Bicycle Mechanics - Mechanical Advantage

As I was reading Sheldon's article about Cantilever brakes
http://www.sheldonbrown.com/cantilever-geometry.html#aa
I became a bit confused reading these 2 seemingly contradicting passages.

"The more mechanical advantage you have, the closer the brake shoes will be to the rim at their rest position."

"On touring bikes with high-mechanical-advantage "æro" brake levers, excessive mechanical advantage may cause the brake to run out of lever travel, so that the lever hits against the handlebar. Shimano makes an extra-wide cable yoke for such applications, but you can achieve the same effect by lengthening the transverse cable, unless the bike has such a small frame that you run out of room."

How can the brake run out of lever travel if excessive mechanical advantage means that the brake shoes are closer to the rim at their rest position?

Because to get greater mechanical advantage, the lever moves more to get the paads to move an equal distance.
Think of your gearing. In low gear you have greater mechanical advantage but you have to pedal more to get the wheel to rotate the same distance as a higher gear.
Brake lever "squeeze" is akin to gearing.

I'll try to illustrated for you

Let put fictional made up number.

Let say brake A when you move the lever 10cm it move the brake pad 2mm

Brake B when you move the lever 20cm it move the brake pad 2mm (or move the lever 10cm and it move the brake pad 1mm)

So brake B has twice as much mechanical advantage as brake A.

You'll notice that in brake B for the same lever movement the pad move less, only 1mm vs 2mm so you need to position the pad closer to the rim since it will only move 1mm

Now let say you go crasy and want to make a brake C with 100X more mechanical advantage than A

So you need to move the brake 1000cm (10cm X 100) so the pad move 2mm (or if you move 10cm the pad will move only 0.02mm)

Now you see the pad need to be at 0.02mm of the rim. That unrealistic. You need a wheel that perfectly true within < 0.02mm tolerance not realistic.

So if you position the pad farther than 0.02mm from the rim with only 10cm brake lever travel you will not have enough reach to make contact with the rim.

Since with brake C 10cm brake reach will only move the pad 0.02mm.

Hence C which has 100 times more mechanical advantage then A but C will run out of travel because realistically it's very very hard to put the pad at 0.02mm of the rim without the pad rubbing against the rim some time or an other since it very very hard to make the rim perfectly true <0.02mm tolerance so you don't have enough brake travel to put the brake pad at a realistic position

Alright. But then I read this:
"Æro levers are generally an improvement over the older type. The pivots are located differently, making it possible to get fairly serious braking from the position where the rider's hand is on top of the lever hood. Non-æro levers would permit the use of this position for gentle deceleration only."
That means that brake levers don't have to move much to get 'serious" braking. See the contradiction?

Alright. But then I read this:
"Æro levers are generally an improvement over the older type. The pivots are located differently, making it possible to get fairly serious braking from the position where the rider's hand is on top of the lever hood. Non-æro levers would permit the use of this position for gentle deceleration only."
That means that brake levers don't have to move much to get 'serious" braking. See the contradiction?

The amount of cable pulled for a given motion of the brake is fixed. How much force you have to apply varies depending on your hand position. Brakes changed their pivot points to allow for better leverage from the hoods.

The more mechanical advantage you have, the less the brake calipers move for each complete stroke of the brake lever (eg, relesed to all the way to the bars). So if you don't run the calipers really close to the rim, you can run out of lever.

How can the brake run out of lever travel if excessive mechanical advantage means that the brake shoes are closer to the rim at their rest position?

Because that's not what mechanical advantage means. (Geez, does no one take basic science in school any more? Remember simple levers?) Sheldon wasn't giving you a definition, he was showing you a side effect. Try this version:


"The more mechanical advantage you have [at the shift lever], the closer the brake shoes will have to be to the rim at their rest position."

Bolt cutters are a good example of this. Bolt cutter handles require quite a bit of travel while its cutter blades only squeeze just a few millimeters.

Awesome, I guess it was a semantic misunderstanding. Thanks for your help.

yeah, and always remember, that the angle of the dangle is equal to the sag of the bag.

Alright. But then I read this:
"Æro levers are generally an improvement over the older type. The pivots are located differently, making it possible to get fairly serious braking from the position where the rider's hand is on top of the lever hood. Non-æro levers would permit the use of this position for gentle deceleration only."


By the way, this particular point is an opinion rather than definitive.