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.

A look at energy use in my life and how it applies to others' lives

## Sunday, December 21, 2008

## Sunday, December 07, 2008

### 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.

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.

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.

## Saturday, November 29, 2008

### 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.

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.

## Saturday, November 22, 2008

### 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.

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.

## Sunday, October 26, 2008

### 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.

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.

## Saturday, October 18, 2008

### 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).

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).

## Saturday, August 30, 2008

### 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.

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.

## Friday, August 29, 2008

### 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.

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.

## Monday, August 18, 2008

### 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.

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.

## Sunday, August 10, 2008

### 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?

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.

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.

## Sunday, June 01, 2008

### 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.

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.

## Sunday, April 20, 2008

### 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.

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.

## Friday, April 04, 2008

### 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.

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.

## Saturday, March 29, 2008

### A simple way to save a little fuel

I know that most people won't use the extreme methods of fuel consumption minimization that I've used to achieve a five tank moving average fuel efficiency of 21.09 m.p.g. in my Land Rover LR3 HSE, at least until it's a matter of taking extreme measures or not driving at all. People are repelled by the thought of (and if they're in my vehicle, the experience of) driving 55 m.p.h. on the freeway, coasting wherever possible, etc. But what about a minor adjustment that will save a little fuel?

I've previously detailed my policies on stoplights, including when I turn my engine off, coasting to minimize fuel waste when approaching red lights, whether or not it pays to speed up to attempt to make it through a green (or yellow) light, etc. Possibly, no one will adopt any of the measures I've outlined in those posts. But what about just shifting from drive to neutral? When sitting still with the vehicle in drive and brakes applied, more fuel is used than with the vehicle in neutral. I know this to be the case because I can see it on my Scan Gauge II. As I usually do, I'll run a few calculations to estimate my fuel savings from this policy, and then I'll add some more estimates to see what the effect might be on nationwide energy consumption, trade deficit, etc.

On my LR3 HSE, I typically use about 0.5 gallons/hour at idle in neutral. The absolute manifold pressure is about 4.8 p.s.i. Putting the car in gear (drive) and holding it still with the brakes causes the manifold pressure to increase to about 5.8 p.s.i. Since increasing manifold pressure results in a proportional increase in air mass flow through the engine, and hence a proportional increase in fuel consumption, we can assume that the 20.8% increase in manifold pressure results in a similar increase in rate of fuel consumption. However, we're looking at what could be saved by a driver who adopts the policy of shifting to neutral at stoplights so the appropriate way to look at the situation is that this driver will reduce his or her fuel consumption by 17.2% (1/5.8*100%).

Using estimates detailed previously (slightly modified) for stoplights hit per day, time spent per light, idling fuel consumption, etc. for the average car and driver, it looks like my "average driver" could save about 2.56 gallons/year. At current rates in Southern California, that would amount to a savings of $8.70 at the pump. I guess that would cover a single high-end caffeine product at your local Starbucks. It's probably not enough to save a homeowner headed for foreclosure though. As readers of this blog will readily infer, I certainly do it.

What about the results of nationwide application of this policy? I estimate that somewhere on the order of 333 million gallons of fuel could be saved. This is the gasoline from about 17.5 million barrels of oil. And since the other 23 gallons of oil in a barrel are not discarded when gasoline is produced at the refinery, I'll estimate that something like 8.8 million barrels could be left for other countries to purchase. This would reduce our trade deficit by just shy of $1 billion at current oil prices (about $105/barrel). Hmmm... According to the U.S. Census Bureau the January 2008 trade deficit was $58.2 billion. And here I thought I'd solved the problem.

I've previously detailed my policies on stoplights, including when I turn my engine off, coasting to minimize fuel waste when approaching red lights, whether or not it pays to speed up to attempt to make it through a green (or yellow) light, etc. Possibly, no one will adopt any of the measures I've outlined in those posts. But what about just shifting from drive to neutral? When sitting still with the vehicle in drive and brakes applied, more fuel is used than with the vehicle in neutral. I know this to be the case because I can see it on my Scan Gauge II. As I usually do, I'll run a few calculations to estimate my fuel savings from this policy, and then I'll add some more estimates to see what the effect might be on nationwide energy consumption, trade deficit, etc.

On my LR3 HSE, I typically use about 0.5 gallons/hour at idle in neutral. The absolute manifold pressure is about 4.8 p.s.i. Putting the car in gear (drive) and holding it still with the brakes causes the manifold pressure to increase to about 5.8 p.s.i. Since increasing manifold pressure results in a proportional increase in air mass flow through the engine, and hence a proportional increase in fuel consumption, we can assume that the 20.8% increase in manifold pressure results in a similar increase in rate of fuel consumption. However, we're looking at what could be saved by a driver who adopts the policy of shifting to neutral at stoplights so the appropriate way to look at the situation is that this driver will reduce his or her fuel consumption by 17.2% (1/5.8*100%).

Using estimates detailed previously (slightly modified) for stoplights hit per day, time spent per light, idling fuel consumption, etc. for the average car and driver, it looks like my "average driver" could save about 2.56 gallons/year. At current rates in Southern California, that would amount to a savings of $8.70 at the pump. I guess that would cover a single high-end caffeine product at your local Starbucks. It's probably not enough to save a homeowner headed for foreclosure though. As readers of this blog will readily infer, I certainly do it.

What about the results of nationwide application of this policy? I estimate that somewhere on the order of 333 million gallons of fuel could be saved. This is the gasoline from about 17.5 million barrels of oil. And since the other 23 gallons of oil in a barrel are not discarded when gasoline is produced at the refinery, I'll estimate that something like 8.8 million barrels could be left for other countries to purchase. This would reduce our trade deficit by just shy of $1 billion at current oil prices (about $105/barrel). Hmmm... According to the U.S. Census Bureau the January 2008 trade deficit was $58.2 billion. And here I thought I'd solved the problem.

## Sunday, March 09, 2008

### The best speed for fuel economy

I calculated in a previous post that my "highway mileage" at 55 m.p.h. is 23.27 m.p.g. It stands to reason that there is an optimum speed for fuel efficiency based on the balance between the low efficiency at low speed due to engine friction and the increase in aerodynamic drag, proportional to the square of speed, as speed increases. Now, my Land Rover LR3 HSE is not the optimal aerodynamic shape, with a coefficient of drag of 0.41 and a frontal area of 33.9 square feet. It makes sense, and conforms with various articles I've read (see the article on HowStuffWorks.com entitled "What speed should I drive to get maximum fuel efficiency?" here for example), that the optimum speed for a box on wheels like my vehicle should have a lower optimum speed than a vehicle designed to have excellent aerodynamics.

I made some conceptual calculations that agree with the form of the equation shown in the "How Stuff Works" article linked above. There, it is stated that the power required as a function of speed is a third degree polynomial, that is, P=as^3+bs^2+cs+d where P is power required, s is speed, a,b, and c are coefficients and d is a constant specific to a given vehicle. Since power is the rate of doing work, or more importantly in this case, the rate of use of energy (burning fuel) in the appropriate units (gallons per hour for example), we can say power is proportional to gallons/mile times miles/hour. Then we can say that gallons per mile (the inverse of miles per gallon) is proportional to power divided by speed. So, substitute the polynomial above for power and divide by speed and we find that the rate of fuel consumption in gallons per mile is a second degree polynomial function of speed. Sorry for the extended math exposition!

In any case, the above leads to the following expression for fuel per unit of distance: f=ms^2+ns+p, where f is fuel consumption per distance (say, gallons per 100 miles), s is speed in miles per hour, and m and n are coefficients and p is a constant different (probably) from the previous ones. I used the same level stretch of freeway in no wind conditions that I used previously to check highway mileage (linked above) over a few weeks to check the instant miles per gallon at various speeds allowed by traffic (when I was able to maintain a set speed long enough for the display to stabilize). I then calculated the inverse in gallons per 100 miles for those speeds, plotted them in an Excel spreadsheet and made the best fit of a second degree polynomial.

From that point, it was a very simple calculus exercise to find the speed at which fuel consumption would be minimized. This turned out to be 43.4 m.p.h. I can plug this into the second degree polynomial, divide by 100, and invert the resulting number to estimate miles per gallon at that speed. The result is 27.47 m.p.g. Not too bad, but remember from the earlier post that it turns out that that stretch of freeway has a very slight downward slope in the direction I used to obtain my measurements. I have to use the method I used in that post to correct the fuel economy. To spare my patient readers the details, the correction yields a final figure of 26.18 m.p.g. at 43.4 m.p.h.

Interestingly, this speed is lower than the one previously calculated for the Jeep Grand Cherokee Limited I used to have, even though that vehicle had (according to various web sites) a higher drag coefficient. And, looking at the vehicles side by side, the Jeep looks sleeker. Even with the higher drag coefficient, the jeep feels a smaller drag force due to the smaller frontal area. But unless the figures are mistaken, the looks are deceiving as far as drag coefficient is concerned. And the estimate I had for that vehicle of optimum speed for fuel efficiency was a little over 50 m.p.h.

So, do I plan to reduce my freeway driving speed from the current 57 m.p.h. (it's 57 because I ran the above calculations based on speedometer reading, not Scan Gauge II's 2 m.p.h. lower reading since the speedometer seemed more accurate over a timed measured mile)? Probably not, since I have to be alive to continue with the experiment.

I made some conceptual calculations that agree with the form of the equation shown in the "How Stuff Works" article linked above. There, it is stated that the power required as a function of speed is a third degree polynomial, that is, P=as^3+bs^2+cs+d where P is power required, s is speed, a,b, and c are coefficients and d is a constant specific to a given vehicle. Since power is the rate of doing work, or more importantly in this case, the rate of use of energy (burning fuel) in the appropriate units (gallons per hour for example), we can say power is proportional to gallons/mile times miles/hour. Then we can say that gallons per mile (the inverse of miles per gallon) is proportional to power divided by speed. So, substitute the polynomial above for power and divide by speed and we find that the rate of fuel consumption in gallons per mile is a second degree polynomial function of speed. Sorry for the extended math exposition!

In any case, the above leads to the following expression for fuel per unit of distance: f=ms^2+ns+p, where f is fuel consumption per distance (say, gallons per 100 miles), s is speed in miles per hour, and m and n are coefficients and p is a constant different (probably) from the previous ones. I used the same level stretch of freeway in no wind conditions that I used previously to check highway mileage (linked above) over a few weeks to check the instant miles per gallon at various speeds allowed by traffic (when I was able to maintain a set speed long enough for the display to stabilize). I then calculated the inverse in gallons per 100 miles for those speeds, plotted them in an Excel spreadsheet and made the best fit of a second degree polynomial.

From that point, it was a very simple calculus exercise to find the speed at which fuel consumption would be minimized. This turned out to be 43.4 m.p.h. I can plug this into the second degree polynomial, divide by 100, and invert the resulting number to estimate miles per gallon at that speed. The result is 27.47 m.p.g. Not too bad, but remember from the earlier post that it turns out that that stretch of freeway has a very slight downward slope in the direction I used to obtain my measurements. I have to use the method I used in that post to correct the fuel economy. To spare my patient readers the details, the correction yields a final figure of 26.18 m.p.g. at 43.4 m.p.h.

Interestingly, this speed is lower than the one previously calculated for the Jeep Grand Cherokee Limited I used to have, even though that vehicle had (according to various web sites) a higher drag coefficient. And, looking at the vehicles side by side, the Jeep looks sleeker. Even with the higher drag coefficient, the jeep feels a smaller drag force due to the smaller frontal area. But unless the figures are mistaken, the looks are deceiving as far as drag coefficient is concerned. And the estimate I had for that vehicle of optimum speed for fuel efficiency was a little over 50 m.p.h.

So, do I plan to reduce my freeway driving speed from the current 57 m.p.h. (it's 57 because I ran the above calculations based on speedometer reading, not Scan Gauge II's 2 m.p.h. lower reading since the speedometer seemed more accurate over a timed measured mile)? Probably not, since I have to be alive to continue with the experiment.

## Sunday, February 24, 2008

### Good question

In my diligent search through the web to find articles of interest about energy, fuel saving measures, and efficiency I happened upon an article from the Technology Review published by MIT entitled Why Not a 40-MPG SUV. The substance of the article was that, despite the remonstrances of (particularly) the U.S. automobile industry, the technology is available now to bring relatively large and comfortable SUV's that achieve a fuel efficiency of 40 miles per gallon.

This was of particular interest to me since I drive a relatively large and comfortable SUV, the Land Rover LR3 HSE that has been the subject of many of the articles I've posted. Now, none of the technologies described in the article can be retrofitted to my vehicle, but they could be brought to market by the time I have to replace the LR3.

Some of the options reflect methods I've already incorporated into my regimen, such as engines that turn off and restart at stoplights, etc. The development is a starter /generator that has sufficient power to start the engine without noticeable lag when a driver steps on the gas after a stop. The current state of the art requires a 42 volt electrical system and is a way out into the future. As detailed previously, I simulate this at relatively long stoplights and on long downhill cruises and make up for the lack of instant starting ability with anticipation.

Some of the developments detailed are already beginning to appear, one example is the continuously variable transmission. Clearly, the ability to run in a narrow band of r.p.m.s regardless of vehicle speed will result in more efficient operation - this is one reason why modern locomotives are hybrid diesel electric propulsion systems wherein the diesel engine runs at a constant r.p.m. to operate electric motors that provide the motive force.

Some are much farther out, including engines that operate without camshafts to operate the valves. Electronic controllers can do a much more efficient job of opening and closing the valves, but are quite hard on them using current technology. Camshafts are more gentle, engineers are investigating various damping systems to reduce the electronically controlled valves impact on valve seats.

There are several more methods under development detailed in the article. Contemplating the individual financial savings as gasoline creeps seemingly inexorably toward $4/gallon and considering the impact on our need to import oil, it's high time we got down to it.

This was of particular interest to me since I drive a relatively large and comfortable SUV, the Land Rover LR3 HSE that has been the subject of many of the articles I've posted. Now, none of the technologies described in the article can be retrofitted to my vehicle, but they could be brought to market by the time I have to replace the LR3.

Some of the options reflect methods I've already incorporated into my regimen, such as engines that turn off and restart at stoplights, etc. The development is a starter /generator that has sufficient power to start the engine without noticeable lag when a driver steps on the gas after a stop. The current state of the art requires a 42 volt electrical system and is a way out into the future. As detailed previously, I simulate this at relatively long stoplights and on long downhill cruises and make up for the lack of instant starting ability with anticipation.

Some of the developments detailed are already beginning to appear, one example is the continuously variable transmission. Clearly, the ability to run in a narrow band of r.p.m.s regardless of vehicle speed will result in more efficient operation - this is one reason why modern locomotives are hybrid diesel electric propulsion systems wherein the diesel engine runs at a constant r.p.m. to operate electric motors that provide the motive force.

Some are much farther out, including engines that operate without camshafts to operate the valves. Electronic controllers can do a much more efficient job of opening and closing the valves, but are quite hard on them using current technology. Camshafts are more gentle, engineers are investigating various damping systems to reduce the electronically controlled valves impact on valve seats.

There are several more methods under development detailed in the article. Contemplating the individual financial savings as gasoline creeps seemingly inexorably toward $4/gallon and considering the impact on our need to import oil, it's high time we got down to it.

## Thursday, February 21, 2008

### Stoplights (stop me if you've heard this before)

Never one to leave well enough alone (as an aside, this is one of the many expressions I never really understood until well into adulthood - another is "you can't have your cake and eat it too"), I've started sporadically keeping track of my stoplight experiences. I've tracked how many greens, how many reds, and approximately how much time was spent waiting. I say approximately because it's not so easy to determine when to start the timing at a light - do you start the stopwatch at first brake application? Or at a complete stop? What about slowing down but not having to stop? I'm trying to tie the timing to time not using fuel as efficiently as cruising, but there's a lot of judgment involved.

But it's looking like the earlier estimates I made (see here and here)for stoplight durations are fairly close. In the time I've been recording this data (only sporadically because it's quite distracting), I've encountered 59% green lights. I've suffered an average delay of 32 seconds. I've passed through an average of 32 lights each day. So that means that I'm losing an average of about 10:06 per day while stopped at 19 stoplights.

I try to minimize driving on weekends (though I haven't succeeded in eliminating it entirely) so I'll figure 280 days per year of losing 10:06 per day, for a total of 47.13 hours per year lost at stoplights. Burning about 0.5 gallons of fuel per hour at idle, if I don't turn the engine off at any lights, I'll burn 23.6 gallons of fuel. In my Land Rover LR3 HSE, that's a little over a single tank full and at $3.39/gallon (today) it's worth just barely less than $80.00.

This underestimates the loss, however, because it only counts idling fuel and not the fuel wasted in regaining energy lost to braking that has to be added by burning fuel. I estimated that in the second of the two posts listed above, so I'll just refine it here. I estimated stopping at 12 lights for 45 seconds each day for a loss of 9:00 per day, apparently a slight underestimation.

To finally squeeze the last blood from this turnip, I'll estimate that I slow from 35 m.p.h. to 0 on average at each of the 19 stoplights. It's not perfect, but it's as good as I know how to do. In any case, this wastes 322,150 joules of energy which takes, at 25% efficiency, 1,288,600 joules of heat energy from burning premium grade fuel to regain.

Using the figures above, and estimating 125,000,000 joules of heat energy available in a gallon of gasoline, I burn 54.84 gallons of fuel per year adding kinetic energy to my vehicle that I've wasted to heat my brakes stopping for stoplights. The total then is 78.4 gallons of fuel, or about 3.6 tanks full wasted. This number is quite close to my previous estimate, but now there's data to back it up. To me, the interesting aspect of this is the fact that well over 2/3 of the fuel wasted is due to getting back up to speed rather than to burning fuel while sitting still. Since kinetic energy is proportional to the square of speed, this stands to reason but it's still interesting to see it documented.

I'm still anticipating an experiment to determine fuel lost in restarting, but this data shows the potential savings from coasting to a stop without brakes (thus using instead of wasting kinetic energy) and turning off the engine - ideally as soon as the coasting begins. As with most of the other measures, it won't eliminate our need to import oil but it could help delay the crash.

But it's looking like the earlier estimates I made (see here and here)for stoplight durations are fairly close. In the time I've been recording this data (only sporadically because it's quite distracting), I've encountered 59% green lights. I've suffered an average delay of 32 seconds. I've passed through an average of 32 lights each day. So that means that I'm losing an average of about 10:06 per day while stopped at 19 stoplights.

I try to minimize driving on weekends (though I haven't succeeded in eliminating it entirely) so I'll figure 280 days per year of losing 10:06 per day, for a total of 47.13 hours per year lost at stoplights. Burning about 0.5 gallons of fuel per hour at idle, if I don't turn the engine off at any lights, I'll burn 23.6 gallons of fuel. In my Land Rover LR3 HSE, that's a little over a single tank full and at $3.39/gallon (today) it's worth just barely less than $80.00.

This underestimates the loss, however, because it only counts idling fuel and not the fuel wasted in regaining energy lost to braking that has to be added by burning fuel. I estimated that in the second of the two posts listed above, so I'll just refine it here. I estimated stopping at 12 lights for 45 seconds each day for a loss of 9:00 per day, apparently a slight underestimation.

To finally squeeze the last blood from this turnip, I'll estimate that I slow from 35 m.p.h. to 0 on average at each of the 19 stoplights. It's not perfect, but it's as good as I know how to do. In any case, this wastes 322,150 joules of energy which takes, at 25% efficiency, 1,288,600 joules of heat energy from burning premium grade fuel to regain.

Using the figures above, and estimating 125,000,000 joules of heat energy available in a gallon of gasoline, I burn 54.84 gallons of fuel per year adding kinetic energy to my vehicle that I've wasted to heat my brakes stopping for stoplights. The total then is 78.4 gallons of fuel, or about 3.6 tanks full wasted. This number is quite close to my previous estimate, but now there's data to back it up. To me, the interesting aspect of this is the fact that well over 2/3 of the fuel wasted is due to getting back up to speed rather than to burning fuel while sitting still. Since kinetic energy is proportional to the square of speed, this stands to reason but it's still interesting to see it documented.

I'm still anticipating an experiment to determine fuel lost in restarting, but this data shows the potential savings from coasting to a stop without brakes (thus using instead of wasting kinetic energy) and turning off the engine - ideally as soon as the coasting begins. As with most of the other measures, it won't eliminate our need to import oil but it could help delay the crash.

## Tuesday, February 05, 2008

### Humans as generators

I was watching the show "Invention Nation" on the Discovery Science Channel. The hosts visited a company that, apparently, is working on a revolving door that, when operated by patrons, generates electricity by moving neodymium magnets across coils of copper wire. The mechanism is exposed, so that patrons of an establishment that has such doors will be able to see the means by which they are generating power.

I was skeptical as to the significance of such a device, the show hosts used a prototype to light a small bank of L.E.D.'s. So I performed a Google search on the terms "generating power with revolving doors." I found several sites that mentioned the use of various human activities to generate useful power, including revolving doors and other methods (e.g., piezoelectric crystals in floors). This led me to consider the possibilities (quoting Marcellus Wallace, "All I'm doing is contemplating the 'ifs'").

As best I can tell, the human body, when purposefully performing work (riding a bicycle, lifting, etc.) has an efficiency of somewhere between 11% and 14%. That counts only how many calories (actually kilocalories) of food it takes to do a given amount of "useful" work. It does not count the sun to plant to animal to slaughterhouse to processing plant to distributor to store to house to stove to mouth efficiency (leave out some of those if you're a vegetarian). So, unless someone is exercising to remain physically fit, utilizing the human body to convert sunlight to electricity is quite inefficient.

Let's run some "back of the envelope" calculations though. There are about 3*10^8 people in the U.S. Say 1*10^8 of them walk on office, factory, or school floors, walk through revolving doors, etc. Now, the average adult uses something like 2500 kilocalories per day, let's say 100 of those are used putting feet on floors, using doors, etc. (very generous in my opinion). At 14% efficiency by the human and 50% efficiency by the generator (piezoelectric, magnetic, etc.) we have: 100 kilocalories*0.14*0.5 kilocalories of useful work per day per person to be captured.

Work divided by time is power so the above can be converted to watts per person (I typically use Google's calculator). This yields 0.339 watts per person. This is the effective continuous power output per person on average. Multiply this by 1*10^8 to total 33,900,000 or 3.39*10^7 watts available nationwide calculated on a continuous basis. According to the CIA World Factbook, in 2005 we used electricity at the rate of 3.816 trillion kilowatt hours/year, or 4.353*10^11 watts. Hence, using these extremely optimistic assumptions, this scheme could generate 0.008%, or 8 one thousandths of 1% of our electricity.

As I said though, when we do this, we're converting solar power inefficiently into electricity. Better to invest the money into more efficient generation schemes, except at health clubs, etc., where people are working out into a load and it might just as well be an electrical load that serves a purpose.

I was skeptical as to the significance of such a device, the show hosts used a prototype to light a small bank of L.E.D.'s. So I performed a Google search on the terms "generating power with revolving doors." I found several sites that mentioned the use of various human activities to generate useful power, including revolving doors and other methods (e.g., piezoelectric crystals in floors). This led me to consider the possibilities (quoting Marcellus Wallace, "All I'm doing is contemplating the 'ifs'").

As best I can tell, the human body, when purposefully performing work (riding a bicycle, lifting, etc.) has an efficiency of somewhere between 11% and 14%. That counts only how many calories (actually kilocalories) of food it takes to do a given amount of "useful" work. It does not count the sun to plant to animal to slaughterhouse to processing plant to distributor to store to house to stove to mouth efficiency (leave out some of those if you're a vegetarian). So, unless someone is exercising to remain physically fit, utilizing the human body to convert sunlight to electricity is quite inefficient.

Let's run some "back of the envelope" calculations though. There are about 3*10^8 people in the U.S. Say 1*10^8 of them walk on office, factory, or school floors, walk through revolving doors, etc. Now, the average adult uses something like 2500 kilocalories per day, let's say 100 of those are used putting feet on floors, using doors, etc. (very generous in my opinion). At 14% efficiency by the human and 50% efficiency by the generator (piezoelectric, magnetic, etc.) we have: 100 kilocalories*0.14*0.5 kilocalories of useful work per day per person to be captured.

Work divided by time is power so the above can be converted to watts per person (I typically use Google's calculator). This yields 0.339 watts per person. This is the effective continuous power output per person on average. Multiply this by 1*10^8 to total 33,900,000 or 3.39*10^7 watts available nationwide calculated on a continuous basis. According to the CIA World Factbook, in 2005 we used electricity at the rate of 3.816 trillion kilowatt hours/year, or 4.353*10^11 watts. Hence, using these extremely optimistic assumptions, this scheme could generate 0.008%, or 8 one thousandths of 1% of our electricity.

As I said though, when we do this, we're converting solar power inefficiently into electricity. Better to invest the money into more efficient generation schemes, except at health clubs, etc., where people are working out into a load and it might just as well be an electrical load that serves a purpose.

## Sunday, January 13, 2008

### Highway MPG

My 2006 Land Rover LR3 HSE with its 4.4, Liter V8 engine is rated by the EPA at 18 m.p.g. highway mileage. In fact, the spreadsheet provided by the EPA in zipped files shows the so-called "uncorrected" fuel economy as 23.3 m.p.g. They correct this by the simple expedient of reducing it by 22%. Now, don't misunderstand. They don't do some arcane analysis that leads to a 22% reduction, they just multiply the measured number (found by measuring carbon emitted during the dynamometer test) by 0.78. Very scientific. That leads to the "18 HWY" on the window sticker. Since my driving is mixed and I'm able to achieve a higher average mileage (currently about 20.5 m.p.g.) than the EPA highway estimate I think that my highway mileage must be considerably better than the 18 m.p.g estimate, and possibly higher than the 23.3 m.p.g. uncorrected measurement. I determined to find out.

The LR3 does not have an instant m.p.g. indication in its instrumentation, however, the Scan Gauge II with which I've equipped my Land Rover does have this instrumentation through the OBDII port. I'm not sure of the mechanism by which this is determined, though I would guess that it uses the metering of the fuel through the injectors and the speed. If it's this method, it may be unreliable because the speed readout on the Scan Gauge II appears to be inaccurate. It reads 55 m.p.h. when the analog speedometer in the dash reads about 57 m.p.h. I had always assumed the ODBII reading was accurate, but there is a series of measured miles for the use of the highway patrol on interstate 15 on the way to Las Vegas and stopwatch timing over these measured miles indicated that the analog gauge on the dash is a better indicator of actual speed. Never mind, I'm going to calculate using the ODBII.

So, what I need is a stretch of level highway where I can just look at the readout on the instant mileage indicator, wait for it to stabilize, and there's my answer. The complicating external factors might be an undetected slope, and wind. As it happens, there's a stretch of the 405 freeway through Seal Beach that appears to be suitable for this determination. Conveniently, there's a power plant visible from this portion of the freeway, and its smokestack gives an excellent signal of wind conditions. When northbound on the freeway, the average stabilized reading over several trips is about 24.8 m.p.g. Woo Hoo! But when southbound, it's more like 21.9. Hmm.... Must be an undetected slope.

How much might there be and what effect might it have? I looked to Google Earth to try to find out. I located the stretch in question and measured the distance and logged the elevations. I tried to find end spots for my measurement where the elevation clicked from one integer foot to another (e.g., 17 feet to 16 feet) and assumed that this was the location where the actual elevation was halfway from one to the other. Now, this may not be completely accurate, but as long as the algorithm used by Google Earth is consistent, this is the best I can do since I'm not interested in absolute elevations but rather in elevation changes.

It turns out that the elevation change is 5 feet over 0.71 miles. That means that, in the downhill direction, I gain 39,948.6 (I always carry a lot of digits) joules of kinetic energy by converting gravitational potential energy, and turn the same amount of chemical energy (assuming I maintain the same speed) into gravitational potential energy in the uphill direction. It's straightforward to determine how much fuel is saved and burned respectively, if I assume that the car is able to utilize 25% of the heat energy of burning gasoline for propulsion at this speed.

Since I haven't had readers of this blog clamoring for more mathematical detail, I'll just give the results. Factoring out the "free" energy provided by going downhill, the car should be producing 23.74 m.p.g. Factoring it out in the uphill direction, the resulting mileage is 22.79 m.p.g. Closer but not identical. I'm not sure where the error is, so I'll just average the two numbers and say that my level highway average m.p.g. is 23.27 m.p.g. This is still a healthy increment above the 18 m.p.g. estimated by the EPA but, amazingly, it rounds precisely to their uncorrected number of 23.3 m.p.g.. I know that the test protocol does not involve simply running in cruise control on level highway in no wind conditions but it still pleases me to beat the window sticker estimate by over 29%, as arbitrary as that EPA estimated number seems to be.

Another lesson is that such a slight hill has so much effect on mileage. Five feet over 0.71 miles is 0.076 degrees; almost undetectable. To get an idea, if you're hanging a 24 inch wide picture and it's off of level by this amount, the low side will be 0.03 inches lower (about 1/32 inch) than the high side. And yet climbing it reduces fuel economy by 5.9%. The lesson? ALWAYS make sure that your destination is at a lower elevation than your starting point.

The LR3 does not have an instant m.p.g. indication in its instrumentation, however, the Scan Gauge II with which I've equipped my Land Rover does have this instrumentation through the OBDII port. I'm not sure of the mechanism by which this is determined, though I would guess that it uses the metering of the fuel through the injectors and the speed. If it's this method, it may be unreliable because the speed readout on the Scan Gauge II appears to be inaccurate. It reads 55 m.p.h. when the analog speedometer in the dash reads about 57 m.p.h. I had always assumed the ODBII reading was accurate, but there is a series of measured miles for the use of the highway patrol on interstate 15 on the way to Las Vegas and stopwatch timing over these measured miles indicated that the analog gauge on the dash is a better indicator of actual speed. Never mind, I'm going to calculate using the ODBII.

So, what I need is a stretch of level highway where I can just look at the readout on the instant mileage indicator, wait for it to stabilize, and there's my answer. The complicating external factors might be an undetected slope, and wind. As it happens, there's a stretch of the 405 freeway through Seal Beach that appears to be suitable for this determination. Conveniently, there's a power plant visible from this portion of the freeway, and its smokestack gives an excellent signal of wind conditions. When northbound on the freeway, the average stabilized reading over several trips is about 24.8 m.p.g. Woo Hoo! But when southbound, it's more like 21.9. Hmm.... Must be an undetected slope.

How much might there be and what effect might it have? I looked to Google Earth to try to find out. I located the stretch in question and measured the distance and logged the elevations. I tried to find end spots for my measurement where the elevation clicked from one integer foot to another (e.g., 17 feet to 16 feet) and assumed that this was the location where the actual elevation was halfway from one to the other. Now, this may not be completely accurate, but as long as the algorithm used by Google Earth is consistent, this is the best I can do since I'm not interested in absolute elevations but rather in elevation changes.

It turns out that the elevation change is 5 feet over 0.71 miles. That means that, in the downhill direction, I gain 39,948.6 (I always carry a lot of digits) joules of kinetic energy by converting gravitational potential energy, and turn the same amount of chemical energy (assuming I maintain the same speed) into gravitational potential energy in the uphill direction. It's straightforward to determine how much fuel is saved and burned respectively, if I assume that the car is able to utilize 25% of the heat energy of burning gasoline for propulsion at this speed.

Since I haven't had readers of this blog clamoring for more mathematical detail, I'll just give the results. Factoring out the "free" energy provided by going downhill, the car should be producing 23.74 m.p.g. Factoring it out in the uphill direction, the resulting mileage is 22.79 m.p.g. Closer but not identical. I'm not sure where the error is, so I'll just average the two numbers and say that my level highway average m.p.g. is 23.27 m.p.g. This is still a healthy increment above the 18 m.p.g. estimated by the EPA but, amazingly, it rounds precisely to their uncorrected number of 23.3 m.p.g.. I know that the test protocol does not involve simply running in cruise control on level highway in no wind conditions but it still pleases me to beat the window sticker estimate by over 29%, as arbitrary as that EPA estimated number seems to be.

Another lesson is that such a slight hill has so much effect on mileage. Five feet over 0.71 miles is 0.076 degrees; almost undetectable. To get an idea, if you're hanging a 24 inch wide picture and it's off of level by this amount, the low side will be 0.03 inches lower (about 1/32 inch) than the high side. And yet climbing it reduces fuel economy by 5.9%. The lesson? ALWAYS make sure that your destination is at a lower elevation than your starting point.

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