Braking Equations

[Danny B]

Hey everyone, im new to the forums and the team for that matter. Another team member and i are designing the braking system for our car. We set up an excel program that calculates system pressure and pedal forces, etc... based on certain car parameters. I have already spoken to a braking engineer from stop tech who confirmed all of our equations and what not. Anyway... theres a couple of things i am caught up on as far as the brake pedal travel and movement in the master cylinder.
How much will the push rod in the master cylinder move in relation to pedal travel. What i am asking here is if we have a master cylinder with a 1" stroke, how much of that stroke is going to be used up on full lock up? And is there any way to vary how much of the stroke will be used in order to change pedal travel... Or is pedal travel dependant upon pedal advantage. Also, we were looking into using different size master cylinders for front to rear but we are not sure at what speed most of the stopping is going to be done at which will dictate front to rear pressures (weight shift). Obviously we can only optimize braking from a certain speed. Does anyone have any opinion on the in the car dial that adjusts the balance bar? From what i have read they can only make fine tuning adjustments and do you think it would be worth it to buy and install this dial. Any help or point in the right direction here is greatly appreciated, thanks...

[Danny B]

Hey everyone, im new to the forums and the team for that matter. Another team member and i are designing the braking system for our car. We set up an excel program that calculates system pressure and pedal forces, etc... based on certain car parameters. I have already spoken to a braking engineer from stop tech who confirmed all of our equations and what not. Anyway... theres a couple of things i am caught up on as far as the brake pedal travel and movement in the master cylinder.
How much will the push rod in the master cylinder move in relation to pedal travel. What i am asking here is if we have a master cylinder with a 1" stroke, how much of that stroke is going to be used up on full lock up? And is there any way to vary how much of the stroke will be used in order to change pedal travel... Or is pedal travel dependant upon pedal advantage. Also, we were looking into using different size master cylinders for front to rear but we are not sure at what speed most of the stopping is going to be done at which will dictate front to rear pressures (weight shift). Obviously we can only optimize braking from a certain speed. Does anyone have any opinion on the in the car dial that adjusts the balance bar? From what i have read they can only make fine tuning adjustments and do you think it would be worth it to buy and install this dial. Any help or point in the right direction here is greatly appreciated, thanks...

[Denny Trimble]

Danny,
On pedal travel: the only reason the brake pedal actually moves when you press on it, is:
-any clearance between the pads and rotor
-compression of the pads
-flex in the calipers
-flex in the brake lines
-flex in the brake pedal and mount system

So, the stiffer your system, the less pedal travel, the better. Drivers like to brake by "Force control" rather than position control, which is what they do with the gas pedal.

Your "pedal ratio" determines the relationship between force and displacement from the bias bar / master cylinders to the pedal pad.

As for brake bias, you don't adjust it for a certain speed, you adjust it for a certain deceleration (g's). If the conditions change and it gets wet, you need more rear bias.

We don't use cockpit-adjustable bias, it clutters up our brown go-kart.

[TomF]

Well there is also the factor of bulk viscosity, which relates to the compressibility of the fluid. If air gets trapped inside the system your brake travel increases, without providing actual brake power. This means the brakes feel spongy. But as Denny remarked, brake pedal force is of much more importance to the driver than pedal travel. Just make sure you get your forces sorted out, and minimize any friction in the system. Than under operation bleed the brake system regularly to prevent air bubbles getting into you brake lines.

[Agent4573]

As stated in one of the carrol smith books, most drivers prefer the brake pedal to feel like thier pushing against a brick wall. Hopefully, like the others have said, once you get everything situated there should be almost no pedal movement in your brake. This shouldn't be a problem as long as you can bleed your system well, and all your caliper/brake pedal assemblies are rigid. Also remember when you design your pedal that you don't want to over shoot your maximum input force in your master cylinder.


My philosiphy for designing our braking system was as follows:
1. Calculate maximum needed braking torque.
2. Choose reasonable pad/rotor combo.
3. From Cf, rotor size, calculate line pressure
4. From line pressure, calculate master cylinder bore size
5. From bore size and line pressure, calculate input pressure and pedal ratios.
6. Iterate process until rotor/pads/torque all work without overheating/underheating

As far as the balance bar goes, you can get quite a bit of adjustment out of it. Before you chose to run different size master cylinders we need to know if your running two rotors out back or one. We run two rotors up front and one on the diff in the back. Because of this we can get away with the same size master cylinders because even with exact rotors front and rear, the front still does twice as much braking as the rear. If your running dual brakes front and rear, then a size smaller master cylinder for the fronts would probably help get you closer to where you need to be w/ front to rear brake bias.

[Sam Zimmerman]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Denny Trimble:
We don't use cockpit-adjustable bias, it clutters up our brown go-kart. </div></BLOCKQUOTE>

Sorry, Travis. Denny now has you beat for the funniest post I have seen in a long time.

[MikeWaggoner at UW]

I got used to our old car with nice spongy brakes, and I've always driven passenger cars with nice, spongy brakes. This whole brake by force thing is stupid.

[TA]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by MikeWaggoner at UW:
This whole brake by force thing is stupid. </div></BLOCKQUOTE>

Trust me, the first time you burn up your brakes and the pedal hits the stop with NO effect on speed, you'll begin to appreciate the "brake by force" thing -- after you change your shorts http://fsae.com/groupee_common/emoticons/icon_smile.gif.

Cheers, Ted

[Sam Zimmerman]

TA,

i"¢ro"¢ny
n. pl. i"¢ro"¢nies
1.
a. The use of words to express something different from and often opposite to their literal meaning.
b. An expression or utterance marked by a deliberate contrast between apparent and intended meaning.
c. A literary style employing such contrasts for humorous or rhetorical effect.

http://fsae.com/groupee_common/emoticons/icon_smile.gif I think you must have missed the steering column thread. http://fsae.com/groupee_common/emoticons/icon_smile.gif

[TA]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Sam Zimmerman:
TA,

i"¢ro"¢ny
</div></BLOCKQUOTE>

As an engineer -- I think you should avoid irony and stick to simpler concepts such as "sarcasm" http://fsae.com/groupee_common/emoticons/icon_wink.gif.

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">http://fsae.com/groupee_common/emoticons/icon_smile.gif I think you must have missed the steering column thread. http://fsae.com/groupee_common/emoticons/icon_smile.gif </div></BLOCKQUOTE>

Yeah, missed it entirely...

And I own a Moke, that I'm building up as an autocross car -- does that make me a bad person?

http://fsae.com/groupee_common/emoticons/icon_biggrin.gif

[Sam Zimmerman]

A bad person, no. A strange person, yes.

Post pictures, please. I gotta see it.

Now back to the braking equations discussion.

[Dr. Bob Woods]

My textbook "Modeling and Simulation of Dyanmic Systems" from Prentice Hall gives a complete analysis and design parameters for a FSAE brake system in Chaper 10. It should answer the questions being asked.

Dr. Bob Woods
Faculty Advisor, UTA

[Danny B]

Yeah we already have all of our equations set up and before we went ahead and decided on master cylinders we wanted to know what deceleration rate we should be looking at for most of our driving. If we are looking at a high deceleration rate then our front and rear pressures will get close to evening out with the weight shift. Yet if we will be declerating at a slower rate then the front and rear pressures will differ significantly. What i am trying to decide on is will a different size master cylinder be helpful in evening out our pressure numbers and leave the fine tuning to the brake bias adjustment dial.
Either way, we are going to need a pedal advantage of at least 4:1 in order to keep pedal effort below about 170, and even 170 is too high. The reason for such high effort is we are using wilwood ps-1 calipers (with 1" diameter pistons) and 6" diameter rotors and only one caliper and rotor on the rear diff.
Also, with such a small brake set up does anyone think we will have a major problems with brake fade. The calipers are mounted outboard so that will dissipate heat but they still need to work hard since they are quite small granted our car is pretty light.

[Agent4573]

we assume 1.5 g's of braking. At least this is what are accelerometers tell us. If you want, we have an excel sheet that an alumni wrote for us, it calculates brake temp given rotor mass, vehicle mass, % of forward velocity going over brakes, and some other things. If you want to give me the details of your system and car, i should be able to let you know pretty reasonably what temp your rotors will run at. This way you can see if you're gonna boil your brakes or not.

[Psychosis]

@ Dr. Bob Woods
That really is a shameless plug!

@ back to the topic...
My thesis was on brake design for FS cars and i would agree with what has been said so far. Our weight distribution was 50:50, and with a measured decel of 1.4G. using Wilwood ALMMC rotors front and a single rear with Wilwood Dynalite rotors, i worked out that the brake balance should be exactly 60:40 (using same Dia master cylinders). and with a pedal ratio of 4:1, and a C.O.F. of 0.45 pedal effort (for 4-wheel lock up) would be 600N. Then after a ton of analysis and transient FEA, arrived at my new discs that weigh in a 0.45kg. what weights are everyone else looking at?

hope this helps!

[Marshall Grice]

Our front rotors weigh in at just about 2.5 lbs. They overheat like crazy. I don't know the specifics about our design. I didn't do it.

[TomF]

Front rotors: about 275 grams, no overheating experienced; Then again to stop 200kgs of car, you do not need to use a lot of friction. Weight is everything!!!!

[Danny B]

1.5 g's of deceleration? That seems like more than the tires can handle before locking (assuming about a 1.3 tire to road coefficient). Ok heres whats up: With .55" bore master cylinders (front and back) we are looking at 120 pounds of foot pressure (5:1 pedal advantage) assuming a deceleration rate of about 40 ft/s^2. Front and rear pressures are about 1250 psi.
If however we cut the decelration rate down to... 20 ft/s^2, the system pressure favors the rear by about 400 psi (less weight shift).
My question is, Would the balance bar be able to even pedal pressure to the MC's out if there is a difference of this much??? I plan on doing temperature analysis within the next few days to make sure our brakes wont overheat massively due to our scaled down brake components having to work extra hard.

[Dan B]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Danny B:
...we are looking at 120 pounds of foot pressure...
</div></BLOCKQUOTE>
Too much peddle effort (IMO)

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Danny B:
...If however we cut the decelration rate down to... 20 ft/s^2...
</div></BLOCKQUOTE>
You do know that this is a race right??? Not just a Sunday drive? Why would you ever want to stop slowly in a race car (trail braking asside).

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Danny B:
...the system pressure favors the rear by about 400 psi (less weight shift)...
</div></BLOCKQUOTE>

This is why some people like the inline proportioning valves. They are non-linear.

[Danny B]

Im thinking that 120lbs is about the point we want under max acceleration... thats what the professional engineers i have talked to have said

[Agent4573]

If you want to know if the balance car can adjust that much, do the equation. Assumme you can get about 3/4 an inch of movement(i think its actually close to an inch of movement) in the balance bar, and do a simple statics problem to see how much imput force is going into each master.

[Buckingham]

Back on travel:

Every MC that uses a resevoir will have a "travel to cutoff" distance. i.e. the mc will stroke a finite distance before pressure is allowed to build. Its possible that this can account for more of your travel than any amount of flexure.