Weight transfer vs brake bias

[RallyJon]

EDIT: While this thread may make amusing reading, it turns out there is an error in Fred Puhn's formula. Tom Tweed ferreted it out and posts a correct analysis here:
Master cylinder affects brake bias?
Cliffs's notes: The calculated bias ratio IS actually about 1.4. Porsche must have used 1.6 to allow for weight transfer, braking downhill, etc.

I've been comparing the various brake combinations on 911s and their front/rear bias. I ran some calculations based on my own car and it seems like the ideal bias would be somewhat more towards the rear than stock.

Key assumptions:
1) maximum braking is 1G
2) CG is 18" off the ground
3) ignoring any prop valve, which would make the brakes even more front biased beyond a certain point

                               G's of Braking 
Weight: 2471lbs      Static   0.2    0.5    1.0 
Front Weight (lbs)     944   1043   1193   1441 
Front Percent         38.2%  42.2%  48.3%  58.3% 
Rear Weight (lbs)     1527   1428   1278   1030 
Rear Percent          61.8%  57.8%  51.7%  41.7% 
Bias Ratio            0.62   0.73   0.93   1.40  
CG height (inches)    18.0    
Wheelbase (inches)    89.4    
CG ratio              20.1%

Given the above, why would the stock Bias Ratio of 1.6 be ideal and not something closer to 1.4? It seems like there would have to be much more weight transfer to justify that much front bias.

What am I missing?

[SC-targa]

Where's Bill V when you need him?

Jerry Kroeger

[djmcmath]

This sounds like a great discussion topic! I have two questions, though:
1 - Why would you ever brake at 0.2g? More accurately, isn't the only time that anyone really cares about brake bias at the adhesion limits of the tires, which ought to be something over 1g for braking?

2 - How did you determine these numbers for your car? That's some fantastically useful data!


TIA,

Dan

[Bill Verburg]

What works has been determined by years of trial and error, by the factory engineers and the racing community at large. As w/ many things one can calculate for ever but unless you factor in a large # of often not obvious variables the answers you get only having a passing resemblance to reality. Keep in mind that the more a car is modified from stock and particularly when changes are done disproportionatly at on end or another the more likely a change in bias is needed.

Lower a car and there is less forward weight bias on braking so you can use more rear brake,

Proprortionatly larger front spring rates less forward weight bias on braking so you can use more rear brake,

Proprortionatly more front aero force means more front bias is wanted

Changes in tire size or compound, changes in driver technique, changes in lsd %s, changes in shock valving, type of event, type of course, weather, alignment all affect desired bias (some more than others).

Can you run Carrera brakes( w/ 1.3 bias sans p/v)? Sure, it might even be desireable for some drivers in an A/X type event, but go to Lime Rock you you will be very unhappy.

I have experimented w/ bias on my own car from 1.7 to 1.5 w/ the proper tires, aero package, and suspension they all work fine, but you will want to optimize for what is on your car and it's intended use.

In general it is easier to correct for too much rear bias than too much front, You always want the fronts to lock before the rears(except in A/X).

[RallyJon]

The weights are from my car. The CG height is a guess. Everything else is calculated.

I really don't know what the range of maximum decelleration is on varying surfaces. If your brakes are biased for slicks on a very high friction racetrack, you'll be locking up your fronts way too early in the rain.

I think that's why manufacturers used proportioning valves. You set the system up for perfect balance at a more modest level of traction, then the prop valve limits pressure to the rears above that point. If you take that into consideration, a bias ratio of closer to 1.0, combined with a prop valve, might give better braking under all conditions.

I'm just saying that the stock bias ratio of 1.6 seems to indicate that the fronts will lock up way too early in the dry--and even more so in the rain. Actual experience bears this out.

[RallyJon]

Good point--the formula for weight transfer excludes spring rate and aero. I can imagine that a soft suspended stock car would have more weight transfer.

[Tim K]

I've been thinking about sizing of dual master cylinders for adjustable bias lately. I'm looking into a setup for my car. Should you take into consideration the tire contact ratio front and rear, (assuming they are different)? Maybe I'm crazy.

What do you think!

Tim K

[Bill Verburg]

The Carrera(first use of a p/v) got brakes w/ p/v because all the yuppies buying 911s at the time were whining that the pad wear was uneven, they felt that f/r ought to be changed at the same time.

p/v continued to be used on later car because they allowed the ABS to be tuned more aggressively. ABS cars end up w/ bias well into the 2s

I'm just saying that the stock bias ratio of 1.6 seems to indicate that the fronts will lock up way too early in the dry--and even more so in the rain. Actual experience bears this out.

Again every car and driver is that little bit different, it could be anything from shocksor alignment to tires or springs.

Step 1 is to be sure every component is optimal, then if you have the tire and suspension and aero package you want, and it's still not satisfactory to you, then install an adj. p/v on the rear.

[Bill Verburg]

I've been thinking about sizing of dual master cylinders for adjustable bias lately. I'm looking into a setup for my car. Should you take into consideration the tire contact ratio front and rear, (assuming they are different)? Maybe I'm crazy.

Absolutly, but dual m/c has its own set of drawbacks, not the least of which is cost.

[jluetjen]

Here's my $0.02 on two points, so I guess I'm putting in $0.04...

Proprortionatly larger front spring rates less forward weight bias on braking so you can use more rear brake,

Bill, this statement doesn't make sense since stiffer springs WILL transfer more weight to the front tires under braking as they resist dive. That being said as a general statement, I then need to add the following disclaimer and $0.02 to Juan's initial post...

Everything is transient. So let's take a car travelling at 100 MPH down a straight...
Case A) The driver "Stomps" on the brakes (aka: Brakes agressively): Initially the braking force will be roughly proportional to static weight distribution, but as weight transfers forward (a function of the spring rate ratio F/B as well as the shock valving) the proportion of braking will move forward. This can also be impacted by anti-dive geometry at the front or anti-lift geometry at the back. In some cases it can result in the front tires prematurely locking up even if the brake bias is set ideally.

Case B) A more subtle driver who applies the brakes less abruptly will experience a differerent transient response which will impact the brake balance. In this case I doubt that the driver will experience premature lock-up at the front. While potentially not impacting the maximum brake bias, the braking style of the driver may impact the initial bias selection for the brakes. For example, depending on the braking system the brakes may start at an 40/60 bias for light brake applications and then transition to 45/55 under hard application. This is most likely especially true in systems which have a pressure limiting valve.

One of the drills that they taught us when I took Skip Barber was proper braking technique which included (especially in the rain) the proper application of the brakes.

So, I suspect that there are many acceptable solutions within a certain range, and the ideal solution may change substantially based on the tires, suspension set-up and driver's style -- especially if he trailbrakes. The introduction of rain or low grip situations will change it also.

BTW Jon, I estimated the overall CG height for a 911 at 15 inches based on the height of the crank above the floor. Is this for a rally car or a track car? Running some equations against my car's set-up using a 15 inch CG height seemed to result in a fairly close result to what the car actually handles like when cornering.

[TimT]

Besides calculating weight transfer and guessing how the brakes will react, you need to test, take rotor temps after a hot session and see how the brakes are sharing the load.

In my 914 I had a heck of a time with rear brake lock up!!

Turn one at Watkins Glen approaching at about 120 or so down hill and bumpy, I would lock my rear brakes. (NOT FUN AT ALL).

The car doesnt exhibit any significant weight transfer signs, corners flat, no pitching forward when on the brakes hard. but weight is transfering.

I stated dialing rear brake out till I could get on the brakes and not worry about lock up.

I started taking rotor temps, and found a trend that the fronts were 400 deg rears 200 deg, my rear brakes were just along for the ride basically.

After some head scratching, I talked with a set up guy from ALMS, he said "rear wing", as did a few other people

So i stuck a really deep splitter on the car, extended the 914 duck tail, and went out and started increasing rear brake bias.. the car is stable, brakes like its hitting a wall, and my rear rotor temps are up.. about 300 deg last time out...


Im still tuning the brake bias but I was going in the wrong direction, untill I started gathering hard data

dont know if this nugget is any help, but you need to get rotor temps

[Bill Verburg]

John, relatively stiffer front springs will prevent the shift of weight forward, weight shift is the result of the ctr of mass being raised and shifted forward a bit do to the compression of the front springs, less compression means less lift for COM means less forward shift.

Don't confuse weight shift w/ the increased downforce at the front to the couple(inertia acting forward through the COM and brake force acting back o/s from the inertial vector) causing the car to try to rotate through the z plane. This couple does increase the vertical force at the front but is not the same as weight shift. Stiffer front springs will transmit more of the coupling moment vertically through the tires.

Actual weight shift is more influential than the couple.

[RallyJon]

Using a 15" high CG, the theoretical departs from the empirical even farther, with a max-braking bias ratio of 1.22:

                        
Weight: 2471lbs      Static   1.0 
Front Weight (lbs)     944   1359 
Front Percent         38.2%  55.0% 
Rear Weight (lbs)     1527   1112 
Rear Percent          61.8%  45.0% 
Bias Ratio            0.62   1.22  
CG height (inches)    15.0    
Wheelbase (inches)    89.4    
CG ratio              16.8%

[masraum]

This is another on of those "cool threads". You guys need to keep it coming.

[Bill Verburg]

I've detected front lockup to be less prevalent with the stiffer front springs,

The reason is that the CoM isn't moving as much.

[jluetjen]

Bill;
I'm still not on the same page as you on this subject. I'd argue that the location of the COM doesn't change unless you can get out of the car while braking and move the battary to the back of the car or something like that (we'll exclude for now the sloshing of the fuel and oil towards the front of the car). The COM is what it is and doesn't move much without the physical redistribution of the components of the car that constitute it's mass.

The forces on the tires are merely the sum of the acceleration vectors on the car. When the car is standing still (or travelling at a constant speed on a smooth surface) the forces on the tires are strictly vertical and the result of the acceleration resulting from the force of Gravity -- so 1 G. When you are braking, you are transitioning from that state to a state where there are the additional forces of braking on the contact patches of the tire. Since the COM is generally above the contact patch the tire, there will be the couple that you described that results in the car pitching forward. The only movement of the COM is a result of the arc that the COM travels based on the angle of the pitch. I can't see how that movement (let's say forward by 2 inches or about 2% of the car's wheelbase that I'm guesstimating would result in a shift forward of ~2% of the cars weight or 48 pounds) would dwarf that of the pitch couple which can transfer about 10% of the cars weigh (off of the back and onto the front for a total change of 20%) as Juan is describing.

I'd still argue (but my wife maintains that I do that a lot ) that what Noah is describing is the result of those springs resisting the pitching motion which results in that pitching force being transfered to the front contact patches sooner.

The other thing to keep in mind is that as a 911 pitches forward it will gain some negative front camber which can reduce the front tire contact patches in extreme situations which can also cause front brake lock-up. The difference is that this will be a lock-up after the car pitches forward which is generally at full braking. Lock-up resulting from to aggressive application of the brakes for a given spring stiffness will tend to occur at intial application and then linger afterwards since a locked tire won't unlock without the reduction in braking force.

[RallyJon]

So what's the answer? Either I'm missing something significant and the actual weight transfer is much greater than the calcs suggest, or there is a huge safety margin on the order of 20-30% designed into the stock system.

[Bill Verburg]

John & John, The CoM moves when ever the car rolls either in pitch or yaw. I have been writing from memoory but will dig out my Adams, Smith and Racecar Engineering where I picked most of this up. Never did get a Puhn but am looking. Also there is a New Nascar oriented treatise by Boll? looking for that as well.

All sources indicated that the vast majority of so called weight transfer either in acceleration, deceleration or lateral acceleration is due to the changing height of the CoM.

I do know for a fact that spring rate does not enter into any weight transfer function that I have ever seen,

Only wheelbase, height of CoM are involved and probably something else that I have forgotten but certainly not spring rates.

iIwill dig out my tomes and do some further research. I do know that the empirically derived #s I use for bias are valid.

[RallyJon]

By Puhn, do you mean Brake Handbook? Whaddaya know, he has a formula, and sure enough the ratio comes out at (surprise!) 1.6. I plugged in the numbers in Excel to get the answer, but I'm not sure I really understand the formula. The car actully weighs more under braking???

     Static     1G
WC     2471   2471
I      89.4   89.4
YCG    15.0   15.0
XCG  55.248 55.248
µ       0.0    1.0

FF    944.0 1773.1
FR   1527.0 1112.4
               1.6

[masraum]

Imagine that.