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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: markortizauto@windstream.net. Readers are invited to subscribe to this newsletter by e-mail. Just e-mail me and request to be added to the list.

OFFROAD SUSPENSION

I am currently designing a new off-road race car. My current race car uses trailing arm suspension both front and rear.

For the new car I plan to increase the suspension travel, and want to change the front suspension to parallel equal wishbones, and retain semi-trailing rear suspension.

I have been told that the combination of these two suspension types will cause the car to pitch (bounce), and become unstable.

By changing the front suspension, I am trying to eliminate the issue of camber change during cornering. This can cause the wheels to "tuck under", and roll the car in short course racing, where wheel ruts have developed.

I have also noticed with VW beetle based race cars that bounce seems to only occur at certain speeds.

Is there a way of calculating trailing arm length/angle to control the pitch of the car, and would reducing the size of the rear tyres also reduce the bounce?

I am not as conversant with off-road cars as with oval track and road race ones, but I think I can help a bit.

There is no suspension that can keep the car from bicycling or rolling over if it hooks a rut really hard. The best we can hope for from the suspension is that it not make a bad situation worse. And even that is a bit tricky. If the roll center is low, i.e. if there is little geometric anti-roll, the c.g. will translate more toward the wheel(s) hooking the rut as the car rolls on the suspension, and that may make the car more prone to rollover. If the roll center is high, there will be more tendency for the car to jack when it hooks the rut. This will raise the c.g. and make the car more prone to rollover that way.

The suspension on VW beetles that really has a tuck-under problem is the swing axle rear suspension, not the trailing arm front. That’s why VW went to a semi-trailing arm design for late beetles, and most off-road cars nowadays likewise use either pure trailing arms or semi-trailing. I doubt that VW-style trailing arm front suspension makes the car more prone to rollover upon hooking a rut. It does have zero camber recovery in roll: the wheels lean with the sprung structure.

However, parallel control arms also have zero camber recovery in roll. As seen in off-road vehicles, they usually slope upward toward the frame, and therefore create more anti-roll than pure trailing arms, but not more camber recovery in roll. If anything, the increased anti-roll makes the car more inclined to jack up when it hooks a rut.

The anti-roll and the jacking are inescapably related. The geometric roll resistance comes from the jacking forces. The outside wheel’s suspension tries to jack up when the tires make lateral force, and the inside wheel’s suspension tries to jack down, and that fights the roll. In hard cornering, the outside tire makes more ground plane force than the inside one, so the car jacks up overall.

It is possible to arrange A-arms or trailing arms to produce some camber recovery in roll. This involves making the A-arms non-parallel, or making the pivot axes of the upper and lower trailing arms non-parallel in front view (Porsche actually tried this, shortly before they abandoned trailing arm front suspension). I generally recommend doing that. As ballpark recommendations, for independent suspensions I suggest front view swingarm lengths between 65 and 100 inches (two to three meters or a bit less), or camber gain as measured on the shop floor around 0.6 to 0.9 degrees per inch. This strikes a reasonable compromise between camber change in ride and camber change in roll, for a wide range of vehicles. The wheels then lean about three quarters to a bit more than half as much as the sprung structure in cornering, plus a bit more due to various compliances.

Longer front view swingarm lengths may be desirable where camber control in ride is a priority.

Off-road tires tend to be relatively camber-insensitive, due to tall sidewalls, compliant carcass design, and low inflation pressures. Some are also made with rounded tread profiles to make them even more camber-insensitive. Even so, it is better to have good camber properties in the suspension than not.

However, minimized camber change in roll should not be counted on to keep the car from overturning when it hooks a rut. It is doubtful that it provides any benefit at all in that regard.

Suspension geometry does influence pitch due to ground plane forces – forward, rearward, and lateral forces at the contact patches. However, suspension geometry has little influence on oscillatory behavior in response to bumps. That’s mainly a matter of springing and damping. I would not shy away from using A-arms in front to avoid problematic oscillations due to bumps.

I would, however, study the science of oscillatory behavior in suspension systems. This is a subject for a least a chapter in a vehicle dynamics text, but I will try to address it a little.

First of all, there isn’t just a single way that things in the system can oscillate. There are multiple masses and compliances in the system, and different ways things can move. I think the questioner is describing an oscillation of the sprung mass, especially at the rear, in response to either a single sequential disturbance at the front axle and then the rear one, or a series of these.

All oscillations in suspension systems are sensitive to excitation frequency. The system has natural frequencies for its various modes of oscillation, and when the system is excited at a frequency close to any of those, resonant reinforcement will occur. Excitation frequency on bumps depends on the frequency of bumps with respect to distance, and the distance the car travels with respect to time, which is its speed.

Pitch and bounce have specific meanings in vehicle dynamics, and they are not the same. Pitch can have at least three meanings, although all of them are somewhat related. It can mean angular movement of the sprung mass about the transverse (conventionally the y) axis. It can mean equal and opposite displacements of the front and rear suspensions. It has a third meaning in ride engineering, which is the one that concerns us here.

In ride engineering, pitch is the movement of the sprung structure in response to the application of a pitch moment, with no vertical or other forces. In all cases, one end of the car will go up and the other will go down, but usually not equal amounts. There will then be some point along the wheelbase where vertical displacement is zero. This is called the pitch center. Its location depends on the wheel rates in ride at the two ends of the car. It does not depend on the location of the sprung mass c.g., nor on the suspension geometry. Note that this is not pure pitch in the sense that we would use the term in describing modal suspension displacements. It normally involves some heave (synchronous displacement at all four corners) in addition to pitch. Therefore it is a somewhat different use of the word.

In ride engineering, bounce is the movement of the sprung structure in response to a vertical force applied at the sprung mass c.g., with no rotational or other force. This will always cause same-direction displacements at the front and rear, but again usually not in equal amount. The unequal front and rear displacement implies an instantaneous center of rotation either ahead of the car or behind it. This is called the bounce center. Its location depends on the wheel rates in ride at the two ends of the car, and the location of the sprung mass c.g., but not on the suspension geometry.

For cars with no front/rear interconnective springing, the best ride is obtained when the pitch center is near the middle of the wheelbase or slightly aft, and the bounce center is a considerable distance behind the car – say three to five times the wheelbase. To get this, the front static deflection (sprung weight divided by wheel rate) has to be greater than the rear, yet front and rear wheel rates need to be similar. This is only possible when the car is at least somewhat nose-heavy.

In a very tail-heavy car, we cannot have both at once. If the pitch center is near the middle of the wheelbase, the bounce center will be ahead of the car. If the bounce center is behind the car, the pitch center will be well to the rear of the wheelbase midpoint.

A pitch center near the rear axle will result in the front of the car rising a lot under power and dropping a lot in braking. This is a problem if we have a splitter, valance, or front wing that needs to be kept a controlled distance from the ground. On an off-road car, it may be okay, but the front suspension has to have lots of travel. Unless the rear tires are much larger than the fronts, a large

front anti-roll bar and/or a high front roll center will be needed to curb oversteer. Of course, on rear-engined buggies, the rear tires often are much larger than the fronts.

By far the more common approach with a tail-heavy car is to have the front static deflection a good deal smaller than the rear; the front end is stiffer than the rear, relative to the weight it carries. The bounce center is then ahead of the car. This works decently, provided the bounce center isn’t too far ahead of the car. As a rule of thumb, we want it one to two wheelbase lengths ahead of the front axle line. That is, we want the front static deflection around ½ to 2/3 of the rear.

In other words, we need a front static deflection that is either moderately greater than the rear or considerably smaller. If the front static deflection is similar to the rear or just slightly smaller, we get a lot of rear suspension movement on the second oscillation following a large, short disturbance such as a speed bump or raised railroad crossing.

If the suspension is fairly heavily damped with respect to its springing, i.e. if it has a fairly high damping ratio, there won’t be much of a second oscillation, and all this won’t matter very much.

The questioner mentions the role of tires. Certainly when the tires are very compliant, they become a significant part of the overall springing. In off-road vehicles, this is the case, although the rest of the suspension is soft too. The tires need to be big and compliant to provide ample traction and flotation. Unfortunately, it’s hard to damp a tire. The shock can’t act on the tire sidewalls. They have some damping internally, but not enough. The only way to damp oscillation on the tires is by inertia damping. That’s why inertia damping was hot in F1 for a while, until it was banned. (I understand some teams are still incorporating inertial elements in the suspension, but that’s not really equivalent.) The tires are a large part of the springing on those cars, not because the tires are highly compliant but because the rest of the system is very stiff.

Lightly sprung and damped passenger cars do quite often use inertia damping. The engine/transmission assembly has soft rubber mounts, and these and the front suspension are deliberately tuned to have natural frequencies that create interference rather than reinforcement. It would be quite possible to apply the same principle at the rear of a buggy.

This would involve knowing the spring rate of the tires, and a representative rate for the rubber motor mounts, which are quite nonlinear. A given set of mounts would only be right for a particular range of wheel rate and tire spring rate combinations. Still, if done right, this could offer some advantage.

Returning to the original question, I would not shy away from using A-arm front suspension, but I would be careful, when taking advantage of the longer arms to use more travel and softer front

springing, to not get the front static deflection or natural frequency in the range that creates an unfavorable relationship with the rear.