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BMW 3-Series (E90 E92) Forum > BMW E90/E92/E93 3-series General Forums > General E90 Sedan / E91 Wagon / E92 Coupe / E93 Cabrio > Does the 330 actually stop more quickly becuase of its bigger brakes?



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      02-01-2006, 07:21 PM   #67
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Quote:
Originally Posted by Laplacian
No, no, I understand that warm/hot pads have a smaller mu than cold ones. I was just choosing to fix the temperature (fix mu) at a certain warm (but not melting) practical temperature point.

Okay, I should have been more clear. I was referring to the normal force that the pad can exert on the disc, not the frictional force which depends on mu. The normal force is dependent on pressure and surface area only. Fb = mu*N and I thought you were referring to a fixed value of mu previously and meant that the maximum N can vary. Now I see that this is not what you meant. Sorry.
I think we're almost there. One little detail we have to clear up is that there are two frictional coefficients floating around. My original Mu was the normal force friction coefficient between the TIRES and the GROUND. Your Mu is the coefficient of friction between the BRAKE PAD and the BRAKE DISC. I would prefer to call this Cfbrake. Perhaps this clarification might reduce some confusion. I've been alluding to Cfbrake, but never explicitly mentioned it or introduced it in the previous posts. Sorry if it caused some confusion.

As a first approximation, it would be sufficient to keep Mu and Cfbrake constant for normal driving conditions - the arguments don't change much.

Quote:
Originally Posted by Laplacian
You argue that mu is so high in most cases (all but the hottest temps) that Fbmax will always be greater than Fmax*Rt/Rd. I wouldn't have thought this to be true.
I think you meant Cfbrake here. And, yes, this is true. (Note that Fmax was derived from Mu, not Cfbrake.) The brake pads can lock up the wheels at practically any speed. The trick for brake designers is to balance the pedal sensitivity such that it's not so sensitive the brakes lock immediately (poor stopping distance since you are sliding) or so insensitive that you have overexert yourself trying to reach that impending brake lock point (a situation where you don't utilize the full traction between the tires and the ground - hence a longer stopping distance.). This is why I keep bringing up the modulation issue. Either you or the computer needs to modulate the brakes to maintain the impending brake lock point for minimal stopping distance. (To live on the edge, if you will.) If you don't modulate, you will either lock up the wheels or under-brake. Also modulation doesn't just mean ABS. There are four wheels on the car, and each wheel brake must be modulated to be at its impending lockup point. (I believe BMWs have electronic brake force distribution as well.) A lot of cheap cars have brakes biased towards the front wheels (having cheap drum brakes in the rear), so the rear wheels don't do much braking, and you don't get optimal braking performance. There's another reason for the front bias - it's more stable, i.e., safer, for the front wheels to lock first than rear wheels, but that's another story.

Quote:
Originally Posted by Laplacian
[Here's why I thought this not to be true: how can Fb >> Fmax*Rt/Rd if the ABS is not kicking on? Maybe Fb = Fmax*Rt/Rd + epsilon with no ABS, but >>? This is really the main issue--I think we're in perfect agreement on everything else.
What I meant is that the MAXIMUM capability of modern brakes to generate Fb is >> Fmax*Rt/Rd. Of course, when the ABS is not on, the ACTUAL Fb to stop the car is < Fmax*Rt/Rd! When the ABS is on, Fb = Fmax*Rt/Rd. If Fb exceeds Fmax*Rt/Rd at any point in your braking, you've locked your wheels.

Thanks Laplacian for your great discussions. I haven't thought about brakes much until now, and I'm learning more about them as I type!
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      02-01-2006, 07:44 PM   #68
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I don't see why people has such a hot argument on which component in the brake system to stop the car. It is all common sense, a larger brake kit will stop the rotor quicker and a more gripper tire will help stop the car quicker too. They all have to work together in order to stop the car. So, which component stop the car, it is the brake system (consist of brake fluid, brake line, brake caliper, brake piston, brake pad, rotor, wheel and tire) but not just one single component in the system.
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      02-01-2006, 08:08 PM   #69
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Living on the east coast, I sure miss a lot of good discussion during business hours and late night.

Laplacian and e90wraith: I feel like I need to get back into the engineering texts I haven't used in 10 years. You've already got me interested in doing a triple integral I haven't done since 1989...

In order to calculate the friction force of the brake pads you'll need to know the temp range. Pad type and characteristic has a large bearing on the temp range for stopping. The carbon metallic pads I used on my racecar didn't start working well until a few warm-up applications whereas street pads typically work better at lower temps. The calipers on the two cars differ as well. This would change the normal force put on the disc by the pads.

Practically speaking from race track experience, the cars with larger rotors and pads to match will have more brake left at the end of a session. Of course you could have the same brakes and a lighter car, and that would be even better. Lose the runflats, put on some light wheels, and you will take off some 80 lbs of rotating mass. This loss of unsprung weight would make this entire discussion mute.

Cool discussion.
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      02-01-2006, 08:43 PM   #70
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Modulation is not an issue if you're putting the pedal to the floor to test maximum braking response at a certain speed. (Of course, modulation as you describe it sounds absolutely essential to any good system, but not important to our discussion about maximum braking power.)
Quote:
Originally Posted by e90wraith
What I meant is that the MAXIMUM capability of modern brakes to generate Fb is >> Fmax*Rt/Rd.
This is what I was questioning. Is this really true under most normal driving conditions? I know you said that Fb < Fmax*Rt/Rd with super hot pads, but I thought Fb < Fmax*Rt/Rd also in situations where the pad is sufficiently warm. I'm no expert so I guess I'll have to take your word for it. However, if this were true, then brake disc size would be determined by the tire traction of the car itself. (A manufacturer would want to put the smallest discs possible so that the pads don't heat up too much.) This would make maximal braking almost completely independent of the brakes themselves! Again, I don't anything about tire traction so I'll have to trust you on that.

Maybe the way that the way mu_brake (isn't Cf heat capacity?) varies with temperature has much more to do with braking than I originally thought. In other words, the lower brake temperature due to the larger disc has more to do with better stopping than the greater amount of energy that the larger brake can dissipate.
Quote:
Originally Posted by e90wraith
Thanks Laplacian for your great discussions. I haven't thought about brakes much until now, and I'm learning more about them as I type!
Same here. Funny thing is that some people are seeing our exchange as an argument. That's certainly not the case--only a few miscommunications due to the format of the board. Working out the details is always interesting. Wish we had more data though. Then we could compute the real answer.
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      02-01-2006, 10:06 PM   #71
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Quote:
Originally Posted by Laplacian
Modulation is not an issue if you're putting the pedal to the floor to test maximum braking response at a certain speed. (Of course, modulation as you describe it sounds absolutely essential to any good system, but not important to our discussion about maximum braking power.)
If you put the pedal to the metal (the brake pedal), what you'll get is a brake lock. Of course there is a little lag because you have to physically push down on the brake pedal, but if you push the brake pedal to the floor when you're driving, you will lock the brakes if you don't have ABS. *Disclaimer - don't try this at home!* When the magazine reviewers test the brakes on non-ABS equipped cars, they don't push the brake pedal all the way down. They do threshold braking - just backing away from brake lock. If you push the brake pedal all the way down on a modern car at any speed, the brakes WILL lock.

Quote:
Originally Posted by Laplacian
This is what I was questioning. Is this really true under most normal driving conditions? I know you said that Fb < Fmax*Rt/Rd with super hot pads, but I thought Fb < Fmax*Rt/Rd also in situations where the pad is sufficiently warm. I'm no expert so I guess I'll have to take your word for it. However, if this were true, then brake disc size would be determined by the tire traction of the car itself. (A manufacturer would want to put the smallest discs possible so that the pads don't heat up too much.) This would make maximal braking almost completely independent of the brakes themselves! Again, I don't anything about tire traction so I'll have to trust you on that.
Yes, my assertion is that the maximum Fb that the brakes can generate when warm is > Fmax*Rt/Rd. I'm not sure I follow your argument about why you would use smallest discs. You want to use larger discs so you have better heat dissipation (fade resistance) and use lower brake pad pressure (less stressed system).

Quote:
Originally Posted by Laplacian
This would make maximal braking almost completely independent of the brakes themselves! Again, I don't anything about tire traction so I'll have to trust you on that.
Indeed, as long as your brakes are capable of generating brake force, Fb > Fmax*Rt/Rd, it doesn't matter how powerful your brakes are. This ignores the reduced Mu_brake (I used your terminology - I usually use Cf to denote Coefficient of Friction.) due to heating which comes to affect when the brakes are used repeatedly. Hence the argument that 330i and 325i have same stopping distance when the brakes are cold or used intermittently.

Quote:
Originally Posted by Laplacian
Maybe the way that the way mu_brake (isn't Cf heat capacity?) varies with temperature has much more to do with braking than I originally thought. In other words, the lower brake temperature due to the larger disc has more to do with better stopping than the greater amount of energy that the larger brake can dissipate.
I'm not sure I follow the first sentence, but the second sentence right on. It's the ability of larger discs to dissipate heat that gives it resistance to brake fade (reduced mu_brake) - hence stop quickly, repeatedly. The car with a smaller brake disc scan initially stop just as quickly as the car with larger brake discs, but not repeatedly.

Quote:
Originally Posted by Laplacian
Same here. Funny thing is that some people are seeing our exchange as an argument. That's certainly not the case--only a few miscommunications due to the format of the board. Working out the details is always interesting. Wish we had more data though. Then we could compute the real answer.
I feel like we hi-jacked this thread. Perhaps we need to apologize to the other members. Maybe we should have discussed this off-line, but it was sure entertaining...

P.S. Look what you made me do! I even made some graphs... See if you agree with the three graphs for three different situations, normal stop, threshold braking, and emergency panic stop.
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      02-02-2006, 12:35 AM   #72
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Quote:
Originally Posted by e90wraith
I'm not sure I follow your argument about why you would use smallest discs. You want to use larger discs so you have better heat dissipation (fade resistance) and use lower brake pad pressure (less stressed system).
Perhaps I didn't word it correctly. I am simply saying that the manufacturer would want to use the smallest discs possible that still give an appropriate temperature under heavy braking situations (to save on materials/money, of course).
Quote:
Originally Posted by e90wraith
I'm not sure I follow the first sentence...
Seeing a plot of mu_brake vs. temperature would be interesting.
Quote:
Originally Posted by e90wraith
I feel like we hi-jacked this thread. Perhaps we need to apologize to the other members. Maybe we should have discussed this off-line, but it was sure entertaining...
Nonsense. Our discussion directly addresses the topic of this thread: Does the 330 brake better?
Quote:
Originally Posted by e90wraith
P.S. Look what you made me do! I even made some graphs... See if you agree with the three graphs for three different situations, normal stop, threshold braking, and emergency panic stop.
Very nice plots. In the second one I like how you have the emergency braking (red) line plateau out indicating that the brakes have locked and static friction has taken over. Took me a second to realize that's what you were indicating. But isn't mu_static > mu_dynamic? So shouldn't the plateau be at the highest part of the graph? In fact, it should be higher than the Fmax*Rt/Rd threshold (dashed) line indicating that the brakes have locked up. Also, if the brakes have locked up, then Fmax (the frictional force of the tires on the ground) has moved from the static to dynamic range. So this bar should be lowered upon break lock up. Maybe something like this. (By the way, I don't understand your third plot.)
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      02-02-2006, 02:25 AM   #73
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Quote:
Originally Posted by Laplacian
Perhaps I didn't word it correctly. I am simply saying that the manufacturer would want to use the smallest discs possible that still give an appropriate temperature under heavy braking situations (to save on materials/money, of course).
Yes, this is true. There is definitely a disc size at which a manufacturer would say "that's good enough," beyond which the added benefit of a larger size is "only" better fade resistance. The next section might clarify a little bit why.

Quote:
Originally Posted by Laplacian
Very nice plots. In the second one I like how you have the emergency braking (red) line plateau out indicating that the brakes have locked and static friction has taken over. Took me a second to realize that's what you were indicating. But isn't mu_static > mu_dynamic? So shouldn't the plateau be at the highest part of the graph? In fact, it should be higher than the Fmax*Rt/Rd threshold (dashed) line indicating that the brakes have locked up. Also, if the brakes have locked up, then Fmax (the frictional force of the tires on the ground) has moved from the static to dynamic range. So this bar should be lowered upon break lock up. Maybe something like this. (By the way, I don't understand your third plot.)
Ah - I now understand the misunderstanding after seeing your statement and graph! If you remember, when the tires are rolling, traction is determined by the STATIC friction coefficient (the speed at the bottom of the tire where it meets the ground is zero!). Once the brakes lock, the tires are sliding, hence the DYNAMIC friction coefficient takes over. And as you noted, mu_dynamic < mu_static. That's why Fb exerted by the brake pads actually drop once the wheels start sliding, i.e., brakes lock. Hence, you actually have longer stopping distance once the brakes lock. Does the third plot now make sense? Once the brakes lock, it takes longer time to stop since you have lower deceleration. (I guess I could have done a little better job of plotting in the third graph. For the emergency braking, the initial downward slope should be high and immediately transition to a gradual downward slope when the brakes lock. But I think you still still get the point with the current graph.)

[EDIT] Thinking more about it this morning, I think I now REALLY understand what you wrote. The previous paragraph was a false start, although the arguments are still relevant and valid. I think you meant that mu_static_brake should take over when the brakes lock. Since mu_static_brake > mu_dynamic_brake, the force applied by the brake pads, Fb, should increase when the brakes lock. (This explains your graph.) However, this is incorrect. If you balance the forces (torque in this case) between the tire/ground and applied by the brake pads/disc, the brake pads must apply Fb = Fmax*Rt/Rd, where Fmax is determined by mu_dynamic of the ground and the tires. Remember, mu_static_brake is the maximum potential friction between the pad and the disc that can be generated, and Fb is NOT the normal force between the brake pad and the disc. Fb is a tangential force applied perpendicular to the normal force between the brake pad and the disc. Think of a wooden block sitting on a table. Before it starts sliding, it only pushes back with the same amount force (direction perpendicular to the normal force) you apply. Only when you apply a force greater than m*g*mu_static, does it moves. Any force less than that, it just pushes back with the same level of force as the applied. The brake pads don't just generate their maximum force, they generate just enough to balance the force the tires and the ground generate, i.e., balance the torque.

So looking back, I now see why you had difficulty believing that Fb never exceeds Fmax*Rt/Rd. Once it's exceeded, the wheels lock and Fb, the tangential force applied by the brake pads onto the disc, actually drops to a level proportional to mu_dynamic/mu_static (of the ground versus tires) which is < 1.

Last edited by e90wraith; 02-02-2006 at 02:09 PM.
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      02-02-2006, 02:43 AM   #74
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I took one look at the graphs above and I said... "Whoah whoah... let me find a new thread to post in."
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      02-02-2006, 01:52 PM   #75
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It was late when I posted last night, third plot makes sense of course.

And when dealing with static friction, the force of static friction can equal the opposing force UP TO mu_static*N. That doesn't mean that it equals mu_static*N. It matches the opposing force exactly, up until you cross the mu_static*N threshold. This was my mistake and the reason that the red line should dip down. Again, it was late .

Showing Fmax during the brake lock-up range is not relevant, however--that's what was throwing me off (if I have to blame something ). I added the actual tire friction thresholds to your second plot. Just added these for my own understanding.
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      02-02-2006, 02:16 PM   #76
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You know, I just edited my last post just as you were writing your new message. I think the mu confusion got us again... Anyway, maybe we can actually plug in the numbers and compute everything one day.

But then again BMW's gonna have to pay us to re-analyze and redesign their brakes...
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      02-02-2006, 02:26 PM   #77
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Quote:
Originally Posted by e90wraith
You know, I just edited my last post just as you were writing your new message. I think the mu confusion got us again... Anyway, maybe we can actually plug in the numbers and compute everything one day.

But then again BMW's gonna have to pay us to re-analyze and redesign their brakes...
Seriously...although I think their money would be better spent on us reprogramming their iDrive (which I would almost want to do just to get it the way I like ). Although I haven't really used the new 4-point iDrive on the 3/5/6 (and didn't order it on mine); I've just used the 8-point iDrive on the 7.
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