# Race car vehicle dynamics and design applied to formula student

• E.J. Goodman

Student thesis: Master's ThesisMaster of Philosophy

### Abstract

[Master of Philosophy]. Part 1: This thesis is divided into two distinct parts. The first of these builds upon a list of terms commonly used in the discussion of vehicle dynamics. The list is supplied by the Society of Automobile Engineers (USA), and the Institute of Mechanical Engineers (UK) to teams participating in the Formula Student competition. These terms and the implications that their respective values have on the design and performance of a race car are considered to be essential. The objective of the first part of this thesis is to explain, discuss and evaluate the theoretical effects of the terms covered in the list.

The leading chapter begins with an introduction to the challenges associated with racing and the basic tools needed to understand and evaluate vehicle performance. The discussion then passes on to the tyre and tyre-road interface. The mechanisms by which the tyre generates friction are investigated and the subsequent consequence of load sensitivity is discussed. Analysis of the contact patch and an explanation of slip angles and generation of lateral and longitudinal forces then follow. The by-products and effects of slip and friction forces in the contact patch are
further evaluated to explain tyre deformation, pneumatic trail and self aligning torque. Analysis of the tyre concludes with an explanation of tyre parameters, practical testing methods and results, as well the principles behind a detailed mathematical model of lateral force and self
aligning torque curves.

A discussion on steady state balance is then entered with reference to slip angle, lateral force and instantaneous radius of turn. Theoretical states of understeer, neutral steer and oversteer are discussed along with consequences on driver input and ultimate limits of performance. Terms
such as understeer gradient and the Ackermann steering angle are also related to cause and effect.

The next chapter covers terms related to basic vehicle geometry values of track and wheelbase. Firstly, defining them and then relating their effects on steady state balance, lateral weight transfer and longitudinal weight transfer.

Delving further into a vehicle’s geometrical values, suspension kinematics are then covered. Roll centres and swing axle lengths are graphically defined and related to suspension performance in roll and bump motion. As a consequence, measures of roll and bump performance are then explained. Anti-squat and anti-dive parameters are also defined along with an evaluation of their value in a high performance suspension system, whilst considering the adverse effects that they might have.

Weight transfer and its effects are fundamental to vehicle performance. Consequently, the next section gives an in-depth explanation and breakdown of weight transfer as a result of lateral and longitudinal acceleration.

The next three chapters cover the definition of suspension rates and the respective necessary control motion of both suspended and unsuspended masses. Wheel rates are derived from motion ratios and spring rates. The suspension system is then represented as a simple mass spring system in order to explain oscillatory motion and the need for damping. The discussion then progresses with a definition of critical damping and a description of the ride versus handling compromise. Basic damping principles are covered along with the advantages and disadvantages
of damper design for different applications. The notion of high and low speed damper motion is explained and related to system stimuli.

All of the previous investigations have been into individual systems that comprise a race car. Each system could be theoretically perfect but if incorrectly interfaced it will not function well. Hence, the chassis can be looked at as a system with a purpose of linking all other systems together in a manner that they are allowed to perform optimally. In this chapter important performance measures, chassis fabrication and chassis material are investigated and related to the performance increases they may give to other systems.

Part 2: The second part of this thesis looks at applying the theoretical information contained within the first part to the practical example of a Formula Student car. The process begins with some background on the design process and the numerical tools needed for analysis of the problem. A process of performance data collection is outlined along with a description of the hardware and analysis techniques needed to asses a current design. A mathematical simulation of a lap of the Formula Student circuit is developed.
Date of Award May 2009 English

• race
• car
• Dynamics
• formula
• student

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