I just completed a 150 km ride on a fixed gear bike (never again)! Actually it wasn't that bad, just not the most comfortable setup on this particular bike, gears or no gears. Anyway, during the ride, one of the other riders was trying to figure out, off the top of his head, how many revolutions of the pedals we would complete by the end of the ride. His math and reasoning seemed kind of strange, possibly due to the heat and the onset of fatigue, as it was late in the ride. I decided to try and figure it out after I got home. Now I'm no math wiz, but here's what I came up with:
39/15 gear x 27" wheel = 70.2 inches
70.2 x 2.54 = 178 cm x PI(3.14) = 560 cm
This means that with each full turn of the pedals, the bike travels 560 cm, or .0056 km.
150 km/.0056 km = 26786 revolutions
My heart rate monitor claims I burned 5299 calories on the ride. Assuming that's correct, which I know it isn't, that would be 1 calorie burned for every 5 pedal revolutions. Doesn't seem like much of a payback when you look at it that way.