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2023 | Book

# The Science of Vehicle Dynamics

## Handling, Braking, and Ride of Road and Race Cars

Author: Massimo Guiggiani

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This textbook offers a comprehensive treatment of vehicle dynamics using an innovative, compelling approach, suitable for engineering students and professionals alike. Written by an authoritative contributor in the fields of applied mathematics and mechanics, it focuses on the development of vehicle models paying special attention to all the relevant assumptions, and providing explanations for each step. Some classical concepts of vehicle dynamics are revisited and reformulated, making this book also interesting for experienced readers. Using clear definitions, sound mathematics, and worked-out exercises, the book helps readers to truly understand the essence of vehicle dynamics for solving practical problems. With respect to the previous edition, which was the recipient of a 2019 TAA Textbook Excellence Award, this thoroughly revised third edition presents a more extensive and in-depth analysis of braking and handling of race cars.

##### Chapter 1. Introduction
Abstract
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.
Massimo Guiggiani
##### Chapter 2. Mechanics of the Wheel with Tire
Abstract
All road vehicles have wheels and almost all of them have wheels with pneumatic tires. Wheels have been around for many centuries, but only with the invention, and enhancement, of the pneumatic tire it has been possible to conceive fast and comfortable road vehicles [5].
Massimo Guiggiani
##### Chapter 3. Vehicle Model for Handling and Performance
Abstract
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
Abstract
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
Abstract
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. Map of Achievable Performance (MAP)
Abstract
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 7. Handling of Road Cars
Abstract
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 8. Handling of Race Cars
Abstract
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. The handling of Formula cars is addressed by means of the Map of Achievable Performance (MAP). With this new approach it is possible to better understand the effects of different vehicle setups at steady state and also in power-on/off conditions. The relationship between steady-state results and transient behavior is analysed in detail.
Massimo Guiggiani
##### Chapter 9. Handling with Roll Motion
Abstract
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
Abstract
Real roads are far from flat. Even freshly paved highways have small imperfections that interact with the vehicle dynamics by exciting vehicle vertical vibrations.
Massimo Guiggiani
##### Chapter 11. Tire Models
Abstract
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
##### Backmatter
Title
The Science of Vehicle Dynamics
Author
Massimo Guiggiani