That is a LOT of assumptions and very minimal facts ...
it's really not.
It's a bunch of actual, known, facts, and then the only conclusion we can draw from that fit all of those facts.
Again- if you think you can draw a DIFFERENT one that fits all the actual facts- please let us know what it is.
So far nobody else has one.
Alex, can I get partial understanding of the problem for $1000?
The answer is... what you're about to say
You have part of the equation correct.
No, all of it.
Here it is-
d= v^2/2ug
d=distance for car to stop
v=velocity of car
u=coefficient of friction between tire and road
g= acceleration due to gravity (9.80 m/s^2)
Notice how the formula doesn't ask about your brakes, but DOES ask about your tires?
Because the maximum deceleration (which would be what's going on during a panic stop) is
every single time limited by the friction of the
tires... and MOAR BRAKES!! does not change that. At all.
The braking system and tires work in concert to stop the car. Driver's foot (or electrically controlled driver aid) to pedal to master cylinder (which is mounted to the firewall) to fluid through hoses to ABS controller to brake caliper to brake pad to rotor to hub through bearings to wheel to tire (all supported by chassis and suspension) to the road.
I'd encourage you to read the article I posted from the guy who designs brake systems for a living.
He covered what each part of the system does, and why
none of them stop the car (other than the tires).
It was in fact the entire point of the article- with math, physics, and everything included.
If we take it to the extreme, a vehicle with the stickiest race tires ever made (lets say LC0 Hoosiers) and carbon to carbon brakes with infinitely stiff calipers, uprights, suspension links, chassis, and bushings/bearings, perfectly calibrated ABS, and the best aero in the world (Formula 1 car?) will not do a damn thing in a vacuum with a frictionless road surface - ever
Sure. In fact I already gave the same type of example earlier (though making the tires instead of the road frictionless) to make the same exact point. The tire/road friction is
what actually stops the car
It's weird you're trying to repeat back my own example to me.
watch a car hit black ice, or hydroplane into a wall? So, it must be that the road that stops the car, not the tires.
I think you're getting lost now... it's the friction between the tire and road that does it.
See, again, the actual formula for stopping distance. It's the only part of the equation that cares about any actual parts on the car.
Better brakes can help a vehicle stop shorter.
This is 100% completely wrong.
Period, full stop.
Brembo says you're wrong (already quoted them doing it)
Car and Driver says you're wrong (already quoted them doing it)
So does stoptech and a ton of others... here's Road and Track for example debunking your claim-
Road and Track
How Changing Tires Can Improve Your Braking & Stopping Distances - How Tires Upgrade Your Braking System
Road and Track said:
When ABS is activated, this tells the onboard systems that your wheel has stopped rotating, meaning that you’ve exceeded the maximum stopping force of the tire. In other words, your stopping distance is limited by the tire. Your brake was likely perfectly capable of applying more pressure, however the tire lost grip, so more pressure serves no purpose
In fact- they even toss in some math not entirely unlike what I gave you earlier... pointing out that u (the coefficient of friction of the tire) is the single thing that
dictates the stopping distance of the vehicle. Because that's the
maximum force the tire can apply to the road. Which is the force that
actually stops the car
And since the stock brakes can already maximize that by engaging ABS, well, let's quote them again-
Road and Track said:
With μ equal to 0.7, the car would stop in nearly 172 feet. No matter how expensive or advanced the brakes are, if a car’s tires have a frictional coefficient of 0.7, there’s no way for it to stop in less than 172 feet using the disc brakes alone
Then (somewhat like the Pulp Friction article) then mention some of the OTHER things changing brakes parts CAN do for you... but that stopping shorter is
not one of them
Then they reiterate:
Road and Track said:
If you want to definitively improve stopping distances, whether at the track or on public roads, buy nice tires.
Because- as (most of us) understand- the
tires are what stop the car.
Why? Stiffer assemblies (think awesome calipers, brake lines, brake pads, and pedal boxes) flex less and allow the working fluid to more directly apply pressure through the system to the brake pad and rotor combo. This lets the ABS system function more effectively (better response time) which can shorten stopping distances.
100% nonsense.
It's explicitly debunked in the GRM pulp friction link in fact where he discusses compliance and why that
can't stop you any shorter
GRM Pulp Friction said:
Although those cool-looking stainless steel brake lines alone will not make your car stop any faster, the decrease in compliance and improvement in pedal feel can make a driver much more confident.
Same with the other parts you mention- each of which he explains what they CAN do for you and what they CAN NOT (spoiler: stop shorter is one they can't do)
Dynamic characteristics of the system matters.
To feel? Sure.
To stopping any shorter? 100% nope.
Weirdly- they do not provide their testing methodology or their raw data.
I bet it's because what they did was test from speed like 10 or 20 times in a row with no cool down....
Meaning they were testing fade resistance- not stopping distance.
(they don't mention that of course because they don't want the average sucke^h^h^h^h^h customer to realize their pads won't do jack to stop them any shorter in a normal highway panic stop- because they can't.)
Because, as physics (and Brembo, Stoptech, Road and Track, Car and Driver, professional Braking systems engineers, and more) tells us- brake pads
can't change that second one for a normal single panic stop.
The National Law Enforcement and Corrections Technology. Center does tests like that... (because they expect that unlike a normal civilian driver, a cop might need to repeatedly be braking hard from 100 mph or more over and over)... Interestingly they too make the point you are wrong about this when they explain why they do
not measure stopping distance in such a normal civilian panic stop situation-
https://www.justnet.org/pdf/EvaluationBrakePads2000.pdf
NLECT said:
When braking to a targeted deceleration rate, where the speed of the vehicle at brake application is the same, the stopping distance should also theoretically be the same, making any measurement of stopping distances irrelevant
Instead they test fade- by repeating braking from 90 mph over and over, heat soaking the system to see how much abuse it can take.
This type of thing matters for police work- and for race tracks- but not normal, legal, civilian street driving.
Plus- of course- fade measures how much
longer stopping takes after things get very hot... the stopping distance is never
shorter than the first normal panic stop- no matter how great the brakes are- it can't be...since it's the tires that stop the car
Riddle me this: If its only tires that stop the car, how come Edmunds was able to demonstrate excessively long stopping distances in their long term test Model 3 which was then rectified by an over the air update? The tires didn't change.
Glad you asked!
Because the code controlling the ABS computer had a bug in it. (and as we established- in a
correctly working car ABS engages when the tires are at their limit of friction.... so if it's NOT correctly working it's failing to maximize the tires friction limit- and will take longer to stop).
Notice how they fixed it with computer code- and not changing
any hardware (including brake parts).
Once they did that, the tire was able to once again maximize available friction and distance got shorter.
Here's a better question for you-
Why does the non-P model 3 with 19s stop shorter than with 18s?
The only difference after all? The tires.
For that matter, why does a P3D+ with BIG BRAKES stop in the
same distance as an LR AWD
without BIG BRAKES once you swap PS4s tires on the LR AWD?
(Spoiler- it's because the
tires are what stop the car)