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ATZ , 58 10 —, Dunlop Tyre Company. Wobble and weave. Lateral dynamics of the uncontrolled motorcycle. In 2 nd Int. Congress on Automotive Safety , San Fransisco, Evangelou, D.

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Limebeer, R. Sharp, and M. Steering compensation for high-performance motorcycles. Control of motorcycle steering instabilities: passive mechanical compensators incorporating inerters. An h-inf loop-shaping approach to steering control for high-performance motorcycles. In Bruce A. Francis, Malcolm C. Smith, and Jan. Mechanical steering compensators for high-performance motorcycles. Motorcycle handling and chassis design-the art and science. Tony Foale Designs, Spain, Frezza and A. Simulating a motorcycle rider.

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Vehicle System Dynamics , 17 4 —, Koenen and H. The influence of frame elasticity, simple rider body dynamics, and tyre moments on free vibrations of motorcycles in curves. Swets and Zeitlinger. Limebeer, S. Evangelou, and R.

Stability of motorcycles under acceleration and braking. Limebeer and R. Bicycles, motorcycles and models: Single-track vehicle modeling and control. Sharp, and S. The stability of motorcycles under acceleration and braking. Motorcycle steering oscillations due to road profiling. Louam, D. Wilson, and R. Optimal control of a vehicle suspension incorporating the time delay between front and rear wheel inputs. Vehicle System Dynamics , 17 6 —, Motorcycle dynamics — fact, fiction and folklore. Meijaard and A.

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Application of non-linear dynamics to instability phenomena in motorcycles. Abe, editor, Proc. Vehicle System Dynamics. Numerical continuation of solutions and bifurcation analysis in multibody systems applied to motorcycle dynamics. Nonlinear Dynamics , 43 1—2 —, Mitiguy and K. The definition of product of inertia.

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Tire and Vehicle Dynamics

AbeBooks Bookseller Since: May 31, Items related to Motorcycle Dynamics Second Edition. Stock Image. For a given displacement of the front wheel, due to some disturbance, the angle of the resulting path from the original is inversely proportional to wheelbase. Another factor that can also contribute to the self-stability of traditional bike designs is the distribution of mass in the steering mechanism, which includes the front wheel, the fork, and the handlebar.

If the center of mass for the steering mechanism is in front of the steering axis, then the pull of gravity will also cause the front wheel to steer in the direction of a lean. This can be seen by leaning a stationary bike to one side. The front wheel will usually also steer to that side independent of any interaction with the ground. The role of the gyroscopic effect in most bike designs is to help steer the front wheel into the direction of a lean.

This phenomenon is called precession and the rate at which an object precesses is inversely proportional to its rate of spin. The slower a front wheel spins, the faster it will precess when the bike leans, and vice versa. Hence gyroscopic forces do not provide any resistance to tipping.

Thus a fast bike may feel stable even though it is actually not self-stable and would fall over if it were uncontrolled. Another contribution of gyroscopic effects is a roll moment generated by the front wheel during countersteering. For example, steering left causes a moment to the right. The moment is small compared to the moment generated by the out-tracking front wheel, but begins as soon as the rider applies torque to the handlebars and so can be helpful in motorcycle racing.

Between the two unstable regimes mentioned in the previous section, and influenced by all the factors described above that contribute to balance trail, mass distribution, gyroscopic effects, etc. However, even without self-stability a bike may be ridden by steering it to keep it over its wheels. Longitudinal acceleration has been shown to have a large and complex effect on lateral dynamics. In one study, positive acceleration eliminates self stability, and negative acceleration deceleration changes the speeds of self stability.

In order for a bike to turn, that is, change its direction of forward travel, the front wheel must aim approximately in the desired direction, as with any front-wheel steered vehicle. Friction between the wheels and the ground then generates the centripetal acceleration necessary to alter the course from straight ahead as a combination of cornering force and camber thrust. The radius of the turn of an upright not leaning bike can be roughly approximated, for small steering angles , by:.

However, unlike other wheeled vehicles, bikes must also lean during a turn to balance the relevant forces: gravitational, inertial, frictional, and ground support. A slight increase in the lean angle may be required on motorcycles to compensate for the width of modern tires at the same forward speed and turn radius. It can also be seen however that this simple 2-dimensional model, essentially an inverted pendulum on a turntable , predicts that the steady-state turn is unstable.

Motorcycle Dynamics (Second Edition)

If the bike is displaced slightly downwards from its equilibrium lean angle, the torque of gravity increases, that of centrifugal force decreases and the displacement gets amplified. A more-sophisticated model that allows a wheel to steer, adjust the path, and counter the torque of gravity, is necessary to capture the self-stability observed in real bikes. A rider can lean with respect to the bike in order to keep either the torso or the bike more or less upright if desired. The angle that matters is the one between the horizontal plane and the plane defined by the tire contacts and the location of the center of mass of bike and rider.

This lean of the bike decreases the actual radius of the turn proportionally to the cosine of the lean angle. The portions at either edge of a motorcycle tire that remain unworn by leaning into turns is sometimes referred to as chicken strips. The finite width of the tires alters the actual lean angle of the rear frame from the ideal lean angle described above.

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The actual lean angle between the frame and the vertical must increase with tire width and decrease with center of mass height. Bikes with fat tires and low center of mass must lean more than bikes with skinnier tires or higher centers of mass to negotiate the same turn at the same speed. It has been shown that the couple created by gravity and the ground reaction forces is necessary for a bicycle to turn at all. On a custom built bicycle with spring-loaded outriggers that exactly cancel this couple, so that the bicycle and rider may assume any lean angle when traveling in a straight line, riders find it impossible to make a turn.

As soon as the wheels deviate from a straight path, the bicycle and rider begin to lean in the opposite direction, and the only way to right them is to steer back onto the straight path. In order to initiate a turn and the necessary lean in the direction of that turn, a bike must momentarily steer in the opposite direction. This is often referred to as countersteering. With the front wheel now at a finite angle to the direction of motion, a lateral force is developed at the contact patch of the tire.