“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)

Saturday, December 29, 2007

Going renewable (part 2)

In my previous post I discussed what it would take for me to harvest the entirety of my family's energy usage on our own property using renewable sources. This resulted in the determination that I'd need to install 9,400 square feet of solar collectors at an approximate cost of $900,000. Clearly, this isn't a practical calculation for an actual plan. Nor was it meant to imply that photovoltaics are impractical or a waste. Rather, the point was that for the U.S. as a whole to be free of the need for fossil fuel, it will take more than panels on rooftops.

A reader (Mark) was kind enough to leave a comment. His point was that I'm being misleading in producing such figures. He also pointed out that using solar power in a grid connected system to produce more electrical energy than is used by a homeowner is a waste, at least in a financial sense, because the utility purchases such excess power at wholesale rates (tied to what they pay per kilowatt hour from their normal sources). Up to that point, they effectively pay the homeowner retail, since they utilize so-called "net metering" and when the system is producing more power than is being used, the meter literally spins backward.

In order to determine the figures for what I'd need to net out our household electrical use, I can use the figures from the post referred to above and my post on my family's total energy use. Using this data, I'd need 660 square feet of collector area (say 22' X 30') to supply a system capable of delivering about 8 kilowatts for about $64,000. Much more realistic, but I better goose it up a little bit because we're now talking about "practical" systems, and such systems don't convert sunlight at 20% efficiency today. Let's say a 10 kilowatt system for $80,000. Tax credits and other government inducements might cut this cost in half. So I could, in theory, free myself from paying for electricity by spending $40,000. Obviously, every single thing I can do to reduce energy usage will pay off massively.

Now, let's dig into the figures from part 1 a little more deeply. In my post totaling my family's energy use, I determined that we currently spend something like $35,000 per year on total energy costs. To offset that, I'd need to spend $900,000. Let's ignore maintenance costs and figure that a $900,000 investment would return $35,000/year for a system life span of 20 years. Finally, let's assume that my cost of capital is about 6.5%, about the going rate for a second trust deed (not that I have $900,000 in equity). So what's the net present value of using $900,000 at 6.5% interest to generate an income of $35,000/year? Clearly it's going to be negative since 20 times $35,000 is only $700,000. Thus, at current energy prices, it doesn't pay to go totally renewable, even if it were possible to do so.

Finally, let's figure what energy would have to cost in order for an investment of $900,000 to pay a reasonable rate of return. Let's call that rate 10.5%, that's a break even return on money that costs 6.5% with inflation at 4%. And we'll assume a lifespan of 20 years. The investment would have to return about $109,000/year. That implies that the cost of energy would have to increase by $109,000/$35,000 or a little over three times to make it "calc out." With the government offering to pay half my costs (sort of) it might only have to increase by 50%.

Of course, all of these figures are theoretical because my energy figures incorporate embedded energy in food and goods, all transportation costs, etc. And the $35,000 per year includes gasoline, coal burned and uranium decayed to make electricity for the house and factories, etc. all accounted for at a single rate of probably questionable accuracy. Nevertheless, the ratios are approximately correct, so the implied price increases of energy (or, inversely, the implied decrease in the cost of renewables) should be about right. It won't be long, since both numbers are heading quickly in the "right" direction.

Tuesday, December 25, 2007

Going renewable (part 1)

My last couple of posts have dealt with my family's overall use of energy. I've calculated it in terms of equivalent continuous power and included transportation, food, durable and consumer goods, and household energy use. For those unclear on the distinction between power and energy, an analogy would be that power in watts (and kilowatts, etc.) is to speed in miles per hour as energy in kilowatt hours (or, equivalently, 3,600,000 joules) is to distance in miles. Or, alternatively, power is to energy as speed is to distance. You can go a long way by going fast for a little while or going slowly for a long time. Equivalently, you can use a lot of energy by using a lot of power (watts) for a short time or a little power for a long time. So my calculation of our family's use of energy at the rate of around 40 kilowatts is the average "speed" of constant rate energy use that would use the same amount of energy at the end of, say, a month that our actual sporadic use totals.

In thinking about what it would take to go completely renewable, several factors must be considered. First is that I don't really need to be able to supply power at the rate of 40 kilowatts. A lot of the energy conversion in that number is from the consumption of food and consumer goods. However, if I'm really intending to be entirely sustainable, I should put energy into the grid to compensate for that used in those types of consumption. The same rationale applies to transportation fuel. For this reason, I'll proceed as if that's what I'm going to do.

Next, what renewable sources are available to me? Such exotics as geothermal and tidal are not scaleable to my needs, even if they were geographically and geologically available. Wind is not practical because wind of sufficient velocity is infrequent and the (%$#&*&^%) homeowners' association would never let me put in a tower. (Note to self: NEVER buy a house where there's a homeowners' association). So solar seems to be my only "realistic" option. The reason for the quotation marks will become clear later.

So, should it be photovoltaics? How about a concentrator heating a liquid to boil water and run a turbine? Passive solar for water and home heating? All of the above? Well, what can the sun deliver to me? I'm in Southern California at a latitude of about 33 degrees 50 minutes. Using the U.S. Solar Radiation Resource Map from the National Renewable Energy Laboratory I find that with a two-axis tracking flat plate collector during the worst months of the year I should be able to collect, on average, about 5.5 kilowatt hours/square meter/day of solar energy.

Suppose that I can use, in some fashion, this insolation with 20% efficiency (difficult on my scale but certainly possible on an industrial scale). I'd have 1.1 kilowatt hour/square meter/day available to me. Now our 40 kilowatt rate of consumption is equivalent to 960 kilowatt hours/day, so I'll need to collect solar radiation at 20% efficiency over an area of 960/1.1=873 square meters. Hmmm... That's about 9400 square feet, or an area 94 feet wide by 100 feet long. Our south-facing roof is not that big. Our whole two story house's floor area is only 2480 square feet. I do think that our lot is big enough to encompass such an area of 0.22 acres, but not by much. OK, so I'll erect a structure that spans corner to corner both ways on our lot and top it with some as yet to be determined type of collector.

Now that my needs are defined, what about the type of system and the cost? This is a complex area in which I am by no means an expert. But that has never stopped me before, so let's give it a go. I speculate that setting up a solar to steam turbine system in my suburban neighborhood that can deliver the kind of power I'm discussing here won't be permitted so it appears that photovoltaics is my only option (note that I've dropped the "realistic"). It's impossible that I could cover my lot with photovoltaic panels, so I'd have to use the strategy of concentrating the energy. Maybe mylar sun-tracking reflectors to concentrate the incoming solar energy onto a much smaller set of panels.

Now in June at local noon, I might expect something like 1,300 watts/meter^2 over my 873 meter^2 or a capacity for output of about 227 kilowatts at 20% efficiency. So at an installed rate on the order of $8,000 per kilowatt, I'm looking at spending about $1,800,000. This overstates the requirement by a little bit, since I've sized my system to supply the energy we use in the short, low-sun days of December and January. So I'll cut this in half, to $900,000. I wonder if they take VISA?

Obviously, before getting out the plastic or taking out a second on the house, etc. the most economical thing by far is to reduce consumption. This is easy to say and, in my experience, difficult to do. Compact fluorescent bulbs, turning off lights in rooms not being used, reducing the amount of time the pool filter runs, etc., only nibble at the margins. The biggest consumer is my wife's use of automobile fuel, the next two largest are her and the children's "stuff" consumption and my automobile fuel. Dramatically reducing these would be a huge lifestyle change. But it's going to have to be done.

As discouraging as this is, there's a positive element to it. My family is a fairly hefty consumer of energy, and yet the sun provides enough energy to supply us with our needs over the area of the property we own. If we extrapolate that nationwide, the possibility exists that we could actually become self-sufficient and sustainable. There are many, MANY, MANY hurdles to be overcome but there's reason to think it just might not be impossible. It's now up to us to figure out how to make it happen.

Sunday, December 16, 2007

Carbon footprint adventures

I made some calculations in my last post regarding my family's use of fossil fuels. I attempted to determine as complete a picture as I could, including such things as goods consumption, food, etc. I also utilized a very simplistic model, assuming all our fossil fuel consumption could be modeled by the chemical combination of n-heptane with atmospheric oxygen to produce carbon dioxide and water to estimate our production of carbon dioxide as a result of our energy use. While this undoubtedly leads to inaccuracies, I think it is "in the ballpark."

Since publishing that post, I've played a little bit with the so-called "carbon footprint calculators" to be found all over the web. I've also been as thorough with them as I know how and as they will allow. The results are rather disturbing, if one buys into the theory of anthropogenic global warming by way of carbon dioxide emissions. My "ground up" calculations indicated that my family produces 96 tons per year of carbon dioxide emissions, whereas the calculator linked above shows about 44 tons. This is a rather significant under estimation by more than half, if my calculations are correct. And though they may be off, I don't believe that they are off by that amount.

Now I suppose that those who model climate do so using a better estimate of carbon dioxide emissions than a summation of everyone's output from the carbon footprint calculator. Nevertheless, I imagine many people log on to such sites to determine their footprint and what they can do about it. Based on my results, they severely underestimate the extent of the emissions for which they are responsible and the remedial measures they would need to take.

Assuming that the averages shown on the calculator site are off by the same extent as the results of my calculations, my family of four emits carbon dioxide at a rate of about double the national average, a little under four times the average for so-called "industrial countries," about ten times the world average, and about twenty times the worldwide goal. That is, my family would have to reduce its emissions by about 95% to bring us into accord with that goal.

Wow. If both my wife and I stopped driving, and I stopped flying my airplane, we'd reduce our footprint by just over 50%. In fact, our food consumption alone represents over 8% of our carbon footprint, and thus we would have to eliminate all carbon emissions not involving eating and change our eating to less carbon intensive sources to reduce our footprint by 95%. And as I pointed out in the previous post, this does not take into account our pro-rata share of institutional use of fossil fuels such as military, etc.

If this is truly an accurate representation of our situation and only differs from others in the United States by degree but not basic nature, we aren't going to be able to meet such goals no matter how many conferences in Bali are flown to by worldwide climate diplomats. So what then?

After calculating our footprint, we're given the option of "offsetting" all or part of our carbon dioxide emissions. What would I have to do? I'm given three options: contributing $598 to a "Clean Energy Fund;" contributing $777 to Reforestation in Kenya; and contributing $1,304 to "UK Tree Planting." I get a certificate and everything. Keep in mind, however, that these amounts reflect the carbon dioxide calculated by the calculator at the site, not the ones I calculated from scratch. Those would require over double the expenditure. I guess this is how Al Gore flies around the world and lives in a mansion and yet has a positive effect on climate change. Somehow, I don't feel that everyone buying these offsets will solve our problems.

Saturday, December 08, 2007

Total energy use in my family

In an earlier post I utilized data in the World Almanac and Book of Facts to determine that the total per capita rate of energy consumption in the United States is a little over 11,000 watts. I decided to see where my family and I fall into this. I approximated all of the electrical consumers in the house, the fuel consumption of my vehicle, my wife's vehicle, my airplane, the power I use at work, the power she uses at work, the energy content of the food each of us eats, and the energy content of the items each of us "consumes."

Obviously, many approximations and estimations were necessary but the results are quite interesting to me. It appears that my family of four consumes energy at the rate of about 40,094 watts. This is all-inclusive as best I can make it, but does not include our pro-rata share of government expenditures (this could be significant, considering it would include our share of military expenditures of energy, etc.). Surprisingly, this amounts to 10,023 watts per capita in my family. I find this agreement with the figures from the Almanac to be downright startling and, frankly, quite gratifying. It's a little misleading though, since the Almanac figures are the total of U.S. energy use whereas, as we'll see later, a significant portion of my family's energy consumption likely takes place offshore.

The largest single item is my wife's use of automobile gasoline in her Grand Cherokee Laredo. This came to 11,880 watts. She uses a LOT of gas.The next is her consumption of "stuff." I don't know exactly what she buys, so I used the the money she spends as a proxy. I excluded food, since it's included separately, then figured one third the cost represents energy input. In earlier days it would have been less, since there would be more input of labor but in this automated day and age, I figure one third. Then I estimated the cost of a joule of energy (about $2.778*10^-8) and worked back to rate of consumption normalized to represent continuous consumption. Since the two children that share our house are hers, I lumped all consumption that is not mine into hers. The total for this category is 10,400 watts. This is the where the "offshore" portion mentioned above comes in, since a significant portion of the energy input for our "stuff" purchases is in places like China.

Next came my use of automobile gasoline at 5,049 watts, followed by aviation gas for my airplane at 3,961 watts. The house consumes energy at the rate of about 2,812 watts. I used a separate spreadsheet to go item by item in the house, the largest consumer on the continuous, annualized basis is the refrigerator, followed by the swimming pool pump. My goods consumption comes in at 2,400 watts. Total food for the four of us is 3,294 watts. Amazingly, taking my house completely "off the grid" would only reduce our family's total fossil fuel energy expenditure by about 7%. As an aside, I should point out that I'm carrying many more digits of accuracy than my approximations justify, the best of them are probably good for two significant figures.

From a carbon footprint point of view, I assume that 100% of our energy use comes from burning fossil fuels, and that 6 pounds of fossil fuel provides 125,000,000 joules of energy and produces 19 pounds of carbon dioxide. That means that our rate of energy consumption results in the annual addition to the atmosphere of 96 tons of carbon dioxide. From an economic point of view, my family spends something like $35,000 per year on energy.

I mentioned in my article about the Almanac that I was confident I could reduce my rate of energy consumption by half. I'm less confident now that it would be relatively easy, but circumstances will surely force us to do this and much more. At least I now know where to start looking for the savings.

Sunday, November 25, 2007

A year's worth of data

For those of you who would prefer to see actual data rather than read my descriptions of what it indicates, I'm publishing a Google spreadsheet that shows the complete data set for my Land Rover LR3 HSE. The Excel spreadsheet is, of course, more extensive and informative, particularly with respect to the charts. But this should certainly be enough to let those who would like to know more about the actual numbers I've achieved satisfy that desire. I apologize for my current inability to format the spreadsheet to the width of the blog, I'll work on it.

Average speed

My Land Rover LR3 HSE has a fairly extensive menu of data on display. One of these displays is "Average Speed." Like all the numbers on the display, it resets when the mileage on the trip odometer (actually one of the two trip odometers) is reset to zero. I do this at each fill up, so the average speed on the indicator shows the average for the current tank full.

The average speed should reflect, among other things, the amount of time I spend on the highway at 55 m.p.h. versus the time I spend on streets and in traffic jams. It crossed my mind eight fill ups ago to add the average speed data for the tank full to the myriad of other data I collect when I fill up. Since highway mileage should be higher, it's reasonable to expect that higher average speeds for a tank should correlate with higher miles per gallon for that tank.

To check this theory, I've plotted m.p.g. on the vertical axis versus average speed on the horizontal axis. As expected, higher speeds are accompanied by higher mileage numbers. The linear trendline, calculated by Excel, has a slope of about 0.32, meaning that each mile per hour increase in average speed over a tank full yields an increase in 0.32 m.p.g. for that tank full. The coefficient of determination ("R squared"), however, is low at 0.48. Thus, while there is a positive correlation between average speed and gas mileage, average speed is a weak predictor of gas mileage. More data will enable a deeper analysis.

For those who are curious about what the actual numbers are, the lowest average speed has been 31.7 m.p.h. and the highest has been 39.1. The latter number was for a tank full the bulk of which was expended on the interstate from Las Vegas to Los Angeles. That tank full produced a fuel economy of 23.41 m.p.g. The lowest average speed produced a fuel economy of 19.82 m.p.g.

Saturday, November 24, 2007


The only way to my house is to select one of two hills to climb. As I make my choice and climb, I watch the average mileage for that tank full (the LR3 clears the average mileage at fill up when the trip odometer is reset) decrease. And quite a few web sites that discuss gas mileage state that, when possible, use the least hilly route available. This got me to wondering what the effects of hills actually are so, as usual, I decided to do some calculating.

To start, I found the elevation at the bottom and top of the hill I usually climb by getting the latitude and longitude from Google Earth and then plugging the coordinates into the height/elevation tool of EarthTool: Webservices. I determined that I climb 123 meters. Doing this in a vehicle whose mass is, on average, 2,673 kilograms means that I add 3,222,000 joules of potential energy to the vehicle in climbing the hill. This energy comes from burning gasoline, but since I'm only able to use about 25% of the heat of the combustion of fuel, I need four times this amount, or about 12,890,000 joules of heat energy from gasoline. This is the amount in about 0.1 gallons. This is in addition to the fuel I burn just to drive the 2108 meters of road (as measured by Google Earth) to climb the hill.

Since I typically drive this hill at about the speed limit of 35 m.p.h., on level ground I'd get something like 21 m.p.g. and use about 0.062 gallons. Thus, I use much more fuel to climb the hill than I do to drive the distance. Adding the two numbers, I use 0.062 + 0.1 gallons to drive 1.31 miles for a gas mileage number of about 8.1 m.p.g. This squares nicely with what the readout on the panel display says.

BUT... When I go down the hill, I turn my engine off and coast to the bottom of the hill. The distance down is the same as the distance up, so if I drove it on level ground, I'd use the same 0.062 gallons. Instead, I use none. So driving up the hill and coasting down uses 0.162 gallons, driving the same distance on level ground would use about 0.124 gallons. Thus, the necessity of climbing the hill requires the expenditure of 0.038 gallons of fuel. Since I typically do this about five times per fill up, I put something like 0.19 extra gallons of fuel in the tank because I live at the top of a hill.

So how does this affect my fuel economy? Well, let's say I fill up at 340 miles and put in 17 gallons. This is fairly representative, and equates to exactly 20 m.p.g. The extra 0.17 gallons would reduce my mileage to about 19.8 m.p.g. I'm kind of surprised by this result, as I intuitively expect that I'll convert the potential energy going down the hill. If I didn't have to brake going down the hill and if I could hit the bottom, turn the corner and coast down to cruising speed I'd be able to recover a lot more of it, but these actions aren't possible. This means that I end up using the stored potential energy gained by burning fossil fuel to heat the metal in my brakes.

The hill seems pretty steep. Running the trigonometry, it turns out to average 3.34 degrees. It turns out that going up the hill and down adds eight meters to the distance I would travel if there were no elevation change from the location of the beginning of the hill to my house. While I will always turn off my engine and coast the last eight meters into a parking space where possible, it isn't saving much. The extra eight meters driven five times for a fill up use about a thousandth of a gallon. Anyway, traveling up and down hills clearly does not help fuel economy. I guess I should move downhill. Better yet, move next door to my job.

Monday, November 05, 2007

Stoplights revisited

I get frustrated when I'm cruising down a major thoroughfare at the speed limit on cruise control, say at 40 m.p.h. and the light turns yellow at a point that forces me to stop. Often, a lot of cars behind and in front of me will also have to stop and a single car will pull out from the cross street. Or I'll stop and there's nobody at the light on the cross street. What a waste!

So, it's frustrating, it loses time for me (and others of course), and it does waste fuel. But how much? And if we could figure out a way to eliminate them altogether, what could be saved? Sounds like a time for estimates and calculations since I can't find figures on how many stoplights are stopped at each day. I've repeatedly mentioned Fermi and so-called Fermi problems where plausible estimates are made. I'll give it a try.

Fuel is wasted in two ways at a stop light. First, the kinetic energy at speed is wasted, though the waste from this can be minimized by utilizing coasting to a stop. While your kinetic energy still goes to zero, you use less gas in getting there. But you still have to extract the potential energy from the gas to change to kinetic energy in getting back to speed. Then, you waste fuel idling at the light. I mitigate this to an extent by shutting off the engine at some long lights (the efficacy of this is controversial and the subject of future experimentation). But I'll ignore that technique for this analysis.

I'll calculate figures for what I think are average cars, drivers, and routes. I'll figure a 3000 pound car (including fuel and payload)and accelerating to 32 m.p.h. (my typical average speed over a tankful). I estimate that the average driver stops at 12 stoplights each day (is this high?) and spends 45 seconds at each. Finally, I'll estimate that an average car burns 0.35 gallons of fuel per hour at idle.

Using these numbers, I have to add 139,350 joules of kinetic energy to get the vehicle up to speed. This means I need to burn about 557,400 joules worth of gasoline, about 0.00446 gallons to add back this lost energy (since I have to burn four joules worth of gasoline to get a joule of useful work, with the 25% efficiency of the engine). And 45 seconds of idling at 0.35 gallons per hour burns 0.004375 gallons of fuel. I'll add another 0.00097 gallons for the fuel used during the coast to a stop. Thus, as an approximation, a single stoplight will waste about 0.009805 gallons of fuel. In a day of 12 stoplight encounters, this is 0.11766 gallons.

Now, I'll figure about 125,000,000 people do this in a day, for a burn of 14,707,500 gallons nationwide, representing $44M. At 19 gallons of gasoline in a barrel of oil, this is represents the gasoline in 774,000 barrels of oil. Of course, the other 25 gallons of oil are used, so all of this wouldn't be saved. Figure 1/2 of this, or 387,000 barrels. This is about 1.8% of our daily oil use.

Of course, it's not possible to have no traffic lights, so if proper sequencing and traffic management logic could reduce stops at lights by a third, 0.6% of our oil use might be saved. And the carbon in a gallon will combine in the engine with atmospheric oxygen to create about 19 pounds of carbon dioxide, so this would save 139,700 tons of CO2 per day.

For me, adjusting the figures to reflect my vehicle, I waste about 0.195 gallons per day at an approximate cost of $0.59. A little under a nickel per light. In a year, this is about $213. Not a fortune, obviously. In fact, my time at the lights is worth considerably more (depending on whom you ask). And, as above, it's impossible to live in a world with no traffic signals, so reducing my stops at lights by a third would save me about $71. Again, not a huge amount of money. But, if asked, I'd rather have $71. than not have it.

Sunday, October 21, 2007


I live in Southern California, and we experience a phenomenon known as "Santa Ana Winds." These winds can literally reach hurricane speeds, I heard that a gust reached 108 m.p.h. today. These winds are invariably extremely dry and typically result in a rash of wildfires. Such has been the case today.

I was driving back to my house from Lakewood, an easterly trip down the 91 freeway. Santa Ana Winds originate in the Great Basin and thus are typically northeasterly. As I tooled down the freeway at my usual 55 m.p.h., I noted sand, pebbles, leaves, etc. blowing into my windshield as my car experienced significant buffeting. Looking at my miles per gallon display, on a level stretch where I expect to see 21.5 m.p.g. I noted 17.2 m.p.g. I had heard that the sustained winds in this area were on the order of 30 to 40 m.p.h. with possibly something like a 22 to 29 m.p.h. headwind component (it was off my nose by maybe 45 degrees), and so presumably that's the sort of gas mileage I could expect in the range of 80 m.p.h. (using the average of 22 and 29 as the headwind component).

Needless to say, I wasn't pleased but I wasn't willing to slow down to, oh, say, 30 m.p.h. to attempt to save fuel. Even my compulsiveness has limits. Besides, I didn't want a crash or a ticket. I've been pulled over for driving 55 m.p.h. in the right lane. Though the officer wouldn't say why he pulled me over, I'm sure he thought I'd been drinking (I've been sober for 28 years) and that I was trying to avoid being pulled over. He didn't even ask for my license and registration, he just shined his light in my eyes, told me to drive carefully, and left.

So what's to be learned from this headwind experience? There's not much to be done about it, but I can at least plug the numbers into my fuel consumption versus speed equation and see if they fit. Maybe my mileage gauge can serve double duty as an anemometer.

Sunday, October 14, 2007

More on A/C

With the Scan Gauge 2 I can find out a lot about what my engine is doing. I have it set to provide a continuous display of speed (it's about 2 m.p.h. slower than the dashboard speedometer display), r.p.m., instant mileage, and absolute manifold pressure. The manifold pressure is a very sensitive indication of throttle position, since throttling is accomplished by restricting the flow of air through the throttle body.

I've found a few stretches of freeway where it seems like the road is level, or at least its slope is constant (constant slope will suffice for this). Thus, with cruise control on, manifold pressure will remain quite constant on these stretches. This is an ideal time to experiment with turning the air conditioning on and off to see if there is an effect on manifold pressure, indicating that throttle position is increased in order to operate the compressor while still maintaining the selected speed.

So what happens? Well, the manifold pressure increases by approximately 0.4 p.s.i., typically from 9.1 p.s.i. to 9.5 p.s.i. I found this to be a consistent and repeatable result. What does it mean in terms of fuel consumption? I can run a few calculations and come up with a number, but I'm not extremely confident in the accuracy because the indications on the instant gas mileage display are not as dramatic, consistent, or repeatable.

But let's proceed anyway. PV=nRT in an ideal gas, we'll assume (inaccurately) that that's what we have. Since, for a given length of time the volume, V, and the temperature, T, are fixed, and R is the universal gas constant and thus never changes, a change in P means that n, the quantity of the gas (number of moles), must change by the same proportion. A change from 9.1 p.s.i. to 9.5 p.s.i. represents an increase of about 4.4%, so fuel consumption should increase by a similar amount. Since I'm typically looking at about 21.7 m.p.g. or so, I should see a decrease to something like 20.8 m.p.g. It doesn't seem like I see this much of a decrease, but I'm going to be doing some more checking.

In another post I determined the LR3 uses something like 24.5 horsepower to cruise on a level highway at 55 m.p.h. Since burning fuel provides this horsepower, the additional fuel burn should reflect the increased power required to run the air conditioner. How much power? It works out to be just a tiny bit over 1 horsepower, and as I concluded in my previous post on air conditioning, I find that to be a number that squares nicely with my intuition.

Tire pressure and the last 1%

Regular followers of my blog (mythical creatures though they might be) will have noted that I have compulsive tendencies. This character trait has expressed itself in various ways through my life, some destructive and others not. I consider my pursuit of maximum mileage from gasoline in my vehicle to be in the latter category. For that reason, I'm glad to continue my activities and analysis in this area.

I've had my Land Rover LR3 HSE for just shy of a year (324 days to be precise). I haven't spent a lot of time checking tire pressure, how important might this be? Various sites (see no. 4 here for example) give percentages of 2% to 4% as the excess consumption caused by under-inflation. Edmunds conducted some testing of various "tips" to save fuel, reported in a column entitled "We Test the Tips." Tire pressure is number 5 in their list of tested tips. They were unable to find consistent savings, though they did find what they termed "modest savings" in two vehicles.

What about the physics? Well, it's quite a complex topic to solve analytically, but I utilized a tool called "Dimensional Analysis" to make an approach to the problem. I concluded that rolling resistance is inversely proportional to the square root of tire pressure. This would mean that there might be approximately a 5% difference between overfilling by 2 p.s.i. versus being under-inflated by 4 p.s.i. Keep in mind that rolling resistance is only one of the external forces acting on the vehicle and that it decreases in relative importance as speed increases, since aerodynamic drag increases with the square of speed. Interestingly, tire rolling resistance is independent of vehicle speed, at least insofar as the depth of the analysis I performed.

So at highway speeds, it's likely that an increase in rolling resistance of 5% might contribute about a 2% increase to overall resistive forces, exactly in line with what many of the fuel saving sites indicate. I'd better get that gauge out of the glove box.

Sunday, September 30, 2007

Bottled water

So... I'm walking into my local Von's grocery store. Outside on the sidewalk, on my left is a 6' wide by 8' long by 5' high display of 24-count packages of bottled water. On my right, I see a similarly sized display of another brand of bottled water. When I check out, I notice a "sale" display of Propel Fitness Water. It's being sold for two 8-count packages with 20 fluid ounces of fitness water for $10. I burst out laughing, much to the dismay of the clerk and some other customers. That's $4/gallon for water with a little vitamins thrown in. It's on sale from $5.60 per gallon. And in one way, it is a bargain. Evian is close to $7 per gallon.

Well. I really like water. It's far and away my favorite drink. I drink a lot of it. And I drink it right out of the tap, from the same source (city water) from which a lot of these purveyors of boutique water acquire the elixir. Now and again there's a source of tap water with a small odd taste, but that's quite rare. Our refrigerator at the house and the one at my company have filters. What would possess someone to pay a third more for water than they pay for gasoline? (To be fair, it looks like Evian really is imported from France. That makes it even more decisively stupid in my opinion.)

I often say that if you were to go back in time and tell someone from, oh, say, 1950 that in 57 years water would be put in small bottles and sold at stores for twice the price of gasoline they'd lock you up. The inefficiency and silliness of this water craze is hard to put into words. To draw water from a city supply, filter it, put it in plastic bottles, ship it to stores and sell it is an incredible waste. Then it's drunk and the bottle discarded or recycled using more energy. Well, I'm not going to say it should be outlawed, but my Lord, how can we have hope when such insanity prevails?

Anywhere in the United States, one can turn on the tap and receive tested, safe water for less than 1 penny per gallon. In some cases, way less. So Evian at the equivalent of $7/gallon or Propel at $4/gallon is simply ludicrous. The energy used in plastic, the transportation, etc. only makes it that much worse. When will it end?

Data and Statistics

I've collected data on the fuel consumption of my LR3 HSE since I purchased it in November of 2006. I've missed a couple of fill ups and a few miles when my wife has used it when I've been out of town, but by and large it's a pretty complete data set.

I've driven the vehicle in a way that most people would consider normal in terms of speed, acceleration, behavior at lights and on hills, etc. and I've more recently driven it in a way that most would regard as extreme with respect to such matters. It's obvious on the surface that my fuel economizing techniques are effective, I need only look at the graphs. But what do the statistics say?

I keep track of mileage at the most recent fill up, as well as three tank, five tank, and ten tank moving average. I track the standard deviation of the mileage (separately for before and after resumption of fuel economy maximization). The "before" data consists of 35 points, the "after" of 21 points. Surprisingly, the standard deviation of the "before" data is 0.66 m.p.g., that of the "after" is 1.20 m.p.g.

Standard deviation is a measure of "central tendency," that is, of the tendency of a data set to be clustered closely to the mean (the mathematician or statistician's term for average), or scattered far from the mean. For a so-called "normally distributed" population (that is, a population that when plotted exhibits the classic "bell curve"), about 68% of the data points will lie within plus or minus one standard deviation of the mean, about 95% within two standard deviations.

We're actually looking at an experiment here though, the question is how accurately does the mean of my mileage calculations reflect the actual gas mileage I've achieved? What we're looking for is the standard error of the mean. It's the standard deviation of the population (as computed above, itself an estimate) divided by the square root of the sample size. So, for the pre-economizing driving it's 0.66/sqrt(35)=0.11. For the post-economizing driving, it's 1.20/sqrt(21)=0.26. This latter number means the true mean gas mileage for this driving methodology, vehicle, and driving regime has about a 95% probability of being within 19.61 +/- 2*0.26 m.p.g. Or, there's about a 5% chance that the actual population mileage is outside of this range, that is, there's a 2 1/2% chance it's less than 19.09 m.p.g. and a 2 1/2% chance it's greater than 20.13 m.p.g.

This is far higher than the EPA estimate, and the graphs of my mileage show the improvements leveling off. Well, I can probably begin to make deductions based on the data I have regarding what can be done.

Behind the Power Curve

As I've mentioned previously, I'm a pilot. There's a concept in aviation called being "behind the power curve." It's a situation wherein induced drag caused by a high angle of attack means that going slower requires more rather than less power. The only way out is to lower the nose.

I've also mentioned that I'm philosophically aligned with libertarianism (small letter l). My core beliefs involve personal choice, personal responsibility, freedom, and right to privacy. Thus, I don't typically look to government to solve societal problems. However, I think that it's possible that we've reached a situation analogous to being behind the power curve, where it's going to take more unified and possibly directed action to get through the next few years without the societal equivalent of an aerodynamic stall.

What I mean is that the changes in infrastructure and industry that will be required to succeed in the establishment of a new paradigm for energy conversion have a huge energy requirement of their own. This need becomes more and more difficult to supply in light of the (possible) passing of so-called "peak oil" and the ever increasing demands on fossil fuel from the developing nations as they compete to achieve what we in America regard as (to paraphrase Dick Cheney) our non-negotiable birthright to the American lifestyle.

I love the American lifestyle of flat screen TV's (we have two), a vehicle for everyone of driving age (we have three for two people), a nice house (four bedrooms for four people), a swimming pool, and my Piper Saratoga. So what am I doing talking about saving energy and government action? And more poignantly, how do I reconcile this lifestyle of profligate energy expenditure with my attempts to squeeze a few extra miles per tank full from what is, after all, a fuel-guzzling, oversized SUV?

In a way, this is the reason that I'm afraid governments will need to step in. I have these things and live this way because I can and I like it. There are millions more like me. By the time the free market makes it impossible for me to continue to live this way, it may well be too late to matter. The market is very good at sending signals in some circumstances - it's certainly sending some clear signals about our trade deficit and our export of jobs that actually create things with the price of a dollar in Euros or Canadian Dollars. But the market seems ill equipped to send a signal that will cause us to take actions that will cost us in lifestyle and whose payoff is years into the future. Unfortunately and in contradiction to my philosophical inclination, I'm afraid that government intervention is the equivalent of putting the nose down.

Sunday, September 16, 2007

The effect of "philosophy" on the interpretation of factual information

I like to listen to all viewpoints. I listen to KPFK, Pacifica Radio's Southern California outlet, for the farthest left point of view, and to KRLA, Salem Radio's Los Angeles area station, for the right point of view. The other day someone asked Michael Medved, an afternoon host on KRLA, about peak oil. Medved said "it's nonsense." Now, listening to him, one realizes he's an intelligent man and must be capable of understanding facts. What would cause him to say such a foolish thing?

I've concluded that Medved and many, many others (both on the radio and in "real life") decide what the facts must be to fit their viewpoint. They read books and articles and listen to people who will "confirm" the facts that support their philosophical beliefs. They form a self-reinforcing feedback loop of confirmation. I believe that talk radio, blogs, etc., have exacerbated this phenomenon. Thus, for example, people with a conservative outlook now believe that the peak oil phenomenon is nonsense because Medved said so, and he's a smart guy with a radio talk show.

The potential for disaster is huge. In my opinion the only chance, and it's a slim one, that we have of avoiding really very large trauma in the way we live our lives is the sort of single minded, participatory, nationwide goal-oriented behavior that we last exhibited during World War 2. As I've mentioned several times in my blog I have a libertarian orientation philosophically, but I don't see how we're going to get through this with everyone acting in his or her own enlightened self-interest. Nor do I see how growing population, growing energy use, growing "standard of living" (when measured in standard terms) can continue. And the denial of this will hasten and worsen the crash.

So, back to the question at hand. What can be done to help seemingly intelligent individuals to objectively evaluate facts rather than bend the facts to fit the way they think things "must work?" Unfortunately, I see a stronger tendency for this behavior from the conservative hosts on Salem Radio than from the liberal (actually liberal is far too weak) hosts on Pacifica. This saddens me, as I don't align myself with Pacifica's point of view in general. I'd like to feel that conservatives deal with facts, but this is not the case.

For another example, EVERY conservative host I know of is a "global warming denier." Now, I will definitely concede that there are intelligent climate scientists who argue that global warming caused by mankind's release of greenhouse gases is not yet a proven fact. There are many, many more who disagree. But Dennis Prager, Michael Medved, et al, will hear none of it. This is a sad commentary on their ability to deal with reality.

I wish peak oil were nonsense, I wish anthropogenic climate change were a myth, but as I had to learn as a child, wishing won't make it so.

Tuesday, July 24, 2007

Saving the world ..... again

As mentioned in a previous post, I've restarted my efforts to reduce fuel consumption in the LR3 by driving techniques. When I got the vehicle, I attempted to do so but had little success. Now, however, I've carried it to the next level, the most extreme to which I can safely and practically go. I've managed to get my average m.p.g. to slightly above 19.5 in my five tank moving average.

As I've opined over the last couple of posts, the fossil fuel situation is far too dire for such measures alone to save the day. And I've posted earlier estimates of how much fuel might be saved. But if I assume that what I'm doing now more accurately represents what can be done by the average driver than the extremes I achieved in the Grand Cherokee, what does that indicate can be accomplished?

My current three tank moving average of miles per gallon is at 19.55. The LR3 is rated by the EPA at 14 city, 18 highway. I estimate that 60% of my mileage is highway, 40% city, so the blended average mileage should be 0.4*14+0.6*18=16.4 m.p.g. I exceed this by about 3.15 m.p.g., or 19.2%.

As before, based on the complaints I hear and read, I assume that very few people are getting the mileage estimated for their vehicle by the EPA. I'll guess at 90%. I exceed this estimated average by 119.2/90=1.324, or 32.4%, so I use 1/1.324 or .755 (75.5%)as much fuel as the average person would in my vehicle driving my routes. If everyone did this and achieved the same results, it would be a reduction of 24.5% in transportation fuel usage in the personal vehicle sector.

According to this wonderful web site two thirds of U.S. oil use is in the transportation sector. I have read (I can't find sources right now) that half of transportation fuel use is in private (as opposed to commercial) vehicles. And about 19.5 gallons of gasoline comes from each of the 21 million barrels of oil we use daily. So of the 409,500,000 gallons of gasoline used each day, 24.5% or right at 100 million gallons could be saved. This is the gasoline from 5,145,000 barrels of oil.

Of course, the other 22 or so gallons of product from a barrel of oil aren't thrown away when gasoline is refined, so we wouldn't save that many barrels, but I estimate that well over two million barrels per day could be saved, 10% of our consumption and about 15% of our imports. Obviously, we won't achieve the chimeric goal of energy independence by these measures, but they could buy us some time. A side benefit would be the reduction of our trade deficit by over $4 billion per month.

As I've often pointed out in these articles, these savings won't come free, the payment will be in hours of time spent on the road instead of at work or with family, friends, etc. That price will seem more and more worth paying as scarcity increases and prices rise.

Saturday, July 21, 2007

Exponential growth versus exponential decline

I would like to direct my readers' attention to a web site created by an organization called "Negative Population Growth." As its name implies, the organization is devoted to bringing attention to and finding solutions for the problems of humankind caused by overpopulation (pretty much all the problems, as nearly as I can tell). The link above is to a presentation of exponential growth by Dr. Albert Bartlett, who has become famous in peak oil circles and rightly so.

I would direct the reader's attention to section II, subsections IV and V. These address the mathematics of exponential growth of consumption of a finite resource. Obviously, here I'm thinking of growth in energy (specifically, fossil fuel) use versus the finite total of recoverable fossil fuel resources. Dr. Bartlett presents the concept of the "exponential expiration time," a mathematical expression relating the size of a resource, the consumption rate of the resource, and the rate of growth of consumption of the resource.

While none of the numerical quantities involved (population growth, economic growth, total recoverable resources) are known precisely and the growth rates are not constant, the conclusions will hold qualitatively as long as the rates are positive and the resource is finite. Let's calculate a model scenario that doesn't even require an estimate of what is referred to in the peak oil community as "ultimately recoverable resources" or "URR."

The idea is to determine the rate at which so-called "renewable energy" production must increase to make up for a shortfall in availability of energy derived from fossil fuels. I'll make some assumptions, based on the best information at my disposal, regarding rate of growth of demand for fossil fuels, rate of decline of fossil fuel production, and the current rate of fossil fuel consumption. I'll cite the sources of data and the pertinent dates. The reader should keep in mind that experts have done these calculations with better models and more accurate information (not to mention higher IQ's) than I have at my disposal, so my results are meant only to help grasp the magnitude of the dilemma we face.

I found an absolute goldmine of data on energy consumption and production - BP (the old British Petroleum) has a downloadable excel spreadsheet that has a spectacular amount of information. I utilized it to find a trend line for worldwide primary energy consumption and determined that, based on data from 1965 through 2006, we have a doubling time on the order of 36 years at an annual growth rate of 1.9%/year. It's certainly possible that many developed countries could moderate their growth in energy consumption, but India and China combined are exhibiting a growth rate on the order of 5% on a curve form 1965 through 2006, and represent about a third of the world's population. It doesn't look good on the consumption side.

On the "production" side (in quotation marks because energy is never produced, it is only converted) the sum of oil plus natural gas production has every appearance of increasing linearly. The peak oil community contends that this curve will plateau (or has plateaued), but the data I see doesn't show it. Unfortunately, the situation is plenty grim even without the plateau. Assuming present trends continue, we must make up the shortfall between exponentially increasing consumption and linearly increasing production with alternative sources of primary energy (hydroelectric, wind, solar, geothermal, tidal, nuclear, etc).

This gap increases exponentially as well, and though energy production through means other than fossil fuels also is increasing exponentially, it is not doing so at a rate that will enable the shortfall to be overcome. I estimate that, in 2010, the shortfall will be on the order of 500 MTOE (million tonnes oil equivalent). In fact, my crude estimates and calculations indicate that alternative sources will be required to be equal to fossil fuel sources in about 2026. If, that is, the plateau and decline don't happen. A mighty big if.

Further, it must be noted that this quick estimate takes no account of the myriad other fossil fuel "sinks" such as plastic products, fertilizer, pharmaceutical products, etc. I believe that the time has come, and possibly gone, for a radical restructuring of how we live our lives. Every assumption and simplification I've made has underestimated the magnitude of the crisis (no other uses of fossil fuel, continuing increase in primary energy production, etc.) I'm neither a socialist nor a utopian, however, every trend I've analyzed indicates that we're whistling past the graveyard and that only the most extreme measures will suffice to avoid catastrophe.

And driving more slowly in an LR3 is not going to get it done.

Y2K was an epic disaster after all

You all remember the approach to Y2K don't you? There were books, magazine articles, web sites, etc. devoted to the inevitability of system wide disaster to be caused by the Y2K bug and to the consequences thereof. Then disaster struck - Y2K came and went and nothing of any consequence happened. Now, there are many explanations. Chief among them is that hundreds of billions of dollars and millions of person-hours were spent and that that expenditure, which for some reason was invisible to the average person, saved us. Therein lies the true disaster.

The Y2K non-event has persuaded many people that predictions of imminent threats to our entire society and way of life are merely the yammerings of wolf-crying doom sayers. In some cases, that may be true. Unfortunately, when it comes to our ability to fuel our society on petroleum products, it is false. This threat is real, and dire consequences are, in fact, unavoidable. The problem is that warnings fall on deaf ears, in part because the average person thinks "yeah yeah, I've heard it all before. They said the same thing about Y2K." One would like to think that a brief application of common sense would cause people to realize that exponentially increasing consumption of a finite resource is a dead-end street, but that brief application is missing.

I live in a so-called "McMansion" (a 2500 square foot four bedroom house) in Anaheim Hills, and as extensively noted in this blog, I drive a 60 mile round trip to work in a segment (inspection and materials testing) of an industry (construction) that will surely go away in the tsunami of economic dislocation caused by the unavailability of imported fossil fuels to "feed the beast." Further, much of my net worth is tied up in the equity in my house and my equity in the company for which I work and in which I am a partner. My vulnerability is huge, I'm a perfect example of what won't work.

The simultaneous trends of exponentially increasing consumption and the peaking of production of fossil fuels would be bad enough. However, quoting the infomercials, "but wait, there's more!" As explained here, as exporting countries' fuel resources begin to suffer the effects of depletion while their citizens demand the things we assume we will always have here (cars, air conditioning, etc.), those countries will divert exports to internal consumption. So even if production doesn't slide as quickly as some predict, oil available for export to the U.S. will decline steeply in the very near future. To call the consequences dire is to understate them dramatically.

Thus, my playing with a Land Rover LR3 to see if I can coax 20 m.p.g. out of it is truly a hobby and almost irrelevant to the fossil fuel situation we face. As far off as James Howard Kunstler was in his Y2K predictions and as bombastic as he is in his prose, I'm afraid that this time he's right. So the true disaster of Y2K was that it blinded many of us to the real doomsday scenario we now face, and prevents us from taking any meaningful steps to mitigate the inevitable tragedy ahead.

Sunday, July 15, 2007

Alternative transport redux

In a previous post I discussed the benefits of using an electric scooter for the bulk of my commuting to and from work. The analysis there was based on my fuel use in the Jeep Grand Cherokee Limited I had when I started this blog. It should be even more beneficial with the Land Rover LR3 HSE that I'm driving now, since the LR3 achieves about 4 m.p.g. less than the Grand Cherokee.

Further, there's a scooter available from Zap!, called the Zapino that, with their optional 60 volt 40 amp-hour battery, claims a range of "up to 65 miles." My commute, as I would have to ride it on surface streets, is 25.57 miles (according to Google Earth) so, in theory, I could make the round trip on a single charge. I wouldn't do it, because the very last part of my trip home is up a very severe hill. I wouldn't want to try it on a dwindling charge. But if I charge it at work, my hope is that it would have sufficient charge remaining to take me up the hill to my house.

There are various factors to consider, even if I stipulate (I've been around lawyers too much lately) that the Zapino is well-built and reliable and will climb the hill at the end of a workday. Most importantly, I need to know the financial impact (the Zapino retails with the standard battery for $3,495, I can't find the price of the optional battery I'd need), and how much time my commute would take.

I can run the route I'd have to take on the scooter but I think it would be foolish to do it in the LR3 at the speed to which I'd be limited in the scooter. So I'll estimate that it would take about 75 minutes each way. My current commute is about 40 minutes. Am I willing to spend 70 extra minutes per day commuting? I wouldn't be able to listen to books on tape or podcasts or even talk radio - such a vehicle requires close attention in city traffic. It's possible that it could be "reasonably" safe to carry a bluetooth ear piece and do limited cell phone business. In most cases, I think I'd have to pull off the road and consequently increase the commute time. It sounds like a non-starter at this point.

For the financial impact, most of the figures in my previous post can, with slight modification, be applied to the use of the Zapino in lieu of the LR3 for the bulk of my work commutes. Of course, these will only be rough estimates, but they should suffice for a "go/no-go" decision. I calculate that the Zapino should cost about $0.10/mile to operate or about $850/year for 180 commutes versus about $4,700/year to operate the LR3 for those commutes. Thus, the potential cost reduction is $3,850/year.

Combining these figures, I'd spend 210 extra hours per year to save $3,850. This means that I'd be paid at the rate of $3,850/210 or $18.33/hour. Unfortunately for my Company, my hourly rate exceeds this by a considerable margin. Thus, in order to make it attractive, I would have to regard the excess time spent on the scooter as personal time, something like a hobby. I think that, to start, it would feel that way. But that would likely get old quite quickly.

These types of tradeoffs are endemic to alternative transport, or even to adjustment of driving techniques to minimize fuel consumption. Professor Steven Dutch, whom I have cited extensively in this blog, makes a cost benefit analysis of public transportation that makes it clear why, for most people, mass transit is not a compelling choice.

Future economic considerations may change the calculus here, and in fact, may make the choice of commuting in a vehicle like the LR3 impossible at any price. Until then, I'm afraid that I just can't justify alternative transport.

Friday, June 29, 2007

The practicalities of drafting

As I've mentioned previously I do some drafting of trucks to increase my gas mileage. I did some estimations and calculations, described in that post, that indicate that, done with extreme caution, it could be safe and that it should be effective. But how practical is it? It's turned out that I'm only able to find a truck to draft between 10% and 15% of the time I'm at freeway speed. Trucks are frequently going too fast for my fuel saving regime, thus leading to the question of what the break even point would be for the fuel used in speeding up to draft a fast-moving truck versus maintaining a leisurely 55 m.p.h. with no truck in front of me. More on this later.

But the fact is, there is rarely a suitable truck around when I need one. I look for trucks with the following characteristics, just based on intuition: low trailer; as square a back as possible (preferably not a milk or cement tanker); not hauling rock, dirt, etc. (no dump trucks); maintains a reasonably steady speed; doesn't do a lot of lane switching, I guess that pretty much covers the candidates. But at 55 m.p.h. I'm not doing much passing of them, so I have to wait for a truck that has the listed attributes to pass me. It is rarer than I would have guessed, though if I see a likely prospect in the rear view mirror, I can slow down to let him catch me.

So when does it pay to speed up to draft? There are two aspects to this - the fuel used in accelerating to a new speed, and the balance between the reduction in drag from being behind the truck (this would be in the density term in the drag equation) and the increase in the speed. Additionally, road loads would increase by a small amount, but I assume this to be linear, and thus the increase in road load force is compensated by the increase in distance covered.

There will be a number at which my fuel savings from reduced density (the low pressure zone behind the truck) will be overcome by the increase from the speed term, since it's squared in the drag equation. For the purposes of this post, I'll ignore the fuel used to get up to a higher speed - this fuel is used to increase the kinetic energy of the vehicle, I'll assume I can recapture this energy (though of course I can't, at least not with 100% efficiency).

I have to use the figures in my previous post on drafting to calculate the reduction in drag to attribute to the truck's wake, and calculate from there. Using my best estimate of the increase in gas mileage while drafting, from 21.5 m.p.g. to about 25 m.p.g., I can calculate that air density is decreased by about 14.0% (from about 1.16 kg/m^3 to about 0.998 kg/m^3). Again, unless I receive a huge outcry demanding the details of the mathematics involved, I'll only outline the process and give the results.

Plugging these density results into the drag equation and realizing that I want to minimize fuel/distance (gallons per mile) = energy/distance = work/distance = force * distance/distance = force, I merely need to determine when drag using the decreased density behind the truck but an increased speed exceeds drag at normal density and 55 m.p.h. As it turns out, that speed is a little over 59 m.p.h. So if I have to go faster than 59 m.p.h. to draft a truck, I will lose fuel efficiency compared to driving 55 m.p.h. in the clear.

Thus, the battle becomes one of finding a truck with all the characteristics listed above AND that is not going faster than 59 m.p.h. This has turned out to be extremely difficult. As I refine my data, I'll revisit these figures.

Tuesday, June 26, 2007

Turning resources to refuse

I read somewhere, I don't remember where, something to the effect that "an economy is a system for turning natural resources into refuse." Obviously, that's hyperbole, but it's not completely without basis. A couple of posts back I looked at national and global energy consumption, comparing time frames and comparing countries and the world. I thought that I could pursue that a little further and see what the energy requirements are to "turn natural resources into refuse."

As I stated in the post linked above, in 2006 the United States consumed 100.41*10^15 btu, or 1.059*10^20 joules of energy. In that time, we produced 245 million tons, or 222*10^9 kilograms of "MSW," municipal solid waste. I can't find an authoritative source for total air pollution in 2006, but in 2005 the total was 141 million tons. Now, that number is on a strong downward trend, it was 188 million in 1995 and 160 million in 2000. Bearing this in mind, I'll use 136 million tons or 123*10^9 kilograms in 2006. I can't find good numbers for water pollution and liquid waste, so I'll blithely assume it's negligible. With that in mind, I'll say we produced 345*10^9 kilograms of waste. So for a start, we used 307 million joules of energy per kilogram of waste. Now, 307 million joules is the amount of energy in about 6.5 kilograms or 2.5 gallons of gasoline.

So our economy used the energy available in 6.5 kilograms of gasoline to produce a kilogram of waste. Let's be optimistic and assume that the combined efficiency of all the energy conversion processes we use is 40%. That would mean that we really needed 16.25 kilograms of gasoline or equivalent to produce a kilogram of waste. Now what does that mean? Good question. From one point of view, if our energy to waste ratio were high, it could mean we didn't waste much, that that energy went into useful things. On the other hand, if our energy to waste ratio were low, it could mean we were efficient, since it wouldn't have taken much energy to produce our byproducts. But I suspect a big number is what we'd like to see.

The complexity of the situation comes from the fact that, taken independently, we'd like to produce small amounts of waste, and we'd like to consume small amounts of energy. I think the way to get a handle on this would be to find out how much energy in joules is contained in an "average" kilogram of manufactured product. In the end, what we want is as little of our consumed energy as possible to go into things that are discarded.

Taming the LR3

As I've mentioned repeatedly, I have had very little success in utilizing driving techniques to make a large impact on the fuel economy of the LR3. This lack of success led me down a road of trying to understand the aerodynamics of the vehicle, the specifics of the engine and transmission, and the effects of driveline friction. It's been educational, but not satisfying with respect to enabling me to goose my gas mileage.

As my brother said, "it kinda takes the fun out of it." Hence, for several months, starting around the beginning of 2007, I stopped using fuel economy maximizing techniques. I didn't go "hog wild" and floor it from the light, drive as fast as traffic would allow, etc., but I would accelerate with the traffic, drive at typical speeds, eschew coasting in neutral and turning off the engine, etc.

The last three weeks or so, however, I have renewed my efforts. I've managed to bring my three tank moving average of gas mileage from a little under 16 m.p.g. to a little under 19 m.p.g. My most recent fill-up indicated 19.37 m.p.h. The improvement is probably a result of 55 m.p.h. or slower, drafting where possible, stoplight shutdowns, and coasting with the engine off. I did most of these before, but I tried being ultra aggressive in doing them.

So fuel can be saved. The LR3 is rated by the EPA at 18 highway, 14 city. By my best estimate of the relative amounts of highway and city driving in my regime (about 60/40) the EPA thinks I should see overall mileage of 16.4 m.p.g. (0.6*18 + 0.4*14). That means that the 18.85 m.p.g. in my most recent three tank moving average is 14.9% over the weighted EPA estimate.

As a point of comparison, in the Jeep Grand Cherokee Limited in which I started this experiment, I was able to achieve about 30.6% better mileage than the weighted EPA estimate. I don't know the reason that the LR3 has only allowed me to exceed the EPA estimate by about 1/2 as great a percentage as the Grand Cherokee. It may be that the LR3, about six years newer, incorporates engine management techniques that make the vehicle more efficient when driving normally. If this is the case, I will have to assume that all manufacturers utilize these management techniques and hence reduce my estimate of the impact on national fuel consumption of universal adoption of extreme mileage enhancing driving techniques. I'll save that for another post.

I will say that I am pleased that I can exceed the 19 m.p.g. barrier, and 20 m.p.g. is in my sights.

Cuantos caballos?

In my last post I tried to calculate the top speed of my Land Rover LR3 HSE. In doing so, I used the horsepower found in the vehicle's specifications, i.e., 300 horsepower. Earlier in my musings about the LR3, I was marginally successful in some calculations relating to the car's (truck's?) fuel consumption. Now I'd like to calculate the vehicle's horsepower using known facts. These facts are the engine displacement and red line r.p.m. (6200)and the r.p.m. at which it was rated as specified (5500).

I'll use the method that was employed before, i.e., I'll determine how much fluid volume (air is a fluid) is going through the engine at those r.p.m.'s and how much fuel would be in this fluid. From there, I'll use the energetic content of the fuel and some thermodynamic calculations of efficiency to see what's available at the flywheel. Here we go. One advantage I'll have is that I can estimate the efficiency by figuring out how much heat energy per second comes from putting air/fuel mixture through the engine at 5500 r.p.m. and utilizing the rated brake horsepower of 300 at that r.p.m. This should give me an approximation of how many joules per second go to the flywheel versus how many are discarded to the environment.

A straight ratio of (6200/5500)*300 tells me that I should be able to produce 338 horsepower at 6200 r.p.m. As mentioned in the earlier post linked above, Car and Driver stated that the LR3 is governor limited to a top speed of 121 m.p.h. Let's see what kind of overall efficiency is indicated if 5500 r.p.m. produces 300 horsepower. To do so, I need an estimate of manifold pressure - for starters I'll assume wide open throttle and maybe something like 0.2 p.s.i. losses for an absolute pressure of about 14.3 p.s.i.

So at 5500 r.p.m., the engine (as per my policy, I'll spare readers many of the actual calculations) will pump about 0.0147 kilograms of fuel air mixture through the engine each second. This takes into account manifold pressure of 14.3 p.s.i. as mentioned above. Oxidation of this mass of gasoline will release about 705,000 joules of energy each second. Since joules/second are watts, a measure of power, we can convert to horsepower. Doing so, if the heat of oxidation of that amount of gasoline could be converted to mechanical energy with 100% efficiency, we would develop 946 horsepower. The rated horsepower at 5500 r.p.m. is 300, implying an efficiency of about 32%. This seems very reasonable.

OK, so what's available at 6200 r.p.m.? Well, since all these calculations are based on mass flow of fuel air mixture through the engine, the simple calculation above gets close, at 338 horsepower. However, I assume that there's a slight improvement in volumetric efficiency, in other words, a slightly higher manifold pressure than at 5500 r.p.m. Making this assumption and calculating as above, it seems possible that, if full throttle at redline can be achieved, an absolute maximum of 358 horsepower could be measured at the flywheel.

Sunday, June 24, 2007

Top speed

Those who may have stumbled upon my little blog have probably noticed that I enjoy putting numbers to things. The Land Rover LR3 HSE is certainly an example, though the figures that I've been able to derive have borne only a passing resemblance to measured values. So I think I'll derive one that I won't be able to disprove myself - the maximum speed of the vehicle.

As we've previously noted, in unaccelerated travel the sum of the forces acting on the vehicle must be zero. The rated power of the 4.4 liter V8 engine in the LR3 is 300 horsepower. We'll convert that to 223710 watts using the Google Calculator. Now I'm going to estimate, based on various sites I've visited, that the efficiency of transmitting the engine's power at the flywheel to the road is 78%. This may seem a little low to some, typical figures are often in the 80% to 85% range. But this is a full time four wheel drive vehicle, so losses will be higher.

That leaves 174794 watts to the road. Now, power is force times speed, so if I add the external forces and multiply them by the speed, I'll have the power being utilized to overcome forces. The aerodynamic drag reduces to 0.7491*s^2 and the road load is estimated to be 14.65*s, where s is the speed of the vehicle. If anyone leaves a comment that they would like to know where these figures came from, I'll be happy to oblige.

In any case, since those are forces and speed times force equals power, we'll multiply by speed (s) and equate it to 174794 Thus: 174794=0.7491*s^3+14.65*s^2. I have various computer algebra systems, but the simplest is called Derive 6. Much to my regret, Texas Instruments will stop development and shipment of the program this week. I've had most versions, and where truly exotic math isn't required, I prefer it to Mathcad, Maple, and Mathematica, as capable as those programs are.

In any event, Derive easily solves this cubic equation and determines that s=55.65 meters per second, or 124 miles per hour. For purists, this is the solution in the real domain. I'm not sure how realistic this is - I haven't come anywhere close to topping out the speed in the LR3, nor do I intend to do so. This is the basis of my contention at the outset of this post that I won't be able to disprove the number. However, Car and Driver's site gives the top speed as 121 m.p.h. but refers to it as "governor limited." According to my calculations, you'd have to be going down a hill to exceed this by more than 2.5% so I'm not sure why a governor is needed. I still find this published number satisfying.

Saturday, June 23, 2007

The Almanac

One of my favorite books is the annual World Almanac and Book of Facts. Some of the book covers topics which don't interest me in the slightest, e.g., entertainment facts and much (but not all I hasten to admit) sports information. But it is chock full of nuggets to please a fact and number junkie such as myself.

I thought I'd look into per capita energy consumption in the United States and see how it's increased in the range of time covered by the Almanac for such information. In 1960 the U.S. consumed 45.09 "quads." A quad is a quadrillion, or 10^15, btu's (british thermal units). This is total consumption of every kind - industrial, agricultural, commercial, transportation, etc., and from all sources. In 2006 the consumption was 100.41 quads.

To get these figures to a unit with which we are familiar, energy per time (quads/year) is power, so the figure for 1960 converts to 1.51*10^12 watts. In 2006 the figure is 3.36*10^12 watts. The population in 1960 was 179,323,175 for a per capita power usage (that is, rate of energy consumption per unit of time) of 8421 watts per person. In 2006 with a population of 298,444,215 we consumed energy at the rate of 11,248 watts per person, a 33.6% increase in consumption rate. Frankly, this is a smaller increase than I would have guessed.

Just to put this into perspective, this is as if, in 2006, each of us had 112 100 watt light bulbs lit 24 hours per day, seven days per week. Or, since 11,248 watts is 15.1 horsepower, each of us had about 15 lawn mowers following us around 24/7.

Let's take a look at a comparison of the U.S. with China. In 2006, the U.S. consumed energy at a rate of 11,248 watts per capita. China, with a total consumption of 59.57*10^15 quads and a population of 1,313,973,713 consumed energy at a rate of 1,514 watts per capita, or about 13.4% of the U.S. rate of consumption. I'd be curious to know how much of China's figure relates to production of consumer goods for shipment to the United States.

Worldwide, in 2005 humanity consumed 446*10^15 quads, or used energy at the rate of 1.49*10^13 watts. With a population of about 6.4 billion, we consumed energy at the rate of about 2330 watts per capita, about 21% of the U.S. rate. This is very scary stuff. Standard of living is very strongly correlated with rate of energy consumption, so to bring the world to "our" standard of living, we'd have to approximately quintuple our rate of energy consumption on a worldwide basis. This seems ludicrous. Never mind climate change, there is no chance of converting (all human energy use is conversion, never creation) energy at such prodigious rates.

How about looking at it from the other direction? How much energy consumption could we, as a society, forgo? I think I personally could struggle by on 1/2 the personal energy consumption. Remember, though, that this would include reducing the energy content of my consumer purchases, my food, etc., since the numbers above are all-inclusive. As I look around, listen to the television on downstairs, listen to the waterfall in my pool as water is pumped through the filtration system, listen to my wife in the shower as the heater provides hot water, etc., I know there's a long way to go.

Sunday, June 17, 2007

Turning off the engine

I have linked a blog called "Daily Fuel Economy Tip in the right column of this blog. I enjoy reading it, and have left quite a few comments. Brian Carr's (the host of the blog) most recent post is a follow up to a previous post regarding turning off the engine at stop lights. I also do this, and I have done a fair amount of googling on the topic.

As anyone reading this will likely be aware, the web is awash in sites discussing fuel saving methods. A lot of these discuss avoidance of idling, and there are large differences in the "break even" times for turning off the engine and avoiding burning fuel while idling versus extra fuel used to start the engine. Brian estimates an increase in m.p.g. of about 5.8% from this technique alone. On his site, I left a comment contemplating whether that was a plausible number, I'll copy the comment here:

"I also do this, however, I wonder if a significant portion of your increased mileage in the second period comes from this. Let’s see if it’s plausible:

If you had driven the 1559.9 miles in the second period with the miles per gallon (31.25) from the first, you would have used 49.9 gallons. Instead you used 47.2 gallons, a savings of 2.7 gallons. Now, I’ve had a Jeep Grand Cherokee Limited with a 4.7 liter engine and now have a Land Rover LR3 with a 4.4 liter engine. The Grand Cherokee used 0.38 gallons per hour at idle, the LR3 about 0.5 gallons per hour. Your car probably uses less than either of these at idle but let’s assume 0.4 gallons per hour. It would have taken you 6.75 hours of idling at stoplights to burn 2.7 gallons. In a 30 day month, that would be about 13.5 minutes of sitting at stoplights each day, every day. Assuming that a stop is an average of 40 seconds (don’t have data, just a guess), that would mean that, every single day, you were stopped at a little over 20 stoplights.

Now, if you have a much smaller engine (I forgot what you drive), that would mean you’d have to be spending even more time at stoplights to have turning the vehicle off at stoplights be primarily responsible for your savings. Do you think that this is the case?

Also note that these calculations assume absolutely NO extra fuel use on startup. I’ve searched the web and can find no figures for extra fuel used on startup, but the assumptions above are clearly the most favorable for fuel savings by engine shutoff."

It would seem that his savings must be due to some other factors as well, yet the numbers above aren't completely out of the question. As mentioned there, I know well how much fuel I'm burning as I sit at a light (or coast to it) but it's been very difficult finding any information on extra fuel used to start a spark ignition internal combustion engine. Various sites claim six seconds, 10 seconds, 30 seconds, and one minute as the break even point. No one cites any data to back up their number, and they vary by a factor of 10. This is not especially helpful.

However, after replying to Brian Carr's post, I tried changing my google search string to "idling versus shutting down engine". This led me to this site. It's the closest I've found to giving me the answer I need to determine whether shutting off the engine at stop lights is a fuel saver. It says the following: "Our research showed that a V6 restart takes about the same fuel as 5 seconds of idling. We expect a V8 to save more and a 4-cylinder less." It doesn't state the nature of the research, whether it was actual measurement by the authors, by associates of the authors, or was located in a literature search. It ain't much but it's all I've found.

As I've mentioned before, I haven't done experiments by varying a single parameter and keeping all others as constant as possible to determine the effect of that parameter. Brian Carr says he has done so and the article from the ASME Florida Section provides some verification. So I suspect that, while Brian's entire 5.8% increase in fuel economy isn't due to this procedure, a significant portion of it is.

I am going to run an experiment to determine this once and for all. I don't have a way to directly measure the fuel consumption on startup, but I'll find a vacant stretch of road forming a closed course a couple of miles long. I'll run it for an hour or so stopping and idling for a measured period every mile and find the total fuel consumed. Then I'll drive the same distance, turning the car off and back on every mile - it won't matter how long the shut off period is. I'll be concentrating very hard on duplicating the acceleration, cruising, and deceleration regime of the first series. I'll start both with a full fuel tank.

At the end of this process, I should have enough data to approximate the break even time and from there, the excess fuel used on startup. No doubt this number won't reflect what's happening before the car warms up, but it should provide reasonably definitive data on the question of turning the car off at lights. I can't take credit for formulating this methodology - I read it on someone's web site. I'd credit the site, but I can't find it now.

Saturday, June 16, 2007


In thinking about what I've done to attempt to minimize fuel consumption there are three things that stand out in my mind as potentially dangerous. I say "potentially dangerous" because for all three of them it is "common knowledge," stated all over the web, that they are. For the sites and blogs that I frequent (devoted to fuel saving measures and techniques) this is typically in the context of "while this may save fuel, it is very dangerous and no amount of fuel savings is worth a serious injury or your life."

So what are the three? The first is filling my tires (slightly) beyond the recommended maximum. The second is turning off the engine on long downhills. The last and most controversial is drafting trucks. It is this that is the subject of this post.

There are two obvious question. The first is "does it work?" The second is "is it dangerous?" As to its value in fuel savings, while there are some naysayers, most references agree that it is quite effective. Coincidentally, the Discovery Channel hit show Mythbusters covered this topic recently. Their results are summarized here. As is their common practice in such "myths," Kari, Tori, and Grant started with a scale model in a wind tunnel and achieved very encouraging results. Their full scale testing, while it didn't achieve quite the drag reduction of the wind tunnel tests, indicated significant fuel savings even at a following distance as large as 100 feet.

I have played with this idea off and on, both in the Grand Cherokee and in the LR3. However, because I have been so very unsuccessful with the LR3 in achieving the dramatic enhancements to gas mileage I was able to accomplish in the Jeep, I recently decided to pursue this avenue more aggressively. I know that this is controversial, many will call it selfish - if I crash, it will cause a huge backup for those behind me. I agree that this technique is extremely selfish if there is any significant chance that I will crash into a truck and tie up a freeway. I'll get back to that momentarily.

But does it work? According to the information from my Scan Gauge II, it does. I attempted to judge how far I was behind trucks by using my stopwatch to see what fraction of a second elapsed between the back of a truck crossing a highway mark and the front of my car crossing the same mark. Needless to say, tailgating a truck while looking at a Scan Gauge II reading and timing intervals with my stopwatch is sort of living on the edge, but I concluded that I was about 35 feet behind the truck. According to Mythbusters' results, I can look for an increase in miles per gallon of somewhere between 20% and 27%. As best I could tell, I saw an increase from about 21.5 m.p.g. to about 25 m.p.g., an increase of about 16%. These are pretty fuzzy figures - the readouts are constantly changing with changes in slope, etc., and the trucks typically don't maintain a particular speed quite as efficiently as the LR3 (due to the huge mass of the trucks no doubt). Nevertheless, every time I try it I get significant indications of increased fuel efficiency.

So apparently it works, how dangerous is it? Obviously, the worst case scenario is for the truck to apply maximum braking suddenly with no advance indication to me. I don't know if trucks have anti-lock braking systems, for the analysis to follow I won't assume they do. Judging from the condition of a lot of the trucks I see, this is a valid assumption. It should go without saying that, when following a truck at 35 feet, my eyes are focused on the truck's brake lights and my foot is ready to instantly hit the brake pedal. So the question is, when I see his (male pronouns are to be understood as gender-free) brake lights when he implements maximum braking, can I avoid hitting him?

I have to calculate the circumstances under which the distance between my front and his rear decreases to zero. The data necessary for this calculation is his maximum deceleration rate, my maximum deceleration rate, and my time to go from his brake lights on to my application of maximum braking. I will obviously limit my calculations to dry pavement in good condition - I'm not suicidal.

Truck braking, like everything else when looked at by academics, is ridiculously complex, see here if you are skeptical. But the nugget for my purposes in that paper is that the best that an empty semi-tractor trailer can do in deceleration is right at 20 ft/sec^2, or 6.10 m/s^2. For my LR3, it's (maybe, subject to correction) about 8.0 m/s^2. My reaction time, when paying close attention (as I do when tailgating a large truck) was determined using this online reaction timer to be 0.303 seconds in an average of 10 trials. With a lot of practice and knowing what to expect, I was able to bring the average way down, to around 0.20 seconds, but I'll leave it at 0.303 to be conservative.

All right then, we have what we need. The initial conditions are that the truck and my LR3 are each going 60 m.p.h. or 26.8 m/s. The truck hits his brakes maximally and decelerates at 6.10 m/s^2. 0.303 seconds later, I hit my maximum brakes and decelerate at 8.0 m/s^2. How far back must I be to avoid hitting the truck? I suspect that detailed expositions of mathematics bore those who read here (though I'd certainly appreciate any feedback on this). So I'll just state that the answer is that I must be a minimum of 9.67 m or 31.7 feet behind the truck. Now, this assumes I can meet my reaction time and instantly apply maximum braking. I should add, say, a 50% safety factor for a total of 47.6 feet. Call it 50 feet. For those that would say that that's not enough of a safety factor, remember that I assumed that the truck applied perfect braking as well.

While I won't proselytize that drafting trucks is safe and should be done by one and all, I do think that with extreme caution and maximum alertness it can be safely done. I wouldn't want to try to get closer than 50 feet, and I will adjust my procedures accordingly, but I'm keeping this weapon in my arsenal.

Tuesday, June 05, 2007

Another comparison

I'm still trying to understand the differences between the Jeep Grand Cherokee Limited I had until late November of 2006 and that was the topic of many of my posts, and the Land Rover LR3 HSE I have now. Right now, I'm thinking about the 31 m.p.g. the Jeep exhibits at 55 m.p.h. versus the 21.5 shown by the Land Rover. My last post dealt with the LR3 from the point of view of a big fuel burning air pump. I decided to compare what the two vehicles "should" require.

I gave some figures that should help out in this effort a few posts back. Let's run a few numbers. The LR3 has a frontal area of 3.15 m^2 and a coefficient of drag of 0.41. We have a dynamic pressure at 24.6 m/sec (approx. 55 mph) and air density of 1.16 kg.m^3 of 351 newtons/m^2. Thus, for this condition and drag coefficient, my aerodynamic drag is approximately 453 newtons (dynamic pressure times frontal area times drag coefficient).

Tire rolling resistance (as best I've been able to find) is about .015 times vehicle weight, or about 392 newtons. Total external forces to be overcome by the engine at 55 mph are therefore about 743 newtons or 167 pounds force. Now, force times speed is power, so the engine must provide 743 newtons at 24.6 m/s or about 18,280 watts. This equates to about 24.5 horsepower.

Obviously, much of the energy in the gasoline is lost to heat, engine and driveline friction, and pumping various fluids (refrigerant if the a.c. is on, water in the cooling system, air through the fan, oil, etc.). So enough gas must be burned per second to overcome all of these "dissipative" forces and still provide 24.5 horsepower.

For the Grand Cherokee, frontal area is 2.48 m^2, coefficient of drag is 0.44. Running through the same calculations, I get the external forces to be overcome by the Jeep at 55 mph are 383 newtons of aerodynamic drag and 289 newtons of rolling resistance for a total of 672 newtons or 151 pounds force. Enough energy must come from the fuel per second to overcome the dissipative forces and provide about 22.1 horsepower to maintain 55 mph against the external forces. So, if all else were equal, the LR3 should burn about 10.9% more fuel per mile at 55 mph. In fact, it burns about 44% more fuel. Or so the gauges say. So obviously, all else isn't equal.

These are the types of things I'm trying to understand.

Saturday, June 02, 2007

First principles

This post is a continuation of the previous one in which I tried to reason the cause of my inability to coax better mileage out of the LR3. I was able to show through an analysis of manifold pressure, engine frequency (r.p.m.) and the chemical mixture requirements for combustion that the vehicle was burning fuel at a rate that equated to 13.3 m.p.g. at 55 m.p.h. on level ground. While this is in the ballpark, it's certainly not close to the base, so I tried reasoning from first principles, as the mathematicians say.

I started with the assumption that the fuel/air mixture in the manifold (and the cylinder during the intake stroke) is an ideal gas. I carried through an analysis on that basis (from the details of which I'll spare my patient readers) utilizing the absolute pressure and the manifold air temperature as reported by the Scan Gauge II I have attached to my engine.

I ran my analysis using the approximation that gasoline is normal heptane and that air is 22% O2 and 78% N2. From there, I proceeded to calculate from the ideal gas law. As Scotty used to say on Star Trek, "you canna change the laws of physics." I didn't expect to determine a fuel consumption number that matched the indicated m.p.g. from the Scan Gauge II to the nearest 0.1 m.p.g., but I did hope for something within, say, 10%.

Nope. The calculated result was worse than my previous calculation, coming in at 11.06 m.p.g. So what gives?? I have begun reading a treatise entitled "The Internal-Combustion Engine, Theory and Practice" by Taylor, since it's obvious that my level of understanding of the physics of internal combustion engines is inadequate to the problem at hand. It's a two volume tome, and exhaustive in scope and detail. When I learn enough to see where I've gone astray with my analyses, hopefully I'll also understand the mysteries of the LR3 vs. Grand Cherokee Limited engine comparison.

Saturday, May 26, 2007

Understanding a new engine

I mentioned in my last post that I'm trying to understand the factors that make it impossible for me to achieve the fuel savings in my Land Rover LR3 that I did in my Jeep Grand Cherokee Limited. I'm beginning to think my understanding of the internal combustion engine is sadly lacking.

For example, in the post linked above, I tabulated some of the relevant numbers for each vehicle. The LR3 uses a smaller engine to produce a higher rated horsepower than the Jeep. In the highest gear (at freeway speeds) the engine rpm is lower as well so one would think that the smaller engine turning more slowly would burn less fuel and hence derive heat to perform work at a slower rate. I know that the LR3 has a higher compression ratio. Could this be the explanation?

It's well known that the maximum theoretical efficiency, E, of an engine using an idealized Otto cycle is E=1-r^(1-y) where r is the compression ration and y (should be be the Greek letter gamma) is the ratio of the constant pressure to constant volume heat capacities. For the LR3 with its 10.5:1 compression ratio, this works out to 0.61. For the Grand Cherokee Limited at 9.3:1 it is 0.59. So what does this mean?

It means that for a given amount of heat from burning fossil fuels, the LR3 engine would be able to do ((0.61-0.59)/0.59)*100%=3.4% more work per joule of heat from burning gasoline than the Jeep if they were both working at the maximum theoretical efficiency. In order to see what how this affects our consumption, let's see how much heat per second from burning fuel is available to each engine.

In one second, at 1750 rpm in the Jeep, the engine moves 68.5 liters ((1750/2)/60) * 4.7 liters of fuel/air mixture through the engine. (The division of 1750 rpm by two is necessary because the rpm readout is crankshaft rpm, the crankshaft in a four stroke engine revolves twice for each engine cycle). The LR3 at 1660 rpm will move 60.9 liters per second. In these mixtures will be fuel, and I will assume that the richness of the mixture is the same for each engine, since the ECS (engine control system) will try to maintain the so-called "stoichiometric" ratio (14.7:1 by air mass to fuel mass). This mystifies me because the LR3 should burn less fuel since it's moving a smaller volume of fuel/air mixture through the engine at a presumed identical mixture. Yet the Grand Cherokee indicates instant mileage of approximately 31 m.p.g, the LR3 shows about 21.5.

The density of air at typical temperatures, pressures, and relative humidities is about 1.16 kilograms/meter^3 or 0.00116 kilograms/liter. This density is reduced in the intake manifold due to throttling effects, in fact, that's how the throttle works. I have equipped my LR3 with a Scan Gauge II so that I can measure absolute manifold pressure. At a steady 55 m.p.h. on level ground, manifold pressure is 68% of ambient. Since density is proportional to pressure, the ambient density of 0.00116 kilograms/liter is reduced in the cylinders to 7.84*10^(-4) kilograms/liter. We'll assume that the mixture is air as an approximation, since it's about 94% air in reality. Therefore, in one second, the LR3 moves 0.0477 kilograms of mixture through the engine and in that fluid, there should be (1/15.7)*0.0477=0.00304 kg. of gasoline. Burning this gasoline will release about 143,000 joules of heat energy. Hats off to me, this is great information. There's only one problem.

Since a gallon of gasoline weighs about 2.65 kilograms, this implies that I'm burning (0.00304*3600)/2.65=4.13 gallons/hour. At 55 m.p.h., this is about 13.3 m.p.g. The LR3 is no economy car but it isn't as bad as that. As I stated earlier, I expect about 21.5 m.p.g. at 55 m.p.h. on the freeway. Clearly, something is wrong in my assumptions. I'm not sure what it is, the mass flow calculation seems pretty straightforward.