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Constrained testing in traction

Constrained testing in traction

Constrained testing in traction

Constrained testing has been used, for many years, to conveniently obtain cornering performance data. (See Chapter 8 of Race Car Vehicle Dynamics). The concept of replacing an inertial force with a static force is even older, of course. But, to my knowledge, constrained testing has not been done to evaluate rear tire loading of a live axle car during acceleration. The following is the basis for a presentation which I'll be making, Lord willing, at the Motorsports Conference later this year. Your comments will help me prepare for those I will receive at that time.

So, the concept is very simple: Replace the inertial force generated during acceleration with a static force. This reduces to simply pulling, in a negative X direction, with a chain or cable. But, of course, the force must be resisted. In other words, the engine must be restrained from rotation. This can be accomplished by any one of a number of means. A driveshaft torque is then generated and that brings us to the reason for the procedure. The reaction to the driveshaft torque which acts on the pinion gear is absorbed by the chassis through the engine and transmission mounts. It is then distributed, front-to-rear, in proportion to the relative roll stiffness. And, at this point, some of you are probably already aware of the possibilities.

Suppose a chain is attached, in the XZ plane and at the CG height, to a car and then further suppose that the chain is extended horizontally out the rear, where it is attached to a "come-along" and then to a stout post. With a couple of transmission gears engaged to prevent engine rotation, the chain tension is then increased. The loading is then the same as when the car is accelerating. (Well, not exactly, for there's the matter of unsprung mass, but there's a "work-around" for that.)

Next, suppose that the aforementioned car's front wheels are supported by wheel scales. It is then possible to measure the left-to-right front tire load differential necessary to overcome the driveshaft torque reaction at any given chain tension. With measurements at 3 or 4 levels of tension, nonlinearities can be determined.

Okay, what can we get out of all this? With a little calculation, we can determine the load removed from the front wheels (what the drag racers call "weight transfer") and, with a bit more effort, we can calculate the driveshaft torque. Since we can measure the torque absorbed by the front suspension, we can then calculate the roll stiffness distribution. That's probably of more interest to most of you than the primary reason for my development of this procedure.

My primary interest was to validate my efforts to achieve equal tire loading with an asymmetrical suspension. With the proper asymmetric setup, the front wheel loads will remain equal (assuming they were equal originally) as the chain is tensioned. And that means, of course, that the rear tires are also equally loaded. I intend to have data, at the Conference, to indicate the effectiveness of such a setup. Non-dynamic means of load equalization -- such as preloads -- could also be studied.

Incidentally, you don't need to have a sturdy post available. A device could be fabricated, having an appearance similar to that of an engine hoist, which would react on the underside of the axle housing and on the shop floor ahead of the axle. Compression links could react against "levers" replacing the rear wheels and extending downward while a hydraulic chain tensioner would replace the come-along and sturdy post. This would allow leveling of the car with any height of front wheel scales.

Braking reactions could also be measured by reversing the chain force.

So, what are your comments?

RE: Constrained testing in traction

Hi Billy
My name is Richard Malmlöf, i live in northern Sweden.
I compete in something called "RallyCross".
It´s an arenasport with gravel and asphalt, the course is 1km long and we drive for 3 laps clockwise.
Its a standing start with 6 cars in a row(so the launch is crucial for the outcome)
I have been looking for an some improvement to my car, and I found your article on racingarticles regarding a 3 link with offset to the right. It´s currently a basic 4-link
This theory seems to me like a very good concept especially for my applikation were I could benefit at the launch and the curves to the right.
I recently bought RCVD but to my dissapointment the student workbook which you mentioned didn´t accompany the book.
How can I get the formulas to calculate the offset, or is this something you could help me with?(I´m no king with maths)
The gearing in the rearend is 5:43 and the links are 22.8" long, the lower links I would like to have horisontal to get near zero rear steer.
The track width is 59", wheelbase 100"
I would be very thankful for any reply´s regarding this matter cause you seem to have the knowledge and idea´s.
I recently got myself a scale for wheel loads, so I could try the pull test. I have a tree standing in front of my garage so I could just winch a load and measure the front wheels.
My own idea wold be a 18" long upper link with 10dgr angle,
4" offset to the right from the center.
Sorry for any bad spelling or wrong technical terms.
Any other reply´s to this matter would be greatly appriciated
Best regards

RE: Constrained testing in traction

Richard, sounds like an entertaining form of motorsports.

Before giving the setup equation for a 3link, I must warn you of something I failed to mention in the racingarticles.com description. The loads carried, by the links and housing, in an asymmetric suspension, are quite large. As I type this, I realize that you're not going to be using the very "sticky" dragrace tires, so, perhaps, this warning is not really needed, but I'll continue. The stresses in the links can be minimized with a proper choice of material, but the torsional shear stress in the axle housing is another matter. I would suggest that you regularly inspect for any signs of deformation or imminent failure.

Haven't looked at that racingarticles. com piece for a while and can't remember if I included any kind of correction for unsprung mass. If I did, please ignore it as it was slightly in error. (I say "slightly" in that the normal error would probably be within the fabrication and setup error tolerance.) The following is correct:

tangent = (Mh + mR)/(Ml) - KR(M + m)/(yGM)

where "tangent" refers to the tangent of any of the link angles, measured positive up from the horizontal at the rear pivot; "M" is the sprung mass; "m" the unsprung; "R" the rear tire loaded radius; "l" the wheelbase; "y" the offset, from car centerline, of the "odd" link; and "G" the axle ratio. "K" requires a bit more to explain. First, define points where lines through the links intersect a vertical plane at the rear axle centerline. "K" has one value for the 2 symmetrically located links and another for the "odd" link. "K" is unity for the 2 symmetrically located links and is equal to the ratio of the vertical distance, from the track surface, to the previously defined point for the "odd" link to the vertical distance to the point for the symmetrical link pair. The "odd" link can be either above or below the link pair.

While roll under/over steer is usually not desired, keep in mind that its effects are largely psychological. That is, the wheel loads and, thus, the car's performance potential are affected minimally, if at all. (Unfortunately, this is covered in that student workbook.)  

RE: Constrained testing in traction

Richard, it occurs to me that you might wish to consider an alternative solution. You mentioned that you're presently using a 4link. Instead of fabricating an entirely new setup, you might consider using different spring rates up front and a slight asymmetry of the 4link for final "tuning" to achieve equal rear tire loading during launch. This would, of course, provide different, though not insurmountable, handling problems. I would suggest a right front spring rate about 30% to 50% greater than the left front. Then, using a chain and that tree you mentioned, you could make an instant center change, on one side, to fully achieve equal rear tire loading. As indicated, you solve one problem and create another, but the ease with which this might be implemented (I'm assuming you're using adjustable coilovers up front) could warrant further consideration.

RE: Constrained testing in traction

Billy, the 4link is not with any bushings that can flex so the the links are parallel, because of the binding condition that come in play with non parallel links.
All the links are uniballs(I think you call them rod ends)
Therefore it would be better with a 3-link setup, where the binding never comes in to play.

It´s seems a little to complicated for me with the equation.

I´m fabricating an adjustable mount sideways for the upper link but it only goes about 4 inches, its from the center and to the right.Do you think it is enough or should I try to make even more to the right?

In case of the stresses, the car weight is 1050kg and have about 300hp and the tires are race slicks.

RE: Constrained testing in traction

If I understand you correctly, the link pair on each side is in a plane parallel to the XZ plane. I would hope that the links, while parallel to each other, are not parallel to the track surface (horizontal), for that would cause a large amount of squat during acceleration. If they are angled, as a pair, so that the tangent of the angle is equal to the ratio of sprung mass height to wheelbase, you will get no squat or rise and there will be no binding during cornering.

So, here's yet another way to achieve equal rear tire loading. In this case, the front spring rates can remain equal, left-to-right. The right side link pair should be about 5 degrees greater than the previously defined angle and the left side, about 5 degrees less. The easiest means of achieving adjustability is to tie the front link ends together with a single bracket and then make that bracket adjustable on a bracket attached to the frame. (Hotrodders here call this a 4 "bar" setup, as opposed to a 4 "link.") Again, you'll need that stout tree to finalize the adjustment.

The 3link is still to be preferred, for that which I've just described requires deflection of the main suspension springs, resulting in oscillatory loadings.

RE: Constrained testing in traction

It´s even worse the links are about 2" lower at the frame than the rear end, but parallel to each other.(compared to the floor)

If my understanding is correct this generates pro squat?

It´s the general idea that if a car squats a lot it is a fast starter among all other racers.

Do you think 4 inches offset is enough or should I try to make the mount even more to the right?

Based on the 4 "bar" is it possible to achieve equal rear tire loading in a 3-link by raising the right lower link about 5 degrees? (with the single upper link in center)

RE: Constrained testing in traction

Squatting at the rear during the start will result in less traction and consequently, a slower start.  Don't be misleading by the appearance of weight transfer from the squatting response.  This is because the rear springs are absorbing the vertical force applied to the rear wheels instead of allowing the forces to be used at the tire contact patches.  For quick launches I suggest you angle the lower arms up from back to front.  The drawback is that the rear suspension will have roll oversteer (rear wheel will steer opposite the front during cornering.)  This may not be a problem for you though.  If possible, make the lower arm angle adjustable to tune your anti-squat/roll steer characteristics.

RE: Constrained testing in traction

First, I would agree with Joest: Either squat or rise will generate oscillatory loading which will reduce the performance potential of the rear tires.

The no squat/no rise line is defined by a line, projected on the XZ plane, which passes through the rear tire patch and 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 of that portion of the car mass which includes everything but the rear axle assembly. (This is defined for a RWD beam rear axle car.) If the instant center of the rear suspension lies above the line, the car will rise on acceleration; if below, it will squat. If the instant center (as in your case) lies behind a vertical plane, parallel to the YZ plane and passing through the rear axle centerline, the situation is reversed (i.e., above, squat; below, rise).

As for your idea of a 3link with a centrally located single upper link and a right side lower link angled up at a steeper angle than the left side lower link, the answer is, yes, that could be used to gain equal rear tire loading, but, again, this scheme is inferior to the asymmetry we were previously considering, for the main suspension springs would be employed to obtain the balanced condition.

RE: Constrained testing in traction

I'm  sorry, Richard. I misread your last post. I got the idea that your links were no longer parallel to each other. You wrote, however, that they were, but both were angled down. Although, mathematically, you could consider the instant center to be at an infinite negative X, there's certainly no reason to consider it so. By angling them down, the squat simply becomes more pronounced.

RE: Constrained testing in traction

Thank you Joest for joining the discussion.

Okay, I´m going with a 3-link setup were the lower outer links are almost horisontal maybe a bit angled up towards the front. The single upper link will be angled down about 10 dgr (to try to hit the no squat no rise line with the intersection point), it will also be adjustable from center to 4" to the right (to get the equal tire loading).
Pros and cons?
There is also the matter of lateral restraining, it´s currently a watts link with the pivot mounted on the axel housing 11" from the ground(RC height)non adjustable. I am thinking of replacing it with a panhard bar mounted on the axle too the right and to the left on the frame with easy adjustable height from 6" to 10".(RC height at front will be 5")
Pros and cons?
I really value the knowledge and idea´s you guys share, cause it seems to be a lot of misconceptions in this sport.

RE: Constrained testing in traction

Richard, I don't have all the information on your car, but it would appear that you have not satisfied the relationship I gave you earlier and you will not, therefore, have equal rear tire loading. Again, I don't have all the dimensional information, but it would seem that you need far more than 4 inches of offset.

RE: Constrained testing in traction

What offset do you think would be the right one? (the mount will then be adjustable 4" from that point). I have a packaging problem with the exhaustsystem which is around 4 inches to the right. It is possible to replace it with a smaller silencer.

Do you need more dimensional information?
If so just tell me what measurements you need.


RE: Constrained testing in traction

Sorry to butt in on this conversation, but if the assymetric links are arranged to give equal wheel loading on acceleration, won't it tend to lift the right wheel on braking?


RE: Constrained testing in traction

Jeff, braking would be affected only at the limits of adhesion. This concerned the Ramchargers (a Chrysler dragrace team of the sixties) sufficiently that they incorporated a telescoping 4th tube to take braking loads. But, on the other hand, Jaguar didn't see it as a problem on their early C-Types. And, the Jaguar situation was far more critical, I'm sure you'd agree, than the typical braking chore for a drag car.

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