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Discussion Starter · #1 ·
Brake upgrade information:

Over the last few years on the Vortex there have been a multitude of posts arguing about the benefits and disadvantages of big brake kits. The most popular “disadvantage” is that a larger diameter rotor means it has a bigger rotational inertia, or moment of inertia. What this means in laymen’s terms is that a, say, because a 12” rotor is bigger, it “saps” more power from your engine than, say, a stock 9.4” set up. This is indeed true. However, how big a factor is it? I was doing some project work on this kind of thing so I decided to diverge a little and do something that might show me and those of you who are interested something pretty interesting. If you couldn't be bothered with the technical explanation, scroll down to "conclusion". I sort of rushed through this stuff, so if there are calculation errors, please don't kill me, I'm just trying to help, educate and illustrate


The basic equation to calculate the moment of Inertia of a solid (as opposed to “floating” disc and assumed to be a constant-thickness disc) is:

Where m is the mass of your disc, and d is the diameter of your disc.
To interpret this, it means that the moment of Inertia increases with the square of diameter. This looks like a really scary thing! But again, we ask, what does it actually mean?
More useful than the simple moment of Inertia equation for demonstration is the Kinetic Energy (KE) which is required to rotate this disc to a specific speed, due to moment of Inertia. This is given by:

where is angular velocity of the disc, ie. how quickly it is required to spin at a given point. What this means is that the energy required to rotate the disc at that velocity is a factor of the square of velocity, and the square of diameter, as before.
What we will assume:
Car weighs 1100kg
Car has 16” wheels which aren’t coming into the equation
Car is on a flat road
9.4” rotor weighs around 3kg
Decent 12” rotor weighs around 5kg (this is pretty conservative)

If we take a test subject, let’s say a 12” non-floating rotor weighing in at 5kg, we calculate:
I = 0.0581kg/m^2
And the energy at a car velocity of 100km/h (62mph) is
KE = 412.175 joules
Since the measure of energy that the engine puts out is simplified to be the energy your car has at a particular speed thanks to the energy the engine transferred, we can actually go and find out exactly how big a difference this EXTREMELY SUPER SIZED OVERKILL TRUCKLOAD MOTHER DISC WILL MAKE!
The graph below shows the ratio of the Kinetic Energy required to reach a vehicle speed of 100km/h starting from 0. The speed of the car signifies the energy that the engine was able to produce from burning fuel (simplified version of Kinetic Energy of the car).

Interpreting this, the curve shows that most of the energy that is ever used to accelerate the rotors is used at the lower speed band, and as you get progressively fast, the rotors rotate quicker and are thus are not as “difficult” to rotate.

CONCLUSION
What the data and the graph shows is that most of the energy that is ever used to accelerate the rotors is used at the lower speed band, and as you get progressively fast, the rotors rotate quicker and are thus are not as “difficult” to rotate.
I’ve shown all the rotor energies in the table just for the hell of it – so you can see how the energy required by the rotor goes up exponentially with speed. In this table for TIME SPLITS (not the same as the above graph), the various energies for rotors and energies of the car at various speeds, the ratio of required rotor energy compared to energy from the engine, is the same at all speed splits. This percentage is 0.007494%. That isn’t a hell of a lot!!! So finally there is some evidence that even big brakes aren’t such big factors in “power loss” from the engine! Woot!
A typical 9.4” rotor would have a ratio % value of around 0.00276%. Calculating a percentage ratio of these two ratios, we land up seeing that from changing from a 9.4” rotor to a slightly heavier 12” rotor, you are increasing your energy “wastage” from the engine by 36.78% compared to the original value.
While this may seem sort of high, you have to understand that everything in tuning is a trade-off. I’ve highlighted the negative side-effect of going to bigger brakes, and in my opinion, 36.78% increase is really not much, because you’re looking at heat capacity improvements of up to like 120%.
Also, all the calculations have been done assuming the 12” is of one-piece construction, and weighs 2kg more than the 9.4”. 1.9..16vTurbo weighed his 12” AP’s and the floating rotor was actually lighter than the 9.4” stock rotor!! This brings that 36.78% down quite a margin, and it also reduces your unsprung weight which is great news for cornering performance.
Also, while I have used the term "big brake kit" in this article quite loosely, in automotive aftermarket brake systems, 12" isn't that big and is certainly the maximum diameter I would suggest for a Mk2. I saw an Audi A4 running around with some 14" Wilwoods, and the energy sapping of that size rotor is really going to be bad.
While wheels haven't featured in this, I think I'll do a similar article on energy that wheels require sometime in the future. A lot of people say that the upgrade to bigger brakes means needing bigger wheels and THAT is the big deficit, and I don't agree, because of the mechanics of them, they aren't as influential on inertia as one might think... But that, ladies and gentlemen, is a story for another day...
Hope you enjoy, and it isn't too technical :/
Edited so I could write this line


Modified by Jezztor at 1:04 AM 4-4-2006
 

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Man... now I remember why I bailed on my Physics degree!
But seriously, very good information for those that are able/willing to digest it.
Looking at what you've said there, I would estimate that the losses in time through acceleration are considerably out weighed by the benefits of shorter braking distances and times.
If you consider this (and I don't have equations to back this up) the fact that your average velocity point to similar point say A - B (and to exagerate the point A being V =0) will be reduced, granted. If you need to be stoped/at a reduced velocity by point D, with the larger brakes you will not need to brake until point C therefore it would be interesting to see the difference in the A - D avergae velocitys.
Meh... Food for thought.
edit: Bah who am I kidding, I can't chat science like Rico!

Modified by top fuel at 11:33 PM 4-3-2006


Modified by top fuel at 11:34 PM 4-3-2006
 

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Re: (top fuel)

Quote, originally posted by top fuel »
edit: Bah who am I kidding, I can't chat science like Rico!

That's why I just chat women and hot air balloons with him


Damm Rico you put your time in on this one. Now I have a damm good theory explanation thread to post a link to when this topic comes up.
Damm fine job Sonny Jim http://****************.com/smile/emthup.gif
 

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Discussion Starter · #9 ·
Happy to help!
Adam, in studying this stuff we often see so many numbers that we forget what letters are used for... This is the right thread for spelling mistakes! http://****************.com/smile/emthup.gif
 

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Re: (dubweiser1)

I know this is an old topic, but... what does it do to unsprung mass? (One of the big reasons for alloy wheels...)
Less inertia on the suspension makes for a tighter setup. Rotate the mass around the a-arm points...
 

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Re: (branden89golf)

i am happy I upgraded to my 280mm rotors. From a driver's standpoint, I didnt even notice a difference in the available power during accereration.
Now it totally isnt an issue, but I was of course referring to before my engine had a snail bolted to it.
 

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Discussion Starter · #14 ·
Re: (zanakas)

Quote, originally posted by zanakas »
I know this is an old topic, but... what does it do to unsprung mass? (One of the big reasons for alloy wheels...)
Less inertia on the suspension makes for a tighter setup. Rotate the mass around the a-arm points...

There definitely is un unsprung mass deficit. OEM rotors are like 18mm thick, my 12" ones are 28mm thick, as a guide to how heavy they'll be. The calipers are only 1.9kg each which is lighter than stock IIRC, but the rotors most definitley are heavier and the difference in transient response time is there if you know what to look for. But that's why I went for the lightest, strongest wheels I could get my hands on for a semi-reasonable price.
 

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Re: (91gti_wolfsburg)

So, correct me if I'm off on this; Given the results of your experiment and concluding that the difference in the rotors is under 0.09% making it negligible, but identifying that the larger rotor needs more KE to rotate it at lower speeds...
Can I safely reason that although I can brake much later into a turn, carry the same speed as a smaller rotor car through it, but out of the turn I need more KE to return to the entry speed (IDK if I'm using the correct terms in the correct places, feel free to learn me up one).
This is the possible disadvantage to bigger rotors? But negated by the fact that I did not have to brake as soon to slow down for the turn? This is only a concern because the MKII is not exactly a power house vehicle and of the available power, would not want ot lose it in turning something I don't need to.
If that made any sense please respond. And THANK YOU Jezztor for a thread like this. Haven't seen something this good since the rear suspension thread. http://****************.com/smile/emthup.gif
 

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Re: (Funkatollah Insaney)

^^^ That's what someone else was getting at before (point a-b-c-d averaging etc).
Yes, the disadvantage is going to be slower acceleration, notably at lower speeds (more KE required). So yes, it is going to take an amount more energy to come back to speed. But what we haven't found to this point is if the extra time to reaccelerate is made up by the extra time the car can remain at entry speed before braking. I would suspect it is. Keep in mind that there was evidence presented that 12 AP floating rotors in fact weighed LESS than stock solid 9.4. The advantage of that is twofold: less KE is needed than in the calculations (the acceleration loss will be less than predicted by the equations), and possibly more important, less rotational unsprung mass! That allows better cornering abilities as less weight is effectively transfered.
There are plenty of options other than larger rotors that offer PLENTY of braking power and consistency for street and autox use. I would think the real benefits of this article are for those on track, who are beyond the limits of better rotors, pads, fluids, ducts etc. Track racing is going to lend more towards higher consistent speeds, so the acceleration loss is going to become even more negligible (note the inverse curve).
Nice write-up. http://****************.com/smile/emthup.gif
 

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Re: (VWGolfDriv3r)

Nice, that's why I always loved my physics classes ( those numbers don't give me a headache, they make me smile... and make me take resolutions towards bigger brakes )
Funny thing is all those with basics college physics could've calculated this but none ever thought about doing it ; leading for a long time to an ocean of debate and ignorant stupidity... once again you rico showed people undeniable proof for future disc-ussion!
 

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Discussion Starter · #19 ·
Re: (Funkatollah Insaney)

Quote, originally posted by Funkatollah Insaney »
So, correct me if I'm off on this; Given the results of your experiment and concluding that the difference in the rotors is under 0.09% making it negligible, but identifying that the larger rotor needs more KE to rotate it at lower speeds...

Essentially, yup.
Quote »
Can I safely reason that although I can brake much later into a turn, carry the same speed as a smaller rotor car through it, but out of the turn I need more KE to return to the entry speed (IDK if I'm using the correct terms in the correct places, feel free to learn me up one).

Well, the data shows that even though it takes more KE (exponentially) to accelerate from low rotating speeds, the difference between a larger rotor and a smaller rotor in terms of the KE needed is really insignificant. What the curve represents is the way rotational acceleration of a mass works. So if we are to neglect fractional differences, an efficient big brake upgrade will allow you to brake later, carry the same speed through the corner and accelerate at the same rate as a car with smaller rotors. The difference comes in where there's change of terrain (ie. bumps, camber change etc) mid-corner and this affects the actual handling during the corner, all because of the increased unsprung mass.

Quote »
This is the possible disadvantage to bigger rotors? But negated by the fact that I did not have to brake as soon to slow down for the turn? This is only a concern because the MKII is not exactly a power house vehicle and of the available power, would not want ot lose it in turning something I don't need to.

The real disadvantage is the added unsprung mass. The disadvantage is going to be much more pronounced in a rally car, because of the same principle as above. The extra mass basically "delays" the response time of a bump. So let's say with a stock 9.4" rotor it takes a suspension system 0.05 seconds to respond to a speed-bump, it might take 0.1 seconds for the same system with bigger rotors (= bigger mass) to respond to the same bump at the same speed. I hope that makes sense... and the numbers are only for arguments sake.

Quote, originally posted by VWGolfDriv3r »
Yes, the disadvantage is going to be slower acceleration, notably at lower speeds (more KE required). So yes, it is going to take an amount more energy to come back to speed.

The disadvantage is there, but it's really not noticeable. Regardless of mass and size of rotor/brake setup, it's always harder to accelerate a rotational mass from low speed than it is at higher speed. This DOESN'T take into account engine acceleration, just acceleration for the same energy input.
[/quote]But what we haven't found to this point is if the extra time to reaccelerate is made up by the extra time the car can remain at entry speed before braking. I would suspect it is. Keep in mind that there was evidence presented that 12 AP floating rotors in fact weighed LESS than stock solid 9.4. The advantage of that is twofold: less KE is needed than in the calculations (the acceleration loss will be less than predicted by the equations), and possibly more important, less rotational unsprung mass! That allows better cornering abilities as less weight is effectively transfered. [/quote]
Well, in my opinion we have found that out. The point of the calculations and my own tests with my 12" AP's was to demonstrate that larger diameter rotors don't affect acceleration much at ALL. As with anything in engineering, it's always a performance compromise, but the larger brake thing is actually a question of handling vs. braking, not acceleration vs. braking. My rotors are solid rotors, they aren't floating rotors, and I doubt my engine puts out more than 110-120bhp.
Quote »
There are plenty of options other than larger rotors that offer PLENTY of braking power and consistency for street and autox use. I would think the real benefits of this article are for those on track, who are beyond the limits of better rotors, pads, fluids, ducts etc. Track racing is going to lend more towards higher consistent speeds, so the acceleration loss is going to become even more negligible (note the inverse curve).
Nice write-up. http://****************.com/smile/emthup.gif

Yes, absolutely right. I'm very performance-oriented and the write-up is more for track drivers. Though I think it goes without saying, because anyone who spends $1000+ on a set of brakes for street aesthetics has a screw loose
. Girling 54's even with a good DOT4, braided lines, DS2500 pads, brake ducts and good quality slotted rotors is a fantastic OEM brake setup that can take punishment.
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Discussion Starter · #20 ·
Re: (bassman1987)

Quote, originally posted by bassman1987 »
Nice, that's why I always loved my physics classes ( those numbers don't give me a headache, they make me smile... and make me take resolutions towards bigger brakes )
Funny thing is all those with basics college physics could've calculated this but none ever thought about doing it ; leading for a long time to an ocean of debate and ignorant stupidity... once again you rico showed people undeniable proof for future disc-ussion!

That's the thing, it's all basic physics, nothing fancy at all... I wrote this a long time ago after a longstanding argument with someone who said big brakes are retarded. Glad you enjoyed bro http://****************.com/smile/emthup.gif
 
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