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

Sunday, November 19, 2006

"Optimum" economic speed

For a math guy like me, this one will be strictly fun. In "Use of time" I discussed various matters related to the time "lost" by traveling at 55 m.p.h. on the freeway. One of the comparisons I developed was that, at the fuel prices in effect at that time (April of 2006), the time I lost in a day was valued by my company at $12.39 whereas I saved fuel valued at $4.57.

This would seem to indicate that, from a purely "dollars and cents" point of view, the faster I go, the better. Let's take an analytical look at that. I'll ignore limits on engine performance, speed limits and law enforcement, the physics of negotiating curves, and all other real-world matters.

The aerodynamic force resisting my vehicle's forward motion is proportional to the square of velocity (I insist) so additional speed increases fuel use dramatically. The time gained increases as my speed increases. Can I go so fast that I burn extra fuel worth more than the dollar value of my time savings?

Since I do in fact have to go to work and must use fuel, I can't merely calculate when fuel burned per minute equals my salary per minute. I have to use a baseline. I'll choose to use 55 m.p.h. So the problem is to determine how fast I must go to burn so much more fuel than I would burn at 55 m.p.h. that it is worth more than the value of my salary for the time that I'm traveling at the high speed.

The reader should note that I typically contemplate the problems about which I write "on the fly," hence I don't know what the answer will be until I have set it up in the blog. This is no exception, but I anticipate that the the speed will be a ludicrously high one.

So let's get started. I can easily calculate that the value of the time saved by driving faster than 55 m.p.h., as determined by my salary (and hence by my company's valuation of my time) to be $62.95-(3462/x) where x is my speed in miles per hour and the result is the savings for a single day's driving to and from work. So, for example, at 75 m.p.h. I save time worth $16.79.

The excess gasoline costs are not nearly so easy. To get a handle on this, I started with the model on the "How Stuff Works" web site. There, Marshall Brain models the power required as p = a*v + b*v^2 + c*v^3. Now, using some physics definitions and the chain rule from elementary calculus, we get to c = d + e*v + f*v^2, where c is "consumption" in appropriate units (say, gallons per mile) and d, e, and f are constants for a given vehicle. To determine the three constants, I need to know the consumption in gallons per mile (the inverse of miles per gallon) at three different speeds.

Well, I have 31 m.p.g. or 1/31 gal./mile at 55 m.p.h. so there's one. I can't use my idling fuel consumption since it is at zero m.p.h. and consequently would lead to an undefined consumption in gallons per mile, since we would be dividing by zero. So I acquired two more points, one at 40 m.p.h. and one at 70 m.p.h. Utilizing those numbers in the same way and solving the three simultaneous linear equations for the constants d, e, and f, and plugging them into the equation enables me to equate the dollars saved on my salary to the dollars spent in extra fuel, assuming gasoline at $3.40/gallon. At that speed, any faster and I would start losing money since losses on the fuel side would exceed gains on the salary side.

I hope I've built the suspense enough. The break even point occurs at 170 m.p.h. Now, if someone were to think that a Jeep Grand Cherokee Limited isn't capable of those speeds, that person would be correct. So what does it mean? It further emphasizes the need to be productive on the road, because gas isn't expensive enough, by far, to make up for the time lost in driving slowly.

Of course, I'm relatively well paid and gas could go up, so I guess the next step would be to develop a table for the break even speed at different salaries and fuel costs. But even then, a change in the miles driven at freeway speeds (such as 170 m.p.h.) would change the table. But it is clear that, from a purely economic point of view, I'm not doing myself any favors.

Saturday, November 11, 2006

Run for the light?

Of course, some of the modifications to my driving technique save gallons per tank full; in particular, slow acceleration to a maximum of 55 m.p.h. Without getting into statistics, there's no question that large improvements in fuel economy have been made - I used to have to fill up at about 280 to 290 miles, now it's more like 430 to 450. I'm reasonably sure most of it comes from the speed and acceleration reductions.

Some of the things I do may save, literally, only milliliters per tank full. For example, my driveway slopes severely to the street. I can roll down, turn into the street, use the momentum to turn 180 degrees onto the adjacent street, and roll to the stop sign for the main road before turning on the engine, saving about 30 seconds and 180 feet of running the engine. In a tank full period I may do this 6 times, thereby saving something like 2.5 fluid ounces of fuel. In a year, the savings could amount to a gallon. Not enough to save the world.

And I do other things whose savings make that seem huge by comparison, such as turning off the engine and coasting into a parking space when I have the space made. People chuckle, shake their heads in pity and say "tsk tsk" when they see me do this, but I'm strong and can take it!

But I do these things because I'm trying to do everything possible, no matter how trivial. In so doing, I often am faced with the decision of how to treat stoplights. There are several issues to contemplate but the one I have in mind today is how to treat a light that is currently green but that may change to red before I get there. Under what circumstances should I accelerate and run for it?

It's clear that the question is the balance between fuel wasted while stopped at a red light versus that wasted by hitting the throttle to get through the light. Looming in the background is the horrifying risk of hitting the throttle to get through the light and missing it anyway. Worse still is the doomsday scenario of running for the light, having it change, being unable to stop and getting a traffic ticket. We'll ignore this remote possibility.

It's a complicated problem since lights have different durations, my knowledge is typically imperfect (though I know some lights quite well and can therefore make more informed decisions), I may or may not be able to keep the speed I generate in running for a light (depending on traffic conditions, whether or not I am turning, etc.), the continuum between a slight, gentle acceleration and "stomping on it," and many other factors.

But to at least get started, let's suppose I estimate that, if I run for it there's an 80% chance I'll make it. If I don't make the light, I'll spend 35 seconds stopped while it's red. For the purposes of the analysis, let's say that I'm going 25 m.p.h. Let's further assume that I use hard but reasonable acceleration - say, 2.7 meters/second^2, or 0.28g to accelerate to 45 m.p.h. For this scenario, let's assume that I am not turning and can keep my momentum or at least coast to the appropriate speed without braking if I make the light. For the accelerate and make it scenario, we have to make still more assumptions. I'll assume that I'm at 25 m.p.h., I accelerate to 45 m.p.h. at 2.7 m/s^2 and coast back down to 25 m.p.h. at 0.22 m/s^2. Finally, let's assume that, without acceleration there's a 30% chance that I will make the light.

OK, we should be able to get some comparative numbers here. It will be probabilistic and deal with so-called "mathematical expectation" since I have to incorporate the 20% chance of not making the light if I accelerate and the 70% chance of not making it if I don't. I'll spare my patient readers (reader?) the details of most of the calculations, but there are 4 situations: accelerate, make it; accelerate, miss it; don't accelerate, make it; don't accelerate, miss it. These scenarios have probabilities 80%; 20%; 30%; 70%.

I think the easiest way to go about this is to figure how much fuel is used in each case to get, say, one mile past the light with no further stopping given each of the scenarios above. So without further ado:

Don't accelerate, make light uses 0.0458 gallons

Don't accelerate, miss light uses 0.0523 gallons

Accelerate, make light uses 0.0546 gallons

Accelerate, miss light uses 0.0611 gallons

Surprisingly, acclerating and MAKING the light uses more fuel than not accelerating and missing the light. Therefore, it could not possibly pay to try to make the light using this specific scenario. Obviously, other assumptions regarding light durations, speeds, accelerations, etc. could change this. And in case anyone incorporates my driving techniques, the numbers above were derived using fuel consumption numbers for my Grand Cherokee Limited. As they say in chatrooms, ymmv (your mileage may vary).

To close the chapter, the mathematical expectations (under this set of assumptions) are:

Don't accelerate: 0.3*0.0458+0.7*0.0523=0.0503 gallons

Accelerate: 0.8*0.0546+0.2*0.0611=0.0559 gallons.

So there you have it. If I accelerate to make a light, I can expect to use about 11% more fuel at the intersection than if I just maintain my normal speed. Again, the circumstances for this calculation are quite specific but not abnormal. Every now and again though, at lights where I know the duration of the red is long and where I know a short burst will get me through and the lack thereof won't, I'll give it a try.

Sunday, November 05, 2006

Traffic jams

Though I've had trouble finding the original source, it seems that the consensus on the web (see here for example) is that Americans waste 2.3 billion gallons of motor fuel in traffic jams annually. Another figure that seems to be well accepted is that Americans use about 100 billion gallons of fuel. So approximately 2.3% of the motor fuel in the United States is wasted in traffic jams.

This is truly awful, but is it significant? As noted in a previous post a barrel of oil produces 19 gallons of motor fuel, so we waste the gasoline from 2.3 X 10^9 / 19 = 121 million barrels of oil per year in traffic jams. We use about 21.9 million barrels per day or 7.9 billion barrels per year. Thus, fossil fuel wasted in traffic jams represents about 1.5% of our annual fossil fuel usage. Of course, the barrels of oil producing the 19 gallons are actually 42 gallons each. The remainder goes to various other uses and thus this figure of 1.5% overestimates the reduction in oil usage that could be achieved by the elimination of traffic jams. Figure about half of that or so.

In an earlier post I noted that the United States could save almost 29% of our personal transportation motor fuel if everyone implemented the measures I have undertaken to save fuel. Of course, I have also explored the likelihood that all, most, or even a significant portion of the population of U.S. drivers would take these measures. In the current vernacular: I'm sure we'll do it..... NOT!!

Still, if a way could be found to motivate Americans to take up these driving habits, to avoid unnecessary car trips by telecommuting, carpooling, combining trips, etc. I believe we could cut our use of fossil fuel for personal transportation by 50% and our overall fossil fuel usage by upwards of 20%. Increasing the so-called "CAFE" (corporate average fuel economy) requirements could increase this further still.

But in order to accomplish anything like this, a general awareness of the urgency of the situation would have to be generated. These things could be done at one time, the sacrifices of World War II come to mind, but in today's completely fragmented society, I am more than skeptical. The facts of our spiralling trade deficit, increasing population, and diminshing availability of cheap and easy fossil fuels will have to hit us on the head.

It will not be painless.

Sunday, October 29, 2006

New car considerations

I've had the 2000 Jeep Grand Cherokee Limited that has been the subject of the experimentation described (ad nauseum) in this blog since August of 2000. It has about 142,000 miles on it and has been a truly wonderful car. I know some have had lots of trouble with their Jeeps, but I've changed the oil in mine, and the brake pads and rotors once. Other than that, it's been maintenance free. But it's getting a little long in the tooth, with no navigation system, the cd changer in the back of the truck rather than in dash, etc. I decided to start looking for a replacement.

Most who are aware of what I've been doing to minimize fuel consumption in the Jeep assumed I'd look at Prius, Insight, Civic Hybrid, or other mileage maximizing vehicles. Today I looked at the Acura RL, the Acura RDX, and the Lexus RX350. Huh? The best of these achieves E.P.A. ratings of 20 city, 26 highway. Isn't this hypocritical?

Well, for starters, they all are rated higher than my Jeep (15/20). But the fact of the matter is, I like big engines, acceleration, and luxury. The fact that I never utilize the horsepower available to me in the Jeep doesn't mean that I couldn't (and haven't). And there are those who say "you've squeezed all the blood out of that turnip" in reference to my experiment. Occasionally, I do think it would be nice just to drive, enjoy the performance of a nice car, and not concern myself with trying to extract the last possible foot out of each milliliter of gasoline.

But the fact is, none of the vehicles I looked at today excited me. The RL is nice, high tech, has real time traffic through XM satellite radio, is comfortable, and handles well. The RDX just didn't thrill me at all, nor did the RX350. In fact, my experience today led me to realize how much I really do like my Jeep. It's exceptionally comfortable, has power in case I should ever decide to go back to using it, and has demonstrated flawless reliability. I'd like to have satellite navigation, but that can be achieved with a Garmin portable unit or similar. Blue tooth hands free calling would be nice, but I can get an earpiece. An iPod port would be great but I can get an adapter. XM satellite radio is cool, but I can get a portable unit. All in all, I'm just still very pleased with my Jeep.

One of my business partners got a BMW X5 last week, though I haven't been in it yet. I'm not a BMW kind of guy. They seem like a "look what I can buy" kind of vehicle, though Brian assures me that he isn't a "look what I can buy" kind of guy. It's been suggested that I look at the Infiniti M class. I don't know much about the car, either in terms of features or gas mileage. But unless it knocks my socks off, I'm thinking very seriously of staying with old faithful.

Sunday, October 22, 2006

Effects of weight

I've scoured the internet for the last year (plus) looking for mileage and fuel economy related sites. One of the "rules of thumb" I've seen quoted is that "you will lose 1% to 2% of your gas mileage for every 100 pounds of excess weight you carry" (see here for example). Since I tend to be a pack rat and that tendency extends to the cargo area of my Grand Cherokee, it's one of the areas where further savings may be possible.

First, suppose it is true. In that case if I removed, say, 200 pounds of stuff from the car I could expect to improve from the 23.6 m.p.g. I am currently averaging to about 24.1 m.p.g. In the course of the approximately 20,250 miles I drive per year, I could expect to save about 17.8 gallons. At current Southern California prices, that represents a savings of a little over $43. Maybe dinner at Islands for two, but no movie afterward. Of course, long-term readers of my blog (lol) will realize that this likely exceeds the savings realized by eschewing the drive through window. That means I MUST do it if I can demonstrate that it's a plausible number. Let's see what we can do.

A couple of posts back I discussed mass as it relates to mileage. As related there, I think there are probably three detrimental effects of a more massive vehicle on gas mileage. Only two can be controlled by eliminating weight from a given vehicle: the energy cost of lifting mass up hills and not receiving full repayment on downhills; and tire rolling friction.

I will make an educated guess that increased dissipative losses on hills due to increased weight are a so-called "second order effect" and that the primary effect of increased weight on fuel economy is based on the increased rolling friction. I have cited a web site several times where the author discusses the physics of automobiles, and on that site the author contends that rolling friction is approximately 1.5% of vehicle weight at freeway speed. His discussion is actually more detailed, but that's my estimate based on the information he provided. In another post I've shown that his calculations agree with the ones I've made based on fuel consumption, so I think it's reasonable to use his figures.

Thus, I can estimate that 200 extra pounds would result in 3 extra pounds of rolling friction. Since fuel expended to maintain speed is proportional to the total resistive force, which I calculated using the rate of fuel consumption in a previous post as approximately 139 pounds, and that I will calculate in a subsequent post using a different method as 170 pounds, 3 pounds represents somewhere between 2.2% and 1.8% of total resistive force. The "second order effect" mentioned above will only add to the savings, though likely by a minor amount. But that's pretty close to the 2% to 4% predicted by the rule of thumb, so, out comes the junk.

Sunday, October 15, 2006

Efficient speed

It's been well over a year since I began my experiment to increase gasoline mileage in my Jeep Grand Cherokee Limited. Without any doubt, huge increases can be achieved. At the outset of the experiment, in August, 2005, my average mileage indicator on the display was at 14.9 m.p.g. It is currently at 23.6 m.p.g., a whopping 58.4% increase, and an estimated 31.1% above the EPA estimate for the vehicle (18 m.p.h. combined). I should add that the information on the average mileage indicator is confirmed by an extremely detailed, tank full by tank full spreadsheet. I calculate mileage by tank full, five and ten tank full moving averages, standard deviation, and estimated annual savings in gallons and in dollars.

In an earlier post (More on acceleration) I estimated that about 14% of my savings come from reduced rate of acceleration. It might be wondered where the rest comes from. As loyal readers may recall, the other steps I've taken are to utilize cruise control at 55 m.p.h. on highways and freeways; anticipate stops and slowdowns to enable coasting to stops and speed reductions so as not to waste energy by braking; minimize use of "appliances" (air conditioning, headlights, seat heaters, defroster, etc.); coasting downhill out of gear (the savings here are controversial - some maintain that modern computerized cars are more efficient coasting in gear); filling the tires to 2 p.s.i. above recommended maximum; avoidance of drive through windows; and turning the engine off on long downhills and at long stoplights.

Of these, I think it's very clear, based on both theory and the evidence of the instant mileage indicator, that the main contributor to my increased fuel efficiency comes from my reduced highway speeds. My understanding of the physics involved leads me to conclude that the reason for the dramatic decrease in mileage per gallon at speeds above 55 m.p.h. is that aerodynamic drag increases as the square of speed (as noted previously, others say cube, which would make it even more dominant).

I have done a lot of "googling" using search terms involving fuel efficiency, minimizing fuel consumption, etc. and there are many people on forums and blogs who contend that their vehicles are much more efficient at 70 m.p.h., and even 80 m.p.h. than at 55 m.p.h. As I noted in my original article on acceleration (To floor it or not to floor it) there is general agreement that fuel efficiency (m.p.g.) increases as speed increases up to a point where the aerodynamic drag increase overrides the increase in efficiency from utilizing fuel for motion rather than merely running the engine. A further complication is that the gearing and engine parameters for a particular vehicle may make it utilize fuel to develop power more efficiently at some relatively high engine speed.

So is it possible that the above-mentioned posters are correct? It would imply an extremely low coefficient of drag, combined with an engine and drivetrain combination that would lead to terrible low speed performance. Since I don't have such a vehicle, I can't do any experimentation, but I suspect it's wishful thinking on the part of the drivers of those vehicles in an effort to rationalize their behavior. I'm not a psychologist, so I have no comment on why they would have a need to engage in such rationalization.

Saturday, October 07, 2006


It's been almost two months since my last post due to some surgery that made writing and typing difficult. I hope I haven't lost my devoted readers. Right. In any case, onward and upward.

The trend in my mileage has been a significant increase in standard deviation, together with a slight decreasing trend in mileage. This, despite the installation of the K&N high flow air filter noted in my last post. Starting June 19, there was a major downtrend in my mileage from which I've never really recovered, followed by a trendless few tank fulls with large variation.

A comment was left in my post about Dr. Steven Dutch and his article about the 200 mile per gallon car. At the end of that post, I stated that it was my belief that "in order to achieve major reductions in oil consumption without going to vehicles such as the scooter I discussed a couple of posts back, large-scale changes must be made in the technology of internal combustion engines or other propulsion methods must be employed."

Bill Anderson, host of the blog entitled "mental radiation," commented that large gains can be made in automotive gas mileage by reducing the weight of vehicles. He stated that two thirds of the energy used at the wheels is used to overcome weight, and concluded that by reducing weight the amount of energy required to get from point A to point B can be reduced. Dr. Dutch implied a similar conclusion.

What about this? Well, obviously, since F=ma, that is, Force equals mass times acceleration, it takes more force to get a heavier (more massive) vehicle up to a given speed. But at speed, on level road, acceleration is zero and hence, the sum of forces acting on the vehicle must be zero. These forces are dissipative (drag, rolling friction, driveline friction, engine friction) and force applied to the road by the engine. With the likely exception of rolling friction, seemingly none of these are a function of mass, though engine friction must increase with engine size, which in turn typically increases with vehicle weight. Though this is probably not necessary by the laws of physics, a certain capacity for acceleration must be provided by its manufacturer to make the vehicle saleable.

And since I concluded in a series of earlier posts that engine friction is a very significant component of energy usage, heavier vehicles must use more fuel even in unaccelerated travel, though it isn't a direct correlation. Added to this, it takes more fuel energy to lift a heavier vehicle up a hill, energy which is not fully recovered in the descent due to disspative forces. Further, it seems very likely that heavier vehicles produce higher tire rolling resistance. In fact, this is almost certainly the largest contributor to increasing fuel consumption with increasing weight. Finally, unaccelerated travel on level roads for long periods is not the norm.

Thus, I agree that weight reduction is an effective means of increasing fuel economy, but at freeway speeds a large percentage of the force the engine must overcome is produced by drag. Reduction in "flat plate area" can be achieved by making cars smaller as well, but there is a limit - we still want a driver's seat and a passenger seat. I doubt we'll see tandem seating anytime soon.

Saturday, August 19, 2006

Mixed messages

After my fill-up on August 10 (calculated miles per gallon of 23.90 so climbing back up where I had grown to expect) I installed a K&N high performance air filter. I wanted to see if such a product could increase my fuel efficiency. I was amazed to see that the instant mileage indicator, which I consult frequently when driving, seemed to show a distinct and significant increase. For example, on normal, relatively level stretches of freeway at 55 miles per hour I typically see the indicator jump between 31 and 32 miles per gallon. After installing the K&N filter, the same stretches yielded indications of 33 and 34 miles per gallon. Amazing and quite significant. This should be my best tank full yet, huh?

Think again. Though the driving I did for this tank full was quite typical of my average driving regime, the fill-up from yesterday (August 18) yielded 21.16 miles per gallon. This surprised me as the instant mileage indications led me to expect something like 24 miles per gallon early in the tank. As the fuel quantity indicator went down though, it was clear that I wasn't going to see a good number.

I surmise that one of the major contributors to the variance I see in my results (current standard deviation, the square root of variance, in calculated miles per gallon evaluated at fill-up is 1.71) is inablility to fill the tank to a precise level. That is, if my previous fill-up was short of normal and the current one is above, I'd calculate a lower mileage. The opposite is also true. Such effects clearly average out over a period of time and thus I follow my five tank and ten tank moving average to account for this.

But it's hard for me to see how it could be the entire explanation of this particular fill-up. I put 19.104 gallons in the tank after driving 404.2 miles, thus getting 21.16 m.p.g. For me to have gotten 23 m.p.g. I would have to have only needed 17.565 gallons. That's a difference of 1.539 gallons. It could have happened if the earlier fill-up was, say, about 0.77 below the "average" spot and the most recent was 0.77 above that spot. But it seems like that's an awful lot of variation.

Because I'm aware that the fill-up point is so important to the calculated mileage, I fill it absolutely as full as possible because that seems to be the most accurately repeatable amount. Though I know one is not supposed to "top off," I invariably do. I top off until it's only possible to add a couple of cents worth of fuel (say 0.006 gallons) before the automatic shut-off turns it off. I know that if I didn't top off, the variations would average out to an accurate number over time but I'm too impatient to wait for the averaging out process.

But I'm having a hard time reconciling the low mileage calculated for this tank full with the noticeably higher freeway instant miles per gallon readings. I guess I'll give it another tank full or two before I delve into it more deeply, though I don't know what that delving would invlove.

Monday, August 07, 2006

Cruise horsepower

This will be a short one. I cited a web site a couple of posts back that has some very interesting articles on automobile physics. The author uses coefficient of drag, estimates of tire rolling friction, etc. to determine that his Corvette needs about 26 horsepower to cruise the highway at 60 miles per hour.

I can get at this problem from a different point of view. I get about 31.5 miles per gallon at 55 miles per hour. This is using fuel at the rate of 55/31.5 or 1.75 gallons per hour. Those 1.75 gallons contain about 1.75*125,000,000=218,000,000 joules of heat energy in the chemical bonds I release by burning them in my cylinders. About 25% or 54,600,000 joules goes to maintaining my 55 miles per hour, the rest is wasted as heat expelled to the environment (an inevitable consequence of the second law of thermodynamics, i.e., you can't break even).

So I'm using 54,600,000 joules per hour to maintain motion, or 54,600,000/3600=15,200 joules per second, otherwise known as watts. Now a horsepower is 746 watts, so I'm using 15,200/746=20.4 horsepower. Pretty darn close to the web site author's number, especially considering I'm looking at a speed 5 miles per hour lower. I really love it when different approaches to a problem confirm each others' results.

To carry the analysis a little further (at the risk of causing any remaining reader to throw up his or her hands in despair), force X speed = power, thus power/speed=force. So: 55 miles per hour is 24.6 meters per second; 15,200 watts/24.6 meters/second = 618 Newtons (the metric unit of force). 618 Newtons is 139 pounds of force. That's all it takes, applied continuously, to move me down the highway at 55 miles per hour in my Jeep Grand Cherokee Limited. I'm going to take an informal survey. I bet most people think it's a whole lot more.

Sunday, August 06, 2006

More on fuel used to run the engine

I've spent a couple of posts attempting to determine where the heat energy in the cylinders from burning fuel is used. I talked about the air conditioner and about the fuel used to keep the engine turning. I was rather surprised at the amount used for the latter and decided to look into it a bit more.

Several posts back I wrote about the web site of Dr. Steven Dutch, a Professor at the University of Wisconsin at Green Bay. He has an article debunking the fantasy 200 mile per gallon car. To be clear, he doesn't claim that no such vehicle exists or is possible, only that it's not possible to use simple bolt-on parts or additives to achieve this kind of mileage with "off the shelf" cars.

In any case, Dr. Dutch uses several strategies to infer the force required to turn the engine against the friction of the moving parts (probably primarily the pistons in the cylinders I would guess). The one I'm considering is his analysis involving the cranking power of an automotive battery. He concluded that turning the engine over requires 3600 joules per second or 3600 watts.

If that's true, it means that the energy needed to turn the engine for an hour is 3600*3600 or 12,960,000 joules. However, the engine only uses about 25% of the heat energy in gasoline to do useful work, the rest is wasted as heat expelled to the environment. In fact, some of the "useful work" is turning the fan and the water pump to dissipate the heat. In any case, this means I need the energy of 4*12,960,000 or 51,840,000 joules of heat. This is the amount available in 51,840,000/125,000,000 or about 0.41 gallons of gasoline.

Let me repeat that. Dr. Dutch's calculations imply that I consume about 0.41 gallons per hour to turn the engine. My observations on the road lead me to conclude it's about 0.38 gallons per hour. Absolutely amazing that the agreement is so close. And it reinforces my conclusion that a large amount of the fuel burned in a car is used to operate the engine.

Saturday, August 05, 2006

Dissipative forces

There's a principle in physics called "conservation of energy" which is of awesome utility. There are also what are termed "conservative forces" (gravity is one). Please note carefully that I am talking about PHYSICS and NOT POLITICS. Anyway, gravity being a conservative force, theoretically, I can get all of the energy I use to climb a hill back when I descend. As we all know, this isn't the nature of our real world. The fly in the ointment is the phenomenon of dissipative forces. Such forces in our example include friction of all types and fluid mechanical drag.

I was reading a site that discusses the physics of automobiles (a very interesting site by the way) wherein the author stated that "Mechanical Drag is due to all the moving mechanisms in the vehicle that have frictional losses, most specifically the wheel bearings, but is actually nearly entirely due to the action of the tires on the road surface. In nearly all actual situations, all the other causes of mechanical drag factors can be ignored, and just the Tire Resistance considered, regarding the Mechanical Drag."

I don't know about that. As I discussed in my last post, my Grand Cherokee burns about 0.38 gallons per hour when idling or coasting in neutral. It idles at 650 r.p.m. I think it's reasonable to assume that: a) all of the fuel burned while idling goes to overcome engine friction and pumping losses; b) these losses are directly proportional to engine r.p.m.

At 55 miles per hour, the engine turns at 1750 r.p.m., so assumption b) above would indicate that I'm burning (1750/650)*0.38 or 1.02 gallons per hour to overcome engine friction and pump fluids. As I also showed in the previous post, I burn 1.75 gallons per hour at 55 miles per hour. This would indicate that 58% of my fuel consumption goes to keeping the engine running at 1750 r.p.m. and 42% goes to overcoming aerodynamic drag, driveline friction and tire rolling friction.

This seems very surprising to me, and I'm sure it would be extremely surprising to the author of the article cited above. Could it be true? Let's suppose that the engine friction and pumping losses are proportional to the square root of r.p.m. If so, I'd use 0.62 gallons per hour at 1750 r.p.m. and about 35% of the fuel burn is to overcome engine friction and pumping losses. If fuel used to overcome these losses doesn't increase at all with r.p.m., an extremely unlikely scenario, it would still mean that almost 22% of the fuel burn at 55 miles per hour is used in keeping the engine going. Very surprising indeed.

It's possible that the fuel is used for something other than overcoming these dissipative forces when idling, but I'm not sure what it would be. Unless there is a governor that absorbs the mechanical energy and turns it into heat, if there is an excessive amount of fuel for the state of energy use in the engine, the r.p.m.'s would increase. In other words, since the r.p.m.'s stay at 650, the system is in equilibrium. So, surprising as it may be, I think the conclusion is accurate, i.e., that a whole lot of fuel is burned to keep the fuel burner burning fuel.

Friday, August 04, 2006

Air conditioning?

Though I doubt anyone reads this blog so carefully (hidden assumption: anyone reads this blog at all), it's possible that someone could have wondered, reading earlier posts, how I estimated the idling fuel consumption of my Grand Cherokee. When coasting in neutral down a mild grade, the car will sometimes reach an equilibrium speed. When this happens for long enough for the instant gas mileage reading on the display to stabilize, the speed in miles per hour divided by the mileage in miles per gallon gives the consumption in gallons per hour. I think this is reasonably accurate since the car is only burning fuel to maintain idling r.p.m. (650).

The number is typically pretty close to 0.38 gallons per hour. However, coasting down the typical grades where I check that, I've noticed lately that I'm burning closer to 0.48 gallons per hour. Now, although my most recent fill-up indicated an improved mileage of 22.1, my previous post was pretty much of a rant about my declining gas mileage of late. Is the increase in idling fuel consumption indicative of a systemic problem that could cause my overall decrease in efficiency? Perhaps it's a symptom of dirty injectors or a clogged air filter.

But another possibility is air conditioning. I try to minimize its use, but it's been quite hot in Southern California and I've had it on quite a bit of late. Could it be that this is the difference I'm seeing? If so, it would indicate that the air conditioner uses about 0.1 gallons per hour when it's on. It certainly seems reasonable that air conditioning fuel use would be a constant function of time and independent of vehicle speed, therefore, the faster I'm going, the less deleterious the effect would be on my fuel consumption per hour.

Let's see if this makes any sense at all. A gallon of gasoline contains heat energy of about 1.25*10^8 joules. Thus, 0.1 gallons per hour would be 1.25*10^7 joules per hour, or about 3500 watts. But the internal combustion engine wastes most of that heat energy - something like 75%. So that means only about 25%, or 875 watts (a tad over 1 horsepower) would be available as mechanical energy to cool the air. This squares niceley with my "gut feeling" about air conditioning.

If it is the air conditioner, I can calculate the effect of a.c. on my gas mileage at , say, 55 miles per hour. Let's see what we find: when driving at 55 m.p.h. on stretches of freeway that appear to be level (i.e., 0% grade) I typically see the instant mileage display oscillate between 31 and 32 miles per gallon. Let's say it's 31.5 m.p.g. This indicates I'm burning 1.75 gallons per hour. But if the air conditioner then burns an additional 0.1 gallons per hour for a total of 1.85 gallons per hour, it should reduce my gas mileage to about 29.7 m.p.g.

This number should be quite noticeable and I don't notice it. It could mean that the 0.1 gallons per hour useage noted above comes from some other cause (e.g., the clogged injectors or air filter) or it could mean that the fuel consumption of the air conditioner is not merely a constant function of time. Or finally, it could be an indication of the error in my determination of the relevant numbers while also performing driving tasks (tuning the radio, answering the cell phone, checking my schedule on the pda, etc.).

I guess I need to get a tune up, see about getting the injectors cleaned, and change the air filter. Then it would be reasonable to check the numbers, followed by a day trip out to the desert somewhere to do some experimentation under more controlled conditions. Stay tuned...

Friday, July 28, 2006


It's been a very frustrating period. Over the last few weeks, my five tank moving average mileage has decreased by more than two miles per gallon. The troubles began with the brake job reported in an earlier post. The pads definitely dragged on the rotors for a few hundred miles after that - I could feel it in the behavior on coasting to a stop and, in the beginning, I could smell the burning pads. But these are no longer the case. The car rolls just like it always has, the highway instant miles per gallon seems normal, and yet my mileage has deteriorated. Why?

I got involved in an argument with a guy who has a blog called "mental radiation." (Note that that link is to the argument, I believe he actually maintains his blog at a wordpress site here.) The nature of the argument was over the extent to which the use of ethanol as a motor fuel eliminates the impact of driving on fossil fuel usage. As is common in internet arguments, neither of us was convinced. But in the process of our discussion, he looked at my blog and made several comments.

One of them was in response to my posting about my learning curve, in which I opined that the increasing trend in my mileage, as shown by the five and ten tank moving averages, indicated that I was learning to better maximize fuel efficiency. Bill Anderson, publisher of "mental radiation," was skeptical. His belief is that there are likely other reasons, e.g., different brands and different seasonal blends. I'm beginning to wonder.

I've bought Chevron, mostly from the same station, for the duration of the experiment. There have been perhaps three exceptions when I patronized Arco. The Arco purchases are not distinguishable on the graphs or in the raw data, but the downward trend from the last few weeks is obvious. I don't know if there has been a change in gasoline blends in June and July, certainly I haven't read of one. Maybe something's wrong with the vehicle. But even at that, why does my highway instant mileage still indicate what it did when my trend was upward?

Thursday, July 13, 2006

$4.85 per gallon

Today I paid $4.85 per gallon for fuel. It was a very painful fillup since I needed almost 40 gallons. In context, that means I had used about 3/8 of a the fuel in my tanks. I mentioned in an earlier post that I'm a pilot, and I'm referring to the fuel in my airplane.

Because much less "avgas" is refined as contrasted with the vast quantities of automobile fuel, avgas is more expensive. My particular airplane, a Piper Saratoga, cruises at about 168 knots (193 statute miles per hour) while burning about 18 gallons of fuel per hour. That works out to about 10.7 statute miles per gallon.

I took it out for some "pattern work," that is, executing touch and go landings for the purpose of staying sharp and probably burned about 10 gallons or so. In light of my extraordinary efforts to save an ounce of gasoline here and a teaspoon there, how does my flying fit in?

It certainly enables me to accomplish things I otherwise couldn't. For example, I have an employee in the field, working a project in Fresno. He will work Sunday night until about 6am Monday morning and needs to be back at our office in Long Beach by 9am. This could not be accomplished without the airplane, but the cost of doing it will be about $500.00. That figure values my time at zero (which many who know me say is appropriate).

But in the end, I really do it because I like it. What will my breaking point be? I'm not sure yet but I know it's out there somewhere. The aiplane holds 102 gallons of fuel, and I was told by someone that avgas is going for $6.25 per gallon in Las Vegas. When I fly there, I burn around 25 gallons each way, so figuring half the trip at $4.85 Long beach prices and half at $6.25 Vegas prices, the fuel for that trip costs about $280.00. That's a steep price if I fly alone. The airplane has six seats. It's really only comfortable for four, though I've had as many as five. But with four, including me, that's $70.00 per person. Of course, being a private pilot, not commercial, I can't charge my passengers. They're allowed by regulations to share the cost, however.

Now, I can fly at a considerably more efficient airspeed and use less fuel to make the trip, but you get an airplane to GO FAST and it's beyond my tolerance to pull the power back and cruise at 120 knots (138 statute miles/hour)to save fuel. To drive there and back using my current technique would use 20 gallons and cost something like $65.00. I could take the same three passengers and make the round trip for a little over $16.00 apiece, leaving everyone an extra picture of Ulysses S. Grant for the tables, should they be so inclined. That trip would take not quite 5 1/2 hours each way and would be a major test of my passengers' patience.

I am currently projecting that, in the year following the start of my driving experiment, I'll use 884 gallons of automobile gasoline. Had I used my pre-experiment driving techniques, I estimate I would use about 1310 gallons in the same time. I estimate that I use about 1,080 gallons of avgas per year.

I guess my flying negates any ability I might have thought I had to brag about diminishing my use of fossil fuel or my "carbon footprint." Still, at the end of the year I will have saved 426 gallons of auto gas. That's better than if I hadn't done it.

Thursday, July 06, 2006


Two weeks ago, I took my Jeep in for some brake work. I patronized the place to which my company takes its vehicles (we have a fleet of about 28) for service. When it was returned, I was told that they had had to replace the rotors because they had gotten too thin (after about 134,000 miles) as well as the pads. The mechanic told me to go easy on it for a hundred miles or so to give the rotors and pads a chance to set. Little did he know - what he would think of as going easy would be insanely abusive to me these days.

But as I drove, the smell of burning brakes suffused the cabin. I could feel the brakes grab as I would attempt to coast to a stop. The instant mileage indication was at about 60% of what I had come to expect in any particular driving situation. OH NO!!! I'm burning fossil fuel to heat metal for no reason. My five tank moving average had been at 24.23 m.p.g, and my last two tanks were 21.98 and 20.36 m.p.g. The bottom line is that I'M WASTING GASOLINE! I was so horrified that I took the Jeep to the dealer to have them make sure the installation was performed properly. They confirmed that it had been and verified that, even after 400 miles, the symptoms I was experiencing were not unusual.

I believe that it's over now - when I let the car coast I feel no resistance and the numbers seem to be back where they should be on the display. But I now realize how sensitive I have become to the behavior of the car. Even after the smell of the brakes was gone and the car was close to being back to normal, I could tell it wasn't quite right. I'm conscious of every aspect of its behaviour by both feel and by the numbers. I think if there were problems with fuel injectors, spark plugs, etc. I would be able to quickly sense and remedy them.

Now it's back to trying to get the averages to 25 m.p.g. It's starting to look like that's the practical limit for this car. I'm going to change the air filter to a more nonrestrictive after market type (Air Hog or something) to see if that has a measureable effect. My IT guy is very interested in that experiment but I had to wait until the Great Brake Job Catastrophe had abated.

Saturday, July 01, 2006

Economic choices

The other day I stopped at the bank to get some cash. The particular branch I chose to patronize had a drive through window, and I watched the action for a few minutes. I saw a Hummer (H2) use the window and it set me to thinking about the motivation.

In an earlier post I gave some fairly detailed estimates of the consequences of drive through windows, estimating that if they all went away we could save about 350,000 barrels of oil per year. Clearly, this is not a huge amount. What about the Hummer pilot?

The engine is a 6.0 liter V8. My Grand Cherokee has a 4.8 liter V8 and uses about 0.38 gallons per hour at idle. It seems very reasonable to assume that fuel consumption at idle is directly proportional to engine displacement so I'll estimate that the H2 uses (6.0/4.8)*0.38=0.475 gallons per hour at idle.

I don't know what the driver's bank transaction was but let's assume that it was something she (I saw that it was a woman - no implications intended) could have done at the walk-up ATM. This matters since it is clearly worth more to avoid going inside the bank than to avoid the walk-up ATM.

I think the estimates I made for times at a window in my earlier post would be applicable here, so I'll say that she burned a net three minutes worth of fuel that could have been saved had she parked and walked up. That three minutes of pistons going up and down in cylinders used about .024 gallons of fuel which cost about $0.074. So her use of the drive through meant that it was worth at least about seven cents to avoid going to the trouble of parking and walking to the ATM.

I'll guess that she might use some sort of drive through window four times per week, so she might burn about five gallons of fuel per year while driving through, worth about $15.00. If she were to be presented with these numbers, do you suppose she'd immediately cease use of the drive through? I'm thinking that this is one of the few answers of which I can be sure. Actually, she'd have two answers: "no" and "HELL NO!!"

I wonder where her "point of indifference" would be? Surely she wouldn't use the drive through if it cost, say, $100.00 per use versus the walk-up ATM. What about $10.00? $1.00? I'm going to hypothesize that an average H2 driver would drive through for a dollar and walk up if the price differential were any higher. That would imply that a gas price of (100/7.4)*3.12=$42.16 per gallon would be the threshold of removing her from her car. There's a lot of room for gas prices to go up before certain lifestyle choices would change. I don't think drive through windows will be shuttered anytime soon.

Thursday, June 22, 2006

More on acceleration

I timed some of my snail-like starts, timing how long, on average, it takes me to go from 0 to 10, 10 to 20, etc. and finally from 50 to 55 (the fastest I ever go). I took the average of four times for each interval and plugged them into a spreadsheet. Then I graphed them and found a regression curve that had the best fit.

It turns out that it takes me, on average, about 53 seconds to go from 0 to 55 m.p.h. I'm guessing, from their wailing and gnashing of teeth, and their honking, flashing of lights and gesturing, that this seems kind of slow to many of my passengers and fellow drivers. Ah well, anything for science.

In any event, I took the regression curve and integrated it twice from 0 to 53 seconds and determined that it takes me about 890 meters, or about 2900 feet to accelerate from a stop to 55 m.p.h. I then plugged times into my spreadsheet that fit the same shape of curve but that totalled 9.7 seconds (I was looking for about 10 seconds) to model fast acceleration from a standstill. This isn't flooring it, I determined a long time ago that the Jeep will go from 0 to 60 in about 7.4 seconds minimum.

Utilizing the same mathematics, I determined that it would take about 150 meters or 490 feet to go from 0 to 55 m.p.h. Now, in each case, I have changed the potential energy of the chemical bonds in gasoline into an amount of kinetic energy of the car that is identical for each acceleration regime (a little over 600,000 joules). As I mentioned in an early post in this blog, the energy of burning fuel goes to overcoming the forces working against the motion of the car and to adding kinetic energy to the car.

So I've gone about 2400 feet farther on the same amount of fuel by accelerating slowly. That's about 0.45 miles. Supposing I do the equivalent of this amount of accelerating about 15 times per day, I get something like 6.75 miles extra by accelerating slowly. At 32 miles per gallon on the highway, that's about 0.21 gallons of fuel saved.

I'm saving something like 1.5 gallons per day compared to my old driving methods, so I'm estimating that about 14% of my fuel savings come from leisurely acceleration. The rest come from some combination of lower freeway speeds and extremely conservative energy management, that is, coasting to stops, coasting in neutral when going downhill, turning off the car on long downgrades and at long stops, etc. I'm not sure of the division here, but I'll try to figure it out.

Sunday, June 18, 2006

Negative externalities

I've turned to trying to determine some of the major effects that would result from "everyone" adopting my driving methods. I've discussed the potential economic savings in previous posts, but there are many other possible ramifications. It seems to be extremely difficult to really determine what the results would be.

At first blush, I'd think that everyone driving more slowly would lead to greater traffic congestion if the same number of people made the same trips. I've searched the web for information relating to this hypothesis using google's beta site for searching the scholarly literature. While I found lots of articles about traffic congestion and driving speed, none seemed to confirm my intuition. Nor did they seem to refute it.

There would likely be less accidents, following distances could close. On the other hand, the same number of people spending longer on the same length of pavement argues that densities would be higher and congestion more likely. I'm calling it a wash until someone points me to information that would make a strong argument one way or the other.

Economic losses due to added time on the road, however, seem to be unambiguously negative. An earlier post assessed the effects of lower speeds on my personal time in vehicle, and I've mentioned that I'm intrigued by the notion that one should be able to come up with an estimate of almost anything. So, if everyone adopted my driving techniques, how much time would be lost each year?

Using estimates of number of personal vehicles and annual mileage, combined with an estimate that 30% of these miles would be driven more slowly than otherwise with drivers adopting my techniques, my estimate is that about 468,000,000,000 miles would be driven more slowly. I estimate that this would result in 1.8 X 10^9 (1.8 billion) extra hours on the road. Does this make sense?

Well, I'm one of 200,000,000 drivers and I calculated in an earlier post that I'll lose about 47 hours per year. If each of the 200 million drivers lost that much, the total would be 9.4 X 10^9 hours. But I estimate that I probably drive something like 30% more than average so adjust this down to 7.2 X 10^9 hours. Figure somewhere between these numbers is right, I'll use 4.5 X 10^9 or 4 and one half billion hours.

I'll say the average hour is worth $30.00, in that case the lost time is worth $135 billion. Considering I calculated we'd save $36 billion in oil imports, it would seem not to be worth it. Are there any mitigating factors?

Not many. First would be finding ways to avoid productivity loss when on the road. Talk radio? Books on tape? Cell phones? These all may help but they certainly won't eliminate the lost productivity. Most workplaces have required hours, so the lost time would come from drivers' personal time. Thus, it wouldn't be strictly an economic loss.

One thing's for sure. There's no free lunch.

Saturday, June 10, 2006

Professor Steven Dutch, Ph.D.

I'm fascinated by the web site of Professor Steven Dutch at the University of Wisconsin Green Bay. The portion of his site entitled "Science, Pseudoscience, and Irrationalism" has dozens of articles, most of which I find interesting. Some I agree with, others I don't but they are interesting reading.

To the point of this blog, he has an article debunking the "200 m.p.g. car" that the conspiracy theorists claim has been suppressed by the oil industry. His article aims to use rough and ready methods to show the impossiblity of a simple "gizmo" that, bolted onto the engine, would enable an ordinary car to achieve extraordinary gas mileage.

Dr. Dutch uses a 1000 kilogram mass car in his calculations, mine is about twice as massive. As it happens, my vehicle has a big (4.8 liter) engine and I think it's reasonable to estimate that internal friction and pumping and throttling losses are directly proportional to engine displacement.

Surprisingly, Dr. Dutch converges on about 40 miles as an estimate for what can be extracted from a gallon of gasoline for the car in his example. My car, being twice as massive, having at least twice as large an engine as the car Dr. Dutch analyzes and probably 40% larger "flat plate area" (the area presented to the oncoming air to develop drag), etc., should get half of that. My actual results are amazingly close to this.

What does it mean? Well, it means that in order to achieve major reductions in oil consumption without going to vehicles such as the scooter I discussed a couple of posts back, large-scale changes must be made in the technology of internal combustion engines or other propulsion methods must be employed. It means that I'm probably approaching the limit of what I can achieve by driving methods alone, though I'm sure that slight gains are still possible.

The other eye-opening aspect of Dr. Dutch's debunking of the 200 m.p.g. carburetor is his demonstration that exotic test methods and advanced mathematics aren't necessary to derive useful information about practical problems. His analysis utilized a car, a stopwatch, some easily available information (such as the cold cranking capacity of lead acid batteries), high school level physics and experience to come to a conclusion that my real-world tests seem to confirm.

Wednesday, June 07, 2006

The curve

I've been playing with the numbers from my fuel consumption generated over the last 275 days. It appears there is strong evidence of a learning curve on fuel minimizing driving techniques. I placed the numbers for my fuel consumption in a post a couple of weeks back. Since then I've filled up twice.

I graphed the miles per gallon for each fill up and the five tank moving average of mileage at fill up. I then had Excel calculate a linear regression for each data set. The linear least-squares line for the per fill up data is y=0.1008x+20.251 and for the five tank moving average it's y=0.0777x+20.845 where y is the miles per gallon and x is the "fill-up number."

Obviously, the 20.251 and 20.845 (the "y intercepts") can be interpreted as the mileage I was achieving at the outset of the experiment. The 0.1008 and the 0.0777 (the "slopes") can be interpreted as my average increase in miles per gallon achieved per tank full, in other words, my learning to minimize fuel consumption.

The majority of my mileage is on my commute which has not changed and there hasn't been any significant change to the remainder of the vehicle usage, so I think these positive slopes really do represent my increasing ability to drive in a maximally fuel-efficient manner.

The fact that my last four fill ups have resulted in the five tank moving average being above the trend line indicates that my learning is still in progress. Clearly this will have to come to a halt, since otherwise in five years I could expect to be getting 46 miles per gallon. I somehow doubt that that will occur. But I will be very interested in seeing what the number looks like when the learning curve levels off.

On another note, I achieved a milestone (pun intended) today when the average mileage reading on the display clicked to 23.0. Starting from 14.9, I'm amazed. I'm not sure if 24 miles per gallon on the display is in the cards, the current five tank moving average is 23.88. But I'll be trying. Right now it seems to take a couple of weeks or so to goose the display up by a tenth of a gallon, so if I can make it to 24 it will take at least something over four months. I should have been keeping a log of dates that the display changed.

Oh well, I can't think of everything.

Sunday, June 04, 2006

Alternative transport

I've determined that, at current prices in Southern California ($3.32/gallon) my daily commute costs about $9.00 in fuel alone. Clearly, regardless of anything else relating to the efficiency of my driving technique, I'm spending most of that money on moving a large vehicle (about 4000 pounds) to carry little ol' me (190 pounds). That can't be a good use of fossil fuel.

Pondering this seeming waste, I've been looking into alternative means of transport. Human power, though I could certainly use the workout, is not feasible because I'd be lucky to spend less than five hours on the road each day. So I've looked at electric scooters. The ones I'm contemplating are the EVT (Electric Vehicle Transport) Ion and Equinox models. These little scooters claim a range of about 50 miles at about 30 m.p.h.

I would have to ride it to the office and plug it in. A full recharge takes four hours so there's not a problem with time. How does the cost compare? Well, the battery pack consists of four 12 volt 40 amp-hour sealed lead acid batteries. Therefore, charging from 20% to 100% should use 4*12*40 = 1920 watt hours or 1.9 kilowatt hours of energy. Say 2 kilowatt hours, then figure that losses in the charging system and heating of the batteries would account for about 20% losses, meaning I would need 1.25 x 2 = 2.5 kilowatt hours. I'd need to do this at work and at home, so figure that I would pay for about five kilowatt hours per day. The cost, at my current rates, would be around $0.50.

So I should be able to save $8.50 per day that I am able to use the scooter. I wouldn't want to ride it in the rain, so out of about 250 work days per year, that would leave maybe 230 days where the weather would permit riding. Some of those days I might have to take care of business where the scooter wouldn't be appropriate - figure maybe one such day per week or about 50 per year. That means I should save 180 days x $8.50 per day, or $1,530.00 per year. Note that this is on fuel alone, no accounting has been made for vehicle maintainance, depreciation, etc.

Let's look into that a bit. In my Jeep, I spend about $0.145 per mile on fuel, the I.R.S. allows about $0.44 per mile deduction for business related driving. Not having a better proxy, I'll use $0.295 per mile for expenses other than fuel in my Jeep. What about the scooter? The literature says the battery pack is good for about 500 charge cycles. I'd use two charge cycles per day of use of the scooter, so I'd get about 250 days per battery pack - maybe a year and four months. That's not so bad.

What about the cost per mile? 500 charge cycles times about 30 miles per cycle gives 15,000 miles per battery pack. I don't know but I'll estimate that a battery pack costs something like $400.00, yielding about $0.026 per mile in battery costs. Let's triple that for tire replacement, bearings, controller and anything else that may go wrong and round up to $0.08/mile. Adding that to the electricity charge of about $0.50/62 miles or $0.008/mile for a grand total on the order of $0.088/mile. Thus, an estimate of the total savings on the scooter is about $0.352/mile.

So I can save about (180 days/year) x (62 miles/day) x ($0.352/mile) or about $3,928.00 per year. The link above is for a dealership in Oakland who sells the scooters for $2,450.00 so a scooter would pay for itself in about 7 1/2 months.

I can't afford not to buy one!

Thursday, May 18, 2006

Raw data

For posterity, I thought I'd post the results from the beginning of my effort. You'll see the dates, miles and gallons for each fill up. Also, you'll see the cumulative days of the experiment and the standard deviation in mileage based on the results of each fill up. Note that no pre-experiment data exists, so you'll just have to take my word that the average mileage at that time was 14.9 m.p.g. based on the "average mileage" readout of the display unit in the car. I'd like to include graphs, but I haven't yet been able to figure out how publish them in a readable fashion. Sigh...
Date Miles Gallons to fill Mileage 5-tank mov. Avg.
9/5/05 377.2 18.714 20.16
9/9/05 346.7 19.541 17.74
9/16/05 381.5 18.948 20.13
9/24/05 404.3 20.126 20.09
10/1/05 401.3 18.293 21.94 20.01
10/8/05 414.1 19.821 20.89 20.16
10/14/05 429.6 18.545 23.17 21.24
10/28/05 401.0 20.399 19.66 21.15
11/6/05 446.1 20.703 21.55 21.44
11/16/05 443.8 19.190 23.13 21.68
11/23/05 403.2 19.821 20.34 21.57
12/3/05 425.2 19.299 22.03 21.34
12/14/05 434.1 19.044 22.79 21.97
12/21/05 414.7 19.484 21.28 21.92
12/29/05 442.2 17.604 25.12 22.31
1/6/06 404.4 19.777 20.45 22.34
1/14/06 415.8 18.904 22.00 22.33
1/19/06 438.9 18.739 23.42 22.45
1/27/06 454.7 20.066 22.66 22.73
2/5/06 415.0 19.402 21.39 21.98
2/14/06 432.3 20.252 21.35 22.16
2/21/06 437.8 20.282 21.59 22.08
3/2/06 454.2 20.261 22.42 21.88
3/9/06 435.2 19.351 22.49 21.85
3/22/06 444.0 20.321 21.85 21.94
3/30/06 456.7 21.321 21.42 21.95
4/6/06 456.4 21.361 21.37 21.91
4/17/06 444.7 19.291 23.05 22.04
4/25/06 475.5 20.099 23.66 22.27
5/2/06 416.0 16.217 25.65 23.03
5/11/06 416.8 19.624 21.24 22.99
5/20/06 482.3 20.322 23.73 23.47
Totals: 13645.7 625.1 21.83
Standard deviation: 1.60 m.p.g.
Days of experiment: 257

Tuesday, May 16, 2006


I'm having trouble now deciding if I'm in the midst of an experiment or just trying to save all the gas possible. If it's the former there are several things I'd like to try, but I'm loathe to see the "average mileage" display creep down as I test hypotheses.

What hypotheses? The least likely to reduce my mileage has to do with fuel in the tank. I've always heard gas mileage is better during the first half of a full tank. The fuel gauges of all the vehicles I've owned act this way, but I suspect that that behavior is an artifact of the gauging mechanism. After all, half a tank weighs less than a full tank, and though the air doesn't know how much the car weighs so drag won't change, it does take more fuel to accelerate a heavier car. Further, increased weight adds to the tire loading, thus increasing road loads. I suppose it's possible that a larger hydraulic head in a full tank could somehow improve pumping efficiency but it seems far-fetched.

I'm a pilot, and I know from that avocation that fuel weighs about 6 pounds/gallon, so a full tank (21.5 gallons) in my car weighs about 129 pounds, the weight of an extra adolescent or perhaps female passenger. So it stands to reason that mileage would improve as fuel is used.

Finding out would take quite a while, filling and emptying to half a tank is not as exact as topping off to measure fuel usage. I'd fill to full, drive until I get as close as possible to, say, 5/8 full and refuel. I'd do this maybe 15 times, and calculate the mileage at each fill up. Then I'd drive down to 1/8 tank, add fuel to bring it to 1/2 full, drive down to 1/8, repeat, etc. Again, I'd do it maybe 15 times and compare. It wouldn't be exact because of the difficulty of filling and reading to exact level using the gauge but after sufficient trials, a conclusion should be possible.

Or perhaps the best way to measure this, since full tank is the easiest level to which to accurately fill, would be to run a series of trials, always filling the tank but alternating between using about 1/2 of a tank and close to a full tank. This way the accuracy of the miles per gallon achieved would be maximized, but the difference in the results would be minimized. Well, if I do the experiment I'll put a lot more thought into its design.

What else? I've achieved what I regard as a drastic reduction in fuel consumption by taking many different steps, as detailed elsewhere in this blog. Which of the measures are most effective and which are minor? Is it the slow acceleration that contributes the most, or perhaps the reduced freeway speed? The way to find out is to eliminate each measure I've taken, one at a time, and measure the result. Unfortunately, at least one or two of the experiments would likely lead to my having to watch the "average mileage" indicator show significantly deteriorating results, and I just hate to give back my hard won tenths of a mile per gallon.

Maybe I AM eccentric.

Saturday, May 13, 2006


In my previous post I expressed my skepticism that the U.S. would find the will to take even a significant portion of the measures I have undertaken to save gasoline. Part of my skepticism stems from a general feeling about "the way things go" and part from my experiences with friends, family and people at my company.

I've made no secret of my program. To some of the people I mentioned above saving something like $1,500.00 per year doesn't mean much. To others, it's a large amount, enough to make a difference in their lifestyle. But to a person, they all shake their heads and tell me they couldn't do it and explain to whomever is around that "Rob (I'm Rob) is eccentric."

A man who works at my company drives a big Ford dually pickup with a large diesel engine. He's put a chip in it to maximize performance and that sucka will most definitely hurry up. He commutes from Riverside, CA to Long Beach each day, a round trip I'd estimate at about 100 miles. He makes decent money but he just bought a house and at times is strapped.

I asked him today what it costs him to fill up and he told me $120.00. He's known from the outset of my experiment, he and I used to race each other. He's always just shaken his head about what I'm doing now, so I thought I'd present it to him and his buddy in a different way today. I said "you know Tim, driving this way I get the equivalent of every third tank of gas free." He acknowledged that that was an interesting way of looking at it, but it didn't change his behavior.

There was a song a while back called "I Can't Drive 55" by Sammy Hagar. I know that the vast majority of people feel that way and even with government action I don't see how people will adopt these habits. And as I mentioned in a previous post, I tend toward Libertarianism. So all in all, I'm probably tilting at windmills. But I'll continue to tilt at these and to look for others at which to tilt.

I think next I'll spend some time thinking about "unintended consequences."

Tuesday, May 09, 2006

Best case scenario

In my last post, I conservatively estimated that the U.S. would be able to immediately reduce its need for imported oil by about 5% by changing non-commercial driving technique in a mostly benign way. What about an optimistic yet not, in my opinion, pie in the sky estimate?

Well, I'm now at 22.7 m.p.g. in my 2000 Jeep Grand Cherokee Limited. The E.P.A. says I should get 15 m.p.h. city and 20 m.p.h. highway. I estimated in an earlier post that 36 out of every 60 miles I should be getting "highway mileage" and 24 out of every 60 miles I should be getting "city mileage." So a weighted average E.P.A. estimate for my driving regime would be (36/60)*20+(24/60)*15=18 m.p.g. But I've demonstrated that it's possible, with this driving regime, to get 22.7 m.p.g. at least.

Now, the vast majority of people to whom I've talked, about whom I've read, etc. complain that they don't achieve the E.P.A. estimates. Let's say the average is 90% of the E.P.A. estimate. I'm getting 126.1% of the E.P.A. estimate for my car. Suppose everyone went from 90% to 126.1% of the E.P.A. estimate. That would result in a 40.1% increase in gas mileage nationwide or a decrease to (1/1.401) times 100% = 71.4% of the fuel used before the change. That is, personal transportation fuel use would be reduced by 28.6%.

Using the figures in my previous post, that would result in a reduction of .286 times 6.4 Mbbl/day or 1.83 Mbbl/day. That's about 13.9% of our daily oil imports. Now we're getting someplace. All this without a single person driving a single mile less than they are currently driving or buying a more fuel efficient vehicle. And remember, this completely leaves out commercial use of transportation fuels.

Can it happen? Yes, of course. Look at the rationing during World War II. Will it happen? Probably not, but something much more onerous surely will.

Wednesday, May 03, 2006

So what?

OK, so I started this driving experiment in August 2005 and I've saved 15 tanks of fuel or so. What does that mean? It's a difficult subject. It's not likely to postpone the onset of the effects of so-called "peak oil," even if I could get everyone in the country to do it. A case can be made that, if everyone in the U.S. started driving the way I've driven during this experiment, it would have a very measurable effect on the need for imported oil. Alone, it wouldn't stop it but it would be significant.

But what would it accomplish? Well, reduction in the U.S. demand for imported oil would presumably lower the price or at least influence prices in a downward direction, thereby encouraging consumption in China, India, etc. Clearly, the path these "developing nations" are on is leading them to find plenty of ways to use oil, and a lower price would accelerate that process. Even so, I believe that huge advantages would still be gained for the United States.

Let's look at some numbers. It's not easy (for a layperson such as myself anyway) to find definitive numbers for some of this, but I've given it my best shot. Should anyone have better information, I would welcome it.

Of the approximately 20.5 Megabarrels/day (Mbbl/day) of oil used in the U.S., about 13.7 Mbbl/day goes to transportation. As best I can determine, something like half of that, or 6.4 Mbbl/day goes to "non-commercial" transportation. This is where I make my impact. Suppose all the drivers in the U.S. took the "realistic" approach I mentioned in my first posting in this blog and that my estimates are correct. I had felt that a 15% gain in average fuel economy was reasonably achievable, but let's be more conservative. I believe that 10%, or .64 Mbbl/day could easily be saved. That amounts to about 5% of our oil imports.

What??!! Reducing speed from 70 m.p.h. to 55 m.p.h., avoiding drive-through windows and other unnecessary idling, judicious use of the gas pedal, etc. is only good for a 5% reduction in import demand? And EVERYONE would have to do it?? Well, it is one of many relatively painless steps that can be taken.

Suppose we really wanted to end our dependence on oil imports. If, instead of increasing our oil consumption annually, we reduced it by 5%, we would eliminate our dependence in 18 years. This assumes that U.S. petroleum production remains constant.

Of course, the reduction attained by conservative driving techniques represents 5% of imports, not 5% of consumption. So that, along with some other measure, would be the steps to be taken on the first of the 18 years. They only get harder after that.

I've carefully avoided controversial political aspects of oil use. In particular, I've brought up neither "peak oil" nor "greenhouse emissions" in this blog prior to this post. I started my experiment simply as a way to see how much gas (and money) I could save and at what cost in terms of frustration. The answer is that I can save about 500 gallons or over $1,500.00 per year. And though I've experienced very little frustration, I suspect I have frustrated some of those who have ridden with me and I'm certain that I've frustrated some of my fellow drivers.

Still, I believe that this is important. It has genuinely changed my outlook on my energy budget. I have become much more aware of my personal "energy leaks" and the leaks of my business and those around me. Much more will be required, but I won't dismiss the value of this small experiment in efficiency.

Saturday, April 29, 2006

Use of time

One of the problems of maintaining a maximum speed of 55 m.p.h. is that it seems to waste a lot of time. Of course, use of the mobile phone, listening to books on tape, etc. can make this time less unproductive than it might seem at first. But it's a constant challenge to find ways to be productive during commutes, whether on a professional basis (phone conversations with business associates, etc.) or a personal basis (books on tape).

But what about the time itself? How much is actually lost? I drive about 60 miles per day on average, I estimate that 36 of those miles are spent driving at 55 m.p.h. when I could drive 70 m.p.h. That's faster than the speed limit but probably about what would be considered "normal." At 55 m.p.h. I spend 39 minutes, 16 seconds driving more slowly than "normal." If I were driving at 70, I would spend 30 minutes, 51 seconds driving the 36 miles. So I seemingly lose 8 minutes, 25 seconds per day.

However, I also only have to refuel about every 8 days instead of every 5.3 days (on average). I estimate that pulling off the road, fueling and getting back on the road takes about 8 minutes, so I save an average of 31 seconds per day stopping for fuel less often. Thus, the grand total loss is 7 minutes 54 seconds per day. In the course of a year, I lose 33 hours and 11 minutes behind the wheel (assuming 252 such days per year).

Looking at this time another way, my company values the 7 minutes and 54 seconds at about $12.66. An interesting comparison is that, on a given day, I save about 1.4 gallons of fuel compared to what I would have consumed using my pre-experiment driving style, which, at current Southern California prices, is worth about $4.57.

Or, yet another way is that I try to sleep 7 hours per night. Thus, the extra time spent driving amounts to 0.77% of my waking hours.


Wednesday, April 26, 2006

Ween us from imported oil? Maybe not...

One of the things I've done in my quest to get the maximum out of a tank of gas is to forgo the drive-through window. In so doing, I began to wonder how much gasoline is burned in the United States idling at drive-through windows. I decided to try to figure it out - maybe outlawing drive-through windows (something a person with a libertarian bent such as myself would never advocate) would end our reliance on imported oil.

I've read that Enrico Fermi felt his students should be able to come up with an estimate for almost anything. The classic example is to estimate how many piano tuners there are in New York City. There's even a competition to come up with order of magnitude estimates ("Fermi Answers") to obscure questions. Though I've never entered any sort of formal competition of this nature, the idea fascinates me. Anyway, such skills helped me with my answer to the query mentioned above.

Though "google is my friend," I wasn't able to find every piece of data I needed in my fairly brief search. I couldn't find statistics on how many fast food drive-through window visits occur in the U.S. in a day (or a year). Using estimates based on how many drive-through windows I think there might be, how often the people I know use them, what I've seen at the restaurants, etc. I decided maybe 1.5 million such visits occur each day. I estimated that an average visit is four minutes, and an average car burns 0.25 gallons per hour at idle (mine burns 0.38). I subtracted a minute because that was my guess as to the idling equivalent of pulling into a parking space, stopping and then starting the car after going into the restaurant.

Using these figures, I estimate that 18,750 gallons of fuel are wasted in drive-through window visits per day in the U.S., or about 6.84 million gallons per year. I was able to find a very informative site from a consulting geoscientist. I learned that a barrel of oil produces 19.5 gallons of fuel, so 6.84 million gallons require 350,000 barrels of oil.

I also learned that we use 21.93 million barrels PER DAY of which 13.21 million barrels are imported. So we import 4.82 billion barrels of oil per year. Thus, elimination of all fast food drive-through window stops could eliminate maybe .007% (that is, 7 one-thousandths of 1%) of our oil imports.

Well, ya gotta start somewhere...

Tuesday, April 25, 2006

To floor it or not to floor it

I'm trying to understand the effects of rate of acceleration on minimizing fuel consumption over a given distance. We've all read and heard that "jackrabbit starts" waste fuel. How can this be shown? Well, fuel contains energy in hydrogen and carbon chemical bonds. We oxidize fuel to release this energy. The energy does two things in our vehicle - it adds kinetic energy, thus changing the potential energy of the chemical bonds to the kinetic energy of the moving vehicle, and it does the work of moving the car against the sum of the forces acting to resist motion. These include engine and driveline friction, pumping fluids, aerodynamic drag, tire rolling resistance, etc. For the purists, it also can increase our potential energy by utilizing chemical potential energy to raise our position in the Earth's gravitational field (i.e., take us up hills). But since, on average, our vehicle stays at one elevation (that is, at the elevation of wherever it lives) we can ignore this.

It's easy to show that the more slowly we accelerate, the farther we go in the process of adding a given amount of kinetic energy to the car (that is, getting up to a given speed since kinetic energy is one half the product of the mass of the vehicle and its contents times the square of the velocity or speed). Thus, if we accelerate from 0 to 60 in twice the time, that is, accelerate at half the rate, we will go twice as far to add the same amount of kinetic energy, which comes from burning the fuel. So, the same amount of fuel will take us twice as far while getting us up to the same speed. It will take longer but be more fuel efficient. As I said, this is quite easy to show mathematically.

So it seems like a no-brainer. But... It's also true that there is a speed at which an automobile gets the best fuel economy. Because it burns fuel while idling (my Grand Cherokee burns 0.38 gal/hour as nearly as I can determine), the car gets 0 m.p.g. standing still. As we start moving and achieve higher speeds the fuel economy, that is, the m.p.g., increases. Above some speed, different for each vehicle, the aerodynamic drag, which increases approximately with the square (at least according to my calculations - others say cube) of speed begins to take its toll and the efficiency decreases. So, the vehicle is more efficient (gets better gas mileage) the faster you go, up to some speed at which efficiency begins to decrease. I'm still working on the mathematics of this but it seems intuitively reasonable and agrees with the nuggets I've found on the web (see here for example) and some "back of the envelope" calculations.

So let's say, for conversation's sake, that for my Grand Cherokee, the most efficient speed is 50 m.p.h. I think this isn't too far off, based on my experiments and a website I found (but since lost). And let's say I'm going to take a 20 mile trip. To make it easy, the trip is on a level road, no stops. I could, in principle, accelerate so slowly that I don't get to 50 m.p.h. before reaching my destination. Or, I could floor it and reach 50 m.p.h. as quickly as possible and drive the greatest possible portion of my trip at the most efficient speed. So flooring it gives me the maximum number of miles at the most efficient speed. On the other hand I could, in principle, accelerate so slowly that I only get to, say, 5 m.p.h. before reaching my destination and drive the entire trip at a very inefficient speed. This seems to imply that quick acceleration is most efficient. So which is best?

I'm still working on it, so more to follow.....

Saturday, April 22, 2006

The Goal

I'd like to welcome myself to the world of blogging. I have a hard time with the term "blogos.....," maybe in time I'll come to accept it.

The intent of the blog, in the beginning, will be to document my efforts to minimize my use of energy, particularly auto gas. I drive a 2000 Jeep Grand Cherokee Limited with a 235 horsepower V8.

Until August of 2005, I drove it like I used to drive my 1970 Roadrunner in high school, that is, as fast as traffic would allow (and sometimes faster). As for acceleration, I used to say "I don't need an accelerator pedal, I just need a switch." It was full throttle all the time. The Jeep is equipped with a display of "average mileage" and "instant mileage." As nearly as I can tell, the average represents mileage over the last several tanks - maybe 4000 or 5000 miles. It can't be from 0 on the odometer - it changes too quickly for that. Or so I think.

In any case, at the start of my experiment, the average m.p.g. was 14.9, reflecting my extreme driving habits (according to the E.P.A. the car is rated for 15 m.p.g. city, 20 m.p.g. highway).

In August of last year, as gas prices in the Los Angeles area approached $3.00 per gallon, I started toward the opposite extreme of driving, incorporating snail-like acceleration, coasting down hills in neutral, shutting the engine off at long stops, cruise-controlled 55 m.p.h. and attempts to look ahead and put the car in neutral to coast to a stop for traffic, etc. The brake pedal became my enemy, I pictured burning gasoline to heat chunks of metal. I filled my tires to 2 p.s.i. over the maximum rating (don't try this at home).

My current average is 22.5 m.p.g., a 51% increase. I estimate that I have saved approximately 350 gallons of fuel. Obviously, someone starting from a more normal driving technique could not expect as great an improvement. But even for someone getting average mileage consistent with the EPA estimate, say 18 m.p.g., which many do not achieve, a 25% improvement would be possible. Again, most would not take it to the other extreme as I have, but a 15% improvement would seem to be easily achievable.