Bicycling Downhill

We’ve been talking here and here about the effects of weight, speed, and grade on climbing hills on a bicycle.  Now, let’s reverse direction and think about coasting down a hill. 

We can examine this case by simply setting the total energy term to zero.

Now, the force to overcome rolling resistance and air drag is provided by the energy from decreasing elevation.  Using the same rolling resistance and drag assumptions from before, and setting the total energy term to zero, we get this figure for the velocity as a function of mass. 

Now, of course, the heavier cyclist has a significant advantage.  Although the lines are non-linear  (apparent for the 3% grade line), and the slope changes somewhat with grade, a rough average for the entire 3%-11% grade span is a velocity increase of about 1/6 mph  per kg. Might as well have another cheeseburger.