ABSTRACT
As a preliminary to analyzing vehicle motions while it is on its wheels, Chapter 2 discusses how forces are generated “where the rubber meets the road” at the contact patch. Rolling resistance in level straight-line unaccelerated driving is presented as a concept that involves deformation of the tire, friction in the power train, and even aerodynamic forces. Longitudinal tire slip is defined and analyzed. The relationship between tire slip and force due to torque that is positive (traction) or negative (braking or engine drag) is presented. The phenomenon of a wheel binding up in a crash is discussed. The concept of lock fraction is introduced; how to calculate it as a function of braking demand, friction coefficient, engine drag, tire deflation, and being bound up is presented. A vehicle’s crab angle is defined as the difference between its heading angle and its velocity vector angle. In similar fashion, a tire’s slip angle is defined as the angle between its center line and its tangential velocity vector at the contact patch. The relationship between lateral force and slip angle is discussed, along with the notion of cornering coefficient or cornering stiffness. When longitudinal and lateral forces exist together, they are not independent; rather, they are related through the concept of the friction circle, which limits the ability of a tire to generate forces. In simulations, this greatly complicates the analysis, and often forces the analyst to devote more effort to get the run-out right, as compared to the impact phase, which is where the damage to vehicles and occupants is more likely to occur.
It is the case that reconstructions work backwards in distance. That is, they start where vehicle positions and velocities are known (at the end of the run-out), and work backwards towards the beginning of the run-out, where the positions are known but the velocities (linear and angular) are not. Classically, this is done assuming straight-line trajectories between the end and the beginning. For the frequent occurrences where the path is curved, and the crab angle varies, subsequent chapters will build on this one to facilitate a more generalized distance-backwards analysis.
