Z, Thanks for this exposition. I understand this approach. The downside of it is that to get it right you must do some trig to keep track of the variation in the tangent force magnitude. The tension in the straddle wire increase the flatter it gets. Of course you never get near the theoretical infinity but it does increase, and to get the right answer from your approach you have to keep track of that and balance it correctly with the variations of alignment with your axis tangent.
Please consider another approach that I think is simpler, particularly if you want qualitative insight. Keep the other half of the brake in the back of your mind. It's important because it balances the side forces that are inherent in any feasible straddle cable. In stead of decomposing the cable force into axial and tangent (or perpendicular), go with up and sideways. You do this with both the straddle and the arm. The vertical component of tension in the two halves of the straddle wire must balance the tension in the brake cable. Call the brake cable tension T, then the up force one each brake arm is T/2. This is true regardless of what the straddle cable height is, and that fact is what gives this approach its advantage. Now unless the straddle cable is vertical there will be a side force towards the centerline of the bike. The flatter the cable the larger the force. To get the torque about the pivot post, decompose the brake arm axis into sideways and upwards components (dx and dy if you like). The net torque is the sum of the up force times the sideways offset plus the side force times the upwards offset. The part of the torque from the up force times the sideways offset does not change when you alter the straddle wire height. The part of the torque from the side force times the sideways offset always helps and always get larger when you lower the straddle wire. Q.E.D. Furthermore, if you look at the sideways and upwards offset lengths of different brakes in light of what you know about the forces induced on them by the straddle cable you get an accurate intuitive sense of what is going on. With 720s or Neo-Retros the sideways offset is sizable and the vertical offset is small. Because of this these brakes are relatively insensitive to changes in straddle cable height. With low profile brakes like the Paul Touring model the sizes of the sideways and upward offsets are about reversed. They need the sideways force from the flatter straddle cable to generate significant torque, and the torque you get depends quite a bit on the straddle height. High profile cantilevers do not need a high straddle wire to maximise leverage, on the contrary raising the straddle wire always reduces the leverage. High profile cantilevers need high straddle wires to clear the tire/fender/rack. Luckily the leverage they get is relatively insensitive to straddle wire height so raising the straddle to clear whatever you need to clear is not a problem. On Friday, February 20, 2015 at 10:42:22 PM UTC-8, Z wrote: > > Ted, > > Envision one half of a cantilever brake setup. There is an axis between > the points where the straddle cable attaches and the brake pivots. We'll > call this The Axis. Now envision a force vector along the straddle cable. > If you conceptually break down that vector into components which are 1) > perpendicular to The Axis and 2) parallel to The Axis, you will realize > that any force parallel to The Axis will be working against the rigidity of > the cantilever brake mount. So, you really want to maximize former vector > component... that is, by applying the straddle cable's force perpendicular > (90 degrees) to The Axis. Of course, you want to be maximizing this force > vector as the brake pad is touching the rim. > > It's true that you can apply a great deal of tension to a straight cable > by applying a force perpendicular to its axis. However, the theoretical > infinite tension doesn't really affect braking when you consider the brake > pivots (and the steel frame to which they attach) resisting most of that > tension, which is what you would likely achieve with a high profile > cantilever and shallow straddle cable angle. > > > Z > > On Friday, February 20, 2015 at 7:35:52 PM UTC-7, ted wrote: >> >> Michael, >> >> I am confused. >> Are you saying that not enough mechanical advantage causes the lever will >> bottom out, or that too much will? >> Do you agree with Mark that 90 deg. gives the best stopping power, and >> say that 45 degrees gives the most power? >> Are you distinguishing between "pure power" and "stopping power", and if >> you are how do you define them? >> What exactly is the "hence" that makes neo retros require a higher >> straddle cable? >> Could you please elaborate? >> >> On Friday, February 20, 2015 at 4:40:16 PM UTC-8, Michael Hechmer wrote: >>> >>> I too agree. Mechanical advantage is important to avoid having the lever >>> bottom out before the brake fully engages, but pure power will be maximized >>> when the straddle cable is 45 degrees to the arm. Hence the neo retros >>> require a higher straddle cable than the touring cantis to maximize >>> stopping power. >>> >>> Michael >>> >>> On Friday, February 20, 2015 at 5:25:28 PM UTC-5, Mark Reimer wrote: >>>> >>>> Deacon, >>>> >>>> I agree with you on this. Getting the straddle as close to 90 degrees >>>> has always been the position which yielded the greatest stopping power for >>>> me. With my neo-retro's (Aka the 'weaker' of the paul canti's) I have the >>>> cable long and up high, and I have enough power to lift up the back wheel >>>> if I really wanted. >>>> >>>> Lower straddle usually results in less power, and obviously less mud >>>> clearance as well. >>>> >>>> As I understand it, the idea is to get the cable as close to 90 degrees >>>> as you can WHEN the brakes are in contact with the rim. >>>> >>>> To read a much more exhaustive explanation than I'm willing to >>>> regurgitate, take a look at BQ's great write-up on setting up canti's. >>>> >>>> In the end, I'm sure we can all agree that Paul canti's are awesome. >>>> >>>> On Fri, Feb 20, 2015 at 4:18 PM, ted <ted....@comcast.net> wrote: >>>> >>>>> Deacon, >>>>> >>>>> I am glad that you were able get your brakes to work the way you want. >>>>> I suspect you were told the opposite of what I am telling you, and that >>>>> you >>>>> understood what they were saying. Sadly they told you wrong. But happily >>>>> they still steered you to something that worked for you. >>>>> >>>>> The phrase "slushy brakes" suggests to me low effort producing large >>>>> brake lever travel with little braking effect. If that's what you had it >>>>> was likely due to elasticity in the brake system, which is a separate >>>>> thing >>>>> from leverage. If you experience that sort of thing, look for what moves >>>>> when you squeeze the lever hard after the pads hit the rim. For example, >>>>> I >>>>> found the steel front cable hangers flex a lot. Replacing mine with the >>>>> aluminum ones improved the feel of my brakes significantly. Cables that >>>>> change shape as the brakes are applied can be another source of excess >>>>> travel. >>>>> >>>>> >>>>> On Friday, February 20, 2015 at 4:21:44 AM UTC-8, Deacon Patrick wrote: >>>>>> >>>>>> Ted, et al engineer types: I happily bow to your knowledge on the >>>>>> angles and leverage, though I was told the opposite (as I understood it) >>>>>> before I made the change. Interestingly, either way, the experience went >>>>>> from slushy brakes (short saddle cable, < 90˚ intersection with the >>>>>> brake >>>>>> arm) and salmon pads, to passable strength except in single track steep >>>>>> descents (long saddle cable, close to 90˚ intersection with the brake >>>>>> arm). >>>>>> But that point is mute now, as the Paul's are wonderful! I look forward >>>>>> to >>>>>> snow-free trails so I can try them out! >>>>>> >>>>>> With abandon, >>>>>> Patrick >>>>>> >>>>> -- >>>>> You received this message because you are subscribed to a topic in the >>>>> Google Groups "RBW Owners Bunch" group. >>>>> To unsubscribe from this topic, visit >>>>> https://groups.google.com/d/topic/rbw-owners-bunch/5HXsqAEXrWM/unsubscribe >>>>> . >>>>> To unsubscribe from this group and all its topics, send an email to >>>>> rbw-owners-bun...@googlegroups.com. >>>>> To post to this group, send email to rbw-owne...@googlegroups.com. >>>>> Visit this group at http://groups.google.com/group/rbw-owners-bunch. >>>>> For more options, visit https://groups.google.com/d/optout. >>>>> >>>> >>>> -- You received this message because you are subscribed to the Google Groups "RBW Owners Bunch" group. To unsubscribe from this group and stop receiving emails from it, send an email to rbw-owners-bunch+unsubscr...@googlegroups.com. 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