What is the physics of bicycle design

Once the bike rolls, it rarely tips over. But why a bicycle is so stable in motion has been an empirical value for the manufacturers for around 150 years and a mystery to science. An international team of researchers is now presenting a physical bicycle model that can predict the driving behavior and stability of a bike.

Delft (Netherlands) - With this, new designs can be tested quickly, but also individual bicycles can be created much more easily than before - even for disabled cyclists. Various companies have already expressed their interest, the researchers report.

"Bicycle manufacturers could never say exactly how a bicycle worked - they always had to refine their design by trial and error," explains Arend L. Schwab, Professor of Mechanics, Maritime and Materials Research at the Technical University of Delft. "With our model, however, you can enter all the various factors into the computer that affect the stability and guidance of your bike. The model then calculates how the bike will react at certain speeds." In collaboration with colleagues from the University of Nottingham and Cornell University, the Delft team created a mathematical model for bicycles: four rigid individual parts, symmetrically connected to each other on ideal hinges - two axially symmetrical tires, a frame and a movable front axle. The mass distribution and frame geometry were otherwise variable. The researchers recently published their model in the Proceedings of the Royal Society, Series A.

In comparison with the theoretical bicycle models of numerous earlier studies, they found matches and deviations in their formulas. Practical tests in the Delft bicycle laboratory helped to check the variants and to test the dynamic behavior of different models in reality. For the physicists, the assumption that the bicycle can be a conservative system with asymptotic stability is confirmed. For manufacturers such as the long-established Dutch company Batavus, completely new possibilities are opening up: "So far we have always worked with three parameters when designing bicycles: the overall geometry, the distance between the axles and the angle at which the front fork points downwards," explains Rob van Regenmortel, Batavus chief developer with great interest in the new model. Because such bicycles seemed to work, one seldom deviated from it; "But with the new model we hope to soon be able to design bikes that are much better geared towards specific target groups." Even people with balance problems are no longer dependent on tricycles. Van Regenmantel wants to participate in an upcoming project when it comes to investigating human control and the influence of leadership on driving behavior.