I thought this was nifty, and should allow for testing tomorrow. Recently, I made a very long trip, and should return to the same gas station by dropping ~1500ft. Since going uphill hurts mileage, going downhill should help.
But by how much. We know potential energy is expressed as mgh, with mg equaling ~15,000 Newtons in my case. Over 1500ft, or ~450 Meters, this should be equal to ~15,000*450=~6800000W=~6800kW, or ~2kWh. Now, since the engine only operates at ~10-20% efficiency at most, those 2kwh are equal to ~10-20kwh worth of gasoline. If every gallon has ~34kWh, that's a third to two thirds of a gallon of gas worth of PE. If I get ~33mpg at a cruise, over 100 miles I'll use ~3 gallons. But, since I'm getting that PE boost, I'll only need two and a third to two and two thirds, and will probably see ~40mpg. This isn't exactly exact, but I though it was neat approximating how much elevation can change mileage. And it's testable too!