Why are there different brake cable pull ratios?

[Twilkes]

Rode V-brakes for the first time in a couple of years yesterday, and yes they'd just been set up and one of the brake calipers was new, but great stopping power and I didn't notice that I was missing out on any modulation. A recent thread here said that V-brake pull ratio is 1:1, whereas road caliper is somewhere up near 4:1 i.e. you have to move the lever four times as far to get the same movement in the caliper. I think the pull ratio was even changed when the cables were routed under the handlebar tape, was it increased or reduced? Is the increased pull ratio purely to increase modulation, or are there other reasons?

By contrast my mechanical discs feel like they have too much modulation and not quite the same stopping power at the other end - would they have benefitted from a lower pull ratio, maybe 2:1, rather than the same as road calipers?

To keep top braking power I would need to regularly tweak the pads as the tolerances are so fine, fractions of a millimetre it seems. I know people recommend compressionless brake housing, which I might try next time the outers need replacing, but they seem like a faff to cut and aren't as flexible in routing, especially around the handlebar bend.

 

[fossyant]

It's not as marked difference from 4:1 to 1:1 but just enough to say, not make the switch from cantilever to v brake possible. As for stopping power, that's all down to quality of parts, pads, rim condition. My wife's hybrid stops on a sixpense with basic shimano levers and tekro v brakes. Pads make a huge difference.

The only bike I have that's not so good stopping was my old MTB with canti's, but that's been massively improved with new wheels (others wore out) and new pads.

The Tekro mechanical discs on my son's bike are fine, stop well enough, but aren't a patch on the hydraulic brakes on mine and MrsF's MTB's. Even they feel very different, shimano SLX is a bit on/off so modulation is finer, mine is Guide RS which have more modultion, but it's very 'fine', unlike mechanical - remember these are designed for single finger braking.

 

[keithmac]

I'd always go Hydraulic disk brakes personally.

 

[presta]

When I bought my Horizon 21 years ago I was a bit unimpressed with the brakes after my old Raleigh racer, (cantis with aero levers compared to callipers with non-aero levers), so I decided it would be an interesting and useful pastime to see if I could improve them. I quickly realised that tinkering around blind wasn’t going to get me anywhere fast, so I picked up a pencil and paper to find out what matters and what doesn’t.

A fair bit of maths later I discovered what I should have realised in the first place: Shimano aren’t as wet behind the ears as I assumed, and also something a bit less obvious: the difference between the brakes is not where you think it is.

The typical efficiency of a brake is >95%, and higher still for the brake lever, but the cable is a different kettle of fish: a rear cable can be as little as 20% efficient. So, if you’re on a quest for brake efficiency there’s only really one game in town: what affects the cable? Bends, yes, but the other factor that has a critical effect on cable efficiency is cable travel. About half your effort goes in friction, but another half goes in stretching the cable, which depends on tension, and hence travel. It turns out that the optimum travel for maximum efficiency is about 60mm, so for all practical purposes you’re always going to be below the optimum, and anything you can do to increase travel will improve efficiency:

So that’s the difference between my new and old bikes: the aero levers only pull 10mm of cable and the non-aero ones pull 12mm, and that’s also why V-Brakes are so efficient: they use a cable pull of ~30mm. Different brakes have different efficiencies, but that’s due to the effect they have on cable travel, and not a difference in the efficiency of the brake itself. The reason that aero levers pull less cable is that the load arm of the lever is rotated 90° relative to the non-aero lever, so it has to be shorter to fit it in under the hood. If you want to look like Bradley Wiggins with your aero levers, Shimano will make what you want, but there’s a price to pay.

(Note that all this assumes you’re using a lever and brake that are compatible with each other, there’s no point increasing cable pull at the lever if that makes it incompatible with the brake.)

Meanwhile, there are bends in the cable, and everyone knows that tight radii and longer cables increase friction, don’t they? Well, yes, sort of….

The ratio of tension out to tension in is given by

Where µ is the coefficient of friction, L is the length, and R is the radius.

So friction losses do increase with length and reduce with increasing radius, but the eagle-eyed will have noticed that L/R is just the angle of the bend in radians, so we’re actually left with the result that the losses in a cable bend depend only on the angle of the bend, θ, because for any given angle, L and R are not independent:

A short cable round a tight radius will have the same losses as a longer cable round a gentler radius if the cable materials have the same coefficient of friction, and the angle of bend is the same, so given that the angle of a bend is mostly determined by the frame, the options for reducing friction by adjusting cable routing are fairly limited.

 

[Twilkes]

When I bought my Horizon 21 years ago I was a bit unimpressed with the brakes after my old Raleigh racer, (cantis with aero levers compared to callipers with non-aero levers), so I decided it would be an interesting and useful pastime to see if I could improve them. I quickly realised that tinkering around blind wasn’t going to get me anywhere fast, so I picked up a pencil and paper to find out what matters and what doesn’t.

A fair bit of maths later I discovered what I should have realised in the first place: Shimano aren’t as wet behind the ears as I assumed, and also something a bit less obvious: the difference between the brakes is not where you think it is.

The typical efficiency of a brake is >95%, and higher still for the brake lever, but the cable is a different kettle of fish: a rear cable can be as little as 20% efficient. So, if you’re on a quest for brake efficiency there’s only really one game in town: what affects the cable? Bends, yes, but the other factor that has a critical effect on cable efficiency is cable travel. About half your effort goes in friction, but another half goes in stretching the cable, which depends on tension, and hence travel. It turns out that the optimum travel for maximum efficiency is about 60mm, so for all practical purposes you’re always going to be below the optimum, and anything you can do to increase travel will improve efficiency:

View attachment 640129

So that’s the difference between my new and old bikes: the aero levers only pull 10mm of cable and the non-aero ones pull 12mm, and that’s also why V-Brakes are so efficient: they use a cable pull of ~30mm. Different brakes have different efficiencies, but that’s due to the effect they have on cable travel, and not a difference in the efficiency of the brake itself. The reason that aero levers pull less cable is that the load arm of the lever is rotated 90° relative to the non-aero lever, so it has to be shorter to fit it in under the hood. If you want to look like Bradley Wiggins with your aero levers, Shimano will make what you want, but there’s a price to pay.

(Note that all this assumes you’re using a lever and brake that are compatible with each other, there’s no point increasing cable pull at the lever if that makes it incompatible with the brake.)

Meanwhile, there are bends in the cable, and everyone knows that tight radii and longer cables increase friction, don’t they? Well, yes, sort of….

The ratio of tension out to tension in is given by
View attachment 640133
Where µ is the coefficient of friction, L is the length, and R is the radius.

So friction losses do increase with length and reduce with increasing radius, but the eagle-eyed will have noticed that L/R is just the angle of the bend in radians, so we’re actually left with the result that the losses in a cable bend depend only on the angle of the bend, θ, because for any given angle, L and R are not independent:
View attachment 640134
A short cable round a tight radius will have the same losses as a longer cable round a gentler radius if the cable materials have the same coefficient of friction, and the angle of bend is the same, so given that the angle of a bend is mostly determined by the frame, the options for reducing friction by adjusting cable routing are fairly limited.

So what's the reasoning for less cable pull on the road bike levers, is it just the shape and positioning of them that means they will never be able to pull as much cable as a flat bar V-brake lever, they just can't design in enough pivot to the mechanism?

 

[Ajax Bay]

The typical efficiency of a brake is >95%, . . . .

Thank you for that post. Could you share the source of the graph, please?
"The typical efficiency of a brake is >95%." Please define "efficiency"? Is this the force exerted on the rim divided by the force exerted on the lever?
"A rear cable can be as little as 20% efficient." Do you define this as the force exerted by the cable on the caliper divided by the force exerted on the cable at the lever?
"About half your effort goes in friction, but another half goes in stretching the cable, which depends on tension, and hence travel."
There are going to be friction losses but am surprised by "about half". Where have you got this from? For a rear brake cable of 1m length, how many mm does the cable stretch (elastically) and does it matter? "Effort" implies "work": presumably this is force (cable tension times the amount of travel). So it's not "hence " travel. Tension and travel are multiplied to get 'effort'.
The force applied by the hand on a lever times the distance that lever travels = cable tension (varying/increasing) times the distance cable travels x efficiency (friction losses in the brake pivot). Given that, depending on the design of the brake lever, the lever travel is limited, a longer cable travel implies a mechanical advantage is needed which will reduce the force (and therefore tension) in the cable. These considerations affect the choice of brake calipers/V-brakes as these design characteristics need to match.
"It turns out that the optimum travel for maximum efficiency is about 60mm." I assume you get this from the graph so it would be good to read the context and definitions used for that graph. How can the curve be randomly declined beyond the 60mm point without any other datapoints?
If using cable operated disc brakes, (agreeing with fossy) it makes entire sense to use compressionless outers as the initial lever movement is not spent compressing the outer and can be used to operate the caliper: the modulation is surely better.

 

[Ajax Bay]

I have dug up an old post and rehashed to offer some quantitive analysis, in case anyone is interested.
Cables stretch. A brake outer compresses far more than the cable stretches.
All materials stretch when a strain is induced therein. A brake/gear cable stretches every time it is operated and returns to its original dimension when the lever is released (removing the tension). They never breach their elastic limit so there is no plastic stretch, ever.
Stainless steel cables do not stretch any more than normal when new.
1) The length of pull on a brake cable with a STI (brake lever) is about 9mm max (ie from 'resting' position to lever touching the (drop) bar. Proper adjustment means that full strength braking is effected (with my pads and pad/rim gap adjustment) at 5mm of lever operation (ie with 4mm 'spare').
2) Wire ropes/cables do not possess a Young’s Modulus but an ‘apparent’ Modulus of Elasticity can be used and the various generic steel cable types have working Moduli of Elasticity. So using Hooke's Law:
Elastic Extension = FL/EA where F = load applied (N), L = rope length (mm), E = elastic modulus (N/mm2),A = metallic cross section (mm2)
F The 'full' (ie 4 fingers in opposition to the thumb) grip of an adult is in the range 250N-500N. Even from the drop bars (the strongest braking position for the hand (and for other reasons)) the full grip cannot be exerted so, say, a force of 200N can be applied. The mechanical advantage of the levers is 3 (vector distances from axis are 54mm and 18mm) so this implies an applied force of 600N on the cable (ie max cable tension).
L 1300mm is a typical rear brake cable run for a normal bike (580mm TT) and cables under tape on drop bars. Hybrids/MTB cable run will be a little less.
E General Elastic-modulus of the cable construction
Spiral strand, type 1x7 EM = 126000
A The area of a 1.6mm dia brake cable = 2.0mm2
3) That gives an elastic extension of 3.1mm for a 600N load on a rear brake cable.
I have made assumptions to get this result: I hope they are valid (for the useful level of accuracy).
PS I had a great ride out in the sunshine over the Severn Bridge and to Usk and beyond yesterday.

 

[T4tomo]

So what's the reasoning for less cable pull on the road bike levers, is it just the shape and positioning of them that means they will never be able to pull as much cable as a flat bar V-brake lever, they just can't design in enough pivot to the mechanism?

The pull at the lever is different because the pull at the caliper pivot is different. Just look at a v brake and a road caliper - mechanically they work very differently.

That is why, as is oft stated, you must match the lever to the brake type, and why swapping a bike between flat and drop bars is more complex and costly than some people think.