Brake bias calculation

[renalpete]

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!

[renalpete]

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]

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]

Oh dear, I've used the circumference of the pistons instead of the area!

[renalpete]

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" :-)

[renalpete]

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!

[renalpete]

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 :-)

[renalpete]

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!