Does ABS shorten stopping distance of a car? ABS, from German Antiblockiersystem, is a device put in almost every new automobile. The web has lots of explanations about the system, how it works, but I don't understand how it shortens the way of stopping.
The system (a Wikipedia link) is intended to prevent locking of wheels and thus allows keeping control of the car (this I understand).
When I push a brake pedal, there are metal parts that touch a wheel. Because of friction force between these metal parts and wheel, the latter stops rotating and its kinetic energy is dispersed as thermal energy and both parts are hot. It does not matter how strongly I press the pedal, if only it makes wheel stop rotating. When it happens, there is a friction force between a tyre and ground. This force depends on (among others) car's mass.
The kinetic energy of moving car is (please confirm) dispersed as thermal energy. Sometimes stopping car leaves a black trace on the ground.
If now ABS starts to work, it moves the metal parts away, so the wheel can rotate again for some angle, even if I am still pushing the brake. This is intended behavior, and again the ABS stops the wheel.
I heard that such act can shorten the time to stop a car, but I don't know why. If the ABS allows the wheel to rotate for some angle, in this moment there is no friction between wheel and ground (well, actually there is, because the wheel rotates, but in this case it is useless friction). So the way to stop the car should be longer.
Again, I understand how the ABS prevents wheels from blocking and allows maintaining control, but I don't how it shortens this distance.
The only thing I can imagine is that this small angle of rotation prevents tyre from getting hot. If it would be hot too much, it becomes more liquid and the friction force is smaller (this is why these tracks come from). So the ABS changes "used" part (hot) of tyre to a "fresh" part (cold).
This explanation is not confirmed by experiment which I performed myself on ice with the speed ca. 10 km/h, and it shortened the stopping distance, but with this speed we should not think about thermal destruction of tyres.
 A: I am not 100% sure. But the way I think ABS decreases the stopping distance, is that the static friction between the tires and the road will be higher than the kinetic friction. So locking the tires by breaking hard, without ABS, will mean that there will be an kinetic friction between the tires and the road. However letting the tires just break hard enough to reach the maximum static friction (what ABS basically does) will mean that you will have a bigger force acting on the car and therefore the car will come to a stop in a shorter distance.
A: Without ABS, an experienced driver will go lighter on the brakes as soon as they feel it lock up.  Some time later, he'd press the break again, perhaps not as hard this time.  The computer, on the other hand, can apply a HUGE braking force, up to the point that the wheel's JUST BARELY lock for a fraction of a second, then let go and repeat.  If you think in terms of impulse and momentum, the larger breaking force can make up for the shorter overall time it is applied.  If the impulse of the breaking force of each pump of the ABS is larger than what a person would deliver, this means less time and distance is required to stop the car.  It turns out that this is the observed behavior when real people drive cars in most conditions, although it's not always the case.
A: There are a few points to consider:


*

*Driving is not only done on pavement. The friction in the braking system is predictable, because the materials do not vary. But driving surfaces vary. Anti-lock braking systems are particularly useful on ice or loose gravel. If the wheels lock up on ice, the car glides forward on a thin layer of water, with little friction. Preventing lock-up allows the wheels to stay bonded with the ice, so the brakes can dissipate kinetic energy. The idea is to try to maintain whatever grip that the tires are able to muster, so that the wheels move with the road, and the friction between brake pads and rotors/drums can dissipate energy.

*Braking is not just about slowing down or stopping, but maintaining control while doing that. Locked wheels can lead to a a dangerous skid. Wheels don't necessarily lock up at the same time on both sides, particularly if there is weight transfer from steering while braking.

*In manual transmission cars, when the drive wheels lock up, the engine can stall. On a slippery road, this can happen at speeds at which the driver is not accustomed to stepping on the clutch while braking.
A: ABS is not intended to shorten the braking distance, this system is for prevention of sliding when it occurs between roar and tire due to the exerted force exceeds the friction force. ABS triggered by sensors' signals to control panel and cosequently control panel commands to decrease the braking fluid thus slightly allowing acceleration. Then it again increases fluid amount i.e. hydraulic force increasing fluid through pump installed. 
Therefore if you own some basic physics, you can see actually ABS manages the braking, but some negligible increase in braking distance is in place. 
A: The whole point of braking is to dissipate kinetic energy. Not the kinetic energy
of the wheel as you said, but the kinetic energy of the car, even though you may
do that through transmission to the wheel.  Some trucks or busses
actually brake by transforming part of their KE into electricity,
which may sometime be reused, or is dissipated into heat as eddy (or
Foucault) currents.
However, the most common way to dissipate kinetic energy is
friction. In the case of cars there are two possible frictions :
bretween the brake and the wheel (not the rubber itself hopefully) and between
the rubber and the road.
But there is energy dissipation only if there is motion with (kinetic)
friction creating a resisting force (in the case of friction braking).
The word kinetic is in parentheses, because it may require some further precision (see below).
When the car is rolling normally, there is no (or marginal) kinetic
friction because the wheel is at rest relative to the road in the
contact part.  If you brake, this may no longer be true, because the wheel
may not turn fast enough. On some surfaces, like a wet road (but
apparently not all surfaces) the friction is more important if the
speed of the wheel part in road contact is not too important relative
to the road.  Beyond a certain speed, the tire can even sort of surf
on a thin layer of water, and the friction goes down, thus dissipating
less energy. This happens much faster if you block the brakes.
So, with the brakes blocked, there is no energy dissipated by friction
in the brakes, and the wheels may be skidding too fast to dissipate
energy efficiently. Hence, it take a longer time to dissipate, meaning
a longer time to stop.
The ideal situation is dissipating energy both in the brakes and in the rubber.
But that is not easy to attain, because the static friction coefficient is usually greater than the dynamic coefficient. As soon as the wheel starts slipping, the friction reaction force of the wheel that preserved some motion in the brakes may become too low for the brakes to allow for motion, and the brakes block, no longer providing any dissipation, and increasing further the  skidding speed of the wheel.
ABS prevents blocking the brakes by removing briefly the friction, and allows the wheels to turn some,
so that the relative speed of their contact with the road does not
get too high.
But why should it work on a dry road ?  According to Wikipedia, there
is another phenomenon to be considered. The transition from static to
dynamic friction coefficient is not a discontinuous
phenomenon. Apparently the "maximum braking force is obtained when
there is approximately 10%-20% slippage between the braked wheel's
rotational speed and the road surface", beyond which "rolling grip
diminishes rapidly" to kinetic friction. So that is where the heat
dissipation is at its maximum, since maximum dissipation requires maximum motion with
the greatest motion compatible friction (actually, it is the product that is to be maximized). The role of ABS will be to
let go when the slippage becomes too important so that the slippage
remains in the optimal range (in addition to above issues).
But apparently some surfaces behave differently, and ABS may actually
brake more slowly. I would guess that this is due to the specific properties of the function that relates the friction force and the slippage speed for
that kind of surface in contact with rubber wheels. But on such surface, the advantage of keeping
better control of the car, by slipping less, is also an issue.
Another role of ABS systems is to distribute the braking effort
between front and rear wheels. Front and rear wheels have different
internal pressure, thus different contact surface with the road. They
are also subjected to different forces as the car is braking (more
force in the front), so that the friction coefficient acts more
effectively where the force is greater.  Hence slippage control has to
differ in the front and in the back. It may also balance left and
right if for some reason the two sides behave differenlty.
A last issue was actually raised by @tohecz. Where should the energy
be dissipated, or according to what ratio between brakes and
rubber-road? His opinion is that it should be in the braking system,
not in the wheel-road contact. I did not find any information stating
that, if there is a choice, it should one more than the other, but it
may indeed be preferable to spare the tires (I do not really know).
It is however worth considering the issue and the degree of freedom of
choice.
We can analyze somewhat this ratio by considering extreme cases.  If
you block the wheels (assuming no ABS), no energy is dissipated in the
brakes. Thus it is all dissipated in the rubber-road contact. On the
other hand, if you brake slowly, the wheels surface remains in static
contact with the road (no ABS needed) and all the energy is dissipated
in the brakes. This runs contrary to some belief that violent braking
could heat the braking system: frequent and slow braking will,
while violent braking without ABS will heat and wear the rubber.
So the question of the ratio, with an ABS system, occurs really only
when you brake strongly enough so that wheel slippage will occur and
the ABS can be used to control it. Here a proper analysis would really
require working on actual figures, as there are many possible
scenarii.
It should be the case that optimal braking, with fastest energy
dissipation, will impose a precise pressure on the brakes resulting in
a precise dissipation ratio between brakes and rubber. However, given
the hiccup behavior of ABS system, this corresponds probably to an
unstable setting requiring a dynamic control of the pressure so as not
to leave the optimal dissipation zone. I did not find any information about this ratio.
If the pressure on the brake pedal does not indicate urgency for fast
braking, the ABS system can probably choose, according to its programming,
what amount of pressure to apply, and when, so as to determine where
most of the energy will be dissipated, between brakes and rubber.  But
there does not seem to be much public information on that.
A last remark is that the choice of optimal pressure for whatever
result is desired should also depend on the current speed of the car.
It is probably hard to get any slippage from a very slow car. Hence
the process has to be dynamically controlled for that reason too.
Note: In this analysis of ABS braking, the careful reader will have noticed that I
talk of forces, when actually it should be torques in many cases. My
reasons for doing this are the following:


*

*the main issue is friction and friction forces, which become torques
because of the structure of the devices considered;

*talking of torque would necessarily require the description to
introduce size considerations (wheel and brakes radius), which
would complicate the analysis without bringing in any essential
insight regarding ABS;

*this is just a qualitative analysis, without using any actual
figures. Developing complete formulae would of course require to
bring in size issues, and to consider torques. But I deemed it simpler
not to do that here.
To dissipate any misunderstanding and any heat that could result from
it, I should make it clear that this looked to me like an interesting
problem to work on, but that I have no particular expertise, and I did what I could with the information I could find. Comments and criticisms are welcome.
A: TLDR: ABS provides more stable handling, and improves friction with the road by ensuring static (rather than dynamic) contact. This can improve stopping distance.

ABS (antilock brake system, in English) measures the rotation of the wheels, and adjusts the braking pressure (either continuously, or in a pulsating manner) to prevent the wheels locking up. This improves handling and braking distance.
When brakes lock, the direction of the (small) force between the road and the tire is directly opposite to the direction of the motion; by contrast, when the wheel is rolling, the direction of force is at right angles. The latter means that if the car ends up pointing away from the direction of motion (starting to skid), the rolling rear wheel tends to provide a restoring force; a locked rear wheel does not prevent the car from continuing to turn. This is why it is important to brake harder with the front wheels than the rear wheels: it provides stability (if the front wheels lock, you continue in a straight line and can no longer steer; if the rear wheels lock, you spin). Ensuring that the wheels don't lock, therefore, improves handling.

Regarding braking distance: Braking removes kinetic energy from the car. This energy has to be dissipated - either between the tires and the road, or between the brake pads and the rotors. On a wet road, the profile of a rolling tire ensures that water is being pushed away, so there is some contact between the rubber and the road. When the tire locks, the water tends to build up in front of the wheel, and provides a continuous "film" of water on which the wheel can slide with minimal friction. With low friction between the wheel and the road, no energy is dissipated during braking. By restoring the rotation of the wheel, contact friction is increased. This is particularly striking case of the general difference between kinetic and dynamic friction: when two surfaces are not moving relative to each other, the force to start them sliding is greater than the force needed to keep them sliding if they are already moving.
A: The kinetic friction coeffictient is ALWAYS lower than the static friction (stiction) coefficient (by definition/virtue of the matter). Except for on loose gravel and snow, ABS ALWAYS provides higher acceleration than breaking with locked up wheels. Granted, for tires on asphalt, stiction vs. friction is a simplified model but the correct model, which uses slip, says exactly the same: Maximum acceleration for 10% slip, which is what ABS keeps the tires at, is ~ 1.1 g on dry roads whereas acceleration by dynamic friction (locked up wheels, so no ABS) is ~ 0.85 g. For wet roads, the ratio is about the same: ~ 0.75 g vs. ~ 0.55 g.
I found this source, which unfortunately is in German, but the graph should be interpretable easily enough:
https://www.leifiphysik.de/mechanik/reibung-und-fortbewegung/ausblick/reifen-aus-gummi-ein-kompliziertes-reibungsproblem
Note that your conclusion: "If the ABS allows the wheel to rotate for some angle, in this moment there is no friction between wheel and ground" is incorrect. ABS does not fully release the brakes intermittently - only until slip decreases and during that time, acceleration is not zero. It's just a tiny bit lower than acceleration by pure dynamic friction and only for a very short time. After slip increased again, acceleration is a lot higher and for a longer time.
Of course, ABS can be beat but only by ~ 0.05 g (for normal cars) and you have to be very accurate. Race car drivers do that all the time when approaching a corner. But
this is a completely different situation than an emergency break in traffic by everyday people. Actually, I'm pretty sure that even many a professional race car driver would panic floor the brakes in such a situation.
