hoffman
07-08-2003, 07:46 PM
(in now way is this my own or trying to pass this off as my own writing, enjoy)
Brakes:
1) The ultimate determinent of the amount of deaccelerative force that the chassis
can see is the amount of grip provided by the tires. This grip is determined
by:
a) The compound/construction of the tire
b) The area and shape of the contact patch
c) The amount of instantanious download on the tire (a function of static weight
distribution, dynamic weight transfer, and aero downforce/lift)
d) The instantanious camber angle of the tire
e) The instantanious temperature of the tire at the contact patch
f) The nature of the road surface at the contact patch
g) The ability of the tire to remain in contact with road irregularities, itself
a function of the natural frequency of the suspension, the impulse frequency,
and the damping ratio
h) The current slip angle of the tire. (which implies the direction of the load
vector)
Notice that NONE of this has anything to do with the brakes!
So we work all this out, and we come up with some level of grip at each tire,
which, when summed, tells us the maximum amount of deaccelerative force the
car can use under those conditions.
If the brakes are capable of producing this much force at each wheel, than we
are tire-limited. If the brakes cannot deliver this much force, then we are
brake-limited.
2) Our job as brake engineers is to ensure the car is tire-limited, not brake
limited, under all operating conditions. This means the driver has the ability
to lock the brakes at will, which we hope will translate into the driver ALMOST
locking the brakes at will. Give him the tools and hope for the best.
3) The amount of brake force produced by a brake is a function of:
a) The CoF of the brake pad, itself a function of pad temperature
b) The clamping pressure on the pad, itself a function of the caliper piston
area and the line pressure in the brake line, itself a function of the master
cylinder piston area, the brake pedal lever arm, and how had the driver is pressing
the pedal.
c) The torque arm between the pad and the axle
4) So simple, right? Just mix and match between the items in #3, and come up
with a combo that provides more braking force than the tire can ever generate.
Well, that works for bikes, where the driver has a separate control for each
(and every!) tire. But we have cars, and that means ONE control for FOUR tires.
So now we need some sort of mechanical interconnection between the tires and
this one control - and it means we have to start thinking "whole car" instead
of individual wheels.
To make things a little bit easier though, we can pretend that the car is really
a bike with only one brake control - we'll just pretend that the left and right
sides of the car are identical.
For now, we'll also pretend that most of the tire grip functions are identical
front and rear - camber, contact patch, temperature, road compliance, etc etc
etc. All we're going to care about is the braking force APPLIED to each wheel,
and the braking force GENERATED at the contact patch - which for the sake of
our simple example, is a function of static weight distribution + dynamic weight
transfer.
5) This leads us to the concept of "brake bias".
Strictly speaking, brake bias is the ratio of the line pressure in the front
brake circuit to the line pressure in the rear brake circuit - one control,
remember? But that's not a particularly useful way to think of it.
Instead, it is far more useful to think of brake bias in terms of the amount
and location of excess tire grip capacity when one end or the other has locked
up. If both wheels (remember, we're using a bicycle model) lock simultaniously,
then there is no bias. If the front locks first, it is front biased, and if
the rears lock first, it is rear biased. If the front locks first and there
is a lot of capacity still in the rears, it is strongly front biased, and so
on and so forth.
Now, let's consider a car that is strongly front biased. The driver hits the
pedal, weight transfer happens, and the fronts reach incipiant lockup. This
is the maximum level of braking that this car can stand. Adding more braking
force to the fronts on this car will not add any more deacclerative force, because
the fronts are already at incipiant lockup.
OK, so instead we do something to send more pedal pressure rearward - the rears
have all that extra capacity, so let's make use of it. The car now makes more
deacclerative force, and stops quicker.
Note, however, that there's a wrinkle here. When we increase the amount of deaccelerative
force, we increase forward weight transfer, which translates into more grip
at the fronts, less at the rear. This means we can press a little harder now
before we get the fronts to incipient lockup (we have more front grip) but we
also have less rear capacity too - in a way, sending brake force rearward "ate"
more rear capacity than we thought it would.
Note too that with a front-heavy car, forward weight transfer results in a net
loss of POTENTIAL braking force - we have something analogous to acceleration
in a WWD.
OK, so we keep sending brake force rearward until both front and rear lock together,
and we have maximised deaccelerative force, and we're done. Right?
6) Now we get to talk about STABILITY. When a tire is right at the point of
incipiant lockup, it can only produce braking force, not lateral force. If any
lateral load intervenes, that tire will lock unless the braking force is reduced
at the same time.
If the front locks, you get instant understeer. If the rear locks, you get instant
oversteer.
Now consider: nobody EVER brakes in a straight line. There is ALWAYS some measure
of lateral force on the tire. This means that not only do you want the fronts
to lock up first (understeer is stable, oversteer is not) but you ALSO have
to have sufficent rear excess capacity to be able to deal with unexpected lateral
loads. Because if you don't - around you go.
This is why brake bias is driver-adjustable in real race cars. What might be
acceptable bias in turn 1 may be too far rearward in turn 6. (And if you're
Michael Shumacher, you actually make those adjustments every lap, rather than
just setting the best compromise)
Without the ability to adjust bias directly, you have to ensure enough front
bias that the rears never lock first under any situation - which is what the
OEMs do.
In a nutshell, sending bias rearward trades stability for braking performance.
7) Now let's look at a modified car.
First, it was stock. The OEM set the car up so that the front brakes could be
locked - just - with enough pedal pressure. The car is tire-limited, and front-biased
Then you go out, and put great big sticky Hoosiers on the car. Grip goes WAY
up, to the point where you can't lock the brakes any more. The car is now brake-limited.
So you buy a set of performance brake pads with a much higher CoF, and you can
lock wheels again. The car is back to being tire-limited. Note, however, that
overall deaccelerative force is much higher, so you have more front weight transfer,
meaning less load on the rears, meaning less rear reserve grip capacity. This
means you have effectively moved the brake bias REARWARD (although it is probably
still front-biased)
At this point THE BRAKING POTENTIAL OF THE CAR IS MAXIMISED, or very nearly
so. It might be able to stand a little more bias movement rearward, but not
much (from my experience in DSMs, very, very little) and then you're giving
up stability.
So then, why aftermarket brakes?
3 reasons:
1) HEAT REJECTION - remember how brake CoF is a function of brake temperature?
That means the brakes must be able to maintain a certain temperature, or performance
falls off (fade) To do that, you add mass (as a heat sink) and surface area
(to speed cooling) - in other words, you make the rotors bigger. For cars that
see lapping use, this is essential. For street/autox cars, not at all.
2) WEIGHT - aftermarket parts can use aluminum instead of cast iron. I've got
TCE/Wilwood 6-pots with aluminum hats; they saved 9lbs per wheel
3) FEEL - anything that reduces brake system flex and swell means better pedal
feedback - although the OEM brakes aren't bad.
That's it - heat, weight, and feel.
Are there any questions?
DG
(written by Dennis Grant, DSM suspension guru)
Brakes:
1) The ultimate determinent of the amount of deaccelerative force that the chassis
can see is the amount of grip provided by the tires. This grip is determined
by:
a) The compound/construction of the tire
b) The area and shape of the contact patch
c) The amount of instantanious download on the tire (a function of static weight
distribution, dynamic weight transfer, and aero downforce/lift)
d) The instantanious camber angle of the tire
e) The instantanious temperature of the tire at the contact patch
f) The nature of the road surface at the contact patch
g) The ability of the tire to remain in contact with road irregularities, itself
a function of the natural frequency of the suspension, the impulse frequency,
and the damping ratio
h) The current slip angle of the tire. (which implies the direction of the load
vector)
Notice that NONE of this has anything to do with the brakes!
So we work all this out, and we come up with some level of grip at each tire,
which, when summed, tells us the maximum amount of deaccelerative force the
car can use under those conditions.
If the brakes are capable of producing this much force at each wheel, than we
are tire-limited. If the brakes cannot deliver this much force, then we are
brake-limited.
2) Our job as brake engineers is to ensure the car is tire-limited, not brake
limited, under all operating conditions. This means the driver has the ability
to lock the brakes at will, which we hope will translate into the driver ALMOST
locking the brakes at will. Give him the tools and hope for the best.
3) The amount of brake force produced by a brake is a function of:
a) The CoF of the brake pad, itself a function of pad temperature
b) The clamping pressure on the pad, itself a function of the caliper piston
area and the line pressure in the brake line, itself a function of the master
cylinder piston area, the brake pedal lever arm, and how had the driver is pressing
the pedal.
c) The torque arm between the pad and the axle
4) So simple, right? Just mix and match between the items in #3, and come up
with a combo that provides more braking force than the tire can ever generate.
Well, that works for bikes, where the driver has a separate control for each
(and every!) tire. But we have cars, and that means ONE control for FOUR tires.
So now we need some sort of mechanical interconnection between the tires and
this one control - and it means we have to start thinking "whole car" instead
of individual wheels.
To make things a little bit easier though, we can pretend that the car is really
a bike with only one brake control - we'll just pretend that the left and right
sides of the car are identical.
For now, we'll also pretend that most of the tire grip functions are identical
front and rear - camber, contact patch, temperature, road compliance, etc etc
etc. All we're going to care about is the braking force APPLIED to each wheel,
and the braking force GENERATED at the contact patch - which for the sake of
our simple example, is a function of static weight distribution + dynamic weight
transfer.
5) This leads us to the concept of "brake bias".
Strictly speaking, brake bias is the ratio of the line pressure in the front
brake circuit to the line pressure in the rear brake circuit - one control,
remember? But that's not a particularly useful way to think of it.
Instead, it is far more useful to think of brake bias in terms of the amount
and location of excess tire grip capacity when one end or the other has locked
up. If both wheels (remember, we're using a bicycle model) lock simultaniously,
then there is no bias. If the front locks first, it is front biased, and if
the rears lock first, it is rear biased. If the front locks first and there
is a lot of capacity still in the rears, it is strongly front biased, and so
on and so forth.
Now, let's consider a car that is strongly front biased. The driver hits the
pedal, weight transfer happens, and the fronts reach incipiant lockup. This
is the maximum level of braking that this car can stand. Adding more braking
force to the fronts on this car will not add any more deacclerative force, because
the fronts are already at incipiant lockup.
OK, so instead we do something to send more pedal pressure rearward - the rears
have all that extra capacity, so let's make use of it. The car now makes more
deacclerative force, and stops quicker.
Note, however, that there's a wrinkle here. When we increase the amount of deaccelerative
force, we increase forward weight transfer, which translates into more grip
at the fronts, less at the rear. This means we can press a little harder now
before we get the fronts to incipient lockup (we have more front grip) but we
also have less rear capacity too - in a way, sending brake force rearward "ate"
more rear capacity than we thought it would.
Note too that with a front-heavy car, forward weight transfer results in a net
loss of POTENTIAL braking force - we have something analogous to acceleration
in a WWD.
OK, so we keep sending brake force rearward until both front and rear lock together,
and we have maximised deaccelerative force, and we're done. Right?
6) Now we get to talk about STABILITY. When a tire is right at the point of
incipiant lockup, it can only produce braking force, not lateral force. If any
lateral load intervenes, that tire will lock unless the braking force is reduced
at the same time.
If the front locks, you get instant understeer. If the rear locks, you get instant
oversteer.
Now consider: nobody EVER brakes in a straight line. There is ALWAYS some measure
of lateral force on the tire. This means that not only do you want the fronts
to lock up first (understeer is stable, oversteer is not) but you ALSO have
to have sufficent rear excess capacity to be able to deal with unexpected lateral
loads. Because if you don't - around you go.
This is why brake bias is driver-adjustable in real race cars. What might be
acceptable bias in turn 1 may be too far rearward in turn 6. (And if you're
Michael Shumacher, you actually make those adjustments every lap, rather than
just setting the best compromise)
Without the ability to adjust bias directly, you have to ensure enough front
bias that the rears never lock first under any situation - which is what the
OEMs do.
In a nutshell, sending bias rearward trades stability for braking performance.
7) Now let's look at a modified car.
First, it was stock. The OEM set the car up so that the front brakes could be
locked - just - with enough pedal pressure. The car is tire-limited, and front-biased
Then you go out, and put great big sticky Hoosiers on the car. Grip goes WAY
up, to the point where you can't lock the brakes any more. The car is now brake-limited.
So you buy a set of performance brake pads with a much higher CoF, and you can
lock wheels again. The car is back to being tire-limited. Note, however, that
overall deaccelerative force is much higher, so you have more front weight transfer,
meaning less load on the rears, meaning less rear reserve grip capacity. This
means you have effectively moved the brake bias REARWARD (although it is probably
still front-biased)
At this point THE BRAKING POTENTIAL OF THE CAR IS MAXIMISED, or very nearly
so. It might be able to stand a little more bias movement rearward, but not
much (from my experience in DSMs, very, very little) and then you're giving
up stability.
So then, why aftermarket brakes?
3 reasons:
1) HEAT REJECTION - remember how brake CoF is a function of brake temperature?
That means the brakes must be able to maintain a certain temperature, or performance
falls off (fade) To do that, you add mass (as a heat sink) and surface area
(to speed cooling) - in other words, you make the rotors bigger. For cars that
see lapping use, this is essential. For street/autox cars, not at all.
2) WEIGHT - aftermarket parts can use aluminum instead of cast iron. I've got
TCE/Wilwood 6-pots with aluminum hats; they saved 9lbs per wheel
3) FEEL - anything that reduces brake system flex and swell means better pedal
feedback - although the OEM brakes aren't bad.
That's it - heat, weight, and feel.
Are there any questions?
DG
(written by Dennis Grant, DSM suspension guru)