Steven Carter wrote:
JamesShort wrote:
Maria Winslow wrote:
Steven Carter wrote:
Also, if you want some nerdy reading the Stoptech Brake White papers are pretty cool...
http://www.stoptech.com/tech_info/tech_white_papers.shtmlThanks for posting this - it will keep James so busy with over-analysis that we will continue to beat him
Everyone else, don't bother to read it because James will be able to explain it all next time.
Too late, I've read those a few years ago
. When my father in law worked at performance friction, I had to learn up so I could talk the talk with him
.
Too bad with all that information, I can't explain why I saw a sliver mini in the middle of the grass on Sunday.
Why am I not surprised by that? You let me down, though. I expected a post with lotsa equations...you off your game today?
Well smartass, I guess a braking conversation to have is how surface area means nothing. Way too frequently am I hearing people talk about surface area when it comes to brake pads or rotors and it is immensely irrelevant.
From a low level there are 3 major concepts/points with braking systems: compound characteristics, heat capacity (thermal mass) of the system, and cooling ability of the system.
First and most applicable to this post is compound. If you can't increase the heat capacity of the system or add cooling mechanisms, you must have a compound that operates (well) at the average temp that your braking system is going to be. The coefficient of friction (mu) has a somewhat bell shaped dependency with temperature for a given compound. So prior to this temp (or small range of temps) it will have a lesser mu and mu will rise to it's peak and then drop off again as temperature rises. That's why track pads suck on daily drivers and why OEM pads suck on the track. Also, compound price general goes up as the peak mu temperature increases (it's much easier to design a compound where peak mu is at 200 degC than 800 degC for example so costs go up). Generally your brakes operate in a range of temperatures and not a single temperature so that must be designed into the braking compound as well. The broader the range, the more expensive the compound and the faster wearing the compound is (generally). Initial bite as we have been talking about generally means the brake compound has absolute peak mu at a more steady state temperature of the car (your brakes stay much warmer than ambient just driving on the highway because the pads are very lightly touching the rotors and creating frictional heat). So the instant you apply more braking, you are at peak mu and therefore peak clamping force and then almost instantly the temperature shoots up of the rotor to pad interface and the mu drops slightly (not to the point of fade but to the point you can modulate it easily). Some say slotted rotors increase 'initial bite' significantly due to the trailing edge of the slot 'grabing' the brake compound.....I feel this effect is lightly minimal. Mu will be important in a bit.
Second is heat capacity. You could track any car you want on crappy OEM pads without fade if you had an immense amount of mass in your braking system (let's pretend the hypothetical mass didn't mess with acceleration/decel). Mass or heat capacity (has a material dependence) acts as a buffer to temperature rises of the system. For a given braking scenario you will need dissipate X joules of heat. If you have 20 lbs of braking mass, the temp of the system will increase by Y degC and if you have 40 lbs of braking heat capacity, the temp of the system will increase by Z degC where Z < Y. In the case of assuming a constant braking compound, in the former scenario, the temp increase might have caused the system to be above the ideal range for that given braking compound such that mu has decreased which means the clamping torque has decreased and the rotor will have to spin more times to dissipate the same amount of energy (ie to get to the turn entry speed you want) which means even more heat and more temperature and mu drops and drop and drops: FADE. So simply having bulky rotors and calipers and hubs etc can reduce fade all things the same. (however we all hate unsprung weight so that always isn't ideal).
3rd big concept is the ability of the system to remove heat (cool the system) from the system per unit time. As your rotor spins there is convective heat transfer from the rotor to the fluid it is spinning in (air). Another nice thing about the air the rotor spins in is that it is constantly betting 'renewed' with new air as the car move. Convection (heat xfer though a moving fluid) is much more efficient at removing/adding heat than conduction (heat xfer purely through contact between to dissimilar temperature objects). This is why formula 1 brakes get awfully hot and smoke when their pit teams take forever swapping tires because A) the system is stationary and the fluid is stationary and B) the air around the brakes is not moving either and constantly getting warmer and warmer (the closer the air temp gets to the system temp, the less heat xfer via conduction). Another form of convective cooling is just the flow of air over the caliper, tie rods, hub, lugnuts, wheel etc.....all the metallic heat capacity that gets affected by the heat generated during braking. You can force a greater flow of air into the brake system with ducts to increase the convective cooling ability of the system too. 2 piece rotors generally have cast iron rings and aluminum hats since aluminum has a much higher convective and conductive ability than steel or cast iron. Also the design of 2 piece rotors adds more flow paths for cool air to get into the rotor and hot air to get out of the rotor. So all this basically says is the faster you can remove heat from the system, the lower the average temperature will be per braking event of the braking system. So this does something similar to having a lot of mass.......without actually having a lot of mass.
Another thing you can do for better braking and heat capacity is larger diameter rotors. The larger the rotor the larger the moment arm is (distance from rotating axis to point of effective clamping force). The effects are two fold. Generally the larger diameter rotors will have more mass/heat cap AND your braking torque is greater. So per revolution of the wheel you dissipate more kinetic energy (and convert it to thermal energy) that spreads it self across the increases heat cap for slightly lower temps than had the mass remained the same).
So as you can see there are a ton of variables and ways to design a braking system using these 3 (+1 small) main elements once you know your design conditions (temps, weight requirements, braking zones on a track, average speeds at braking, exits speeds etc).
So back to mu and surface area. The clamping force is purely a function of the temperature dependent mu(T) and the normal/perpendicular force exerted on the rotor by the caliper piston(s) a la F_clamp = mu(T)*F_normal. Surface area has no direct affect on braking. Ok so someone will say that a tiny kidney bean sized pad will not exert as much braking force as a 360 degree circular brake pad. Well if that kidney bean pad could be made of out Kryptonite that holds has a specific heat of 10^6* that of steel backing plates with braking compound, AND they had the same mu, then both of those pads would apply the same clamping force. However, the kidney bean pad is not made of Kryptonite has less mass to hold the heat generated so mu will drop drastically for small braking inputs because the temperature of the pad increases fast since it is less massive and therefore it'll fade. So as you see the surface area of brake compound has nothing to do with fade or clamping force....its the heat capacity (and in turn the cooling ability of the system) to moderate the temperature of the pad and compound to keep mu in the designed range.
Steve, you satisfied
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