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Re: anybody explain Sheldon's straddle wire MA?

Posted: 10 Nov 2011, 12:38pm
by 531colin
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 :D
...............


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

Re: anybody explain Sheldon's straddle wire MA?

Posted: 10 Nov 2011, 2:57pm
by snibgo
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.

Re: anybody explain Sheldon's straddle wire MA?

Posted: 10 Nov 2011, 5:01pm
by rjb
Phew - got there in the end 8) , must go for a lie down :mrgreen:

Re: anybody explain Sheldon's straddle wire MA?

Posted: 10 Nov 2011, 5:08pm
by 531colin
rjb wrote:Phew - got there in the end 8) , must go for a lie down :mrgreen:


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

Re: anybody explain Sheldon's straddle wire MA?

Posted: 10 Nov 2011, 6:50pm
by Cyclenut
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. :oops:

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!

Re: anybody explain Sheldon's straddle wire MA?

Posted: 9 May 2012, 10:36pm
by Brucey
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

Re: anybody explain Sheldon's straddle wire MA?

Posted: 13 May 2012, 5:32pm
by 531colin
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

Re: anybody explain Sheldon's straddle wire MA?

Posted: 14 Sep 2019, 5:02am
by 9494arnold
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.