“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 25, 2007

A year's worth of data

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

Average speed

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

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

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

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

Saturday, November 24, 2007


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

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

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

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

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

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

Monday, November 05, 2007

Stoplights revisited

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

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

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

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

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

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

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

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