[Originating question: "Are V-Brakes more efficient than Cantilevers"
- A previous poster answered "Yes" ]
> > > > >
> > > > > You say that V-brakes are more efficient than cantilevers.
> > > > >
> > > > > Efficiency = work input / work output.
> > > > >
> > > > > (work = force * distance moved)
> > > >
> > > > The efficiency of V-brakes and cantilevers is practically identical ( = work input - a bit
> > > > of loss due to cable friction, viscosity in the brake arm bearings, and stretching it a bit,
> > > > hysteresis in the brake arm return springs). Very close to unity for both, I'd guess.
> > >
> > > I'd guess that the upward force on the vertical cable is in fact wastefully converted into two
> > > forces at an angle to the first.
> >
> > Where's the waste? Is the work being converted into heat, sound, light, or what?
>
> Bound to be heat. As its only a few joules you'd not notice.
>
> > Answer: None of the above. They (V's & cantilevers) are equally efficient.
>
> A bold statement, see below.
>
> > > Then - unless perfectly aligned (and even then doubtful) - the two cables to the top of the
> > > cable might not be pulling perpendicular to the pivot/attatchment.
> > >
> > > > Now, if V-brakes are more efficient than cantilevers, where is the extra work coming from?
> > >
> > > Wrong way round.
> >
> > You really ought to expand this section of your argument.
>
> Cantilevers are inefficient - your force and your distance are "wasted". The same is less true for
> V brakes. So the right way round is rather than: " if V-brakes are more efficient than
> cantilevers, where is the extra work coming from?" " if V-brakes are more efficient than
> cantilevers, where is the wasted work goin in cantis?"
>
> > > > Who is supplying the free (working) lunch?
> > >
> > > Cantilevers are less efficient and V brakes aren't magical.
> > >
> >
> > In what way are cantilevers less efficient? How are you measuring or defining efficiency?
>
> Right... lets start with the part where the cable goes three ways.
> A) forces: Top one vertical, side ones at about 45 degrees to the horizontal. Do a force diagram
> and you'll find that a force F on the vertical cable is needed for a force half-F/root 2. As
> there's two, you are basically losing 30% of your force for no benefit.
>
> Force lost in %= cos angle to horizontal of two cables going to end of cantis. So, horizontal, you
> have 100% loss of that vertical force, 30 degrees 50% etc.
>
> B) Distance. You pull the vertical cable by 5mm and each side arm comes in by more or less that
> distance, but in many cases less.
>
> C) The pivots. Unless the side cables are pulling tangentially to the arc of the calipers, force
> is being wasted by pulling away or towards the
pivot.
>
> SO: With perfectly set up canti's some of your force is lost - not a leverage effect, just lost,
> pulling against pivots etc. As brake wear makes the set up different, it gets worse without a lot
> of mucking about.
>
> Even with wildly out V-brakes, you are pulling more or less tangentailly to the pivots directly,
> so there is far less of these "force wasting" effects.
>
>
>
> > But the original claim was that V's are more efficient that canti's.
>
> Yes
>
> > Mechanical efficiency is the ratio of work output to work input.
>
> Ye
>
> > You haven't shown an efficiency gain for V's over cantis.
>
> W?
>
> I have mentioned qualitatively and semi-quantitatively how in various
parts
> of a canti set up have losses in force and distance, hence work. There is hardly any such loss in
> the V-brake. So, V-brakes will be rather close to 100%, most canti setups at best 70%.
>
Come on WK, you just pulled those numbers out of thin air. And my claim was supposed to be bold!
The dominant difference between cantis and V's is that V's have a higher mechanical advantage.
That's it.
If you're going to tot up elastic deformations of the braking system and count 'em as losses, don't
forget that V's have much longer, thinner (and hence bendier) arms, and also rely on compression of
a longer section of cable housing. But, so what? These factors are irrelevant.
You note that in the case of canti's, the angle of the straddle cable decreases as increasing
pressure is applied at the lever (once the blocks are in contact with the rim). But not by much: The
stiffness of a unit length of 2mm brake cable is of the order of 8e-7 metres per Newton, which is
pretty damn stiff!
Decreasing ridge angle is of no account in any case: As the angle at the ridge of the straddle cable
decreases, the mechanical advantage of the brake system is lowered yet further, so that further
increments of force at the brake lever result in increased braking force for progressively smaller
displacements at the brake lever.
The work performed by you applying both cantis and V's for the same pad pressure on the rim is:
integral of force (applied at the brake lever) wrt displacement (of the lever). You're saying that
canti's suffer from a lower overall "stiffness", for want of a better term, than V's, and so the
Canti's lever displacement is increased. I'm not convinced: In my view, the compliance of both the
braking systems is a second order effect, ie noise.
Tim.
[I'm punting this over to RBT as well. Might get a few o' the resident engineers involved to throw
some light on the topic...]
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