Brake test failure

[apoorv]

Hello, I am SUSHIL RAI from SRM University, India. I am working in brakes domain and we are testing our vehicle for 2015 FSAE Italy event. While brake test wheels are not locking. We tested at 60 Kmph and none of the wheels locked. we are using Solid EN353 Steel grade rotor with diameter 196.85 mm and 6.375 mm thickness. We are using fixed calliper system from willwood. the weight of our vehicle is 394kg with driver.
Pedal ratio is 4:1. We are using wet type tyres with the configuration 185/60 R14

Before testing we checked line pressure which was 47.25 bar for front and 31.52 bar for rear under 60:40 brake bias. Theoretical clamping force is
7314.3 N for front rotor and 4879.29 N for the rear rotor. the pedal is having decent pressure and there is no leakage problem from the lines. I decided
to change the biasing ratio but still the brakes locking was not showing up. I changed the brake pads and properly did the bleeding.

what could be the possible reason for wheels not locking?

[CWA]

When it comes to problem solving, what catches you out isn't always what you don't know, sometimes it's what you think you know that isn't so. For starters, re-check those specs, calcs and measurements of yours. Get someone else to do it, no harm can come from it.

On the other hand, my own sanity check calculations make your outcome seem quite realistic. I have made the following assumptions:

50/50 WD
You achieve at least 1g braking
Your CG height / Wheelbase ratio = 0.25
Road surface to tyre mu = 1.5 (quite conservative, I would say)

The above assumptions and your listed tyre / brake specs equate to a requirement of 4350N front brake force (at the disc) to lock a front wheel.

I can't verify your claim that 47 bar gives 7300N of clamp force as I don't know your caliper piston diameter, but these numbers imply it is ~45mm which seems reasonable.

My very brief search-engine research of 'brake pad to steel disc coefficients of friction' returns values of around 0.5. Assuming this is the case with your system, this would explain why you are not locking your front wheels. In this case you would need 8700N of clamp force to lock your front wheels with a pad/disc mu of 0.5, 20% more than what you say you have.

These assumptions are of course very general and ignore some subtle behaviours that will be seen in the real world (transient braking effects vs caliper piston friction, to name two). But it does tell you that the numbers you have presented could be valid in explaining your real world results.

On a personal note - this ties in with my own experience of the brake test, where our team (for 2 years in a row) very seriously underestimated the performance required from the brake system in order to pass the brake test. You need to be very honest and objective when assessing the system loads and making your coefficient of friction assumptions. Adding factors of safety / ignorance is also advisable when you have limited confidence in these assumptions.

Failing the brake test is a brutal way of being forced to admit that the system your team has designed is insufficient, but it is better finding out this way than mid-corner. Hopefully at least you found the results above whilst testing your car, with some development time available to make modifications, rather than finding it out on the weekend of an event.. ?!

[Claude Rouelle]

Apoorv,

1. 394 Kg with driver? That is 326 Kg (717 lbs) without a 68 kg drive. Did I read this correctly?

2. I am afraid you will have to expect several other things than your brake to fail.

3. Have you and your team members ever considered participating at Formula Student India to better prepare yourself (at lesser transporting cost) for a quite competitive European competition?

4. On the brake issue: what are your master cylinder and your caliper piston diameters?

[BillCobb]

One of my first engineering projects many blue moons ago was to display the pressure distributions of the inside and outside pads in a disc brake using a very large array of strain gauges. If you think the pad physical area is the number to use for brake effectiveness calculations, then the stuff you are taking to make yourself ignorant is sure working good ! Make a brake dyno and correct your system parameters.

[Charles Kaneb]

What's your master cylinder diameter? 47 bar (4.7 MPa, 600ish PSI) is below the upper limit of most brake system hardware, so are you reaching the limit of your brake pedal assembly's strength and breaking stuff? Are you reaching the limit of assembly stiffness and having the brake pedal strike the impact attenuator plate? Is the driver reaching the limit of his/her strength, being forced out of or cracking the seat (I have seen karters of both genders do this - some kart brake hardware is trash!), or simply not believing how much force is necessary to lock the tires?

A car with a single braking circuit can be simplified to a lever for a first pass through the problem: Force at pedal * travel at the pedal = Force at caliper * travel at the caliper. Make it four calipers and assume constant pressure in the system and Force at pedal * travel at pedal = Sum of (Force at caliper * travel at the caliper). Add a bias bar and you now have one more lever: Force at pedal * travel at pedal = Force at MC1 * travel at MC1 + Force at MC2 * travel at MC2, and so on. I'm wondering if the total work input to the system is just inadequate.

[apoorv]

@claude
Sir, we are formula student electric not combustion team and this our first car. Hence we cannot participate in FS India.
area of the calliper piston: 0.001548384 m^2
area of the master cylinder: 0.00019996 m^2

[Ahmad Rezq]

apoorv
In order to get proper help you should provide proper data.
The simple answer to your question " Because your brake system cannot provide the required torque to lock the wheels"
Please in a single comment provide the following data.
- wheel base
- CG Location ( Height/Weight distribution)
- Front/Rear rotor size
- Front/Rear Caliper piston numbers and piston size
- Calipers Pads COF as stated from the supplier.
- Front/Rear Master Cylinders piston size

[Jonny Rochester]

Reasons for not locking:
1. You don't have enough water on the road.
2. Compliance in the brake pedal or pedal tray. Your brake pedal maybe flexing so you can't transfer the pedal force to the wheels.
3. Your 185-60-14 tyres are the size I use on my road car. Yes they are small, but a large diameter and probably heavy for FSAE.
4. Do all pistons slide freely and able to move the pads against the disc without restriction?
5. Your brake pads are too new. You have to brake a few times to wear them in so their surface perfectly matches the surface of the disc.

Can you show a picture of your system?

[Claude Rouelle]

Sushil,

1. 394 KG with driver even for an electrical car is way to heavy. F=Ma. The heavier it is for a given lateral or longitudinal acceleration the bigger the forces on the chassis and suspension. I am pretty sure that something else than the brakes will fail.If you pass Tech.


2. You have one master cylinder or 2 master cylinder? If one that is not legal. If 2 of the same size that is wrong especially of you have the same caliper front and rear.

3. As suggested by other readers (and without any pictures or additional information) I bet there is a compliance issue: your driver is using his leg force to deform the brake pedal, or to flex the brake pedal assembly or its attachment to the chassis or to flex the caliper attachment on the uprights, or to inflate your brake hose (You would not have rubber brake hose by any chance?) or all of the above instead of using his leg force to push the brake pads on the brake discs.

[CWA]

A few questions from me - firstly, did you clean the oil from your discs, if you bought them new??

Second, can you make an estimate of your longitudinal decceleration ('braking g') with the system as is? Just repeat your brake test events again and measure the distance travelled to fully stop from a set speed. This will help clarify whether you are close to locking up, or way off. Telling us the exact brand of tyres you have and the road surface you are driving on will also be useful (if you are not on race track tarmac with event-legal slicks now, you are going to struggle even more at comp!). Similarly, have you tried shifting full brake bias to each axle to check you have enough system force to at least lock each axle independently? This is another useful way of finding out how 'close' you are. If you can't even lock the rears with full rear bias you know you are in trouble. Same for the fronts on their own really..

Thirdly, can you clarify how you gathered your quoted brake system pressures? Was this driver-in-the-car braking-as-hard-as-possible with pressure gauges at the master cylinder outputs? Or was some other method used?

My further comments would echo what Charles has mentioned. It appears your driver is applying 41kg of force to your pedals. Simply asking for more foot force might not be a responsible design decision. What are the practical implications of allowing for increased pedal displacement (either by changing your mechanical or hydraulic ratio)? This will more than likely be your winning solution at this stage in the game, you may have to alter your packaging situation (and assembly stiffness) to allow for it.

Finally, can you throw up some pictures of how your caliper and pads are mounted against your discs. As I think Bill has alluded to, perhaps there are some practical issues with your mounting method, changing the pad centre of pressure moment arm that we are ignoring in our estimations.

A quoted brake pad coefficient of friction estimate from the supplier would also be interesting to see too..

[Charles Kaneb]

Even with rubber lines, too-hard pads, and a heavy car you're not doomed to failure. I have locked the brakes on my 900kg Honda CRX road car with a failed vacuum line to the brake booster. You have a friction or compliance issue, or a driver who is simply not pushing the pedal hard enough.

The master cylinders could be the same size and be right if the leverage ratio of the pedal is different on each cylinder, but I'm not aware of an off-the-shelf brake bias bar that would let you get away with a difference of leverage ratio that large.

[CWA]

I don't see why you'd need to have each master cylinder mounted at a different height on the pedal Charles. Won't a standard bias bar distribute the forces between your circuits enough to achieve the front/rear axle bias split you want, even if your cylinders are the same diameter? That is the point of a bias bar. Perhaps having equally sized master cylinders is not optimal, it may require a less conventional, perhaps more extreme bias bar setting, but I wouldn't call it wrong.

And perhaps I am ignorant of the practical implications of compliance in a braking system. But why does compliance / excess displacement at the pedal have to imply reduced forces seen in the system? As long as steady-state is achieved, and the drivers foot force is reacted by the pad on the disc as we have discussed, how much the pedal travels before balance is achieved shouldn't be an issue, should it?

Obviously there are practical implications in having a pedal travel too far depending on your local component packaging, and I can understand that excessive movement of the driver's braking foot would be an undesirable attribute. But I can't see how improving system stiffness in this regard without changing any other parameters will improve the primary function of getting more brake force into the tyres..

[Ahmad Rezq]

Theoretically having Same Master Cylinders Front/Rear + Same Calipers Front/Rear is possible .
As mentioned from Charles & CWA It requires large bias in some cases almost near to 80% to one MC.

[Claude Rouelle]

Sushil,

Other considerations (on top of the very good and generous other observations already made by other persons)

1. Do you have an adjustable brake balance bar? So obvious question that i forgot to ask

2. I hope you do not have floating calipers. Please confirm

3. Are you sure you did bleed your brakes properly? Are you sure you do not have trapped air for example on a long part of your brake line that would be above the master cylinder and calipers level?

[Charles Kaneb]

One thing I forgot to ask - do you have two meters of flex line from master cylinder to rear calipers? Hard line has two orders of magnitude less expansion than flex line. Air is worse than either. If there are no leaks and the master cylinder can be lifted to be the highest point in the system the system can be bled (my kart needs to stand up against a wall for this). Master cylinders need to be bench-bled; I have made the mistake of failing to do so and got really frustrated when the calipers wouldn't bleed.

On paper, compliance should not prevent lockup. Paper is a lousy racing surface. Most drivers I know don't like the "pock" of the piston hitting the end of the master cylinder, nor the "clunk" of the pedal striking the bulkhead.

400N force at the master cylinder seems REALLY low. With even 3:1 leverage on the pedal, that's only 150N (30 lbs) force at the pedal. Prof. McDermott was able to exert 1200N brake pedal effort at age 70 when he measured it in the Texas A&M gym.

[CWA]

Funny jokes are funny.

The line pressures and piston diameters given equate to 1600N at the master cylinder, which is 400N at the foot. Although having just stood on a foot myself (my own) and lifted myself up a few times (I weigh around 80kg) I guess 40kg at the foot pedal isn't really that great. I look forward to the OP clarifying how he gathered the line pressure values that he mentioned, and how hard the driver felt he was pushing on the pedal at the time.

And yes, the proviso is already stated, if compliance / displacement is so great that things are touching when they shouldn't, of course it is bad. These are obvious issues that I'm sure the OP would have noticed and mentioned if they were present in his case. I thought you were trying to imply that compliance had a more direct correlation with brake force, hence the clarification..

[apoorv]

- wheel base 1.6m
- CG Location ( Height/Weight distribution) .768m from front & .832m from rear.
-piston/caliper/disc front and rear are same
single piston and single caliper
caliper piston size - 0.001548384m^2
- Calipers Pads COF 0.46
- Front/Rear Master Cylinders piston size - 0.00019996m^2

@claude
sir we have same master cylinders for front and rear.
yes we have adjusting brake balance bar and fixed calipers.
We are quite confident on bleeding.

@cwa
our discs are not that new. There is no oil on them.
we took this pressure at calipers with pressure gauge with driver applying full force.

I was going through my calculations again & I got
11061.7N as the required clamping force at front at 1.4g.
for brake calculation I noticed that I got 53 bar of pressure and then when multiplied by area of piston and mu I got 3841.66N of clamping force at one wheel. i.e. 7683.33N of clamping force at front. Thus wheels should not lock.
I have doubt here. I have read stoptech's paper where they multiply the force at piston by a factor of 2 because of the brake pads will apply the force from both the sides. In that case I have 15400N of clamping force. In this case it should lock.
Can u tell me is it correct to multiply it by 2 or not becoz that can give me just opposite results. I noticed in your calculations that u also didn’t multiply it with 2.

Thanks

Link to the stoptech: http://www.stoptech.com/docs/media-center-documents/the-physics-of-braking-systems.pdf

[CWA]

I haven't read the whole of that article (too much pride and stubbornness [I must be getting old] makes me want to derive these calcs myself). But yes, you are right, I did forget to double the clamp force at the caliper. Out of interest, as Claude asked, are you using sliding or fixed 2-pot calipers?

Anyway, let me revise some assumptions and run through the numbers again:

Your parameters:
400kg = Car & driver
50/50 = Static WD
1.6m = Wheelbase
0.23m = Wheel radius
1.4g = Braking decel - seems reasonable

50 bar = Front brake circuit pressure
0.5 = COF (mu) pad/disc
0.1m = Disk radius (centre of pressure lever arm taken to be 0.075m)
0.00155m^2 = Caliper piston area

My assumptions:
2 = COF (mu) tyre/road
0.4m = CGH (determines front axle grip due to load transer due to assumed Ay)

1. Decel when full brakes applied (1.4g) with your car would give:
Front axle normal load = 340kg
Rear axle normal load = 60kg

2. Tyre/road mu of 2 means:
EACH FRONT WHEEL must be producing 3400N to lock

3. Wheel size and brake disc size (effective radius of pad) means:
10,420N required of TANGENTIAL brake disc force to lock EACH front wheel

4. Brake pad/disc mu of 0.5 means:
20,840N of CLAMP force (NORMAL to the disk face) is required to look EACH front wheel

Now working back from the front line pressure you stated:

A. 50 bar acting on your caliper piston area gives:
7,750N of force acting at one piston NORMAL to the disc face

B. Whether you have sliding or fixed calipers, this force is effectively doubled, giving:
15,500N of clamp force NORMAL to the disk face

When comparing step B with step 4, we can see that your system still may not produce enough force to lock the (front) wheels under certain assumptions.

My results here are of course different to the first set of results I posted because my assumptions have become more ambitious (or, realistic?). Whichever way you look at it, I do believe my assumptions are still reasonable (I welcome criticism, and I'm sure I'll get it where it's due). I hope these numbers help make clear why it is still plausible that you just don't have enough system pressure.

Although having said that, with these revised calcs and your values for rear brake system pressure, I do believe the predictions should state that at least your rear axle locks up. As you have said that not even your rear axle locked, it is clear that these predictions do not tell the whole story, we are sure missing something.

Additional thoughts - after discussion with Charles above, I too am surprised to hear that 400N (40kg) is the most that your driver could apply to your brake pedal. To expand, I can squat my own bodyweight (80kg) on my right (braking) foot from bent knees all the way up to tip toes quite easily and I am by no means fit.

Can you post up some pictures of your pedal box layout, preferably your caliper/upright layout too? It would be nice to take a look and verify what you have told us.

Also please do some sanity checks when you are out testing next - how much decel are you actually managing to achieve even without locking the wheels. I suspect 1.4g as an estimate is really a bit keen.

[Ahmad Rezq]

apoorv

- Since you are running same master cylinders Front/Rear and same calipers Front/Rear (As i understood from your comments) and as discussed in previous comments it seems your system needs around 80% bias to your front master cylinder.



I have doubt here. I have read stoptech's paper where they multiply the force at piston by a factor of 2 because of the brake pads will apply the force from both the sides. In that case I have 15400N of clamping force. In this case it should lock.
Can u tell me is it correct to multiply it by 2 or not becoz that can give me just opposite results. I noticed in your calculations that u also didn’t multiply it with 2.

You need to multiply the clamping force pressing each brake pad against the disc by two to calculate the total braking force from caliper.

[Claude Rouelle]

Sushil,

397 Kg car (with driver) and about 800 mm CG height. Let's be serious guys..... this is an engineering competition. I know how hard it is to design and manufacture a car in India but sorry guys, even for a first car you should have better expectations.

A passenger car and even a SUV has a lower CG than that! How did you calculate a front and a rear CH Height of 768 and 832 mm? Really? How do you manage to make a car of over 300 kg with a CG height of 800 mm? Did you measured that CH height and if you did can you explain how you did it? Unless your batteries are placed at the diver helmet height, does this number of about 800 mm makes sense to you?

FYI I have seen brake pressure on professional race cars (no power brake) going as high 900 psi (65 bars).

[apoorv]

@claude
sir our CG height is 350mm, and what I have mentioned above is the location of CG from front and rear i.e. 0.832m from front and 0.762m rear with 48:52 WD front to rear. wheelbase 1.6m

[Ahmad Rezq]

Claude
aproov didn't mention the CG Height he's just mentioned the weight distribution 768 longitudinal distance from front wheel center and CG , 832 longitudinal distance from RWC to CG.
i.e 52-48% weight distribution i can't imagine by any way that the car can have a CG height of 800 mm !

[Z]

This thread reminds me of one of those parties where you turn up really late... And everyone is just stumbling around bumping into things. And when you try chatting to someone you find they only speak Braille...

So, discussions of CG Height aside...
~~~o0o~~~

Apoorv (Sushil),

So far you have shown your THEORETICAL Engineering Design skills for "Brakes" to be an UTTER FAILURE.

This is most obviously seen in your choice of bicycle-brakes for a truck, which, quite naturally, makes them incapable of locking-up the tyres. (Here I agree with CWA's assessment in the second post of this thread. Namely, your design is simply one big COCK-UP!)

But your lack of Engineering nous really stands out here (and similar in subsequent posts).


... rotor with diameter 196.85 mm and 6.375 mm thickness...
... clamping force 7314.3 N ... 4879.29 N ...

As you have now found out, your use of "theoretical" numbers of 6 significant digit precision DOES NOT MAKE YOUR CAR WORK BETTER!!!

Nevertheless, you still have a chance to redeem yourself. I guess you still have a few weeks in which you can show whether you have any PRACTICAL Engineering Development skills.

You can start by noting that your rotors are ~0.2 m diameter, and your thus far calculated clamping forces are ~7 kN and ~5 kN. These, quite clearly, are not enough!

So go through all your numbers, accurate to only ONE significant digit (or maybe 2, at most), and see which changes to which numbers make the biggest difference. Then think about which changes you can actually change. Then change them. Quickly!
~~~o0o~~~


I welcome criticism, and I'm sure I'll get it where it's due.

CWA,

You were doing so well... (Apoorv, listen to CWA!)

Until this.

3. Wheel size and brake disc size (effective radius of pad) means:
10,420N required of TANGENTIAL brake disc force to lock EACH front wheel

4. Brake pad/disc mu of 0.5 means:
20,840N of CLAMP force (NORMAL to the disk face) is required to lock EACH front wheel

I know the standard "brake-design equations" make it look that way, but the above is very misleading. (This because ... "failed education system"+++ :)). So, just for the record.

Your 10 kN of required tangential-force Ft is, for a typical brake-disc, split into 2 x 5 kN Fts, ONE ON EACH SIDE of the disc. If pad-Mu = 0.5, then clamping normal-force Fn required, PER SIDE, is 5/0.5 = 10 kN (from Ft = Mu x Fn). There are, of course, TWO of these Fns acting from the caliper, through the pads, and onto the disc. One leftward Fn acts on the right-face of disc, and another rightward Fn acts on left-face of disc.

Am I splitting hairs?

Well, in my way of figuring it, a "compliance FEA" of the caliper would start with a 10 kN "spreading force" acting on the caliper. That is, TWO forces, L&R, of 10 kN each (-> draw the FBD!). Your way, as above stated, has only ONE force of 20 kN acting on the caliper. Somewhere. Err..., or is it 2 x 20 kN forces??? Aaaarghhh... poor FEA-Guy!!!

Also, if analysing, say, an "N-face disc-brake", similar to a multi-plate-clutch, then my way suggests much lower clamping-force Fn is needed for a given Ft (ie. Fn = Ft/(N x Mu), were N = number of faces). Which is what actually happens.
~o0o~

Now, back to the party... :)

Z

(PS. Apoorv, As per CWA and Charles's comments earlier, if your driver can WALK, then he (even she!) should be able to exert ~0.7+ kN (= ~70 kg) force on brake pedal. If they can hop, then 2 x that... This is NOT rocket science!)

[Claude Rouelle]

Sushil,

About the CG location; I did not read it correctly and I mixed Z and X location description. I apologize.

Claude

[K. Edwards]

A 4:1 pedal ratio is pretty low for a brake system. I believe "Think Fast" suggests a pedal ratio of between 6:1 and 8:1.

Why are you trying brakes test with rain tires, on what I assume is dry pavement?

In future years, don't use the same size master cylinders front and rear with the exact same calipers at every corner. The required size difference of your rotors would be too difficult to package. You will have too much trouble making the rear rotor incredibly small without hitting the hubs, and/or the front rotor incredibly large and fit inside a 13" wheel.

Also, did you take into account weight transfer into your calculations? This makes using the same master cylinders and calipers for both systems even more ridiculous.

1.4g deceleration? With a car as heavy as yours, given how you have the master cylinders and calipers configured, reduce that number to 0.75 - 1.0g and retry your calculations. Some of the better FSAE cars are decelerating at 1.5g, so it's a little daring to assume you could achieve something similar.

[CWA]

Thanks Z, yes I could have described that step with a bit more clarity. I hope it hasn't caused any confusion, thanks for the correction.

Sound comments from K.Edwards too.

Sushil, have you got any CAD / pictures to add? Do you have any news from tests as to:
- actual deceleration values achieved
- swapping bias to maximum front then rear - do you lock up either axle?
- what surface are you testing on?
- what are your tyres? (manufacturer, brand)
- any reason why your driver isn't applying more than 40kg to the pedal??

If this is just a theoretical exercise where you don't actually have a car built yet and you wanted comments on your predicted numbers / system design then just let us know that. If you really do have a running car and this is a practical exercise then in your own interests try and provide some answers for the above so we can consider how to help you further..

[Z]

Apoorv,

Again, listen to CWA above. Post some photos of your car...

Given you have an E-car, and given its current state (haha), are you sure you are turning the electric motors OFF while braking?

Given your car's total-mass, CG position, and 14" wheels/tyres, your Front-Brakes are WOEFULLY UNDERSIZED!

Theory time is now over. Time now for ACTION!

Z

[K. Edwards]

If your caliper mount is simple enough, you could add a second set of calipers to the front wheels. The rotors could then be "woefully undersized", but you could make up for your lack of radius with an overwhelming amount of clamping force with multiple calipers. It's a heavy solution, but it seems you aren't worried about a lightweight car.

[apoorv]

@cwa in your calculation u have considered the mu to be 2, I think its way to high. If u calculate with mu=1.5 (which i guess should quite correct) our brake system is sufficient to lock the wheels. Also we checked our brake bleeding and did find some air trapped hence we did bleed again, now the brake pedal feels very stiff and we are hoping that the car will stop in our next testing.

@Z
I dont have any pics of brake system right now...I will put it ASAP.

Thanks

[K. Edwards]

A mu of 2 is reasonable with a gritty concrete surface (Fsae Lincoln) with good race tires. If you guys are doing this with rain tires, your coefficient could be even higher if on a dry surface.

[CWA]

I don't believe that to be true Sushil. A tyre/road mu of 1.5 makes 15,630N of front disc CLAMP force required. When the clamp force delivered by your stated 50 bar of front system pressure is 15,500N, that's still a fail. You may be on wets now, but I don't think (for the sake of hand calcs) that a COF of 2 for slicks (at comp aren't these mandatory for the brake test if it's dry?) on race track tarmac is an unreasonable assumption.

That said, my own further calcs confirm you do have an abundance of rear system pressure. If 47 bar front and 31.5 bar rear (60/40) is what you are delivering during your tests, you should at least be locking your rears only. So let's take another step back. A small benefit of you having equal discs and caliper sizes front to rear means we can consider your performance on paper in a more fundamental way, that negates the need for us to know your actual decel, axle load transfer and brake bias:

- Assuming your brake pedal input force (and ratio) remains constant as you have told us, you will always have a total system pressure of 78.5 bar to play with.
- Common caliper pistons mean this system pressure gives a total system CLAMP force of 48,670N which is distributed amongst all four discs regardless of the bias you set.
- To negate the need to know axle load transfer, let us consider the 4 corners of your car as one wheel/tyre unit and one disc, with similar dimensions. The total weight of the car always acts vertically on this analogized 'single-wheel car' regardless of any deceleration under braking (there is no dynamic load transfer considered). So a brake system that can cause our analogized single wheel to theoretically lock is representative of a brake system that has bias optimised to lock all four wheels on a standard two-axled four-wheel car.
- Your car (and driver) weighs 400kg. Knowing wheel and disc size, there are two options for CLAMP force required at the disc to lock our theoretical tyre, depending on which tyre/road COF we choose:

- Option A, COF=1.5; 36,800N of total system CLAMP force required to lock
- Option B, COF=2; 49,067N of total system CLAMP force required to lock

As you have alluded to Sushil, when comparing these options against the 48,670N of total force your system can deliver, all your wheels will lock in one situation (COF=1.5), but not in the other (COF=2).

_____

Now you might think that in real life you have closer to a mu of 1.5 than a mu of 2. Consideration of some tyre data would help to confirm whether this is reasonable or not. Let us consider your mu is indeed 1.5. But let's also consider for a moment that your pad/disc COF is closer to 0.4 when you go to complete your brake test (perhaps temp isn't nominal yet, the surface of your steel isn't ideal) rather than the quoted 0.5. In this case you would need 46,000N of total system clamp force.

On top of this, let's now consider a transient effect which we haven't considered so far; the rotational inertia required to decelerate your wheels:
- Radius of gyration of 0.2m for a 0.23m radius wheel/tyre assembly
- Wheel/tyre unit mass of 10kg
- 40mph vehicle speed = 390 rad/s wheel speed
- At 1.4g decel; your car should be stopped within 6 seconds. Assuming you want the wheels to lock within 3 seconds (judges will probably prefer it is no later), each brake must also resist 52Nm of inertia torque. This works out to be a further 1,390N of disc clamp force at EACH corner, adding 5,560N of clamp force requirement to the full system.

In this case you would need 51,560N of full brake system clamp force at the calipers. In this case, your system will not deliver. And remember we have still assumed a tyre/road mu of 1.5.

Further to this we could consider the tyre/road mu is actually 1.6, which is quite possible because let's be honest, you're not sure that it isn't. In this case you would need 54,630N of clamp force, which is well in excess of the 48,670N that we know your system delivers.

Btw, do you have an aero-package; are you producing downforce? If so, don't forget to add the grip provided by this to your brake system requirements.

You can nit-pick at the numbers all day to make them tell you what you want. The point of my posted calculations is to show that when there can be so much variation between assumptions, and you don't have the engineering resource to find more accurate values, the only real sensible option is to provide an abundance of brake force (a good level of 'ignorance factor'), which I do not believe your system does.

______

As for the air in your system, I wonder if this will truly be the root cause of your issue. Air in the system just acts to reduce system stiffness. Assuming you do not have stiffness related issues like bottoming of your MC, or contact of the pedal with surrounding components, I wonder how removing the air will actually increase brake force sent to the tyres. Sure you will now feel a stiffer pedal, but how will this translate into more clamp force at the discs?

And another comment; if you had air in your system when you measured 47 bar and 32 bar, and you have lead yourself to believe, according to your own hand calcs, that these pressures are enough to cause your wheels to lock, air in the system cannot be the root cause of your problem.

_____

Nevertheless, all the best with your re-tests, it would be nice if I'm wrong and your system is good enough as it is. Believe me I know the frustration of failing brake test (at events! not just in testing). I do still look forward to seeing some CAD / pictures too.

A final, general question from me. I've not been involved with the full process of designing a brake system, from hand calcs through to verification of performance at an event. So I would be curious to know (Charles?) what assumptions for the parameters (COF's mainly) we have discussed above are reasonable to deliver a successful system in FSAE?

[apoorv]

@cwa
Your calculations are quite correct I know.
Today we tested our car and our brakes locked all the four wheels :) :) . Now this could mean that the mu value is not more than 1.5. Even the speed of the car was also high. Well thanks for all the help. I guess then I brake system is sufficient for our car and the main problem was the trapped air in the line which led to less stiff pedal.

[CWA]

@cwa
Your calculations are quite correct I know.
Today we tested our car and our brakes locked all the four wheels :) :) . Now this could mean that the mu value is not more than 1.5. Even the speed of the car was also high. Well thanks for all the help. I guess then I brake system is sufficient for our car and the main problem was the trapped air in the line which led to less stiff pedal.

That is good news Sushil. I do wonder where the disparity between our predictions and the real-life results lie, but I suppose I'll never find out over the interwebs. I'm glad your tests were successful, but if you do nothing else between now and your competition, at the very least please please please consider how representative your test tyre/road surface interface is of the brake-test scenario at the event you will be attending.

You are using wet tyres for your brake testing now; at competition I am fairly sure that if the conditions are dry the marshals will make you fit slicks for the brake test. Similarly, if you have not been conducting your brake tests on race track tarmac, the surface you brake test on at competition may offer a lot more grip. If you do not know how close to the limit of your brake system's capability you are currently operating to achieve lock up, you need to make dam sure that there won't be more grip at comp.

Underestimating the difference in grip levels between our test track and the brake test area at Silverstone was the main reason we spent so long on the competition weekend struggling to pass the brake test. I really hope you don't need to experience this yourselves.

[Ahmad Rezq]

apoorv
You didn't consider any change in the system ?
Only the trapped air in the line was the brakes problem . ?
I'am not quit sure about your car stability during braking.
Anyway congratulations and good luck.

[JT A.]

That is good news Sushil. I do wonder where the disparity between our predictions and the real-life results lie, but I suppose I'll never find out over the interwebs. I'm glad your tests were successful, but if you do nothing else between now and your competition, at the very least please please please consider how representative your test tyre/road surface interface is of the brake-test scenario at the event you will be attending.

You are using wet tyres for your brake testing now; at competition I am fairly sure that if the conditions are dry the marshals will make you fit slicks for the brake test. Similarly, if you have not been conducting your brake tests on race track tarmac, the surface you brake test on at competition may offer a lot more grip. If you do not know how close to the limit of your brake system's capability you are currently operating to achieve lock up, you need to make dam sure that there won't be more grip at comp.

Underestimating the difference in grip levels between our test track and the brake test area at Silverstone was the main reason we spent so long on the competition weekend struggling to pass the brake test. I really hope you don't need to experience this yourselves.

When I was in school we would usually mount a really old, almost worn out set of slicks for brake test, and pump them up to 30psi, and max out the camber settings just to eliminate any doubt :)

[Jay Lawrence]

^ and roll the car through as much dirt and oil and crap as possible on the way to brakes ;)

[MCoach]

When I was in school we would usually mount a really old, almost worn out set of slicks for brake test, and pump them up to 30psi, and max out the camber settings just to eliminate any doubt :)

^ and roll the car through as much dirt and oil and crap as possible on the way to brakes ;)

Gosh, kids. Breaking out all the tricks in the book now. :P

Sushil, was the test attempted with your dry tires? I'd go find the highest friction surface you have available to you and attempt there to make sure that even being capable of locking the tires does not become the issue and that they are comfortable to use at the limit as well!

[Bemo]

You are using wet tyres for your brake testing now; at competition I am fairly sure that if the conditions are dry the marshals will make you fit slicks for the brake test.

The rules don't require slick tires. You will have to use whatever you define as your dry tires. So what you should do is do the test with the tires you are planning to use as dry tires at comp and look for the surface with the most grip you can find. As others have stated before you want to be really sure that brake test isn't a problem at comp. So you should verify it is still no problem when doing the test under circumstances which make it difficult to pass. At the Italian competition you have to consider the brake test to be done on really hot racing tarmac on which several other teams already did their brake tests. Therefore there will be a lot of rubber left on the tarmac, increasing the grip level even more.

[Alumni]

Gosh, kids. Breaking out all the tricks in the book now. :P


You forgot the best of them all - a small spot weld or two on each rotor!



Seriously though kids, don't try that.

Unless it's baja.