Saturday, 2 November 2013

Vehicle Dynamics II: Cornering

By Univ.-Prof. Dr.-Ing. Martin Meywerk ,Helmut-Schmidt-Universität - Universität der Bundeswehr Hamburg

From Bugatti Veyron to Volkswagen Beetle, from racing to passenger car: Learn how they corner and drift, under- and over-steer!

About this course
The mobility has influenced many areas of a human's life since the invention of the wheel. While, in the early days of motorized vehicles, technical developments concentrated on simple mechanical or electrical issues , in the past decades, the electronics and with it, the microprocessor technology have become a central part of innovation in vehicles. Future developments of trendsetting style will be the conversion of the drive train from purely internal combustion engine to hybrid or alternative powertrain systems, the car-to-car communication and the autonomous vehicles. Challenges that make these technical developments partly necessary, come from a desirable reduction in CO2 emissions and an increase in the active safety. To understand the recent developments, especially in the field of alternative propulsion strategies and also in the area of autonomous or semi-autonomous vehicles, a knowledge of the basic driving physics is essential, as these innovations can be understood solely as the underlying laws of physics are known.
For this reason three parts of the vehicle dynamics, the longitudinal, the lateral and the vertical dynamics are important.
In this second part lateral dynamic aspects of vehicles will be illuminated, that means the cornering of a car will be explained.
We will start with a simple single-track model, then we will describe the slip angle of a wheel. The slip angle results in cornering forces, which are essential for understanding lateral dynamics. After that, we will look at the dependency between longitudinal and lateral forces using Kamm’s circle and Krempel’s diagram. Then we will illuminate steady state cornering, stability and the influence of different weight distributions between inner and outer side wheels of the car. The course will be finished by two applications from automotive mechatronics.
Course Structure
  1. Single Track Model
  2. Slip Angle
  3. Cornering Force
  4. Kamm's Circle, Krempel's Diagram
  5. Steady State Cornering
  6. Stability
  7. Influence of Left/Right Weights
  8. Application: ESP, DSC
Learning Outcomes
  • You will understand basic principles of cornering of a car
  • You will know slip angle and cornering forces
  • You understand the single track model
  • You understand the steady state cornering, stability and the influence of different weight distribution between inner and outer side of the car
  • You are able to calculate simple properties of a car
Per week: 135 - 260 min.
  • one video divided in 5 to 7 portions: 45 min.
  • 5 – 7 question-clusters for knowledge: 20 -30 min.
  • 2 – 3 question-clusters for comprehension: 25 – 50 min.
  • Guided calculation for application
  • P2P-problems to train analysis and synthesis skills: 45 min.
  • wrap-up: 0 – 90 min. (depends on your previous knowledge and your comprehension) Preparation of the exam: 30 h
Course Format
The course uses a mixture of Screencasts (with handwritten derivations, drawings, formulas), Powerpoint slides and videos from real cars, simulated cars and testrigs.
To assess the different levels of learning this course will use different form of assessments:
  • Knowledge: Multiple choice,
  • Comprehension: correlation between statements and parts of diagrams, formulas or driving maneuver (visualized by short simulation videos);
  • Application: short guided calculations (open office),
  • Analysis: P2P-problems: longer calculations or drawings
Prior Knowledge
You should have been successful in university courses in basic mathematics and in basic engineering mechanics, especially you need:
  • Algebra
  • Trigonometric Functions
  • Differential calculus
  • Linear Algebra: Vectors, Coordinate systems etc.
  • Force, Torque, Equilibrium
  • Mass, Center of Gravity, Moment of Inertia
  • Method of Sections, Friction, Newton's Law
  • (Lagrange’s Transf., Stability, ODE)


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