alexjc4

Using some high school physics I've tried to do the calculations to look at the effect of brake upgrades.

Leaving brake balance, pedal effort and pedal length to one side, the reason big brakes are good is because they can absorb more energy without overheating (boiling the brake fluid and/or cooking the pads), this is also the reason Aluminium brakes are good, as Al can absorb twice as much energy as Iron for the same rise in temperature. Edit: this turns out to be right for Al discs but not for Al calipers where the benefit is the reduction in unsprung mass - the Al caliper actually has some detrimental heat soak effects compared to Fe and also the pad is a very bad conductor of heat so the caliper doesn't see much heating in the initial braking event anyway.

Sure a bigger disc and a caliper with more hydraulic "leverage" can let you grip the disc with more force and leverage, but since with stock brakes you can engage the ABS at will (or lock the brakes if your ABS is defunct), we know its not force and leverage that we are lacking.

I've made some reasonable assumptions about masses etc, I've also made some more shaky assumptions about how braking energy is spread through the system; front vs rear, caliper vs rotor etc. Finally I've made some obviously wrong but convenient assumptions eg all the kinetic energy is transferred to the rotor and caliper, no cooling during the brake event, no energy transferred to tyres, wheel, hub or road, no engine braking etc etc. All round these fudges shouldn't ruin the maths but let me know if you think they do, and more importantly what would be better assumptions.Edit: Turns out the incorrect assumptions aren't just in the parameters but also the model and therefore the calculations themselves which need to be more sophisticated

So using my fudge riddled maths we find that, say for a 1500kg car stopping from 130mph you might see a rotor temp increase of say ~164 deg C and a caliper temp increase of ~82 deg C.

Increasing the caliper mass by 50% and rotor mass by 22% (as per a move to Big Reds and 322mm rotors) could decrease the these to 124 deg C and 62 deg C respectively. Interestingly this is the same sort of size of effect that you get by dropping the weight of the car from 1500kg to 1100kg. To summarise, as you double the mass of the brakes, you double their ability to take on heat, so you halve the temperature rises associated with braking. So the Big Reds offer ~22% more mass and therefore reduce temp rises by ~22% - which means you can carry ~10% more velocity (e=1/2 mv^2) into the braking zones and maintain the same brake temps. Which is a similar result as you'd get from the more involved process of removing 400kg weight from the car.


Attached are a pdf of the maths and a zip of the spreadsheet with the workings. Feel free to have a play and/or shoot me down in flames

EDIT: So... it turns out the simplistic model I've used is some way off reality for a number of reasons pointed out below and some others too! Basically the way the kinetic energy is converted into heat in the brake components is not instant (eg. it takes a few seconds to slow the car, during which time convection cooling occurs), or homogeneously spread through rotor and caliper (the rotor actually takes most of the heat, and the heat is very unevenly distributed through the rotor- concentrating in the area contacted by the pad, so in reality the temperatures at the section of disc under the pad vs the opposite side of the disc vary by 100 deg C)

Better physics and more realistic numbers appear on page 3 onwards.

SuperUser

very cool data

My dad has been working on and selling Fans that cool brakes for some time. I have been thinking about making a turn key kit of our cars but was not sure how much of a market there is. Nascar, Daytona Prototypes, and some Rally guys are using them with great results.


I am also thinking about making a rear heater tube with one in it, they are super light, something like 5oz
http://ejfracing.com/#high_flow_fans

alexjc4

Oo thats interesting, I wonder what the air cooling effect maths would work like.

Google, here I come.

Porsche964FP

Nice one Alex.

max3.2

I think there are a bit too many assumptions in there (but Im an mech. engineer so maybe Im a bit too cautious..)

The heat is generated at the interface between pad and rotor. I think using the cars kinetic energy is maybe not the best way. There's a lot going on while braking (e.g. deformation processes, damping, spring forces....) - all that stuff takes out energy. My first approach would be something like:

-say speed decreases linear, then take braking time. compute rotor speed as f(t), compute.
-coulomb friction will yield a brake power, integrate over time to get energy.

Lets neglect heat dissipation (which is, for the rotor, mostly heat transfer and convection. both rely on a big surface area -> big rotors!) and assume caliper and rotor have the same temperature. then the braking. now there's energy. no time scale here. bit bad because while the rotor spins and heats evenly, the caliper dosn't..
now the heat flux depends on T-difference (same for pad/caliper and rotor) and thermal conductivity (high alloy steel ..20, aluminum ..250!) and area (!not on mass!). but whats the rotor area now? just the pad area? caliper area will be way smaller since it is touching the pad only with its pistons...its getting complicated...

if i find the time i'll run a FEA this weekend. just a generic rotor, 2 sizes, steel. with two blocks of aluminum pressing against it....instationary braking...could be interesting..

now tear me a new one. Im more the fluid dynamics guy so the stuff is a bit foggy..

alexjc4

Hurray, thanks for you feedback max3.2!

Yup lots of assumptions, but then we're not putting a man on the moon, just looking at the basic effects of changing the mass of brake components, so a fair bit of error is acceptable

The kinetic energy has to go somewhere; heat and sound and I'd say most of it (say 95%) goes into the brakes as heat, that's what they are designed for after all. The suspension, will generate some heat in the damping, the springs are just temporary stores of energy and will release that back when the car settles. My gut tells me the heat transferred to the oil in the dampers during braking isn't that significant compared to the amount going into the brakes. I'd guess the tyres and wheel (and road surface) are probably the biggest areas that I'm not accounting for, as there is a fair amount of mass in a tyre and wheel and its fairly well coupled thermally to the brakes.

Good point about the thermal conductivity. I wonder what the net effect would be, as you say the energy conducted will also be proportional to the contact area and it wouldn't be mad to suggest the rotor has 10x the surface contact with the pad compared to the caliper - leaving no net effect. In my first calculations I just assumed equal amounts of energy being transferred to rotor and caliper, but went for linking it to mass in the end, as you say that's probably nonsense, maybe assuming equal amounts to rotor and caliper is a cleaner fudge, as it goes I don't think it changes the deg C delta very much.

In fact thinking about it there's some tricky couplings going on;
pad friction material vs rotor
pad friction material vs pad backing material
pad backing vs piston (a composite material in our case)
piston vs seal
piston vs brake fluid
seal vs caliper
fluid vs caliper
caliper vs hub

Would be really interested to see what you come up with, if two different methods come up with similar results you always know you're in the right ball park!

Of course it wouldn't be terribly hard to verify this experimentally .... (Alex goes looking for infra-red pyrometers and a long straight bit of road)

alexjc4

BTW Max have you got any thoughts on the fluid dynamics/ thermodynamics of air cooling the brakes (normal and forced convection)?

For example things like the effects of increasing the mass and velocity of air directed onto the brakes.

alexjc4

Good point, another improvement with bigger brakes is the increased surface area increases cooling, would be interesting to calc the extra cooling effect, maybe the extra cooling is at least as important as the extra heat sink capability. Lol, only I don't have a clue where to start to do that.

Though mass increases with the cube of scale, whereas surface areas only increases with the square, so the heat sink effect of the extra mass becomes more and more important as you get bigger and bigger.

max3.2

Well but you are not braking once. Yes, more mass = less T increase for the same amount of heat generated, but at some point you will have to dissipate. And then it comes to area (which is linear in the governing equations..)

What do you mean by forced or normal convection? Brake ducts?...

Your question is really nonspecific, so I will try to answer as general as possible. The main mechanism of heat transfer for in a moving fluid submerged bodies is convection. The actual amount depends mainly on flow conditions (leaving the area constant). That's an endless topic...

Big factor is laminar / turbulent flow (factor 10..). If you are not driving, you will have natural convection->laminar. I assume turbulent flow for driving conditions (haven't double checked..wheelhouse flows can be quite interesting), then in comes down to flow velocity, I actually don't think mass flow rate is that important as long as it is over a certain value to not have the air itself heat up before it passed the rotor.
If you want to look around (wiki etc..) search for: Heat transfer coefficient, Reynolds number, Nussel number, Prandtl number, Grashof number (for nat. convection)

If you want more informations, please help me out where to start. Sometimes its hard to find the point where non-crazy-people stopped learning about engineering, no offense

Captain Ahab Jr.

I can't do the maths but I am a design engineer.

Adding material weight to the caliper and disc would be the last thing I would do to improve braking performance, well at least until all the other options have been exhausted first.

I think I'd design a sealed brake duct cooling system ducting fresh air from a high pressure area on the car. Most of the aiflow would be directed to the centre of the disc so it exits out through the internal turning vane gap of the brake disc. I would also split off some air flow to blow across the brake disc surfaces and across the pad and brake disc contact areas.

If this wasn't enough to drop temperatures then you could cross drill the brake pads and blow air through the brake pad material and direct some cooling air at the brake caliper pistons.

Also add a more agressive pad material and high temperature brake fluid.

If this still wasn't enough I would lighten my car which would in turn uprate the brake system for free.

alexjc4

I'm thinking about the maths needed to calculate the effects on brake temperatures of metal to air cooling. It could be the natural cooling of anything from a solid rotor in basically stationary air (normal convection) through to vented rotors in a airflow ducted from the front bumper (forced convection), even taking into account the wheel well aerodynamics.

I'd already quickly googled and zero'd in on the heat transfer coefficient as a key lynch pin in the calcs but it seems the velocity of air makes a difference here and I can't find formulas or constants to correctly adjust for this.

When it comes to ducting design I seem to remember there are some rules of thumb regarding inlet and outlet size to get optimal flow. Along the lines of inlet area = 1/2 outlet area. This was relating to oil coolers, so maybe it doesn't apply, but we still basically dealing with heat exchangers of a fashion.

I wouldn't make any assumptions about me being in the cohort of non-crazy-people but I have no formal engineering education so, I'm falling back on Alevel (age 16) Maths, Physics, Chemistry.

Bill Verburg

The temps aren't the thing to look at, either system can be driven to extremes by use

a bbk say 964RS vs oe964 gives you
1) increased brake torque at a given line pressure
stock f/r @70bar line pressure 1974/1217N
RS f/r @70bar line pressure 2381/1390N

2) increased thermal mass which delays temperature rise

3) more efficient internal air ducting which enhances cooling ie delays temp. rise

4) pedal feel will depend on the mc used, the smaller the m/c the worse feel but lesser effort and more travel is found

alexjc4

Thanks for joining in Ahab

I hear you Ahab, but we're not dealing with a cost no object/clean sheet here, we've got some simple/bolt on options available in the form of;

Fluid
Pads
Ducted cooling
Increased size calipers and rotors from newer/higher performance cars
Reduced weight

If you use/abuse you car to the point of thinking about all of this the first two are mandatory. But as Boxsey has found you can still run out of brakes if you're good enough.

The second two are proven in practice but I'd like to understand the physics about why they work and what the relative merits are. Sounds like you favour the ducted cooling route as the first port of call (based on race team experience?).

The third is a matter of practicality and taste. But from my cigarette packet maths it looks like you'd need a helluva lot of weight loss to for the same sort of gain you'd get from larger brakes. Obviously you get a load of other gains from weight loss too, but that's not what we're talking about here.

alexjc4

Woohoo, Bill V too!

Pound for pound you can subject bigger brakes to more extreme use though, right?

1) comes back to my point about being able to lock the brakes at will, if you can already apply enough force to lock the brakes what's the gain in adding brake torque? perhaps with sufficient tyre width and downforce you can reach a point where you need that extra torque, but is that point reachable in a 964?

2)is basically the same as what we're talking about - isn't it?

3)is the extra factor Max introduced and that I'd like to understand how to calculate

4)there is a certain amount of personal preference in pedal feel, and practicalities of control-ability, rather than a direct performance gain, but there is scope for altering this with properly sized MC and piston sizes as you know.

Captain Ahab Jr.

My pleasure, always enjoy a good technical post

Wasn't thinking clean sheet, no cost options at all even though I've seen first hand one team spending over $1 million in one season on pads and discs alone but thankfully those crazy days are over.

I try to keep my feet in the real world so was thinking ideas that the guy at home could do with some basic DIY skills, a bit of thought and a little bit of tracfine tuning at the track.

Sorry don't believe in complicating things with electric fans etc., simple works best but is harder to do.

Alex, agree with your order of priorities

Fluid and pads - easy fix
Ducted cooling - not so easy but not an expensive fix if you have basic DIY skills to make a few MDF/wood patterns and a bit of laminating
Increased calipers and rotors - expensive, easy fix but will compromises unsprung weight and can effect pedal feel, brake balance etc
Reduced weight - can be the hardest and most expensive fix but you can get part of the way for free if you compromise on creature comforts

Even if the ducted cooling doesn't lower temperatures enough it will help minimise what size up you go to make an uprated sytem work. It could add up to be a huge cost saving and reduce the extra weight you need to add.

In my experience any engineering problem needs attacking from all angles not try and solve it with one fix. A lot of little changes can add up to being more effective fix with less knock on compromises than one big change.

I like where this thread is going