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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.
ANTI-SQUAT FROM TOP-VIEW DRIVESHAFT ANGULARITY?
I have a question about drive axle inclination in plan view. A friend who does off road racing pointed out that if the wheels are in front of the driven inner axle, the tendency will be anti-squat and if the wheels are behind, the tendency will be to squat on acceleration. Embarrassed that I never thought about it, but it seems very obvious. Is this correct? The attached photo shows a car with the opposite geometry, or pro-squat.
Assuming it is correct, will the anti-squat action be the same as that resulting from anti-squat A-arm geometry?
How does anti-squat affect corner exit traction? On the one hand I would expect the greater load on the tires to cause oversteer, while at the same time it seems that a pro-squat rear would also increase oversteer by jerking the tires up. Or would both be a short lived dynamic lasting only as long as the effect took to equilibrate (move the springs)? To experiment would mean a change in wheelbase + F/R weight balance + polar moment or a change in F/R weight balance and polar moment, giving unwanted variables.
As a kid, I experimented with a dirt bike and varied the rear geometry so that I could have the wheel lift or push down with power. On the bike, the lifting rear tire made the bike easy to control - and slide, but wheelspin slowed it down. - interesting, but slow.
Plan view driveshaft angularity (in independent or DeDion suspension) does not create anti-squat or pro-squat. What your friend is probably thinking is that the system is subject to a torque about the ring gear axis, and that tries to force the diff down if the wheel axis is behind the diff axis, or force the diff up if the wheel axis is ahead of the diff axis. That would only be true if the shaft were not jointed – but of course in that case the car couldn’t go anywhere; any movement at all would only be the result of compliances and clearances in the components.
When a shaft has universal joints in it, and has some provision to accommodate plunge, each segment can only transmit torque, and only about its own axis, since the assembly moves freely in bending and in tension and compression. The stub axle at the diff transmits torque about its axis, the shaft transmits torque about its own axis, and the stub axle at the upright transmits torque about its axis. The shaft cannot act as a lever or crank since it is flexible in bending.
As with any suspension, jacking force induced by longitudinal force at the contact patch depends on the instantaneous rate of x (longitudinal) displacement at the contact patch with respect to z (vertical) displacement at the contact patch. For drive with a sprung differential, and also for braking with inboard brakes, this is the same as the instantaneous rate of x displacement with respect to z displacement at the wheel center, unless there is gearing at the upright.
In the case of a car under steady forward acceleration, anti-squat only increases rear tire loading slightly. The increase results from the c.g. being slightly higher under power.
The same applies to a motorcycle, except that motorcycles have a lot more longitudinal load transfer than cars because the c.g. is so high and the wheelbase is so short. I’m not sure just how the rear geometry was adjusted on the bike mentioned. Generally we can’t move the swing arm pickup very much with respect to the frame unless we add some form of chain tensioner. If we can’t do that, then we would be adjusting the ride height of the whole bike to change the anti-squat, and that would have a bigger effect on rearward load transfer than the change in anti-squat would.
Things get a bit more complex when we consider abrupt application of power, as opposed to steady forward acceleration. In such situations, both the suspension and the sprung mass have velocities and accelerations, in heave and in pitch. These are affected by suspension geometry, springing, and damping. In general, however, the rear wheels will have more load momentarily with anti-squat than without it, but this may then be followed by the rear wheels having less load as the car reaches dynamic equilibrium. In some cases this can create wheel hop.
Adding weight (adding mass) at the rear adds oversteer. Adding tire loading at the rear through dynamic load transfer (colloquially misleadingly called weight transfer), without adding mass at the rear, adds understeer. Adding normal force to a tire increases its friction force capability, but at a decreasing rate. Adding mass increases inertia linearly, and also increases normal force linearly, which increases frictional force capability less than linearly. Thus the increase in frictional force capability does not keep pace with the increase in inertia, and decreased acceleration capability results.
Am still fabricating away on my Exoskeleton race car. About 120Kw rear wheel drive with engine and gearbox at the back.
The rear end is now complete with about 2 Deg of camber gain at full roll of 50mm of wheel travel from normal ride height.
I need now to start on the front suspension.
Double wishbones, top 2/3 the length of the bottom and scrub radius about 20mm, based on some rims I already have.
I have read that it is beneficial to have the front track wider than the rear for a car that is going to be used purely on track and a very small twisty track on top of it.
First question… Is this statement correct?
Second Question… How do I determine how much wider the front track should be compared to the back?
Third question…What can I design into the chassis to help the understeer prone design of this type of car?
Fourth question… Do I have to get the same camber gain in the front for the same amount of wheel travel, planning on a 50:50 weight distribution front to back?
Making the rear track narrower than the front is popular for cars that are purpose-built for American autocross and Formula SAE/Formula Student, where the courses are extremely tight and are laid out with traffic cones in a parking lot. The idea is primarily to place the wide end of the car in the driver’s view and make it easier to avoid collecting cones with the inside rear wheel. There is no magic correct number or formula for how much narrower to make the rear, but a commonly accepted rule of thumb is to make the overall width at the outside of the tires about four inches (100mm) narrower at the rear than at the front.
Making the rear track narrower also reduces the tendency of a locked axle or limited-slip diff to add understeer.
Actually, a car with 50/50 weight distribution is not inherently prone to understeer, at least if the tires are equal size. However, all cars tend to understeer more in tight turns than in larger-radius ones, mainly because the rear tires tend to track on a smaller radius than the fronts in tight turns. This is called off-tracking. In this situation, the combination of drag force from the front tires and thrust force from the rears tends to create a couple that adds understeer. Making the car more tail-heavy, while keeping front and rear tire sizes identical, helps. However, that may not be an option if the car is at a stage where the locations of most components have already been defined.
Making the wheelbase shorter reduces off-tracking.
Giving the rear more roll resistance than the front reduces understeer. This can be done by giving the front less geometric roll resistance (lower roll center), and/or less elastic roll resistance (softer springs and a/r bar) relative to the rear. It is not uncommon in FSAE cars for the car to corner with the inside rear tire almost completely unloaded, and even then teams often run toe-out at the rear to try to kill understeer in the very tight turns.
Choice of differential matters. Probably the best type available is a worm-gear limited-slip, with viscous fluid in it and little or no preload. This produces little torque transfer or locking torque when power application is modest and the wheels are turning close to the same RPM, yet still can transfer enough torque even with the inside rear very light if wheel speeds start to differ by a lot, as when the inside rear starts to spin. Note that some wheelspin has to occur for this to happen, so traction control can prevent this strategy from working. The aggressiveness of the viscous locking effect can be tuned by changing the viscosity of the fluid.
Having similar camber change properties front and rear is generally a good idea.
For tight turns, it is generally advisable to have considerable Ackermann geometry (toe-out with steer) in the front end.
If the car will have to negotiate high-speed sweepers as well as tight turns, it will often have excessive oversteer in the higher-speed turns when it’s happy in the tight turns. Rules permitting, this can be addressed with aerodynamics: a preponderance of downforce at the rear.