The Schwitters Memorial Problem: A Car Speeds Across a Triangular Bump

Abstract

Most drivers slow down for speed bumps, sometimes to almost a stop, as if each speed bump were a stop or yield sign. The late Roy Schwitters and I shared the view (here called the Schwitters Doctrine) that one should take the bumps at a speed of at least 60 or 70 kph (35 to 45 mph), not because we were scofflaws, but because we found, based on informal experiments, that the traverse was less jarring at high speeds than at low. Here, the problem is worked in terms of the geometry of the wheels on the road and two coupled, damped harmonic oscillators representing the suspension of the car and the driver's cushioned seat. The Schwitters Doctrine is recovered, but not in the way that one expects.