Vittore Cossalter - Motorcycle Dynamics
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- Book:Motorcycle Dynamics
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I am deeply indebted particularly to Roberto Lot, Mauro Da Lio, Alberto Doria, who helped to make this book possible.
This book was written thanks to the enthusiastic participation of PhD students of the Motorcycles Engineering Course: Alessandro Bellati , Roberto Berritta, Francesco Biral, Daniele Bortoluzzi, Mario Dalla Fontana, Giovanni Dalla Torre, Davide Fabris, Pasquale De Luca, Stefano Garbin, Giuseppe Lisciani, Fabiano Maggio, Massimo Maso, Matteo Massaro, Luigi Mitolo, Martino Peretto, Nicolay Ruffo, Jim Sadauckas, Mauro Salvador, Riccardo Toazza
Coordinate systems
| ( P r , x , y , z ) | mobile triad with the origin in the rear contact point P r , according to SAE J670 |
| x | forward and parallel to the longitudinal plane of symmetry |
| y | lateral on the right side of the vehicle |
| z | downward with respect to the horizontal plane |
| ( C , X , Y , Z ) | mobile triad with the origin in the turn center point C |
| X | parallel to x axis |
| Y | parallel to y axis |
| Z | parallel to z axis |
| ( A r , X r , Y r , Z r ) | triad attached to rear frame |
| ( A f , X f , Y f , Z f ) | triad attached to front frame |
| r | suffix for parameters of rear frame |
| f | suffix for parameters of front frame |
Kinematics and dynamics parameters
| C | turning center point |
| C | path curvature |
 | path radius of rear wheel |
 | path radius of front wheel |
| V | forward velocity |
| steering ratio | |
| steering angle | |
| kinematic steering angle | |
| * | effective steering angle |
| pitch angle of the main frame | |
| yaw angle of the main frame | |
| thrust chain angle respect to the ground plane | |
| transfer load angle respect to the ground plane | |
| i , j | velocity ratio |
| yaw angular velocity about the z -axis | |
| frequency | |
| p | natural frequency of pitch vibration |
| b | natural frequency of bounce vibration |
Motorcycle parameters
| A | frontal area of the motorcycle |
| a | mechanical trail (trail) |
| a n | normal trail |
| b | longitudinal distance from rear axis to the motorcycle mass center |
| c | viscous damping coefficient of suspension |
| c | viscous damping coefficient of steering damper |
| C D | aerodynamic drag coefficient |
| C L | aerodynamic lift coefficient |
| d | fork offset: distance from the center of the front wheel to the steering axis |
| h | height of motorcycle mass center |
 | moment of inertia of motorcycle about the x -axis through its center of mass (roll inertia) |
 | product of inertia of motorcycle about the x - z -axes through its center of mass |
 | moment of inertia of motorcycle about the y -axis through its center of mass (pitch inertia) |
 | moment of inertia of motorcycle about the z -axis through its center of mass (yaw inertia) |
| k | suspension stiffness |
| L | swinging arm length |
| m | motorcycle mass |
| p | wheelbase |
| P | tire contact point with the ground |
| G | motorcycle center of mass |
| r p | radius of drive sprocket |
| r c | radius of rear sprocket |
| h | lowering of the steering head |
| caster angle | |
| swinging arm angle respect to the ground plane | |
| roll angle of the rear frame (camber angle of the rear wheel) | |
| roll angle of the front frame (camber angle of the rear wheel) | |
| chain angle respect to the ground plane |
Front frame parameters
| b f | distance of the mass center of front frame from steering axis |
| h f | distance of the mass center of front frame from the line passing through the rear wheel center and perpendicular to the steering axis |
| G f | mass center of front frame |
| k f | effective (reduced) front suspension stiffness |
| m f | front unsprung mass |
| M f | front frame mass |
 | moment of inertia of the front wheel |
 | moment of inertia of front frame about the x f -axis through its center of mass |
 | product of inertia of front frame about the x f - z f -axes through its center of mass |
 | moment of inertia of front frame about the y f -axis through its center of mass |
 | moment of inertia of front frame about the z f -axis through its center of mass |
Rear frame parameters
| b r | longitudinal distance of the mass center of rear frame from rear wheel axis |
| h r | height of the mass center of rear frame |
| G r | mass center of rear frame |
| k r | effective (reduced) rear suspension stiffness |
| m r | rear unsprung mass |
| M r | rear frame mass |
 | moment of inertia of the rear wheel |
 | moment of inertia of rear frame about the x r -axis through its center of mass |
 | product of inertia of rear frame about the x r - z r -axes through its center of mass |
 | moment of inertia of rear frame about the y r -axis through its center of mass |
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