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ANTI-SQUAT IN A STRUT REAR SUSPENSION
What follows is an exchange with a correspondent who is getting free consulting from me in exchange for his permission to edit and publish the material.
I read your article on independent rear suspension for dirt track racing in a recent edition of Racecar Engineering. We run a mid-engined rear-wheel drive rally car on gravel hillclimbs and sprints. The original car was written off and we are in the process of designing a replacement. We have always suffered from excessive wheelspin so are trying to come up with a better rear suspension setup. Our first car had the rear suspension as per early Subaru WRX Ė two parallel arms and a forward link with McPherson strut. We are looking to improve the rear suspension setup from a traction point of view only. Everything else works really well, but we suffer from excessive wheelspin. We have good struts (MCA Australia) and have tried various roll centre adjustments etc.
We are considering a wishbone bottom arm with a steering link. Here are the rest of the car details:
- Turbo Subaru engine 400+hp, mid-mounted with Albins sequential transaxle
- 65% rear weight bias (heavy transaxle behind rear axles)
- Big shaft McPherson struts front and rear (MCA Suspension Ė Australia)
- Springs 250lb Front, 180lb Rear, no swaybars
- Small Subaru Justy body, 950kg total
- Subframes front and rear, have tried various rollcentres
- Have tried adjusting anti-squat by moving forward link pickups
- Outboard brakes
Are struts inferior to double wishbones for traction? Which is going to be our best option?
Starting point for anti-squat on dirt? Angle top of strut in more, or forward or back? In front or behind hub centre at the bottom?
Assuming we stay with the Macpherson strut, which is going to be the best bottom arm setup for traction? Stay with the 2x parallel lower arms and a forward link (early Subaru WRX), single lower arm with steering link and forward link (early Toyota MR2), or an A-arm bottom with steering link? And where should we mount the top of the strut in relation to everything else in terms of anti-squat etc?
Any advice would be greatly appreciated. See photos attached and video link below.
A few additional questions from me:
1. Do you run just the course in the video, or is there a whole circuit?
2. Are there ever asphalt bits, or does the car always run on gravel?
3. Can you provide your rules, or a link to them?
4. What does that transaxle have for a diff?
Every course is different, the events are rallysprints or hillclimbs around our local area, probably 10 or 12 different courses each season. So the road surface changes a bit, but always gravel. We run in the Unlimited class so there are basically no rules. The diff is a plate-type LSD, I think around 60lb breakaway from memory. Here is another video link on a different course, obviously the wet weather doesnít help but you can see how quickly it lights up when it comes on boost.
So why are you running a steel sedan with two wheel drive and an FIA-legal wing?
At Pikes Peak they have a class they call unlimited where the car has to be production based and I guess there are some body and wing rules but practically anything goes mechanically, and another class they call open, where the cars can be scratch-built single seaters but have to be two wheel drive and canít have forced induction.
I am happy to help you with the suspension, but that will only get you a little. If you really want a huge improvement, quick and cheap, add a big splitter on the front and a giant wing above the roof. Better yet, build an open wheeled single seater with your existing powertrain and as much wing as you can hang on it.
Or am I missing something?
Ok, we do have some rules, I guess it would be similar to Pikes Peak Unlimited. The wing can only be 100mm above the roofline and the width of the body. We are limited on the size of the front
splitter due to it getting ripped off on rougher roads or cutting corners. We run a flat underfloor and rear diffuser so our aero is pretty well balanced. More aero wonít help with getting traction off the start line though. The car is very quick on fast open roads, but it is the slow speed traction that is costing us. Most of our events are timed from a standing start, and getting off the start line or out of tight corners with 400hp in a 2wd is the issue. Our closest competitor runs a Toyota MR2 AW11 with a mid-mounted 500hp Nissan engine. We are very closely matched but his car is much faster off the start line or out of hairpin corners Ė it gets more traction and we canít figure out why. We run the same tyres. His car has a single lower arm with a steering link and forward link on the rear. In theory the things that will affect our straight line traction are tyres, shock absorbers, spring rates, diff, suspension geometry? We have tried several variations of all of the above. Changing shock absorbers has made the biggest difference so far in getting the rear tyres to bite. So we are just thinking that while we are rebuilding the car, is there a better rear setup we can use? Or will the design of the arms have nil effect?
Thank you for the clarification. Now I see why youíre focusing on the suspension.
Is the attached picture the type of suspension the MR2 has? [will attach and send with newsletter] If so, Iíd say he doesnít have any edge over you there, at least in terms of basic layout. My guess would be that heís simply got more static rear percentage than you have. Ordinarily, your 65% is considered to be about the practical upper limit, but on a slippery surface you could probably get away with a bit more. I donít know how the engine weights compare but I would expect a V6 to be heavier than a boxer 4. If he has a similar transaxle to yours, and similar total car weight, he would then have more static rear.
I take it you have no minimum weight, and no ballast?
I will get to your original question. I just want to make sure we donít overlook anything that might get us a bigger payoff.
A few more questions: do you set the brake balance so the rears lock before the fronts, so the driver can use the brakes to toss the car on entry? Do you do any handbraking to turn the car?
As set up now, does the car corner on three wheels?
How much of the bodywork is plastic or lightweight material?
Yes that is the rear suspension setup in the MR2. His car runs a 4-cyl Nissan engine mounted east-west, so the engine and gearbox is essentially the same as a front-wheel drive setup but mounted in the back. So all of his weight is above or in front of his rear axle, whereas we have a lot more weight hanging out the back and a higher polar moment. His car is about 150kg lighter and probably closer to 55/45 rear split I would imagine. I would have thought the extra weight over the rear wheels would help us with traction. It may be all to do with shock absorbers.
We run the same brakes front and rear with more rear bias to help with turn in, and use handbrake for hairpin corners. The car does not lift a wheel when cornering. Most of the panels are original steel or alloy but have been gutted as light as possible (doors, boot lid etc), fibreglass bonnet, plastic bumpers. We should be able to get the new chassis a little bit lighter but not much, the transaxle is pretty heavy. No minimum weight or ballast. And probably donít have the means or funds to make the whole bodyshell from carbon, especially when itís likely to get ripped apart the first corner you cut.
It may be that you can get some further improvement with shocks. It may also be that control of power delivery can be improved. I donít know what your rules are on traction control. Certainly if a lot of power comes on suddenly for any reason, that will break traction, and beyond a certain point thereís nothing the tires or suspension can do about it. Perhaps Iím belaboring the obvious, but I thought I should mention this.
Now, letís get to the original question: is it worthwhile trying to increase the anti-squat; how do you do that in a strut suspension; what is the best configuration for the lower control arm and the system as a whole?
First, is it worthwhile? Anti-squat helps by raising the car and therefore increasing the amount of rearward load transfer for a given forward acceleration. Itís tempting to think that the jacking force loads the wheels more than it really does; it makes the suspension push the car up, so that must push the wheels down. But since thereís nothing keeping the sprung mass from just rising, all we really do is unload the springs and raise the car a bit.
How much improvement are we talking about? Suppose the c.g. height is 1/6 of the wheelbase, the static rear percentage is 65%, and the car can accelerate forward at 0.4g. That would be a coefficient of friction between 0.5 and 0.6. Then 0.4/6, or 1/15, or between 6% and 7% of the carís weight transfers rearward. If we can raise the c.g. by ten percent, or about an inch and a half, we increase that by 10% of its previous value, or about two thirds of a point. That will get us about 1% more, or about .004g more, forward acceleration. Not much, but it canít hurt.
Note that how much the car lifts depends not only on how much the rear squats or lifts but also on how much the front lifts. Front suspension geometry doesnít affect this in a rear-drive car (except for the motion ratio on the springs) because there is no significant ground plane force at the front contact patches. How much the front lifts depends on the front springs, or more precisely the wheel rate. With softer springs it lifts more. With soft rebound damping it lifts faster, but the springs determine how far it lifts. Therefore, you might consider going softer on the front springs and adding an anti-roll bar to get the elastic roll resistance back to where it was with the stiffer springs. In fact, if you are currently running no anti-roll bars you might consider having them at both ends.
It looks like your current front springs are really stiff for dirt. Assuming a 0.9 spring to wheel motion ratio, 240 lb/in springs would give a wheel rate just under 200 lb/in. You have about 300
pounds of sprung weight per wheel in front, so thatís a static deflection of only about an inch and a half, or around 150 opm (2.5 Hz) frequency. Thatís stiff pavement car territory.
At the rear, assuming the same motion ratio youíve got around 150 lb/in and 600 pounds sprung weight per wheel, for a static deflection of around 4 inches and a frequency of about 90 opm (1.5 Hz). Thatís even a little stiff for dirt, but not extremely.
You could set the car up so it has a lower frequency in front than in back, as is common in front-engined cars. With the same rear springs as at present, youíd want about a 5 inch static deflection. That would call for a wheel rate around 60 lb/in or a spring rate around 75 or 80 lb/in. Youíd get about three times the front end lift under power that you get now. Youíd then need to add an anti-roll bar that would provide around 135 lb/in/wheel at the wheels to get similar cornering balance to what you have now.
In any independent rear suspension, the jacking coefficient under power depends on the side-view motion path of the hub as the suspension moves. For anti-squat, you want the motion path to lean backward at the top and forward at the bottom. Itís also best if the path is concave rearward. Given a free hand, with a strut I would want a lateral link and toe link, and a leading link in place of the Toyotaís trailing link. This should anchor somewhere near hub height at the hub carrier and back and lower than that at the frame. Its angle should be adjustable.
I would try for at least 100% anti-squat as a middle setting, and try to provide adjustment from there. That would be a link angle of around nine or ten degrees from horizontal, nose up. Increase the anti-squat until you get wheel hop, and then back off a bit.
If the longitudinal link anchors to the hub carrier fairly close to hub height, the side view strut angle has little effect on anti-squat. If the strut is close to vertical in side view and the system has anti-squat, the strut will swing rearward at the bottom as the suspension compresses, and forward as it extends. This is okay as long as nothing runs out of angular travel.
However, the side view angle of the strut matters for anti-lift under braking. This is why I wanted to know if you turn the car with rear brake. With outboard brakes, if the system has anti-squat and the strut is close to vertical in side view, the system will have a greater jacking coefficient in braking than under power. This means that as you increase anti-squat, you will very likely be limited by wheel hop in braking before you are limited by wheel hop under power.
To get away from this, you need to incline the strut back at the top. The leading link and the strut need to make an angle of less than 90 degrees. The strut should lean back around 20 to 30 degrees. This gives a side view instant center behind and below the hub. The hub carrier should rotate rearward as the suspension compresses and forward as it extends.
It is possible to achieve similar effects with a lower control arm and a toe link. You incline the armís pivot axis up at the front. Ideally you would also like it angled in top view, in at the front, out
at the rear. That makes the hub motion path concave rearward. However, I would opt for the leading link instead, because it would probably be easier to provide anti-squat adjustment that way.
Of course, all of this will be affected by considerations of packaging and load paths. The leading link would have to have frame structure to attach to, and this has to be adequately rigid. This may or may not be practical.
Front-view inclination of the strut does not affect anti-squat or anti-lift. It does affect camber properties and roll center height.