Cycling UK Forum

Phil_Lee wrote:This is exactly the kind of applied mathematics problem I need to keep my 12 YO son interested in maths - nothing he's been getting at school seems to be stretching him at all.
It's tough staying ahead of him - it won't be very long before He's trying to explain stuff to me that I can't understand
...............

I just googled "maths club for kids cambridge".............OMG..
As I said at the start of this thread, I'm sure mathematicians are born, not made.....but a little nurturing can't hurt?

Divide straddle distance by twice the height from ruler to brake block centre (usually about 25mm nowadays, so divide by 50) and you have your MA. In this case 140/50 = 2.8.

Yup. However, dividing by twice the height is to consider only one side of the brake. I wouldn't take twice the height, to give me the MA of the entire brake.

Is this equivalent to the circlecaycles (http://www.circleacycles.com/cantilever ... ometry.pdf) maths? Yes, it is. Here comes the proof.

In the circleacycles diagram, extend YA and OP until they meet. Call that point M. Then MP is CJ's "straddle distance".

Consider the triangle MAP. The sine rule gives us:

MP / sin (180-Beta) = PA / sin yoke_angle

But sin(180-Beta) = sin(Beta) so

MP / sin (Beta) = PA / sin yoke_angle

MP = sin (Beta) * PA / sin yoke_angle
MP = sin (Beta) / sin yoke_angle * PA

So the circleacycles expression
MechanicalAdvantage = sin Beta / sin yoke_angle * PA / OD
becomes:
MechanicalAdvantage = MP / OD

QED.

Phew - got there in the end , must go for a lie down

rjb wrote:Phew - got there in the end , must go for a lie down

You mean you can understand that stuff? I'm wondering if I could borrow Phil's 12 year old lad........

snibgo wrote:

Divide straddle distance by twice the height from ruler to brake block centre (usually about 25mm nowadays, so divide by 50) and you have your MA. In this case 140/50 = 2.8.

Yup. However, dividing by twice the height is to consider only one side of the brake. I wouldn't take twice the height, to give me the MA of the entire brake.

You're right, my mistake: both brake blocks move so the mechanical advantage of the brake is cable tension divided by TWICE the brake block force.

EDIT (some months later): No, you're wrong! Why did I fall for that? Probably because my results differ from those of Circle Cycles, whom I mistakenly assumed to know what they were doing since they've gone to all the trouble of building a whole web page around it. Go back and read the maths like Brucey did and you'll see that my calculation of forces takes account of both arms of the brake at the outset. Unlike Circle Cycles, apparently!

Thank you Brucey, for having more confidence in me than I have of myself!

I think CJ got it right the first time; take the case of flat arms and b = 2h. This yields a caliper MA of 1:1 not 2:1... Think of cable force x distance = brake pad force x distance. If not then energy is not conserved.

The applet in the link gives MA values that are exctly double those of the whole caliper. This doesn't matter for comparing cantis with other cantis but it does when comparing cantis with other brakes like DPs etc. as I have tried to do here;

http://forum.ctc.org.uk/viewtopic.php?f=5&t=63112

cheers

Because this thread is in "too good to lose" I'm adding a link to a later thread in which "Brucey" reviews MA in some detail
http://forum.ctc.org.uk/viewtopic.php?f=5&t=63112&start=30

Last picture shows a graphic illustration of the "triangle of forces" involved in this. Well done to the poster.
Had to deal with a friends tandem that had the cantilevers set up incorrectly. Plus whoever fitted the cantilever bosses had got one offset on the fork blade (compared to the other) . A post frame build upgrade error sadly.

A late reply to this thread:
To get the best MA the straddle cable should be perpendicular to the line between its point of attachment to the canti and the canti pivot, on each side, WHEN THE BRAKE IS APPLIED. Ideally, the straddle cable length should be constantly shortened as the pads wear.
This method ignores some of the more complicated geometrical implications, but it works for me and is relatively easy to set up.
The limit is when the cable touches the mudguard or tyre (if no mudguard don't forget to rig a catcher in case the brake cable breaks).
If anybody's still interested I hope this helps.

The lower the yoke angle, the higher the MA. Sheldon was right. Unfortunately, adjusting a brake that way puts the pads way too close to the rims and gives a crummy feel at the brake lever. I found the ideal is to have the straddle cable at right angles to the brake arms when the brakes are applied (anchor angle in Sheldon's diagram).

right angles between the arm and the cable is a practical approach with many brakes simply because it doesn't challenge the cable mountings on the ends of the brake arms. However it

a) cannot be achieved with some brakes at all and
b) it is fairly meaningless on others (eg most using post-mount brake blocks) because the arms can be adjusted through a range of angles.

So my vote is 'no cigar'.

cheers

Brucey wrote:right angles between the arm and the cable is a practical approach with many brakes simply because it doesn't challenge the cable mountings on the ends of the brake arms. However it

a) cannot be achieved with some brakes at all and
b) it is fairly meaningless on others (eg most using post-mount brake blocks) because the arms can be adjusted through a range of angles.

So my vote is 'no cigar'.

cheers

No on b. Adjust the straddle cable after adjusting the post mount pads.

the point is not that you can't usually set the straddle at 90 degrees (although you can't always) after you have set the arms, more that the brake MA is different depending on the way you have set the arms. So it isn't a 'one size fits all' setup method.

Fundamentally any method used to 'simplify' canti setup will not work some of the time and/or will deprive you of one of the key features (missing with most other brakes BTW), which is that you can adjust the MA.

Every canti brake manufacturer supplies some fairly straightforward instructions which will apply to their particular brakes. Follow them and you should get reasonable performance. However if you understand what is going on you can nearly always make the brake work slightly different to that, in a way that better suits you.

cheers

Brucey wrote:the point is not that you can't usually set the straddle at 90 degrees (although you can't always) after you have set the arms, more that the brake MA is different depending on the way you have set the arms. So it isn't a 'one size fits all' setup method.

Fundamentally any method used to 'simplify' canti setup will not work some of the time and/or will deprive you of one of the key features (missing with most other brakes BTW), which is that you can adjust the MA.

Every canti brake manufacturer supplies some fairly straightforward instructions which will apply to their particular brakes. Follow them and you should get reasonable performance. However if you understand what is going on you can nearly always make the brake work slightly different to that, in a way that better suits you.

cheers

You might want to edit your post because it is not intelligible (at least to me). How about an example?

The only way I can see that you can't make the yoke angle approach 90 degrees is because you are using fenders or the tire is too tall and the brake arms too short. I don't use fenders and have used cantis on mountain and touring bikes back in the day and had no problems setting them up correctly, so I'm not following you.

I was commenting on the suggestion that all that is required is to 'set the straddle at 90 degrees to the arms'. For reasons I have already explained this will not give a reproducible setup.

I don't know how to explain what I have already explained any differently.

cheers