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.
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.
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
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
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
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?
The typical efficiency of a brake is >95%, . . . .
Thank you for that post. Could you share the source of the graph, please?
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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?
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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?
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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.
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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.