The Physics of Bicycle Suspension on

In their attempt to explain the physics of bicycle suspension, the folks at Dave Weagle’s dw-link site lay this egg:

Newton’s Third law of Motion states that “Every action has an equal and opposite reaction.” When a bicycle accelerates forward, the rider’s mass is transferred rearward. Without something to counteract this mass transfer, the rear suspension on most bicycles will compress under acceleration.

The most glaring error is the misinterpretation of Newton’s 3rd law. As any undergraduate Engineering Mechanics textbook will explain, the “mutual forces of action and reaction between two particles are equal, opposite, and collinear.” That quote is from Engineering Mechanics by Hibbeler. Engineering Mechanics by Schmidt, Engineering Mechanics by McGill and King, Engineering Mechanics by Bedford and Fowler, Dynamics by Tongue and Sheppard, Engineering Mechanics by Meriam and Kraige, and Vector Mechanics for Engineers by Beer and Johnston all agree.

Thus, the only possible reaction, by Newton’s 3rd law, to the friction force acting on the rear tire contact patch, which is responsible for a bicycle’s forward acceleration, is the friction force acting on the ground that accelerates the earth in the opposite direction.

Of course, the law they should invoke is Newton’s 2nd law, or more specifically, Euler’s 2nd law, which describes the acceleration of a body in response to the sum of external moments.

The next error is in suggesting that load transfer actually requires the movement of mass. Tony Foale, in his Motorcycle Handling and Chassis Design, on page 9-1 explains why he doesn’t even like the expression weight transfer, let alone mass transfer.

This is normally referred to as weight transfer, but that is really a misnomer. Weight is the gravitational attraction of all the particles in the bike towards the centre of the earth, and for convenience we usually consider the sum of these forces to act through the CoG. Neither acceleration nor braking can cause this weight to transfer elsewhere. As a result the use of the term ‘load transfer’ is preferable.

I tried explaining all this back in 2009 to a wikipedia user named Tremanaps, who I suspect was either Dave himself or a surrogate, but made no progress. In both cases, I was able to provide multiple reliable sources to support my interpretation, but Tremanaps could not. You can read the contemptuous tone in his replies on the Wikipedia bicycle suspension talk page.

One can only hope that the actual dw-link suspension design is better than their ability to explain it.




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