UPDATE -- Computers in Racing
Chapter in Race Car Engineering and Mechanics

(See index at http://www.pvanvalkenburgh.com/Race Car Tec/engineer.html


The use of computers in the production of race car hardware is commonplace among the major designers. However, there may be some confusion in the proper terminology, between the acronyms of CAD, CAM, CAE, CNC, CFD, and FEM. Computer Aided Design (CAD) implies using a terminal to work out the geometries and relationships of individual components, as a draftsman would with pencil and paper. CAM can mean either Computer Aided Manufacturing (production components), or Computer Aided Machining, which takes these digitally-defined dimensions and uses them to automatically form the components. More recently, this is called CNC, for Computerized Numerical Control. But since few readers of this book have such facilities, this section will concentrate on the more useful application of strength analysis, using Finite Element Modeling or Analysis (FEM or FEA), and Computerized Flow Dynamics (CFD) which is a developing substitute for the wind tunnel or flow bench. Actually, all the above techniques, as well as vehicle dynamics modeling from the previous section, may be lumped under Computer Aided Engineering (CAE). So much for the alphabet soup.

As engineering software has evolved into comprehensive packages, the root function seems to be "solid modeling." That is, before any kind of development can be done, the first item of business is to get a numerical 3-D model of the object -- whether a bracket or a complete chassis -- into the computer. Once that is done, many analysis operations can be performed on it. FEM can be used to determine its strength, once boundary conditions are defined, such as space and geometry limitations, material properties, and all load inputs. In fact, there are even automatic optimization routines which can identify weak areas, reconfigure the design, and rerun the analysis, the same as an engineer would. If airflow is involved, say it's an intake manifold, CFD may be available to study different flow path designs. If it's a moving mechanism such as steering components, a combination of parts may be joined and then animated, to see what interferences may exist. If high temperatures are involved, as in header pipes, a thermal analysis can show how that heat is transferred and dissipated. Then, as the design is finalized, cumulative tolerance checks can be run automatically before having components fabricated. The final digital model can then be sent directly to a CNC machine such as an automatic mill or lathe -- or even the latest rapid prototyping methods of stereolithographic production, or the laser-generation of models layer-by-layer out of fluid materials.

The Theory of FEA

Finite element analysis is simply a mathematical technique of doing strength analysis with a computer. Before computers, it could take engineering man-years to perform such an analysis on aircraft or automobiles -- and the results were very often questionable. Now software packages are available which can reduce the process to a matter of days. Even relatively inexperienced engineers can learn such systems, although a basic course in structural analysis is highly desirable first.

There is nothing magical about the mathematics; it is just a matter of degree. Even without a computer, a good structural engineer can estimate the location of the worst stresses and easily calculate the worst loads. From there he can work down through less and less critical areas. But a computer can just as easily go to extremes of refinement, breaking a structure into hundreds of thousands of "elements," as shown in the computer-generated drawing of Fig 53. In this way it is possible to optimize the strength-to-weight ratio so that no area is either unnecessarily weak or unnecessarily heavy. The process is independent of the type of material or the type of structure. It could be used on a balsa monocoque or a spaghetti-tube frame. With that introduction, let's consider the actual procedure, using the parent program "NASTRAN" (NASA Structural Analysis) as an example.

First you have to define the necessary shape, and certain locating points such as the suspension and engine mounts. You have to provide space for the driver and fuel and a hundred other bits. This is as far as most people get in their consideration of chassis design. But for computer analysis, all of this information must be represented by numbers, and not drawings. Every point must be defined by three-dimensional co-ordinates, which in some cases means locating thousands of three-digit dimensions.

For each point, the computer needs to know what material properties apply. In the case of a sheet metal monocoque, this is relatively simple, because the material will have uniform thickness and symmetrical properties. With fiberglass or graphite composites, however, both the thickness and the direction of maximum stiffness are infinitely variable (as discussed in chapter 10). This is a structural advantage but an analytical nightmare.

The Input Process

This is the tedious part. If manpower is cheap, you can sit down at any computer keyboard and type in those thousands of numbers -- and just hope you didn't make an error. The use of "interactive graphics" however, makes the job faster and more fun -- and less expensive in computer time. Using a video terminal, you can begin by just locating a few overall critical points, and then use stored computer logic to provide more detail. With simple commands, and/or a digitizing tablet, you can identify a point or line; redraw a hand sketch; duplicate, enlarge, or rotate any element; and call up stored shapes. You can define a surface by four points and then "mesh it," or break it down into any number of sub-elements. And if your chassis is symmetrical, you can just create one-half and then double it. The finished image is then automatically digitized, or converted into the necessary data points. Alternatively, if a real model or prototype has already been constructed, a 3-D digitizer can scan the necessary surface points, using either a laser or an electronically located mechanical arm.

The most comprehensive FEA programs can run any conceivable stress test on the structure: static or dynamic, linear or non-linear, impact or fatigue. Dynamic tests are primarily for vibration frequency analysis; non-linear tests are for investigation of structures as they yield; fatigue is not usually a problem in the short life of a race car; and thermal or aerodynamic studies don't apply to the tub. So for our purposes (race cars) the simplest test is adequate--and expensive enough. A simple static torsion test is not only the most appropriate for a race car, but it is the easiest to verify in the finished product--and to compare to previous empirical designs.

At some point it's necessary to make an educated guess as to what loads will be encountered and what stiffness is required. It is commonly assumed that a chassis which is torsionally stiff enough will be adequate in beaming. It also used to be assumed that 3,000 foot-pounds per degree of stiffness provided a rigid enough chassis for the suspension springs and anti-roll bars to balance the handling. With the incredible aerodynamic loads now seen, it's hard to say what is adequate, but the best Formula One cars are probably over 40,000 foot-pounds per degree. The scientific way to determine the loads would be to instrument a car for vertical, longitudinal, and lateral g loads, and get a recording of the conditions at every track in the series. This would provide not only stiffness requirements, but peak bump loads and bump amplitude/frequency plots for fatigue analysis.

Understanding the Output

There are just as many options for the form in which the computed answers are presented. The simplest would be just one figure for stiffness in foot-pounds per degree, or perhaps a plot of stiffness down the length of the chassis. But to get such a number, stresses and deflections must be calculated for every segment, and so all those numbers may be printed out regardless. Naturally it is difficult to comprehend reams of computer paper crawling with numbers, so it may be condensed by requesting only those stresses above some acceptable limit. Another option is a computer-generated drawing of the structure in its unloaded state, over-laid with an exaggerated drawing of its shape in a stress-deformed configuration, showing exactly what is bending where. Finally, stress contour maps may be drawn in color over all the surfaces, giving a vivid visual representation of high stress concentrations. These are almost equivalent to layout drawings for locating extra layers of reinforcement material.

Ideally, a designer could keep modifying the structure, changing the location and thickness of panels until all stresses were equal at the limit. This would give the ultimate optimum strength-to-weight ratio. However, this assumes that the real world loading conditions are accurately known, and that there is only one worst case. In fact, there are unanticipated situations which must be allowed for, like an off-course excursion, or combinations of load such as hitting the brakes and a bump at the same time. When you get right down to it, it's hard to even make a subjective decision: What kind of safety factor does one select? 1.5?...2.5?...ten? But given a complete historical survey of what the vehicle should encounter, and leaving the consequences of deviation up to the driver, continual redesign and rerunning is certainly better than experienced guessing.


Even in Formula One, there is a limit. In the most efficient design and development operation, all possible approaches are compared in terms of cost/benefit ratio. Rumor has it, that in the aerospace business, weight reduction is effective at $100,000 per pound. Even in mass-production automobiles the figure might be about the same, spreading the cost over 100,000 cars. In fact, the auto industry has found finite element analysis to be more cost effective than exotic materials for weight savings so far. After they get the design optimized, then they will start using more aluminum and composites. For just a few Formula cars, however, the cost/benefit ratio may be more like ten thousand dollars per pound.

The actual costs of running a finite element analysis are a little hard to predict, given all the unknowns and the potential complexity. Most teams probably don't even know what it costs to analyze their cars, but we can use one early model as an extreme example for estimation of a professional analysis. The structure was broken down into about 800 elements. Based on computer time and man-hour costs, just the input or setup time would take about two weeks and cost roughly $3,000. From then on, each computer run on each configuration change might be about $500, the number of runs depending on the brilliance of the first layout and the final refinement desired. So the total computer development time could have cost less than $10,000. The weight saving due to graphite fibers was said to be 35% less than an aluminum tub, but how much can be credited to the computer is unknown. However, if we estimate the tub to be around 50 pounds, and the finite element analysis reduced the weight by 10%, that is 5 pounds at $2,000 per pound--which is certainly within reason.

On the other hand, assuming you already have a decent PC, a slightly less ambitious analysis can be done in your spare time for a fraction of the cost. Simplified versions of NASTRAN currently sell for a few thousand dollars, and with them, you can make as many runs as your spare time and deadlines allow. Even if you had to buy a more powerful PC, the extra few grand or so would be easily amortized over a lot of other applications.

The cost/benefit tradeoff is always hard to pin down. If you expect to be doing structural optimization on a lot of race cars, then the equipment and experience will definitely pay off in the long run. But for a few applications, the best value might be hiring out the analysis, or merely making a few simplified calculations on a pocket computer. Or, as is usually the case, relying on intuition.

In any case, the process is not bulletproof. Those who have done FEA a few times recommend experienced specialists who can save a lot of time, money, and mistakes. While the designer can't keep up with the latest in computer technology, neither can the programmer be aware of all the race car design requirements. It takes a combination of talents with expertise in many areas to make it all come together. But with the success of existing examples, the availability of computers, and the weight and safety advantages of finite element analysis, we are going to be seeing a lot more efficient chassis on the track -- whether we know it or not.


To my knowledge, the first computerized structural analysis of a complete race car chassis was the McLaren MP4B Formula One chassis, which was the most sophisticated race car chassis of its time. Perhaps it was supposed to be a secret, and perhaps they just took it for granted, but the first hint was a computer-generated structural drawing which appeared in a press kit at the 1982 Long Beach Grand Prix (See Fig. 54). Since McLaren's success rate that season was largely due to the team and their selection of drivers, the basic tub never did get appropriate recognition. Ordinarily the chassis is hidden beneath body panels, and the team has no reason to make an issue of it -- especially if it is part of the secret of their success.

McLaren had asked Hercules Aerospace of Salt Lake City, one of the largest graphite fiber producers in America, to produce the first one-piece true monocoque structures ever seen in racing. So naturally when Hercules took the job, they decided to use the standard aerospace technique of finite element analysis to optimize the design. Eventually Hercules admitted that the original hand-calculated design by McLaren's John Barnard was intuitively "pretty close," but this was still a dramatic first application.

At the time of this writing, FEA had even reached NASCAR, the last bastion of intuitive race car design. Factory assisted efforts from Chevrolet and Ford were being quietly used to improve the torsional strength-to-weight ratio of Winston Cup cars -- but of course that information is never generally available to privateer racers or constructors. However, a strong racing-oriented engineering program under Harry Law at Clemson University produced a number of valuable publicly available SAE papers (See numbers 983051, -53, and -54), that demonstrated what FEA could contribute. Graduate level students used it, with carefully measured dimensions from some familiar chassis, to establish that the baseline torsional rigidity was about 10,000 foot-pounds per degree. They then ran dozens of cases in which they added or strengthened structure to see what the relative effects were.

The analysis easily showed that the weakest areas were at the cowl and the un-triangulated engine bay. Eventually, repeated computer runs brought the rigidity up to about 23,000 foot-pounds per degree, a number that was felt adequate in maintaining the desired suspension dynamics. Being realistic, they also analyzed the engineering tradeoffs in terms of added weight and CG height. The final configuration was plus 40 pounds and a 1/2-inch higher CG, numbers which could be related to laptimes through the use of a racetrack simulation. However, it appears these handicaps could have been minimized by utilizing just the most cost-effective structural modifications. Finally, to verify the FEA, other students constructed a precise torsional test rig -- also to resolve the precision and repeatability of testing. After running a number of different chassis, their figures indicated that some common chassis were less than 60 percent as stiff as the original baseline chassis in this study.

How To

Computerized structural analysis of race car chassis and components is not totally out of reach of non-factory teams. Software companies do not ignore any market for their products, scaling down their more omnipotent programs to fit lesser budgets and computers. Granted, you still need a basic background (at least a first engineering course in structural analysis) to be able to understand the simplest programs. And if you don't spend more than a few weeks per year in structural design, the familiarization time required will never pay off. So instead of duplicating standard textbook explanations of FEM programs, I will briefly mention how to select and use them with respect to race cars.

Cost and compatibility with your existing hardware may be of first importance to the non-professional non-commercial user, although an engineering professor once told me the most effective strategy for a department of five or more engineers would be to fire one engineer and buy the best software package. At the time of this writing, apparently the most popular and most powerful package was I-DEAS (Integrated Design Engineering Analysis Software), which with all added modules could be in the $50,000 range. Other packages that should be investigated include CATIA (more design and surfaces oriented), Unigraphics (more manufacturing oriented), ProEngineer, and Autocad. The FEA techniques they use may be based on NASTRAN, ANSYS, ABAQUS (primarily non-linear), and STRUDL (civil structures). Although an adequate full-bore program could be in the $5-10,000 range, simplistic training programs are as little as a few hundred. A good mid-range compromise is currently the MacNeal-Schwendler version of NASTRAN, which runs on a PC with enough accessories. This will be adequate for most racers, when selection is based on the following capability considerations:

Types of analysis include statics and dynamics, 2D or 3D, and heat transfer, which is hardly critical in race car structures.

Variety of components that can be modeled includes plates (panels), beams (including tapered beams), and shafts. One small drawback in some scaled-down program is that they only accept point loads. That is, aerodynamic or gravity loads cannot be distributed over a surface, but must be reduced to point loads at nodes or analysis intersections.

Graphics capabilities can include input visualization, zoom/rotation/pan of the image, overlaying of the strain-deformed image, and animation of the image in dynamic analysis. Other features not usually available in these lower cost programs are automatic generation of meshes, or panel breakdowns, and automatic input data error checking.

Output variations beyond graphics include transfer capability to larger computers for more detailed analysis -- a strong point for a NASTRAN-compatible program. And of course there may be CNC-compatible output, which is irrelevant unless CNC machinery is available, even on a contract basis.

Ease of use may be a key question for occasional users. Procedures and commands are easily forgotten without interactive input, or automatic prompting. To reduce memory requirements, some packages have minimal prompting. For initial familiarization, a good interactive package might take a few days to learn, while a poor non-interactive program might take few weeks. But then as procedures become familiar, the repetitive prompting isn't there to slow down the process.

The last consideration might be speed and capacity. At worst, a maximum capacity analysis on a PC might take overnight -- which is human downtime anyhow. But that may still allow a structure with thousands of nodes (the original McLaren example was about 600 nodes). It's simply a matter of learning to live with limitations, by first analyzing with a "broad brush" and then focusing in on critical areas with increased element densities.

As problems are simplified to accommodate smaller computers, accuracy of results may begin to suffer somewhat. Considering that real-world race car loads are only approximated anyhow, errors are probably not significant. But this points out that FEA's greater value is in showing relative effects rather than absolute values. That is, it is better to run a computer analysis on a known, existing chassis (perhaps comparing output to real test results), and then make simulated changes in the chassis, such as thinner material sections, to study the change in performance. In other words, what is the predicted tradeoff in reduced weight versus reduced stiffness?

In the near future, expect to be able to lease software just as needed from application service providers, and to be able to run analyses at home via the Internet. Massively parallel processing will soon make analyses a thousand time faster, and a hundred times more efficient. But in the fast-changing world of software, no book can be up to date. The only way to get the latest information on FEA products is from monthlies such as Mechanical Engineering, Machine Design, SAE Journal, and your own specific PC magazine.