The Back of the Envelope
A series of "back of the envelope" calculations to answer questions in my daily life
BOTE #1: Am I just pissing off my dad, or am I saving the environment? (July 6, 2026)
Every time my dad (or my sister or my mom) gets in my car, they say, "Rohan! Why is your tank empty?!" I reply with, "it's to improve the fuel efficiency of my car!" Today, I explored the veracity of that answer on the back of an envelope.
(1) https://dspace.mit.edu/entities/publication/61ad3ba0-2895-49f1-ba21-b53343224ee1
(2) https://www.epa.gov/system/files/documents/2026-02/420s26001.pdf
(3) https://fueleconomy.gov/feg/bymodel/2017_BMW_X3.shtml
(4) https://www.ornl.gov/news/sensible-driving-saves-more-gas-drivers-think
(1)
(2)
(3)
(4)
(5)
(6)
(1) To understand the relationship between a car's weight and its fuel efficiency, I started with a correlation from Lynette W. Cheah's PhD thesis (Cheah, 2010).
(2) Checking that the correlation described in Figure 2-6 fits for my vehicle, I found that it underestimated my vehicle's MPG.
Correcting this with a factor that accounts for the improvement of average fuel efficiency from 2008 (the last year of vehicle data in the correlation) to 2017 (the manufacturing year of my vehicle), I am able to closely estimate my vehicle's fuel efficiency (~2.5% error)
(3) Using this new scale factor in the fuel efficiency equation (note, it is written incorrectly, and should be applied only after a conversion from L/100km to MPG), I calculate the efficiency for a "light" vehicle (half-tank of gas) and a "full" vehicle (full-tank of gas).
(4) The light vehicle is ~0.68% more efficient
(5) This efficiency boost corresponds to ~4.1 gallons/year saved, assuming 14,000 miles driven/yr, or $15.7/year saved in gas money
(6) Extrapolated to the entire US car-driving population (in true Chemical Engineering fashion), this improvement in fuel efficiency would correspond to a 932 million gallon reduction in fuel consumption (corresponding to ~8.28 million tons of CO2 abated)
Sounds like I'm saving the environment ;)