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MACPHERSON STRUT GEOMETRY AND MODIFICATION STRATEGY

I have been reading your article in Racecar Engineering for numerous years and I have a suspension question that I cannot find the answer to. I have a 1973 BMW 3.0 CSL Group 2 race car with a MacPherson strut front suspension. The geometry of the front suspension is setup with a single lower control arm and a tension rod that attach to a bolt-on lower steering arm on the bottom of the strut. The rear suspension is a semi-trailing arm setup with coil-over dampers. The car races on 16" Hoosier TD-S treaded bias plies with 9.0" wide fronts and 10.5" wide rears.

I am in the process of converting the car from a steering box to a rack and pinion steering system that will require a new steering arm to make the geometry work. This is being done to help stabilize the front suspension especially under braking where the car has a tendency to have significant lateral movements under heavy braking and become very unstable. I attribute this to the compliance in the steering box system as well as the polyurethane suspension bushings. I am in the process of solid mounting all the suspension front and rear and removing the urethane bushings. I am also reinforcing the front and rear chassis to try to eliminate as much compliance as possible.

Since I need to make a custom steering arm already due to the steering rack install, I would like to swap my struts from side to side so that the brake caliper mounts move from the front to the rear. This will make it easier for me to install a brake cooling duct to the front of the strut. My main question/concern is that the stub axle is not directly in-line with the center of the strut housing in the side view. It is offset towards the rear in side view by about 0.50". So when I swap the strut from side to side, this offset will go from being behind the strut centerline to in front of the strut centerline and I cannot figure out if this will cause any negative steering or geometry effects. From my research, I know that the critical locations for a MacPherson strut suspension are the upper strut mount and the lower ball joint mount to determine the steering axis and the pivot radius. Assuming that I can design my new steering arm to replicate the location of the lower ball joint, what else do I need to be concerned with when designing the new suspension setup? In the side view, what does the linear difference between the lower ball joint and the tie rod ball joint control? If I shorten or lengthen this difference, what effect will it have on steering and scrub? I know I can design the

steering arm and upper strut mount to achieve the static caster and camber I desire but is there anything else I need to be concerned with?

I have not been able to find a good source of information regarding vehicle dynamics for a MacPherson strut front wheel suspension. Do you know any good books on this topic? Most racing vehicle dynamics books focus on double A arm suspensions so I have not been able to find a wealth of knowledge on MacPherson struts in a race car. Thank you very much in advance for the help with this topic; I look forward to your response.

A MacPherson strut system can be thought of as being much like a double A arm system. The lower control arm is entirely the same. It has a control arm plane defined by the inner pivot axis and the ball joint center of rotation. The front view projected control arm is the line where the control arm plane intersects the y-z (transverse-vertical) axle plane. The side view projected control arm is the line where the control arm plane intersects the x-z wheel plane (the longitudinal-vertical plane containing the contact patch center).

The system can conveniently be regarded as having an effective upper control arm plane that is perpendicular to the strut axis (not the steering axis) and contains the center of rotation of the strut’s upper pivot. As with the lower control arm, the front view projected control arm is the line where the control arm plane intersects the axle plane and the side view projected control arm is the line where the control arm plane intersects the wheel plane.

As with a double A arm system, the intersection of the front view projected control arms is the front view instant center and the intersection of the side view projected control arms is the side view instant center. These are true instantaneous centers of rotation for the upright or spindle and everything rigidly attached to that. In front view, this includes the wheel and the contact patch center. In side view, ditto, if the wheel rotates with the spindle, as it does with a locked outboard brake.

As with any independent suspension system, geometric resistance to (or encouragement of) roll and pitch arises from jacking (z axis) forces induced by the linkage when ground plane (x or y axis) forces act on the tire at the contact patch. The magnitude and direction of these forces depend on two things: the magnitude and direction of the ground plane force and the magnitude and direction of the instantaneous rate of change of x or y displacement at the contact patch with respect to z displacement of the suspension. For example, if the front contact patch’s instantaneous rate of x axis displacement with respect to z axis displacement is a tenth of an inch forward per inch of suspension compression (wheel upward with respect to the sprung structure), the system generates a pound of anti-dive force for each ten pounds of rearward ground plane force that the road surface exerts upon the tire.

The horizontal distance from the front view instant center to the contact patch directly determines the instantaneous camber gain or instantaneous camber velocity with respect to z displacement. The

horizontal distance from the side view instant center to the contact patch almost exactly determines the instantaneous caster gain or instantaneous caster velocity, although not quite exactly because caster is not measured in the wheel plane.

If we consider a strut suspension and a double A arm suspension with the front view and side view instant centers in the same locations, the two systems will be identical as regards camber velocity, caster velocity, anti-roll, and anti-dive, at the one point in their travel that we’re looking at. However, there will be only one point in the suspension travel where this will be so. Even when the camber velocities are the same, the camber accelerations will differ – and so it is with all the other properties: they change differently as the suspension moves.

The biggest difference is that with the strut design, geometric roll resistance changes much more with ride height, and camber acceleration is positive rather than negative: as the suspension compresses, camber goes toward negative at a decreasing rate, and in some cases may even start to go toward positive near full bump. This means the suspension has little camber recovery in roll when lowered. Consequently, when people make new hardware for the bottom end of the strut, the most common objective is to lower the ball joint. This shortens the front view swing arm length and restores some geometric roll resistance.

In any case, analysis of the suspension’s geometry can be done per above.

In further correspondence with the questioner, not shown here, he told me that the suspension is a rear-steer layout (steering linkage behind the axle line) with a lower control arm running roughly transversely and a compliance strut running diagonally forward from the outboard end of the control arm. He was not able to supply a picture of the suspension, and an image search didn’t turn one up for me either, but he was able to supply a picture of a car with the fender flares he is using to accommodate the wheels and tires he describes. These are not the extremely wide IMSA-style flares some readers may be familiar with. These are more modest. Still, the front wheels and tires are at least two inches wider than stock, and the extra width can only be accommodated by widening the track and increasing the front-view steering offset (SAE scrub radius). Additionally, the racing tires generate considerably greater forces in braking than those the car was designed for. The questioner is probably correct in supposing that deflection steer is producing the braking instability he describes. Chances are the wheels are toeing out. It is also common to run static toe-out when setting a car up for racing, whereas factory settings for street use generally have some toe-in, partly to compensate for deflection steer in braking.

Taking compliance out of the system will no doubt help. However, even cars with solid bushings or spherical joints have some compliance. If a new steering system is being installed, it would be desirable to have the tie rods oriented in top view so that when the ball joint moves rearward, the wheel does not toe out. This would probably involve having the tie rod roughly parallel to the control arm when the steering is centered, not angled back at the outboard end. Packaging constraints will no doubt limit what is possible.

The questioner describes the spindle pin as being half an inch behind the strut axis in side view, and he would like to reverse the struts, placing it half an inch ahead instead. If the ball joint and the upper strut pivot are not moved, this will decrease trail by about an inch. That’s roughly equivalent to a four or five degree reduction in caster. The front wheels will also be about an inch further forward.

Packaging constraints permitting, moving the front wheels forward is good. It makes the car less nose-heavy. This car has a fairly long inline six engine. The front crossmember passes under the rear two main bearings. The fairly long sump hangs entirely in front of the crossmember. The tops of the strut towers are only slightly forward of the firewall. The layout gives good load paths but arguably would be better suited to front wheel drive.

If the struts are reversed, we’d really like to drastically increase caster to get the trail back where it was. Assuming we don’t do major surgery to the strut towers, this would involve moving the ball joints forward over an inch. That would also move the wheels forward something like another inch. The wheels would then be something like two inches forward of their previous location. This would be good in terms of vehicle dynamics, provided packaging constraints permit it. Generally, moving any car’s wheels that much will necessitate fender modification. Probably the car wouldn’t look different enough from stock to attract attention, but I couldn’t guarantee that.

If a complete tubular frame is going to be built, then maybe the upper strut pivots can be moved back with no problem. The weight distribution improvement from moving the front wheels forward an inch or two is not very large – on the order of one percentage point.

In some cases, cars with lots of caster and some pin lead will exhibit steering shimmy, often at low speeds. If this goes away at racing speed, it can be lived with if the car goes faster. A hydraulic steering damper can also be helpful. Many German cars have these as factory equipment. In some cases, there won’t be any shimmy problem.

The front to rear position of the outer tie rod end with respect to the ball joint controls how fast the steering is, together with the pitch diameter of the pinion gear in the steering rack assembly. Shorter steering arms give faster steering. Scrub radius and front view steering offset are not affected. How far inboard or outboard the outer tie rod end is with respect to the ball joint controls how much Ackermann effect the system has. Moving the outer tie rod ends in gives more Ackermann. Rack location also affects Ackermann, primarily at large steer angles. Moving the rack rearward increases Ackermann.

We also want to avoid having really large tie rod angularity with respect to the rack, especially at small steer angles, where the system spends most of its time. The straighter the tie rods are with respect to the rack axis, the less load is induced at the rack bushings by tie rod forces.