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.
Thursday, June 22, 2006
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.
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.
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.
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!
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!
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