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Technical Paper

Moment Method - A Comprehensive Tool for Race Car Development

The MRA Moment Method computer program automates an original approach to the analysis of race car handling. For a given speed and power/braking condition, the computer solution covers the full maneuvering envelope and presents the results graphically in one figure. The model is based on a comprehensive nonlinear vehicle representation utilizing tire, chassis, and aerodynamic input data as available to race car designers and developers. The paper will first explain and illustrate the Moment Method in general terms, with some graphical examples. The ability of the technique to model the behavior of an F.1 car traversing a small bump in mid-corner on a Grand Prix circuit is then reviewed. The results correlate well with the driver comments relative to changes in directional stability (plow/spin) as the car pitches over the bump. It also correlates well with the lateral acceleration/speed that the driver is willing to use in this corner.
Technical Paper

Inflation Pressure Effects in the Nondimensional Tire Model

Inflation pressure affects every aspect of tire performance. Most tire models, including the Radt/Milliken Nondimensional Tire Model, are restricted to modeling a single inflation pressure at a time. This is a reasonable limitation, in that the Nondimensional model forms an input/output relationship between tire operating conditions and force & moment outputs. Traditional operating conditions are normal load, slip angle, inclination angle, slip ratio and road surface friction coefficient. Tire pressure is more like a tire parameter than a tire operating condition. Since the Nondimensional Tire Model is semi-empirical it does not specifically deal with tire parameters like sidewall height or tread compound. Still, tire pressure is the easiest tire parameter to change, and as the air temperature within the tire varies during use so does the inflation pressure. Thus, it is desirable to incorporate inflation pressure into the Nondimensional Tire Model as an input.
Technical Paper

MRA Vehicle Dynamics Simulation-Matlab®/Simulink®

Milliken Research Associates has developed a new simulation tool, named Vehicle Dynamics Simulation-Matlab/Simulink (VD-M/S). Produced for the government's Variable Dynamic Testbed Vehicle (VDTV), VD-M/S is an 18 degree-of-freedom simulation programmed in the Matlab/Simulink environment. It contains a detailed non-linear tire model, kinematic and compliance effects, aerodynamic loadings, etc. as do MRA's other simulation programs. Unique to VD-M/S is its development from Day One as a simulation catered to the inclusion and exploration of active systems within the vehicle.
Technical Paper

Tire Asymmetries and Pressure Variations in the Radt/Milliken Nondimensional Tire Model

The Nondimensional Tire Model is based on the idea of data compression to load-independent curves. Through the use of appropriate transforms, tire data can be manipulated such that, when plotted in nondimensional coordinates, all data falls on a single curve. This leads to a highly efficient and mathematically consistent tire model. In the past, data for slip angle and slip ratio has been averaged across positive and negative values for use with the transforms. In this paper, techniques to handle tire asymmetries in lateral and longitudinal force are presented. This is an important advance, since in passenger cars driving/braking data is almost always asymmetric and, depending on tire construction, lateral force data may follow likewise. In addition, this paper is the first to explore the inclusion of inflation pressure as an operating variable in the Nondimensional Tire Theory.

Race Car Vehicle Dynamics

Written for the engineer as well as the race car enthusiast, Race Car Vehicle Dynamics includes much information that is not available in any other vehicle dynamics text. Truly comprehensive in its coverage of the fundamental concepts of vehicle dynamics and their application in a racing environment, this book has become the definitive reference on this topic. Although the primary focus is on the race car, the engineering fundamentals detailed are also applicable to passenger car design and engineering. Authors Bill and Doug Milliken have developed many of the original vehicle dynamics theories and principles covered in this book, including the Moment Method, "g-g" Diagram, pair analysis, lap time simulation, and tire data normalization. The book also includes contributions from other experts in the field.

Race Car Vehicle Dynamics - Problems, Answers and Experiments

Written for the engineer as well as the race car enthusiast and students, this is a companion workbook to the original classic book, Race Car Vehicle Dynamics, and includes: Detailed worked solutions to all of the problems Problems for every chapter in Race Car Vehicle Dynamics, including many new problems The Race Car Vehicle Dynamics Program Suite (for Windows) with accompanying exercises Experiments to try with your own vehicle Educational appendix with additional references and course outlines Over 90 figures and graphs This workbook is widely used as a college textbook and has been an SAE International best seller since it's introduction in 1995. Buy the set and save! Race Car Vehicle Dynamics