Structural Reasons for Fork Shudder on Bicycles with Cantilever Brake Systems

[KootK]

At the beginning of covid I acquired a version of the bicycle shown below. It's a 1992 Miyata 1000LT. It was the best, production touring bike that one could buy in 1992 for any amount of money. It is legendary for being a sweet, smooth, "steel is real" ride and the legend could not be truer. When I ride the bike, I feel so little discomfort in my body that it's almost as though someone chopped off my head and mounted it to the handle bars. I feel nothing but joy and exertion.

Performance wise, the only non-awesome thing about the bike is the cantilever brakes. As cantilever brakes are prone to doing, hard front braking will induce a pulsating front end shudder that is very disconcerting. Before attempting to fix the problem, I would like to accurately diagnose it. Everywhere this question is asked out in the online Bike-o-Verse, you get the same "bow and arrow" explanation described in detail here: Link. Looking at that explanation as a structural engineer, I find it to be utterly implausible. Some suggested remedies can also be found at that link but I deem them to be questionable because, in my opinion, they are based on a flawed theory of causation.

So my first question here is this: what do you think of the "bow and arrow" explanation? Do you buy it? Do you share my skepticism? I have reasons for my doubt, of course, but I'm going to withhold them for a spell here in the hope of not contaminating the thought pool. I've reproduced part of the "bow and arrow" explanation below for reference.

I've got my own theory about the cause of the fork shudder which we'll get into in more detail on later. The short version is that I think that it's a function of torsional fork twist rather than the front to back fork flexing that the "bow and arrow" theory suggests.

Why does shudder occur?

Brake shudder is widespread because it’s built into the design of almost all ’cross bikes; it’s inherent to the design of a center-pull cantilever brake. To understand the reason why it happens and why reduced pad size, lots of toe-in, and a tight headset help take a look at the chart titled “Brake Shudder in cantilever brakes.”

As the brake is applied, the ground applies a force directed backward on the tire as shown, causing the fork to flex backward. Problem is, the brake cable is fixed at one end at the brake caliper and at the other end at the cable stop above the headset (as you can see in my case, at a cable hanger attached to a bolt on the stem face plate).

Think “bow and arrow” and imagine the fork between the cantilever bosses and the top of the headset is like the bow, and the cable is like the string. As the fork flexes back due to braking, the cable tightens like the string in the bow, because its two ends – the cable hanger and the brake calipers, have moved further apart. So even though you may have pulled the brake lever carefully enough to modulate it properly, as soon as the pad slows the wheel down, the fork flexes back and tightens the cable, which in turn pulls the pads harder against the rim. This in turn flexes the fork back further, which tightens the cable more, which pulls the pads harder against the rim, and so on.

Eventually, something has to give: Either the tire must slip on the ground, the rider must go over the handlebars, or the pads must break free from the rim. It is the latter that creates the shudder, the pads bind and release, bind and release, each time allowing the fork to flex back and forth and the tire to roll and stop, roll and stop. This is why the problem goes away in mud and wet sand, because the pad can break free smoothly. It is also why smaller pads with more toe-in help.

If the headset is loose, the problem is greater, because the length change between the brake posts and the cable stop atop the headset is greater as the fork moves back when the brake is applied.

 

[KootK]

Close up of the brakes. The second pic is the the Shimano CX50 system that I plan to install this summer. The CX50 is basically where evolution stopped with respect to cantis before V-brakes and discs took over. I speculate that the CX50's will improve the brake shudder if I make the straddle wire angle steep but, at present, that's a pretty tentative guess.

 

[phamENG]

Intriguing problem. The "bow and arrow" seems plausible in theory...but looking at that fork arrangement it seems to me it would have to be made of 10000ga aluminum to be flexible enough to make a significant difference.

I used to commute by bike, back before I moved to the exurbs, and I keep telling myself I'll get over to the local bike trail for lunch rides. But my bike was just a cheap Target-grade Schwinn. Never had a shudder problem that I noticed, but then again maybe that's because it's heavy as can be and probably a lot more stiff. If I squeeze the brakes hard I launch myself over the handlebars. Can you describe the phenomenon a bit so we understand better what's happening to the bike?

 

[KootK]

Can you describe the phenomenon a bit so we understand better what's happening to the bike?

It feels very much like a higher frequency version of what you feel in a car when the antilock braking does its thing. As you can imagine, it's much less appealing on a two wheeled vehicle. Does that help?

...but looking at that fork arrangement it seems to me it would have to be made of 10000ga aluminum to be flexible enough to make a significant difference.

Exactly. Your spotting that suggests that you're already on track to arrive where my head is at.

Never had a shudder problem that I noticed, but then again maybe that's because it's heavy as can be and probably a lot more stiff.

An interesting feature of the cycling world's online discussions on this is that they cite things that anecdotally fix the problem and then, retroactively, use that as evidence that they were right about the cause of the problem to begin with. One such "fix" is the switch to V-brakes. I don't buy that because:

1) There are still a few reports out there of fork shudder with V-brakes.

2) V-brakes are linear pull and require more lever end cable pull which, I believe, means that they apply more mechanical advantage to the brake pads.

3) Most importantly in my opinion, by far, is that most V-brakes got installed on true mountain bikes and hybrids which, as you suggested, tend to have sturdier forks.

 

[Compositepro]

I believe it is due the stick-slip, which originates from the difference between static and dynamic friction. The severity and frequency of the shudder is strongly a function of how rigidly fixed the the position of the brake shoes are. More like a violin string where the wheel rim is the "bow" and the brake shoe is the vibrating string. Loose fork bearings can make this shudder very severe.

 

[human909]

I don't like the bow and arrow theory.

I believe it is due the stick-slip, which originates from the difference between static and dynamic friction. The severity and frequency of the shudder is strongly a function of how rigidly fixed the the position of the brake shoes are. More like a violin string where the wheel rim is the "bow" and the brake shoe is the vibrating string. Loose fork bearings can make this shudder very severe.

Agreed.

I believe the primary source of brake shudder is stick-slip type behaviour. The brake pad is vibrating back and forth along the tangential direction of the wheel rim. Toe-in/toe out of the brake pad can promote or suppress this primary source.

The rigidity of the entire brake system will accentuate or suppress this behaviour. I conjecture that the primary source of flexibility is torsional bending flexibility of the brake arm about the brake post and possibly a minor amount in the fork itself. In the case of cantilever brakes P-Delta effects of the tension on the brake cable accentuating the torsion of the brake arm. In a V-brake the P-delta effect would have a restoring affect on the torsion of the brake arm.

They are my first thoughts on this.

Second thoughts:

One such "fix" is the switch to V-brakes. I don't buy that because:
1) There are still a few reports out there of fork shudder with V-brakes.

Agreed. I wasn't immediately aware that cantilevers are more likely to vibrate but it sounds user experience suggests that they might be. My conjecture of P-Delta affects I think offers one explanation.

2) V-brakes are linear pull and require more lever end cable pull which, I believe, means that they apply more mechanical advantage to the brake pads.

It mostly evens out as the user is going to adjust their grip to reach the required force on the brake pads. Also cantilevers have user adjustable mechanical advantage by adjusting the length of the 'bow string'.

 

[phamENG]

Some quick googling to correct my ignorance, and I see my hybrid has V-Brakes, not cantilever.

Given your description of the shudder:

It feels very much like a higher frequency version of what you feel in a car when the antilock braking does its thing.

I tend to agree with Compositepro. Since antilock braking is essentially a rapid cycling of application and release, stick-slip would likely cause similar response. The issue as I see it, is what causes the slip? You apply the brakes and have dynamic friction. If you reach a point where you stick (static friction), the friction force increases, right? Unless you start pedaling again or ease up on the pressure, it shouldn't un-stick. Unless it's coming from imperfections in the rim and minor out-of-roundness. That makes me wonder about your number 2...it seems the greater mechanical advantage offered by V-brakes would help to overcome that.

 

[3DDave]

I feel, as a long-ago cyclist, that this is just stick-slip. Setting toe-in so that as the load on the pad increases the rear of the pad sees less force than the front edge decreases self-amplification of the grip of the pad on the rim.

I recently acquired a trash bike - literally tossed to the curb - with similar brakes and it had no shudder. Mainly because the pads are about as hard as nylon, which makes stopping enough of a challenge that I'll try for new pads to go along with the chain, which I broke. I wonder if using Evaporust was a problem for the chain as it was a rather brittle fracture, but the chain was as furry as a caterpillar with rust before so it was getting replaced one way or the other. With no chain, the brake situation has become resolved.

I do recall it is more likely on plain aluminum rims than on steel rims, but the grip is better on plain aluminum.

 

[human909]

The issue as I see it, is what causes the slip? You apply the brakes and have dynamic friction. If you reach a point where you stick (static friction), the friction force increases, right? Unless you start pedaling again or ease up on the pressure, it shouldn't un-stick.

Its a bit more complicated than that and maybe describing it as stick-slip is glossing over the finer details.

Globally there is clearly no full 'stick' as the wheel is continues to rotate and the pads are globally static. If there is proper stick you'll soon know it as you are launched into a lovely somersault which also gives you a brief moment of contemplating your life choices before pain interrupts such thoughts.

Locally I suspect there is minor stick slip behaviour or at least local fluctuation of effective force due to torsion. This is a common scenario in life. The violin bow across a violin string I think is a good example. The bow is always moving the string is on average static, though there is clearly fluctuations in the lateral force being applied. Other such scenarios occur such a dragging a rubber block across a surface or even dragging a 4 legged table across the floor. In the case of the table you likely do get observable stick slip behaviour, you can see and hear the legs vibrating. But globally the table is moving at a constant rate.

Unless it's coming from imperfections in the rim and minor out-of-roundness. That makes me wonder about your number 2...it seems the greater mechanical advantage offered by V-brakes would help to overcome that.

Out of roundness and out of trueness (axial imperfections) don't seem to significantly affect heavy brake shudder in my experience. I've seen badly out of true wheels brake just fine, the brake callipers do move back left and right following the rim, but they don't induce shudder as they a made to track the rim like this.

 

[phamENG]

launched into a lovely somersault where you which also launches you into a brief moment of contemplating your life choices.

Been there. It was into the woods, too. Still have use of my legs so I guess it wasn't too bad...

I agree my thoughts are a bit simplistic. As a novice cyclist I haven't really taken the time to consider parts of my bike in a rigorous engineering sense. I started typing that before your previous response - the torsional flexibility of the brake arm sounds good and the scale makes flexibility issues more plausible than the fork itself.

 

[human909]

Actually the more I think about it the more I think the table analogy is a good description of the stick slip behaviour. Humour me and forgive me if this explanation is obvious to you.

Consider a table being dragged at a constant rate over a rough surface at a force only slight above the global static friction. Every now and again one leg is going to catch a microscopic edge and move over into stick friction. It continues to stick and bend as the table continue moving until the force & energy builds up in the bending of the leg. Eventually this force exceeds the static friction and the leg slips and springs back. This can be happening on all 4 legs and can be quite noticeable on a table with slender legs because the reduced stiffness means a lower frequency, and higher amplitude & wavelength of slip.

So again to summarise the key ingredients you need is friction, imperfections and non rigidity.

In the case of a cantilever brake, I believe the primary non rigidity is the brake arm itself bending the arm and about the post. (I earlier described this as torsional, though I believe this was an incorrect description.)

 

[phamENG]

No worries. It is pretty obvious, but more often than not stating it doesn't hurt. That's sort of where I was going with the out of roundness (though out of trueness is a better way of capturing my intent), but your statement is much more concise.

 

[human909]

No worries. It is pretty obvious, but more often than not stating it doesn't hurt. That's sort of where I was going with the out of roundness (though out of trueness is a better way of capturing my intent), but your statement is much more concise.

Thanks. My explanation was intended for all rather than you specifically. And like many things it was also intended for myself. I might think I understand something, but until I write it out or try to explain something I often find that I don't fully understand it and I learn things myself in the process.

As a novice cyclist I haven't really taken the time to consider parts of my bike in a rigorous engineering sense.

I'm an enthusiastic cyclist hence my enthusiastic posting. I've also thought a decent amount about the physics of cycling. I still wonder if Kootk has been stalking me as he had earlier singled me out for comments on a bicycle discusion.

Understanding the physics of braking actually improved my cycling significantly when it dawned on me that maximum braking most non slippery surface is achieved at 100% front brake and 0% rear brake. On asphalt in a straight line I don't use my rear brake even in emergency braking scenarios.

 

[phamENG]

Stalking does fit his profile. Watch out for some guy in yellow crocks next time you're out for a ride.

I came to the same conclusion about braking when I launched myself halfway into orbit. As a result, I rarely touch my front brake unless I need to slow down in a hurry. Even then, I always hit my rear brake hard first and then apply the front a little more calmly. Gives me peace of mind that it's taking the edge of the speed before I lock up the front wheel...

 

[human909]

I think you misread my post. I effectively DONT use my rear brake. I can elaborate why if you wish.

Though your approach is definitely common and probably safer until you get adept with feathering the front brake. (Many people on bikes wear out their rear pads far faster than their front. I'm the opposite as I barely touch the rear brake.)

 

[phamENG]

Nope - read it right. I was referring to the 100% effectiveness of the front brake. It scared me...

I've gotten a lot better about feathering it since then, but haven't changed things. I'd be happy to hear the elaboration. Might also help me understand the dynamics going on it KootK's problem a little better.

 

[human909]

I've gotten a lot better about feathering it since then

Yeah I got better at feathering since I forced myself only to use the front brake. When I first tested the approach out I did it in an empty car park at low speed and just practiced it. Now since it is almost the only brake I use my muscle memory is much improved.

I'd be happy to hear the elaboration. Might also help me understand the dynamics going on it KootK's problem a little better.

This elaborates on it well:

https://en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamics#Braking

As per the wiki. "For an upright bicycle on dry asphalt with excellent brakes, pitching will probably be the limiting factor.". Essentially overturning about the front wheel is the limiting factor in braking. Thus maximum braking is achieved at this limit point. At this limit point all weight is on the front wheel and zero weight is on the rear. Thus you can get ZERO effective braking from the wheel wheel at maximum braking.

Naturally you don't want to site at the tipping point of 100% theoretical braking. But with practice getting close is quite possible and if you are close you want VERY little (aka zero) force on your rear brake as you could readily initiate a skid there which will reduce your 'yaw' stability.

All bets are off on loose surfaces and your are back to due handed brake modulation. I do mountain bike and I'm probably 70-80% front 20%-30% rear...

 

[dold]

maybe something like this? And oscillates between bites and slaps until user releases brake? Seems like the bowstring theory would require a huge amount of deflection of the axle relative to the brake mount relative to the head tube to make any sort of noticable difference in cable tension. Like, a catastrophic amount of deflection. I bet against the bowstring theory.

My 'deformed shape' dashed lines are just general. The deformation is probably mostly in the brake assembly joints and not so much the fork itself?

 

[human909]

Exactly that. Far clearer in pictures.

It also helps show why having the break pad "toe in" helps prevent shudder. (You want the pads front of the pad touching the rim before the rear as then you avoid the "bites" section of that diagram.)

 

[dold]

One such "fix" is the switch to V-brakes. I don't buy that because:...

I suggest that v-brakes will disguise the problem based on where the cable pull line of action is relative to our....kern...of braking pressure? . I'd guess this behavior is just inherent in this type of design. The assembly seems about as stiff as me rotating my wrist about the axis of my forearm, holding a toilet plunger, trying to catch a passing car.