Car Skidding

You drivers out there have probably heard of the ABS in your car (at least, if you are driving a car, you had better know about it!). ABS stands for “Anti-lock Braking System,” which should never be written as the “ABS system.” This is not a post about how ABS works, but rather one about the underlying concept behind it.

Generally what ABS does is to prevent wheels from locking up. To understand this, consider what would conventionally occur (i.e. in a vehicle without ABS). If someone were to slam on the brakes in a moving car without ABS, the braking discs or drums would cause the wheel to stop turning. Typically, that is the whole purpose of brakes in the first place, but usually one would gradually brake the car to stop by applying more and more brake pressure until the vehicle stops. If the brakes lock up the wheels suddenly (which is unhealthy for the brakes anyway), wheels lock up. Remember that the car is still traveling at considerable speed. Simply preventing the wheels from turning does not stop a car. The momentum of the car keeps the vehicle moving forward, so we get tire skidding, and we lose traction. That’s a bad thing; we would be sliding and have little to no control of steering.

Fundamentally, ABS adds some electronics (like computers and sensors) in between the brake pedal and brakes and modulates the braking pressure so that tires don’t skid and traction is maintained. We’re going to focus on why it’s so important not to skid by taking a look a friction. If you want to learn about how ABS actually works, you can visit HowStuffWorks’s “How Anti-Lock Brakes Work“ article or About.com’s “How Does ABS Work” article.

There are two basic types of kinematic friction: static and kinetic, but both are a function of the normal force. (Do you remember what the normal force is? “Friction at the Tip of the Finger” talked a little about it a few weeks ago.) The friction force can be loosely described by this relation:

Friction Force

Coefficient of Friction

If you recall from “Friction at the Tip of the Finger“:

The coefficient of friction is a dimensionless constant that takes into account the two surfaces. The higher this coefficient, the greater the friction force. Using everyday experience, for example, the coefficient of friction between leather shoes on ice is much smaller than between sneakers on the concrete sidewalk. (There are tables we can use to looks these coefficients if we really wanted to. And it’s important to note that these coefficients are generally higher at higher temperatures for the same pair of surfaces.)

Note: the coefficient of friction is basically depends on the two types of materials in use, and static coefficient of friction is usually greater than the kinetic coefficient of friction. We’ll see this in a bit.

Kinetic Friction

Sliding Dictionary Example

Let’s take a look at these two cases. Kinetic friction (or sliding friction) is simple. It only comes into play when something is physically rubbing against something else. It is the resistive force that goes in the opposite direction of motion. So, imagine you are successfully pushing a heavy dictionary across your desk. You can clearly feel the resistance, which you’d usually attribute to its relatively heavy weight. In fact, what you are feeling is the kinetic friction that resists the motion (remember, it has to be moving for the concept of kinetic friction to apply). This friction force is a function of the normal force, which, in turn, varies directly with the object’s weight. So, it is generally correct to assume that heavier objects are harder to push (assuming the same coefficient of friction, of course). Does that make sense?

Kinetic Friction Force

Static Friction

Static friction is pretty awesome, but it takes some explaining. Firstly, this friction is present whenever there is no motion (or static). The magnitude (or value) of this force, however, depends on what is acting on it. This can go from 0 to a maximum value that is dictated by the friction formula above. So, for the case of static friction, we have:

Static Friction Force

Let’s go back to our dictionary example. Once the pushing force exceeds the maximum static friction force, the book begins to slide, and we move into the kinetic friction regime. But before that point, it takes some increasing amount of force to get the dictionary to slide. The magnitude of the static friction force is only to the extent that it is needed. Consider the following series of diagrams. (Remember that the Newton is the metric unit for force.) Let’s assume for sake of example, that the maximum static friction force is 10 N. Note that the kinetic coefficient of friction is less than the static one, which we see because the kinetic friction force is less than the maximum static friction force.

Now, how does it apply to ABS and car tires? Keep in mind that as a car tire rolls, there is a patch of rubber that is actually stationary and static friction is in effect. We want to maintain this static friction for as long as possible (for grip, traction, and control). If the rubber starts to slide across the asphalt (when the wheel locks up), we lose the benefit of the static friction force and the stopping force exerted by the tires on the car. That’ll be a bad thing, especially since we usually slam on the brakes when we really, really need to stop (to avoid hitting the ducks crossing the road, let’s say). In order to stop in the shortest time possible, we prefer the greater static force over the kinetic force. In this case, our first instinct of abruptly pressing on the brakes fails us. Thank goodness for ABS. (Or, we can all just pay more attention to the road!)

Car image from: http://www.aa1car.com/library/stability_control.htm

Source: http://en.wikipedia.org/wiki/Friction#Static_friction