Modeling Braking: Braking Harder Means Less Brake Fade

By Khiem Dinh

Khiem Dinh is an engineer for Honeywell Turbo Technologies at the time of this writing.  All statements and opinions expressed by Khiem Dinh are solely those of Khiem Dinh and not reflective of Honeywell Turbo Technologies.

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.

 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.

 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.