EQUALIZING REAR TIRE LOADS FOR DRAG RACING
by Bill Shope ©2003
NOTE: The following applies to suspended rear wheel drive competition drag race cars without independent rear suspension.
The oval track racer realizes the importance of minimizing load differences between inside and outside tires during cornering. As a result, center of gravity heights are minimized and track widths are maximized. While the drag racer is not going around any corners, he is faced with a similar problem in that the driveshaft torque tends to unload the right rear tire. Should he be concerned about this?
While test data for tires in traction are not as plentiful as those for tires bearing cornering loads, those which exist indicate that the drag racer should definitely be concerned! Maximum traction performance is significantly greater when a tire pair is carrying equal loads. In other words, tires act essentially the same, whether carrying cornering or traction loads.
Rear tire loads can be equalized either statically or dynamically. The static solution is to preload the right rear tire. Or, when the car is not in motion (static), the load carried by the right rear tire will be greater than that carried by the left rear. This is normally accomplished by use of an adjustable coilover at the left front and/or link length adjustments of a 4 link suspension. The preload amount can be adequately measured only with wheel scales. (There will be more on wheel scales later in this same article.) If the preload amount is correct, tire loads will be equal when driveshaft torque is applied. This would be true, of course, for only one value of driveshaft torque. If we have a good idea of the friction coefficient as the tires break loose at launch, we can calculate the needed preload and come pretty close to the perfect solution. Unfortunately, the necessary preload will change from strip-to-strip and with changing strip/lane conditions. While it is certainly possible to achieve fairly good results with a preload, it is not surprising that some have sought a solution using dynamic methods.
With a dynamic solution, the forces and deflections associated with the launch are used to cancel some, or all, of the driveshaft torque effect.
First, consider the reaction to the driveshaft torque. From the position of the driver, the driveshaft is attempting to rotate the rear axle housing counterclockwise. The reaction to this torque, acting at the engine and transmission mounts, is attempting to rotate the rest of the car clockwise. This reaction torque eventually finds its way to the front and rear suspensions. It is distributed, front-to-rear, in proportion to the relative roll stiffness. Or, if all the roll stiffness was contained in the rear suspension, all the reaction torque would be fed back into the rear axle housing via the rear suspension springs. Since this reaction torque is equal in magnitude to the driveshaft torque, the driveshaft torque would be completely canceled and rear tire loading would be equal throughout the launch.
So, we come to the first dynamic solution: Increase the rear roll stiffness and/or decrease the front roll stiffness. In terms of hardware, this means installing as large as practicable an anti-roll bar at the rear and/or removing the same from the front. While this will certainly improve launch performance, it immediately becomes apparent that, since the front roll stiffness cannot be completely eliminated, the rear tire loads cannot be fully equalized.
Another dynamic solution does provide equal rear tire loading and, if properly implemented, is undoubtedly the best solution. This design was first used, not in a drag race car, but, in a competition sports car, Jaguar's early C-Type. It is an asymmetric trailing link suspension. By "asymmetric," I mean that the links are not symmetrically positioned about the car's centerline, when viewed from above. The Jaguar design used two symmetrically positioned lower links and a third link, offset to the right and above. While this is a simplification, you can visualize that third link as being angled down from its axle end and, since it is tension during launch, containing a vertical force component. That downward force, acting to the right of the car's centerline, would tend to cancel the driveshaft torque. And, since it is proportional to the driveshaft torque, it is possible to cancel any value of driveshaft torque. Note that this cancelation is achieved without chassis spring deflection and is, in effect, "instantaneous."
But, there are some drawbacks to this design. Anyone familiar with the fragility of some of the 4 link designs would be reluctant to put the same loads through only 3 links. Also, if the "odd" link is above, as in the Jaguar design, there is a packaging problem. With drag race axle ratios and car dimensions, it would normally be necessary to move the rear mounting positions, for the links, forward and up from the axle. The same canceling effect can be achieved if the odd link is below the symmetrical links. This also solves the packaging problem. Unfortunately, that odd link would have to carry some very heavy loads! Picture that single link supporting a stack of cars, say 4 or 5, and you get an idea of the loads involved. Also, it is important that the link angles remain unchanged during launch. This means the instant center must also be on the no squat/no rise line.
(If the reader is interested in the setup equations for the asymmetric trailing link solution, he is encouraged to read my contribution to the "Student Workbook" for the book, "Race Car Vehicle Dynamics," by Bill and Doug Milliken, available through SAE.)
The last dynamic solution I'll discuss is one which occurred to me only recently. If it were possible, the drag racer would enlist the aid of a giant, invisible thumb to push down the right rear fender during launch. While you're envisioning that, consider what would happen to the rest of the car. The whole car wouldn't go down, of course. In fact, the left front would most likely raise. This "cross-corner" effect is very familiar to the oval racer, but is often not considered by the drag racer. While the drag racer has not encountered any giant, invisible thumbs lately, he is familiar with that which occurs at the front of the car during launch. In short, the front end rises during launch. And, there's nothing that can be done about it. Since there are loads, proportional to the tire traction forces, carried through the rear suspension links, it is possible to adjust the angles of those links so that the rear end either squats, rises, or does neither. But, when it comes to the front end, it will always rise. Some drag racers encourage that front end rise by installing lower rate (softer) front springs.
So, let's review: To cancel the driveshaft torque, we need the car to assume an attitude in which the right rear fender is down and the left front fender is up. The front always rises during launch. The front rises even more when lower rate springs are used. Does it not follow, then, that, if we use a lower rate spring at the left front than at the right front, the car will assume the desired attitude? In fact, there exists a relationship, between left and right spring rates, which will accomplish perfect driveshaft cancelation. The following is the necessary ratio of right to left spring rates:
(ThX + QRL) / (ThX - QRL)
where T= front track, h = center of graviy height, X = axle ratio, Q = ratio of front roll stiffness to total roll stiffness, R = effective radius of rear tires (vertical distance from axle centerline to strip surface after wrinklewall "jumps" on launch), and L = wheelbase.
Except for the "Q," evaluation of this relationship is straightforward. I can't provide much help for a value for your car, other than to say that, typically, most of the roll stiffness is at the front. So, a value of, say, 0.6 would certainly get you in "the ball park." If you're using adjustable coilovers at the front, implementation is very simple and cost is low.
It is important, of course, that you start with equal tire loading. In other words, the car, while awaiting launch, will have equal rear tire loading. Upon launch, the left front fender will jump about half a foot higher than the right front. At the rear, the right rear will be dropping lower than the left rear. The result of these contortions will be essentially equal rear tire loading during launch.
I strongly recommend the use of wheel scales for setup. This is true, whether adjusting for equal tire loading with a dynamic solution or measuring the amount of preload for the static solution. Measuring vertical heights of chassis points might get you close, but it's no substitute for wheel scales.
The single disadvantage of the "unequal spring rate" solution is that cancelation requires motion of the sprung mass. This means there will always be load oscillations around the desired values. But, its dynamic properties, low cost, and ease of implementation certainly warrant its consideration.
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