent, etc. Most of these things are are either symptoms or causes (or both) of peak oil and living on credit.

Fundamentally, Kunstler's complaints are always the same, or at least extremely similar though a little topical, and his recommendations are few and simple. We need to rebuild our intercity rail transport system, abandon suburbia and the automobile, farm close to where we eat with dramatically less "inputs," and let broken things (the banking system, the so-called "warehouse on wheels" system, the capital allocation system, the airline system, among others) crash and burn. He's written several fictional and non-fictional books on these topics, such as "The Long Emergency," "The Geography of Nowhere," and "World Made by Hand."

Now, please don't misunderstand, I agree with many of Kunstler's positions and quite a few of his recommendations. As regular readers will know, I've expressed views along these lines and still hold them. But I do reject his strident tone, his incessant badgering and finger pointing, and the repetitiveness of his screed. There's a place for that but it's not everyplace.

To impart the flavor of his writing, Kunstler's column is entitled "The Clusterfuck Nation Chronicles." He uses "Cheez Doodles," the "Banker Boyz," Salad Shooters, and NASCAR as his metaphors for the descent of the nation into hopeless and mindless consumerism and rampant something-for-nothing thievery and grift. He comes across as smug and self-righteous, and clearly thinks he's the smartest guy in the room, no matter the room. He has quite a following, he's often quoted and most people in the peak oil community know of him and read him.

Kunstler also made similar predictions of catastrophe for Y2K and, as I wrote, Y2K WAS a disaster. It just wasn't the kind of disaster he anticipated. As usual, he rationalizes the reasons.

I also detect just the slightest whiff of hypocrisy; he's recently blogged about his trips to Aspen, CO and to Johannesburg, South Africa. He didn't bicycle to Aspen or take a sailboat to South Africa. But I'm sure it was for a good cause.

OK, I get it. We're short sighted, narrow minded, selfish, lazy, arrogant, self-indulgent fools. That's what Kunstler has taught me. I think I've learned all I can from him and I'm moving on. Anyway, John Lennon said it better.

Debt is a commodity too

I've been reviewing some of my posts (self-indulgent but, in a way, gratifying too) and they caused me to wonder. I've complained and I've listened to others complain that the United States is getting out of the business of producing things. We're running out of many natural resources (uranium, crude oil, iron ore, etc.) and we've decided to outsource much of our manufacturing. And yet we have the highest standard, or at least among the highest standards, of living in the world. Certainly we have, by far, the highest per capita rate of energy usage which is a reasonably good proxy for standard of living. The things comprising this standard aren't free, and since we aren't selling manufactured products or raw materials, what are we exchanging?



The answer is obvious, we're exchanging debt. But what is debt? It's the right to collect something of value from us at a future time or at future times. In that sense, it's a commodity. When I buy an "oil future" I exchange cash (not even the actual amount of the quantity of oil I'm committing to purchase times the unit price at which I'm committing to purchase it) for the right and the obligation to accept delivery of the oil at a fixed date and price. In this way, U.S. debt can be regarded as a "production future." China, for example, exchanges yuan for the right to receive dollars at or over a future period of time. The value of those dollars may rise and fall.



U.S. debt's value as a commodity is tied to our ability to, at some future time, produce or extract things of actual value. In this way, it's also like oil. We don't want oil to have it, we want oil to use to do things. The Chinese (and the various other governments, NGO's, pension funds, etc.) buyers of our debt want to use it to do things as well. Given that our ability to extract natural resources, manufacture durable and non-durable goods, etc. is declining, what would these holders like in exchange for the debt that they own?



One thing is intellectual property, but this is quite risky since any such property is easily copied. Ask Sony, the RIAA, any drug manufacturer, Microsoft, etc. One might say the holders of the U.S. debt could want dollars, but only if those dollars can be exchanged for things with some intrinsic utility.



For this reason, U.S. debt is a commodity whose value is dependent upon the perceived ability of the United States to produce a surplus of something of value. It's been amazingly resilient considering the amount of the commodity already produced and the trends for our ability to produce things of value. It's hard for me to see how perception of the ability to exchange U.S. debt for things of real value can withstand the facts on the ground.

Horsepower, fuel efficiency, and thermodynamic efficiciency

I received a comment to my post on the Moller Skycar Volantor suggesting that I "look up the Wankel rotary engine (Mazda RX8) - 1.3L = 200+ HP." I'm not completely sure what the commenter was getting at, but I think he or she was saying that it's possible to get the power claimed by Moller in a package of the type he claims to have it in. Let me be clear (quoting our President): I agree. There's no question in my mind that that's possible. I didn't discount that possibility in my post.



What I did say isn't possible is to develop that amount of power and still achieve 20 miles per gallon of fuel at the speed claimed. That is, the combination of airspeed, fuel economy, and engine power claimed is not realistic. I'd like to delve into this in a little more detail. An internal combustion engine works by taking some combustible fuel into an enclosed space and igniting it. This results in a large temperature rise, and the consequent increase in pressure is used to push down a piston, turn a rotor, or turn a turbine thus converting the potential energy in the chemical bonds of the fuel into mechanical energy and using it to do work.



Any given fuel has a fixed amount of energy available for release by oxidation for any given mass, volume, or number of "moles" of substance. In a perfect world, unencumbered by the second law of thermodynamics, we could harness 100% of this energy to do useful work. Even in such a perfect world, no more could be had. And once the time over which this chemical potential energy is converted by oxidation into internal energy or "heat" is noted, we can divide the energy in the quantity of fuel (energy available is the same as work that can be done) by the time, we have work divided by time, or power.



For example, my Piper Saratoga PA32R-301T will burn about 18 gallons of fuel per hour to go about 170 knots. A "knot" is one nautical mile per hour, and a nautical mile is 6080 feet or about 1.152 statute miles. So, the plane burns 18 gallons in an hour to go 170*1.152 or 195.6 miles. Thus it's achieving 10.9 m.p.g., but more to the point of this post, it's burning 18 gallons per hour. There are a variety of sites with somewhat differing values for the energy density of the 100LL avgas I burn in the Saratoga (see here and here for example) so I'll use an average of 32.6 megajoules/liter or 123.4 (easy to remember) megajoules/gallon.



So, I'm releasing 18*123.4 megajoules/hour of chemical potential energy. Since an hour is 3600 seconds that's 18*123.4/3600 megajoules per second or 617,000 joules per second. By definition, a joule/second is a watt so this is 617 kilowatts or 827 horsepower. This is interesting, my pilot's operating handbook says that the power setting producing this fuel flow is 70% of the 300 maximum continuous horsepower available, or 210 horsepower. Thus, I'm using (210/827)*100% or 25.4% of the heat released by burning the avgas. This is pretty close to the type of efficiency we've come to expect of internal combustion engines in typical applications.



The maximum possible efficiency allowed by the laws of thermodynamics for a "heat engine" was determined in the 19th Century beginning with the work of Sadi Carnot and is determined solely by the temperature of the working fluid (fuel/air mixture as it oxidizes in this case) and the cold reservoir (the atmosphere) and for reasonable temperatures, as stated in my post on the Moller Skycar, is about 82%. For a working internal combustion engine, the maximum efficiency is related to the compression ratio and, for a typical compression ratio of 10.5:1, works out to be about 61%. Various factors involving friction, the operating points of the engine, inefficiencies in the fuel delivery and exhaust, and many other factors cause the actual efficiency to be as low as it is. These considerations apply equally to the Wankel or rotary engines in the Moller Skycar.



But, if the rate of fuel burn in volume/time and the type of fuel are known (or can be calculated) then the maximum available power can be calculated. An estimate of engine efficiency can then give the power available to turn wheels, turn a propellor, turn a ducted fan, etc. This is what I did in the Moller Skycar post, using the miles per hour divided by miles per gallon to give gallons per hour and thus the heat energy available. This enabled me to demonstrate that the claims made by Moller for the Skycar are not feasible.

"Exponentially" really does mean something

In my never ending quest to understand what people believe about the world, and specifically about energy and fuel economy, I run across repeated misunderstanding of the word "exponentially." This or that "increases exponentially." Now some things do, in fact, increase exponentially. Money in a bank account at a fixed rate of interest comes to mind. The population of bacteria in a petri dish or humans on a finite planet (for a while) are other examples.



But it means more than "gets big quickly." People who should know better, or at least should learn better before using it this way frequently use it to mean this. An example is an article at the Planet Green web site entitled "Become a "Hypermiler," Save Even More Gas" by one Collin Dunn of Corvallis, OR. As usual, driving more slowly is first on his list. OK, I agree completely, but then he states that "The amount of drag your vehicle generates increases exponentially with each increase in speed; that is, driving a little faster generates a lot more drag, which requires more gas to overcome."



Well, it's just some guy writing an article for a Cable Channel web site, right? But he got this gem from the Toyota Open Road Blog where they go into detail to precisely state their error: "The amount of drag your vehicle generates is not linear – it does not increase at the same rate as your vehicle’s speed does. Instead, drag is more or less proportional to the square of speed. It increases exponentially." NO, NO, NO!



"More or less proportional to the square of speed" is correct. That is, if you know the drag at some speed, and want the drag at some other speed, take the ratio of the second speed to the first, square it, multiply the drag at the first speed by the squared ratio and there's your approximate drag at the second speed. For example, doubling the speed would approximately increase aerodynamic drag by a factor of four. This is NOT exponential, the mathematically astute refer to it as a power function. The variable (speed) is the base, the power (2 in this case) is the exponent. The exponent is fixed.



An exponential function has a fixed base, and the variable is the exponent. Now, depending on the ranges of the variables and the fixed numbers and the proportionality constants, the exponential function may be smaller than the power function at some values of the variable, but the exponential function is always ultimately larger for large values of the variable. So while something that increases exponentially really does get large very fast, at least after a while, it's not true that anything that increases quickly at any point increases exponentially. This most assuredly does include aerodynamic drag.



And don't even get me started on "mega."

A potpourri of cluelessness

In my reading of various blogs, news articles, forum posts, etc. I've encountered a large number of writings indicative of the strange and distorted ideas people have about the subjects of this blog, that is, of fuel economy, energy use, physics, and life. I've decided to periodically quote some of them along with, where it's relevant, my own comments.



The following is from Physics Forums where the question was "Does RPM affect gas mileage?" An answer was:



"Assume that you travel a set distance at the same speed, first in 3rd gear, then in 4th. Can you see that the engine will turn more times in the lower gear. Each revolution of the engine will "consume" the same amount of air/fuel mixture. Therefore you must consume more air/fuel mixture at the lower gear.



Now a lot of modern engines are getting smarter about feeding fuel so, the assumption of a constant a/f mixture may not be valid. With intelligent fuel metering the millage difference may be small.



The biggest difference to fuel consumption is your rate of acceleration. If you like to feel some acceleration and take pride in your ability to get to 60mph (100kph) then you will see improvement by playing "old lady" for a while.



You do more work when doing 5s to 60 vs 10s to 60. This increased work MUST be reflected in fuel consumption."



Well. The fact is that RPM will affect gas mileage but this guy's argument is full of errors. He (I assume it's "he") correctly states that the lower gear will require more revolutions to travel a given distance than a higher gear, but then claims that each revolution will consume the same amount of fuel/air mixture regardless of the gear. This is false. The lower gear will travel a lesser distance and therefore do less work for each revolution, thus requiring less throttle since the gear ratio will give a greater mechanical advantage. But you'll need to apply this lesser throttle through more revolutions of the engine. Now, due to throttling and frictional losses, you'll be less efficient in the lower gear but it's certainly not true that "Each revolution of the engine will "consume" the same amount of air/fuel mixture." And this was true before cars included computerized controls, it's only a matter of the throttle position.



Next, "Integral" (his screen name, complete with integral symbol avatar) is completely off base with his concept of acceleration and work. Going from 0 to 60 adds the same amount of kinetic energy to the car, and thus takes the same amount of work, regardless of whether it's done in 5 seconds or 10. It's true that taking 10 seconds is more fuel efficient, since the energy is added over a longer distance but Integral confuses work with power. And this is from a Physics Forum where he has enough posts to be a mentor. Further, someone points out his errors and he stridently defends them, even insulting the corrector.



Moving on, "Josh," in reply to a tip at Daily Fuel Economy Tip that suggested minimizing use of electrical accessories said: "This is simply not true …. and alternator is not operated on a clutch therefore it spins at the same speed no matter what is being used in the car. It is not on a clutch like the AC that just kicks in when the compressor comes on."



Of course, this is false. Raising the electrical load causes an increased magnetic field in the alternator field coil, resulting in a larger torque to be overcome by the alternator drive belt, thereby using more fuel.



These are merely misunderstandings of fundamental physical principles and don't reach the heights of looniness achieved by some of the more "outro" world wide web denizens. I'll cover more of each type in subsequent posts.

The Moller Skycar

Since I was a little boy, there has been talk of flying cars. And since I was a little boy, Paul Moller has been a short few years away from going into production on such a vehicle. He still is, though now it's called the Skycar Volantor. It's reminiscent of the wag's remark about fusion energy: "fusion is the energy source of the future, and always will be."



But what about the M400 Skycar? It's "specifications" can be found here. What a fine way to get around! 275 m.p.h. cruise at better than 20 m.p.g. It's stated that the production model will employ eight rotary engines rated at 150 h.p. per engine burning any of a variety of fuels, but ethanol is suggested. This is the power required for the vertical take off capability. At this site, there are a variety of videos, including a hover test of the M400, it apparently will get off the ground. There are also some specifications wherein it's indicated that the "nominal continuous power" is 720 horsepower and the fuel is ethanol. This would be running at 60% power and makes sense. It's not stated whether the engines are turbocharged, but they must be since the operational ceiling is stated to be 36,000 feet (!).



So let's take a look at a vehicle utilizing internal combustion engines to get 20 m.p.g. (the specs. say ">20" so this should be conservative) at 275 m.p.h. This means it's burning 13.75 gallons of ethanol per hour. OK, we find here that ethanol has an energy density of 6,100 watt hours/liter, or about 83,100,000 joules/gallon. So the total available energy in 13.75 gallons of ethanol is 1,143,000,000 joules. Burning this in one hour or 3600 seconds at 100% efficiency will produce 317,395 watts or 426 horsepower. This means the Skycar's engines are using fuel with an efficiency of 169%. I rather doubt it.



Let's suppose, then, that the figures come from burning gasoline. Gasoline has a significantly higher energy density, and would mean the claim is only an efficiency of 106%. Still higher than the figures one typically sees for an internal combustion engine. All right, suppose that the 720 horsepower only applies to the "top speed," listed as 360 m.p.h. Now, with gasoline, we're looking at an efficiency of 81%. Well, at least it's no longer in the category of the "over unity" nut cases, but I've never seen a real engine with such a specification and, unless it's operating at a very high temperature and dumping into a very cold reservoir, thermodynamics won't allow it. If a heat engine is operating from 1500 K into a reservoir of 273 K (about 2240 degrees fahrenheit into 32 degrees fahrenheit) the absolute theoretical maximum efficiency is 81.8%. No real engine comes close.



Is 720 horsepower sufficient to produce a speed of 360 m.p.h.? It's likely that it is. The Piper Meridian, for example, utilizes a Pratt & Whitney PT6A-42A turboshaft engine running at 500 horsepower to cruise at 260 knots, or about 300 m.p.h. It burns on the order of 40 gallons of Jet A fuel each hour to do it though. Speed available goes up approximately with the cube root of power, so 720 horsepower should be able to give an increase of about 12.9% over the Meridian, all else being equal. This would be about 339 m.p.h. Maybe the Skycar is a little aerodynamically cleaner, maybe its ducted fans are slightly more efficient than the Meridian's propeller. I'll call it plausible.



So if the Skycar were to be a real product, what are its claimed advantages? Well, it's driveable at low speed from your garage to an approved takeoff location where it can take off vertically. It's being designed, ultimately, to be fully automated, no pilot intervention necessary, and thus able to be used by those with no flying skills of any kind. You were previously able to buy a place in line for a production Skycar at a cost for delivery of about $400K to $1M (according to some dated web sites) depending on where in line you were. You could put only part of that down to reserve your place. It seems that that's no longer the case though.



Dr. Moller is now stating that, in limited production, the M400 Skycar Volantor will sell for about $500,000 and be available in "about three years." In mass production (i.e., when everyone you know is buying one) they'll sell for $60,000 to $80,000. If you'd rather own the company than the Skycar, it's sold over the counter as MLER.OB on the OTCBB ("Over the Counter Bulletin Board"). You can peruse the financials here. Note the negative book value. No wonder they're not taking deposits. Its market capitalization values the company at $8.27M, with 54% owned by insiders and 5% holders. Pretty thin. You just can't beat the laws of thermodynamics.

More on wind

In my post on headwinds I bemoaned the destruction of fuel economy I suffered in driving head-on into our Southern California Santa Ana Winds. I drove home in the rain last night, and began thinking about the effect of rain soaked roads on fuel economy so, naturally, I Googled it. As commonly occurs when Googling fuel economy related issues, a highly placed hit took me to an ecomodder post. That led me, in turn to a site where a Prius fanatic (zealot?) writes about a "Prius Palm Mileage Simulator." I don't have a Prius, nor do I have a Palm but this software appears to be truly amazing. I can't begin to do it justice in this post, but I'd strongly recommend that anyone reading this take a look.



In any event, the author of that site writes about the effect of wind on mileage. As is common in my reading, he brings up many points I had not considered. The kernel of the information is that wind is much worse than I had considered. For example, to a first order approximation, wind from 70% of the compass will hurt mileage. Even wind with a significant tailwind component hurts, and a direct crosswind of a given magnitude hurts worse than a similar direct headwind. I have to take his word (and that of his software) for this at this time because the analysis would be complex. I assume the reason crosswinds and quartering tailwinds are detrimental is that, in order to maintain a desired track, one must steer into them. This, it seems to me, would have two negative effects: necessitating the force vector applied by the road to the vehicle to be misaligned with the direction of travel; and increasing loss of energy to the tires as they are traveling in a direction outside of their plane. This must increase their rolling resistance.



The tire situation would be, I suspect, quite complex but I can quickly run some numbers and find out, to at least a first approximation, the effect of the force. I'll assume (I always must make assumptions) that I want to move down the road at 55 m.p.h. and that a direct crosswind (i.e., at precisely 90 degrees to my direction of travel) of 15 m.p.h. is blowing. What effect is this likely to have?



I'll need to determine the force on my LR3 from the crosswind. From this Motortrend location I found the dimensions of my vehicle and determined that the area presented to a direct crosswind to be 9.18 m^2. I don't know the coefficient of drag for the LR3 in that direction and at that wind speed, so I'll assume it's worse than the 0.41 for wind on the nose, let's say 1.0, or pretty darn bad. That would mean that the wind is pushing my vehicle to the side with a force of about 248 N (Newtons, or about 56 pounds).



I calculated in this post that it takes a force of about 743 N to propel the LR3 at 55 m.p.h. Working the vector equation (or finding the hypotenuse of the right triangle), it will take about 783 N to produce a resultant force of 743 N in the direction of travel. Since, at a fixed speed, fuel consumption is directly proportional to force to be overcome, this increase of about 5.4% in force would result in a 5.4% increase in fuel used per mile, or just slightly over a 5.1% reduction in m.p.g.



If this is true, and if the Prius fan's program is correct, much of the deterioration in gas mileage caused by a crosswind must come from an increase in tire rolling resistance as the steering wheel is held into the wind since a 15 m.p.h. headwind will certainly result in more than a 5% decrease in gas mileage. I'm not sure how to calculate this effect, maybe I can get the owner of that site to enlighten me.

Off topic (but important)

The problems facing our nation and our civilization are such that well-meaning and intelligent people can differ not only on appropriate policies but on what facts are important. These problems are incredibly complex and highly interrelated. They include, among others, humans' effect on the geophysical environment (climate, erosion, overfishing, pollution, resource depletion, you take it from here), overpopulation, arms proliferation, intolerance (racial, ethnic, religious) and others.



I happen to be watching a bowl game (Utah vs. Alabama) on FOX TV. A pure escapist waste of time to be sure. But during a commercial, there was a promo for the local news, it featured the death of John Travolta's 16 year old son and a guy who makes furniture from empty Budweiser cans. I'm not making this up. This was followed by a promo for another season of American Idol.



Yet we have the turnover of the Green Zone to Iraqui forces, the Israelis bombing the Gaza Strip with tanks and troops on the border, Pakistan (a nuclear power) descending into chaos on the border of India (a nuclear power), Russia (otherwise known as Gasprom) shutting off natural gas supplies to the Ukraine, nearly all of Africa in a state of disorder resulting in starvation, genocide, and cholera, both the U.S. and world economies operating (or failing to operate) in a manner unfathomable by those trained to understand it and those elected or appointed to control it, and a host of other issues that could result in TEOTWAWKI.



I read various blogs (of all orientations: liberal, conservative, those who believe anthropogenic global warming is a fact, those who believe it's wrong, a hoax, or a conspiracy, etc.). The alarming thing is the commentary to these blogs. Much of it is clearly from those who are on the edge of their chairs waiting to see the Budweiser furniture guy on the "news" and who will be the next American Idol. They clearly are uneducated and unthinking. How has this happened? This is not a rhetorical question, I would really like a cogent explanation.



Most alarmingly, these people vote. I don't know if the level of discourse in other countries is as retrograde as it is in the United States, I truly hope to God that it is not. I've blogged before (here and here) about the tendency of spokespersons (of any persuasion) to filter factual information through their own philosophical belief system - that is, to decide what the facts "must be." This is bad enough, but it's compounded by their legions of American Idol watching acolytes who accept it as true. In a thoughtful, educated society this could not happen. And these pathetically uninformed and ignorant, yet highly opinionated people vote.



And every sign I see indicates that it's getting worse, not better. When our Constitution was written, there were many problems but the amount of information to be digested and factual material to be learned in order to address those problems was dramatically lower. Even then, not everyone could vote. Not even every Caucasian male could vote. But now one needn't have the most basic scientific, economic, political, philosophical, or critical thinking background to vote for those who will attempt to solve the problems I listed above. One needn't even speak English or read.



This must be changed, and in both a top down and bottom up manner. This means with educational (or at least knowledge) testing for a "voting license," and a complete overhaul of how Americans are educated. Unfortunately, there are the proverbial two chances of either one happening.

Yet another look at alternative transport

At the risk of redundancy, I'll point out yet again that one of my most common internet haunts is the ecomodder web site. It's a fantastic place for knowledgeable discussion, news, and ideas regarding nearly anything connected with minimizing energy consumption (usual disclaimer, it should be energy conversion since energy isn't consumed). Today, there was a forum post about a new electric motorcycle.



I've posted before about alternative personal transportation, and most recently concluded that, for me at this time, it's impractical. Can this new development change my calculus?



The "Electric GPR" is apparently not yet available, however, one can be ordered at a retail price of $8,000. This is about 2.3 times the most recent cost of the Zapino I evaluated in my previous post. The aspect of the Electric GPR that makes it worth a look is its status as a street legal motorcycle and, at least as claimed by Electric Motorsport, freeway capable. Should it be actually so, I could anticipate a commute time approximately the same as the one I suffer in my Land Rover LR3 HSE. Readers may recall that one of the key negative factors in my evaluation of the Zapino was that it would have to be ridden on surface streets and thus would add dramatically to my commute time.



As to specifics, the Electric GPR utilizes a lithium ion battery with a capacity of 3.3 kilowatt hours (11,880,000 joules - the amount of energy available in a little under a tenth of a gallon of gasoline). It powers a 50 volt Etek RT motor apparently manufactured by Briggs & Stratton. It's advertised as having a range of 35 miles in "power mode" and 60 miles in "economy mode." Obviously, since my freeway commute is a little over 30 miles, economy mode would be the ticket. I'm not able to determine whether economy mode means no freeway riding at 55 m.p.h.; if so, it's obviously disqualifying.



Suppose that it's capable of commuting from my office and climbing the final (steep and long) hill to my house. Do I want to be on a California freeway in the far right lane at 55 m.p.h. on a 285 pound motorcycle that makes no noise? I have a very limited history with riding and no one would imagine that I'm an expert, so there would appear to be a very strong element of danger. Can extreme caution make this a controllable risk? I don't know.



What about the economics? It's not so easy to estimate this, what with the extreme volatility of gasoline prices. This is obviously the largest factor in determining the return on investment in such an asset. Do I use $4.959 (or higher) as I paid in June, 2008 or $1.939 as I paid at my most recent fill up? I'm going to use $3.00. My personal belief is that, in the period of the next couple of years, that number will underestimate the average cost of gasoline and therefore my calculations will be conservative (in the engineering sense).



I would imagine that I'll use about 2.8 kilowatt hours of energy for a 32 mile trip. In order to replenish the battery, I'll have to use 3.3 kilowatt hours of electricity (assuming the charging system is 85% efficient). This will cost me about (because of the tiered system of electricity billing, I have to assume the worst case) $0.4330 for a cost per mile of $0.0135. The LR3 at $3.00/gallon would cost about $0.146/mile or a little over 10 times as much. Assuming I'd be able to use the motorcycle 180 days per year at 62 miles per day, I'd save about $4,600 per year.



The LR3 is under warranty and thus maintenance costs are currently nil, so any maintenance or replacement reserve for the Electric GPR would be a pure cost with no offset. Since the warranty is only one year (!) I suspect that maintenance would not be negligible. But let's make a pessimistic assumption that it would cost $1,000/year. That would mean that it would take something on the order of two years and three months to pay for itself. This is a very simplistic way of looking at return on investment but it certainly indicates that, from a purely economic point of view, the purchase decision should be positive.



The thought of being obligated to ride a light motorcycle on California freeways to make an investment pay off is daunting, however, and I think that will turn out to be the determining factor.

Trade deficit

Because we are consuming significantly less oil and that oil is much cheaper than it was a short six months ago, and because we import a large portion of the oil we use, one would expect a very large reduction in our monthly trade deficit beginning sometime around mid-summer of 2008. In most ways, this is a good thing though it's certainly the byproduct of some very bad economic conditions. Nevertheless, if we continue to import the same fraction of our oil as we did last summer, we should see a net reduction in trade deficit of something like $1.3 Billion per day, or just under $40 Billion per month. This is serious money, even by U.S. debt standards.



It's my opinion that immediate steps should be taken to invest this money in the things that will soften the blow. But since the money isn't really sitting in a pot but rather in the pockets of those who purchase fossil fuel (at any level), what method can be employed to "pool" this money? There are certainly a couple of ways. One would be to place a tax on fossil fuels in one form or another, and let the government determine how to fund the various projects that would be necessary to accomplish the goal of transition to a future of severely limited fossil fuel availability. As regular readers of my blog will know, I'm not a fan of government involvement, being a libertarian philosophically.



So, what else? I'm a strong believer in the innovative capabilities of the entrepreneur. Therefore, I would propose a program of incentivizing this type of entrepreneurial activity with tax incentives, research grants, regulatory encouragement, and team building. Now, I concede that this doesn't sound like laissez faire economics. But as I've mentioned in previous posts, our "this quarter's bottom line" corporate environment (with its consequent risk of shareholder lawsuits and loss of control to pirate capitalists such as Carl Icahn - see here or here) is ill-suited to undertake long term projects that throw off so-called "public goods."



How to evaluate the projects these policies would be meant to encourage? Well, this particular blog isn't about carbon footprints, but I think a good way to determine the extent to which a given project would be effective in reducing our need for fossil fuels would be to estimate the net reduction in CO2 emissions as a result of that project. I haven't worked out every detail (in case anyone hadn't figured that out) but I'd love to get feedback on this proposal. There really is no time to lose.

A stunning drop

No one can have failed to notice the precipitous drop in gasoline prices. I keep complete records and try to always utilize the same pump at the same gas station for every fill up in an attempt to eliminate one possible variable from the data I gather. On June 17, 2008 I paid $4.959 per gallon for fuel. My most recent fill up was at $2.139 on December 3, and the price at that station has declined since then.



But oil prices have dropped from about $147/bbl to $40.81 currently. This is quite remarkable, and so I started doing a little research. A wonderful source for all things related to fossil fuel consumption in the United States is Energy Information Association web site. The link is for a summary page, going deep into the links can provide nearly any statistics one could want.



One revealing table concerns U.S. Crude Oil and Petroleum Products Product Supplied (Thousand Barrels per Day). This statistic stands at 17,796,000 bbl/day in September of 2008. In August of 2007, it was 21,434,000 bbl/day. This is a decline of 17%. Until recently, the question of whether the U.S. was in the midst of a recession was a matter of debate. While that debate seems to have been settled in the affirmative, such a drop in what is the life blood of, literally, every sector of the economy puts an exclamation point on this fact. And, in fact, this reduction in the U.S. amounts to about 4.5% of world wide fossil fuel consumption. Considering how exquisitely balanced supply and demand are, it is small wonder that the contracting economy and the consequent demand destruction for fossil fuel has resulted in a dramatic reduction in prices for forward contracts of crude oil.



What is to be made of this? In my opinion and as I first stated in a previous post, it is, in one sense, a huge opportunity. It gives us a chance (albeit a brief one) to start the process of retooling our economy (and our lives) for a time when cheap and easy energy is a thing of the past. How to do it?



As much as I chafe at his strident language and reject much of his finger pointing, some of the ideas of Jim Kunstler provide a constructive start. He recommends, among other things, rebuilding our intercity rail system and our local farming and manufacturing capabilities. I would add utilizing the (temporary) ability to purchase energy at bargain basement prices to utilize those manufacturing capabilities to invest in our energy infrastructure and localized energy production (bad word - energy is never produced but you know what I mean) and distribution.



But in a nation of Walmart consumers, self-satisfied and self-indulgent baby boomers, MTV, Fox TV, and Lil' Wayne watchers, Obama voters who think "now I don't have to worry about filling my car or paying my mortage" because the government will take care of them, so-called sports fans who brag that "if they (opposing fans) come into our house, they'll get a beer in their grill," what chance is there? I can only hope that Obama (as a point of information, I voted for Bob Barr) is able to parlay his wave of popularity into motivating his constituency (and those who aren't part of that group) to engage in the hard work of rebuilding our economy and our society.

Is it "winter blend?"

My 10 fill-up moving average fuel economy has declined steadily from 21.76 m.p.g. for my September 25 fill-up to 21.03 m.p.g. for my most recent fill-up on November 26. This is quite significant and is obvious in the graph of that statistic. Clearly I'd like to know the cause of this deterioration, which amounts to well over 3%. Among other possibilities are: more traffic jams and city street driving; vehicle maintenance issues (tire pressure, wheel alignment, etc.); and air temperature. But another possibility is the switch to so-called "winter blend" fuel which, as best I can tell, takes place around September 15.



There's a very good article produced by Chevron that discusses many aspects of automobile gasoline. It's written at a level appropriate for a curious layperson, i.e., not as a scholarly journal article but with a higher intellectual content than a brochure or other mass consumer outlet. It discusses a huge variety of issues with respect to gasoline formulation, but for this post I'm focusing on a statement that "The heating value of winter gasoline is about 1.5% lower than summer gasoline because winter gasoline contains more volatile, less dense hydrocarbons."



Heating value is how gasoline chemists and physicists evaluate the energy content of gasoline. There are a variety measurements (i.e., units) for this characteristic: b.t.u./gallon; megajoules/liter; etc. I typically calculate using a bastardized unit of megajoules/gallon. This makes various calculations easier for me, since joules are a S.I. unit of energy and are convenient for energetic calculations, but gallons are what I buy at the pump. Clearly, the less heating energy available in a gallon of fuel, the shorter the distance that gallon will take my vehicle.



So, while it's certainly possible that the switch to winter grade gasoline is a part of the reason for my deteriorating fuel economy, it doesn't seem at all likely that it's the full explanation. Among other pieces of evidence that this isn't the full story, I did not suffer a similar decline in fuel economy in September of 2007. There was a similar declining period in January of 2008, however. Could it be that the switch to summer blend was, for some reason, delayed in the winter of 2007-2008 as compared to 2008-2009? I can find no indication of anything like this.



As to the other possibilities, it is true that I subjectively feel like my recent trips have been more stop and go, and local. But my average speed over the subject tanks has shown a very small decline. Of course, I plot my fuel economy vs. average speed and so I can say that the decline noted above would be equivalent to about a 3.5 miles per hour reduction in average speed over the period of time in question. I don't see this in the data either. That leaves maintenance issues and other random factors. I'll keep looking.

The plunge in oil and gasoline prices

No one can help but have noticed the dramatic fall in prices of fossil fuel and related commodities. Nationwide, regular gasoline is well under $2/gallon. As readers of this blog might imagine, I track the price paid for each tank full, as well as the gasoline cost per mile. I use premium in the Land Rover LR3 HSE and the price for my most recent fill up was $2.459/gallon, down from a high of $4.959/gallon on June 17 of this year.



Does this dramatic drop indicate that concerns about gasoline price and availability are a thing of the past? It does not. These prices are driven by a huge variety of factors, but the number quoted for "oil price" in the news is the nearest month futures price for "light sweet crude" on the New York Mercantile Exchange. There, you can find prices for a huge variety of commodities and a range of contract dates. For example, the closing January, 2009 (the nearest month) price for light sweet crude is $49.93/bbl, whereas the June, 2009 contract closed at $55.05/bbl. There is so-called "open interest" in contracts out as far as December, 2016 which closed most recently at $85.98/bbl.



This last is surprising, given the recent revelations of the International Energy Agency (IEA) report of looming production shortages. The IEA does not have a history of underestimating production capacity, quite the opposite. Yet the price of oil falls.



Already, alternative energy and unconventional (tar sands, etc.) oil projects have been shelved or put on hold because, at current prices, they don't "pencil out." In my opinion, this is ridiculously short sighted. By the time such projects would be completed, the energy produced would surely be profitable. It could be argued that the executives involved know more than I do, and I'm sure they do. But they're constrained by a system that holds them responsible for maximizing results on a quarterly basis so that the price/earnings ratio maximizes share value. Failure to act in precisely that way leaves the company open to shareholder lawsuits.



Such a system makes it nearly impossible to use this incredible opportunity to find rational and sustainable solutions while we can still operate the economy. The opportunity is unlikely to last. So, we've still got the throttle to the floor with the cliff straight ahead.

The purpose of hypermiling

As mentioned repeatedly, I'm a frequenter of a web site devoted to maximizing fuel efficiency through all available techniques. These include the operational techniques I've implemented in my driving as well as minor and major modifications to vehicles. It's a wonderful site, occupied by people with a variety of philosophies.



Mine is to minimize both my cost per mile, and my overall fuel expenditures (given the fuel hog that I drive). But there are others whose goal is to maximize the miles per gallon irrespective of other considerations. Doesn't their goal assure my goal? It doesn't. Many of these hypermilers will choose a longer route if they can achieve higher miles per gallon, even if that route entails sufficient extra mileage to cause an overall increase in fuel consumed. In other words, these hypermilers treat maximizing the miles per gallon realized as something of a sport.



Is there anything wrong with this? Of course not. As the saying goes, "ya pays your money and ya takes your choice." Certainly, these men and women (mostly men) are not using huge amounts of gasoline to make these choices. I suspect that most, if not all, of them use less fuel than I do over the course of a year. And their efforts are communicated to the group, thus giving those of us who seek to minimize total costs additional data.



So what, in my efforts, controls the overall expenditures on gasoline? Two things are key: miles driven and gasoline price per gallon. Note that miles per gallon achieved are conspicuously absent. It's much easier to save on gasoline costs by driving less and by purchasing cheaper gasoline than by utilizing economy maximizing driving techniques.



Lest people conclude that driving technique matters little, I need to clarify. After purchasing my Land Rover LR3 HSE, I attempted to use the techniques that were effective in my Jeep Grand Cherokee Limited. I found that it was difficult to exceed the E.P.A. estimates and that I was hard pressed to make much difference. This led me to drive the LR3 "normally," that is, as most would drive it. As gasoline ran through $3.00, then $4.00 per gallon I redoubled my efforts. It did make a difference, and if one considers the graph of Cost per Mile as a function of Gasoline Price, it literally separates into two distinct data sets. And the average mileages during each of these phases stand at 16.3 and 20.9 respectively.



And actually, that underestimates what can be done, since the "before" data includes my earliest efforts at trying to save fuel in the LR3 and thus is higher than "normal," and the "after" data is significantly higher in the later fill ups, as I refine technique.



But for the "after" data plotted alone with Cost per Mile as a Function of Cost per Gallon, the so-called "coefficient of determination" is greater than 0.81. In other words, more than 80% of my cost per mile is determined by what I pay for fuel, my nibbling around the edges with driving technique accounts for some of the remainder, and the nature of the driving during the tank full (stuck in traffic, city driving, pure freeway driving, etc.), and other random factors account for the rest.



Thus, regardless of what else I do, I'll leave more money in my pocket if I drive fewer miles and buy cheaper fuel. It's a good thing I have a strong mathematics background, it serves me well in deep analyses such as this.

Aero drag and rolling resistance at varying speeds

As I've brought up in many previous posts, the external forces to be overcome by my vehicle at speed are rolling resistance and aerodynamic drag. I've also mentioned that the aerodynamic drag increases with the square of speed, whereas rolling resistance is independent of speed. The latter contention will be, I suspect, debated by experts. I've read extensively and, though several authors contend that rolling resistance increases linearly with speed, I have found none that support that theory with data or analysis.



My admittedly simplistic evaluation revolves around dimensional analysis. While this topic is far too deep to cover in a blog post, I can at least mention the principle involved. In an equation, the units on the left side must be the same as the units on the right side. For example: distance=speed times time. Distance may be in miles, speed in miles per hour, and time in hours. So on the right side, miles per hour times hours is miles, the same as the left side. Physicists will say "length = speed times time" so that they can use miles, centimeters, inches, furlongs, leagues, or parsecs for length, etc. Thus, they deal with the dimension of length rather than the specific unit of miles, for example.



For our problem, we want to know what affects rolling resistance. Resistance on the left side of the equation we're seeking is a force, so we want to know how force is affected by various things that may be on the right side of the equation. Likely candidates for what might affect this force are vehicle weight and speed. So we look for a combination of the dimensions of weight and speed that result in a force. But weight is a force, so if we multiply it by any power of speed, we'll no longer have a force and the dimension on the right side will not result in a force. While dimensional agreement does not assure the correctness of an equation, lack of dimensional agreement assures its incorrectness.



Now, it's true that dimensional analysis cannot, alone, give the entire equation. It cannot account for constants, for dependence on exponential and trigonometric functions, etc. And the method is also highly dependent on the accurate physical intuition of the analyst in determining the factors that may affect the dependent variable. For example, in this case is tire diameter (a length) a possible factor? Inflation pressure? How about bulk modulus of tire rubber? Certainly these could be factors, but a more thorough dimensional analysis indicates that, at least without taking even more arcane factors into account, they are not. For the physicists and automotive engineers reading this, I recognize that this is very simplistic and yet, to the accuracy possible by reading speedometers, odometers, and gas pumps, I believe it represents a valid analysis.



So, we have F[total]=.5*p*C[drag]*A*v^2+C[rolling]*W where F[total]is total external force on my vehicle, p is air density, C[drag] is the coefficient of drag, A is the flat plate area, v is speed, and C[rolling] is the coefficient of rolling resistance. This can be written as a quadratic equation in v, or F[total]=k*v^2+d where k=.5*p*C[drag]*A and d=C[rolling]*(weight). Using a typical value for air density and the other values for my Land Rover LR3 HSE, k=.775 and d=393. So we have F[total]=0.775*v^2+393.



From there, I can produce a graph that shows the fraction of resistive force from rolling resistance and aerodynamic drag at each speed. Below is a plot of each component of resisting force. The aerodynamic drag is the red plot, the blue is rolling resistance. They are equal at about 22.5 meters/second or approximately 50 m.p.h. I took the graph to 40 meters/second, or about 90 m.p.h. (though that speed is irrelevant to me because I never drive that fast).

Moving beyond hypermiling

Several times I've cited the Ecomodder web site. It was started by the owner of a Geo Metro (actually a Suzuki badged as a Pontiac) who'd created a site to discuss modifications both to his car and his driving style to maximize fuel economy. The questions and email he received at that site convinced him that a more general mileage dedicated site with forums, a mileage log, etc., would be popular. He was right. I'm a fairly active participant at the site and recommend it highly. I've acquired a large amount of very informative and sometimes useful information there.



Many of the denizens of that site extensively modify their vehicles. Such modifications range from minor things such as replacing factory original side view mirrors with smaller ones to complete transformations that make the vehicle nearly unrecognizable. Possibly the most extreme is the Honda Civic owned and modified by an Ecomodder using the screen name "Basjoos." He achieves 95 miles per gallon and is frequently stopped by police, queried by bystanders, and even occasionally interviewed by the media.



My vehicle is owned by my company and is used, on occasion, to visit and transport clients and associates and hence is not a suitable candidate for such an extensive makeover. But what could I do to, for example, achieve an overall ("highway" and "city" combined) fuel economy of 25 m.p.g. (I'm currently at 21.6 m.pg.) without making my vehicle a spectacle? I'd have to work to reduce the aerodynamic drag coefficient, or Cd. As I've mentioned in a variety of previous posts, the current Cd of the LR3 is 0.41. If I make some assumptions, I should be able to find out how large a reduction in drag coefficient would be required to achieve a given fuel economy. The assumptions are necessary because drag reduction is most effective at highway speeds. I'll assume that my drag reduction ONLY affects my highway mileage, and that I'm doing highway driving 60% of the time. That should be enough, together with various other estimates, to determine what it would take to get to 25 m.p.g. If I were to be able to accomplish this, it would save me about 147 gallons of fuel annually compared to the current 21.6 m.p.g. I'm getting. Currently, that's worth about $588.



Using my previous calculation of highway mileage and calculating from there, I estimate that my "non-highway" mileage is 19.10 m.p.g. Surprisingly, I've never determined this number before, and it's much higher than I would have thought. Anyway, I now have to determine the Cd that would enable me to achieve a highway mileage of 28.67 m.p.g. Frankly, this seems out of the question, but let's see.



I have to make a few assumptions (as usual). I'll assume that, at 55 m.p.h., 25% of the energy in my fuel turns my wheels and that there are 125*10^6 (125 million) joules of energy in a gallon of gasoline. Thus, a gallon of gasoline delivers (125*10^6)/4 or 31.25*10^6 joules to the wheels. I'll assume that rolling resistance is a function of the tire coefficient and vehicle weight only. I'll assume that the tire coefficient of rolling resistance is 0.12. This may be low. In any case, if I invert the fraction (28.67 miles/31.25*10^6 joules) I'll have energy divided by distance. This is force and, when appropriately converted, will be in newtons. From there, plugging in the known (or estimated) numbers for air density, area, speed, mass, gravitational acceleration, and coefficient of rolling resistance, I can solve for the necessary coefficient of drag.



I know the suspense is killing my readers, the required Cd is slightly under 0.32. Is it possible to reduce the coefficient of drag of my LR3 from 0.41 to 0.32 without making obvious alterations? The only areas I can work with are the grill, under the hood, and the under body. I strongly suspect that grill blocks and belly pans will not result in a 22% reduction in Cd. Still, they will presumably result in a reduced Cd and are cheap and easy. Further, there's a wiki called Instructables that has an article on measuring the drag coefficient of your car. That will enable me to track my progress, which I'll then correlate with my (hopefully) increasing gas mileage.

Google Analytics teaches me something about sociology

This will certainly be outside of my typical topic space. I've plugged in the code to use Google Analytics to see who, if anyone, has visited my little corner of cyberspace and how they might have come here. In looking at the report for the last month, the site has wandered around as usual (I'm too embarrassed to reveal the actual numbers). But yesterday (August 28, 2008) the number of visitors was down by 90%.



This is almost two sigma below the mean. It took but a minute to realize that this was likely to be because people work in the daytime and surf at night. What happened last night? Barack Obama gave his acceptance speech. I was amazed to find that the intersection between fuel economizing web surfers and members of the Obama cult of personality was so large.



I wonder how many of the set of people who would otherwise be perusing my site, or such sites as Ecomodder have actually drunk the Kool-Aid and how many were trying to get to know more about Obama so as to make up their mind?



My gut feeling is that it's more of the former and less of the latter, but the scientist in me is unhappy with leaving it at that. So instead, I've used this opportunity to try a blogger feature I haven't previously used: a poll. Take a moment and let me know, if you surfed less than usual last night, if it was because of Obama's speech and, if so, whether you went there to cheer on your man, or to learn more about a potential recipient of your vote. Clearly this is nonscientific, but it's certainly of interest.

Forces on my LR3 at 56 m.p.h.

There happens to be a hill of, as near as I can tell, constant slope on my commute to work on which I can put my car in neutral and coast down at about an unaccelerated 56 m.p.h. Obviously, the calculations herein will be approximate, these are hardly tightly controlled conditions. But using Google Earth, I can find that in a run of 563 feet, I descend from an elevation of 161.5 feet to 144.5 feet. Assuming that my loaded Land Rover LR3 weighs 5900 pounds force ("lbf"), I can use trigonometry to determine the component of the gravitational force acting to accelerate the truck down this hill. That will give me another estimation of the sum of the external forces acting on my truck, that is, its rolling resistance plus aerodynamic drag.



The calculation is sin(arctan((161.5-144.5)/563))*5900 lbf = Fr where Fr is the total is the total resisting force on the car. Of course, at such a small angle, the sine, the tangent, and the angle itself (in radians) are approximately equal, so what we have is (17/563)*5900 lbf. Thus, the downward component of gravity acting on my car and the total resisting force are each about 178 lbf or 792 Nt (Newtons). Startlingly, my calculations using .5*Cd*rho^2*A*v^2+Crr*m*g (see here) found 743 Nt. Now, this was at 55 m.p.h. rather than 56 m.p.h. and used what I have since determined is likely to be a very slightly low number for air density. Plugging in the appropriate numbers, I get 783 Nt, within 1.1% of the number calculated by determining the component of gravitational force acting parallel to the roadway above. As I've mentioned before, I just love it when different approaches to the same problem yield similar (or almost identical) answers.



So what does it mean? Well, it certainly means I'm on the right track in making calculations based on the resisting forces. I like this because I've made many deductions on that basis. The calculations are fairly limited to the case of analyzing the vehicle as the system and "outside the vehicle" as the environment, that is, the truck is a "black box." This is the case because there's no calculation of the forces involved in the many rotating masses in the vehicle, etc., or of the thermodynamic efficiency of the engine. But it clearly shows that the calculation of the external forces has been accurately performed, and thus the previous two posts are reasonable estimations of what it would take to create a very high mileage vehicle. Oh, and the slope? 1.7 degrees.

Specifics of a high mileage car

In my previous post, I discussed what, outside of the engine and driveline, could be modified to increase fuel mileage. What are the specifics of such a car? Since the laws of physics are unchanging as far as is known and reasonably well known at the macro scale at which cars travel down roads, certain conclusions can be drawn. Let's start with the obvious: fuel is burned to overcome forces acting on the car to take it down the road. So there are two fundamental approaches to high gas mileage, i.e.: put more of the energy in a given amount of fuel to work; and reduce the forces acting on the vehicle.



I'll save maximizing the utilization of energy available in the fuel for another post. Here, I'd like to see what it would take to make a car that gets, say, 75 m.p.g. with currently achievable engine and drive line efficiency by reducing the forces acting on the car. I'll look at achieving this fuel mileage at 55 m.p.h. As I've previously mentioned, force times speed is power, and power is the rate of doing work or, equivalently, using energy.



So, we should be able to say that force times speed equals energy (fuel) divided by time, if the appropriate adjustments are made for units. Or, rearranging, force equals energy divided by speed multiplied by time. And, as would be expected, this simplifies to energy divided by distance. So if I assume 125 million joules/gallon, 25% drive line efficiency, and that I use that gallon in 75 miles, I can determine that the maximum combined force of aerodynamic drag and rolling resistance that I can overcome is about 260 Nt (Newtons). For the SI challenged reader, this is 59.6 pounds.



Referring to my previous post, at a fixed speed the only variables available to control are mass, rolling resistance, frontal area, and drag coefficient. Let's assume that tandem seating isn't a saleable option at this point. What can we do? Well, let's start with vehicle weight. In this article, it's estimated that about 40% of the weight of an average car could be eliminated through replacing steel with carbon fiber. Let's use a conservative estimate of 25%. Then, in this article it's stated that the lowest coefficient of rolling resistance on tires currently available is 0.0062, the highest checked was 0.0152. Let's assume that we can utilize tires with a coefficient of 0.008.



Let's get started. We'll take a small four seat sedan, something like a Toyota Yaris. This vehicle has a curb weight of 2293 pounds, a drag coefficient of 0.29 and a frontal area of (as best I could find) 2.282 meters squared. Let's predict the highway m.p.g. at a steady 55 m.p.h. using, from the previous post, the equation for joules/meter (which is another measure for the inverse of miles per gallon, using the appropriate unit conversions and efficiencies). We'll assume two 170 pound adults to make total weight 2633 pounds. Finally, I'll assume a coefficient of rolling resistance of 0.0115. Running through the calculations, we find that about 355 Newtons are required. To apply this force over a mile, assuming 25% efficiency in the engine, we'd use 0.01828 gallons, or a fuel efficiency of 51.8 m.p.g. Not bad, we're a good part of the way there.



But the car is rated at 36 m.p.g., what gives? Well certainly the EPA tests are more demanding than a steady 55 m.p.h. on level ground. Beyond that, it could be that the new tires with fresh tread have a higher coefficient of rolling resistance. Or, it could be that the engine is able to deliver significantly less than 25% of the energy available in the fuel. If we assume a rolling resistance coefficient of 0.0130 and 20% efficiency, the figure is 36.7 m.p.g. This seems close, and is typical of the types of iterative calculations that are necessary. I'm going to stay in the middle, since I should calculate better than the EPA mileage, due to the rigors of their test. I've verified this in my own LR3. I'm going to assume that the Yaris has a rolling resistance coefficient of 0.0122 and is able to deliver 22% of the energy in the fuel it burns to the wheels. This yields 43.0 m.p.g. Close enough.



Now, what do we get if we reduce the weight by 25%, use tires with a coefficient of rolling resistance of 0.009, and a coefficient of drag of 0.24? Running the numbers, we get 60.8 m.p.g. This is not good, let's see what the maximum credible reductions of coefficient can give us. Using 0.0062 and 0.16 for the coefficients of rolling resistance and drag respectively, we get 90.3 m.p.g. Thus, we conclude that a small car like the Yaris, with the maximally achievable modifications for efficiency, can exceed the target 75 m.p.g. But remember that we've replaced most of the steel with carbon fiber, taken every conceivable measure to reduce drag, and installed tires that are exceptionally efficient and may not wear well, handle well, or be very comfortable. And the fact of the matter is that I very much doubt if a vehicle can be brought to market with a 0.16 coefficient of drag. Let's see what we get with 0.22 and call it good. After all, tires with rolling resistance coefficient of 0.0062 currently exist according to the above-cited article. The answer is 71.5 m.p.g., slightly below the target.



So we conclude that it can be done but the price, both economic and in terms of comfort, is quite high. Clearly, attention to the engine is warranted, as is consideration of drive train modifications. A hybrid engine, combined with pulse and glide driving techniques, could greatly increase efficiency of fuel utilization but it would increase the weight. There is just no free lunch. Tandem seating anyone?

What does a high fuel economy car look like?

To quote Scotty, "you canna change the laws of physics." I'm going to look at what a high fuel economy car would look like, with no assumptions about engine technology breakthroughs. Therefore, there are four fundamental things that we can control: vehicle weight (affects fuel used for acceleration to speed and amount of rolling resistance); tire coefficient of rolling resistance; vehicle frontal area; vehicle shape, reflected in the drag coefficient.



Let's look at cruising. In this case weight only comes in as a factor in rolling resistance, while frontal area and vehicle shape are the factors affecting drag. I've seen an equation that alleges to combine these components - the equation is: Fr=0.5*rho*Cd*A*v^2+Crr*m*g*v where rho is air density, Cd the coefficient of drag, A the frontal area, v is velocity, Crr is coefficient of rolling resistance, m is mass of vehicle, and finally, g is the acceleration of gravity.



I don't buy it. My analysis shows that, at least for first order effects, rolling resistance is not a function of velocity, so let's use Fr=0.5*rho*Cd*A*v^2+Crr*m*g. This is dimensionally correct with both coefficients dimensionless. It is, therefore, plausible and I'm going with it.



So, what can be changed here? We can't change rho or g, and v is whatever the driver chooses to use. I'll list the variables we can change and what would be done:



1. Reduce Cd. This can be done by the manufacturer, there have been vehicles with Cd as low as 0.16, though not many. There are those who modify their vehicles themselves to reduce Cd. To see this in action, visit the Aerodynamics forum at the ecomodder web site. I'd suggest looking for posts by "basjoos" to see the extremes to which this can be taken. A blog post about his vehicle can be found here. If you choose to do this, be careful because aerodynamics can be non-intuitive.



2. Reduce A, frontal area. This means a smaller vehicle in general. For a two-seater, tandem seating might be an option. There are concept vehicles out there that take this route and they will certainly have a low so-called "drag area," the product of Cd and A. Market acceptance is clearly a question.



3. Reduce Crr. This is the amount of force used up by tire rolling resistance. There are low rolling resistance tires out there, and California is contemplating requiring manufacturers to list Crr for tires sold here. The rolling resistance depends in a complicated way on a number of factors, but tires primarily use energy in so-called "hysteresis losses," i.e., flexing portions of the tire without full energy recovery as the tire rotates. Steel wheels on trains have extremely low Crr's since they barely flex at all. For a look at low rolling resistance tires, check here.



4. Reduce m, mass. Obviously, reducing A helps here since, in general, smaller cars weigh less. Lighter materials, less room for storage, smaller fuel tanks, etc. can also be utilized, as can minimally sized engines for the mission at hand. These reductions are synergistic - lighter vehicles need smaller engines, which can utilize lighter drive line components, which can utilize smaller fuel tanks for less fuel weight, etc.



So, a composite, tandem seating car, optimally shaped with little or no trunk and a small fuel tank would appear to be the best prescription. Of course, as is usually the case, the easiest savings coming from driving less and sharing the ride.



As I stated at the outset, this doesn't address possible gains from engine efficiency. In my opinion, dramatic gains aren't likely here. I'll address engine issues in another post.

300 barrels

That's the amount of proven and probable reserves of oil for each person on Earth. Clearly, it's not an exact number but it assumes about 2 trillion barrels and about 6.7 billion people. 300 barrels. That's it.



Now, in the United States we use about 25 barrels of oil per year per person. For those not near their calculator, that means we'll use up our 300 barrels in 12 years. Is it really that bad? Well, yes. Fortunately for us, there are many countries in Africa and Asia, and even in Central and South America who kindly decide not to use as much of their 300 barrels each year as we do. In fact, there are no countries whose citizens use as much of their 300 barrel allotment as we do. For example, the Chinese use around two barrels per year per person.



The question is: when we've used up ours, are they all going to sell us theirs? Sure, if the price is right. But that price will be dear. Only the most essential uses will be able to be accommodated. What we're seeing in the commodity exchanges and at the gas pump is only the beginning - there is no aspect of our lives that will remain unaffected.



Preparation should have begun years ago, this impending calamity is not a new development. It's been predicted for half a century. Preparation at the personal, community, local, national, and worldwide levels with an urgency that hasn't been matched in living memory is the prescription. Look around - do you see it anywhere?



There are those who are preparing, I strongly recommend the Yahoo news group Running on Empty 2. There, you'll find extensive discussions of the issues at hand, of preparations people are undertaking, and answers to questions. You'll find links to pertinent news items, web sites, and fora and blogs. You won't find old school survivalists of the black helicopter variety.



While I work on maximizing the return on my energy expenditures driving my Land Rover to and from my McMansion, I'm working on a total change of lifestyle. I recommend readers do the same.

Michael Medved, Dr. Albert Bartlett, and innumeracy

I was thinking about my post on how peoples philosophy affects their evaluation of factual data. I googled (an unfortunate example of "verbification," a language trend I loathe) "Michael Medved" "peak oil." I came upon a site called The Dead Hand. It seems to be the work of Dr. Robert Williscroft, who has penned a tome entitled The Chicken Little Agenda: Debunking "Experts'" Lies. The theme is that the end of the world as we know it is not approaching, no matter what "they" say. Dr. Williscroft has a flash audio of a Michael Medved segment that included himself and a representative of the group Seattle Peak Oil Awareness (Medved lives in Seattle). The segment occupied an hour of Medved's show.



This post is about the misconceptions about what can be accomplished by finding more oil, something Medved and Williscroft (and most of the callers to the show) think will inevitably happen and will solve our problems, at least for many decades to come. Unfortunately, even should such finds be forthcoming, they'll only postpone our reckoning by a small amount. As an aside, it's not as if most of the world is a vast unknown full of huge undiscovered oil fields and geologists have no clue about where to find them. In any case, Dr. Albert Bartlett has spent his career trying to educate lay people on the consequences of exponentially increasing consumption of a finite resource. I strongly urge everyone to look here for Dr. Bartlett's exposition.



I'd like to spend a little virtual ink to bring some of the salient points to my reader's attention. The world is currently using oil at the rate of about 80 million barrels per day. The spreadsheet from BP I used in my previous post on exponential growth gives enough data to show that the current doubling time for oil consumption is around 45 years. This means that in the next 45 years, we'll use as much oil as we have in all history up until today. Now, this is an exceptionally rosy estimate, if things go as they are going now. We have India, China, Indonesia, and many other developing nations growing quickly both in population and in per capita energy use. This has severe ramifications on the figure of 45 years, since that's based on data from 1982 through 2006.



Let's suppose an annual growth rate of 6% worldwide in demand encompasses the increasing populations and energy consumption rates of the so-called "developing world," and that that leads to an annual increase worldwide of 4%. Both of these are in line with current projections. Now we're looking at a doubling period of about 18 years, meaning that we'll use as much oil in the next 18 years as we've used up until today in all history. Further, it means that if geologists and oil companies double the oil reserves available, only another 18 years of oil use would be added.



Unfortunately, this underestimates the problem, since the second half of the oil is only extracted with much greater effort and with much greater cost, both in energy and monetary terms. I'm not predicting the end of the world as we know it, but Mr. Medved, et al, are whistling past the graveyard. I have no doubt that it's due to the cognitive dissonance between the philosophical framework by which he interprets facts and what is factual reality.

The time factor is worse than I thought

In my post on the use of time, I used some estimates as to how much time I lose with the fuel economizing driving techniques I utilize. I estimated that I lose eight minutes and 25 seconds each day driving 55 m.p.h. instead of 70 m.p.h. I've been browsing the fuel saving websites and blogs, and the "party line" is that very little time will be lost. I decided that I'd see what the real numbers are for my commute.



I used a stopwatch to time the portions of my typical commute each way during which I could have been driving 70 m.p.h. Then, a simple multiplication by 55/70 gave me the time I would have spent driving those miles at 70 m.p.h., and a subtraction yielded the time loss. I did this for two days and averaged the numbers. The days seemed fairly typical so I imagine that the results are representative. Certainly, there are periods during which traffic is worse (say, when school starts in September, when standard time returns, etc.) but during these times, I'm not saving much fuel anyway.



The results are highly disturbing. I'm spending about 10 minutes and 41 seconds longer on the road each day than I would if I drove 70 m.p.h. That's about 44 1/2 hours per year. It's reduced slightly by the fact that I have to stop for fuel less often, and judicious use of my assistant and the mobile phone enables a minimal level of productivity, but even allowing for this, it's just about equivalent to a week of work (or vacation).



A sensible person would give it up, but those who have followed this blog at all will have no fear that I'm a sensible person. I've said it before, but if I'm going to keep this up, I must find a way to be more productive. I have a little tape recorder for dictating things, but that just shuffles the work onto someone else to type it, or slightly reduces the time for me to compose a document. I don't know about the reliability of software that translates spoken word into typed documents, the last time I tried such a product it was worthless for my purposes.



Well, for the time being I guess I'll stick to my "Learn Mandarin Chinese" podcast. But it's clear that nothing comes for free, not even saving fuel.