nerdag said:

I'm certainly no physics guru, but I would have thought that drag increases with a person who has a bigger frontal area.

If you assume that the increase his mass and drag coefficient are by the same proportion, doesn't -k/m end up being the same?

This probably isn't the case, so I guess that a heavier guy would end up being faster if the increase in frontal area was smaller in proportion to the increase in mass.

Not trying to argue, just trying to make sense of it.

n

You're correct. The "k" in the equation is actually equal to Cd (coefficient of drag) times A (surface area normal to the flow.

Let's say that Cd is the same for a big and small rider, and for simplicity that the big rider weighs twice as much as the small one. Let's make one last assumption that humans are kinda, sorta cylindrical in shape. Not entirely true, but true enough for me to make my point.

A cylinder with twice the volume has less than twice the surface area. That is, surface area grows slower than volume. Hence, a bigger person will have an advantage. Here's the math:

Volume for a cylinder is equal to:

V = pi*r^2*z

V = the area of the circle times the height. We also assume that the height doesn't change. Rewritten, we get:

r = sqrt(V/pi*z)

Therefore, doubling the volume increases the radius by 1.4 or sqrt(2).

The surface area, A, for a cylinder is:

A = 2*pi*r*z

In other words, A, is proportional to the radius, r.

Going back to my original point, as you gain weight your surface area only grows 0.7 times as fast as your volume. A person who weighs twice as much only has 1.4 times as much surface area.

John Swanson

www.bikephysics.com