Lockup Pressure Calculations

Hi,

I had a few general questions about brake system design. I calculated the target lockup pressures for our car at 35 miles/hr, which seemed like a good estimate for an average speed (for context, this is an fsae car). I calculated the Hydraulic Bias etc. based on the modules from your course. This would be my bias when the bias bar is centred.

1. I know that the normal forces on the tires change as the speed changes (because downforce changes). How does my bias vary as speed varies during braking and what is a good way to analyse this?

2. The coefficient of friction between the tires and the road that I used for my calculations was 1.2. What do you think of this value?

3. Since the coefficient of friction also changes as the normal forces change, how does that affect my brake calculations? Is there a way to analyse this?

4. Now that i have target lockup pressures at 35 miles/hr, Brake Callipers, MCs and hydraulic bias when bias bar is centred all locked in, what are some things i could do to further analyze my braking system, for different speeds and conditions?

5. I read about deceleration gradient, the deceleration value as a function of the drivers foot force, as an important way of analysing brakes. Could you elaborate a little on that.

My 5 cents, maybe 10 cents, worth of thinking - and I strongly recommend further research. Maybe others can chip in and correct my mistakes, too?

1/ use damper position sensers to establish the loading, per axle, under the different conditions, remembering chassis pitch will also increase the wing(s) angle(s) of attack

2/ can't comment - IIRC they use a spec' tyre (might be wrong), and the CoF (or rather grip) will depend on the surface

3/ the CoF won't change (although mechanical grip may) - I assume you mean the sheer force limit (grip) change? You should get it close using 1/ and very close if you chart/plot it through the load range. Because of 2/ you may need some experimentation on surfaces as close as practical to the test tracks to be used. Don't forget to have a GOOD look through the deata the tyre suppier has on their web site, they're there to HELP the students.

4/ make sure the pedal load is comfortable for the driver, and the ergonomics are such that they have a good 'feel' for the load applied? A sensitive driver can go a LONG way towards maximising braking by holding it at the slight slip angle required, without locking up. Also helps to ensure there is excellent feel through the steering, as a skilled driver will feel the difference across the axle.

5/ I'm not sure what is meant by that? Possibly a comment on some high downforce vehicles having so much mechanical, tyre, grip at high speeds from the downforce that the driver can apply as much pedal force as he can, without worring about locking up. Then, as speed is lost and the downforce lessens, there comes a point where the driver needs to reduce the pedal force to compensate, otherwise the brakes will lock up. FSAE cars tend to have relatively huge wings, IIRC, to maximise downforce, even at the relatively low speeds, so the lock-up may still be a problem.

i'll add some of my thoughts as well. Hopefully you can combine what Gord and I are saying and draw some conclusions.

1. Same thing as Gord said. Best way to understand the downforce that is being generated is from shock-pot data and seeing how the suspension compresses with speed. Compare this to spring rates (adjust for motion ratio) to calculate the downforce.

2. Assuming you're not running on gravel, a good way to get a ballpark figure here is again from data - how much G's are you pulling under brakes. Ignoring aero this is a rough value you can use for CoF. If you don't have data then you'll need to make an educated guess - we need more info on the car and tres you're running to help you here.

3. CoF changes with load due to 'tire load sensitivity'. I've calculated this out for some of our cars and I find the changes are only down to a few percentage. So given the variable nature of braking conditions I don't think it's worth factoring this into your calculations to size the brake package components - unless you're running a very high aero car at high speeds maybe

4. try calculate for a range of different CoF values (for rain etc) or different weight distribution as fuel load changes and see how much moving the bias bar will allow you adjust for.

5. Need a little bit more clarity here. Not sure if you mean what Gord mentioned with having to bleed off the brakes with speed in high aero cars, or maybe how the chassis response to the brake application, or even how this works with the changing of brake pad friction with heat through a stop and how this changes the bias.

This topic goes very deep into the more 'dynamic' behaviour which is what I think you mean by deceleration gradient. We took a much more steady-state approach in the course for simplicity and to make it more achievable for everyone.

Hopefully that helps a bit? let us know