Bicycle and motorcycle dynamics

Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles and their components, due to the forces acting on them. Dynamics falls under a branch of physics known as classical mechanics. Bike motions of interest include balancing, steering, braking, accelerating, suspension activation, and vibration. The study of these motions began in the late 19th century and continues today. Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles and their components, due to the forces acting on them. Dynamics falls under a branch of physics known as classical mechanics. Bike motions of interest include balancing, steering, braking, accelerating, suspension activation, and vibration. The study of these motions began in the late 19th century and continues today. Bicycles and motorcycles are both single-track vehicles and so their motions have many fundamental attributes in common and are fundamentally different from and more difficult to study than other wheeled vehicles such as dicycles, tricycles, and quadracycles. As with unicycles, bikes lack lateral stability when stationary, and under most circumstances can only remain upright when moving forward. Experimentation and mathematical analysis have shown that a bike stays upright when it is steered to keep its center of mass over its wheels. This steering is usually supplied by a rider, or in certain circumstances, by the bike itself. Several factors, including geometry, mass distribution, and gyroscopic effect all contribute in varying degrees to this self-stability, but long-standing hypotheses and claims that any single effect, such as gyroscopic or trail, is solely responsible for the stabilizing force have been discredited. While remaining upright may be the primary goal of beginning riders, a bike must lean in order to maintain balance in a turn: the higher the speed or smaller the turn radius, the more lean is required. This balances the roll torque about the wheel contact patches generated by centrifugal force due to the turn with that of the gravitational force. This lean is usually produced by a momentary steering in the opposite direction, called countersteering. Countersteering skill is usually acquired by motor learning and executed via procedural memory rather than by conscious thought. Unlike other wheeled vehicles, the primary control input on bikes is steering torque, not position. Although longitudinally stable when stationary, bikes often have a high enough center of mass and a short enough wheelbase to lift a wheel off the ground under sufficient acceleration or deceleration. When braking, depending on the location of the combined center of mass of the bike and rider with respect to the point where the front wheel contacts the ground, bikes can either skid the front wheel or flip the bike and rider over the front wheel. A similar situation is possible while accelerating, but with respect to the rear wheel. The history of the study of bike dynamics is nearly as old as the bicycle itself. It includes contributions from famous scientists such as Rankine, Appell, and Whipple. In the early 19th century Karl von Drais, credited with inventing the two-wheeled vehicle variously called the laufmaschine, velocipede, draisine, and dandy horse, showed that a rider could balance his device by steering the front wheel. In 1869, Rankine published an article in The Engineer repeating von Drais's assertion that balance is maintained by steering in the direction of a lean. In 1897, the French Academy of Sciences made understanding bicycle dynamics the goal of its Prix Fourneyron competition. Thus, by the end of the 19th century, Carlo Bourlet, Emmanuel Carvallo, and Francis Whipple had showed with rigid-body dynamics that some safety bicycles could actually balance themselves if moving at the right speed. Bourlet won the Prix Fourneyron, and Whipple won the Cambridge University Smith Prize. It is not clear to whom should go the credit for tilting the steering axis from the vertical which helps make this possible. In 1970, David E. H. Jones published an article in Physics Today showing that gyroscopic effects are not necessary to balance a bicycle. Since 1971, when he identified and named the wobble, weave and capsize modes, Robin Sharp has written regularly about the behavior of motorcycles and bicycles. While at Imperial College, London, he worked with David Limebeer and Simos Evangelou. In the early 1970s, Cornell Aeronautical Laboratory (CAL, later Calspan Corporation in Buffalo, NY USA) was sponsored by the Schwinn Bicycle Company and others to study and simulate bicycle and motorcycle dynamics. Portions of this work have now been released to the public and scans of over 30 detailed reports have been posted at this TU Delft Bicycle Dynamics site. Since the 1990s, Cossalter, et al., have been researching motorcycle dynamics at the University of Padova. Their research, both experimental and numerical, has covered weave, wobble, chatter, simulators, vehicle modelling, tire modelling, handling, and minimum lap time maneuvering.