Al Rotors - The definitive answer (Looong)

[Jeremy R King <kingjer@eng.auburn.edu>]

Here's a lesson on metallurgy/kinetics/heat transfer/fluid dynamics for 
anyone interested - subject to correction as needed.

Glen, you're right on the money with one clarification (I'll get to that 
later).  Eric, you're full of it.  You must be using a solar calculator 
in moonlight to do your "math".  Alan, very correct.

The key to stopping a car from forward motion (ie possessing kinetic 
energy) is to somehow dissipate that energy.  Remember, energy can 
neither be created or destroyed.  Therefore we have to get it to change 
forms.  One way would be to run the car into a wall or a tree or 
something, and share that kinetic energy with the wall and the little 
atoms in the metal of the car itself.  Not good.  So the way we do it 
without destroying everything is through FRICTION.  Friction is the most 
important thing in stopping a car using brakes.  There are two places 
this friction is important - one is between the rotor and pads, the other 
is between the tire contact patch and the road.  If you think back to 
your classes (physics), a frictional force (in our case - stopping force) 
is equal to the normal force (normal as in perpendicular, not everyday) 
times the coefficient of friction.  So, there are ONLY two ways to 
increase a car's stopping force.  One is to increase the coefficient of 
friction.  The other is to increase the normal force.  Before somebody 
(Glen) jumps all over me on that one with, "What about swept area?"  Easy 
- to come up with a total stopping force on one wheel at the rotor, you must 
integrate the normal force at each point over the whole pad area.  Thus 
the bigger the pad surface area is, the bigger the overall normal force 
will be.  

The first thing to look at is the rotor/pad interface.  The rotor/pad's 
job is to overcome the rotation of the tire/wheel/rotor/hub/etc 
(everything that's rotating) period.  The rotor/pad does not directly 
stop linear momentum of the car!  So, Eric, you are correct in saying 
that a lighter rotor would reduce rotational inertia of the rotating 
mass.  But you're dead wrong in saying that the mass difference from an 
aluminum rotor to an iron one will make a significant difference in 
stopping force due to reduced rotational inertia.  This effect will be 
totally insignificant.  Glen is right on the money saying that the wheel 
and tire have a much greater effect on this phenomenon.  The one thing 
Glen left out is the fact that the tire also has a frictional force 
acting on it that wants to continue to rotate the wheel/tire/etc.  This 
force is much greater than the rotational inertia of the rotational mass, 
and much much greater than the rotational inertia of the wimpy little 
rotor!  So where does this frictional force on the tire come from.  
Simple - multiply the normal force on the tire (gee, would that be 
weight?!!! as in MASS times acceleration) times the coefficient of 
friction between the tire contact patch and road surface.  Again, 
integrate the weight of the car over the contact patch - thus if the 
contact patch is bigger, you get more overall normal force.  Also note 
here that the rubber compound of the tire plays a key role in coefficient 
of friction.  So, the heavier the car, the larger the normal force for a 
given Cf and tire patch.  Thus a larger frictional force trying to keep 
the tire/wheel/etc. spinning.

Obviously, if you have a light car with really good brakes (high Cf), you 
can easily lock up the tires.  This is because the normal force on the 
tires isn't big enough (small weight) to create enough friction to keep 
the tire spinning.  OTOH with a heavy car and bad brakes, the tires 
probably won't lock up and the car'll take a while to stop.

We all know that friction works through the generation of heat.  
Friction's job is to take kinetic energy and change it into heat energy.  
So now heat comes into play.  At the rotors, heat can change the compound 
of the brake pads and thus reduce the coefficient of friction between the 
pads and rotor (fade).  Here's where I think Aluminum makes its most 
important contribution.  First of all, Aluminum is a softer metal than 
iron.  Because it's softer, the coefficient of friction between an 
Aluminum rotor and a given set of pads would be significantly higher than 
the Cf between the same pads and an iron rotor.  MORE STOPPING FORCE!  
This is, IMO, the main difference.  Another advantage (though not nearly 
as significant) is Aluminum's higher specific heat.  It was pointed out 
that an Aluminum rotor would get hotter than an iron one.  Not so.  The 
higher specific heat of the aluminum allows it to conduct heat AWAY FROM 
THE PADS to other parts of the rotor.  This keeps the temperature at the 
pad lower than it would be with an iron rotor.  BECAUSE Aluminum also 
dissipates heat to air a lot better than iron.  So now the heat that is 
better conducted away from the pad is now better convected and radiated 
from the rotor into the air, which will carry this heat away.

So why aren't all rotors aluminum?  For one thing, aluminum is less stiff 
than iron.  And the stronger alloys (7075, 7079) tend to be very 
brittle.  But the main drawback is that aluminum has about a third of the 
cycle life of iron.  It is very subject to fatigue.  Since braking is a 
very cycle-intensive process, aluminum is not the best choice for your 
dependable, everyday commuter.  Since the racing life of a part (on a 
race car) is very small compared to a passenger car, aluminum would be a 
viable alternative.  Also, racing applications are tremendously sensitive 
to unsprung weight, where aluminum would provide yet another benefit.  I 
think the answer lies with composite alloys, which would allow the 
benefits and help remedy the weaknesses.

Sorry this was so long.  I hope someone made it to the end.  

Jeremy R. King
Senior Mechanical Engineering Student
Suspension Team Leader - War Eagle Motorsports Formula SAE

'86 VW Quantum GL5
Auburn University, Alabama, USA
Hometown - Reidville, South Carolina, USA