How to brake discs Vs Rims

[Brucey]

I think that the average temperature can be less but the peak temperature may be more (on the rim's surface anyway). This may reduce the risk of problems that arise when the heat has long enough to soak through the structure of a rim.

cheers

[roubaixtuesday]

Re 'forced convection cooling'; the exact heat transfer depends on the flow conditions and they can vary wildly. Also the complete expression contains terms which vary independent of the speed, with the speed, the speed squared, the speed cubed etc, the relative importance of which vary...... hence I said 'roughly'.
cheers

Sure, but heat transfer always increases *less* than linearly with speed.

It's not speed squared or speed cubed, it's typically speed to the power (4/5) or something like that.

As in the graph I posted, note the curve is convex rather than concave. That's always the case for forced convection heat transfer with velocity, regardless of the varying conditions you rightly highlight.

[Brucey]

no, certainly not 'always';



measurements are often taken on surfaces that are designed for good heat transfer (i.e. cooling) and these are intended to work efficiently at low airspeeds and may be limited by conduction through the bulk, boundary layer effects, you name it.

The heat transfer in other cases may be limited by other things. In particular it is worth noting that the heat is generated in the surface of the rim before it is conducted into the bulk; for this reason alone improved cooling is very likely to have a disproportionate effect on the average rim temperature.

cheers

[roubaixtuesday]

what's the source for your graph Brucey?

[Brucey]

what's the source for your graph Brucey?

its taken (fairly randomly) from a scientific journal. You will see plenty like it if you study fluid dynamics and heat transfer processes. [Note that the plot isn't quite as it appears to be; the horizontal scale is actually a log scale.]

cheers

[roubaixtuesday]

its taken (fairly randomly) from a scientific journal.

It is good practice to provide a citation. For very good reasons, as we shall see.

Here it is, through the miracle of google.

https://www.researchgate.net/publicatio ... t_Stamping

Now c'mon Brucey, read the paper. This is a very specialised case where the wall viscosity changes radically with flow due to the ultra high temperatures (950 degrees C!) It's not remotely relevant to the case at hand.

I happily caveat "always," and replace with "heat transfer always increases *less* than linearly with speed for flows similar to those observed around bicycles"

There may be other exceptions (supersonic?), but the point remains: changing speed on a bike will change heat transfer less than linearly. This is in contrast to drag, which will always change more than linearly.

You will see plenty like it if you study fluid dynamics and heat transfer processes.

I challenge you to find a single one, other than for some specialised extreme circumstance such as the one you've posted here.

[Brucey]

as I mentioned earlier the heat transfer rate depends on a lot of things. This includes whether the flow is generally turbulent or indeed whether the boundary layer is turbulent, whether the flow remains well attached to a (blunt-ish) wheel rim or not. There is a school of thought that bicycle wheels move around enough laterally (in even an otherwise steady airflow) that the mean condition is most closely approximated by a transient flow state not a steady state; this will impact heat transfer as well as drag.

Also as I previously mentioned heating of wheel rims is a special case; the situation is additionally dynamic in that heat is developed at the surface before it is conducted into the bulk, therefore improved cooling is likely to have a disproportionate effect on the overall rate of heat transfer into the air and therefore the average rim temperature; getting the heat out of the rim when it has the maximum temperature differential to the surrounding air is definitely the best idea.
[I think even if the cooling rate were constant around the rim circumference, the peak rim temperature difference vs ambient at the brake ought to be about pro-rata with the heated vs unheated length of the rim; i.e. it is likely to be a big spike].

Heat is transferred into the air differently in different parts of the rim and under transient conditions differently vs steady state; also even under steady state conditions, different rim extrusions allow the brake track to be at a different temperature vs the average in the rim, because the part of the rim that is in contact with the tyre is not well cooled, and the heat transfer from the other air-cooled parts of the rim is likely to be limited by the rate at which the heat can be conducted into those rim areas, which will vary with the thickness of the extrusion in those areas.

Note also that if the heat, under transient conditions, takes one or two seconds to conduct to the rim well (where it does most harm, and NB this is not the same as conducting away from the surface per se) then it certainly isn't pointless to pulse or alternate between the brakes at one second intervals rather than drag the brakes; this increases net air cooling for any given mean rim well temperature.

Note further that the freshly heated part of the rim sees high speed airflow (about double the speed of the bike) briefly , provided the brake is somewhere near the top of the wheel. Once the freshly heated part of the rim is close to the road, the average air speed over the rim is close to zero and the heat transfer rate into the air is likely to drop dramatically. Thus having a rear brake on the chainstays is probably a daft idea, in heat transfer terms, anyway. Likewise having a front brake on the rear of the fork crown, together with a fork acting as a shaped duct, is likely to increase rim cooling two ways; firstly by providing more time at high temperature/airspeed (simply by being 'further round' on the wheel), and second by improving the cooling conditions local to the hottest part of the rim.

cheers

[Scunnered]

As this is a difficult problem to solve, it is worth considering the limits.

[*]No braking at all - brakes do not heat up - hill descended in shortest time
[*]Maximal continuous braking (slowest speed at which can remain upright) - brakes barely heat up due to extended time to dissipate heat - hill descended in longest time

At any speed between these extremes the brakes (rim/rotor) will heat up and some particular speed will correspond with the highest brake temperature. Calculating that speed involves some serious equations which I will not attempt now

Whether "pulsed" braking gives lower brake temperatures or not may just depend on whether the average speed of descent is higher or lower than the speed for which continuous braking is being compared with.

[roubaixtuesday]

Brucey,

I agree it's complicated.

However, it remains that heat transfer will increase less than linearly with speed, not to the cube of speed as asserted earlier.

Scunnered,

I agree in all aspects.

[Vorpal]

Brake pads & discs or rims will achieve a steady state temperature at some point, and not just keep increasing. The main problem, of course is that temperature could be high enough that the tyre or inner tube will fail before the steady state is achieved. Speed, however, also makes a big difference to cooling, as the increased air flow helps alot, so the heat transferred to a rim or disc could actually be lower for someone travelling faster, even if more braking energy is required to maintain the speed.

It also makes a difference how quickly one brakes. IMO, having the brakes somewhat on for long periods to maintain a steady speed is far worse than letting the bike freewheel, then braking fairly hard to get the speed down, then letting it freewheel again.

There's quite alot of work done on the surface temperature of automotive disc brakes. Although the systems are somewhat different, the principal is the same, and I would expect that bicycle disc and rim brakes to behave somewhat similarly, even if the scale is different. Folks who are interested can certainly find this information on the internet.

I would expect pulsing (on-off-on-off quickly) to help keep the temperature down significantly, simply because the air running between the pads and rims/discs will cool them.

If I have a long descent, I alternate between brakes, letting each one cool in turn while I use the other, for a few seconds at a time, and freewheel in between.

p.s. I am an engineer, and specialized in heat transferr & fluid dynamics in my bachelor degree, but haven't used it much professionally.

p.p.s. one of those books about the science of the bicycle had a chapter on braking that included some information about the heat transfer and how speed affects it. I don't remember which book, though. I checked it out from the library, so I can't check now.

[roubaixtuesday]

I would expect pulsing (on-off-on-off quickly) to help keep the temperature down significantly, simply because the air running between the pads and rims/discs will cool them.

I think that's unlikely. The area of a brake pad is probably two orders of magnitude less than the rim. The extra heat loss will be very small from the overall system, I think.

p.s. I am an engineer, and specialized in heat transferr & fluid dynamics in my bachelor degree

Me too.

[Brucey]

I would expect pulsing (on-off-on-off quickly) to help keep the temperature down significantly, simply because the air running between the pads and rims/discs will cool them.

I think that's unlikely. The area of a brake pad is probably two orders of magnitude less than the rim. The extra heat loss will be very small from the overall system, I think.

from that effect alone, yes, but in terms of getting the heat into the air from the rim more effectively via any means, probably not; if you pulse- brake (say, twice as hard but for half as long) then the freshly heated parts of the rim surface could be (briefly) about twice as hot as they would be otherwise, thus will be cooled more effectively by the surrounding air.

cheers

[roubaixtuesday]

the freshly heated parts of the rim surface could be (briefly) about twice as hot as they would be otherwise, thus will be cooled more effectively by the surrounding air.

Hmmm. I'm not sure what you mean by "twice as hot". Doubling the temperature difference from air to rim from a brief application of brakes seems very unlikely.

Let's consider the mechanism. It would require a temperature difference across the rim. Let's say you need 20 degrees to make your mechanism significant (the outside of the rim is 20 degrees hotter than the inside).

Aluminium has a thermal conductivity of around 200 Watts per metre per degree. Let's guess the rim is 4mm thick.

20 degrees would drive a thermal flux of (200W/mK)*(20K)/(4mm) = one million watts per square metre

The area of the braking surface of a rim (622mm diameter, say 10mm depth) is ~0.02 square metres.

So the heat flow through per braking surface needs to be 0.02*one million = 20kW per surface, 40kW in total.

A 100kg cyclist descending a 1 in ten hill at 10 metres/second (36kmh) is descending at 1 metre per second vertically so needs to dissipate 100*9.8*1 = 1kW, a factor of 40 less.

Unless I've made an arithmetical error (which is very possible) we can conclude there is no significant effect from the surface of the rim being hotter than the bulk.

Corrections welcome.

[Brucey]

the steady state case is not the one to be considered, I think.

I would be more appropriate to consider the local increase in temperature in that volume of the rim which is heated in an appropriate time period. This volume will vary with the speed of the bike, the width of the brake block and the thermal diffusivity of the rim material.

Thus if, say you are doing about 10 m/s on a 27" wheel then a brake block (say ~50mm long and ~10mm wide) will heat each part of the rim surface for about 1/200th of a second, to a depth that can be estimated (eg using the thermal diffusivity). As soon as the heated part of the rim is exposed to the air it can be cooled by the air, and this will be most effective of course when the temperature differential to the air is highest.

If you are dumping 1kW into a brake (as previously described), and the depth is (say) 50um, this suggests that the surface of the rim is heated to an 'exit temperature' of +80C (above ambient or the 'entry temperature' of an already heated rim) as it leaves the brake block. This seems a realistic estimate in that the temperature is anyway limited by incipient melting in the brake block; if this temperature is reached (even momentarily) then the brake blocks starts to melt and it is this which makes the noise and alerts you to the fact that things are starting to get too hot. Melting/softening points of typical brake blocks are estimated to be between about 120C and 170C.

Experience tells you that if you just start to hear 'the melty noise' as you pull to a halt using most of the braking power available, the rim bulk (~entry) temperature will be hot enough to perhaps cause a blister if you touch it but not so hot that water will actually boil. So between 55 and 95C maybe. This corresponds well with the idea that a ~+80C exit temperature is created, in that this would usually be enough to cause the brake block surface to melt/soften.

In any event if you halve the brake power the exit temperature increase will be about half as much, so +40C instead of +80C, and this means

a) the possibility of getting this heat into the air instead of conducted into the bulk of the rim is greatly reduced. [ Note that the heat transfer coefficient is increased at speed but in addition the exit/rim surface temperature is greatly increased by hard/pulsed braking, so I'd expect the rate at which the brakes transfer heat into the air to be increased more than you might expect otherwise, i.e. it can be a double-whammy if you pulse-brake at speed] and

b) the safety margin is actually reduced, in that you will get warning via incipient melting when the rim bulk temperature is about 40C higher than it would be otherwise.

By the same token if you reduce the brake power to just 250W, by the time you hear the sounds of incipient melting, the rim is liable to be about 60C hotter than if you start to hear the same noise when braking at 1kW. At this point the tyres will be in considerably greater danger of moving around on the rim or failing altogether.

Similar arguments apply to the duration of the braking pulse; if the pulse is short then the rim well (and therefore tyre/tube) temperature will always be considerably lower than the rim surface (entry) temperature; i.e. the heat doesn't have enough time to diffuse into the entire rim, making the brake surface noticeably hotter than the bulk of the rim. Again this effect suggests that shorter pulses are better/safer than longer ones, provided you are alert to incipient melting as you should be.

[Note also that if a rim weighs 500g and is subjected to 1kW for a minute or so, it would -without air-cooling losses- be at about +120C above ambient. This gives a good impression about the actual rates of heat loss from rims via air-cooling; actual rim temperature rises are only about half this, so air cooling may account for about 500W, as a very rough guess.]

cheers

[roubaixtuesday]

I would be more appropriate to consider the local increase in temperature in that volume of the rim which is heated in an appropriate time period. This volume will vary with the speed of the bike, the width of the brake block and the thermal diffusivity of the rim material

The calculation above (caution: back of fag packet, may contain mistakes) shows that the heat loss through the rim by conduction from any such effect is ~40x higher than the increased heat loss to atmosphere.

Interesting figures on softening points of brake blocks.