Brake bias calculation

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Discussion

renalpete

Original Poster:

45 posts

152 months

Sunday 26th February 2017
quotequote all
Hi,

I'm looking to upgrade the brakes on my TVR Tuscan to fix a problem where the rears can lock first under heavy braking. Everything has been checked over by a specialist, but I still have the problem - I guess the back of the car goes very light. I have thought about mixing brake pad compounds or putting a bias valve in, but it seems like a bit of a bodge.

To compare the power of different setups, I'm assuming the brake line pressure is constant, calculating the f:r ratio of piston area * ((disc diameter/2) - (pad height/2)), aiming for something approximating braking force * distance from the wheel centre where the force is applied.

So for the standard front setup of a 291mm disc, AP CP5200 4pot caliper (see spec tab), I get

pi * (38.1+41.3+38.1+41.3) * ((291/2) - (55.8/2))= 58668

For the standard rears with 282mm disc, cosworth 4x4 1pot caliper and pads, I get

pi * 42.8 * ((282/2) - (60.5/2)) = 14891

so 58868/14891 = 3.93 for my current ratio.

I've read that a 330mm front disc in the same caliper tends to sort the problem:

pi * (38.1+41.3+38.1+41.3) * ((330/2) - (55.8/2))= 68397
68397/14891 = 4.59

Typically, my caliper can't take the 320mm disc, so I need new calipers, so I'm considering various other sizes/setups (including floating rear discs),looking for setups that give me a f:r ratio of 4.6 or slightly higher.

Replacing calipers means it's expensive stuff - is my maths right, and is this a reasonable way to compare the braking power of different setups?

If this is a sensible way to work things out, am I likely to see a weight saving going from a 1-piece vented 281mm disc to a 2-piece 300mm replacement?

Thanks!

b2hbm

1,291 posts

221 months

Monday 27th February 2017
quotequote all
If you want to do brake calcs then you've got to take weight transfer into consideration. This varies with deceleration rate and also the physical parts of the car - weight distribution, sprung weights, disc & piston sizes, etc.

There are a few good brake calculators on the web and several sources of info for you to create your own spreadsheet. The most readable source I've found has been Fred Puhn's "Brake Handbook" which is US based but he's got a good way of explaining things. I've done the exercise for my cars and the theory does work, but there's a lot of data to gather if you want to find out the locking points of front & rear axles.

Brian

PositronicRay

26,959 posts

182 months

Monday 27th February 2017
quotequote all
I'm far from an expert but is an adjustable brake bias valve really a bodge? Manufacturers use electronic brake force distribution to optimise braking for different loads/road conditions.

It would also give you the opportunity for a bit of fine tuning, different wheel/tyre set ups or tracks if that's your thing.

renalpete

Original Poster:

45 posts

152 months

Monday 27th February 2017
quotequote all
b2hbm said:
If you want to do brake calcs then you've got to take weight transfer into consideration. This varies with deceleration rate and also the physical parts of the car - weight distribution, sprung weights, disc & piston sizes, etc.

There are a few good brake calculators on the web and several sources of info for you to create your own spreadsheet. The most readable source I've found has been Fred Puhn's "Brake Handbook" which is US based but he's got a good way of explaining things. I've done the exercise for my cars and the theory does work, but there's a lot of data to gather if you want to find out the locking points of front & rear axles.

Brian
Thanks, I was hoping that if I kept the ratio of braking power the same, I could ignore all that complicated real-world stuff and treat two setups as equivalent, as all other factors would remain the same - life is not that simple I guess!

I'll do some more research, but probably just move to the known good setup :-)

renalpete

Original Poster:

45 posts

152 months

Monday 27th February 2017
quotequote all
PositronicRay said:
I'm far from an expert but is an adjustable brake bias valve really a bodge? Manufacturers use electronic brake force distribution to optimise braking for different loads/road conditions.

It would also give you the opportunity for a bit of fine tuning, different wheel/tyre set ups or tracks if that's your thing.
Maybe "bodge" is a bit strong - I think it's a bit extreme in a road car.

renalpete

Original Poster:

45 posts

152 months

Monday 27th February 2017
quotequote all
Oh dear, I've used the circumference of the pistons instead of the area!

227bhp

10,203 posts

127 months

Monday 27th February 2017
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Is this usual for all Tuscans? Do they have some kind of load valve already fitted?

renalpete

Original Poster:

45 posts

152 months

Monday 27th February 2017
quotequote all
It's far from unheard of, but I think there were a number of variations on brake setups over the years, so not everyone has the issue. I have a very early car, with the smallest front discs. I imagine it varies depending on springs, dampers, number of people in the car/stuff in the boot etc.

If I brake very hard from high speed, the rear generally feels very squirmy. If I manage to lock a wheel, it's one of the rears - if there is any lock applied, things get exciting very quickly, but obviously you don't brake like that very often.

I think there is some kind of proportioning valve in the system, but it's not adjustable - like I say, I've had the whole lot checked over and it's working as "designed" :-)


227bhp

10,203 posts

127 months

Monday 27th February 2017
quotequote all
How many brake lines from front to rear?
Aftermarket bias valves aren't as dumb as you may think, maybe you don't know how they work.

renalpete

Original Poster:

45 posts

152 months

Monday 27th February 2017
quotequote all
227bhp said:
How many brake lines from front to rear?
Aftermarket bias valves aren't as dumb as you may think, maybe you don't know how they work.
Apparently there's a line to each of the front brakes, then one line to the back which splits later on - again, I hadn't taken that into account in my sums.

It sounds like the ratio of braking force is already massively weighted to the front - twice the brake line pressure, 4pot vs 1pot, bigger discs, but it still manages to lock the rears first.

You're right, I don't really know how any of this works - I think I'm better off paying someone who properly understands it!

227bhp

10,203 posts

127 months

Monday 27th February 2017
quotequote all
renalpete said:
Apparently there's a line to each of the front brakes, then one line to the back which splits later on - again, I hadn't taken that into account in my sums.

It sounds like the ratio of braking force is already massively weighted to the front - twice the brake line pressure, 4pot vs 1pot, bigger discs, but it still manages to lock the rears first.

You're right, I don't really know how any of this works - I think I'm better off paying someone who properly understands it!
Well you've had a go, that says something. I haven't read the thread you linked to as I haven't had time and they are generally filled with 95% uselessness anyhow, but aftermarket valves often work on pedal pressure i.e, they aren't fixed, not even when the knob is turned to a certain setting are they fixed at that pressure. They take into account pedal pressure and back off the pressure given to the rear the harder you stand on the pedal, which if you think about it makes a bit of sense. Given you have a single line to the rear (as opposed to a proper manufacturers triangulated system), it would be a simple job to incorporate one of these for a play around. It's where I would be going first and it's actually a step up from what you propose which is a fixed pressure system.

Mignon

1,018 posts

88 months

Monday 27th February 2017
quotequote all
Just about everything in your calculations is wrong. You don't have piston area, you don't have pad area, you don't know the coefficients of friction and can't just assume these are the same front and rear. For a road car it's very unlikely that weight transfer will mean you need less than about 1/3 of the braking effort on the rear even under a 1g stop. However you can only work that out with centre of gravity height, wheelbase and static weight distribution.

PaulKemp

979 posts

144 months

Tuesday 28th February 2017
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In the kit car world it is a problem at the IVA test when 4 wheel disc brakes from a heavier donor are put on a much lighter car with different weight distribution.
Older donors have drum rear brakes and generally don't suffer from the rear locking problem
We have used the manufacturers load bias valves and they do work.
Other solutions are an inline brake biassing valve which limits the pressure to the rear all the time or a bias pedal box.
For racing, drivers change bias frequently, for road cars the bias must be set and then locked off.

CrutyRammers

13,735 posts

197 months

Tuesday 28th February 2017
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Op- worth checking as it may have bias adjustment at the pedal end (a bias bar). Many race and kit cars use these for front/rear split systems so yours might too.

Dave Brand

928 posts

267 months

Tuesday 28th February 2017
quotequote all
renalpete said:
twice the brake line pressure,
Two lines to a caliper won't give you twice the pressure! Pressure will be the same throughout the system irrespective of the configuration of the pipework.

Dave Brand

928 posts

267 months

Tuesday 28th February 2017
quotequote all
Mignon said:
you don't have pad area,
Pad area is, within practical limits, irrelevant. The force generated at the pad/disc interface is the product of applied force multiplied by coefficient of friction.

renalpete

Original Poster:

45 posts

152 months

Tuesday 28th February 2017
quotequote all
Thanks for all the comments.

I've done some reading just to try and understand it all a bit betterm though I'm not planning to do anything with the numbers - I will likely find a specialist who can advise on valves etc.

I think I was effectively trying to calculate the ratio of Brake Torque front to rear.

This is not the same as brake bias (which includes other things such as wheel size, distance of axles from CoG etc etc), but all these other things remain constant, so I think this ratio is useful for comparing the f:r balance of raw "braking power" of different disc/caliper setups. This only works I have known bad (rears lock first) and known good (rears dont lock first) values, based on highly reliable forum-anecdote evidence. The actual ratio is definitely not the brake bias, and is only good for "qualitative" less than/greater than/equal comparison with known good/bad values - if two different brake configurations have the same f:r brake torque ratio, they will have the same brake bias (assuming the rest of the car is constant), but a 10% difference in ratio could mean a 0.1% or 1000% difference in actual brake bias.

I think I want:

Brakeline pressure (N/mm^2) * piston area (mm^2) = Brake force (N)

(Disc diameter/2) - (pad height/2) = effective disc radius (mm)

Brake force (N) * effective disc radius (mm) * friction coefficient = Brake torque (Nmm)

I think I can effectively ignore:

)Brake line pressure (as it is the same at both ends (eg always 1N/mm^2)). This is not really correct due to presence of a fixed bias valve in the system, but the error will be a constant factor for each rear calculation. As the value is only used to calculate a ratio which is compared as <, > or = other ratios, a constant error is not an error :-)
)Coefficient of friction, (same pads fitted f:r, no point in multiplying both ends by 0.4)

A comment above said you can't just ignore friction coefficient, but I don't understand why. ditto brake pad area.

Ignoring those things gives:

piston area * ((Disc diameter/2) - (pad height/2))

Which is pretty much what I wanted to calculate initially!

Things I definitely had entirely wrong:

)From earlier posts, schoolboy maths failure of calculating radius!
)From earlier posts, I care about pressure in the brake line, number of junctions is irrelevant
)It seems that for opposing piston calipers, you halve the surface area of the pistons (so count 2 pistons in a 4pot caliper), but in a 1pot caliper you take the complete surface area. Not sure I entirely understand this...

I think I understand what's going on much better, and am much more aware of the things I am ignoring, but I look forward to hearing I still have everything entirely wrong :-)

b2hbm

1,291 posts

221 months

Tuesday 28th February 2017
quotequote all
renalpete said:
A comment above said you can't just ignore friction coefficient, but I don't understand why. ditto brake pad area.
Friction comes into play in 2 main areas that I can think of immediately; the first is the friction between your tyre and road surface and secondly between the pad material and discs.

The first is important because it determines how quickly you stop. If you have lousy tyre friction it doesn't matter how good your brakes are because the wheel locks, skids and you take longer to stop. If you have super grippy tyres then the front digs in and you get a bunch of weight transfer going forward which helps to delay the front brakes locking, but because you now have less weight on the rear axle - the rear brakes lock. Quite a lot of folks told me it's not so much the brakes that stop you, but your tyres.

Brake pads are equally significant, if you have a high friction pad at the front and low at the rear, the rears aren't going to do as much initial work. The range of values isn't large but if you do the sums it makes a heck of a difference in the results.

Brake pad area; you'd think more is better, right ? and it is up to a point, the larger the pad area the longer they will last and the more you can brake before they overheat and move out of their operable range. But it's clamping force that matters and that's down to piston area, not pad area. If the ratio between your master cylinder, pedal leverage and caliper piston will allow you to generate 1000 psi (old school numbers) then that's your clamping force regardless if if your pad has 2 sq ins or 4 sq ins area.

I'm sure there's some advantage with frictional coeffs making larger pads a touch better, but generally what you look for in the calcs I've seen are the caliper piston, disc diameter and the operating radius of the caliper piston (leverage)

I'm quite happy to send you my spreadsheets to show the sort of thing you do to determine when the front & rears will lock, although I'll warn you now it's amateur stuff and not pro standards. PM if interested.

renalpete

Original Poster:

45 posts

152 months

Tuesday 28th February 2017
quotequote all
Thanks - it's all far more involved than you (I) first think, and any mistake makes the results completely useless.

AP helpfully list the effective radius for each caliper/disc combination on their technical drawings, and it turns out to be different enough from the naive calculation based on radius/pad height to reorder all of the results I have.

Complete minefield!

Mignon

1,018 posts

88 months

Tuesday 28th February 2017
quotequote all
I think I can answer a few of your questions.

Effective pad contact radius is not simply half way down the pad from the rim of the disc. (or half way up the pad from the centre of rotation). This is because the effectiveness of the braking increases at greater radii so the bottom half of the pad does less work than the top half. I'd suggest deducting about 1/3 of the pad height from the disc radius plus of course however far inboard the top of the pad is from the rim of the disc.

Yes strictly speaking pad area is not relevant to the calculation if you have the coefficient of friction for that particular pad area. I know the coefficient of friction is not "supposed" to change with contact area but then we'd never find any purpose to fitting wider tyres. Every vehicle on the road would manage quite happily on bicycle tyre thicknesses and clearly that doesn't quite work out.

The reason you only need the piston area on one side of the caliper is because of action and reaction having to be equal or the disc would just snap. In a single piston sliding caliper the piston force is balanced by the opposing pad sliding towards it. In a twin piston, or four piston caliper the force from the pistons on one side is balanced by those on the other side. Think about a set of bathroom scales resting on the floor. You get on weighing 80 kg and the floor pushes back with 80 kg. If some one was holding the scales in mid air and you got on they'd have to push back with 80kg to stop you falling. However the clamping force on the scales is still 80 kg not 160 kg.

Hope that helps.