Originally Posted by rknj
"Say you do a route at a constant speed and you end up with X average speed. If you were to do that same route while constantly accelerating/decelerating, you'd be doing more work in the end to have that same X average speed."
My high school physics teacher would have pegged you with an eraser just now.
Say you're doing a 10 mi. route, with the first 5 miles downhill (10% grade), and the next 5 uphill (10% grade). If you output a constant 200 watts of power, you'll have an ave. speed of 41.64 mph for the downhill, and an ave. speed of 4.46 mph on the uphill. Therefore, the total time for you to complete the trip is 1.2417 hrs (overall ave speed of 8.05 mph). FYI, my algorithm accounts for rolling resistance and aerodynamic drag.
Do the same 10 miles on even ground outputting a constant 200 watts and the overall ave. speed is
18.23 mph.
So it seems to me that you do more work in the hills than you would on flat ground when going the same distance.