Why size matters... Some years ago it seems like it was hot to have as large brakes as possible, particularly at the front. Still one can see ads with the message “buy our BBK, increase stopping power” etc. Even on our ti’s several people recommend swapping the OEM ‘ti front brakes by the e46 330i front setup or even the setup from the e36 m3 3.0. During the recent years several vendors are claiming that bigger is not necessarily better. Especially StopTech has done a good job in advocating this message. This could not be said about all BBK vendors. In experimenting with brake setups, calculating the static bias is probably the first step within the art of brake system analysis, in order to get an overview of how a brake setup is affecting the car. Studying some serious BBK-solutions for e.g. the e36 reveals that they slightly move the static bias rearwards compared to stock. Sadly, not all BBK-kits do that. It seems like the main herd of BBK’s do the opposite, mainly moving the static bias forwards. Since the likelihood for that a BBK system alters the brake bias is quite high, the next step in brake system analysis could be to play around with the equations to see if they could help in an understanding at a level above the static bias analysis. In the following I have played around with the equations given in StopTech’s white papers together with some other published papers (see the list of references at the end), describing the theory in more depth than the StopTech papers. The concept for my analysis is: Several test of an e36 323ti shows a stop length of 38m (see e.g. [4]), going from 100-0 km/h. An assumption is that this stop length is achieved by applying maximum braking force. Accepting this as reasonable, it is possible to determine the average coefficient of friction for the vehicle. When the average coefficient of friction is determined, the maximum deceleration is determined. Further, this also dictates the maximum braking force which can be applied before the front wheels stops rotating (or the ABS intervenes). An additional assumption is that the maximum braking force for the front tires is the same for any brake system setup for the e36 323ti (see e.g. StopTech’s “The brakes don't stop the vehicle - the tires do.”). Knowing the maximum braking force for the front wheels, it is possible to determine which brake pedal force that has to be applied in order to achieve it, given the brake system data. In my analysis I have chosen to present eight analyses reflecting my experience towards choosing brakes for my ‘ti. The purpose was to serve my needs when taking the car to the track as well as a daily cruiser. The first case is the base case, describing the ‘ti with stock brakes. The second case is an analysis considering the use of the popular e46 330i front brakes on the ‘ti combined with stock rear. The third case is the case reflecting my actual choice, AP Racing, 4 piston, 330x28mm vaned, floating disc and stock rear. The fourth case is the same as the third case, however with racing pads up front. The fifth case is AP Racing 4 piston, 330x28mm vaned, floating disc up front and stock rear disc with e34 m5 rear calipers. The sixth is the same as the fifth, but with PFC01 pads (used for the track). The seventh case is AP Racing, 4 pistons, 330x28mm vaned, floating disc up front and a custom made AP Racing 2 piston rear caliper and 294x19mm vented disc from the Z4 3.0. Case eight is the same as the seventh case, however with racing pads. In the analysis I have assumed that the coefficient of friction for my street pads are 0.5, for the track pads (PFC01) 0.6, and finally for the DS2.11 track pad I have used 0.61. For all systems analysis I have chosen to display the static bias, maximum deceleration in g, stopping distance, pedal force needed for the system under investigation to achieve the stopping distance and a guesstimate of the time for achieving the pedal force. dS, dBP and CarLength is explained further down this document. The analysis of the brake systems (cases) are presented in the Table 1 and Table 2 below. Table 1 shows stopping distances and brake point analysis assuming initial speed of 100km/h. Table 2 shows stopping distances and brake point analysis assuming initial speed of 140km/h. Table1.Brake analysis of the brake systems described above. Stopping distance @100-0km/h. http://home.online.no/~krimp/sweb/images/Table1.JPG Table2:Brake analysis of the brake systems described above. Stopping distance @140-0km/h. http://home.online.no/~krimp/sweb/images/Table2.JPG For the OEM brake configuration (Case 1), Table 1 shows that the theory aligns with the stopping distance of 38m as reported. The pedal force needed is 84.4N, and it is assumed that it takes 0.5s to achieve this pedal force. The analysis of the e46 330i disc (Case 2) used on the ‘ti with stock rear, show that the bias is moved forwards by approx. 5%. The stopping distance is estimated to 41m, i.e. increased stopping distance (100-0km/h) by 3m. However, the maximum braking force for the front wheels (tPedalForce) is achieved 0.11s earlier than for the stock system. This time difference corresponds to -3.1 meter (dS). The net change of the braking point (dBP) is however almost zero. Investigating the stopping distance assuming initial speed of 140km/h shows an increase in the net change of the braking point by 2 meter. I.e. we have to apply the brakes 2m earlier than with the stock brakes. The results of swapping the stock ‘ti front brakes with the front AP Racing BBK as mentioned above and maintaining the stock rear brakes is shown as Case 3. The result is almost as sad as for the e46 330i brake setup. The results of swapping the stock ‘ti front brakes with the front AP Racing BBK as mentioned above, using DS2.11 racing pads and maintaining the stock rear brakes is shown as Case 4. The result is now even worse. The bias is moved almost 8% forward. On the track I could feel that the initial bite was eye ball popping, but also that the rear brakes had not much to do. It was as the rear of the car was pushing as if there should be a heavy trailer pushing behind. From Table 2 one can see that I had to start applying the brakes almost a car length earlier than with the stock brakes. Another reflection is that by swapping to the front-only-BBK it felt initially as if this was really good. It felt like the stopping power was increased. By looking at the math, this is probably due to the reduced pedal force needed to lock the brakes. My body had adapted to using more pedal force than that was now needed. I guess this was probably misinterpreted as increased stopping power. So then, was the investment in front BBK a waste of money? Luckily not. Using the static bias analysis I found that by using 38mm rear caliper the stock bias was re-established, with the reduced pedal forced as a bonus. The analysis (Case 5) in Table 1 shows that the stopping distance is close to stock, and that I could theoretically move the braking point -2.5m (negative sign means later). Table 2 shows a theoretically move of the braking point by -3.2m. Further, using the track setup (Case 6) the math predicts less pedal force and even shorter stopping distances. This aligns with my experience using this setup. It simply works very well for me. Last year I participated on a BMW driver training course, where several scenarios were dedicated the use of the brakes. The feedback from the instructors was that the car seemed very well balanced. I could of course have stopped here, but I am curious to if it possible to do it even better than this. Within the next months I am finishing my long term project regarding building vented rear discs on my ‘ti. The calipers chosen are AP Racing CP5211, a very light 2 piston caliper. The math (Case 7 and 8) predicts reduced stopping distances and even later braking. Time will show if the conceptual math as used here supports real experience also with vented rear discs… UPDATE: Did a test run with with my upgraded BBK (Case 7). Used my Performancebox (GPS-based logging system) in deceleration mode (100-0 km/h) to measure stopping distances. Ambient temperature was 8 deg. C. The cold pressure in the tires was front/rear 2.6/2.8 bar. Tires used was Dunlop Sport Maxx, 225/40/18 front, 255/30/18 rear. The e36 323ti is reported to have a stopping distance of approx. 38m (see e.g. [4]). Accepting that as a valid number, my setup should theoretically result in a stopping distance of 37.2m. The results from my test runs show a stopping distance of 37.28m in average. The best was 36.59m and the worst was 37.64m. Peak g was 1.1 m^2/sec. Seems like theory and practice fit... References: [1] http://www.stoptech.com/tech_info/te...e_papers.shtml [2] http://phors.locost7.info/contents.htm [3] http://diss-literatur.lima-city.de/L...oefficient.pdf [4] http://www.monteverdiclub.com/rahmen/stoptbl.htm Disclaimer: Note that the equations and relationships used in this work represent approximations of the real braking system. The results are based on my current level of knowledge and may change without further notice. |
Gotta run to class, but this seems like a really good read. I'll try to post up later |
Just got a chance to read, it's nice to see numbers behind the argument instead of just the idea. I realize how much more my M3 fronts do than the stock rears the most when I'm in the rain/snow/ice. Really have to watch how hard I brake, I can easily lock up the fronts. This is with no ABS, car has none. Dunno if you have the figures, but if you do and could throw em into a calculator I'd love to see the results of the E36 M3 fronts, stock rears with street pads. I take it you're an engineer of some sort? Mechanical I'm guessing. |
A rather thorough analysis, indeed. I'm planning on upgrading my stock front ti brakes to a stock M3 system. My reason for this is not so much to increase stopping distance, which, based on your charts, may actually increase stopping distance, but to reduce brake fade caused by the solid, smaller diameter rotors. Long, twisty downhills are a killer on those thin, solid rotors. Once the brakes heat up, my spirited driving comes to a spongy, choppy halt... it would be nice to not have to worry about that anymore. :smile: |
Fade? I'm barreling down at 115 down 2 straights at the track. Hard on the brakes. 328 brakes up front. I have never had fade except when caused by old brake fluid. I bet my rotors are getting plenty hot. Change your fluid a little more often and get better pads. Use some ATE Gold or Motul if you are experiencing fade. |
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A very well done analysis... I have one question that may or may not impact us US owners as far as your research is concerned... Are you aware of any difference between the euro e36 323ti factory front brakes and the US factory 318ti front brakes? The earlier US models (95-97 I believe) came with a solid rotor, while the later years came with vented rotors, which means slightly different calipers. If there is a difference, how much impact could this have on your findings? I have followed your rear custom brake project and I look forward to the results! |
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Table 3:Brake analysis of the brake systems described above. Stopping distance @100-0km/h. http://home.online.no/~krimp/sweb/images/Table3.JPG Table 4:Brake analysis of the brake systems described above. Stopping distance @140-0km/h. http://home.online.no/~krimp/sweb/images/Table4.JPG As is seen from the tables above the numbers with m3 up front and stock rear (Case 3) does not look good (my opinion). If it had been my 'ti with m3 brake config. up front, I would have tested a rear caliper with 38mm piston (e34 m5 3.6 or similar) (Case 4). I would also have looked for the possibility to use 40mm piston, since it gives the results closest to stock bias (Case 5). Quote:
Disclaimer: Note that the equations and relationships used in this work represent approximations of the real braking system. The results are based on my current level of knowledge and may change without further notice. |
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Yea. Definitely sounds like a brake fluid issue. Not to hijack the thread much. I run cooling ducts directly to the rotors for the track. I remove them on the street. My feeling about bigger brakes up front are that you throw off the brake bias. On a track weekend a few years ago I had track pads up front and street pads on the rear. I went through the rears in one weekend. My feeling is that the rears are working harder than the front. In a normal system, your fronts do more of the braking. |
can u do the calculations with the z3 m coupe rear and the m3 fronts and also the same rear z3 m coupe and a BBK up front? i already have the m3 fronts and i wanna upgrade the rears soon |
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By using the e36 m3 (315mm discs, 60mm piston caliper), Z3m rear and stock 323ti/318ti master cylinder, the numbers are as shown in Table 5 and 6 below. Table 5:Brake analysis of the brake systems described above. Stopping distance @100-0km/h. http://home.online.no/~krimp/sweb/images/Table5.JPG Table 6:Brake analysis of the brake systems described above. Stopping distance @140-0km/h. http://home.online.no/~krimp/sweb/images/Table6.JPG As is seen from the tables above the numbers with m3 up front and Z3m rear (Case 6) looks good. Probably no surprise since this is close to Z3m numbers. Disclaimer: Note that the equations and relationships used in this work represent approximations of the real braking system. The results are based on my current level of knowledge and may change without further notice. |
Wow thanks that's some awesome braking with all the mz3 in the rear and either m3 or bbk up front, sick sick |
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