# Cooling of Brake Discs

## Homework Statement

Ok, I am designing a brake system for a uni project, as part of this i need to specify the size of the disc's, to prevent the brake fluid from boiling during braking.

Does anyone know of an arbitary formula which will help me calculate the rate of heat loss from the system, caused by the airflow over the discs?

obviously it will vary from design to design, but something to give me an appropriate figure would be amazing.

Unknown

## The Attempt at a Solution

many thanks
Ed

I would suggest figuring out what kind of heat you need to dissipate first. As in how much work needs to be done stopping the car and how often, etc.

Because I think you are right that it does vary with designs, but I think you have a number of factors that you need to consider. Not the least of which is how much heat will you be generating that needs dissipating.

i only have very rough figures at the moment, as they are dependant on other parameters of the car, which others are designing, and there not finalised yet, but in simple terms it will be one hell of a lot - its for something weighing ~2000kg from ~400mph (well a parachute brake from 400-200, then wheel and parachute from 200 to stop, however i need to model what would happen should the chute fail), and at present its looking like producing ~100 degrees kelvin per second of full braking without lockup...

I also know i will be using a brake fluid with a dry boiling point of 320 degrees celcius, so there going to need some serious cooling.

Cheers
ed

i only have very rough figures at the moment, as they are dependant on other parameters of the car, which others are designing, and there not finalised yet, but in simple terms it will be one hell of a lot - its for something weighing ~2000kg from ~400mph (well a parachute brake from 400-200, then wheel and parachute from 200 to stop, however i need to model what would happen should the chute fail), and at present its looking like producing ~100 degrees kelvin per second of full braking without lockup...

I also know i will be using a brake fluid with a dry boiling point of 320 degrees celcius, so there going to need some serious cooling.

Cheers
ed

Well that that's a little easier already, because the duty cycle issue disappears. 400 to 0 stops don't crop up that many times a minute in normal traffic.

Except of course you will need to determine the continued resistance contribution from the parachute as it changes between viscosity regimes in slowing down. Which is to say I believe that drag has 2 terms that will play varying roles as you slow the car.

But if you are preparing for chute failure, you have some massive energy to worry about.

In the event of chute failure how much time do you have to stop or is there a distance constraint?

There is approximately 6500m of possible braking distance.

There is approximately 6500m of possible braking distance.

So at the bare minimum you need to supply what breaking force over that distance? That leads to the watts you need to absorb.

As to your original concerns about brake fluid, how do you see that absorbing all this heat? Which is to say are you talking about pads and drums or do you have some other scheme in mind for braking the wheels?

I already have the brake force (or at least a spreadsheet where i will have the accurate brake force once all values are inputted) and the heat generated by the brakes (again the same as the brake force) per second, and in total over the run.

It is simply the amount of heat that the airflow over the disc rotor and caliper removes from the system.

would i be correct in thinking that an equation for forced convection would suffice? I've been doing some reading, and i think the following formula may work

will this formula work?

cheers
ed

I already have the brake force (or at least a spreadsheet where i will have the accurate brake force once all values are inputted) and the heat generated by the brakes (again the same as the brake force) per second, and in total over the run.

It is simply the amount of heat that the airflow over the disc rotor and caliper removes from the system.

would i be correct in thinking that an equation for forced convection would suffice? I've been doing some reading, and i think the following formula may work

will this formula work?

cheers
ed

I think the equation itself is OK, but I think developing the underlying heat transfer coefficient for use with the equation may be challenging.