The Science of Vehicle Dynamics, Softcover reprint of the original 1st ed. 2014
Handling, Braking, and Ride of Road and Race Cars

Vehicle dynamics is often perceived as a quite intuitive subject. As a matter of fact, lots of people are able to drive a car. Nevertheless, without a rigorous mathematical formulation it is very difficult to truly understand the physical phenomena involved in the motion of a road vehicle.

In this book, mathematical models of vehicles are developed, always paying attention to state the relevant assumptions and to provide explanations for each step. This approach allows for a deep, yet simple, analysis of the dynamics of vehicles, without having to resort to foggy concepts. The reader will soon achieve a clear understanding of the subject, which will be of great help both in dealing with the challenges of designing and testing new vehicles and in tackling new research topics.

The book covers handling and performance of both road and race cars. A new approach, called MAP (Map of Achievable Performance), is presented and thoroughly discussed. It provides a global and intuitive picture of the handling features of a vehicle. Moreover, the book also deals with several relevant topics in vehicle dynamics that have never been discussed before.

Massimo Guiggiani is professor of Applied Mechanics at the Università di Pisa, where he also teaches Vehicle Dynamics in the MS degree program in Vehicle Engineering.

Author's website with interactive figures (link: http://www.dimnp.unipi.it/guiggiani-m/interactive.html)

Preface.- 1 Introduction.- 1.1 Vehicle Definition.- 1.2 Vehicle Basic Scheme.- References.- 2 Mechanics of the Wheel with Tire.- 2.1 The Tire as a Vehicle Component.- 2.2 Rim Position and Motion.- 2.3 Carcass Features.- 2.4 Contact Patch.- 2.5 Footprint Force.- 2.5.1 Perfectly Flat Road Surface.- 2.6 Tire Global Mechanical Behavior.- 2.6.1 Tire Transient Behavior.- 2.6.2 Tire Steady-State Behavior.- 2.6.3 Rolling Resistance.- 2.6.4 Speed Independence (Almost).- 2.6.5 Pure Rolling (not Free Rolling).- 2.7 Tire Slips.- 2.7.1 Rolling Velocity.- 2.7.2 Definition of Tire Slips.- 2.7.3 Slip Angle.- 2.8 Grip Forces and Tire Slips.- 2.9 Tire Testing.- 2.9.1 Pure Longitudinal Slip.- 2.9.2 Pure Lateral Slip.- 2.10 Magic Formula.- 2.11 Mechanics of Wheels with Tire.- 2.12 Summary.- 2.13 List of Some Relevant Concepts.- References.- 3 Vehicle Model for Handling and Performance.- 3.1 Mathematical Framework.- 3.2 Vehicle Congruence (Kinematic) Equations.- 3.2.1 Velocities.- 3.2.2 Yaw Angle and Trajectory.- 3.2.3 Velocity Center.- 3.2.4 Fundamental Ratios.- 3.2.5 Accelerations and Radii of Curvature.- 3.2.6 Acceleration Center.- 3.2.7 Tire Kinematics (Tire Slips).- 3.3 Vehicle Constitutive (Tire) Equations.- 3.4 Vehicle Equilibrium Equations.- 3.5 Forces Acting on the Vehicle.- 3.5.1 Weight.- 3.5.2 Aerodynamic Force.- 3.5.3 Road–Tire Friction Forces.- 3.5.4 Road–Tire Vertical Forces.- 3.6 Vehicle Equilibrium Equations (more explicit form).- 3.7 Load Transfers.- 3.7.1 Longitudinal Load Transfer.- 3.7.2 Lateral Load Transfers.- 3.7.3 Vertical Loads on each Tire.- 3.8 Suspension First-Order Analysis.- 3.8.1 Suspension Reference Configuration.- 3.8.2 Suspension Internal Coordinates.- 3.8.3 Camber variation.- 3.8.4 Vehicle Internal Coordinates.- 3.8.5 Roll and Vertical Stiffnesses.- 3.8.6 Suspension Internal Equilibrium.- 3.8.7 Effects of a Lateral Force.- 3.8.8 No-Roll Centers and No-Roll Axis.- 3.8.9 Forces at the No-Roll Centers.- 3.8.10 Suspension Jacking.- 3.8.11 Roll Angle andLateral Load Transfers.- 3.8.12 Explicit Expressions of Lateral Load Transfers.- 3.8.13 Lateral Load Transfers with Rigid Tires.- 3.9 Dependent Suspensions.- 3.10 Sprung and Unsprung Masses.- 3.11 Vehicle Model for Handling and Performance.- 3.11.1 Equilibrium Equations.- 3.11.2 Constitutive (Tire) Equations.- 3.11.3 Congruence (Kinematic) Equations.- 3.11.4 Principles of any Differential Mechanism.- 3.12 The Structure of this Vehicle Model.- 3.13 Three-Axle vehicles.- 3.14 Summary.- 3.15 List of Some Relevant Concepts.- References.- 4 Braking Performance.- 4.1 Pure Braking.- 4.2 Vehicle Model for Braking Performance.- 4.3 Equilibrium Equations.- 4.4 Longitudinal Load Transfer.- 4.5 Maximum Deceleration.- 4.6 Brake Balance.- 4.7 All Possible Braking Combinations.- 4.8 Changing the Grip.- 4.9 Changing the Weight Distribution.- 4.10 A Numerical Example.- 4.11 Braking Performance of Formula Cars.- 4.11.1 Equilibrium Equations.- 4.11.2 Longitudinal Load Transfer.- 4.11.3 Maximum Deceleration.- 4.11.4 Braking Balance.- 4.11.5 Typical Formula 1 Braking Performance.- 4.12 Summary.- 4.13 List of Some Relevant Concepts.- 5 The Kinematics of Cornering.- 5.1 Planar Kinematics of a Rigid.- 5.1.1 Velocity Field and Velocity Center.- 5.1.2 Acceleration Field, Inflection Circle and Acceleration Center.- 5.2 The Kinematics of a Turning Vehicle.- 5.2.1 Fixed and Moving Centrodes of a Turning Vehicle.- 5.2.2 Inflection Circle.- 5.2.3 Variable Curvatures.- References.- 6 Handling of Road Cars.- 6.1 Open Differential.- 6.2 Fundamental Equations of Vehicle Handling.- 6.3 Double Track Model.- 6.4 Single Track Model.- 6.4.1 Governing Equations of the Single Track Model.- 6.4.2 Axle Characteristics.- 6.5 Alternative State Variables.- 6.6 Inverse Congruence Equations.- 6.7 Vehicle in Steady-State Conditions.- 6.7.1 The Role of the Steady-State Lateral Acceleration.- 6.7.2 Steady-State Analysis.- 6.8 Handling Diagram—the Classical Approach.- 6.9 Weak Concepts in Classical Vehicle Dynamics.-6.9.1 Popular Definitions of Understeer/Oversteer.- 6.10 Map of Achievable Performance (MAP)—a New Global Approach.- 6.11 Vehicle in Transient Conditions (Stability and Control Derivatives).- 6.11.1 Steady-State Conditions (Equilibrium Points).- 6.11.2 Linearization of the Equations of Motion.- 6.11.3 Stability.- 6.11.4 Forced Oscillations (Driver Action).- 6.12 Relationship Between Steady State Data and Transient Behavior.- 6.13 New Understeer Gradient.- 6.14 Stability (Again).- 6.15 The Single Track Model Revisited.- 6.15.1 Different Vehicles with Almost Identical Handling.- 6.16 Road Vehicles with Locked or Limited Slip Differential.- 6.17 Linear Single Track Model.- 6.17.1 Governing Equations.- 6.17.2 Solution for Constant Forward Speed.- 6.17.3 Critical Speed.- 6.17.4 Transient Vehicle Behavior.- 6.17.5 Steady-State Behavior: Steering Pad.- 6.17.6 Lateral Wind Gust.- 6.17.7 Banked Road.- 6.18 Summary.- 6.19 List of Some Relevant Concepts.- References.- 7 Handling of Race Cars.- 7.1 Locked and Limited Slip Differentials.- 7.2 Fundamental Equations of Race Car Handling.- 7.3 Double Track Race Car Model.- 7.4 Tools for Handling Analysis.- 7.5 The Handling Diagram Becomes the Handling Surface.- 7.5.1 Handling with Locked Differential (No Wings).- 7.6 Handling of Formula Cars.- 7.6.1 Handling Surface.- 7.6.2 Map of Achievable Performance (MAP).- 7.7 Summary.- 7.8 List of Some Relevant Concepts.- References.- 8 Ride Comfort and Road Holding.- 8.1 Vehicle Models for Ride and Road Holding.- 8.2 Quarter Car Model.- 8.2.1 The Inerter as a Spring Softener 8.2.2 Quarter Car Natural Frequencies and Modes.- 8.3 Shock Absorber Tuning.- 8.3.1 Comfort Optimization.- 8.3.2 Road Holding Optimization.- 8.3.3 The Inerter as a Tool for Road Holding Tuning.- 8.4 Road Profiles.- 8.5 Free Vibrations of Road Cars.- 8.5.1 Governing Equations.- 8.5.2 Proportional Viscous Damping.- 8.5.3 Vehicle with Proportional Viscous Damping.- 8.6 Tuning of Suspension Stiffnesses.- 8.6.1 Optimality ofProportional Damping.- 8.6.2 A Numerical Example.- 8.7 Non-Proportional Damping.- 8.8 Interconnected Suspensions.- 8.9 Summary.- 8.10 List of Some Relevant Concepts.- References.- 9 Handling with Roll Motion.- 9.1 Vehicle Position and Orientation.- 9.2 Yaw, Pitch and Roll.- 9.3 Angular Velocity.- 9.4 Angular Acceleration.- 9.5 Vehicle Lateral Velocity.- 9.5.1 Track Invariant Points.- 9.5.2 Vehicle Invariant Point (VIP).- 9.5.3 Lateral Velocity and Acceleration.- 9.6 Three-Dimensional Vehicle Dynamics.- 9.6.1 Velocity and Acceleration of G.- 9.6.2 Rate of Change of the Angular Momentum.- 9.6.3 Completing the Torque Equation.- 9.6.4 Equilibrium Equations.- 9.6.5 Including the Unsprung Mass.- 9.7 Handling with Roll Motion.- 9.7.1 Equilibrium Equations.- 9.7.2 Load Transfers.- 9.7.3 Constitutive (Tire) Equations.- 9.7.4 Congruence (Kinematic) Equations.- 9.8 Steady-State and Transient Analysis.- 9.9 Summary.- 9.10 List of Some Relevant Concepts.- References.- 10 Tire Models.- 10.1Brush Model Definition.- 10.1.1 Roadway and Rim.- 10.1.2 Shape of the Contact Patch.- 10.1.3 Force–Couple Resultant.- 10.1.4 Position of the Contact Patch.- 0.1.5 Pressure Distribution.- 10.1.6 Friction.- 10.1.7 Constitutive Relationship.- 10.1.8 Kinematics.- 10.2 General Governing Equations of the Brush Model.- 10.2.1 Data for Numerical Examples.- 10.3 Brush Model Steady-State Behavior.- 10.3.1 Governing Equations.- 10.3.2 Adhesion and Sliding Zones.- 10.3.3 Force–Couple Resultant.- 10.4 Adhesion Everywhere (Linear Behavior).- 10.5 Wheel with Pure Translational Slip.- 10.5.1 Rectangular Contact Patch.- 10.5.2 Elliptical Contact Patch.- 10.6 Wheel with Pure Spin Slip.- 10.7 Wheel with Both Translational and Spin Slips.- 10.7.1 Rectangular Contact Patch.- 10.7.2 Elliptical Contact Patch.- 10.8 Brush Model Transient Behavior.- 10.8.1 Transient Model with Carcass Compliance Only.- 10.8.2 Transient Model with Carcass and Tread Compliance.- 10.8.3 Numerical Examples.- 10.9 Summary.- 10.10List of Some Relevant Concepts.- References.- References.- Index.