When comparing the braking performance of various cars, I find it much easier to relate to deceleration g's rather than the stopping distances reported in the various car magazine tests. It doesn't help that they report stopping distances from 60-0 mph, 70-0 mph, 80-0 mph, or 100-0 km/hr, etc., which then makes direct comparisons almost impossible.
This simple formula converts stopping distance to g's, where the initial speed V is in fps and stopping distance SD is in feet.
g = V<sup>2</sup>/(64.4 x SD)
The deceleration rate at 1.0 g is 32 ft/sec<sup>2</sup>. Once you the know the deceleration g capability of a car, you can calculate the stopping distance from any speed with,
SD = V<sup>2</sup>/(64.4 x g)
Using the Enzo as the benchmark, the following results are from a not so random sample of car tests. When someone reported the stopping distance from two different speeds (R&T uses 60-0 and 80-0), I used the higher speed. The deceleration g is calculated, and the 80-0 mph stopping distance is the reported value if available, calculated if not. Obviously these tests were done on different days, on different tracks, with different tires, etc; but I still find the results interesting.
You might be tempted to blame Audi's generally lackluster performance (except for the RS6) on the fact that our cars are nose-heavy. Note, though, that the equally nose-heavy Suburu WRX and Mitsubishi Evo finished near the very top of the list. The Porsches had rather mediocre performance (except for the GT), even though their rear weight bias gives them the capability to be among the best.
Frankly, it looks like it's the rare auto manufacturer that knows how to optimize braking ... and then does it.
Jkay
03-13-2005, 06:58 AM
akula-ssh
03-13-2005, 08:22 AM
Especially when you already start at mid-pack with the S8 on the list? It'd be instructive to see the difference between track pads and street pads too, I think. :)
Acceler8
03-13-2005, 10:52 AM
ryoung
03-13-2005, 12:41 PM
At 80 mph, I'm traveling at 117 ft/sec. Assume I'm driving along at 80 mph, minding my own business, when a herd of deer starts crossing the road in front of me. What has to happen?
Even if it takes only 1/2 second to move my foot from the gas pedal to the brake, I've already traveled 58 ft, and nothing's going to change that. This isn't included in measurements of stopping distance, but I use it as an example to show that things are happening very fast. Next ...
Now that I've got my foot on the brake, I have to apply enough pedal pressure to go from coasting to decelerating at 1.0 g (32.2 ft/sec<sup>2</sup>), the limit of adhesion of the tires with ABS active. Assume that this requires me to move the brake pedal 5" to achieve 1500 psi of hydraulic pressure at the brake calipers. If all of this takes another 1/2 second, I've traveled 29 ft (at an average of 40 mph or 59 ft/sec) just to get to full braking. I can reduce this with,
1. <a href="http://forums.audiworld.com/a8/msgs/75190.phtml">Brake Pads</a>: Compared to the 0.35 cf Audi brake pads, the 0.50 cf Ferodo DS2500 would require only 1050 psi to get enough friction to lock the tire and activate ABS. This would require 1.5" less pedal travel, saving 0.15 sec or 9 ft of stopping distance. The 0.62 cf Ferodo DS3000 racing pad would be even quicker.
2. Master cylinder movement: <a href="http://forums.audiworld.com/a8/msgs/38595.phtml">The Block</a> eliminates 2" of brake pedal travel, saving 0.2 sec or 12 ft of stopping distance. This removed by far the largest source of "compliance" from the braking system.
3. Approx 5% larger front and rear rotors: Like higher friction brake pads, this also reduces the hydraulic pressure required to lock the tires and reduces the amount of time it takes to activate ABS.
4. Braided SS brake lines: This removes another small amount of compliance from the hydraulic system and also slightly reduces the amount of time it takes to activate ABS.
5. Stiffer caliper: The Alcon TA-6 is a more rigid caliper than the OE Brembo, also removing compliance.
6. Brake Bias: The optimum brake bias is 2.2 for the S8 (see <a href="http://forums.audiworld.com/a8/msgs/36145.phtml">Weight Distribution revisited</a>). If brake bias is too high, for example, you have to continue increasing pedal effort, after the front brakes go into ABS, to get the rears into ABS. This also takes additional time; or worse yet, if you assume you're braking at maximum once the front brakes are into ABS, you don't continue increasing brake pressure, and you're wasting stopping power of the rear brakes. Whether street or track, I run higher cf pads in the rear to get as close to a 2.2 brake bias as possible.
Items 1-6 are not additive, but the 12 ft reduction in stopping distance from just The Block is the equivalent of a 0.06 increase in braking g's. So to answer your original question: How did all this affect stopping distance with my S8? I don't know, I never did a braking test, but I definitely wouldn't want to go back to OE brakes :-)
ryoung
03-13-2005, 12:43 PM
As I said below, I never want to go back!
akula-ssh
03-13-2005, 01:54 PM
Jkay
03-13-2005, 09:04 PM
coasTTal
03-13-2005, 09:15 PM
Today, I am about to blaze through the iPASS gate on the exit from the tollroad. There are 2 lanes and iPASS users can just drive through either. There is a slow line moving through the non-pay side, and no one on the pay side, so I slow a bit and plan to go right on through. All of a sudden a big range rover cuts over top the cones directly in front of me and making almost a 90 degree turn even shuts off any area to the right of the lane. I stand on the brakes and stop about 2 feet short of his wife's door.
We are both glad I had Stoptechs on the TT, because even if they only stop 2 feet better than stock, that was a very good 2 feet today.
The idiot got a long blast of the horn.
ryoung
03-13-2005, 11:27 PM
The others would have completed that stop against the Range Rover's door, or worse. Even if you actually need those two extra feet only once every decade, when you do need them, you're sure glad they're there.
msauve
03-14-2005, 05:17 AM
Such a relationship only applies when compressing a gas. Boyle's law does not not apply to fluids. Once the "slack" in the system is taken up, very little movement is required for significant increases in pressure.
You have not given information on the working area of your caliper pistons vs. stock. If it's greater, they take less pressure, BUT MORE FLUID, to operate, and the amount of fluid determines pedal movement more than the amount of pressure.
ryoung
03-14-2005, 06:42 AM
The behavior of a real gas deviates from Boyle's ideal gas law.
Many brake fluid manufacturers brag about the low (not zero) compressibility of their products. DOT 5 silicone brake fluids should be avoided because it's twice (or more) as compressible as DOT 3 or 4 glycol ether brake fluids. Quoting from Stoptech's <a href="http://www.stoptech.com/whitepapers/brakefluid1a.htm">Brake Fluid 1A</a>,
<i>"Now, all fluids have a certain amount of compressibility to start with, but adding even the smallest amount of air into the solution can dramatically increase the amount of elasticity in the system. In the case of silicone-based fluids, air is quite happy to take up residence between the brake fluid molecules, and as a result the fluid compressibility goes down. This is felt at your foot like stepping on a big spring. As you can imagine, more air = more spring."</i>
Last but not least, <a href="http://www.prosystembrakes.com/brembobrakefluid.htm">Brembo</a> shows the effect of a 10% reduction in brake fluid compressibility on hydraulic pressure and pedal travel. Like rubber brake lines or a flexible firewall, the compressibility of brake fluid just makes it another source of compliance in the system.
But it's 99% of the way to the incompressable ideal, vs. a gas, which is what you were basing your argument on. Brake fluid compressibility does not account for 1.5" of brake pedal travel when increasing pressure from 1050 PSI to 1500 PSI (which your argument explicitly claimed).
i.e. you calculated that 1050/1500 = 0.7 and then applied Boyle's law to claim that pedal travel would be reduced to 5" x 0.7 = 3.5", or 1.5" less.
You were clearly applying Boyle's law as if brake fluid behaved like a perfect gas. You were wrong, it is VERY far from it. That real fluids are somewhat compressable doesn't mean they behave like gases.
The chart is of course worthless without more detail, such as the volume of the compressed fluid, which will have a linear relationship with the difference.
ryoung
03-14-2005, 09:53 AM
Since the chart is from an article on Brembo's brake fluid, I believe it's reasonable to assume that this represents data from a test rig that resembles a braking system.
The Brembo curve isn't perfectly linear, but it's close enough to say that hydraulic pressure is proportional to pedal travel. Note that a 1/3 reduction in hydraulic pressure from 100 bar results in about a 25% reduction in pedal travel. My S8 started with 5" of pedal travel; for a 1/3 or 500 psi reduction in hydraulic pressure, the reduction in pedal travel would be more than an inch.
OK ... No one's under my dashboard measuring brake pedal travel during 1g stops, but when I switch to a high friction pad, I definitely feel more than an inch of pedal travel reduction (or at least I did before The Block).
Reason I ask: I don't see stepping on the pedal alone could generate 1kpsi. Now if pedal travel is proportional to the amount of force whatever pump generates to create the pressure, we need something that's not an ideal gas, and the relationship between hydraulic pressure and pedal travel would be linear, or very close to.
ryoung
03-14-2005, 10:10 AM
See <a href="http://auto.howstuffworks.com/brake.htm">How Stuff Works</a> for the basics. The pressure from your foot acts on a lever arm with about a 5:1 mechanical advantage, which pushes on a hydraulic piston in the master cylinder, with a big assist from a vacuum booster. More than 1000 psi at the brake caliper during a maximum effort stop is not at all unusual.
akula-ssh
03-14-2005, 10:21 AM
Or is it "always on" with the same amount of assist all the time?
msauve
03-14-2005, 02:12 PM
they're measuring brake fluid, so in fact it's likely that they've made every attempt to eliminate all other variables, such as caliper flex, brake line expansion, pad compression, etc. It's not reasonable to expect their results to accurately reflect a real braking system.
Furthermore, the simplistic notion that there's a definite benefit from reducing pedal travel is unproven. The goal is not to get to maximum deceleration in a hurry, but to be able to get there repeatably and without overshoot (i.e. without locking the brakes). Reduce the range of pedal motion and your're also reducing the ability to modulate braking, which can work against you.
You still haven't quantified the piston area in your brakes vs. stock brakes. That makes a difference in pedal travel.
Jkay
03-14-2005, 04:46 PM
msauve
03-14-2005, 04:47 PM
If you knew anything about WTF was being discussed, you wouldn't be flouting your ignorace so openly.
Jkay
03-14-2005, 04:57 PM
ill-developed social skills.
Less hammer, more cordial. Following this formula, you might make it out of mom's basement one day.
ryoung
03-14-2005, 07:33 PM
You can feel the effect of the vacuum assist when you start the car. With your foot lightly on the brake pedal, the brake pedal falls an additional amount once the engine's running and providing vacuum to the booster.
I've never taken a vacuum booster apart, but I'm having trouble imagining how it could provide something other than a fixed amount of assist once the brake pedal is depressed a certain amount. Pressure on the pedal pushes forward a rod connected to the pistons inside the master cylinder. Simultaneously, the rod closes a vacuum port to the right half of the booster unit and opens it to the atmosphere. The left half of the booster still contains full vacuum, and atmospheric pressure in the back half of the booster pushes the internal diaphram forward, which applies additional pressure to the master cylinder pistons. Releasing the brake pedal closes the opening of the right portion of the booster to atmosphere and opens it to intake manifold vacuum again.
1) The 0.50 cf Ferodo DS2500 is for operating temperature. Are the DS2500 track pads?. A cold pad would be slightly different.
2) Re: "the optimal brake bias is 2.2" The optimal brake bias isn't static. It changes constantly due to traction (road surface, tire temp, etc), brake pad temp, loaded trunk (an we know the S8 has a huge trunk :), etc.
ryoung
03-16-2005, 06:17 AM
1: The Ferodo DS2500 is suitable for street, autocross, or light track. The coefficient of friction is extremely flat. See my additional comments on pads <a href="http://forums.audiworld.com/a8/msgs/75190.phtml">Here</a>.
<img src="http://www.federal-mogul.com/images/ferodoracing/DS2500Graph.jpg">
2. Absolutely agree. -- With street tires, 2.2 would be about the ideal, but highest, brake bias and is the result of maximum load transfer to the front tires at maximum braking g's. Everything else (rain, rear seat passengers, etc) would result in a lower optimum bias. You can't go lower than 2.2, however, without risking the back end getting squirrelly under maximum braking conditions in the dry. My S8's original brake bias was 2.5.
nirad
03-17-2005, 09:14 PM
yes, i realize you are getting the data from somwhere else. i have driven many of the cars on that list- Audi TT, , Audi A8L, Audi A4 3.0, Audi S4 B5, Saab 9-3, Toyota Camry, Range Rover, MB E320... And the B6 S4 brakes better than all of them, except maybe the TT.
Bauer
03-17-2005, 09:19 PM
The RS6 a very good brake with execellent pedal feel.....but if pushed hard they will fall off pretty bad. They are no good for tracking for several reasons.
1. Piston are too small and concentrate the heat in a small area on the pads, causing them to crack.
2. Poor rotor design does not cool well enough and adds to the problem of the piston design.
I speak from experience when I say the Alcon's are better....I have tracked both, albeit on different cars but the Alcon's have never faded and I am always confident to late brake with them...the Brembo's on the other hand....I would not feel very comfortable after a few laps braking late with them.
ryoung
03-18-2005, 07:23 AM
I don't know what else to say.
nirad
03-18-2005, 10:02 AM
ryoung
03-18-2005, 11:08 AM
70-0 mph in 174 ft. That's 0.94 g and equivalent to a 227 ft 80-0 stopping distance, still rather poor performance, but it's a heck of a lot better than the 0.84 g calculated from Road & Track's 256 ft 80-0 mph stopping distance.
To be completely objective, I'll average the R&T and C&D tests, which is 241 ft resulting in a 0.89 g stop, and change the original post to reflect this result.
BTW: I was also extremely suspicious of the Road & Track results for the S4, and I rechecked it about six times. In their 100 car road test summary (in the back of every issue), a Morgan is the only car listed with worse brakes.