Strange as it may seem, a good starting point may be the U.S. Department of Transportation. As part of their research in understanding basic automotive dynamics, they have sponsored their own computer simulations based on roughly the same original concepts. The most current published information is a seven-volume report titled "Improvement of Mathematical Models for Simulation of Vehicle Handling" (DOT-HS-805-370), available from the National Technical Information Service. Currently, it is being simplified to run on PC's, with a contract to Systems Technology in Hawthorne, California (See SAE paper #2000-01-1620). Regardless of the source, these particular programs are intended for passenger car work. Although the basic framework can also be used to produce realistic race car simulations, it will be necessary to obtain typical race car parameters and formulate typical racing maneuvers.
One of the drawbacks to using a complex computer program is that you seldom learn "why" it came up with a particular "what". Alright, so two-wheel drive gives better laptimes at Sebring than four-wheel drive. Why does it? A human may not be able to comprehend the underlying logic well enough to ever know. The intermediate steps and sub-conclusions may be buried in a stack of printout sheets and plots. Sometimes it is more effective to use a simpler, more comprehensible analysis. The following considerations will define the type of simulation necessary to get significant results:
Suspension simulations are those in which only the mechanical, geometric deflections of the hardware are considered. At the first level, just one wheel location may be modeled, including the wheel, knuckle or upright, all locating links, spring, shock, and anti-roll bar. The model ends at the chassis, which is considered a fixed, solid anchor. This program can give single wheel angular changes with travel, and force paths due to wheel loadings. (See Fig. 50a) The next step is to include the opposite side, to see how one complete end of the vehicle might respond with respect to the ground -- in roll angle and vertical deflection. Then the other end of the chassis and suspension can be added in the same way -- which will require a comparison of front/rear weights, roll centers, and roll resistances to determine true lateral chassis motions. (See Fig. 50b) The next level of sophistication is to include engine and brake torque inputs for their effect on longitudinal suspension motions, as in squat and dive. And the highest level is a consideration of the actual compliance of links, bushings, and pivots as they are stressed, and not simply as assumed infinitely rigid objects.
Vehicle dynamics simulations generally require the above suspension simulations, but are a quantum leap ahead, in that tire models and overall inertias must be incorporated. The ordinary rubber tire is about the hardest thing there is on a car to mathematically model. Good real-world representation requires a tire to be tested in a laboratory in all combinations of load, camber, slip angle, cornering force, and thrust -- while controlling temperature, pressure, and wear. Then these data points must be represented by tables or general equations of relationships. After that, the problem gets complicated. The vehicle inertias -- vertical, longitudinal, lateral, pitch, roll, and yaw (plus the oscillating inertias of the unsprung suspension components) act against the ground through these four flexible tire contact patches. If there were three wheels, the problem would be considerably easier, since four points creates a "statically indeterminate plane," which usually requires "iteration" or repeated approximations to approach a true force balance.
Finally, how is the model used when it is finished? That is, what kind of maneuvers or inputs are used to make it act like a real vehicle? Some simple vehicle test maneuvers such as the "step steer" or sinusoidal steer inputs can be used for comparison with real tests, but they are not representative of very many actual driver behaviors, on the street or on the track. And what kind of results are to be presented? Is a single number adequate, or are complete plots of paths and angles necessary?
Race course simulations are something else. Here we are talking about only the ultimate limits of performance (hopefully), representing a driver with very well-known and repeatable behavior (on the track). None of those sub-limit maneuver niceties such as tire data maps and yaw responses are necessary here. You define the boundaries of the race course, select a "line" just as a driver might (See Fig. 52), and then instruct the computer to travel on that line as fast as it can, restrained only by the theoretical upper limits of the engine and tires.
But of course it's not as easy as it sounds, or everyone would be doing it. First a path must be defined in computer terms to go from a tight radius at the apex to an infinite radius in the straightaway (constant arcs, spirals, parabolic, and hyperbolic paths have been used). Then the computer must be told how to balance cornering versus acceleration to get the best laptime, while considering the effects of weight transfer in determining whether the limit is the front tires, rear tires, or engine torque. And in the real world of race tracks, there may be considerable changes in grade, camber, and surface coefficient from corner to corner. Another major and unique race car consideration is aerodynamics, which can change immensely between 50 and 200 mph. And finally, these days it can be very useful to be able to vary the model between rear wheel drive, front wheel drive, and four wheel drive.
Depth of analysis. Regardless of the type of simulation, you will have to study a candidate program's input variable categories, and the detail within each one. Otherwise the approximations and assumptions will affect results. For example, is tire data represented by a simple friction ellipse, or is it in tabular or coefficient form (TYDEX or Pacejka), and does it go into all the affecting variables of interest, such as temperature or wear sensitivity? Do the required aerodynamic coefficients vary as a function of ride height and ambient conditions? Do the suspension models incorporate bushing compliances? Are shock absorber characteristics required, perhaps varying as a function of speed, travel, or even temperature? And does the program actually use these parameters, responding with appropriate results? Also, the file sizes and the precision of tabulated input such as engine torque curves and tire data should be considered.
Vehicle control input. There are three main types: Most common is a vehicle path controlled by duplicating the output from an actual track test session. This is a simple way of studying the effect of configuration changes and correlating them with testing. More scientific is a path defined by fitting curves to a surveyors track map (including track widths). This allows the prediction of performance and setup change effects on a track that has never been run, or has changed since the last race. Its accuracy will depend on the inclusion of hard-to-define local surface variations such as camber, grade, roughness, and grip. And in a separate category is a path resulting from driver control inputs, either duplicated from test data or standardized "open-loop" inputs such as the step-steer or sine wave. These runs are mostly used to study transient stability as a response to a precise and repeatable simulated driver.
Output presentation. Most common is plotting results in the same format as a familiar data acquisition system - perhaps a host DAS, as they become affiliated with SIMs. Output should also be available as data files such as ASCII or comma delimited files that can be analyzed in other software such as spreadsheets. Output from a simulated run might also include the limiting conditions in every location, such as engine power limit or oversteer/understeer.
Accuracy/correlation. Most SIM companies should warn you not to expect absolute correlation in speeds and laptimes to be too close, unless they reach the point where every important parameter is accurately represented. However, you should expect results to at least indicate the proper direction of results, if not also the approximate relative value of results. Possibly a demo version of the software would allow you to input a change in which you know the likely results from your own experience. Until you have personally verified the predictive value by correlation on your own car, it can be dangerous to have too much faith in it.
All of these race car computer simulations are extremely challenging and therefore as fascinating as the real vehicles. They provide the opportunity to research minor and major changes without the limitations of actual test drivers who sometimes don't repeat too well, may not be sensitive to the immediate question, and can get hurt if someone makes a mistake. The simulation will repeat its maneuver precisely to the nearest fraction of a foot, and determine whether there was a difference of a millisecond between two configurations.
Such programs have given me as much insight about the behavior of race cars as actually driving them. Granted, I can't quote examples of exactly how much they alone have improved laptimes. Perhaps the ultimate step would be to provide real-time inputs, such as computer joy-stick steering, throttle, and brakes, and observe corresponding vehicle behavior represented as images generated on the screen. Very simple versions of this can be seen in any computer-game arcade. But like any other speed equipment, you pay your money and you take your chances. And more and more of the technically sophisticated pro racing teams are taking the chance.
You can expect race car simulations to become more commonly used in the future. There will be more available to choose from, and for much lower prices, for the following reasons: (a) Continual advancements in computer memory and speeds makes it easier to develop and run them. (b) There will be more computer programmers available with an interest in racing. (c) The basic mechanical and dynamics modeling has already been done, and made publicly available by the US Department of Transportation, and it has been well validated. (d) There will be a larger market from more knowledgeable users. (e) The necessary common input parameters, such as vehicle, track, shock, and tire data, will be amortized and become more easily available from outside sources.
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