# Which formulas can I use?

## Main Question or Discussion Point

Hi,
I was reading about bicycles the other day and a question popped up in my head: Does the rider's weight and height affect the speed of the cycle? I have been researching extensively about it but I cannot find any formulae that can be used to measure the effectiveness of the height and weight on the speed of the cycle. If you could help me by providing me some formulae or any sort of references to this topic, it would be highly appreciated.

Thank You :)

The mass of the person is definitely a factor. $F=ma$, which means that $a=\frac{F}{m}$. Acceleration decreases inversely with an increase in mass, thus a greater force is required to keep the bicycle in motion at a constant acceleration. The height of the person (as well as the width) plays a role because the aerodynamic properties are changed. A tall person moves the center of mass of the bicycle-person system to a higher location, and the greater height results in more drag force opposing the direction of motion. Drag force can be written as $F_D=\frac{1}{2}\rho v^2C_D A$, where $F_D$ is the drag force, $\rho$ is the density of the fluid through which one is traveling (air), $v$ is the speed of the object relative to the fluid, $A$ is the cross sectional area, and $C_D$ is the drag coefficient. This is why you see racing bicyclists leaning down toward the handlebars. When they lean down, the bicycle-person system becomes more aerodynamic, and the drag force is decreased.