“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)

## Saturday, October 27, 2012

### Indicated gas mileage

My Lexus CT200h has an indicator that I reset at each fill up that shows an indicated fuel efficiency (in miles/gallon or m.p.g.). I've noted that it consistently (and, now that I've analyzed it, ALWAYS) reads higher than the mileage that I calculate by dividing miles travelled on the odometer versus gallons logged at the pump during fill up.

I thought that I'd have a look at the data and found that every single one of the 56 fill ups I've performed since acquiring the vehicle exhibit this phenomenon. I ran a linear regression between the calculated and indicated fuel efficiency and found the best fit line to have a calculated mileage about 2.6 m.p.g. below the indicated mileage for each fill up. I noted the same error in my previous vehicles (the ones that had such a display), though I never took the time to plot and analyze the data so I can't say if there were no exceptions as I now can with the Lexus.

I don't have an explanation, it doesn't seem credible that it's intentional in order to mislead the driver - the calculation is simply too easy.  Nor can I come up with a theory that attributes the discrepancy to my driving habits. Further, I'm not sure how the indicated m.p.g. is calculated, though I assume that it uses the odometer and integrates a gasoline flow rate. In any case, it seems to exaggerate my actual fuel economy by about 5%. It's a good thing I keep the actual data!

The chart below shows the data points, a line showing where the points should fall, and the best fit line for where they actually fall. The horizontal axis is indicated m.p.g., the vertical is actual (that is, calculated from miles driven and gallons added) m.p.g. Note that every point falls below the upper line, which represents where they'd fall if the indicated and calculated mileages were equal. The vertical distance between the two lines represents the difference between the best fit line for indicated mileages versus a perfect fit between calculated and indicated mileages. In other words, it represents the error in the indicated m.p.g.