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About this book

This textbook covers handling and performance of both road and race cars. Mathematical models of vehicles are developed always paying attention to state the relevant assumptions and to provide explanations for each step. This innovative approach provides a deep, yet simple, analysis of the dynamics of vehicles. 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 deals with several relevant topics in vehicle dynamics that are not discussed elsewhere and this new edition includes thoroughly revised chapters, with new developments, and many worked exercises.

Praise for the previous edition:

Great book! It has changed drastically our approach on many topics. We are now using part of its theory on a daily basis to constantly improve ride and handling performances.

--- Antonino Pizzuto, Head of Chassis Development Group at Hyundai Motor Europe Technical Center

Astonishingly good! Everything is described in a very compelling and complete way. Some parts use a different approach than other books.

--- Andrea Quintarelli, Automotive Engineer

Table of Contents


Chapter 1. Introduction

Vehicle dynamics is a fascinating subject, but it can also be very frustrating without the tools to truly understand it. We can try to rely on experience, but an objective knowledge needs a scientific approach. Something grounded on significant mathematical models, that is models complex enough to catch the essence of the phenomena under investigation, yet simple enough to be understood by a (well trained) human being. This is the essence of science, and vehicle dynamics is no exception.

Massimo Guiggiani

Chapter 2. Mechanics of the Wheel with Tire

The first goal of this Chapter is to describe the kinematics of a wheel with tire, mainly under steady-state conditions. This leads to the definitions of slips as a measure of the extent to which the wheel with tire departs from pure rolling conditions. All aspects are discussed in detail and with a critical approach, showing that the use of the slips implies neglecting some phenomena. The slip angle is also defined and discussed. It is shown that a wheel with tire resembles indeed a rigid wheel because slip angles are quite small. The relationships between the kinematics and the forces/couples the tire exchange with the road are investigated by means of experimental tests. The Magic Formula provides a convenient way to represent these functions. Finally, the mechanics of wheels with tire is summarized with the aid of quite a number of plots.

Massimo Guiggiani

Chapter 3. Vehicle Model for Handling and Performance

At the beginning of this chapter, the simplifying assumptions to formulate a simple, yet significant, vehicle model are listed. Then the kinematics of the vehicle as a whole is described in detail, followed by the kinematics of each wheel with tire. The next step is the formulation of the constitutive (tire) equations and of the global equilibrium equations. A lot of work is devoted to the load transfers, which requires an in depth suspension analysis. This leads to the definition of the suspension and vehicle internal coordinates, of the no-roll centers and no-roll axis, for both independent and dependent suspensions. The case of three-axle vehicles is also considered. In the end, the vehicle model for handling and performance is formulated in a synthetic, yet precise way. A general description of the mechanics of differential mechanisms, either open or limited-slip is included.

Massimo Guiggiani

Chapter 4. Braking Performance

The goal of this chapter is to understand how to stop a vehicle as soon as possible, avoiding wheel locking. This result can be achieved only if the vehicle has the right brake balance. Unfortunately, brake balance is affected by the value of the grip and by the position of the center of mass. This topic is addressed in detail, both analytically and graphically, through the region of all possible braking conditions. The peculiarity of the braking performance of a Formula car is also discussed.

Massimo Guiggiani

Chapter 5. The Kinematics of Cornering

Cars have to negotiate corners. But not all cars do that the same way. This is particularly evident in race cars, where the ability to negotiate a corner is a crucial aspect to minimize the lap time. In this Chapter the kinematics of a vehicle while taking a corner is exploited. At first sight taking a corner looks quite a trivial task. But designing a vehicle that does it properly is one of the main challenges faced by a vehicle engineer. Therefore, there is the need to investigate what really happens during the cornering process. It will be shown that some very significant kinematical quantities must follow precise patterns, for the car to get around corner in a way that makes the driver happy. In some sense, the geometric features of the trajectory must adhere to some pretty neat criteria. The topics covered have never been employed in vehicle dynamics before.

Massimo Guiggiani

Chapter 6. Handling of Road Cars

Road cars are characterized by having an open differential and no significant aerodynamic downforces. These two aspects allow for some substantial simplifications of the vehicle model. With the additional assumption of equal gear ratio of the steering system for both front wheels, it is possible to formulate the single track model. Quite contrary to common belief, it is shown that the axle characteristics can take into account many vehicle features, like toe-in/toe-out, roll steering, camber angles and camber angle variations. The steady-state analysis is carried out first using the classical handling diagram. Then, the new global approach based on handling maps on achievable regions is introduced and discussed in detail. This new approach shows the overall vehicle behavior at a glance. Stability and control derivatives are introduced to study the vehicle transient behavior. Moreover, the relationship between data collected in steady-state tests and the vehicle transient behavior are thoroughly analyzed in a systematic framework. To prove the effectiveness of these results, a number of apparently different vehicles with exactly the same handling are generated.

Massimo Guiggiani

Chapter 7. Handling of Race Cars

Limited slip differential and wings are typical of race cars. Both greatly impact on the vehicle handling (otherwise would not be used). Therefore, the first part of this Chapter is devoted to the formulation of a suitable vehicle model, which, in this case, cannot be single track. As a matter of fact, there is a strong interaction between lateral and longitudinal forces. The concept of handling diagram becomes inadequate and must be replaced by the handling surface. This fairly new tool is introduced in the framework of handling of road cars with locked or limited-slip differential, The handling of Formula cars is first addressed by means of the handling surface. However, an even more powerful description is given by means of the Map of Achievable Performance (MAP). With this new approach it is possible to better understand the effects of different vehicle set-ups at steady state and also in power-on/off conditions.

Massimo Guiggiani

Chapter 8. Map of Achievable Performance (MAP)

The MAP approach provides a way to analyze the steady-state handling behavior of road/race cars. It is completely general, in the sense that is can be employed for any real car, and for any mathematical model as well. Two concepts play a central role in MAP: the achievable region, that is the totality of the achievable trim conditions for a given vehicle, and the level (handling) curves inside the achievable region, to highlight the vehicle peculiar features. The envelope of level curves is often a good practical way to obtain the achievable regions.

Massimo Guiggiani

Chapter 9. Handling with Roll Motion

The vehicle orientation is defined by means of the yaw-pitch-roll elemental rotations. Then, to define the vehicle position, a careful analysis of what happens when the vehicle rolls is performed. The key result is the definition of the Vehicle Invariant Point (VIP) as the best option for monitoring the vehicle position, and also for defining the lateral velocity and acceleration. VIP allows for a simple and systematic analysis of the vehicle three-dimensional dynamics. Among other things, it is shown that the well known roll-axis, as the axis about which the vehicle rolls, is nonsense.

Massimo Guiggiani

Chapter 10. Ride Comfort and Road Holding

The capability to smooth down the road imperfections affects both the comfort and the road holding of the vehicle. Improving comfort means, basically, limiting the vertical acceleration fluctuations of the vehicle body and hence of passengers. Improving road holding means, among other things, limiting the fluctuations of the vertical force that each tire exchanges with the road. In this chapter suitable models for improving the comfort and/or the road holding of the vehicle are developed. Quite interestingly, it is shown that a well tuned vehicle should have proportional dampingproportional damping, although it appears that this aspect is not commonly taken into account in traditional vehicle dynamics. The benefits of inerter in a Formula car are also discussed in detail.

Massimo Guiggiani

Chapter 11. Tire Models

In this chapter a simple, yet significant, tire model is developed. It is basically a brush model, but with some noteworthy additions with respect to more common formulations. For instance, the model takes care of the transient phenomena that occur in the contact patch. A number of Figures show the pattern of the local actions within the contact patch.

Massimo Guiggiani


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