In my previous post, I discussed what, outside of the engine and driveline, could be modified to increase fuel mileage. What are the specifics of such a car? Since the laws of physics are unchanging as far as is known and reasonably well known at the macro scale at which cars travel down roads, certain conclusions can be drawn. Let's start with the obvious: fuel is burned to overcome forces acting on the car to take it down the road. So there are two fundamental approaches to high gas mileage, i.e.: put more of the energy in a given amount of fuel to work; and reduce the forces acting on the vehicle.
I'll save maximizing the utilization of energy available in the fuel for another post. Here, I'd like to see what it would take to make a car that gets, say, 75 m.p.g. with currently achievable engine and drive line efficiency by reducing the forces acting on the car. I'll look at achieving this fuel mileage at 55 m.p.h. As I've previously mentioned, force times speed is power, and power is the rate of doing work or, equivalently, using energy.
So, we should be able to say that force times speed equals energy (fuel) divided by time, if the appropriate adjustments are made for units. Or, rearranging, force equals energy divided by speed multiplied by time. And, as would be expected, this simplifies to energy divided by distance. So if I assume 125 million joules/gallon, 25% drive line efficiency, and that I use that gallon in 75 miles, I can determine that the maximum combined force of aerodynamic drag and rolling resistance that I can overcome is about 260 Nt (Newtons). For the SI challenged reader, this is 59.6 pounds.
Referring to my previous post, at a fixed speed the only variables available to control are mass, rolling resistance, frontal area, and drag coefficient. Let's assume that tandem seating isn't a saleable option at this point. What can we do? Well, let's start with vehicle weight. In this article, it's estimated that about 40% of the weight of an average car could be eliminated through replacing steel with carbon fiber. Let's use a conservative estimate of 25%. Then, in this article it's stated that the lowest coefficient of rolling resistance on tires currently available is 0.0062, the highest checked was 0.0152. Let's assume that we can utilize tires with a coefficient of 0.008.
Let's get started. We'll take a small four seat sedan, something like a Toyota Yaris. This vehicle has a curb weight of 2293 pounds, a drag coefficient of 0.29 and a frontal area of (as best I could find) 2.282 meters squared. Let's predict the highway m.p.g. at a steady 55 m.p.h. using, from the previous post, the equation for joules/meter (which is another measure for the inverse of miles per gallon, using the appropriate unit conversions and efficiencies). We'll assume two 170 pound adults to make total weight 2633 pounds. Finally, I'll assume a coefficient of rolling resistance of 0.0115. Running through the calculations, we find that about 355 Newtons are required. To apply this force over a mile, assuming 25% efficiency in the engine, we'd use 0.01828 gallons, or a fuel efficiency of 51.8 m.p.g. Not bad, we're a good part of the way there.
But the car is rated at 36 m.p.g., what gives? Well certainly the EPA tests are more demanding than a steady 55 m.p.h. on level ground. Beyond that, it could be that the new tires with fresh tread have a higher coefficient of rolling resistance. Or, it could be that the engine is able to deliver significantly less than 25% of the energy available in the fuel. If we assume a rolling resistance coefficient of 0.0130 and 20% efficiency, the figure is 36.7 m.p.g. This seems close, and is typical of the types of iterative calculations that are necessary. I'm going to stay in the middle, since I should calculate better than the EPA mileage, due to the rigors of their test. I've verified this in my own LR3. I'm going to assume that the Yaris has a rolling resistance coefficient of 0.0122 and is able to deliver 22% of the energy in the fuel it burns to the wheels. This yields 43.0 m.p.g. Close enough.
Now, what do we get if we reduce the weight by 25%, use tires with a coefficient of rolling resistance of 0.009, and a coefficient of drag of 0.24? Running the numbers, we get 60.8 m.p.g. This is not good, let's see what the maximum credible reductions of coefficient can give us. Using 0.0062 and 0.16 for the coefficients of rolling resistance and drag respectively, we get 90.3 m.p.g. Thus, we conclude that a small car like the Yaris, with the maximally achievable modifications for efficiency, can exceed the target 75 m.p.g. But remember that we've replaced most of the steel with carbon fiber, taken every conceivable measure to reduce drag, and installed tires that are exceptionally efficient and may not wear well, handle well, or be very comfortable. And the fact of the matter is that I very much doubt if a vehicle can be brought to market with a 0.16 coefficient of drag. Let's see what we get with 0.22 and call it good. After all, tires with rolling resistance coefficient of 0.0062 currently exist according to the above-cited article. The answer is 71.5 m.p.g., slightly below the target.
So we conclude that it can be done but the price, both economic and in terms of comfort, is quite high. Clearly, attention to the engine is warranted, as is consideration of drive train modifications. A hybrid engine, combined with pulse and glide driving techniques, could greatly increase efficiency of fuel utilization but it would increase the weight. There is just no free lunch. Tandem seating anyone?
Sunday, August 10, 2008
What does a high fuel economy car look like?
To quote Scotty, "you canna change the laws of physics." I'm going to look at what a high fuel economy car would look like, with no assumptions about engine technology breakthroughs. Therefore, there are four fundamental things that we can control: vehicle weight (affects fuel used for acceleration to speed and amount of rolling resistance); tire coefficient of rolling resistance; vehicle frontal area; vehicle shape, reflected in the drag coefficient.
Let's look at cruising. In this case weight only comes in as a factor in rolling resistance, while frontal area and vehicle shape are the factors affecting drag. I've seen an equation that alleges to combine these components - the equation is: Fr=0.5*rho*Cd*A*v^2+Crr*m*g*v where rho is air density, Cd the coefficient of drag, A the frontal area, v is velocity, Crr is coefficient of rolling resistance, m is mass of vehicle, and finally, g is the acceleration of gravity.
I don't buy it. My analysis shows that, at least for first order effects, rolling resistance is not a function of velocity, so let's use Fr=0.5*rho*Cd*A*v^2+Crr*m*g. This is dimensionally correct with both coefficients dimensionless. It is, therefore, plausible and I'm going with it.
So, what can be changed here? We can't change rho or g, and v is whatever the driver chooses to use. I'll list the variables we can change and what would be done:
1. Reduce Cd. This can be done by the manufacturer, there have been vehicles with Cd as low as 0.16, though not many. There are those who modify their vehicles themselves to reduce Cd. To see this in action, visit the Aerodynamics forum at the ecomodder web site. I'd suggest looking for posts by "basjoos" to see the extremes to which this can be taken. A blog post about his vehicle can be found here. If you choose to do this, be careful because aerodynamics can be non-intuitive.
2. Reduce A, frontal area. This means a smaller vehicle in general. For a two-seater, tandem seating might be an option. There are concept vehicles out there that take this route and they will certainly have a low so-called "drag area," the product of Cd and A. Market acceptance is clearly a question.
3. Reduce Crr. This is the amount of force used up by tire rolling resistance. There are low rolling resistance tires out there, and California is contemplating requiring manufacturers to list Crr for tires sold here. The rolling resistance depends in a complicated way on a number of factors, but tires primarily use energy in so-called "hysteresis losses," i.e., flexing portions of the tire without full energy recovery as the tire rotates. Steel wheels on trains have extremely low Crr's since they barely flex at all. For a look at low rolling resistance tires, check here.
4. Reduce m, mass. Obviously, reducing A helps here since, in general, smaller cars weigh less. Lighter materials, less room for storage, smaller fuel tanks, etc. can also be utilized, as can minimally sized engines for the mission at hand. These reductions are synergistic - lighter vehicles need smaller engines, which can utilize lighter drive line components, which can utilize smaller fuel tanks for less fuel weight, etc.
So, a composite, tandem seating car, optimally shaped with little or no trunk and a small fuel tank would appear to be the best prescription. Of course, as is usually the case, the easiest savings coming from driving less and sharing the ride.
As I stated at the outset, this doesn't address possible gains from engine efficiency. In my opinion, dramatic gains aren't likely here. I'll address engine issues in another post.
Let's look at cruising. In this case weight only comes in as a factor in rolling resistance, while frontal area and vehicle shape are the factors affecting drag. I've seen an equation that alleges to combine these components - the equation is: Fr=0.5*rho*Cd*A*v^2+Crr*m*g*v where rho is air density, Cd the coefficient of drag, A the frontal area, v is velocity, Crr is coefficient of rolling resistance, m is mass of vehicle, and finally, g is the acceleration of gravity.
I don't buy it. My analysis shows that, at least for first order effects, rolling resistance is not a function of velocity, so let's use Fr=0.5*rho*Cd*A*v^2+Crr*m*g. This is dimensionally correct with both coefficients dimensionless. It is, therefore, plausible and I'm going with it.
So, what can be changed here? We can't change rho or g, and v is whatever the driver chooses to use. I'll list the variables we can change and what would be done:
1. Reduce Cd. This can be done by the manufacturer, there have been vehicles with Cd as low as 0.16, though not many. There are those who modify their vehicles themselves to reduce Cd. To see this in action, visit the Aerodynamics forum at the ecomodder web site. I'd suggest looking for posts by "basjoos" to see the extremes to which this can be taken. A blog post about his vehicle can be found here. If you choose to do this, be careful because aerodynamics can be non-intuitive.
2. Reduce A, frontal area. This means a smaller vehicle in general. For a two-seater, tandem seating might be an option. There are concept vehicles out there that take this route and they will certainly have a low so-called "drag area," the product of Cd and A. Market acceptance is clearly a question.
3. Reduce Crr. This is the amount of force used up by tire rolling resistance. There are low rolling resistance tires out there, and California is contemplating requiring manufacturers to list Crr for tires sold here. The rolling resistance depends in a complicated way on a number of factors, but tires primarily use energy in so-called "hysteresis losses," i.e., flexing portions of the tire without full energy recovery as the tire rotates. Steel wheels on trains have extremely low Crr's since they barely flex at all. For a look at low rolling resistance tires, check here.
4. Reduce m, mass. Obviously, reducing A helps here since, in general, smaller cars weigh less. Lighter materials, less room for storage, smaller fuel tanks, etc. can also be utilized, as can minimally sized engines for the mission at hand. These reductions are synergistic - lighter vehicles need smaller engines, which can utilize lighter drive line components, which can utilize smaller fuel tanks for less fuel weight, etc.
So, a composite, tandem seating car, optimally shaped with little or no trunk and a small fuel tank would appear to be the best prescription. Of course, as is usually the case, the easiest savings coming from driving less and sharing the ride.
As I stated at the outset, this doesn't address possible gains from engine efficiency. In my opinion, dramatic gains aren't likely here. I'll address engine issues in another post.
Sunday, June 01, 2008
300 barrels
That's the amount of proven and probable reserves of oil for each person on Earth. Clearly, it's not an exact number but it assumes about 2 trillion barrels and about 6.7 billion people. 300 barrels. That's it.
Now, in the United States we use about 25 barrels of oil per year per person. For those not near their calculator, that means we'll use up our 300 barrels in 12 years. Is it really that bad? Well, yes. Fortunately for us, there are many countries in Africa and Asia, and even in Central and South America who kindly decide not to use as much of their 300 barrels each year as we do. In fact, there are no countries whose citizens use as much of their 300 barrel allotment as we do. For example, the Chinese use around two barrels per year per person.
The question is: when we've used up ours, are they all going to sell us theirs? Sure, if the price is right. But that price will be dear. Only the most essential uses will be able to be accommodated. What we're seeing in the commodity exchanges and at the gas pump is only the beginning - there is no aspect of our lives that will remain unaffected.
Preparation should have begun years ago, this impending calamity is not a new development. It's been predicted for half a century. Preparation at the personal, community, local, national, and worldwide levels with an urgency that hasn't been matched in living memory is the prescription. Look around - do you see it anywhere?
There are those who are preparing, I strongly recommend the Yahoo news group Running on Empty 2. There, you'll find extensive discussions of the issues at hand, of preparations people are undertaking, and answers to questions. You'll find links to pertinent news items, web sites, and fora and blogs. You won't find old school survivalists of the black helicopter variety.
While I work on maximizing the return on my energy expenditures driving my Land Rover to and from my McMansion, I'm working on a total change of lifestyle. I recommend readers do the same.
Now, in the United States we use about 25 barrels of oil per year per person. For those not near their calculator, that means we'll use up our 300 barrels in 12 years. Is it really that bad? Well, yes. Fortunately for us, there are many countries in Africa and Asia, and even in Central and South America who kindly decide not to use as much of their 300 barrels each year as we do. In fact, there are no countries whose citizens use as much of their 300 barrel allotment as we do. For example, the Chinese use around two barrels per year per person.
The question is: when we've used up ours, are they all going to sell us theirs? Sure, if the price is right. But that price will be dear. Only the most essential uses will be able to be accommodated. What we're seeing in the commodity exchanges and at the gas pump is only the beginning - there is no aspect of our lives that will remain unaffected.
Preparation should have begun years ago, this impending calamity is not a new development. It's been predicted for half a century. Preparation at the personal, community, local, national, and worldwide levels with an urgency that hasn't been matched in living memory is the prescription. Look around - do you see it anywhere?
There are those who are preparing, I strongly recommend the Yahoo news group Running on Empty 2. There, you'll find extensive discussions of the issues at hand, of preparations people are undertaking, and answers to questions. You'll find links to pertinent news items, web sites, and fora and blogs. You won't find old school survivalists of the black helicopter variety.
While I work on maximizing the return on my energy expenditures driving my Land Rover to and from my McMansion, I'm working on a total change of lifestyle. I recommend readers do the same.
Sunday, April 20, 2008
Michael Medved, Dr. Albert Bartlett, and innumeracy
I was thinking about my post on how peoples philosophy affects their evaluation of factual data. I googled (an unfortunate example of "verbification," a language trend I loathe) "Michael Medved" "peak oil." I came upon a site called The Dead Hand. It seems to be the work of Dr. Robert Williscroft, who has penned a tome entitled The Chicken Little Agenda: Debunking "Experts'" Lies. The theme is that the end of the world as we know it is not approaching, no matter what "they" say. Dr. Williscroft has a flash audio of a Michael Medved segment that included himself and a representative of the group Seattle Peak Oil Awareness (Medved lives in Seattle). The segment occupied an hour of Medved's show.
This post is about the misconceptions about what can be accomplished by finding more oil, something Medved and Williscroft (and most of the callers to the show) think will inevitably happen and will solve our problems, at least for many decades to come. Unfortunately, even should such finds be forthcoming, they'll only postpone our reckoning by a small amount. As an aside, it's not as if most of the world is a vast unknown full of huge undiscovered oil fields and geologists have no clue about where to find them. In any case, Dr. Albert Bartlett has spent his career trying to educate lay people on the consequences of exponentially increasing consumption of a finite resource. I strongly urge everyone to look here for Dr. Bartlett's exposition.
I'd like to spend a little virtual ink to bring some of the salient points to my reader's attention. The world is currently using oil at the rate of about 80 million barrels per day. The spreadsheet from BP I used in my previous post on exponential growth gives enough data to show that the current doubling time for oil consumption is around 45 years. This means that in the next 45 years, we'll use as much oil as we have in all history up until today. Now, this is an exceptionally rosy estimate, if things go as they are going now. We have India, China, Indonesia, and many other developing nations growing quickly both in population and in per capita energy use. This has severe ramifications on the figure of 45 years, since that's based on data from 1982 through 2006.
Let's suppose an annual growth rate of 6% worldwide in demand encompasses the increasing populations and energy consumption rates of the so-called "developing world," and that that leads to an annual increase worldwide of 4%. Both of these are in line with current projections. Now we're looking at a doubling period of about 18 years, meaning that we'll use as much oil in the next 18 years as we've used up until today in all history. Further, it means that if geologists and oil companies double the oil reserves available, only another 18 years of oil use would be added.
Unfortunately, this underestimates the problem, since the second half of the oil is only extracted with much greater effort and with much greater cost, both in energy and monetary terms. I'm not predicting the end of the world as we know it, but Mr. Medved, et al, are whistling past the graveyard. I have no doubt that it's due to the cognitive dissonance between the philosophical framework by which he interprets facts and what is factual reality.
This post is about the misconceptions about what can be accomplished by finding more oil, something Medved and Williscroft (and most of the callers to the show) think will inevitably happen and will solve our problems, at least for many decades to come. Unfortunately, even should such finds be forthcoming, they'll only postpone our reckoning by a small amount. As an aside, it's not as if most of the world is a vast unknown full of huge undiscovered oil fields and geologists have no clue about where to find them. In any case, Dr. Albert Bartlett has spent his career trying to educate lay people on the consequences of exponentially increasing consumption of a finite resource. I strongly urge everyone to look here for Dr. Bartlett's exposition.
I'd like to spend a little virtual ink to bring some of the salient points to my reader's attention. The world is currently using oil at the rate of about 80 million barrels per day. The spreadsheet from BP I used in my previous post on exponential growth gives enough data to show that the current doubling time for oil consumption is around 45 years. This means that in the next 45 years, we'll use as much oil as we have in all history up until today. Now, this is an exceptionally rosy estimate, if things go as they are going now. We have India, China, Indonesia, and many other developing nations growing quickly both in population and in per capita energy use. This has severe ramifications on the figure of 45 years, since that's based on data from 1982 through 2006.
Let's suppose an annual growth rate of 6% worldwide in demand encompasses the increasing populations and energy consumption rates of the so-called "developing world," and that that leads to an annual increase worldwide of 4%. Both of these are in line with current projections. Now we're looking at a doubling period of about 18 years, meaning that we'll use as much oil in the next 18 years as we've used up until today in all history. Further, it means that if geologists and oil companies double the oil reserves available, only another 18 years of oil use would be added.
Unfortunately, this underestimates the problem, since the second half of the oil is only extracted with much greater effort and with much greater cost, both in energy and monetary terms. I'm not predicting the end of the world as we know it, but Mr. Medved, et al, are whistling past the graveyard. I have no doubt that it's due to the cognitive dissonance between the philosophical framework by which he interprets facts and what is factual reality.
Friday, April 04, 2008
The time factor is worse than I thought
In my post on the use of time, I used some estimates as to how much time I lose with the fuel economizing driving techniques I utilize. I estimated that I lose eight minutes and 25 seconds each day driving 55 m.p.h. instead of 70 m.p.h. I've been browsing the fuel saving websites and blogs, and the "party line" is that very little time will be lost. I decided that I'd see what the real numbers are for my commute.
I used a stopwatch to time the portions of my typical commute each way during which I could have been driving 70 m.p.h. Then, a simple multiplication by 55/70 gave me the time I would have spent driving those miles at 70 m.p.h., and a subtraction yielded the time loss. I did this for two days and averaged the numbers. The days seemed fairly typical so I imagine that the results are representative. Certainly, there are periods during which traffic is worse (say, when school starts in September, when standard time returns, etc.) but during these times, I'm not saving much fuel anyway.
The results are highly disturbing. I'm spending about 10 minutes and 41 seconds longer on the road each day than I would if I drove 70 m.p.h. That's about 44 1/2 hours per year. It's reduced slightly by the fact that I have to stop for fuel less often, and judicious use of my assistant and the mobile phone enables a minimal level of productivity, but even allowing for this, it's just about equivalent to a week of work (or vacation).
A sensible person would give it up, but those who have followed this blog at all will have no fear that I'm a sensible person. I've said it before, but if I'm going to keep this up, I must find a way to be more productive. I have a little tape recorder for dictating things, but that just shuffles the work onto someone else to type it, or slightly reduces the time for me to compose a document. I don't know about the reliability of software that translates spoken word into typed documents, the last time I tried such a product it was worthless for my purposes.
Well, for the time being I guess I'll stick to my "Learn Mandarin Chinese" podcast. But it's clear that nothing comes for free, not even saving fuel.
I used a stopwatch to time the portions of my typical commute each way during which I could have been driving 70 m.p.h. Then, a simple multiplication by 55/70 gave me the time I would have spent driving those miles at 70 m.p.h., and a subtraction yielded the time loss. I did this for two days and averaged the numbers. The days seemed fairly typical so I imagine that the results are representative. Certainly, there are periods during which traffic is worse (say, when school starts in September, when standard time returns, etc.) but during these times, I'm not saving much fuel anyway.
The results are highly disturbing. I'm spending about 10 minutes and 41 seconds longer on the road each day than I would if I drove 70 m.p.h. That's about 44 1/2 hours per year. It's reduced slightly by the fact that I have to stop for fuel less often, and judicious use of my assistant and the mobile phone enables a minimal level of productivity, but even allowing for this, it's just about equivalent to a week of work (or vacation).
A sensible person would give it up, but those who have followed this blog at all will have no fear that I'm a sensible person. I've said it before, but if I'm going to keep this up, I must find a way to be more productive. I have a little tape recorder for dictating things, but that just shuffles the work onto someone else to type it, or slightly reduces the time for me to compose a document. I don't know about the reliability of software that translates spoken word into typed documents, the last time I tried such a product it was worthless for my purposes.
Well, for the time being I guess I'll stick to my "Learn Mandarin Chinese" podcast. But it's clear that nothing comes for free, not even saving fuel.
Saturday, March 29, 2008
A simple way to save a little fuel
I know that most people won't use the extreme methods of fuel consumption minimization that I've used to achieve a five tank moving average fuel efficiency of 21.09 m.p.g. in my Land Rover LR3 HSE, at least until it's a matter of taking extreme measures or not driving at all. People are repelled by the thought of (and if they're in my vehicle, the experience of) driving 55 m.p.h. on the freeway, coasting wherever possible, etc. But what about a minor adjustment that will save a little fuel?
I've previously detailed my policies on stoplights, including when I turn my engine off, coasting to minimize fuel waste when approaching red lights, whether or not it pays to speed up to attempt to make it through a green (or yellow) light, etc. Possibly, no one will adopt any of the measures I've outlined in those posts. But what about just shifting from drive to neutral? When sitting still with the vehicle in drive and brakes applied, more fuel is used than with the vehicle in neutral. I know this to be the case because I can see it on my Scan Gauge II. As I usually do, I'll run a few calculations to estimate my fuel savings from this policy, and then I'll add some more estimates to see what the effect might be on nationwide energy consumption, trade deficit, etc.
On my LR3 HSE, I typically use about 0.5 gallons/hour at idle in neutral. The absolute manifold pressure is about 4.8 p.s.i. Putting the car in gear (drive) and holding it still with the brakes causes the manifold pressure to increase to about 5.8 p.s.i. Since increasing manifold pressure results in a proportional increase in air mass flow through the engine, and hence a proportional increase in fuel consumption, we can assume that the 20.8% increase in manifold pressure results in a similar increase in rate of fuel consumption. However, we're looking at what could be saved by a driver who adopts the policy of shifting to neutral at stoplights so the appropriate way to look at the situation is that this driver will reduce his or her fuel consumption by 17.2% (1/5.8*100%).
Using estimates detailed previously (slightly modified) for stoplights hit per day, time spent per light, idling fuel consumption, etc. for the average car and driver, it looks like my "average driver" could save about 2.56 gallons/year. At current rates in Southern California, that would amount to a savings of $8.70 at the pump. I guess that would cover a single high-end caffeine product at your local Starbucks. It's probably not enough to save a homeowner headed for foreclosure though. As readers of this blog will readily infer, I certainly do it.
What about the results of nationwide application of this policy? I estimate that somewhere on the order of 333 million gallons of fuel could be saved. This is the gasoline from about 17.5 million barrels of oil. And since the other 23 gallons of oil in a barrel are not discarded when gasoline is produced at the refinery, I'll estimate that something like 8.8 million barrels could be left for other countries to purchase. This would reduce our trade deficit by just shy of $1 billion at current oil prices (about $105/barrel). Hmmm... According to the U.S. Census Bureau the January 2008 trade deficit was $58.2 billion. And here I thought I'd solved the problem.
I've previously detailed my policies on stoplights, including when I turn my engine off, coasting to minimize fuel waste when approaching red lights, whether or not it pays to speed up to attempt to make it through a green (or yellow) light, etc. Possibly, no one will adopt any of the measures I've outlined in those posts. But what about just shifting from drive to neutral? When sitting still with the vehicle in drive and brakes applied, more fuel is used than with the vehicle in neutral. I know this to be the case because I can see it on my Scan Gauge II. As I usually do, I'll run a few calculations to estimate my fuel savings from this policy, and then I'll add some more estimates to see what the effect might be on nationwide energy consumption, trade deficit, etc.
On my LR3 HSE, I typically use about 0.5 gallons/hour at idle in neutral. The absolute manifold pressure is about 4.8 p.s.i. Putting the car in gear (drive) and holding it still with the brakes causes the manifold pressure to increase to about 5.8 p.s.i. Since increasing manifold pressure results in a proportional increase in air mass flow through the engine, and hence a proportional increase in fuel consumption, we can assume that the 20.8% increase in manifold pressure results in a similar increase in rate of fuel consumption. However, we're looking at what could be saved by a driver who adopts the policy of shifting to neutral at stoplights so the appropriate way to look at the situation is that this driver will reduce his or her fuel consumption by 17.2% (1/5.8*100%).
Using estimates detailed previously (slightly modified) for stoplights hit per day, time spent per light, idling fuel consumption, etc. for the average car and driver, it looks like my "average driver" could save about 2.56 gallons/year. At current rates in Southern California, that would amount to a savings of $8.70 at the pump. I guess that would cover a single high-end caffeine product at your local Starbucks. It's probably not enough to save a homeowner headed for foreclosure though. As readers of this blog will readily infer, I certainly do it.
What about the results of nationwide application of this policy? I estimate that somewhere on the order of 333 million gallons of fuel could be saved. This is the gasoline from about 17.5 million barrels of oil. And since the other 23 gallons of oil in a barrel are not discarded when gasoline is produced at the refinery, I'll estimate that something like 8.8 million barrels could be left for other countries to purchase. This would reduce our trade deficit by just shy of $1 billion at current oil prices (about $105/barrel). Hmmm... According to the U.S. Census Bureau the January 2008 trade deficit was $58.2 billion. And here I thought I'd solved the problem.
Sunday, March 09, 2008
The best speed for fuel economy
I calculated in a previous post that my "highway mileage" at 55 m.p.h. is 23.27 m.p.g. It stands to reason that there is an optimum speed for fuel efficiency based on the balance between the low efficiency at low speed due to engine friction and the increase in aerodynamic drag, proportional to the square of speed, as speed increases. Now, my Land Rover LR3 HSE is not the optimal aerodynamic shape, with a coefficient of drag of 0.41 and a frontal area of 33.9 square feet. It makes sense, and conforms with various articles I've read (see the article on HowStuffWorks.com entitled "What speed should I drive to get maximum fuel efficiency?" here for example), that the optimum speed for a box on wheels like my vehicle should have a lower optimum speed than a vehicle designed to have excellent aerodynamics.
I made some conceptual calculations that agree with the form of the equation shown in the "How Stuff Works" article linked above. There, it is stated that the power required as a function of speed is a third degree polynomial, that is, P=as^3+bs^2+cs+d where P is power required, s is speed, a,b, and c are coefficients and d is a constant specific to a given vehicle. Since power is the rate of doing work, or more importantly in this case, the rate of use of energy (burning fuel) in the appropriate units (gallons per hour for example), we can say power is proportional to gallons/mile times miles/hour. Then we can say that gallons per mile (the inverse of miles per gallon) is proportional to power divided by speed. So, substitute the polynomial above for power and divide by speed and we find that the rate of fuel consumption in gallons per mile is a second degree polynomial function of speed. Sorry for the extended math exposition!
In any case, the above leads to the following expression for fuel per unit of distance: f=ms^2+ns+p, where f is fuel consumption per distance (say, gallons per 100 miles), s is speed in miles per hour, and m and n are coefficients and p is a constant different (probably) from the previous ones. I used the same level stretch of freeway in no wind conditions that I used previously to check highway mileage (linked above) over a few weeks to check the instant miles per gallon at various speeds allowed by traffic (when I was able to maintain a set speed long enough for the display to stabilize). I then calculated the inverse in gallons per 100 miles for those speeds, plotted them in an Excel spreadsheet and made the best fit of a second degree polynomial.
From that point, it was a very simple calculus exercise to find the speed at which fuel consumption would be minimized. This turned out to be 43.4 m.p.h. I can plug this into the second degree polynomial, divide by 100, and invert the resulting number to estimate miles per gallon at that speed. The result is 27.47 m.p.g. Not too bad, but remember from the earlier post that it turns out that that stretch of freeway has a very slight downward slope in the direction I used to obtain my measurements. I have to use the method I used in that post to correct the fuel economy. To spare my patient readers the details, the correction yields a final figure of 26.18 m.p.g. at 43.4 m.p.h.
Interestingly, this speed is lower than the one previously calculated for the Jeep Grand Cherokee Limited I used to have, even though that vehicle had (according to various web sites) a higher drag coefficient. And, looking at the vehicles side by side, the Jeep looks sleeker. Even with the higher drag coefficient, the jeep feels a smaller drag force due to the smaller frontal area. But unless the figures are mistaken, the looks are deceiving as far as drag coefficient is concerned. And the estimate I had for that vehicle of optimum speed for fuel efficiency was a little over 50 m.p.h.
So, do I plan to reduce my freeway driving speed from the current 57 m.p.h. (it's 57 because I ran the above calculations based on speedometer reading, not Scan Gauge II's 2 m.p.h. lower reading since the speedometer seemed more accurate over a timed measured mile)? Probably not, since I have to be alive to continue with the experiment.
I made some conceptual calculations that agree with the form of the equation shown in the "How Stuff Works" article linked above. There, it is stated that the power required as a function of speed is a third degree polynomial, that is, P=as^3+bs^2+cs+d where P is power required, s is speed, a,b, and c are coefficients and d is a constant specific to a given vehicle. Since power is the rate of doing work, or more importantly in this case, the rate of use of energy (burning fuel) in the appropriate units (gallons per hour for example), we can say power is proportional to gallons/mile times miles/hour. Then we can say that gallons per mile (the inverse of miles per gallon) is proportional to power divided by speed. So, substitute the polynomial above for power and divide by speed and we find that the rate of fuel consumption in gallons per mile is a second degree polynomial function of speed. Sorry for the extended math exposition!
In any case, the above leads to the following expression for fuel per unit of distance: f=ms^2+ns+p, where f is fuel consumption per distance (say, gallons per 100 miles), s is speed in miles per hour, and m and n are coefficients and p is a constant different (probably) from the previous ones. I used the same level stretch of freeway in no wind conditions that I used previously to check highway mileage (linked above) over a few weeks to check the instant miles per gallon at various speeds allowed by traffic (when I was able to maintain a set speed long enough for the display to stabilize). I then calculated the inverse in gallons per 100 miles for those speeds, plotted them in an Excel spreadsheet and made the best fit of a second degree polynomial.
From that point, it was a very simple calculus exercise to find the speed at which fuel consumption would be minimized. This turned out to be 43.4 m.p.h. I can plug this into the second degree polynomial, divide by 100, and invert the resulting number to estimate miles per gallon at that speed. The result is 27.47 m.p.g. Not too bad, but remember from the earlier post that it turns out that that stretch of freeway has a very slight downward slope in the direction I used to obtain my measurements. I have to use the method I used in that post to correct the fuel economy. To spare my patient readers the details, the correction yields a final figure of 26.18 m.p.g. at 43.4 m.p.h.
Interestingly, this speed is lower than the one previously calculated for the Jeep Grand Cherokee Limited I used to have, even though that vehicle had (according to various web sites) a higher drag coefficient. And, looking at the vehicles side by side, the Jeep looks sleeker. Even with the higher drag coefficient, the jeep feels a smaller drag force due to the smaller frontal area. But unless the figures are mistaken, the looks are deceiving as far as drag coefficient is concerned. And the estimate I had for that vehicle of optimum speed for fuel efficiency was a little over 50 m.p.h.
So, do I plan to reduce my freeway driving speed from the current 57 m.p.h. (it's 57 because I ran the above calculations based on speedometer reading, not Scan Gauge II's 2 m.p.h. lower reading since the speedometer seemed more accurate over a timed measured mile)? Probably not, since I have to be alive to continue with the experiment.
Sunday, February 24, 2008
Good question
In my diligent search through the web to find articles of interest about energy, fuel saving measures, and efficiency I happened upon an article from the Technology Review published by MIT entitled Why Not a 40-MPG SUV. The substance of the article was that, despite the remonstrances of (particularly) the U.S. automobile industry, the technology is available now to bring relatively large and comfortable SUV's that achieve a fuel efficiency of 40 miles per gallon.
This was of particular interest to me since I drive a relatively large and comfortable SUV, the Land Rover LR3 HSE that has been the subject of many of the articles I've posted. Now, none of the technologies described in the article can be retrofitted to my vehicle, but they could be brought to market by the time I have to replace the LR3.
Some of the options reflect methods I've already incorporated into my regimen, such as engines that turn off and restart at stoplights, etc. The development is a starter /generator that has sufficient power to start the engine without noticeable lag when a driver steps on the gas after a stop. The current state of the art requires a 42 volt electrical system and is a way out into the future. As detailed previously, I simulate this at relatively long stoplights and on long downhill cruises and make up for the lack of instant starting ability with anticipation.
Some of the developments detailed are already beginning to appear, one example is the continuously variable transmission. Clearly, the ability to run in a narrow band of r.p.m.s regardless of vehicle speed will result in more efficient operation - this is one reason why modern locomotives are hybrid diesel electric propulsion systems wherein the diesel engine runs at a constant r.p.m. to operate electric motors that provide the motive force.
Some are much farther out, including engines that operate without camshafts to operate the valves. Electronic controllers can do a much more efficient job of opening and closing the valves, but are quite hard on them using current technology. Camshafts are more gentle, engineers are investigating various damping systems to reduce the electronically controlled valves impact on valve seats.
There are several more methods under development detailed in the article. Contemplating the individual financial savings as gasoline creeps seemingly inexorably toward $4/gallon and considering the impact on our need to import oil, it's high time we got down to it.
This was of particular interest to me since I drive a relatively large and comfortable SUV, the Land Rover LR3 HSE that has been the subject of many of the articles I've posted. Now, none of the technologies described in the article can be retrofitted to my vehicle, but they could be brought to market by the time I have to replace the LR3.
Some of the options reflect methods I've already incorporated into my regimen, such as engines that turn off and restart at stoplights, etc. The development is a starter /generator that has sufficient power to start the engine without noticeable lag when a driver steps on the gas after a stop. The current state of the art requires a 42 volt electrical system and is a way out into the future. As detailed previously, I simulate this at relatively long stoplights and on long downhill cruises and make up for the lack of instant starting ability with anticipation.
Some of the developments detailed are already beginning to appear, one example is the continuously variable transmission. Clearly, the ability to run in a narrow band of r.p.m.s regardless of vehicle speed will result in more efficient operation - this is one reason why modern locomotives are hybrid diesel electric propulsion systems wherein the diesel engine runs at a constant r.p.m. to operate electric motors that provide the motive force.
Some are much farther out, including engines that operate without camshafts to operate the valves. Electronic controllers can do a much more efficient job of opening and closing the valves, but are quite hard on them using current technology. Camshafts are more gentle, engineers are investigating various damping systems to reduce the electronically controlled valves impact on valve seats.
There are several more methods under development detailed in the article. Contemplating the individual financial savings as gasoline creeps seemingly inexorably toward $4/gallon and considering the impact on our need to import oil, it's high time we got down to it.
Thursday, February 21, 2008
Stoplights (stop me if you've heard this before)
Never one to leave well enough alone (as an aside, this is one of the many expressions I never really understood until well into adulthood - another is "you can't have your cake and eat it too"), I've started sporadically keeping track of my stoplight experiences. I've tracked how many greens, how many reds, and approximately how much time was spent waiting. I say approximately because it's not so easy to determine when to start the timing at a light - do you start the stopwatch at first brake application? Or at a complete stop? What about slowing down but not having to stop? I'm trying to tie the timing to time not using fuel as efficiently as cruising, but there's a lot of judgment involved.
But it's looking like the earlier estimates I made (see here and here)for stoplight durations are fairly close. In the time I've been recording this data (only sporadically because it's quite distracting), I've encountered 59% green lights. I've suffered an average delay of 32 seconds. I've passed through an average of 32 lights each day. So that means that I'm losing an average of about 10:06 per day while stopped at 19 stoplights.
I try to minimize driving on weekends (though I haven't succeeded in eliminating it entirely) so I'll figure 280 days per year of losing 10:06 per day, for a total of 47.13 hours per year lost at stoplights. Burning about 0.5 gallons of fuel per hour at idle, if I don't turn the engine off at any lights, I'll burn 23.6 gallons of fuel. In my Land Rover LR3 HSE, that's a little over a single tank full and at $3.39/gallon (today) it's worth just barely less than $80.00.
This underestimates the loss, however, because it only counts idling fuel and not the fuel wasted in regaining energy lost to braking that has to be added by burning fuel. I estimated that in the second of the two posts listed above, so I'll just refine it here. I estimated stopping at 12 lights for 45 seconds each day for a loss of 9:00 per day, apparently a slight underestimation.
To finally squeeze the last blood from this turnip, I'll estimate that I slow from 35 m.p.h. to 0 on average at each of the 19 stoplights. It's not perfect, but it's as good as I know how to do. In any case, this wastes 322,150 joules of energy which takes, at 25% efficiency, 1,288,600 joules of heat energy from burning premium grade fuel to regain.
Using the figures above, and estimating 125,000,000 joules of heat energy available in a gallon of gasoline, I burn 54.84 gallons of fuel per year adding kinetic energy to my vehicle that I've wasted to heat my brakes stopping for stoplights. The total then is 78.4 gallons of fuel, or about 3.6 tanks full wasted. This number is quite close to my previous estimate, but now there's data to back it up. To me, the interesting aspect of this is the fact that well over 2/3 of the fuel wasted is due to getting back up to speed rather than to burning fuel while sitting still. Since kinetic energy is proportional to the square of speed, this stands to reason but it's still interesting to see it documented.
I'm still anticipating an experiment to determine fuel lost in restarting, but this data shows the potential savings from coasting to a stop without brakes (thus using instead of wasting kinetic energy) and turning off the engine - ideally as soon as the coasting begins. As with most of the other measures, it won't eliminate our need to import oil but it could help delay the crash.
But it's looking like the earlier estimates I made (see here and here)for stoplight durations are fairly close. In the time I've been recording this data (only sporadically because it's quite distracting), I've encountered 59% green lights. I've suffered an average delay of 32 seconds. I've passed through an average of 32 lights each day. So that means that I'm losing an average of about 10:06 per day while stopped at 19 stoplights.
I try to minimize driving on weekends (though I haven't succeeded in eliminating it entirely) so I'll figure 280 days per year of losing 10:06 per day, for a total of 47.13 hours per year lost at stoplights. Burning about 0.5 gallons of fuel per hour at idle, if I don't turn the engine off at any lights, I'll burn 23.6 gallons of fuel. In my Land Rover LR3 HSE, that's a little over a single tank full and at $3.39/gallon (today) it's worth just barely less than $80.00.
This underestimates the loss, however, because it only counts idling fuel and not the fuel wasted in regaining energy lost to braking that has to be added by burning fuel. I estimated that in the second of the two posts listed above, so I'll just refine it here. I estimated stopping at 12 lights for 45 seconds each day for a loss of 9:00 per day, apparently a slight underestimation.
To finally squeeze the last blood from this turnip, I'll estimate that I slow from 35 m.p.h. to 0 on average at each of the 19 stoplights. It's not perfect, but it's as good as I know how to do. In any case, this wastes 322,150 joules of energy which takes, at 25% efficiency, 1,288,600 joules of heat energy from burning premium grade fuel to regain.
Using the figures above, and estimating 125,000,000 joules of heat energy available in a gallon of gasoline, I burn 54.84 gallons of fuel per year adding kinetic energy to my vehicle that I've wasted to heat my brakes stopping for stoplights. The total then is 78.4 gallons of fuel, or about 3.6 tanks full wasted. This number is quite close to my previous estimate, but now there's data to back it up. To me, the interesting aspect of this is the fact that well over 2/3 of the fuel wasted is due to getting back up to speed rather than to burning fuel while sitting still. Since kinetic energy is proportional to the square of speed, this stands to reason but it's still interesting to see it documented.
I'm still anticipating an experiment to determine fuel lost in restarting, but this data shows the potential savings from coasting to a stop without brakes (thus using instead of wasting kinetic energy) and turning off the engine - ideally as soon as the coasting begins. As with most of the other measures, it won't eliminate our need to import oil but it could help delay the crash.
Tuesday, February 05, 2008
Humans as generators
I was watching the show "Invention Nation" on the Discovery Science Channel. The hosts visited a company that, apparently, is working on a revolving door that, when operated by patrons, generates electricity by moving neodymium magnets across coils of copper wire. The mechanism is exposed, so that patrons of an establishment that has such doors will be able to see the means by which they are generating power.
I was skeptical as to the significance of such a device, the show hosts used a prototype to light a small bank of L.E.D.'s. So I performed a Google search on the terms "generating power with revolving doors." I found several sites that mentioned the use of various human activities to generate useful power, including revolving doors and other methods (e.g., piezoelectric crystals in floors). This led me to consider the possibilities (quoting Marcellus Wallace, "All I'm doing is contemplating the 'ifs'").
As best I can tell, the human body, when purposefully performing work (riding a bicycle, lifting, etc.) has an efficiency of somewhere between 11% and 14%. That counts only how many calories (actually kilocalories) of food it takes to do a given amount of "useful" work. It does not count the sun to plant to animal to slaughterhouse to processing plant to distributor to store to house to stove to mouth efficiency (leave out some of those if you're a vegetarian). So, unless someone is exercising to remain physically fit, utilizing the human body to convert sunlight to electricity is quite inefficient.
Let's run some "back of the envelope" calculations though. There are about 3*10^8 people in the U.S. Say 1*10^8 of them walk on office, factory, or school floors, walk through revolving doors, etc. Now, the average adult uses something like 2500 kilocalories per day, let's say 100 of those are used putting feet on floors, using doors, etc. (very generous in my opinion). At 14% efficiency by the human and 50% efficiency by the generator (piezoelectric, magnetic, etc.) we have: 100 kilocalories*0.14*0.5 kilocalories of useful work per day per person to be captured.
Work divided by time is power so the above can be converted to watts per person (I typically use Google's calculator). This yields 0.339 watts per person. This is the effective continuous power output per person on average. Multiply this by 1*10^8 to total 33,900,000 or 3.39*10^7 watts available nationwide calculated on a continuous basis. According to the CIA World Factbook, in 2005 we used electricity at the rate of 3.816 trillion kilowatt hours/year, or 4.353*10^11 watts. Hence, using these extremely optimistic assumptions, this scheme could generate 0.008%, or 8 one thousandths of 1% of our electricity.
As I said though, when we do this, we're converting solar power inefficiently into electricity. Better to invest the money into more efficient generation schemes, except at health clubs, etc., where people are working out into a load and it might just as well be an electrical load that serves a purpose.
I was skeptical as to the significance of such a device, the show hosts used a prototype to light a small bank of L.E.D.'s. So I performed a Google search on the terms "generating power with revolving doors." I found several sites that mentioned the use of various human activities to generate useful power, including revolving doors and other methods (e.g., piezoelectric crystals in floors). This led me to consider the possibilities (quoting Marcellus Wallace, "All I'm doing is contemplating the 'ifs'").
As best I can tell, the human body, when purposefully performing work (riding a bicycle, lifting, etc.) has an efficiency of somewhere between 11% and 14%. That counts only how many calories (actually kilocalories) of food it takes to do a given amount of "useful" work. It does not count the sun to plant to animal to slaughterhouse to processing plant to distributor to store to house to stove to mouth efficiency (leave out some of those if you're a vegetarian). So, unless someone is exercising to remain physically fit, utilizing the human body to convert sunlight to electricity is quite inefficient.
Let's run some "back of the envelope" calculations though. There are about 3*10^8 people in the U.S. Say 1*10^8 of them walk on office, factory, or school floors, walk through revolving doors, etc. Now, the average adult uses something like 2500 kilocalories per day, let's say 100 of those are used putting feet on floors, using doors, etc. (very generous in my opinion). At 14% efficiency by the human and 50% efficiency by the generator (piezoelectric, magnetic, etc.) we have: 100 kilocalories*0.14*0.5 kilocalories of useful work per day per person to be captured.
Work divided by time is power so the above can be converted to watts per person (I typically use Google's calculator). This yields 0.339 watts per person. This is the effective continuous power output per person on average. Multiply this by 1*10^8 to total 33,900,000 or 3.39*10^7 watts available nationwide calculated on a continuous basis. According to the CIA World Factbook, in 2005 we used electricity at the rate of 3.816 trillion kilowatt hours/year, or 4.353*10^11 watts. Hence, using these extremely optimistic assumptions, this scheme could generate 0.008%, or 8 one thousandths of 1% of our electricity.
As I said though, when we do this, we're converting solar power inefficiently into electricity. Better to invest the money into more efficient generation schemes, except at health clubs, etc., where people are working out into a load and it might just as well be an electrical load that serves a purpose.
Sunday, January 13, 2008
Highway MPG
My 2006 Land Rover LR3 HSE with its 4.4, Liter V8 engine is rated by the EPA at 18 m.p.g. highway mileage. In fact, the spreadsheet provided by the EPA in zipped files shows the so-called "uncorrected" fuel economy as 23.3 m.p.g. They correct this by the simple expedient of reducing it by 22%. Now, don't misunderstand. They don't do some arcane analysis that leads to a 22% reduction, they just multiply the measured number (found by measuring carbon emitted during the dynamometer test) by 0.78. Very scientific. That leads to the "18 HWY" on the window sticker. Since my driving is mixed and I'm able to achieve a higher average mileage (currently about 20.5 m.p.g.) than the EPA highway estimate I think that my highway mileage must be considerably better than the 18 m.p.g estimate, and possibly higher than the 23.3 m.p.g. uncorrected measurement. I determined to find out.
The LR3 does not have an instant m.p.g. indication in its instrumentation, however, the Scan Gauge II with which I've equipped my Land Rover does have this instrumentation through the OBDII port. I'm not sure of the mechanism by which this is determined, though I would guess that it uses the metering of the fuel through the injectors and the speed. If it's this method, it may be unreliable because the speed readout on the Scan Gauge II appears to be inaccurate. It reads 55 m.p.h. when the analog speedometer in the dash reads about 57 m.p.h. I had always assumed the ODBII reading was accurate, but there is a series of measured miles for the use of the highway patrol on interstate 15 on the way to Las Vegas and stopwatch timing over these measured miles indicated that the analog gauge on the dash is a better indicator of actual speed. Never mind, I'm going to calculate using the ODBII.
So, what I need is a stretch of level highway where I can just look at the readout on the instant mileage indicator, wait for it to stabilize, and there's my answer. The complicating external factors might be an undetected slope, and wind. As it happens, there's a stretch of the 405 freeway through Seal Beach that appears to be suitable for this determination. Conveniently, there's a power plant visible from this portion of the freeway, and its smokestack gives an excellent signal of wind conditions. When northbound on the freeway, the average stabilized reading over several trips is about 24.8 m.p.g. Woo Hoo! But when southbound, it's more like 21.9. Hmm.... Must be an undetected slope.
How much might there be and what effect might it have? I looked to Google Earth to try to find out. I located the stretch in question and measured the distance and logged the elevations. I tried to find end spots for my measurement where the elevation clicked from one integer foot to another (e.g., 17 feet to 16 feet) and assumed that this was the location where the actual elevation was halfway from one to the other. Now, this may not be completely accurate, but as long as the algorithm used by Google Earth is consistent, this is the best I can do since I'm not interested in absolute elevations but rather in elevation changes.
It turns out that the elevation change is 5 feet over 0.71 miles. That means that, in the downhill direction, I gain 39,948.6 (I always carry a lot of digits) joules of kinetic energy by converting gravitational potential energy, and turn the same amount of chemical energy (assuming I maintain the same speed) into gravitational potential energy in the uphill direction. It's straightforward to determine how much fuel is saved and burned respectively, if I assume that the car is able to utilize 25% of the heat energy of burning gasoline for propulsion at this speed.
Since I haven't had readers of this blog clamoring for more mathematical detail, I'll just give the results. Factoring out the "free" energy provided by going downhill, the car should be producing 23.74 m.p.g. Factoring it out in the uphill direction, the resulting mileage is 22.79 m.p.g. Closer but not identical. I'm not sure where the error is, so I'll just average the two numbers and say that my level highway average m.p.g. is 23.27 m.p.g. This is still a healthy increment above the 18 m.p.g. estimated by the EPA but, amazingly, it rounds precisely to their uncorrected number of 23.3 m.p.g.. I know that the test protocol does not involve simply running in cruise control on level highway in no wind conditions but it still pleases me to beat the window sticker estimate by over 29%, as arbitrary as that EPA estimated number seems to be.
Another lesson is that such a slight hill has so much effect on mileage. Five feet over 0.71 miles is 0.076 degrees; almost undetectable. To get an idea, if you're hanging a 24 inch wide picture and it's off of level by this amount, the low side will be 0.03 inches lower (about 1/32 inch) than the high side. And yet climbing it reduces fuel economy by 5.9%. The lesson? ALWAYS make sure that your destination is at a lower elevation than your starting point.
The LR3 does not have an instant m.p.g. indication in its instrumentation, however, the Scan Gauge II with which I've equipped my Land Rover does have this instrumentation through the OBDII port. I'm not sure of the mechanism by which this is determined, though I would guess that it uses the metering of the fuel through the injectors and the speed. If it's this method, it may be unreliable because the speed readout on the Scan Gauge II appears to be inaccurate. It reads 55 m.p.h. when the analog speedometer in the dash reads about 57 m.p.h. I had always assumed the ODBII reading was accurate, but there is a series of measured miles for the use of the highway patrol on interstate 15 on the way to Las Vegas and stopwatch timing over these measured miles indicated that the analog gauge on the dash is a better indicator of actual speed. Never mind, I'm going to calculate using the ODBII.
So, what I need is a stretch of level highway where I can just look at the readout on the instant mileage indicator, wait for it to stabilize, and there's my answer. The complicating external factors might be an undetected slope, and wind. As it happens, there's a stretch of the 405 freeway through Seal Beach that appears to be suitable for this determination. Conveniently, there's a power plant visible from this portion of the freeway, and its smokestack gives an excellent signal of wind conditions. When northbound on the freeway, the average stabilized reading over several trips is about 24.8 m.p.g. Woo Hoo! But when southbound, it's more like 21.9. Hmm.... Must be an undetected slope.
How much might there be and what effect might it have? I looked to Google Earth to try to find out. I located the stretch in question and measured the distance and logged the elevations. I tried to find end spots for my measurement where the elevation clicked from one integer foot to another (e.g., 17 feet to 16 feet) and assumed that this was the location where the actual elevation was halfway from one to the other. Now, this may not be completely accurate, but as long as the algorithm used by Google Earth is consistent, this is the best I can do since I'm not interested in absolute elevations but rather in elevation changes.
It turns out that the elevation change is 5 feet over 0.71 miles. That means that, in the downhill direction, I gain 39,948.6 (I always carry a lot of digits) joules of kinetic energy by converting gravitational potential energy, and turn the same amount of chemical energy (assuming I maintain the same speed) into gravitational potential energy in the uphill direction. It's straightforward to determine how much fuel is saved and burned respectively, if I assume that the car is able to utilize 25% of the heat energy of burning gasoline for propulsion at this speed.
Since I haven't had readers of this blog clamoring for more mathematical detail, I'll just give the results. Factoring out the "free" energy provided by going downhill, the car should be producing 23.74 m.p.g. Factoring it out in the uphill direction, the resulting mileage is 22.79 m.p.g. Closer but not identical. I'm not sure where the error is, so I'll just average the two numbers and say that my level highway average m.p.g. is 23.27 m.p.g. This is still a healthy increment above the 18 m.p.g. estimated by the EPA but, amazingly, it rounds precisely to their uncorrected number of 23.3 m.p.g.. I know that the test protocol does not involve simply running in cruise control on level highway in no wind conditions but it still pleases me to beat the window sticker estimate by over 29%, as arbitrary as that EPA estimated number seems to be.
Another lesson is that such a slight hill has so much effect on mileage. Five feet over 0.71 miles is 0.076 degrees; almost undetectable. To get an idea, if you're hanging a 24 inch wide picture and it's off of level by this amount, the low side will be 0.03 inches lower (about 1/32 inch) than the high side. And yet climbing it reduces fuel economy by 5.9%. The lesson? ALWAYS make sure that your destination is at a lower elevation than your starting point.
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.
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 $900,000. I wonder if they take VISA?
Obviously, before getting out the plastic or taking out a second on the house, etc. the most economical thing by far is to reduce consumption. This is easy to say and, in my experience, difficult to do. Compact fluorescent bulbs, turning off lights in rooms not being used, reducing the amount of time the pool filter runs, etc., only nibble at the margins. The biggest consumer is my wife's use of automobile fuel, the next two largest are her and the children's "stuff" consumption and my automobile fuel. Dramatically reducing these would be a huge lifestyle change. But it's going to have to be done.
As discouraging as this is, there's a positive element to it. My family is a fairly hefty consumer of energy, and yet the sun provides enough energy to supply us with our needs over the area of the property we own. If we extrapolate that nationwide, the possibility exists that we could actually become self-sufficient and sustainable. There are many, MANY, MANY hurdles to be overcome but there's reason to think it just might not be impossible. It's now up to us to figure out how to make it happen.
In thinking about what it would take to go completely renewable, several factors must be considered. First is that I don't really need to be able to supply power at the rate of 40 kilowatts. A lot of the energy conversion in that number is from the consumption of food and consumer goods. However, if I'm really intending to be entirely sustainable, I should put energy into the grid to compensate for that used in those types of consumption. The same rationale applies to transportation fuel. For this reason, I'll proceed as if that's what I'm going to do.
Next, what renewable sources are available to me? Such exotics as geothermal and tidal are not scaleable to my needs, even if they were geographically and geologically available. Wind is not practical because wind of sufficient velocity is infrequent and the (%$#&*&^%) 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.
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.
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.
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
Hills
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.
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.
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
Headwinds
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.
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.
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.
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?
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.
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.
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.
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.
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.
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.
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.
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.
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