“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

## Sunday, December 21, 2008

### Yet another look at alternative transport

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

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

The "Electric GPR" is apparently not yet available, however, one can be ordered at a retail price of $8,000. This is about 2.3 times the most recent cost of the Zapino I evaluated in my previous post. The aspect of the Electric GPR that makes it worth a look is its status as a street legal motorcycle and, at least as claimed by Electric Motorsport, freeway capable. Should it be actually so, I could anticipate a commute time approximately the same as the one I suffer in my Land Rover LR3 HSE. Readers may recall that one of the key negative factors in my evaluation of the Zapino was that it would have to be ridden on surface streets and thus would add dramatically to my commute time. As to specifics, the Electric GPR utilizes a lithium ion battery with a capacity of 3.3 kilowatt hours (11,880,000 joules - the amount of energy available in a little under a tenth of a gallon of gasoline). It powers a 50 volt Etek RT motor apparently manufactured by Briggs & Stratton. It's advertised as having a range of 35 miles in "power mode" and 60 miles in "economy mode." Obviously, since my freeway commute is a little over 30 miles, economy mode would be the ticket. I'm not able to determine whether economy mode means no freeway riding at 55 m.p.h.; if so, it's obviously disqualifying. Suppose that it's capable of commuting from my office and climbing the final (steep and long) hill to my house. Do I want to be on a California freeway in the far right lane at 55 m.p.h. on a 285 pound motorcycle that makes no noise? I have a very limited history with riding and no one would imagine that I'm an expert, so there would appear to be a very strong element of danger. Can extreme caution make this a controllable risk? I don't know. What about the economics? It's not so easy to estimate this, what with the extreme volatility of gasoline prices. This is obviously the largest factor in determining the return on investment in such an asset. Do I use$4.959 (or higher) as I paid in June, 2008 or $1.939 as I paid at my most recent fill up? I'm going to use$3.00. My personal belief is that, in the period of the next couple of years, that number will underestimate the average cost of gasoline and therefore my calculations will be conservative (in the engineering sense).

I would imagine that I'll use about 2.8 kilowatt hours of energy for a 32 mile trip. In order to replenish the battery, I'll have to use 3.3 kilowatt hours of electricity (assuming the charging system is 85% efficient). This will cost me about (because of the tiered system of electricity billing, I have to assume the worst case) $0.4330 for a cost per mile of$0.0135. The LR3 at $3.00/gallon would cost about$0.146/mile or a little over 10 times as much. Assuming I'd be able to use the motorcycle 180 days per year at 62 miles per day, I'd save about $4,600 per year. The LR3 is under warranty and thus maintenance costs are currently nil, so any maintenance or replacement reserve for the Electric GPR would be a pure cost with no offset. Since the warranty is only one year (!) I suspect that maintenance would not be negligible. But let's make a pessimistic assumption that it would cost$1,000/year. That would mean that it would take something on the order of two years and three months to pay for itself. This is a very simplistic way of looking at return on investment but it certainly indicates that, from a purely economic point of view, the purchase decision should be positive.

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

## Sunday, December 07, 2008

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

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

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

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

### A stunning drop

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

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

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

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

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

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

## 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.

## 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.

## 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.

## 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).

## 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.

## 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.

## 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.

## 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.