Originally Posted by
ellerbro
I posted the question over on physicsforums.com and the three responses I've gotten are that a heavy and light cyclist will have the same acceleration (a = g*sin(theta)), and therefore speed, when coasting down a hill. That is, until wind resistance comes into play.
Well, that's not very helpful. How fast do you need to be going before wind resistance comes into play? It's always in play, but becomes a big factor at about 15 mph.
Now it happens that while I don't ride a recumbent, I do have both an aerobelly and a degree in physics. I haven't used the physics degree lately and I'm lazy (which is why I haven't thought this through with any kind of rigor up to now), but this is the way I see it:
Let's say rider A weighs 220 and rider B weighs 110. The force due to gravity will vary depending on the slope, but it came be simplified as
F(g)(a) = 2x
F(g)(b) = x
where x is the weight of rider B times a factor to account for the incline. Now lets call the force from wind resistance y. For any given speed it will be about the same for both riders. So the net forces will be
F(net)(a) = 2x - y
F(net)(b) = x - y
Now for simplicity, let's consider the case where the gravitational force in for rider B is twice the force from wind resistance (x = 2y).
F(net)(a) = 4y - y = 3y
F(net)(b) = 2y - y = y
So at that speed (below terminal velocity), the rider with twice the weight will be experiencing three times the force, and therefore will be experiencing greater acceleration, even after you account for his greater weight.
All of the above is completely off the cuff. I may have made some really gross errors. Does it make sense to anyone else?