Tesla Model S And Ford GT Engineer Explains How To Design Oversteer Or Understeer Into A Car’s Suspension

Hello fellow Autopians. If you’re like me, you’ve read lots of articles over the years that talk about something called “oversteer” and “understeer” in cars. And if you’re like most people, you’ve scratched your head wondering what the devil they’re talking about, but were afraid to ask. Or maybe you had no idea whom to ask. Well, fear no more. Your friendly resident Autopian suspension engineer is here to help.

There are three terms often thrown around when talking about how cars handle: Understeer, Oversteer, and Neutral steer. The Society of Automotive Engineers (SAE) defines these terms as “The quantity obtained by subtracting the Ackerman steer angle gradient from the ratio of the steering wheel angle gradient to the overall steering ratio” (source: Fundamentals of Vehicle Dynamics, Thomas D. Gillespie). That’s a lot of fancy words about terms that journalists just casually throw around in every Mazda Miata review ever written. Let’s put the concept of oversteer and understeer into more layperson terms:

Understeer

This is the tendency of a car to want to continue in a straight line when you are in a turn. Some people call it “plowing” or “pushing.” Almost all vehicles on the market today have understeer built into the suspension design, and are tuned so that if you lose control in a turn, you drive off the road nose-first. The nose of a car is designed to absorb impacts much more softly than the side or rear, so if you run off the road and hit a tree you want to do that with the front.

Oversteer

This is the tendency of a car to spin out in a turn. Some racecar drivers prefer their car to be setup like this so they can throw the car into a turn more easily, and then countersteer their way through. NASCAR drivers talk about a car being “loose” when it oversteers. That’s fine if you’re an expert driver, but not so good for Joe public. Don’t confuse what we’re talking about here with what you see in movies or in Hoonigan videos where the car is going full lock sideways around a turn. Those are instances where a driver uses the power of the engine to break traction of the rear axle to get the car to go sideways. This has nothing to do with basic understeer/oversteer characteristics of the vehicle — which is set by geometry, springs, and anti-roll bars, not a driver’s tendency to go full WOT around a 90-degree bend.

Neutral Steer

This is the in-between condition where the car doesn’t understeer or oversteer. It sounds perfect because the car does exactly what you ask it to do, but a car set up for neutral steer can transition into understeer or oversteer unexpectedly and be hard to control.

Personally, I find it easier to understand these terms by looking at how oversteer/understeer/neutral steer is measured. To figure out if a car understeers, oversteers, or neutral steers, there are a few fairly simple tests that can be performed. The easiest is:

• Drive the car at low speed in a large circle. Most OEM’s use about a 200- or 300-foot diameter circle on a skidpad. The steering angle will be equal to L/R where L is the wheelbase of the vehicle and R is the radius of the turn. Note that the steering angle we are talking about here is the angle of the front wheels, not the angle of the steering wheel.
• Slowly increase the speed while measuring the lateral acceleration and steering wheel angle (You measure the actual steering wheel angle, but then you divide by the steering ratio to get the angle of the road wheel, which is what you are interested in). If you can’t measure the lateral acceleration in “G’s,” it is easy to calculate from your speed using the formula V2 / (Rg), where V is your speed, R is the radius of the turn, and g is the acceleration due to gravity
• Record what you need to do with the steering wheel (and thus the front wheel angle) in order to stay on the circle. The skidpads OEM’s use normally have a circle painted on the pavement that you follow.
• Plot the results of front wheel steering angle versus vehicle speed

When you plot the results you will get a graph that looks something like one of these curves:

Image via Indian Institute of Technology

Ignore all the words and formulas for now, just look at the curves. If your car understeers, it means as you increase speed around the circle, you have to keep adding more steering in order to stay on the circle. This makes sense since the car wants to “push” out of the circle and go straight. If the car oversteers, you have to slowly straighten the wheel out in order to stay on the circle. If the car has neutral steer, you don’t have to change the steering wheel angle at all, the car will just stay on the circle no matter how fast you go.

Looking at the curves above at low speed, they are all fairly straight. If we calculate the slope of the curves in this region, we get something called the understeer gradient, K, which is a measure of the amount of understeer the car has. If the value of K is positive, then we have understeer; if K is negative, then we have oversteer; if it is zero, we have neutral steer.

Characteristic and Critical Speed

The other parts of this graph that are important are the Characteristic Speed and the Critical Speed, labeled there on the X-axis.

The characteristic speed applies to an understeering vehicle and refers to the speed at which the steering angle is double the angle needed to keep the vehicle on the line at low speeds. It has no more significance than that.

The critical speed is a bit more important, and applies to an oversteering vehicle. It is the speed at which the steering angle returns to zero and represents the speed at which the vehicle becomes unstable and basically uncontrollable.

Roll Couple Distribution

So now that we know what understeer and oversteer are, let’s talk about how we get a car to understeer or oversteer. Within reason, any vehicle can be made to either understeer or oversteer, and the behavior depends on something called the “roll couple distribution.” In engineering speak, a “couple” is the same thing as a “moment” or “torque,” and refers to a force that is trying to rotate something. In this case, the “roll couple” is the cornering force trying to rotate the vehicle sideways, causing the vehicle “roll” in a turn. The size of the roll couple is determined by the weight of the vehicle, the height of the center of gravity, and the cornering speed or lateral acceleration, and follows this formula:

Cr = Mah

Where M is the mass of the vehicle, a is the lateral acceleration in g’s, and h is the height of the center of gravity above ground. You can visualize the entire mass of the car at the car’s center of gravity, and multiply that by the distance from the ground; that’s what defines the roll couple.

Weight Transfer

Since the roll moment is side to side, it causes the side of the car on the outside of the turn to effectively get heavier and the part of the car that is on the inside of the turn to get lighter. The increase in weight on the outside of the car is the weight transfer that happens in a turn; it depends on the track width of the vehicle, and is calculated using this formula:

Wt = Cr / average trackwidth

Where Cr is the roll moment (see below) we calculated above and average trackwidth is the average of the front and rear track widths since they are rarely the same. This is a bit of an over-simplification since it assumes the front and rear track widths are close and not vastly different, but it is good enough for our purposes. You can picture this formula this way: Imagine a very tall car and narrow car. I think most of us would agree it would tend to tip over very easily in a turn. Now, make the car lower (i.e. lower the center of gravity) or spread the wheel out so the car is wider. Intuitively, the car would naturally be more stable. Looking at the formula, you can see why your intuition would be correct. Lowering the CG height and spreading the wheels out will both reduce the weight transfer.

So far we have only been talking about the weight transfer for the entire vehicle. What we now need to understand is how much of it happens at the front wheels versus how much happens at the rear wheels. This is the roll couple “distribution” I was talking about above. We need to know how the weight transfer is distributed between the front and rear wheels.

Tire Characteristics

tTo understand why we care about the roll couple distribution/weigh transfer, we need to understand a fundamental characteristic of tires. Tires generate cornering (and braking) forces because there is friction between the tire and the road, and the more you push down on a tire, the more friction you create and therefore the more cornering or braking force the tire can produce. It’s the same as pushing a block of wood on a tabletop. The heavier the block is, the harder it is to slide it along the table. A block that is twice as heavy will require twice as much force to slide. Tires work the same way except for one major difference: doubling the weight on a tire does NOT double the amount of cornering force the tire can generate. Here is a graph of a typical tire behavior:

Image via Speed News

Tire-load sensitivity has to do with the complicated physics of the tire-to-road interface and how a tire generates cornering forces. In a nutshell, tires generate cornering force by deforming slightly in the area of the contact patch. This deformation results in a slip angle and means that in a corner, the tire is actually traveling in a direction slightly outward from the direction it is facing (so in the image below, the car it turning left; the tread is deforming and pointing outward while the tire is pointing more inward). The more slip angle a tire produces, the more the direction of travel differs from the direction the tire is facing and the less cornering force it generates.

Image via Mechanics and Industry

But here is where it gets a bit more complicated. For a given tire, the more cornering force the tire is asked to provide, the higher the slip angle gets. In other words, the harder you corner, the larger the slip angle will be that your tires are generating. This is true for all tires, no matter if they are high performance summer, all-season, or winter tires. However, high performance tires will generate cornering force at smaller slip angles than lower performance tires. There are also differences in the slip angles generated by different brands and models of high performance summer or all-season tires. This is why it is always a good idea to have the same brand and model tires on all four corners of your car — and definitely do NOT mix all-season and summer tires on your car. The handling balance the OEM worked hard to achieve relies on having the correct slip angle behavior from all four tires working together.

Now let’s take a look in detail at what the graph above is telling us. The graph is for one particular tire, but it shows the trend all tires follow. Notice that doubling the vertical force on this tire from 200 lbs to 400 lbs increased the cornering force it is capable of generating from 190 lbs. to 360 lbs. In other words, increasing the vertical force by 100%, only increased the cornering force by 85%. This by itself is not terribly interesting, but what makes tires unique is that as you increase the vertical load the tire is carrying, the increase in cornering capacity for the same 200 lb increase in vertical load gets smaller and smaller. Increasing the vertical load from 800 to 1,000 lbs. for instance, only increases the cornering force by 70 lbs, or 35%. It is this tire characteristic that allows suspension and vehicle dynamics engineers to tune certain handling characteristics into vehicles.

How Engineers Tune A Car To Oversteer Or Understeer: The Theory

So how do vehicle dynamics engineers use this characteristic, and how is it related to the roll couple distribution?

If you want to make a car understeer, you want the front axle to slide away from the turn more than the rear axle does. In other words, if you can make the slip angle (the difference between where the tire is pointing and where it’s actually going) of the front axle greater than the slip angle of the rear axle, then we get understeer. Oversteer is the opposite: we want the slip angle of the rear axle to be greater than the front axle.

The way we can change the amount of slip angle each axle generates is by controlling how much of the weight transfer in cornering happens at the front axle vs the rear axle. Let’s take an example to show how this works.

Suppose we have a car that weighs 2,400 lbs and has 50/50 weight distribution, i.e., each axle carries 1,200 lbs. of the vehicle weight. This means each tire is carrying 600 lbs. Let’s also assume we have four tires like the ones in the graph above. Looking at the graph, these tires can generate 510 lbs. of cornering force. This means that at low speeds, each axle can generate up to 2 x 510 lbs. = 1020 lbs.

As we saw earlier, in a corner, there is weight transfer that occurs due to the height of the center of gravity. If we assume the center of gravity of our car is two feet off the ground, this means the roll moment, Cr, is 2 x 2,400 = 4,800 lb-ft. If we also assume the average track width of the car is five feet, then the weight transfer will be 4800 / 5 = 960 lbs. per g of cornering. In a 0.5g corner the weight transfer will then be 960 x 0.5 = 480 lbs.

If both axles share an equal amount of this weight transfer, then the front axle will carry 480 / 2 = 240 lbs. of weight transfer and the rear axle will also carry 240 lbs. of weight transfer. This means that both the front and rear outside tires each carry 240 lbs. more load than they did going straight ahead, and the inside tires each carry 240 lbs less load than they did going straight ahead. Each of the outside tires then carries 840 lbs. (600+240) while each of the inside tires now carries 360 lbs. (600-240) of load.

Looking at the graph again we can see that at 840 lbs. vertical load these tires can generate 620 lbs. lateral force while at 360 lbs. vertical load they can generate 330 lbs. lateral load. The total for the axle is then 620 + 330 = 950 lbs. lateral load capacity. Note that this is quite a bit less than the 1020 lbs. we started with going straight ahead. Since the same thing is happening at both the front and rear axles, this would give a roll couple distribution of 0.5 or 50% since half of the weight transfer is happening at the front axle.

By now it should be clear that to maximize overall lateral grip, you want to distribute weight as evenly as possible among all tires, and that generally means minimize weight transfer.

Now, what if we were able to force more of the weight transfer to happen at the front axle and less at the rear? Let’s suppose we had a method whereby instead of the weight transfer being shared equally between the front and rear axles, we were able to force 70% of the weight transfer to happen at the front axle. That would mean that instead of 240 lbs. weight transfer occurring at the front axle, we would have 480 * 70% = 336 lbs. front weight transfer with the remainder (480 – 336 = 144 lbs.) transferring at the rear axle. The front outside tire vertical load becomes 600 + 336 = 936 lbs. and front inside tire vertical load becomes 600 – 336 = 264 lbs. In the rear, the numbers become 600 + 144 = 744 for the outside tire and 600 – 144 = 456 lbs. for the inside tire. Here is what that would look like on the tire graph where the front weight transfer is shown in green, and the rear in blue:

 

At the front axle, the outside tire now has a lateral force capability of 650 lbs. while the inside tire has a capacity of 250 lbs. for a total front axle lateral load capacity of 650 + 250 = 900 lbs. In the rear however, the outside tire has a lateral load capacity of 580 lbs. and the inside tire has a capacity of 405 lbs. for a rear axle total lateral load capacity of 580 + 405 = 985 lbs. This means that the front axle now has less total lateral load capacity and will have a higher slip angle than it had when the load transfer was shared equally (Remember, as we learned above, a higher slip angle is associated with lower lateral force capacity in a tire). Of course, the opposite is happening at the rear axle where the total lateral load capacity is now higher than it was before, and the slip angle will be correspondingly less. So, in the case of this example, where we forced 70% of the weight transfer to occur at the front axle, we say that the roll couple distribution is 0.7, or 70%.

How Engineers Tune A Car To Oversteer Or Understeer: The Hardware

Now that we know we WANT to be able to control the roll couple distribution, we need to understand how to do it in practice. What hardware is needed in the suspension to control roll couple distribution?

Let’s look at what happens when a car rolls while in a turn. When you enter a turn, the lateral weight transfer changes the load on the tires by passing through the front and rear suspensions. This causes the springs to compress on the outside front and rear wheels and to expand on the inside front and rear wheels. This compression and expansion of the springs is what makes the body of the vehicle roll.  The amount that the body rolls will of course depend on the stiffness of the springs. If the front and rear springs have the same stiffness, then the body roll will cause the same change in force in the front and rear springs and therefore the same change in vertical load at the front and rear tires. This would equate to a 50% roll couple distribution like we had in our initial example.

Unfortunately, the stiffness of the springs is chosen not by how they impact the roll couple distribution but instead are chosen primarily for straight ahead ride. When a car travels forward over bumps, it moves up and down in response to those bumps, and how the car behaves in those situations is determined in large part by the stiffness of the front and rear springs. Do you want a firm sports car-like ride? Choose stiff springs. Do you want a more boulevard soft sedan-like ride? Then choose softer springs. This will be fine for ride but may not be good for cornering. The stiffnesses of the front and rear springs could result in a car that oversteers badly or understeers badly depending on what stiffnesses the engineers wanted for ride. To better understand this let’s take an extreme example. Let’s suppose the straight ahead ride we wanted has resulted in super soft front springs and super stiff rear springs. In a corner, the body roll would then be controlled by the rear springs since they would be doing most of the work. Most of the weight transfer would happen in the rear suspension because they are the stiffest and would control how much the body rolls. The result would be that the slip angle of the rear tires would be much greater than the front tires and the vehicle would oversteer.

So, spring stiffnesses are chosen to control straight ahead ride but the result is most likely a vehicle that is not tuned for optimal cornering performance. What we need is a mechanism that allows us to change the spring stiffness in cornering either in the front suspension or the rear suspension without effecting the spring stiffness in straight ahead ride. We could then use this mechanism to assure that a majority of the weight transfer happens on the front axle so that the front slip angles are greater than the rear and we ensure an understeering car.

Anti-Roll Bars

Fortunately, there is such a mechanism, and it’s called an anti-roll bar. As the name implies, an anti-roll bar resists the forces that cause the body to roll. At the same time, it has no effect when the body simply moves up and down like it does during straight ahead ride events.

Image via Evan Mason/Wikipedia Creative Commons

The anti-roll bar, or sway bar or stabilizer-bar,  is a bent steel pipe or bar that connects the two sides of the front or rear suspensions to each other, usually via a pair of small vertical links. The center portion of the bar is connected to the body at two points that allow the bar to spin freely but not move side to side (on some vehicles, the bar mounts to the moving axle and the links mount to the vehicle — see video below). During a ride event, the body moves up and down and both sides of the suspension are doing the same thing, either moving up or down relative to the body. The movement pushes up or down on the two small links which causes the anti-roll bar to spin on its two body (or axle) attachments. In this case, the anti-roll bar simply moves with the suspension and is just along for the ride.

When the body rolls like it does in a turn, however, the suspension on the outside of the turn moves up relative to the body while the suspension on the inside of the turn moves down. This causes the small link on the outside suspension to push up on the anti-roll bar while the small link on the inside suspension is pulling down. The only thing the anti-roll bar can do in this situation is twist, which it resists based on its design. This has the effect of pushing down on the outside suspension while pulling up on the inside suspension, reducing the amount of roll the body sees, and increasing the share of the lateral load transfer occurring on that suspension, just like stiffer springs would do. By choosing the diameter of the pipe or bar used to make the anti-roll bar, we can tune how much it resists the twisting caused by the body roll and thereby the lateral load transfer that occurs at that particular end of the vehicle. Doing this at the front suspension will have the effect of increasing the share of the lateral load transfer occurring at the front of the vehicle thereby increasing the understeer.

Roll Control

Now. let’s suppose we have installed an anti-roll bar in the front suspension, we’ve chosen a bar diameter that gives the amount of understeer we want but the car rolls back and forth in the turns like an old school Town Car. How do we now control that amount of roll we get in turns without screwing up the understeer we worked so hard to get? If we just increase the diameter of the anti-roll bar in the front, we will add more understeer than we want. But, if we add an anti-roll bar in the rear suspension at the same time as we increase the diameter of the front bar, we could bring the understeer back where we want it while also reducing the amount of roll in turns.

The choosing of the appropriate front and rear springs as well as the front and rear anti-roll bars is a delicate balance that takes time and a lot of trial and error. There are computer models that are used to choose the initial spring and anti-roll bar sizes, but the final values are the result of lots of in-vehicle work under many different road conditions that combine straight ahead ride events with cornering, braking, and acceleration. Anything a customer might do in normal or emergency driving is tried to make sure the vehicle is safe and predictable at all times.

Before we leave the topic of understeer and oversteer, there are two factors that we need to understand and take into consideration in tuning the handling of a vehicle and they are: the braking effect and the weight distribution effect.

The Braking Effect

As anyone who has done any track days will tell you, if you hit the brakes in a turn, the car will understeer less and may even oversteer slightly. Let’s use our example car to look at why that happens. What would happen if we had to hit the brakes hard while in the same 0.5g turn? During braking, there is a forward weight transfer that is very similar to the lateral weight transfer we have been discussing so far. The way to calculate it is the same as we did before except that instead of using the average track width, we use the wheelbase. Just like we did in the case of cornering, we have a 2400 lb. car, with that weight assumed at the CG height, which we multiply by the g level: 2400 x 2 x 0.5 = 2400 lb-ft, which is called the pitch moment in the case of braking.

But now, instead of dividing that by the average track width, we divide it by the wheelbase. If we assume our car has an 8-foot wheelbase, then the forward weight transfer is 2400 / 8 = 600 lbs. This weight transfer is shared equally by the front wheels and the rear wheels so each front wheel vertical load increases by 300 lbs. and each rear wheel vertical load decreases by 300 lbs. The front outside tire now has a vertical load of 936 + 300 = 1236 lbs. while the inside front tire has a vertical load of 236 + 300 = 536 lbs. The outside rear tire would have a vertical load of 744 – 300 = 444 lbs. while the inside rear tire vertical load becomes 456 – 300 = 156 lbs. Here is what that looks like in our graph:

What we now see is that the front axle lateral load capacity is 720 + 480 = 1200 lbs (solid green lines in the graph above). and the rear axle lateral load capacity is 400 + 140 = 540 lbs (solid blue lines in the graph above). Comparing these numbers to the non-braking case, 1200 (braking) vs. 900 lbs. (in a corner not-braking) in the front and 540 (braking) vs. 985 lbs. (not braking) in the rear, we see that the front has gained a significant amount of cornering capacity while the rear has lost a significant amount of cornering capacity. This shows why when you hit the brakes in a corner, the rear tends to step out and the front will “tuck in”.

This is a big reason why vehicles are tuned for understeer. If a driver hits the brakes in a turn, the change in weight transfer cannot cause the whole car to transition into oversteer, because — again — a sideways crash isn’t as safe as a head-on one. There has to be enough understeer built into the vehicle so that even under panic braking while in a hard turn, the vehicle does not lose so much understeer that it oversteers and spins out.

Weight Distribution Effect

In the example above we had a vehicle with 50/50 weight distribution. However, many vehicles on the market don’t have 50/50 weight distribution. Many have more weight in the front than the rear, and in some cases, like Porsche 911’s, there is significantly more weight in the rear than the front. Let’s look at a case where our example car has 60% of its weight on the front. Our 2400 lb. car would then have 1440 lbs. in the front (720 lbs. per tire) and 960 lbs. in the rear (480 lbs. per tire). If we assume the same weight transfer and the same 50% roll couple distribution, the front outside tire would have a vertical load of 720 + 240 = 960 lbs. The inside front tire would have a vertical load of 720 – 240 = 480 lbs. In the rear, the outside tire would have a vertical load of 480 + 240 = 720 lbs. while the inside rear tire would have a vertical load of 480 – 240 = 240 lbs.

From the graph above we then see that the front axle would have a lateral load capacity of about 660 + 425 = 1085 lbs. while the rear axle has a lateral load capacity of 570 + 230 = 800 lbs. However, since more of the weight of the car is sitting on the front tires, they also have to provide more of the cornering force compared to the rears. But, as we learned earlier, as a tire generates higher cornering forces, it also generates higher slip angles. The result is that for front heavy cars, in a corner, the front tires will have a higher slip angle than the rears. And, as we learned earlier, a higher slip angle means the tire is traveling at a greater angle from the direction it is facing. The opposite is true for rear heavy cars like the 911 and anyone who has driven an old 911 can tell you that oversteer is a very real issue in those cars.

Tuning a car for understeer and oversteer is therefore an exercise in controlling the slip angles at the front vs. the rear tires and getting the balance right so that there is just slightly more slip angle on the front axle and that the car understeers. The front slip angles need to be large enough so that the effects of weight transfer during braking doesn’t transition the car into oversteer but not so much that the car isn’t fun to drive. It’s a delicate balance and one that vehicle dynamics engineers spend most of their time trying to get right.