There’s always a “but”, isn’t there?
In order to demonstrate the concept of proper brake balance, it is usually simpler to analyze a car’s handling characteristics and then apply those principles back to the braking system. (For some unknown reason, people seem to have a much better understanding of handling than they do of braking. Brake guys think that’s not fair, but we’ll try to use it to our advantage here.)
In theory what everyone is looking for is that all-too-elusive handling balance which makes the car corner as fast as it possibly can. Generally speaking, this is referred to as the ‘neutral’ car and takes the driver directly to victory circle following the race. Rarely do we ever hear of a winning driver explaining that the car was a handling nightmare.
Of course, no car is ever perfect, so we have ways of expressing how far from optimal the handling balance really is. When a car enters a corner and the front end skids off into oblivion, this is called understeer – the car is turning less than the driver intends. On the other hand, if the rear end breaks free and begins to lead the car through the corner this is called oversteer – now the car is turning more than the driver intends.
In both cases, when one end of the car breaks traction, or begins to slide, the driver can pretty much bet on the fact that he (or she) has found the maximum cornering speed for that particular corner. Yes, there are a million other factors at play which can govern the handling relationship, but the longer each end of the car can “hold on”, the higher the cornering speeds. Conversely, if one end or the other consistently breaks traction early in the cornering event, corner speeds will suffer dramatically.
Naturally, as speeds continue to increase something has to eventually give and slide; however, the very best suspensions do a great job of ensuring that both ends of the car break traction at relatively the same time. How far one end breaks traction in advance of the other is ultimately a function of driver preference (this is just one reason why there is no single “perfect” set-up), but if there are complaints of heavy understeer or terminal oversteer you can rest assured that one end of the car is three steps farther ahead than the other.
Umm…isn’t this an article about brakes?
So, now that we are all chassis tuning experts, let’s look at how this information can be used to understand our braking system. Grab a pop and a bag of chips and hang on.
Like the corner carvers, the brake guys are always looking to achieve maximum accelerations, but of course these accelerations are now really decelerations. Stopping distance is everything and every single foot counts. Remember: outbraking your opponent by just two feet every lap for a twenty lap sprint race can result in a three to four car length advantage at the checkered flag. Attention to detail matters.
As braking force is continuously increased, one end of the car must eventually break traction. If the front wheels lock up and turn into little piles of molten rubber first we say that the car is “front biased”, as the front tires are the limiting factor for deceleration. In the not-so-desirable situation where the rear tires are the first to lock we say that the car is “rear biased”, but the driver would probably have a few more choice adjectives to add. In either case, however, one end of the car has given up before the other, limiting the ultimate deceleration capability of the car.
Just like the car that pushes its way through corners all day long, a car which is heavily front biased will be slow and frustrating, but relatively easy and benign to drive. On the other hand, like the oversteer monster that people are afraid to even drive around the paddock, a car which is severely rear biased will be a scary, twitchy ride resulting in a bad case of the white-knuckle syndrome. Envision an imaginary co-pilot yanking up on the park brake handle in the middle of every corner, and you begin to get the idea. While a rush to drive at speed, it will be horribly slow on the stopwatch.
The car with perfectly balanced brake bias will, however, be the last one to hit the brakes going down the back straight. By distributing the braking forces so that all four tires are simultaneously generating their maximum deceleration, stopping distance will be minimized and our hero will quickly find his way to victory lane. Just like neutral handling, balanced brake bias is our ticket to lower lap times.
All that said, once the braking system has achieved its perfect balance, it is still up to the tires to generate the braking forces. It’s still the tires that are stopping the car, but a poorly designed braking system can lengthen stopping distances significantly, expensive sticky tires or not.
So why is brake biasing necessary?
The maximum braking force that a particular tire can generate is theoretically equal to the coefficient of friction of the tire-road interface multiplied by the amount of weight being supported by that corner of the car. For example, a tire supporting 500 pounds of vehicle weight with a peak tire-road coefficient of 0.8 (a typical street tire value) could generate, in theory, 400 pounds of braking force. Throw on a good race tire with a peak coefficient of 1.5, and the maximum rises to 750 pounds of braking force. More braking force means higher deceleration, so we again see the mathematical benefits of a sticky race tire.
On the other hand, if our race tire was now only supporting 300 pounds, the maximum force would drop from 750 pounds of braking force to 450 pounds of braking force – a reduction of 40%.
Since the amount of braking force generated by the tire is directionally proportional to the torque generated by the calipers, pads, and rotors, one could also say that reducing the
weight on the tire reduces the maximum brake torque sustainable by that corner before lock-up occurs. In the example above, if an assumed 700 ft-lb. of brake torque is required to lock up a wheel supporting 500 pounds, then only 420 ft-lb. (a 40% reduction) would be required to lock up a wheel supporting 300 pounds of vehicle weight.
At first glance, one could surmise that in order to achieve perfect brake bias you could just:
1. Weigh the four corners of the car
2. Design the front and rear brake components to deliver torque in the same ratio as the front-to-rear weight distribution
3. Win races
In other words, for a rear-wheel-drive race car with 50/50 front/rear weight distribution it would appear that the front and rear brakes would need to generate the same amount of torque. At the same time, it would look like a production-based front-wheel-drive car with a 60/40 front/rear weight distribution would need front brakes with 50% more output (torque capability) than the rears because of the extra weight being supported by the nose of the car.
Like most things in life though, calculating brake bias is not as simple as it may appear at first glance. Designing a braking system to these static conditions would neglect the second most important factor in the brake bias equation – the effect of dynamic weight transfer during braking.
The ever-present weight transfer phenomenon
Let’s assume we have a 2500 pound car with a 50/50 static weight distribution. If we are only concerned with the vehicle at rest, it’s easy to determine the weight on each wheel. We just need to find some scales and weigh it. The sum of the front corner weights is equal to the front axle weight (1250 pounds), and the sum of the rear corner weights is equal to the rear axle weight (also 1250 pounds). The weight of the vehicle is of course equal to the sum of the two axle weights (our original 2500 pounds), and this weight can be thought of as acting through
the vehicle’s center of gravity, or CG. Figure 1 sums it up nicely.
Note that when at rest, there are no horizontal (left or right) forces acting on the vehicle. All of the forces are acting in a vertical (up and down) direction. But what happens to the vehicle when we start to apply forces at the tire contact patch to try to stop it? Let’s find out.
During braking, weight is transferred from the rear axle to the front axle. As in cornering where weight is transferred from the inside tires to the outside tires, we can feel this effect on our bodies as we are thrown against the seat belts. Consequently, we now need to add several more arrows to our illustration, but the most important factor is that our CG now has an deceleration acting on it.
Because the deceleration force acts at the CG of the vehicle, and because the CG of the vehicle is located somewhere above the ground, weight will transfer from the rear axle to the front axle in direct proportion to the rate of deceleration. In so many words, this is the effect of weight transfer under braking in living color.
This deceleration force is a function of a mechanical engineer’s most revered equation, F=ma, where F represents the forces acting at the contact patches, m represents the mass of the vehicle, and a represents the acceleration (or in our case, deceleration) of the vehicle. But enough of the engineering mumbo-jumbo – just have a look at these additional factors in Figure 2.
In Figure 3 (the beginning of what we call a “fishbone diagram” – more on this later), we see how our 2500 pound vehicle with 50/50 weight distribution at rest transfers weight based upon deceleration. Under 1.0g of deceleration (and using some typical values for our vehicle geometry) we have removed 600 pounds from the rear axle and added it to the front axle. That means we have transferred almost 50% of the vehicle’s initial rear axle weight to the front axle!
At this point, the brake system we so carefully designed to stop the vehicle with a 50/50 weight distribution is going to apply too much force to the rear brakes, causing them to lock before we’re getting as much work as we could out of the front brakes. Consequently, our hero is going to get that white-knuckled ride we talked about earlier because he creates more tire slip in the rear than the front, and it’s going to take longer for him to stop because the front tires are not applying as much force as they could be.
So what influences brake bias?
If we look at the equations we have developed, we see that all of the following factors will affect the weight on an axle for any given moment in time:
· Weight distribution of the vehicle at rest
· CG height – the higher it is, the more weight gets transferred during a stop
· Wheelbase – the shorter it is, the more weight gets transferred during a stop
We also know from fundamental brake design that the following factors will affect how much brake torque is developed at each corner of the vehicle, and how much of that torque is transferred to the tire contact patch and reacted against the ground:
· Rotor effective diameter
· Caliper piston diameter
· Lining friction coefficients
· Tire traction coefficient properties
It is the combination of these two functions – braking force at the tire versus weight on that tire – that determine our braking bias. Changing the CG height, wheelbase, or deceleration level will dictate a different force distribution, or bias, requirement for our brake system. Conversely, changing the effectiveness of the front brake components without changing the rear brake effectiveness can also cause our brake bias to change. The following table summarizes how common modifications will swing bias all over the map.