My Math Forum Maximum Theoretical Gas Mileage?

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 January 7th, 2008, 10:05 AM #1 Newbie   Joined: Dec 2007 Posts: 3 Thanks: 0 Maximum Theoretical Gas Mileage? Okay, during a recent discussion on gasoline/petrol prices, the subject came up as to what was the "maximum theoretical milage" (whatever that means) you could get out of a gallon of gasoline. So, decided to try and solve it what that would be for a 2000 lb. car. So, I acquired the following data and I'm wondering if I did this correctly: 1 gallon of fuel = ~33 kilowatt-hours of energy 1 kilowatt hour = 2,655,223.74 foot-pounds of work 2,655,223.74 x 33 = ~ 87,622,383 foot-pounds So, one gallon of gasoline at 100% energy conversion (and the absence of all friction), could accelerate a 2000 lb car at the rate of 1 foot per hour squared over a period of 43,811 hours. The distance covered is a triangular series: 1+2+3+4...+43,811 Solve that by n*(n + 1)/2 = (43,811*(43,812))/2 = 959,723,766 feet 959,723,766 feet = 181,765.87 miles. So, the "maximum theoretical gas mileage" for a 2000 lb. car, in intergalactic space, accelerating over a period of about 5 years, is nearly one light-second per gallon.
 January 7th, 2008, 12:21 PM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Yes, but in the absence of friction fuel efficiency is not well-defined, since without braking mileage increases continually. If your example was extended to ten years (without further acceleration, since you're out of gas) then the mpg would triple. More interesting to me would be an estimate of friction from conventional tires/tyres with a given car weight to give an upper bound on the fuel efficiency of a car using those tires/tyres.
 January 7th, 2008, 01:08 PM #3 Newbie   Joined: Dec 2007 Posts: 3 Thanks: 0 Yes, I was kind of stumped on how to set it up. So, I assumed that the purpose of burning fuel is to accelerate against resistance. Even when you're cruising at a steady speed the car is technically accelerating against drag. So, I thought one way to do it would be to see what distance the energy would accelerate the car over. As soon as you add any resistance, the distance starts to drop very quickly. I guess what it really tells me is that we spend an awful lot of energy doing not much mroe than overcoming resistance.

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