Geometry plays an important role in racing. From how a driver apexes the corners of a track to how his team sets up the front end suspension of his race car. If you don't know how to use geometry to your advantage then you will not be a successful racer.
The Oxford American Dictionary defines Geometry as follows: "The branch of mathematics concerned with the properties and relations of points, lines, surfaces and solids. And, the relative arrangement of objects and parts." Sounds simple enough to me. So why is working with geometry one of the most difficult aspects of dealing with a race car?
If a race car remained in a static position then it would be simple to calculate the front-end geometry because nothing would move and the "points and lines" of the car's suspension would not change.
But, as we know, that is not the case. In a race car we deal with all sorts of moving triangles, parallelograms and trapezoids in the suspension system. Each time one of these "points or lines" moves [or is moved] then their "properties or relationships" to each other change. If you change just one "point" in the equation then you change the relationship of all of the others. That turns a simple geometric equation into a complex calculation that can drive setup specialists and drivers crazy if it is not done correctly. I always found it difficult to calculate the angle of the dangle against the swerve of the curve but today's teams have computers and programs to help them do it.
To better understand the complexities of setting up a car's front-end geometry you need to first understand the goal of the setup specialist. His goal is to keep the "tire patch" [the surface of the tire that contacts the track] and the "slip angle" of the tire [the point at which a tire will lose grip and slide across the track] constant and controlled so the driver will be comfortable and confident when he dives into a corner at high speeds.
The variables in this equation are infinite. The positions of the various "pick-up points" in the suspension are critical to achieving the goal of maintaining a constant tire patch and slip angle but so are how a particular driver drives his race car, the type of track he is racing on, the surface of that track, the line or lines that he takes going into and exiting the corners, the type of tire being used, the air pressures in that tire, the braking style of that driver, the car's horsepower, the steering ratio being used and the list goes on and on.
There is an old racing saying that "the simplest adjustment to a race car is the forceful application of a very large wrench to the northern most point of a driver's body." However, as time passed, drivers got smarter and started leaving their helmets on after exiting their cars so the crew chiefs were forced to apply said wrench to the car more to achieve their goals. [There is another old saying that the perfect driver wears a size 14 shoe and a size two helmet but we will explore that theory on another day].
If you were dealing with perfectly vertical and horizontal planes then calculating the interacting geometry of those planes would be relatively simple. But, we are not.
Let's take a simple example of a vertical plane -- the race car's right front tire and wheel -- and connect them to a horizontal plane -- the chassis of the race car. If the relationship between those two planes stayed constant (of equal distance) then things would be easy. But we discover that if we keep the tire and wheel perfectly vertical then the tire will not maintain a constant tire patch as it rolls in and the degree of slip angle will increase as inertial forces and lateral loads are applied.
However, if we lean the top of the tire and wheel in toward the centerline of the car [negative camber] then we can gain a more constant tire patch and a more forgiving slip angle to the tire. We have converted a parallelogram into a trapezoid.
If you draw a vertical line representing the tire and wheel and then draw two parallel lines of equal distance attached to it that represent the upper and lower pick-up points known as A-frames or control arms and you move the vertical line up or down, the two parallel lines will move parallel in concert.
If, however, you want to lean the tire and wheel in toward the centerline of the car and therefore shorten that upper line to achieve it, then the upper line will now move in a tighter arc than the lower arc and you will gain more negative camber when the tire and wheel are moved upwards by the compression of the suspension when the car dives into the corner and turns left.
And, by the way, when you moved the upper part of the tire inward you pushed the bottom of the tire out so now your front and rear tires are not tracking on the same line, which causes other problems that you must correct. You can do that by moving the entire front-end suspension inward so the bottom of the front tire will now be back in line with the rear tire.
Think of a car driving through the snow and how, when it is driven in a straight line, you see only two tire paths [left and right] instead of four. You do not want four lines because that will bind the car up and slow it down.
When you shortened the upper link of the tire and wheel connection [tighter arc] to the frame you brought "bump steer" into the equation. Congratulations! You just created another problem for yourself! You want the driver to control the amount the car turns into the corner versus the suspension doing it. Now you have to go back and figure out how to get rid of that nasty bump steer that the driver is whining about when he turns into the corner and the sudden [and unwanted] added horizontal movement or darting of the nose scares him.
A driver prefers that his car will obediently go where he aims it and not dart around unexpectedly so this is usually the point where his voice becomes very thin and high-pitched and he begins discussing your ancestry on the radio. I would like to take this moment to defend all crew chiefs who I have known. None, who I have known over the years, were either bastard children or had an Oedipus complex.
So, now that you have created unwanted "bump steer" what are you going to do about it? Well, you could just debate your ancestry with your driver or take the easier route and begin working with and manipulating the caster, camber, toe, Ackerman, etc. of the front end until you achieve neutral bump steer and a happier driver. To do that you must sit down and determine all of the factors [some were listed above] that will impact the equation.
Once you have a game plan you need to determine exactly how you will achieve it. It is important to note that there can be more than one plan that will work but that plan must be consistent throughout. For example, you can have aggressive setups or passive setups. An aggressive setup would have stiffer springs and smaller arcs of travel in the suspension whereas a more passive setup would have softer springs that would allow more travel in the suspension and therefore larger arcs for the components. The geometry would be dramatically different between the two setups. A stiffer setup can be faster but is also less forgiving than a softer setup so the driver's talent and experience must be taken into consideration when choosing your setup.
Below are some definitions of the basic elements involved in front-end geometry.
Camber is the relationship of the tire and wheel to vertical. If the top of the tire leans into the centerline of the car then that is called negative camber. If the top leans away from the centerline then that is called positive camber.
Sprint Cup cars usually will run about five degrees of negative camber in the right front and maybe one to two degrees of positive camber on the left front on oval tracks. This helps to compensate and offset for the body roll when the car goes into the corner at high speed and leans toward the outside wall.
You want the camber to be enough to keep the tire patch in constant contact with the track in the corners but not so much that it disproportionately wears the inside of the tread off the right front tire [outside tread on the left] when the car is going straight. Logic would therefore tell you that you can run more camber on shorter tracks with shorter straights than on bigger tracks with longer straights.
The amount of the banking will also influence how much camber you want to run. Flatter tracks require more camber than higher banked tracks because there is more lateral loading of the tire tread on a flatter track. Tire temperature readings across the surface of the tire will tell the setup specialist when he has achieved the correct balance.
Caster is an important component of the front-end setup. Caster is the relationship of the upper and lower pick-up points to vertical but in the opposite direction of camber.
If you manipulate camber east to west then you would manipulate caster north to south. If you move the upper pick-up point forward of the vertical centerline that runs through the two points where the tire, wheel and spindle attach to the arms extending from the frame then you are creating positive caster. Move it back and you create negative caster.
So why is it important? Positive caster helps to minimize or redirect the dive [compression] when the car is turned and goes into the corner.
On an oval track, positive caster on the right and negative caster on the left will also help the car turn through the corner by having the right tire and wheel "reach" forward while the left tire and wheel will pull back. This is because the inside tire and wheel are traveling on a tighter radius than the outside tire and wheel so you want it to turn more than the outside tire and wheel to avoid scuffing it across the track surface.
When you drive your street car in a straight line and let go of the wheel then it will continue in a straight line [or it should[ because the caster is more neutral in your street car's front end. Oval track race cars will go in a circle if you let go of the steering wheel because of the positive caster set into the outside wheel. Oval track race cars are set up to turn left automatically. You have to steer them with the steering wheel and throttle to go straight.
Drag cars, by comparison, will run an excessive amount of positive caster on both sides to help the driver to steer the car in a straight line during a drag run.
Toe is fairly simple. It is the relationship to parallel of the front tires. Most street cars will be slightly toed in [along with caster] to help them go straight when you let go of the steering wheel. Race cars are slightly toed out to help the car turn into and through the corner. It is the same principle as caster. The inside tire and wheel is making a tighter arc through the corner so toeing the left front tire and wheel out helps the car to turn more easily.
Ackerman works in concert with the caster and toe to determine how much more or less the left tire and wheel turns into a corner in relationship to the right tire and wheel when steering is applied.
Stock cars generally have neutral Ackerman. Some open-wheel race cars will have positive Ackerman built into their front-end geometry but stock cars usually will not. If you string lines through the steering points and the lower pick-up points of the control arms on each side toward the rear of the car and they cross in an "X" pattern in front of the centerline of the rear axle then you have positive Ackerman built into your steering system. If they cross behind the centerline of the rear axle then you have negative Ackerman. If they meet dead center over the rear axle then you have neutral Ackerman.
It all sounds simple doesn't it? Just keep in mind that I have only covered the more basic elements that relate to front-end geometry. There are many other factors that can and will influence the geometric setup.
Things like the rake and tilt of the car, wedge, roll center, rear axle alignment, shocks and springs, tire compounds and air pressures (among others) and, finally, there is one very important element that all crew chiefs must deal with. It is called the NASCAR Rule Book.
There is not a lot of humor to be found in that book. In fact, I am sure you can find some tear-stained copies lying around Sprint Cup shops. Part of the current battle that is now being waged between the teams and NASCAR over the new "Sprint Cup" car concern new do's and don'ts relating to front-end geometry. If we could only go back to the good old days when the forceful application of a very large wrench could solve most of a crew chief's problems ...
Bill Borden is a former championship winning crew chief who operated David Pearson's Racing School for many years.