# Physics of ABS brake system

## Main Question or Discussion Point

I was trying to explain the ABS brake system to my daughter, then this question popped up.

http://auto.howstuffworks.com/auto-parts/brakes/brake-types/anti-lock-brake1.htm

I understand the ABS brake system in general, as the above web site says,
The controller monitors the speed sensors at all times. It is looking for decelerations in the wheel that are out of the ordinary. Right before a wheel locks up, it will experience a rapid deceleration. If left unchecked, the wheel would stop much more quickly than any car could. It might take a car five seconds to stop from 60 mph (96.6 kph) under ideal conditions, but a wheel that locks up could stop spinning in less than a second.

The ABS controller knows that such a rapid deceleration is impossible, so it reduces the pressure to that brake until it sees an acceleration, then it increases the pressure until it sees the deceleration again. It can do this very quickly, before the tire can actually significantly change speed. The result is that the tire slows down at the same rate as the car, with the brakes keeping the tires very near the point at which they will start to lock up. This gives the system maximum braking power.
The question I have is, why is the probability of a wheel slipping at time t is higher, if the wheel was slipping at t - $$\nabla$$t?

## Answers and Replies

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jambaugh
Gold Member
In general the coefficient of static friction is usually higher than the coefficient of sliding friction. That means of you try to get something to slip you must apply a greater force than is needed to keep it slipping.

So if its already slipping the force being applied is somewhere between the point were it will stop and the higher point where it started. Call the static friction force F and the sliding friction force f with f< F.

Call the current force g.
You are definitely slipping now if g> F.
You are definitely now slipping now if g< f.
You may be slipping now if f< g < F but only if you were slipping up to now otherwise you are not slipping.

So whatever is the the probability that f< g < F, then that (or twice that?) is how much more probable it is that you are slipping now if you were slipping up to now verses if you were not.

K^2
This is the reason why when you are driving on snow/ice/dirt and you have no ABS, you must tap the brake, rather than depress it. You must keep wheels rolling. It allows you to stop faster, and more importantly, it allows you to maintain control of the vehicle.

If you have an ABS, it's safe to simply press the brakes in pretty much any situation. The ABS will prevent the slip and allow you to remain in control. The main exception is a sharp turn. The traction is shared between braking and steering. In a sharp turn, it's possible to lose grip even with ABS.

If your daughter is learning to drive, right now is a good season to find a snow-covered parking lot, if you live in the area where it snows, and get the feel for what happens when the car loses grip, and how ABS helps prevent it (or how to prevent it yourself if you have no ABS). On fresh snow, you can usually get the same behavior out of the car at 15mph that you'd get on a highway at 70mph, but the mistakes don't cost as much.

it is also worth noting that ABS does not produce optimised braking, a skillfull driver (not me) will do better with the use of threshold / progressive braking techniques

but ABS works well for most drivers in most situations hence it's popularity on road cars

Last edited:
K^2
It's pretty close to optimum. The older systems were easy to outperform if you knew what you were doing. With the new ones, you have to have a lot of professional training to brake more efficiently. But yes, technology is still no replacement for good training. If only people actually received that training before driving...

indeed, they are getting better, and for road use I would always leave it turned on for safety reasons
on loose gravel, rolling wheels are not always effective - trapping debris in front of the tyre can help deceleration - another rare case when ABS is not the best option, but again this is the exception not the rule...

I've always known that static friction is greater than kinetic friction, but that's always been like an axiom.

So the question I put to you is this - WHY? (maybe it has something to do with friction being a non-conservative force).

Adhesion. When something is static parts of it begin to adhere, these little links between two materials don't have time to form if the part is constantly moving.

You can get coefficients of friction of >10 for incredibly smooth contact surfaces with no contamination. As the two parts effectively begin to weld themselves together.

Do you know if the delta of static to kinetic friction is similar across all materials or is there a massive variance in the ratio between the two variables depending on material type? (eg plastic, metal, smooth surface, rough surface etc)

rcgldr
Homework Helper
Do you know if the delta of static to kinetic friction is similar across all materials or is there a massive variance in the ratio between the two variables depending on material type?
Teflon on teflon is almost the same, .04 for static and kinetic.

BobG
Homework Helper
The ratio between static coefficient and kinetic (sliding) varies depending on the material.

http://www.engineershandbook.com/Tables/frictioncoefficients.htm

I don't think it's humanly possible to outperform an ABS regardless of how much training a driver has. ABS can pump the brakes more times per second, therefor maintaining a closer tolerance between static/kinetic than a human can, period.

Additionally, modern ABS can pump each brake individually (except then it's called an Electronic Stability Control program). The ability to control the braking of each tire individually reduces the chance of rollover accidents in addition to reducing the chance of going into a skid.

If you're teaching her how ABS affects driving, try practicing in an empty icy parking lot. Whether you're driving a non-ABS vehicle or an ABS vehicle, the best way to understand is to do it. (The empty part is very important even if you know, or think you know, what you're doing.)

Do you know if the delta of static to kinetic friction is similar across all materials or is there a massive variance in the ratio between the two variables depending on material type? (eg plastic, metal, smooth surface, rough surface etc)
There are many, many variables affecting the difference between static and kinetic friction.
The surface finish, the material, the lubrication/contamination of the surfaces. Minor changes can cause large differences.

As a generalization materials that adhere less will be more likely to have a similar value for friction coefficient. As above polymers such as PTFE and polyethylene doesn't adhere as they have low surface energy and tend to have similar values.

bcrowell
Staff Emeritus
Gold Member
I've always known that static friction is greater than kinetic friction, but that's always been like an axiom.

So the question I put to you is this - WHY? (maybe it has something to do with friction being a non-conservative force).
It's not logically possible for kinetic friction to be stronger than static friction (assuming the standard equations). If you had a combination of surfaces with $\mu_k>\mu_s$, then imagine the situation where you start by applying zero force, then increase it, and finally just barely exceed the maximum force of static friction. The model then can't predict what happens.

I don't think it's humanly possible to outperform an ABS regardless of how much training a driver has. ABS can pump the brakes more times per second, therefor maintaining a closer tolerance between static/kinetic than a human can, period.
It would depend on how sensitive the ABS is to a wheel locking up. I've had systems that went ape when you just pressed the pedal hard even though there was tons of grip left (a cheap system basically in a Corsa). It wouldn't even let you get close to the optimal braking point as the ABS kicked in too early.

A tuned system, or at least a more expensive one would be better though. I don't think anyone is saying that a driver could outperform an ABS system after a wheel has locked up though.

If you're teaching her how ABS affects driving, try practicing in an empty icy parking lot. Whether you're driving a non-ABS vehicle or an ABS vehicle, the best way to understand is to do it. (The empty part is very important even if you know, or think you know, what you're doing.)
If he's going to teach anything it's how to deal with lift-off oversteer. Not knowing what to do can lead to catastrophe, the amount of people that I saw hit the brakes after the back end had gone this winter was just... wow.

It's why I say there should be a mandatory skid pad test for anyone wanting to drive.