Brakes and Physics. [Jason's Next Lecture]

[Larry" <rocco16v@netzero.com (Larry)]

42 psi;  too much
----- Original Message -----
From: 16V Jason <jason@scirocco.org>
To: Brian McGarvey <brianm@zbt62.eastnet.gatech.edu>;
<scirocco-l@scirocco.org>
Cc: Riley Mcdowall <RileyM@sanmarcanada.com>; <DOKTEROH@aol.com>;
<jetthis@hotmail.com>
Sent: Monday, March 25, 2002 6:16 PM
Subject: Re: Brakes and Physics. [Jason's Next Lecture]


> At 08:40 PM 3/25/2002, Brian McGarvey wrote:
> >Ok Folks...
> >I got tired of the argument. So I've whipped out the Physics book. Any
> >ME's out there or ppl that are better at ACTUAL REAL non-Relativistic or
> >mumbo jumbo my ass
> >tells me... physics
>
> 3.5 years of MechE and 18 credits away from graduating with a BS in MechE
> -- couldn't deal with the idea of designing toilet valves for the rest of
> my life; switched majors.  I'm also CC'ing this to a friend of mine with a
> PhD in Physics to make sure he doesn't find any inconsistencies.
>
>
> >So that means that in order to get a larger negative acceleration a
larger
> >F is required.
>
> Correct.
>
> >Assumption. Your tires are not crap. Your tires are relatively sticky. ie
> >they have a decent coeffienct of friction and maximum force point before
> >they turn to
> >dust/liquid/gas.
>
> Okay, I'll one-up you.  More than decent -- let's take a Z-Rated
> Bridgestone Potenza RE-71 in 195/50-15 on a Scirocco, inflated to 42psi on
> a 7x15" wheel.  Or the stickiest road tire you can find.  Either one.
>
>
> >so now you are trying to increase the force to increase the negative
> >accleration. no mind you were are still living in the linear force
section
> >of the friction curve.
>
> Right.  Your argument is that you have to increase the force acting on the
> car; thus the force created by the brake; in order to increase the
negative
> A and therefore decrease the stopping distance.  (s=v1t + 0.5at^2) where
> s=distance in meters, V1 is the starting speed, a is acceleration in
ms^-2,
> and t is the time.
>
>
> >(FORCE lesson)
> >IF the force applied to the disc is constant. the ONLY method for
> >increasing the torque applied to the rotating mass is to increase the
> >distance from the center.
>
> Right.
>
> <snip>
>
> >so now you know that to get more force with the same pads, calipers, and
> >discs it takes a bigger master clyn to get more force.
>
> Right.
>
>
> >What does increasing the size of the rotors/discs do?
> >by using the SAME size calipers on a larger diameter disc with the same
> >CONTACT patch. ie. the Force being applied to the brakes using the same
> >master clyn and
> >caliper are the same, but the distance from the center of the disc is now
> >longer. so now with a
> >little simplified physics magic. Im sure the ME's here will expand on the
> >physics.
> >so there..
>
> So there!?
> Uh, Brian, you're neglecting one hugely important part of this equation,
> i.e. the limits of adhesion of the tire.
>
> Let's do a little experiment.  You can do this in real life if you want
> (Kids, don't try this at home).
> Take a stock Scirocco 8V with 9.4" brakes on the front of it.  These,
> according to your (correct) logic, put out the lowest amount of braking
> force because they're the smallest.  Now, shod the front wheels with the
> stickiest tires you can think of.  The RE71s I mentioned before will serve
> as a wonderful example.
>
> Accelerate the vehicle to its top speed of approximately 108mph.  Then,
> STOP on the brakes.  What happens?
> The wheels lock up immediately, and you hear a loud, screetchy sound
> (technical term).  If you're lucky, you stop in a straight line and don't
die.
>
> Now, tell me:  Of what benefit would it be if you increased the braking
> force by 2?  Or 10?  Or 500?
>
> None.  Absolutely nothing.  Why?  Because even the small 9.4" rotors are
> able to put out enough force to lock a turning RE-71 at top
> speed.  Therefore, the bottleneck here -- or the "weakest link" is the
> amount of force that the tires can transmit to the ground.  Once that
wheel
> is locked, your brakes have nothing more to do with the equation:  It
> becomes a function of the dynamic coefficient of friction of your tire on
> asphalt.  If your brakes are powerful enough to lock your wheels while
> driving, that means that they are capable of creating more braking force
> than the tires can handle.  Increasing the force from the brakes will do
> nothing at all; the only thing you can do to increase A (and shorten
> braking distances) is to increase the tire's grip or reduce the weight of
> the car.
>
> And if your brakes aren't strong enough to lock a wheel?  Well, then your
> car shouldn't be allowed on the road.  In fact, on a healthy brake system,
> it should be quite easy to do so.
>
> So again, by moving the caliper further out on a larger disc, you are
> increasing the distance out from the axle, and therefore increasing the
> torque acting on the axle, increasing braking force - up to the point
where
> the tire locks up.  Since you should be able to lock up your wheels under
> any circumstances, it's a fruitless effort.
>
> What it *does* do is (as you stated), increase braking force for any given
> pedal pressure.  So the brakes will feel more responsive.  But as I said
in
> my previous post, if you don't adjust the proportioning of the system,
your
> rear wheels will be doing proportionally less work and therefore overall
> braking distance is increased.
>
>
> >and fade can occur for several basic reasons.
> >* the amount of force at the wheel decreases due to losses in the system
> >   -- ie. the master clynder hits the stops and has no more volume of
fluid
> >to press.
> >      -- losses can be due to a leaky master clyn, leaky wheel clyn.
> >      -- the rubber hoses expanding enough to lower the volume of fluid
> >transferred to the wheel clyn there by reducing the force applied.
>
> All of which are mechanical problems that should be addressed before even
> considering to upgrade the system.
>
>
> >* the coefficient of friction decreases at the disc/lining interface.
> >   -- get better pads.
> >   -- cool the system.
>
> True, although there is no such thing as a fade-free pad; so there is a
> limitation here.
>
>
> >           they actually pick up loose dirt.
>
> The RE71s do that dirt thing too. :)  It's cool to have a 150hp vacuum
> cleaner. :)
>
>
> >does improving the front brakes alone make a difference.
> >I suppose its time to try it out.
>
> In theory, as long as your existing front brakes can lock your wheels, it
> cannot help you.  And without ABS or an adjustable brake proportioning
> valve, it can only hurt.   Here's why:
>
> [Larry, this is your cue to pay attention] :)
>
>
> The amount of weight on a wheel is part of the equation on how much grip
> the tire will have.  The more weight, the more grip.  (Counter-intuitive,
I
> know but think about it this way:  Take a tire, stand it up, and drag it
> across the floor.  Now have your friend sit on it and try to drag it
across
> the floor.  Your friend's fat ass will make it a lot more difficult to
> drag.  'Nuff said.)  Under braking, there is a large transfer of weight to
> the front axle.  However, in most cars, including ours, there is still a
> significant amount of weight on the rear axle.
>
> As you approach 100% weight transfer, you come to a situation where, under
> full braking, the rear wheels are providing only negligible braking.
Under
> these conditions, a front-only brake upgrade (assuming that the brakes
were
> not powerful enough to lock up the wheels throughout the whole stop
before)
> would help shorten the braking distances.
>
> If you have any significant weight left on the rear wheels, however, those
> rear wheels are still contributing somewhat to braking.  You can see this
> demonstrated very clearly in the early and mid-1980s leaflets that auto
> manufacturers were required to put in new vehicles showing braking
> distances with fully functional braking systems and comparing them with
> front-only and rear-only functioning systems.  (Don't ask why our stupid
> government required these when braking systems, by their own law, are
> dual-diagonal anyway, not dual front-rear).
>
> So let's use an example to illustrate.  You know that most cars are
> proportioned so that the front wheels will lock up before the rears.  So,
> let's say (for math's sake) that you need 100psi of pressure in the brake
> lines to lock the front wheels.  And let's say you need 20% more pressure
> to lock the rears as well, so 120psi.
>
> So, let's say you want to threshold brake -- so you hold the pedal at a
> system pressure of, say, 95psi.  To get the rears at 95% braking, you'd
> need to provide 95 x 1.2 = 114psi of pressure.  Follow me?
>
> So therefore, at the 95% lockup threshold on the front wheels, the system
> is at 95%, which is (95/114 = 0.83) at 83% of the rear wheels' braking
> ability.  Again, 95psi will put the front wheels at 95% of their ability
> and the backs at 83%.  You want that -- you don't want your rears to lock
> up first, lest you lose directional stability. (We all know what happens
> when you yank the E-Brake and the rear wheels lock).
>
> Okay, so now let's say you upgrade the front rotors and calipers to larger
> units.  As we discussed above, we now need less pressure to perform the
> same amount of braking... let's say 80psi is now enough to lock the front
> wheels.  The rear wheels still need 114psi to lock, mind you.  So now, you
> want to perform 95% threshold braking on the fronts.  That means you want
> to have (80 x 0.95) = 76psi of pressure in the system at front lockup.
>
> Just like last time, you're managing 95% of the front tires' traction.
But
> now where's the back?  At a reduced system pressure of only 76psi
(compared
> to 83psi before), you're now working at (76/114) = 66.7%  So now, instead
> of providing 83% of the tire's maximum braking force before locking,
you're
> providing less than 67%.  That's a 16% drop!  Granted, the majority of the
> weight is on the front of the car, so that doesn't mean overall braking
> force will be reduced by a full 16%, but by that logic, it _will_ be
reduced.
>
> Okay, this simplified illustration assumes a few things; most importantly
> that braking force increases linearly with brake system pressure.  While
> this is not a perfectly linear relationship, it doesn't matter.  As long
as
> it's not an inverse relationship (which it can't be -- that would mean
> applying less pressure to the pedal increases system pressure), the exact
> nature of the relationship is unimportant.... the effect can either be
> negligible or negative... not positive.
>
>
> >we'll have to have everybody with all the diff combinations all get the
> >same pads.  change em. and bed them in properly. verify that all brake
> >systems work
> >properly. and do panic brake tests on the runway measuring distance. with
> >different
> >drivers swapping cars.
>
> If we had ABS (which would be a completely different ballgame), that would
> be a good idea.  But not only is it dangerous, but it's a waste of
> time.  With a properly working system, the only factors involved are the
> tires, the surface, the weight, and the suspension geometry.
>
>
> >but my prediction based on the number of times ive panic braked on
> >motorclcyes where i get to actually modulate the rear brakes seperately
> >from the front is that as
> >long as the rear brakes are adjusted properly according to the bently the
> >larger brakes in
> >the front will decrease the stopping distanc.
>
> Um, but brake proportioning is not adjustable on our cars...
>
>
> AND NOW THE CONFESSION:
> ---------------------------------------
> There is one argument that no one has brought up yet -- and that is the
> real reason why manufacturers actually DO put in larger brakes for better
> braking.  And that is for better heat dissipation -- for all the reasons
we
> discussed yesterday.  The problem is that, while all braking systems (when
> working properly) are more than capable of locking up all 4 wheels under
> any conditions, they heat up quickly on full-braking stops from high
> speeds.  So much so that in fact, on a full stop from 120mph in a Toyota
> Tercel, you're likely to have so much fade that you can't lock up the
> wheels at all by the time you hit 40.  That calls for brakes with better
> heat dissipating abilities.
>
> Remember, German cars can't get away with that.  They need to be able to
> stop from their top speeds on Autobahnen without experiencing enough fade
> to prevent the brakes from extracting the most grip possible from the
> tires.  So rev your Scirocco 16V up to 123mph and threshold brake back
down
> to 20mph.  Chances are, if you then mash the pedal, you'll still have
> enough braking ability left to lock up the front wheels.  If you jumped
> back up to 80 as fast as you could and did it all again, would that still
> be the case?  Probably not.  And if that's what you need to do, then you
> need to get brakes with better heat dissipation abilities... not
> necessarily brakes with a further fulcrum length from the axis of
rotation.
>
>
> Phew.  Sorry for the long post guys, but you know how I get. :)
> Jason
>
> PS:  If you're not long on the Scirocco List long enough to remember, this
> brings us full-circle to a debate a few years back over the efficacy of
> Anti-Lock braking.  ABS's ability to modulate each wheel individually
> regardless of weight transfer, split-Mu surfaces (where one side of the
car
> is on different pavement than the other, or on ice for that matter), or
> each individual brake pad's ability to grip.  In theory, you could put 4
> different brake pads, rotors, and calipers on an ABS-equipped car, and as
> long as they don't fade to the point where they can't lock up, overall
> stopping distance would be the same.  Scary as shit from a handling
> perspective, but the same.
>
> PPS:  And from this argument, you should also see why cars with more
> rearward weight bias (Rear-wheel drive cars, for example -- or rear-engine
> cars), have a huge braking advantage -- less weight transfer onto the
front
> wheels means more braking ability from the rears... and less need for
> uneven brake proportioning and smaller rotors in back.
>
>
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