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Simulation of race circuit performance had a significant impact on the design and development of the Dodge Stratus North American Touring Car Championship (NATCC) entry. The analysis involved utilization of the Milliken Research Associates, Inc. (MRA) Lap Time Simulation (LTS) program which predicts lap time based on data describing the vehicle, tires, and race track. Input data for the simulation was obtained from several sources. Chrysler Vehicle Engineering provided vehicle design information and engine power data. Tire characteristics were measured at Calspan Corporation. Aerodynamic coefficients were derived from scale model wind tunnel tests performed by Reynard Racing Cars Ltd. at the Houghton Wind Tunnel, Royal Military College of Science Shrivenham, Wiltshire, UK. X-Trac Ltd. provided transaxle specifications and race line data was derived from on-board measurements and circuit maps. Parametric studies of the vehicle variables were performed for various tracks.

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.

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.

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.

Designing for optimal performance across a variety of situations involves compromise decisions. Through the investigation of a two-variable optimization of a vehicle for two different “races” the importance of this compromise design is underscored. The use of Pareto-minimal solution techniques, borrowed from game theory, aid in the design process by limiting the number of possible compromise designs, highlighting which solution applies for a given situation and providing some insight to the sensitivity of the design.

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.