Bicycle and Motorcycle Dynamics - Longitudinal Dynamics - Stability

Stability

Though longitudinally stable when stationary, a bike may become longitudinally unstable under sufficient acceleration or deceleration, and Euler's second law can be used to analyze the ground reaction forces generated. For example, the normal (vertical) ground reaction forces at the wheels for a bike with a wheelbase and a center of mass at height and at a distance in front of the rear wheel hub, and for simplicity, with both wheels locked, can be expressed as:

for the rear wheel and for the front wheel.

The frictional (horizontal) forces are simply

for the rear wheel and for the front wheel,

where is the coefficient of friction, is the total mass of the bike and rider, and is the acceleration of gravity. Therefore, if

which occurs if the center of mass is anywhere above or in front of a line extending back from the front wheel contact patch and inclined at the angle

above the horizontal, then the normal force of the rear wheel will be zero (at which point the equation no longer applies) and the bike will begin to flip or loop forward over the front wheel.

On the other hand, if the center of mass height is behind or below the line, as is true, for example on most tandem bicycles or long-wheel-base recumbent bicycles, then, even if the coefficient of friction is 1.0, it is impossible for the front wheel to generate enough braking force to flip the bike. It will skid instead, unless it hits some fixed obstacle, such as a curb.

Similarly, powerful motorcycles can generate enough torque at the rear wheel to lift the front wheel off the ground in a maneuver called a wheelie. A line similar to the one described above to analyze braking performance can be drawn from the rear wheel contact patch to predict if a wheelie is possible given the available friction, the center of mass location, and sufficient power. This can also happen on bicycles, although there is much less power available, if the center of mass is back or up far enough or the rider lurches back when applying power to the pedals.

Of course, the angle of the terrain can influence all of the calculations above. All else remaining equal, the risk of pitching over the front end is reduced when riding up hill and increased when riding down hill. The possibility of performing a wheelie increases when riding up hill, and is a major factor in motorcycle hillclimbing competitions.

Read more about this topic:  Bicycle And Motorcycle Dynamics, Longitudinal Dynamics

Other articles related to "stability":

Stability - Entertainment
... The Stability EP, a 2002 three song EP by Death Cab for Cutie "Stability", a song by Debbie Harry from the album Debravation "Stability", a short story by Philip K ...
Spectasia - Code - Stability
... On Mac OS X systems it has been noted that on occasion Spectasia fails to launch ... No work-arounds have been reported other than restarting Spectasia ...
Lax–Friedrichs Method - Stability and Accuracy
... method is stable if and only if the following condition is satisfied (A von Neumann stability analysis can show the necessity of this stability condition.) The Lax–Friedrichs method is classified as having ...
Stability Constants Of Complexes - History
... the first general method for the determination of stability constants of metal-ammine complexes in 1941 ... titration of a mixture of M and HL with base, and knowing the acid dissociation constant of HL, the stability constant for the formation of ML could be determined ... Bjerrum went on to determine the stability constants for systems in which many complexes may be formed ...
Stability Spectrum
... The stability spectrum of T is the class of all cardinals κ such that T is stable in κ ... For countable theories there are only four possible stability spectra ... those for total transcendentality, superstability and stability ...

Famous quotes containing the word stability:

    No one can doubt, that the convention for the distinction of property, and for the stability of possession, is of all circumstances the most necessary to the establishment of human society, and that after the agreement for the fixing and observing of this rule, there remains little or nothing to be done towards settling a perfect harmony and concord.
    David Hume (1711–1776)

    Every nation ... whose affairs betray a want of wisdom and stability may calculate on every loss which can be sustained from the more systematic policy of its wiser neighbors.
    James Madison (1751–1836)

    Traditions are the “always” in life—the rituals and customs that build common memories for children, offer comfort and stability in good times and bad, and create a sense of family identity.
    Marian Edelman Borden (20th century)