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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers. This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr., Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by e-mail to: firstname.lastname@example.org. Readers are invited to subscribe to this newsletter by e-mail. Just e-mail me and request to be added to the list.
DROOP-LIMITED REAR SUSPENSION
I have a question for you, and it's related to something I recently discovered on my race car, and something that you've been talking about a lot lately - droop limiting.
My car is a Mustang with a strut front, 3-link in the rear, 3100#, 400+rwhp, 275 DOT race radials all around, etc.
In a search for lots of bump travel I made some changes to the upper (chassis side) shock mounts in the rear. When my shocks arrived, I never noticed that they were shorter than I thought, and I ended up with a car that has less than 1" of droop travel in the rear. For reference, the car is relatively softly sprung (400# wheel rate in front, 300# wheel rate in the rear) and uses lots of travel with a relatively high CG (about 17" or so).
I was wondering how you thought this lack of droop travel might affect handling? Under braking? Into and through a corner?
I can say this with certainty: when the inside rear suspension tops out, the rear roll resistance increases dramatically, and that makes the car looser (produces oversteer). I cannot say with any certainty when this is happening with a particular car. Data acquisition is very useful for determining this. (The questioner here is an engineer with a NASCAR team, but the question concerns his own personal race car. Presumably he will not be allowed to borrow team data acquisition gear for his own races. He didn't mention whether he has his own.)
If the 3-link rear is set up for moderate anti-squat and anti-lift, and the springing is fairly soft, it is highly probable that the car tops out the inside rear shock when trail-braking. I would also expect that the shock would top out in steady-state cornering.
It is possible to have so much anti-squat in a beam axle rear suspension that the suspension tops out under power, even when the car is running straight. It is not uncommon to see this in dirt cars, even with as much as four inches of droop travel. I do not recommend this, but I see it when I go to races.
It is also possible to have so much anti-lift that the rear suspension compresses rather than extending in braking.
With a simple three-link rear, ample anti-squat implies fairly ample anti-lift. This does not mean that the car necessarily compresses the rear suspension in braking if it extends it under power. The percent anti-lift in braking will generally be considerably less than the percent anti-squat under power, because the rear tires have to provide all of the propulsion force, but only about a quarter of the retarding force. If the questioner's Mustang were set up to actually lift the rear under power, the rear suspension would very probably still extend under braking. It would be possible to have a situation where the only time the rear suspension wasn't topped out would be when there was little forward, rearward, or lateral acceleration.
This is probably academic, because in general road racing cars are not set up with extremely severe anti-squat.
With the more complex suspensions sometimes used in dirt cars, it is possible to have a lot of anti-squat and also have severe pro-lift in braking. I really do see dirt modifieds and Late Models that appear to lift the left rear to the droop limit most of the way around the track. The left rear only comes down momentarily when the driver is transitioning from power to braking at the end of the straights.
How do you calculate the roll center for a Satchell link rear end?
For readers unfamiliar with the Satchell link suspension, it is a form of triangulated four-bar linkage for a beam axle. This family of systems use diagonal semi-trailing links to provide lateral location of the axle, rather than purely lateral links such as a Panhard bar.
The most common version of triangulated four-bar, sometimes called the Chevelle style, has two upper links that are angled around 45 degrees in plan (top) view, and two lower links that are closer to parallel in plan view. The upper links are further apart at the front than at the back. Their centerlines converge at a point above and behind the axle center section. The lower links converge to a point well ahead of the axle. The two convergence points, or instant centers, define an instantaneous axis of rotation, about which the axle moves in roll. The roll center height is the height at which this axle roll axis intercepts the axle plane: the vertical, transverse plane containing the axle centerline.
Note that this is not the midpoint height of the axle roll axis, or the point midway between the instant centers, which at least one author has suggested should be taken as the roll center. Indeed, as we will discuss, there are cases where no such midpoint can be defined.
It is also fairly common to see this system used upside down. When a low roll center is desired, it is possible to have the lower links converge toward the axle center section rather than the upper links.
The Satchell link system is basically a Chevelle system, turned upside down and back-front, or turned upside down by rotating it about a transverse axis rather than a longitudinal one. That is, it has lower links that attach to the axle near its outboard ends and come close together near their front ends. The upper links also attach near the outboard ends of the axle, and are either parallel or close to parallel in plan view.
Finding the roll center is the same as with other triangulated four-bar systems. Find the instant centers for the lower and upper link pairs, define a line connecting these, and find the height at which this line intercepts the axle plane.
There are cases where the link centerlines will have no intersection. Even if they do at static position, they won't in a rolled condition. Generally, the link centerlines will pass over and under each other when the suspension has some roll displacement. In such cases, the best approximation is to find where the lines cross in plan view, and then find a point midway between them in height. In other words, find where the lines have the same x (longitudinal) and y (transverse) coordinates, and average their z (vertical) coordinates for those points.
It is also possible for one pair of the links to be parallel in plan view. They then will not cross at all in plan view. The axle roll axis then passes through the instant center of the non-parallel links (lowers in a Satchell link), and has a side view inclination parallel to the side view inclination of the links that are parallel in plan view (uppers in a Satchell link). If those links do not have the same inclination, we take an average of the two. Note that in this case we have only one link instant center to work with, and it becomes impossible to define a midpoint between two instant centers.
If both upper links in a Satchell system are horizontal and parallel, the roll center is at the same height as the lower link instant center. However, if the uppers are not horizontal and parallel, the roll center height is different from the lower link instant center. As the car moves in ride, the roll center stays about the same height from the ground if the upper and lower links have similar side view projected length. This is important, because the front roll center in most independent front ends moves up and down with the sprung mass, though not necessarily the same amount as the sprung mass. If we supposed that the roll center is at the lower link instant center in the Satchell system, that might lead us to suppose that we'd have better compatibility with an independent front suspension than we have with more conventional triangulated four-bar systems. Unfortunately, that turns out not to be so. However, the system is no worse than conventional triangulated four-bar designs in this regard.
We also do not escape the interrelatedness of roll steer, anti-squat, and geometric anti-roll, as some have suggested. But again, this aspect is no better or worse than in other triangulated four-bar systems.
Advantages and disadvantages of the Satchell system mainly come down to packaging and load paths, both in the axle and in the frame. Whether we gain or lose in those regards will depend on the particular installation.
A WORD FROM THE INVENTOR
After I originally mailed this newsletter, I received a note from Terry Satchell, who originated the suspension bearing his name. He contributes some interesting background on the history of the design and his views regarding its advantages. He writes:
…I had done a Lotus Super 7
type rear for a Trans Am car where the lower A-arm has a pivot under the axle
with two upper longitudinal arms. After running it for a year we kind of
got the impression that the rear roll center was too low, it being at the pivot
of the A-arm to axle joint. Since I had designed four bar link rear axle
suspensions for General Motors for several years, I knew how to analyze them
and create what I wanted. I wanted a geometry with a roll center
basically midway between the bottom of the axle housing and drive axle
centerline. By reversing the lower arms to converge to the center ahead
of the axle I was able to achieve a good geometry. It worked well on the
track, and in fact one of the neat parameters was that the anti-squat increased
on the inboard wheel with roll giving a tightening effect on power that helps
I did a version of this geometry for Herb Adams who did all of Walker Evans truck suspensions and they were very happy with it. They in particular liked the anti-squat difference across the back with roll on throttle for their Stadium racing trucks.
Since then I have done several versions for various disciplines and now there is a company in Pennsylvania that provides aftermarket conversions for Mustangs, Camaros and Firebirds to get rid of the leaf spring suspension and use this four bar link with coilovers.
I have also had success with several of the "Locost" builders using it. [The Locost is a kit car similar to a Lotus 7.] One in particular used it to control his deDion beam.
Just thought you might like to know a little more of the story.
By the way, I never intended to put my name to this version of a four link. Herb Adams named it in one of his books and that is how it got started being call the Satchell Link.
I'd like to thank Terry for his contribution, and also mention that he was the person who taught me the right way to determine the front-view and side-view projected control arm geometry in independent suspensions.
I concur about the roll center height, and the desirability of having more anti-squat on the inside rear wheel than on the outside rear.
In fact, this latter property is a characteristic of most trailing arm rear suspensions, including independent ones that use trailing arms. Strictly speaking, in the case of independent systems, we usually have less pro-squat on the inside wheel with roll, and more pro-squat on the outside wheel, rather than anti-squat as such. However, the effect on roll and on wheel loads is similar: the difference in longitudinal "anti" produces an outward roll moment, or pro-roll moment, in the rear suspension that adds wedge to the car – adds load to the inside rear and outside front wheels.
It is a bit risky to generalize about this subject purely on the basis of general suspension type. Exceptions can be found to most such generalizations, and the dynamics of any actual car will depend on the specific design of that car.