Combining a couple of topics, M7R has raised the point about brake pad areas in this thread here, and I've started to think more about brake pedal / master cyl / brake piston diameters and the leverage involved. There's some maths involved in this, but I'm just starting to scratch the surface. Say a brake pedal ratio is 5:1. This combines with the master cylinder area, and the net effect (in conjunction with any servo) has to be matched with the area of brake caliper pistons pushing on the pad. Then the pad is of a certain size and has X-amount of friction on the disc, a coefficient of friction dictated by the pad type. (I think?). Does anyone have any equations? In theory (?) the effectiveness of any brake set up should be worked back to a number?
Chris, heres something similar, but totally different, move to somewhere else, but It will pass a while for anyone who reads it. I just thought of it on opening this thread. (sorry)! BG http://www.ferrarichat.com/forum/showthread.php?t=274088 Ps, you are correct on the above really, but one thing people forget, stopping is nothing to do with the pad catching the disc after a point, its about the tire catching the road. This is sometimes forgotten. No point being able to lock the disc in a nano second if the tire and road interface cant back it up too.
also the leverage of the pedal length makes a difference to the pressure asserted to the master cylinder I have read a sum, somewhere in one of my many books I've not learned anything from!
Awesome Dave, just what was needed I'll just type it out, working it through from your great illustration, from the initial pedal press to the wheel effect. Braking torque 1) Master cyl Force (Fm) = Pedal force (Fp) x pedal ratio (pedal length x distance from fulcrum to master cyls) This force applies itself to the master cylinder area. Two components: force combined with basic leverage. Force is unknown - it's the foot! 2) Master cylinder pressure = Fm / Master cyl area (Am) This net force translates directly (barring flexible brake line losses) to pressure at caliper (Fp). 3) Force at caliper (Fc) = Fp x Piston area (Ac) 4) Braking torque = 2 x Fc x Coefficient of friction of pad/disc (μ aka 'mu') x Radius from disc centre to centre of pad (R) Qs: There must be an accepted range of human pedal input to expect to be delivered? X kgs? Is the effect of pad area variability all merely summarised within μ ?, Pad size I believe has a heat resistance/endurance role, but I assume a greater friction role? Is there some maths for friction involving a declared μ figure by the pad manufacturer (assuming a given friction on steel) x pad area. Pedal travel Far easier! Dictated by pad clearance from disc during normal running (C) 1) Caliper piston distance moved is 2 x C (twin pot caliper) 2) Fluid moved at caliper is 2 x C x Area of caliper (Ac) 3) Master cylinder travel (Tm) [Per (twin-pot) caliper] = Fluid moved / Area of master cyl (Am) 4) Pedal travel (Fp) = Tm x Pedal ratio (L/P) Q: The unknown in this calculation is 'C'. Clearly in a 4-pot system, this is multiplied by 2 or 4 (if comparing with a single / twin pot set up), albeit it's then reduced by the smaller overall pot diameter.
Great, so 40 kgs. Quite a force. Will look for more data Great, more from M7R here: What I assume μ really is, is a coefficient per unit area of pad compound, so the area of the pad in total will vary from caliper design to design & hence μ masks several components of friction, being: 1) inherent pad friction against an average steel 2) overall area where it's deployed (multiple of 1)? Or does a larger area mean less pressure? 3) heat friction variables
Lets not also forget the stuff that will alter your end figure> Cross-sectional expansion of the flexi brake lines. Stiffness of the calipers. H20 In the brake fluid. Co-efficient of friction between the pads and discs at high temperatures. Stiffness of the pedal box. Condition/thickness variation of the disc surface. Condition of the wheel bearing. I know what your getting at Chris, and perhaps I have pulled it off the original basic calculation your after, but these all factor in there too and can alter things enough to be disappointed once you enter the workshop.
Yes, indeed, but for the purposes of this, components can be assumed to be in optimal/new condition. I notice on the Pedal force maths, the servo effect is not in the equation. Is this a simple linear multiplier?
All of the above points exist in the new condition also As for the servo, Im not sure, I sometimes find it of no use if I left foot brake on the road as there is Little manifold vac at part throttle. Im not sure, for that reason, that Id want to include it. The servos action effectiveness also depends on the cam fitted, and if its advanced or retarded, so Im not sure how you'd factor all that in? Few links, http://sports.racer.net/brake_bias.htm Calliper flex as mentioned, should not be ignored> http://www.eng-tips.com/viewthread.cfm?qid=95841 Interesting none the less, BG
if you want I can find a copy of Reg 13H which is whats used for braking approval, it has some info on pad etc - I THINK.... been a while since I read it!!!, also Reg 90 has some info too on the mu of pads etc etc... this too has a limit of 50daN for pedal input but on modern stuff from my testing unless there is no servo you wont get this high with out the ABS goning mental! for more modern stuff from my testing it more like 27 - 36 average, but I was up at high 30s on a few stops looking back at my results... but I was right on the ABS limit there and that was in a car with some VERY fancy carbon ceramic brakes and more pots that you can shake a stick at in the calipers! this is Reg 13h, there are also updates but they wont really change anything we are interested in, http://www.unece.org/trans/main/wp29/wp29regs/r013hr1e.pdf another thing to chuck in the mix is this... smaller pad = higher force per area clamping on the discs, and from the testing and comapnies I work with it seems to be that pad area when its reduced doesnt make too much differance untill it comes to overal heat capacity... ie a cut down pad will do a high speed stop with little differance to a lager one in the same caliper and system provided the material can take the energy per area... the test comes with repeated stopping, ( check your cars brake pads, they will have a chamfer to help with noise and bedding in.... the chamfer can be as much as 30% or so of the overall area when new) reg 90 - http://www.unece.org/trans/main/wp29/wp29regs/r090r2e.pdf again its beena while since I read it, as we have a test report we follow and unless the customer wants to do something thats not normal we just follow the test report and rutine so to speak. all Reg 90 pads have to pass a spead sensitivity test and a cold peformance test, the speed sensensitivty test shows how the decel varys with speed for a given pressure, and this is rarely flat... it normally drops on the higher speed. Im not on my works lap top at the mo but when I am ill go through the regs properly looking for any info on leaver ratios etc. (im not sure if thats covered thinking about it other than a passing mention...it might just be assumed that the brake maufacture can get it right with the verhicle maker) Servos are normally a fixed ratio iirc, but this is working on a full vac normally around -0.45 I would guess from the mk2, - servo relationships http://www.classicperform.com/PDFs/BoosterBrakePressureChart.pdf also some info on MC to piston relationships http://www.ducatimeccanica.com/brake_ratios.html
flex is a big issue on older cars, you can feel the floor etc move. similarly as brian says the calipers/carriers will move -path of least resistance etc [powerdubs may move more than others]
I appreciate there are a significant number of variables creeping in, but I'd like to derive the base maths and then pepper it with the less precise unknowns. I assume 'flex' in theory affects both pedal travel and then torque at the disc.
Thats the thing with theory, the end figure is useless without the variables factored in. The real world end product can be a fair bit off than what you have calculated. Dont hate me Chris,(please!!) I know what you are on the quest for, but its the 'less precise unknowns' that are the most Important. The rest is just basic math.
the servo is a vac store... it is charged up pretty much instantly the engine is started, and then holds this vac via a 1 way valve untill its used, and it can do 2 or 3 pedal applications before the assistance is gone. also on a nat asp engine there is ALWAYS lower manifold pressure than atmos so even if the throttles wide open there will be vac that will help to charge up the servo.. not as fast as on a closed throttle granted, but its still charging, hence why with the size of the store and the fact a nat asp will always be seeing vac you notice no differance when left foot braking. on a turbo the servo is charged up on closed and part throttle use, if you were to brake on boost then you would get 2 or 3 boosted applications and the the asistance would drop off, but if you braking repeatedly when on boost you have other issues to worry about! servo failed stops are bloody hard work!! we have to do these for approvals the pedal effort applied then is higher, up around the 50 limit for an average pressure, and this si where the leaver length comes into it as this will improve the stopping (servos can compensate for a short leaver length, but you will then fail the stopping distance limit for a servo failed)
I'm interested in the theory - aswell as practice. I'm personally trying to understand the brake system I have, and put some numbers in place. Even with the variables, it means folk in this situ can adjust a known factor, and predict the direction this adjustment will have on the outcome, even though the variables remain in the system.
What you need is a pumped pressure system with accumulator. A la the 90 20V Q. I think I have posted this before somewhere on here? Fast as you can, down 'Moll's Gap', empties the servo, and fades the brakes, uber quick. Just ask our Audi 100 Avant! Down 'The Corkscrew', in Clare, is even better, for fading brakes, when you are pushing it!
Maybe this is another Brian G mod.... the fitting of a vacuum pump from a Diesel to eliminate servo fade during left foot braking twisty runs.
Thought about it Saves making a dissy plug hole cap thingy too Dave, indeed, you need to drive the roads here to truly get the meaning of 'very bad turns' Its no wonder Porsche bring their test cars to Bellmullet for road/suspension testing
