Brakes: What They Do & How They Work
We'll start out with my system: the brakes. The sole purpose of the brake system is to stop the car and prevent the driver from going off into the wild blue yonder. The more technical explanation of the brake system is that it's an energy conversion system. The rotors and calipers convert the kinetic energy of the car into stopping power and heat. How exactly does this happen and what the heck is going on with those spinning razor blades? That's what we're here to figure out.
The Event of Braking
From start to finish, here we go.
Driver mashes the pedal
Pedal moves, pushing the pistons of the master cylinders in and moving the bias bar.
Cylinders compress the brake fluid, pushing in the pistons in the caliper.
Caliper pistons squeeze the brake pads in, grabbing the rotors.
Brake pads have grabbed onto the rotor, they now begin to heat up as the rotor slides against them.
The rotor begins to slow down and heat up at the same time.
Pads, calipers, and brake fluid all begin to heat up.
The car stops.
Super simple stuff, right? On the surface, yes. This is a simple conversion of kinetic energy into thermal energy to stop the car. But this is a racing blog. Why the hell would we stop at simple? Onward to theories and math!
The Physics First, some basic physics and a conversation about Newton and his famous laws.
An object in motion tends to stay in motion until another force acts upon said object.
Force = mass x acceleration
For every action, there is an equal and opposite reaction.
The above are Newton's three laws. They are always in play and can't be ignored, but they can be used to your advantage. They will come in handy later, so hold on to these. The basis of the brake system is torque. There are torques everywhere in this system. If these aren't calculated correctly and the suspension guy gets the wrong numbers from the brakes guy, stuff like this happens. Don't do this. This is wrong. Basic equations and numbers you'll need:
Equations
F = ma
Torque = force x distance
Kinetic Energy = 1/2 mass x (velocity squared)
Pressure = force / area
Numbers
Mass of the car
Weight distribution
Center of mass height
Tire radius
Effective brake radius (how far the pad is from the center of rotation)
Pedal ratio
Front/Rear master cylinder size
Friction of the tires and pads
Brake bias
Brake Temperatures and their Effects
When your brakes are put to use, they heat up. The harder you push, the faster you stop, but the brakes heat up faster and to a higher temperature. In racing, a common phenomenon if the brakes are done wrong, or the track is thick with long straights followed by tight turns, is brake fade. Brake fade is caused by several things, mostly due to extreme and prolonged high temperatures. Pads and rotors can melt and brake fluid boils. If this happens, your driver will complain the brakes feel "soft" or "aren't there" or "I need new underwear."
While it may seem like these extreme temperatures are the last thing you want (and you would be right), it's ok to have some high temperatures. In fact, as brakes get hotter, they can grip better. Most rotors and pads you can buy come with a temperature vs friction chart. These tell you where the optimum temperature is for your components. Some are good at low temps, some at high, others are ok all around. In SAE, you'll want something that is good when cold and maintains its performance through higher temperatures.
A video of our brakes at night. I'd like to mention here this was an unusual occurrence that only happened once.
Thermal Simulations and Data
Now, I've been speaking in very general terms: "high temperatures", "low temperatures", etc. Well, hold on. What is high and what is low? This depends entirely on the car and its setup so I can't answer that. Well, is there a way to predict temperatures? Yes and no. I'm sure the gurus of F1 do simulations all day long, but for FSAE, you're better off not trying to figure it out in SolidWorks. There are a lot of time-dependent variables that require many levels of calculus and Greek to begin to understand what is going to happen. And even then, the variables that go into the simulation will be a one in a million case; track temps might be different, tire temps, tire pressure, brakes temps... There is a heck of a lot going on down there that just isn't worth the time to go through and figure it all out.
BUT, there is hope. There's something out there called brake paint. No, it's not to make your rotors all pretty and sparkly. This small, $80 container has temperature-sensitive paint inside that changes color based on how hot your rotors get. So grab some of this paint, put a dab on the rotors, and take the car for a drive. This will give you a good idea of how hot your brakes are getting.
Calculations
Although the goal of the system is to convert one form of energy into another, the actual math behind thermal calculations involves double integrals, derivatives, and many time-dependent variables that require inputs that are nearly impossible to get a hold of accurately. When you do get the variables, they’ll change based on track temp, wind direction, morning breakfast, or any number of other factors that can change on race day. So the better way to go is to calculate the required torques that will lock the tires. This is fairly easy to find out. I’ll give a general workflow of what I did for my system, but if you’ve gone through Physics I you should be able to figure this all out on your own.
What your brakes can actually do can be calculated as well. You’ll need: master cylinder sizes; effective brake radius; tire radius; pedal ratio; pedal force; friction coefficients; brake bias. To actually calculate the force the brakes can exert on the wheels, think of how the chain of events goes, then work that way.
If you did the calculations right, you’ll have two different numbers for the front and rear.
Conclusion
Brakes take the energy of the car and change it into stopping power and heat. While the physics behind the brakes are simple, the thermodynamics get quite complicated and can vary so much in the span of a race weekend that empirical testing is better than trying to spend many hours smashing your head against the wall because you can’t find the temperature graphs of your chosen material. As far as cut patterns and funky designs go, play around and see what works. Important things to keep in mind are the forces your brakes need to overcome and the possible heat they may see. Good luck and happy building!
- K
