The following is the result of a post in a dragracing forum in which the poster questioned the definition of the 100% antisquat line. Specifically, he felt that the location of the 100% antisquat line should not be affected by a change in wheelbase, so long as the center of gravity remained in the same location.
I attempted to explain the situation, but quickly realized that I would have to resort to free body diagrams.
(If you have gone through the "Getting Started" section on the home page of this site, you're already familiar with use of the free body diagram in the analysis of dynamic forces.)
The following diagrams illustrate that a change in wheelbase does require a repositioning of a line of constant percent antisquat, even though the center of gravity location is unchanged.
Above, we have a nice symmetrical car accelerating, to the right, at 2 Gs. Statically, there were 1500 pounds on the rear tires. An extra 1200 is transferred during acceleration. Note that there is a horizontal force balance and a vertical force balance. There is also a moment balance. If you take the moments about the rear tire patch, with counterclockwise moments positive, 20(6000) + 100(1500) - 100(1200) - 50(3000) = zero.
In the diagram above, the wheelbase has been increased from 100 inches to 600 inches. Somehow, the original weight has been retained and the center of gravity location...relative to the rear wheels...is unchanged. Initially, there are 2750 pounds on the rear wheels, with an additional 200 pounds added during acceleration. Again, vertical and horizontal forces are balanced. As for the moment balance, 20(6000) + 600(250) - 600(200) - 50(3000) = zero.
This last image shows the forces on the rear axle assembly of the 600 inch wheelbase car during launch.
I will assume that the car was initially set up for 100% antisquat. That is, when the wheelbase was 100 inches, all the weight transfer was carried through the links and there was neither separation nor squat. This would mean the slope of the line representing the line of action of the force acting at the rear tire patch would have a value of 20 (the center of gravity height) divided by 100 (the wheelbase). This would explain the 1200 pounds of vertical force acting at the instant center.
Since the instant center can be located anywhere along the line of constant percent antisquat, I have arbitrarily placed it 40 out and 8 up. For a moment balance, 8(6000) - 40(1200) = zero. The 2750 and 200 pound vertical loads are acting at the tire patch as in the previous picture. The additional 2750 pounds, with opposite sense, represents the static load being carried through the suspension springs.
Now, what about that extra 1000 pounds? Note that it's essential for a vertical force balance, but what is its source? It develops because the rear of the car has been elevated, causing a force reversal in the suspension springs.
This is separation, which means that the car is no longer at 100% antisquat.
That force...and the separation involved...can only be eliminated by placing the instant center on the new 100% antisquat line. This line has a slope of 20 divided by 600. This reduces the vertical component from 1200 pounds to 200 and that extra force from the springs is no longer needed.
Some of you might have noticed that I have ignored the inertial force resulting from the mass of the rear axle assembly. With production sedans, the axle weight is a relatively small part of the total weight, so automotive suspension reference books often ignore its effect. In a light weight race car, however, there is greater justification for including it. If you wish to do so, the following equation includes the effect of axle weight and defines a line of constant percent antisquat:
Y = (P/100)(HM + mr)/(LM)X - (mr)/M where:
- P = percent antisquat
- H = center of gravity height
- M = total car weight less axle assembly weight
- m = axle assembly weight
- r = rear tire radius
- L = wheelbase
- X and Y are horizontal and vertical distance components as measured positive forward and up from the rear tire patch