“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, January 13, 2008

Highway MPG

My 2006 Land Rover LR3 HSE with its 4.4, Liter V8 engine is rated by the EPA at 18 m.p.g. highway mileage. In fact, the spreadsheet provided by the EPA in zipped files shows the so-called "uncorrected" fuel economy as 23.3 m.p.g. They correct this by the simple expedient of reducing it by 22%. Now, don't misunderstand. They don't do some arcane analysis that leads to a 22% reduction, they just multiply the measured number (found by measuring carbon emitted during the dynamometer test) by 0.78. Very scientific. That leads to the "18 HWY" on the window sticker. Since my driving is mixed and I'm able to achieve a higher average mileage (currently about 20.5 m.p.g.) than the EPA highway estimate I think that my highway mileage must be considerably better than the 18 m.p.g estimate, and possibly higher than the 23.3 m.p.g. uncorrected measurement. I determined to find out.

The LR3 does not have an instant m.p.g. indication in its instrumentation, however, the Scan Gauge II with which I've equipped my Land Rover does have this instrumentation through the OBDII port. I'm not sure of the mechanism by which this is determined, though I would guess that it uses the metering of the fuel through the injectors and the speed. If it's this method, it may be unreliable because the speed readout on the Scan Gauge II appears to be inaccurate. It reads 55 m.p.h. when the analog speedometer in the dash reads about 57 m.p.h. I had always assumed the ODBII reading was accurate, but there is a series of measured miles for the use of the highway patrol on interstate 15 on the way to Las Vegas and stopwatch timing over these measured miles indicated that the analog gauge on the dash is a better indicator of actual speed. Never mind, I'm going to calculate using the ODBII.

So, what I need is a stretch of level highway where I can just look at the readout on the instant mileage indicator, wait for it to stabilize, and there's my answer. The complicating external factors might be an undetected slope, and wind. As it happens, there's a stretch of the 405 freeway through Seal Beach that appears to be suitable for this determination. Conveniently, there's a power plant visible from this portion of the freeway, and its smokestack gives an excellent signal of wind conditions. When northbound on the freeway, the average stabilized reading over several trips is about 24.8 m.p.g. Woo Hoo! But when southbound, it's more like 21.9. Hmm.... Must be an undetected slope.

How much might there be and what effect might it have? I looked to Google Earth to try to find out. I located the stretch in question and measured the distance and logged the elevations. I tried to find end spots for my measurement where the elevation clicked from one integer foot to another (e.g., 17 feet to 16 feet) and assumed that this was the location where the actual elevation was halfway from one to the other. Now, this may not be completely accurate, but as long as the algorithm used by Google Earth is consistent, this is the best I can do since I'm not interested in absolute elevations but rather in elevation changes.

It turns out that the elevation change is 5 feet over 0.71 miles. That means that, in the downhill direction, I gain 39,948.6 (I always carry a lot of digits) joules of kinetic energy by converting gravitational potential energy, and turn the same amount of chemical energy (assuming I maintain the same speed) into gravitational potential energy in the uphill direction. It's straightforward to determine how much fuel is saved and burned respectively, if I assume that the car is able to utilize 25% of the heat energy of burning gasoline for propulsion at this speed.

Since I haven't had readers of this blog clamoring for more mathematical detail, I'll just give the results. Factoring out the "free" energy provided by going downhill, the car should be producing 23.74 m.p.g. Factoring it out in the uphill direction, the resulting mileage is 22.79 m.p.g. Closer but not identical. I'm not sure where the error is, so I'll just average the two numbers and say that my level highway average m.p.g. is 23.27 m.p.g. This is still a healthy increment above the 18 m.p.g. estimated by the EPA but, amazingly, it rounds precisely to their uncorrected number of 23.3 m.p.g.. I know that the test protocol does not involve simply running in cruise control on level highway in no wind conditions but it still pleases me to beat the window sticker estimate by over 29%, as arbitrary as that EPA estimated number seems to be.

Another lesson is that such a slight hill has so much effect on mileage. Five feet over 0.71 miles is 0.076 degrees; almost undetectable. To get an idea, if you're hanging a 24 inch wide picture and it's off of level by this amount, the low side will be 0.03 inches lower (about 1/32 inch) than the high side. And yet climbing it reduces fuel economy by 5.9%. The lesson? ALWAYS make sure that your destination is at a lower elevation than your starting point.