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Page 45
DEFINING THE INSTANT CENTER LOCATION

Dragracers commonly refer to their rear suspension instant center location as being so many inches forward of the rear axle centerline and so many inches up from the track surface. There's nothing wrong with this, of course. Many experienced racers are so comfortable with this means of location that they can accurately predict the performance change from small changes in "forward" and "up" dimensions. If this system is to be faulted, it is because it serves as an obstruction to the understanding of the dynamics of the rear suspension. There is another means of specifying the instant center location which more closely defines the car's launch performance and...at the same time...can be more readily associated with the suspension's configuration.

Before the launch, loads on the rear suspension links are balanced. That is to say, vertical loading up is the same as vertical loading down, forward is the same as rearward, and there is no net moment (torque) acting on the car. If this were not the case, the car would be moving. This is called "static" equilibrium. That with which we need to concern ourselves is the loading which occurs as the car is launched. This loading...involving only the additional forces which cause the car to accelerate forward...is the "dynamic" loading. The dynamic loading must also be balanced. For instance, the forward force...acting at the rear tire patches...is exactly equal to the inertial force acting rearward at the car's center of gravity. And, the moment resulting from these two forces is exactly cancelled by the moment which causes the weight transfer to the rear.

With a single link with freely rotatable pivots, it's clear to see that a force balance can be achieved only if equal and opposite forces are acting on a line which passes through the two pivots. A torque simply cannot be applied at the pivots. The link, then, either experiences a pure tension or compression from the dynamic fores during the launch.

If, however, the link is not straight, it is possible to introduce a moment into the link, but the forces remain equal in magnitude and opposite in sense and continue to act on a line through the pivots.

This configuration amounts to the same thing as the curved link. It has more components, but, like the curved link, it is rigid and carries loads in exactly the same way.

Does it remind you of something? How about a ladder bar car? Think of the pivot near the letter "A" as the rear tire patch and the pivot near "B" as the front attachment point of the ladder. The entire rear axle assembly and associated ladder can be considered to be one large, rigid link. The force acting along the line A-B has a horizontal componet which is accelerating the car forward and a vertical component which is the weight transfer (plus or minus that portion of the weight transfer which is carried through the suspension springs.) More on this later.

The link angles shown in the above illustration are arbitrary. I could have chosen any two of the links...in the illustration to the right...and the effect would have been exactly the same. So, the frequently seen question in the forums, "Should my ladder bar be horizontal?", is a question that obviously cannot be answered. The ladder bar can be at any angle.

Note, also, that, since the force is going to act along the line A-B, the point on the line at which all those links are pointing could be any one of an infinite number of points on the line.

You might have expected this illustration. If the preceding could be interpreted as a schematic of a ladder bar car, this, then, would be a 4link (or 3link) schematic. The triangular plate represents the remainder of the car. I show that which appears to be a pivot near "B," but this would, of course, be merely that point in space (the instant center) defined by the intersection of the two link lines. The instant center...with the rear tire patch...continues to define the line of action of the force resultant at the rear tire patch.

More needs to be said about the line A-B. It has been stated that the couple created by the horizontal force pushing the car forward...acting at the tire patch...and the horizontal inertia force...equal in magnitude, opposite in sense (direction), and acting at the height of the center of gravity...is cancelled by a couple which results in the weight transfer. In other words, the product of the forward force at the tire patch and the center of gravity height is equal to the product of the weight transfer and the wheelbase.

A line A-B which has a tangent (slope) equal to the center of gravity height divided by the wheelbase is particularly significant. To understand this, consider the case where the line A-B intersects the intersection of two other lines: one a vertical line through the front tire patch and the other a horizontal line through the center of gravity. Since the tire patch force can be considered to act anywhere along its line of action, we'll move it to this point directly above the front tire patch. It can then be seen that the horizontal forces and vertical forces are simultaneously cancelled WITHOUT the creation of a moment.

If the line A-B crosses the vertical line through the front tire patch BELOW the height of the center of gravity, a moment is formed which tends to rotate the rear of the car downward during launch. If, on the other hand, the line passes ABOVE, there is a tendency to rotate the rear of the car upward. These are the reasons, then, for squat or rise during launch.

Here's another way of looking at it: If the line A-B passes through the vertical line at the center of gravity height, 100% of the weight transfer is being carried through the suspension linkage and NONE is being carried through the rear suspension springs. This is why the car neither squats nor rises. This is why, also, that particular A-B line is called the "100% antisquat" line. (Yes, I suppose it could have been called the "100% antiRISE" line, but it wasn't.) Those A-B lines with lesser tangents (slopes) have antisquat values less than 100% and, of course, those with greater, more than 100%. To determine the percent antisquat, the ratio of the A-B tangent is divided by the ratio of the center of gravity height to the wheelbase and the result is then multiplied by 100.

I've added some more lines of constant percent antisquat. It's obvious that, if I had changed the link angles, I could have placed the instant center on any one of these lines. Suppose I had wanted to move the instant center from the line A-B to the line directly above it. (This would be going in the direction of more "hit" or "separation.") It should be obvious that there exists an infinite number of paths from the point to the line above. One could, for instance, move the point either directly up or directly to the left. Or, the point could be moved to the left until its above the line and then dropped to the line. Or, it could be moved to the left, but short of the line, and then moved upward. Another infinity of paths exist which involve moving the point forward.

So, how can these experienced racers predict the launch performance change with a change in instant center location forward and/or up? Do they have this map of antisquat lines memorized? No, of course not. They have simplified the adjustment procedure by keeping the lower link of a 4link horizontal (or nearly so). With the adjustment limited to angle changes of the upper link, the problem of moving to the line directly above is greatly simplified. The only way to get there is to increase the downward angle of the upper link.

Unfortunately, this adjustment simplification has some bad side effects. Not only does it complicate the development of an understanding of the suspension dynamics, it also reduces the utilization of all that the 4link adjustability can provide. Rather than rely on "distance forward" and "distance up" measurements, I would encourage you to invest in 4link software (or use the free spreadsheet available on this site) and determine the full capabilities of your adjustment options IN TERMS OF PERCENT ANTISQUAT. In other words, select a value of percent antisquat (I recommend 100% for dragracing) and then determine...with the 4link software...which adjustment hole combination gets you closest to the percent antisquat value you've selected.

(I must warn that there exists at least one 4link software package that calculates 100% based on a line passing through the center of gravity. This makes no sense dynamically and is certainly not used in the automotive industry. If you already have 4link software, be certain that the 100% line is as defined in an earlier paragraph.)