The Moments of Bicycle Pedaling

Getting a bicycle to move requires the rider to apply forces to the pedal. In doing so the rider's force is transmitted over a distance by the crank, creating a moment which rotates the sprocket, moves the chain and rotates the rear wheel. Use the applet below to examine this process in greater detail.

The applet above simulates pedaling a bicycle. It operates in two modes: user mode which animates the pedal based on forces applied by the user; and experimental mode which animates the pedal based of experimentally determined forces applied by an actual rider. The buttons control which mode is operating, if any. Clicking in the selection boxes at the left allows you to see various quantities as vectors acting on the pedal.

View the experimental animation. Examine how the total moment (torque) varies as the forces on the pedal vary. What happens to the moment when the pedal is on the left side of the sprocket? Keep in mind that the moment being displayed is due to only one pedal (even if two are being displayed).

Stop the experimental simulation. Position the crank at the top of the cycle (12 o'clock). Click and drag on the center of the pedal to define a 50 N force in the x- direction (be sure to have checked "Force, x"). What is the total moment on the pedal (assume units of N-cm)? By knowing the force and the total moment, can you determine the length of the crank?

Now move the crank so that it points to the right (3 o'clock). Redefine the force so that it is still 50 N in the x- direction. Now what has happened to the moment?


You can also vary the angle of the pedal with respect to the crank by clicking on the pedal and rotating it. See how the pedal angle affects the total moment. For example with the crank pointing toward the right and with a 50 N force in the x-direction, how does rotating the pedal affect the total moment.

Do you now have a better understanding of how the forces acting on just one pedal affects the moment that is created? Use the space below to explain how the forces on both of the pedals act together in a cycle to propel the bicycle.

Copyright 1998 Rensselaer Polytechnic Institute. All Rights Reserved.