When countersteering to turn right, the following is performed: direction depending on forward speed, bike geometry, and combined bike and rider mass distribution.
Need to lean to turn A bike can negotiate a curve only when the combined
center of mass of bike and rider leans toward the inside of the turn at an angle appropriate for the velocity and the radius of the turn: :\theta = \arctan \left (\frac{v^2}{gr}\right ) where v is the forward speed, r is the radius of the turn and g is the acceleration of
gravity.
Stable lean (in this case 6 m/s), to a positive steer torque (to the right) that begins as an impulse and then remains constant. It causes an initial steer angle to the right, a lean to the left, and eventually a steady-state lean to the left, steer angle to the left, and thus a turn to the left. As the desired angle is approached, the front wheel must usually be steered into the turn to maintain that angle or the bike will continue to lean with gravity, increasing in rate, until the side contacts the ground. This process often requires little or no physical effort, because the
geometry of the steering system of most bikes is designed in such a way that the front wheel has a strong tendency to steer in the direction of a lean. The actual torque the rider must apply to the handlebars to maintain a steady-state turn is a complex function of bike geometry, mass distribution, rider position, tire properties, turn radius, and forward speed. At low speeds, the steering torque necessary from the rider is usually negative, that is opposite the direction of the turn, even when the steering angle is in the direction of the turn. At higher speeds, the direction of the necessary input torque often becomes positive, that is in the same direction as the turn.
At low speeds At low speeds countersteering is equally necessary, but the countersteering is then so subtle that it is hidden by the continuous corrections that are made in balancing the bike, often falling below a
just noticeable difference or threshold of perception of the rider. Countersteering at low speed may be further concealed by the ensuing much larger steering angle possible in the direction of the turn.
Gyroscopic effects One effect of turning the front wheel is a roll
moment caused by gyroscopic
precession. The magnitude of this moment is proportional to the
moment of inertia of the front wheel, its spin rate (forward motion), the rate that the rider turns the front wheel by applying a torque to the handlebars, and the
cosine of the angle between the steering axis and the vertical. For a sample motorcycle moving at 22 m/s (50 mph) that has a front wheel with a moment of inertia of 0.6 kgm2, turning the front wheel one degree in half a second generates a
roll moment of 3.5 Nm. In comparison, the lateral force on the front tire as it tracks out from under the motorcycle reaches a maximum of 50 N. This, acting on the 0.6 m (2 ft) height of the center of mass, generates a roll moment of 30 Nm. While the moment from gyroscopic forces is only 12% of this, it can play a significant part because it begins to act as soon as the rider applies the torque, instead of building up more slowly as the wheel out-tracks. This can be especially helpful in
motorcycle racing. ==Motorcycles==