Chris_W

I'm wondering how much of an effect switching from a 203mm to a 185mm rear disc brake rotor will have. My search has only revealed the common knowledge that bigger rotor = more heat capacity, but has not revealed any actual quantities showing what the real-world difference is. Does anyone know a source for such data?

The reason I'm asking it that we have an Avid BB7 disc brake with 203mm rotor on the rear of our tandem. Because it's a 2008 Co-Motion Speedster, the disc mounting bracket is on the seat-stay, and so the disc brake interferes with the rack (they've moved the bracket to the chain-stay on newer models, which solves this problem). I had managed to find a random rear rack that didn't interfere with the brake when I mounted it with an extra kit from Tubus. However, the rack was a temporary solution - pretty low quality and not that strong - so I want to upgrade to a fancy Tubus rack. Unfortunately, I've found no way to mount a Tubus Logo rack without interfering with the disc brake. I've tried using two different-shaped mounting brackets from Tubus, but using all possible orientations of those parts puts the rack in various positions, none of which provides a solution. The one thing that would solve the problem would be to use a 180mm or 185mm disc rotor because then the disc brake would mount nicely between the Logo rack's stays when using a certain combination of mounting brackets.

So, it seems that we can have a 203mm rotor and a crappy rack or a 185mm rotor and a super-nice rack (or a 203mm rotor with the super-nice rack mounted in a really precarious way, making it no better than the crappy rack, so I'm not considering this as an option).

Since I couldn't find objective data on the difference in heat capacity, I did some calculations to compute the difference in mass and surface area of different rotor sizes. I assumed that the braking surface is always 15mm wide, the rotors are 1.9mm thick, that rotor density is constant (so mass is proportional to volume), and for simplicity I ignored holes in the braking surface. If my geometry skills are sufficient, the 185mm rotor has 9.6% less mass than the 203mm, the 180mm has 12.2% less than the 203mm, and the 160mm has 22.9% less than the 203mm. The formulas on this Wikipedia page suggest that heat conduction is a linear function of surface area, and the differences in surface area are the same as the percentages above.

Therefore, my best estimate is that assuming zero heat loss, the 203mm disc would absorb 10% more heat (i.e., braking power) than the 185mm disc before they both reach the same temparature (due to the difference in mass). However, when factoring in heat loss we must consider the surface area difference also, so the larger rotor should actually handle more than 10% more braking power than the 185mm rotor, but I don't know how much more - I am at the limit of my skills here

There are probably other factors that I haven't considered, so some real test data would be very nice to see. Also, our current 203 mm rotor is just the stock Avid Roundagon. I'm wondering whether I could get a fancier 185mm rotor that has better cooling properties than the stock 203mm rotor, which might cancel out the difference in mass and surface area. Can anyone recommend something?

Chris_W

I've now gone one step further to try to figure out how to combine the difference in mass and the difference in surface area between the 203mm and 185mm discs. Let's assume a situation of a constant braking force being applied to the rotor.

First, I considered how fast the rotors would gain heat, using the simplification that this is a linear function of the rotor's mass. So, if the 185mm rotor is increasing by 10 degrees per second then the 203mm rotor will increase at 9 degrees per second (10% less), given the same braking force.

Second, I considered how fast the rotors can lose heat, using with the simplification that this is a linear function of the rotor's surface area. We're worried about a situation in which heat is building up much faster than it can be lost, so let's assume that the 185mm rotor can only lose heat at 2 degrees per second, and then the 203mm would lost heat at 2.2 degrees per second (10% more).

Therefore, net heat gain of the 185mm rotor would be 10 - 2 = 8 degrees per second, and for the 203mm rotor would be 9 - 2.2 = 6.8 degrees per second. The 203mm rotor is therefore heating up 15% more slowly (1.2 / 8) and so should take 15% longer before reaching a heat at which braking performance will fade and/or the rotor will be damaged (i.e., it can withstand the same braking force for 15% longer). Unfortunately, I then realized that this conclusion depends greatly on the relative difference between the rate of heat gain and the rate of heat loss, as I demonstrate below.

I assumed above that heat is lost by the 185mm rotor at one fifth the rate at which it is gained (2 degrees per second versus 10 degrees per second); I re-did the calculation assuming that this ratio was one half. The 185mm rotor would therefore lose 5 degrees per second, and so the 203mm rotor would lose 5.5 degrees per second (10% more). Net heat gain would then be 10 - 5 = 5 degrees per second vs 9 - 5.5 = 3.5 degrees per second. This now suggests that the 203mm rotor would heat up 30% more slowly (1.5 / 5) than the 185mm rotor.

Therefore, we need an accurate estimate of the ratio of heat loss rate to heat gain rate before making any solid conclusions about which of these values is more realistic (a 15% difference, a 30% difference, or something else). I'm therefore hoping that someone can point me to some solid test data that addresses all this.

Chris_W

Before I was only talking about heat capacity, but I should acknowledge that there is also a difference in braking power achieved with different rotor sizes. Because braking power is linearly related to rotor diameter, the 185mm rotor will give 10% less braking power for the same amount of force applied at the lever. Continuing this line of thought, to achieve the same amount of braking force at the tyre, the brake will have to squeeze the rotor 10% more tightly and so the brake pads will wear faster with the smaller rotor.

I wish I could find a way to mount this rack and use the 203mm rotor. Maybe I'll give it one more shot!

WebsterBikeMan

No solid test data here, but a note or two about your assumptions.

First, the rate of heat loss is generally proportional to the difference in temperature between the object losing the heat, and the surroundings. Assuming it isn't blisteringly hot out, your talking a linear increase in cooling as the disc heats up. If both discs in your example were the same temperature throughout the thought experiment, you could just talk in terms of degrees of cooling per second, but that approximation doesn't really work here.

Second, the amount of heat the two absorb per unit temperature increase is the heat capacity, as you know. But the amount of heat they need to absorb is the same as the braking power. So if the smaller one has truly 10% less braking power, there is 10% less heat being dumped into it.

I suspect that when it matters, cooling is much slower than heating, and can almost be neglected in the calculation. Rate of cooling has more to do with how soon you can dump more energy into it. Which matters too, but is less of a factor in determining whether you're getting close to catastrophic failure.

joe@vwvortex

I have a 2004 Speedster with a rear 203mm disc and a great Bontrager rack. It works with their Interchange trunk bags which simply snap on and off. The rack is designed with disc brakes in mind and fits perfectly with a just a couple of small aluminum spacers/washers to spread it just a tad more to clear the caliper. The larger diameter disc will also have more braking power.

Chris_W

I spent a couple more hours fiddling last night and finally found a way to mount my Tubus rack with the 203 mm disc and without any interference between the two. It took a bit of inventiveness, and a different mounting method for each side, but it is now super-sturdy and lined up nice and straight, so I'm happy. Taking another stab at it with fresh eyes was apparently the best plan. I still enjoyed my little exploration into estimating rotor heat capacity differences, I hope others people did, too.

BTW, I prefer a rack with three widely-spaced stays to give side pannier bags lots of support, so the two closely-spaced stays of that Bontrager rack don't look like they would work that well for me.

sine

Let us know what you did.

We have a CoMo with the same disc mounts and I need to figure a way to get our Tubus rack (from our old canti brake tandem) to fit. In the meantime, I'll check the Tubus site to see what sort of mounting brackets they have.

Thanks

joe@vwvortex

My panniers fit fine on the Bontrager race - as they have reinforced panels on the inside and mount up nicely. However - I do understand your concern and I might have considered a different rack if they were the priority. We use it more for the trunk rack then panniers.

Chris_W

I've attached some photos of my solution below. Click on the images to make them larger. As you can see in the first photo, the rack is not very level, but it should be good enough. I think it would be more level with a 180 or 185mm rotor, but I decided not to make that compromise. The attachement method at the dropout is different on each side.

On the non-drive / disc side, I've used the upper bolt hole on the rack and I've bolted it onto the lower disc brake mounting hole (only the fender is attached to the normal fender/rack mount hole). The bolt for the disc brake mount is an M6, but the upper hole on the rack is an M5 size (only the lower hole is M6), so I had to drill out the upper hole on the rack so that an M6 would fit through, but that was easy enough. I still had to space the rack out a little to make it clear the disc brake, especially to clear the cable housing entry point. I therefore used some spacers between the rack and the frame, I believe there is about 10mm of spacers, which is the most that I would want to use, but I could not use less. These spacers came with the Tubus rack extension kit shown below (see product page here). I did have to find a longer M6 bolt to secure everything with, and the one I did find was actually slightly too long, and touched the disc rotor, so I had to put another small spacer behing the bolt's head. In the future, I may trim this bolt and get rid of this spacer.

On the drive side, I had the task of making a mounting point similar to the other side so that the rack would be straight. This is where one of the metal plates from the extension kits came in handy. When I bolted this extension plate onto the rack in the way shown in the fifth photo and then clamped the bottom hole of the plate with the quick-release skewer, it was in just the right spot. Tubus sell a very similar kit that is designed to be bolted on using a QR, so I assume this will not be an issue. The bolts used to connect the extension kit to the rack would have pushed up against the frame, so I had to put a small spacer behind the extension, also on the QR skewer, this one is probably only 3-4 mm wide.

It's certainly not ideal (I'd like the top of the rack to be flat and I'd like to not need to use any spacers), but I'm pretty sure that it's the best I can do with this combination of frame, rack, and brake.

BTW, yes I know the bike and chain need a good cleaning, that is the next job on the list. And the frame is really not as pink as it appears in some of these shots, it's just a bright red.

mtnbke

Um...the real world difference? Not going into a wall at over a hundred MPH, from the past sixty years of engineering data from Ferrari, Mercedes, Honda, etc.?

aixaix 

Um... not exactly. Most of what makes modern brakes work better than old ones is design & materials, not size. The increase in leverage from using a larger diameter disc (with the same size pads) is exactly offset by the increased speed of the larger disc, i.e., a point on the swept area of a disc 2x the diameter of a smaller disc gives you twice the leverage over the hub, but is traveling twice as far per revolution. I.e., for a given pad size, rotor diameter makes no difference at all in force required to slow it down. The advantage of a large diameter disc over a small one is the ability to increase the size of the swept area (larger pads). The greater mass of a larger disc means it will both heat up and cool down more slowly than a smaller one, unless it is constructed differently. Depending on how it is used, this could be an advantage or a disadvantage.

As far as real-world considerations go, automobile brake technology research and testing is the most available and thorough, but is of limited relevance, since the power, speed and weight of a car is many times greater than a bicycle. It is about all we have, since there isn't enough incentive (money, liability, legislation) to get bicycle brake manufacturers to do more than basic testing. (Motorcycle brake testing might be relevant. I know nothing about this.)

Check out "Brake Handbook" by Fred Puhn. It came out about 25 years ago. It is well worth reading for its clear and thorough treatment of theory, as well as practical considerations. It may be dated, but the theory hasn't changed much, as far as I know.

2ering

Have you considered a rack specifically designed for rear discs, e.g. OMM Sherpa https://www.oldmanmountain.com/Pages/...earRacks.html? Co-Motion recommends this rack (or at least did while they were using the seat stay mounted caliper bracket). You could sell your Tubus & avoid a lot of hassle.

vik 

This is the only disc brake overheating data I know of:

https://thelazyrandonneur.blogspot.co...im-brakes.html

...may not address your question 100%, but may be interesting reading.

mtnbke

I hope its changed. I'm a layman, and even I understand that the argument of rotor speed, as a function of the ability to stop the wheel is a fool's errand, the efficacy of the disc, for larger discs, has to do with the increased surface area the pads have to slow the wheel down, per revolution of the wheel. You can't begin to compare a smaller rotor to a larger rotor, all other things being equal. One simply works 'best'. Besides, you measure rotational speed in radians (radians per second, actually), and when doing so you'll learn that effective rotational speed with a larger rotor is slower (lower angular speed per second) even though "more" rotor is passing through.

I really doubt that a 25 year old book on brakes didn't intuit that. Maybe we should both read that book!

aixaix 

I see I didn't make my point very well.
A larger rotor will be more efficient than a smaller one, not because the force required to slow it down (given the same size brake pad), but because it has more surface area to give off heat. For a given input (100psi at the pads, e.g.), the initial *********** will be the same. The value of a larger disc is twofold. First, being larger means it can radiate more heat. (For our purposes, this is an advantage, although there are some applications where this is not.) Second, the swept area can be made larger still by increasing its width. My point was that the increase in swept area doesn't give a mechanical advantage in terms of leverage. It absolutely does for other reasons (heat transfer, e.g.).
I'm sorry I didn't make that clear the first time around. By the way, what usually limits the size of a rotor on a car is interference with the rim or other component, just what the original poster was having trouble with.

The theoretical basis for designing brakes, the physics of changing motion into heat, has not changed in any fundamental way since 1986. Technology, practice, engineering & materials have all come a long way, however. Puhn's book is probably out of print, but I'm sure copies are still available at Alibris, Powell's or Amazon.

sine

Thanks for posting instructions & pictures.

stapfam

I went disc on the offroad Tandem in 2006. Not much was known about what brakes to use at that time and I went for Hope Mono M4 with 203mm discs front and rear. Hard braking on the road and the rear wheel will lift- they are that effective. But we also had an imbalance problem. The rear brake was more effective than the front.

A change to a 185 rear disc worked. The tandem is balanced on braking effect and we don't lock the rear wheel quite as often.

On the over heating- we used to do night rides. Those discs took on a dull orange glow after some of the steep twisty descents and we never noticed a reduction in braking effect- or any warping of the disc. May be the quality of the material used in the hope discs but I have used the same thickness of disc in motor sport and never had a problem then either.

aixaix 

That is cool and scary in equal measure! I had no idea you could do that on a bicycle. GT cars often got their rotors red hot back in the day (maybe still do). The rotors didn't care, and as long as the pads could deal with the heat and the fluid didn't boil (or ignite), this wasn't a problem. They looked great in night races like Sebring & Daytona. No fun doing brake pads during pit stops, although you could see what you were doing by the light of the rotors!

joe@vwvortex

That's impossible - since rotor size has no affect on braking if the same caliper and pads are used...........

stapfam

It does- The rear brake and we were locking it up on hard braking. By decreasing the rotor size you reduce the Leverage on the braking effect on that wheel. I used to make my own Caliper units When I was Karting. Increase the disc size and you got a far more effective brake for the same leverage- but it was a balance between making the brakes effective enough and too effective.

If it were the case that rotor size has no effect of braking effect- there would be no need to use discs larger than 100 mm.

This has been noted on many MTB's where in the main you do most of your braking on the front wheel. With rim brakes this just means using harder pressure on the front lever- but with Disc brakes using the same caliper and Master cylinder size- you just fit a larger disc on the front.

joe@vwvortex

Not according to aixaix who posted this above........

Um... not exactly. Most of what makes modern brakes work better than old ones is design & materials, not size. The increase in leverage from using a larger diameter disc (with the same size pads) is exactly offset by the increased speed of the larger disc, i.e., a point on the swept area of a disc 2x the diameter of a smaller disc gives you twice the leverage over the hub, but is traveling twice as far per revolution. I.e., for a given pad size, rotor diameter makes no difference at all in force required to slow it down. The advantage of a large diameter disc over a small one is the ability to increase the size of the swept area (larger pads). The greater mass of a larger disc means it will both heat up and cool down more slowly than a smaller one, unless it is constructed differently. Depending on how it is used, this could be an advantage or a disadvantage.

Chris_W

I understand why the larger disc would heat up more slowly, but why would the larger disc cool down more slowly? It has more mass, but that is offset by the larger surface area. I would expect cooling rate to therefore be approximately equal.

aixaix 

Joe@vwvortex was being tongue-in-cheek about my earlier, somewhat lame post. Larger diameter rotors are more effective than smaller diameter rotors because more swept area means more heat transfer is possible and braking is the business of turning motion into heat. The rate of cooling depends on the surface area vs the volume. A cube 1" on a side has six square inches of surface area. A cube 2" on a side has 8 cubic inches and 24 square inches of surface area. The volume goes up 8 times but the surface area only goes up 4 times. This isn't especially relevant because a larger bike rotor isn't a magnification of a smaller one in all dimensions. The cooling rate will be a lot closer if the rotors are the same thickness, e.g.

The point of the post Joe quoted had to do with leverage. Again, I'm sorry it was badly stated. I realize it reads like I think a larger rotor is no better than a small one at slowing down. It is better, but that has nothing to do with leverage.

Joe, forgive me!

joe@vwvortex

Well - in the case of his MTB brakes - the ONLY difference is rotor diameter. Caliper is the same, as are the pads and rotor thickness is the same. It's like the 12" rear rotors on my TT. They are upgraded from 10.1" stock - but the only thing different is the diameter of the rotor - thickness is the same because the same caliper and pad is used. I understand the whole heat thing - even though I'm not an engineer. When I upgraded my front brakes on the car - the balance was upset - so I upgrade the rears and balance was returned and braking was improved.

mtnbke

I just wanted to posit that this post is wrong. I'll let a mechanical engineer in the forum make the appropriate arguments. Something I'm not interested in doing. However, using larger rotors isn't just effective merely to dissipate heat. They simply work better as a brake, do to the mechanical advantage of the larger rotor size. Kind of similar to how a small cog is your go fast gear, but the large cog provides better mechanical advantage (for a given rider's wattage) to get up the big hill. To say there is no mechanical advantage, or variance, between the small and large cog is absurd. Just as it is to say there is no mechanical advantage between a small and large rotor. It ain't all about the heat.