More on disk brakes and quick release failure



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In article <[email protected]>, James Annan <[email protected]> wrote:

> [email protected] wrote:
>
> >
> > This never involved disk brakes, it was always with reference to bicycles with rim brakes and
> > conventional QR's. These do not loosen from use as John Howard claimed in his expert testimony
> > that brought "lawyer lips" to bicycling.
>
> Just out of interest, I wonder if the much reviled John Howard had used disk brakes himself prior
> to his testimony.

That was quite a while ago- I doubt he'd had the opportunity.
 
[email protected]:

> Jose Rizal writes:

> > Well, Answer (Manitou forks) gives the reason as the cast lower legs of their non-DH specific
> > forks are not designed to handle the "bigger leverage of the larger rotors". Not sure what this
> > means, but it may have something to do with the strength of the mounts for the calipers, which
> > are integral to the lower legs.
>
> Whoa! The larger the disc, the smaller the forces, aka rim brakes (also disk brakes o a sort).
>
> > What of the forces in the mounts, though? My understanding of it is that the moment about the
> > axle of the caliper force on the rotor (say Fc) must equal the sum of the moments about the axle
> > of the forces acting on the two mounts (F1 and F2). That is, Mc = M1 + M2. If a larger diameter
> > rotor is used, Fc is less and its moment arm is longer, while keeping Mc the same. Although Mc =
> > M1 + M2 still, the mounts are longer (ie the caliper is further away from the axle) and this
> > will result in a greater bending moment for each of the two mounts. What have I missed in this
> > analysis?
>
> Whoa! The larger the disc, the smaller the forces, aka rim brakes (also disk brakes o a sort).

Yes, but the moment about the axle is the same. Consider a free body diagram, and assume that the
caliper mounting posts are parallel to the radial line from the axle to the center of the caliper
contact area. This does not affect the validity of the analysis since the mounting posts can be
looked upon as moment arms. Also assume that the caliper center is exactly between the tips of the
mounting posts.

Now in the case of a small rotor with diameter Ro, the force exerted by the caliper Fo is taken up
by the two mounting posts. Assume that each post takes up exactly half the caliper force, or 0.5*Fo.
The moment about the base of each post will then be

1) 0.5 * Fo * Lo,

where Lo is the length of the mounting post.

Now consider the case of a larger rotor, say R1. Assume that the mounting posts are lengthened by
the same amount as the increase in radius for the larger rotor, that is,

2) R1 - Ro = L1 - Lo

and the posts are still parallel to the axle-caliper radial line.

Since the moment about the axle needs to be the same as with the smaller rotor, then

3) F1 * R1 = Fo * Ro.

and so

4) F1 = Fo * Ro/R1.

The moment about the base of each post will now be

5) Moment = 0.5 * F1 * L1 = 0.5 * Fo * Ro/R1 * L1

But L1 = (R1 - Ro + Lo) from 2) above, so the moment on each post is

6) Moment = 0.5 * Fo * Ro/R1 * (R1 - Ro + Lo).

Plugging in typical numbers show clearly that the larger the disc brake rotor, the greater the
moment exerted on the fork leg brake mounts.

Example: let Ro = 80mm (160mm rotor), Lo = 15mm, and R1 = 330mm (26" rim diameter)

Plug into 1) and 6) above and it's clear that the moment on each mounting post is about 6 times
greater for the larger rotor than for the smaller rotor.

Hence I believe the fork manufacturers' recommendation against using larger rotors.

Unless someone shoots holes in the above analysis.
 
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