Brake Pedal Ratio

I am working on an FSAE car and am in the process of setting up brake system calculations. I am wondering if there is a way to determine a pedal ratio (or maybe even an acceptable range of pedal ratios), using a mathematical formula. I understand the pedal ratio can be derived geometrically, but I found a mathematical formula for single MC setups in the book, Race Car Vehicle Dynamics by Milliken and Milliken as follows:

Pedal Ratio = Brake line pressure * Area of MC/Foot force.

It goes onto mention that a dual cylinder system (like mine) will need to factor in the balance bar ratio as well. Could you help me with that calculation?

I meant we have two master cylinders, one for the front and one for the rear. How would that change the formula I mentioned above

Brake line Pressure * Area of MC = Force at MC

That's why the pedal ratio = Force at MC/Foot force

The same stands for a dual master setup and a bias bar.

With the bias bar fully centred, we have equal force in each. Since they're 'in parallel' they would get half of the force from the pedal multiplied by whatever the pedal ratio is.

Basically you need to factor in the bias bar position and separate the MCs. So let's say for example the bias bar 10% closer to the front MC. (60:40 bias bar ratio).

I think you could use... Pedal Ratio = (Front Pressure*MC Area Front*0.6 + Rear Pressure *MC Area Rear*0.4)/Foot force

TBH, I'm a little surprised an FSAE student is asking, but...

The Milliken formula is simply establishing the force required at the master cylinder pushrod, and the ratio for the pedal effort one wihes to work with.

With a dual system, simply work out the force required for each master cylinder and add them together for the pushrod forces, and then you can decide on the pedal ratio.

There are a few ways you can write the formulae, if you can't, one of the folks more into writing code should be able to make up a simple program which allows all but one variable to be entered and the unknown to be given as the answer.

As Connor said, the bias bar will alter the balance but, as it's in essence a simple supported beam, that calculation can be done before, or after, the pushrod stress calc's - it isn't needed for the basic ratio.

I would suggest giving the operating angle some thought, though, together with the ergonomics, as that will affect the force and control that can be applied.