“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, April 29, 2007

### New car for "free"?

As mentioned in a previous post, the Jeep Grand Cherokee Limited that is the subject of a large part of this blog was purchased in July of 2000. It has well over 150,000 miles on the odometer, and has been everything I could reasonably want in a vehicle. But to quote George Harrison, "All Things Must Pass."

So, given that I'm able to drive the Grand Cherokee for 23.5 m.p.g., can I purchase a vehicle that, through savings at the pump, will pay for itself? I'm speaking purely of the cash cost to me and not of the impact on overall fuel consumption for "the universe" (fuel to produce and deliver the car, etc.). I expect to write about that aspect in another post.

I'll also leave out insurance and other extraneous considerations. Any vehicle that could conceivably pay for itself in fuel savings would be much smaller and possibly less costly than the Cherokee was. But it would be new, and so insurance might be a wash. Anyway, that's not what this blog is about.

So, in any case, the Grand Cherokee gets about 23.5 m.p.g. at $3.29 per gallon currently. That amounts to$0.14 per mile, and I average about 56.13 miles per day, 365.25 per year. Therefore, the monthly gas expenditure is (365.25 * 56.13 * 0.14)/12 or $239.18. Now, suppose I could get a vehicle in which I could achieve an average of, say, 45 m.p.g. My monthly fuel expenditure would be reduced to$124.91 for a savings of $114.27. Hmmm... that won't buy much of a car I guess. What if gasoline went to$4.00/gallon as I hear predicted, and by extreme techniques, I could get 50 m.p.g.? Well, the Cherokee would then cost $0.17 per mile and total$290.80 per month and the new car would cost $136.67 per month and save$154.13. Not there yet, though it is starting to eat significantly into the monthly payment for an economy car with very low fuel consumption.

As I've mentioned, my company actually owns the Grand Cherokee, so "business finance" and considerations of internal rate of return, net present value, and payback period are appropriate. I found a 1995 Geo Metro on line for $2,200. The payback period, exclusive of necessary repairs, is on the order of 14 months. I don't know if I can quite deal with that type of accommodation, but it's the only way I can see to getting a car for free. After the 14 month payback period, I'd be essentially adding to the retained earnings every time I drove. ## Saturday, April 28, 2007 ### Searching the journals As is my wont, I have spent a bit of time on the web googling (I've come to accept this term as a verb) on "mathematical model automobile fuel consumption." This search produces 612,000 hits today. Many of them are irrelevant to my obsession ("Pricing for Environmental Compliance in the Auto Industry" for example). Some of them are to abstracts of journal articles and not relevant enough to my interest to cause me to spend the money to buy them. But there is a Ph.D. thesis from 1992 entitled " Automobile fuel economy and traffic congestion" by Feng An. Its abstract is reproduced here : "An analytical model for automobile fuel consumption based on vehicle parameters and traffic characteristics is developed in this thesis.^This model is based on two approximations: (1) an engine map approximation, and (2) a tractive energy approximation.^This model is the first comprehensive attempt to predict fuel economy without having to go through a second-by-second measurements, simulation or a regression procedure.^A computer spreadsheet program based on this model has been created.^It can be used to calculate the fuel economy of any motor vehicle in any driving pattern, based on public-available vehicle parameters, with absolute error typically less than +/-5%.^Several applications of this model are presented: (1) calculating the fuel economy of motor vehicles in 7 different driving cycles, (2) determining the relationship between fuel economy and vehicle average velocity, (3) determining the vehicle optimal fuel efficiency speed, (4) discussing the effect of traffic smoothness on fuel economy, (5) discussing how driving behaviors affect fuel economy, (6) discussing the effect of highway speed limit on fuel economy, (7) discussing the maximum possible fuel economy for ordinary cars, and finally, (8) discussing the impact of vehicle parameters on fuel economy." Now that's what I'm talking about. I ordered it from the source referenced on the page and am looking forward to reading it and seeing what it can teach me. Now, there is another hit from the journal "The Engineering Economist." The title of the article is "The Economic Impact of Obesity on Automobile Fuel Consumption." Fascinating. In the abstract, it is stated that "results indicate that, since 1988, no less than 272 million additional gallons of fuel are consumed annually due to average passenger weight increases." Talk about hitting the jackpot on constructive ways to save fuel! An extremely quick and dirty calculation indicates that, if the above is true, 0.18% of our annual oil consumption can be attributed to weight gain since 1988. So, in addition to adopting the driving methods I've described over the past months, we can all resolve to achieve our ideal weight. This will not only reduce our oil imports, trade deficit, and carbon footprint (are you getting this Al?), but it will increase our health, reduce our health care expenditures, and make us more attractive to the opposite sex (or, for those so disposed, to the same sex). Further, the fuel savings don't stop with the reduction in automobile gas consumption. Food that needn't be produced needn't be fertilized, shipped, cooled, etc. I haven't yet set up estimates for the potential savings here, but they have to be huge. So my recommendation is that, if you are overweight, get on a weight reduction program. It's the patriotic thing to do! ## Tuesday, April 24, 2007 ### At what point will fuel prices justify low speed? The last couple of posts have dealt with the trade off between the value of the fuel saved at low speeds versus the value of the time "wasted." I determined that, for my trip, at my salary, in my vehicle, at$3.40/gallon for gasoline, the speed at which my total cost (my salary + fuel to make the trip) was minimized is 110 m.p.h. Clearly not practical,especially if everyone ran a similar calculation and decided to drive at what I will call their "minimum total expenditure speed (mtes)."

But the process and the mathematics of determining those numbers led me to wonder what gasoline price would make the fuel savings balance the time costs at reasonable speeds. It turns out that the number is extremely high. For example, for gas at $5.00/gallon, the mtes is 97 m.p.h. At$8.00/gallon, the mtes is 87 m.p.h. The mtes never gets to the most efficient speed because the m.p.g. as a function of speed curve is fairly flat in the range near the maximum, which I determined analytically to be 50.8 m.p.h. for the Grand Cherokee Limited.

It is reminiscent of the earlier post where I contemplated the point of indifference for a woman in a hummer at the bank drive-through window. There, as here, the gasoline price that would economically cause a behavioral change was ludicrously high.

There are many actions that can be taken to reduce consumption, some of which do not have the down side associated with maximally efficient freeway speeds. And there are forms of income other than monetary, so-called "psychic income." This involves benefits such as fulfilling the desire to protect the environment, feeling as if one is doing the best one can to leave a better world for one's children, and other non-monetary considerations that comport with one's philosophy or desires. In my case, it has been the satisfaction of pursuing the goal of minimization of fuel consumption for its own sake. Some call me obsessive, and they are probably correct.

These things are difficult, if not impossible to quantify in a meaningful way, other than the extent to which someone is willing to forgo things that can be quantified to receive the benefit. In my case, it is clear that the enjoyment of running the experiment and writing about it in this blog compensates me for the opportunity cost of getting to my destinations more slowly.

## Monday, April 23, 2007

### What's REALLY the best speed?

My last post looked at possible savings utilizing costs with 55 m.p.h. as a basis. I decided I had enough information to look at what speed minimizes total cost with salary and fuel consideration only. The elimination of the 55 m.p.h. baseline had a surprising effect.

I calculated using the constants developed in my previous post, which enabled me to determine the total fuel cost as miles of the round trip (freeway part only) divided by miles per gallon at the speed in question, times $3.40 per gallon. My salary was easily calculated at miles travelled (36, as noted previously) divided by miles per hour times salary per hour. As it turns out, the resulting equation has a global maximum at about 110.5 m.p.h., a speed that I can drive (and have driven) in the Grand Cherokee. I will concede that there are many downsides to the strategy of driving 45 m.p.h. over the speed limit and that time lost at the side of the road talking to the Highway Patrol, time lost in court, money lost paying for traffic school, fines, and insurance increases (assuming that, after a few reckless driving tickets, insurance could be obtained at any price) would have a severe impact on the accuracy of the cost calculations. For these reasons, I am unlikely to adopt this habit. Nevertheless, I am going to become dramatically more aggressive in reducing the impact of the salary component by finding ways to produce on the road. Failing that, the emphasis may have to fall back to those aspects of fuel consumption reduction that do not result in increased trip times. Unfortunately, as best I can estimate, all of those together have approximately 25% of the impact of low freeway speeds. This is beginning to feel like a manifestation of the second law of thermodynamics ("you can't break even"). I ran the numbers for someone making$60,000 per year (significantly less than my salary) and the optimum speed for that particular drive in that particular vehicle is 80 m.p.h. So presumably, for a minimum wage worker, 55 m.p.h. might be the right choice.

These are all rather fuzzy numbers, since I will get to work and complete my job, and the hourly wage guys will put in their hours. Therefore, it's actually "personal time" that is being used during the commute. However, the best surrogate I have for that is the rate at which people are paid, since that amount of money will cause them to leave home and family to go to work. In any case, it is clear that there is a high price to be paid for minimizing fuel consumption by driving slowly.