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spdracerut posted on November 02, 2011 00:00 
Modeling Braking: Braking Harder Means Less Brake Fade
By Khiem Dinh
Almost every novice to track day driving exhibits the same fault; they do not brake hard enough. I was guilty of this myself and I remember vividly plowing through many corners at my first auto-x killing a few cones along the way. Whenever I do driving instruction, I almost always have to tell the student to brake later and harder. It should be obvious that braking harder and later improves lap times. However, braking harder versus braking lightly and longer can also reduce heat buildup in the brake system reducing fade. To prove this theory, I made a little mathematical model.
Before I get into the math, I want to share a little story where I experienced this phenomenon. Four years ago, I was in Europe for work and happened to be within driving distance of the Nurburgring. So what's a driving enthusiast to do? Take their rental car to the 'Ring of course! It was an overcast fall day with the occasional slight drizzle and my track toy for the day was a Citroën C5. It was a 3200lb, 4-door thing that looked like an overgrown Toyota Tercel with 110hp of diesel fury residing under the hood. It was there that I experienced something first-hand that I knew conceptually but I had not encountered previously.
I had never driven the 'Ring on any driving simulator, never watched a lap video, and my rental was wearing some all-season tires that squealed at 30mph. Fortunately, the built-in navigation system had the track on the display and I had a brave friend to play navigator calling out the corners for me. I took the first lap very cautiously due to my unfamiliarity with the track, slick weather conditions (a new Civic Type-R and 911 GT3 were both totaled), and the unknown limits of the car.
In driving cautiously, I tended to brake early and light dragging the brakes all the way to the apex until I could see the track-out point of the unfamiliar corners. Despite the cold and wet weather with ambient temps hovering around 50F, I got the mushy brake pedal about three quarters of the way through the first lap. Well, that just wouldn't do. Having now seen the track, it was time to man up and drive it hard. No more tip-toeing through the braking zones! My following three laps were driven more aggressively with harder and shorter braking zones and the result was no brake fade. Braking harder resulted in less fade? Here's the math to prove it.
I made a model to replicate what I experienced out on the race track. It is not meant to provide accurate numbers, but only serve to provide a way to compare different driving techniques with regards to braking. The job of the brakes is simple, slow down the vehicle by converting the kinetic energy of the vehicle into heat. The heat generated by the brakes is then rejected to the surrounding environment through heat convection and radiation.
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| Some of the heat transfer equations used. |
I used my S2000 as a rough physical model to use for numbers. My model only looks at one corner of the car, so I took one quarter of the weight to use as the mass of the vehicle. To model the brake rotor, I only took into account the braking surface part of the rotor, so the outer ring; I ignored the mass and heat transfer from the 'hat' of the brake rotor setup. I also ignored the mass consisting of the vanes in the vented rotor between the two braking surfaces. I did however try to account for them in the heat transfer. I calculated a surface area of the rotor which was the two surfaces in contact with the brake pads. I said that the surface area for convection was four times that of the two braking surfaces. So this accounts somewhat for the surface area in the middle/vented part of the rotor and somewhat takes into account the turbulence created by the vanes which increases heat transfer. Again, this model was not meant to accurately predict rotor temps, but just to provide a tool to compare different driving habits.
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| These are the values for the properties of the brake rotor and air used. |
I created three cases to analyze. The first case was using lazy braking. The second case was braking harder and shorter which was also the fastest method for completing my test. The third case was braking harder and shorter, but completing the test in the same time as the first case. This required lower top speeds in the third case as compared to the other two cases.
Posted in: Magazine, Tech
Wednesday, November 02, 2011 12:59 AM
I wrote a similar paper once about aero load effects on brake heat. Interesting to see a purely mechanical case written up.
Wednesday, November 02, 2011 2:37 AM
Any tips on stomping the brake pedal on non-abs equipped cars? My worst nightmare is locking up the brakes and totaling my car on a barrier...
Wednesday, November 02, 2011 8:26 AM
“When braking, think of “squeezing” the brake pedal down-and easing off it. The smoother you are with the brakes, the better balanced the car will be, enabling you to drive at the limit. Three-time World Driving Champion Jackie Stewart claimed one of the reasons he won so many Gran Prix was because he eased off the brakes more smoothly than any of his competitors. Hard to image how that could affect the outcome of a race so much, isn’t it? But it allowed him to enter corners a fraction of a mile per hour faster because the car was better balanced. Obviously, this squeezing on and easing off the brake pedal must be done quickly-and it can be done very quickly with practice-but always emphasizing smoothness.” -Quote from Speed Secrets by Ross Bentley
Wednesday, November 02, 2011 11:46 AM
@a6killa: You have to be your own ABS. You have to train your brain to let off the brakes for a moment to unlock the tire, then hit the pedal again (but not quite as hard so you don't lock the brakes again). It takes a lot of practice, but eventually you should work up to threshold braking where you brake to the point just before the brakes lock. The best drivers are the ones who have mastered braking. Jackie Stewart was also incredibly smooth and I remember one auto editor who got to ride with The Wee Scott and he said that Jackie was so smooth, even on the street, that as a passenger you could barely feel him turn, accelerate, and brake. Being nice to the car will make it consistently fast for a longer time period. That's why jenson Button can run far longer than Lewis Hamilton: Button is nice to his tires and car and can get more out of them. He may not have as many fast laps as Hamilton, but Button will have more consistent laps and stretch a set of tires further. I wonder how the model would change for progressive braking as opposed to on/off.
Wednesday, November 02, 2011 12:38 PM
I also wonder how a carbon fiber wheel covers and brake ducting or brake shrouds would affect temperature or are the benefits mainly in aero gains
Wednesday, November 02, 2011 12:54 PM
on off is for those still learning the track & sequences the smooth sq
Wednesday, November 02, 2011 12:54 PM
squeezers is for the guyz already blending the dance moves
Wednesday, November 02, 2011 5:47 PM
Since you mentioned autocross and braking. One of the top ten rules is BRAKE EARLIER AND LESS. That is proven times and times by pretty much any national champ. 3[ Brake "earlier…and less. Waiting until the last possible second approaching a turn and then dropping anchor at precisely the correct place so that the desired entry speed is reached exactly as you come to the turn-in point is quite difficult to execute consistently. Especially when you consider that you get no practice runs on the course, and the surface changes on every run, and you aren’t likely to be in exactly the same position with the same approach speed on every run, etc. Better to start braking a little earlier to give some margin of error. And by braking less you can either add or subtract braking effort as you close in on the turn-in point. This will make you consistent and smooth."]
Wednesday, November 02, 2011 5:48 PM
"4[ Lift early instead of braking later. Continuing with the philosophy of #3, when you need to reduce speed only a moderate amount, try an early lift of the throttle instead of a later push of the brake. This is less upsetting to the car, is easier to do and thus more consistent, and allows for more precise placement entering the maneuver (remember #1 above)."]
Wednesday, November 02, 2011 7:43 PM
Ok Khiem, at first I wasn't quite sold but now I'm with you! I couldn't get over the simple fact it takes as much force or energy to stop what's been put into a system. But looking at the heat transfer you've shown, I now understand how the drug out braking technique could cause daster brake fade. I thought of a good analogy for this scenario (I may have been hungry at the time). Imagine three bowls of soup: #1 was heated to temp in a microwave for 3 mintues. #2 Was heated to temp on a stove top in ten minutes. #3 was heated to temp and simmered in a crock pot over 4 hours. Which bowl stays warm the longest? Just like brakes, the one where the most sustained heat was put into its respective system. Ine question though
Wednesday, November 02, 2011 7:45 PM
One question though, why don't we see more track guys placing shims between the pads and calipers to minimize heat transfer to the fluid?
Wednesday, November 02, 2011 7:51 PM
@mx5, notice it says, "difficult to execute consistently" and also, "start braking a little earlier". If a machine where driving, then later is better because it can do it consistently. Also, a 'little earlier' is different than a lot earlier :) I think the advice you listed is valid for competition auto-x because of the so few number of runs that you get. Also, auto-x often involves some pretty abrupt transitions where car stability can be more important overall than a quick entry into a section only to lose time due to car instability. Road course is another story though where the turns generally require much less abrupt steering/brake/throttle inputs as compared to auto-x. And of course, an auto-x run only lasts 40-70 seconds or so. Endurance races can go for hours and hours, and 24 hours even where brake wear and fade can play a very big factor.
Thursday, November 03, 2011 7:17 AM
@Der Bruce: Probably because nobody thinks of it. Also, space can be kind of tight with a fresh set of pads, so you would need worn pads or pads that are slightly thinner than stock. On most of the cars I've worked on there's barely enough room to fit brand new brake pads, let alone shims behind them.
Thursday, November 03, 2011 8:59 AM
@Der Bruce, We use titanium shims with moderate success. Also stainless steel or titanium can be used for brake caliper pistons for the same effect.
Thursday, November 03, 2011 12:06 PM
As far as shims, or trying to keep the fluid cool -some cars, like the Nissan GT-R actually have air cooling channels in the brake pistons. I first saw these on a set of race Brembos for the World Challenge car. I was surprised to see them on the street car Nissan GT-R. They do seem some help slowing the big thing. If you run them hard, some good fluid goes far, if the car is heavy. I see the shims as a bit of a gimmick. Thanks for the article Khiem, it was a good read.
Thursday, November 03, 2011 12:32 PM
When racing wheel to wheel, braking later, even if you mess up corner entry a little, is better than braking sooner. Braking early invites people inside, and unless you're protecting the inside, you're gonna have a friend to share the next corner with.
Thursday, November 03, 2011 12:35 PM
BTW, brake later and FUBAR corner entry isn't going to win you races either. :-)
Thursday, November 03, 2011 8:13 PM
I do not see how titanium or SS shims wouild help. Both of these metals conduct heat very well, most certianly better than the pad material. If the goal was to suck heat out of the pad and transfer it to the fluid mission accomplished. I think teflon or a wafer made from mineral wool would be a much better choice.
Friday, November 04, 2011 8:29 AM
@DaGou Teflon would never survive braking temperature. Mineral wool might. The pad also transmits heat through the sides as well as through the pistons. I don't think mineral wool sheet would support the sliding. My wilwoods have stainless pistons as well as stainless supporting the sides of the pads. Stainless has roughly 7 times less thermal conductivity than the aluminum the calipers are cast from. Titanium is an even worse conductor. Every little bit helps.
Friday, November 04, 2011 11:55 AM
@DaGou Titanium has a very low thermal conductivity as does SS. Ti is around 11-13 Btu/(hr*F*ft) and SS is around 7-26. For reference Gold is around 186 and Aluminum is 114ish. There's a reason why Ti shims have been used by track rats and race teams alike. It's because although they do not have the lowest thermal conductivity they will survive the heat, are relatively cheap, and it does reduce the heat transferred.
Friday, November 04, 2011 11:33 PM
BTW, brake later and FUBAR corner entry isn't going to win you races either. :-)
Thursday, November 10, 2011 12:21 PM
Interesting thread. Was on track with a young fellow for a first time NASA Hyperdrive at NJMP. Before we rolled he told me about the engine upgrades he had planned for his new STI. There was no mention of the brakes. He was a quick learner so I worked him a bit. When we returned at the end of the session I asked him what he was now thinking for modifications. He said something to the effect, "I don't need more power, I need much better brakes!" He learned what we all know or should know. To go fast, you need to be able to slow the car quickly for each corner. In today's race classes where the cars have been largely equalized, where do drivers overtake? They mostly do it in the braking zones. Overtaking is done with the brakes! It's one reason why pads, fluids, calipers and rotors are the subjects of ongoing discussion on motorsport sites like this one. Having the best brakes is one thing. Knowing how to use them is something else. If you've been watching F1 you'll see how even top drivers (like Hamilton) have trouble slowing. Slowing a car properly for turn in, may well be the most challenging aspect of trackcraft to master. Especially if it rains. These days, ABS and self blipping transmissions ease the driver's task somewhat but can't compensate for not going deep enough, overslowing, or heavy entry braking. One of the best discussions of race braking and corner entry theory can be found in the Skip Barber "Going Faster" book. These guys instrumented their cars. They've got the data to show what's quicker. Definitely worth a second read even by front runners. I tell my students to buy a copy and leave it in the bathroom!
Thursday, November 10, 2011 7:34 PM
@Phil, I have that book. Or rather, HAD that book. I loaned it to a friend four years ago and haven't gotten it back yet! Definitely a great reference.
 
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