# Why is braking action (with Anti-Skid) best when the wheel rotates at ~85% of the actual speed?

During my ATPL training the subject of tires and braking was discussed.

• I understand the principle of the anti-skid and also the differences between aircraft and similar systems in cars.
• Physics also thought me that static friction is greater dynamic friction.

The script mentions that it has been shown that the maximum braking efficiency is obtained when the wheel rotates at a speed of 85% of the ground speed. [Clarification: imagine a identical tire wich rolls on the surface without any resistance/braking, this would be 100%. Every bit of slip therefore reduces the rpm. ]

Why would this be beneficial?

My ideas so far are:

1. that if some slip occurs braking is mostly in the static friction range but some energy during braking is also put into deforming the tire (and thereby heating it) and possibly ripping small pieces of rubber (on a really small scale) off the tire.
2. In order to find out where the tire begins to slip it actually has to slip, so in this process of: raising the pressure on the brake and if slip occurs, reducing the pressure, on average a slip of 15% occurs- whixh means a tire speed of 85%.

Is one of these correct?

Are there any other factors and processes?

• this is unclear " the wheel rotates at a speed of 85% of the ground speed." one is a rotational speed (deg/s or rad/s) and the other is a linear speed (m/s). Did you mean " the wheel rotates at a speed such that the outer rim has a speed equal to 85% of the ground speed." ? Commented Aug 6, 2018 at 11:31

Tire-road dynamics at speed are described by the Pacejka's "Magic Formula", so called because

there is no particular physical basis for the structure of the equations chosen, but they fit a wide variety of tire constructions and operating conditions.

This empirical description was developed using regression analysis and consequently has no theoretical basis as to why it works, but it does work and is widely used. You may not like the answer that 85% is best because that is what the formula says.

The reference gives the parameters necessary for calculating the peak longitudinal force and corresponding slip. ABS systems attempt to balance a peak slip ratio with vehicle directional control, resulting in an ideal ratio between 0.1 to 0.3. (which is 70-90% of ground speed using your terminology)

source

I would modify your statement #2 to say that in order for the ABS to know when the tire begins to slip it has to know when the tire does not slip, which allows the determination of unbraked tire speed from which the desired slip can be calculated. I think this is one reason for pulsating brakes when ABS is active; the ongoing determination of zero slip speed as the vehicle decelerates.

• Great find on that graph. Commented Aug 7, 2018 at 0:21
• In the case of Maxaret, the pulsing was purely a mechanical side-effect. It turned off the brake every time the wheel slipped 60 degrees, so it pulsed at 6 times the current RPM. Commented Aug 8, 2018 at 21:21
• @MauryMarkowitz What does 'slipped 60 degrees' mean? Commented Aug 8, 2018 at 21:43
• Too long to explain here, see: en.wikipedia.org/wiki/Maxaret Commented Aug 8, 2018 at 21:47
• Maxaret is a now obsolete purely mechanical ABS designed in the 50's that used a control disc with a one way clutch that would spin up with wheel on landing. When brakes were applied and the tire began to skid (the wheel began to lock) the disc would advance relative to the wheel. At 60 degrees of advance the disc activated a hydraulic valve dumping pressure from the brake circuit stopping tire slip and the cycle repeated. Commented Aug 8, 2018 at 22:10