decceleration curve

[sprior]

was going to give up with my math course as it is too hard, but have got to an interesting bit about braking performance, and whether or not braking decceleration is (or should be) linear.

Loads of interesting stuff comes to mind like wind resistance, brake temp, tyre temp, tyre rolling speed, disc speed, weight transfer etc.

Anyone got any curves for decceleration v time?
Would be ace if the ruf 0-100-0 curves were available!

simon

[GreenV8S]

Pretend that maximum decelleration is independant of speed and you won't be far wrong. There are various factors that do depend on speed but for conventional roadgoing cars these would only have a very small effect and will tend to cancel each other out. For example:

Coefficient of friction of the tyre will increase as it gets hot (this is probably the biggest speed-dependant factor).

If the brakes overheat, the brake balance will be thrown out which means it will no longer be possible to achieve maximum braking on all four wheels.

Aeodynamic drag will decellerate the car (but only by about 0.05 G at terminal speed for a typical car).

Aerodynamic lift will reduce the weight on the wheels at high speed (but only a 1% change for a typical car).

Once you get far enough away from a conventional car or typical road speeds, some of these factors start to become more important. For example an F1 car generates so much downforce that it can pull around 6G under braking at 180 mph but only 1.5G at 30 mph. Similarly, the effect of drag will be more important on very light cars with poor aerodynamics. I've been in a high speed convoy behind a Caterham where I had to brake fairly hard each time the Caterham driver lifted off the throttle, to avoid running into the back of him.

[sprior]

It seems logical that retardation is pretty much constant, regardless of speed for a road car, but is it my imagination that makes me think that it's easier to look up (or invoke abs) at lower speeds than higher ones?

[neon_fox]

sprior said:

It seems logical that retardation is pretty much constant, regardless of speed for a road car, but is it my imagination that makes me think that it's easier to look up (or invoke abs) at lower speeds than higher ones?

Completely correct, as to invoke ABS you have to lock up a wheel (or come close).

As the ability to lock the wheel is dependant on a number of factors which are basically constant for a given application (e.g. frictional coefficients, which we shall ignore) leaving one factor which varies as the square of the speed, the rotational energy of the wheel. This energy must be converted into other forms of energy (mostly heat) by the application of friction between the brake pad and the disk.

The faster the wheel is spinning, the harder it is to dissipate that energy quickly enough to lock the wheel against other factors - mainly the friction of the tire against the road surface acting as a conduit for the kinetic energy of the car to spin the wheel back up again...

Hence "yes", the faster you are going the more difficult it is to lock a wheel.

Fox
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Caveat emptor: this explanation is intentionally much more simple than Real Life(TM), but hopefully makes enough sense to back up the initial proposition.