Talk:Capstan equation

Hi all!

I am new to this as you may notice, and it took a while with the LATEX Editor. Maybe it needs some tidying up if there is say a convention for enumerating steps in a proof or for how to denote unit vectors. Certainly there should be some illustrations. I have them in a MS Word document. Any volunteers who could help me with that?

--Laelele (talk) 04:50, 31 January 2009 (UTC)

Hey

I just wanted to say that the proof is really hard to follow and understand. Please define all variables and constants as soon as they are introduced. For example what is phi? It is possible to understand If you have background knowledge but not everyone does. Furthermore it is confusing when you give two equations and somehow derive another from them as in (6) and (7) ⇒ (8). Please state exactly what you do to get to the next step.

Zippypic (talk) 06:12, 23 November 2009 (UTC)

Hi Zippypic,

Some illustrations would help. I have them, but in a word document. Can you give me som advice as how to convert them to something that Wikipedia can digest? As I tell my students: always read scientific text with a pencil and some paper at the side. When it says "one can easily see that..." you are supposed to do some filling in yourself.

--Laelele (talk) 22:00, 24 November 2009 (UTC)

The Table

The table is terrific, but I'm afraid it's misleading. Suppose I want to find numbers for the jib sheet on my sailboat's winch. Just looking at the table, I might be tempted to assume a middle value for \mu\ the coefficient of friction (COF), say 0.5. But this is unrealistic in the real world, since the COF for synthetic rope on steel is in the range 0.08 to 0.15 (Handbook of fibre rope technology, by H. A. McKenna, J. W. S. Hearle, N. O'Hear, page 138; retrieved from Google Books 12/28/09). Thus I should be using the first column in the table, for the smallest COF, and getting the smallest results from the table. In particular, the example involving the baby and the supercarriers assumes a COF of 0.6, without specifying what kind of rope on what kind of capstan can provide that, or whether a COF of 0.6 is even resonable in the real world. (If we're going to provide examples, shouldn't they relate to the real world?) Jedwards01 (talk) 05:41, 29 December 2009 (UTC)

Thank you Jedwards01

for enlightening me about the COF for synthetic on steel. Certainly if you have a monofilament synth line, such as a fishing line, and try to wind that up on a fishing reel you will need a lot of turns and maybe even riding turns to make it lock fast. About the example you may envision a hemp rope around a tree or a granite bollard. The reason for us interested in maths/physics at all to consider this is that the capstan equation is one of very few examples of exponential functions that isn't nuclear physics, solid state physics or from the world of economics.

Laelele

I had to take away the Amontons thing since Amomtons' law is any friktion not specifically a line around a capstan. Can anyone help me with the phi: it is a phi in the code but a varphi is shown.

Laelele —Preceding unsigned comment added by Laelele (talk • contribs) 08:38, 30 September 2010 (UTC)

"It is both ancient and modern practice for anchor capstans and jib winches to be slightly flared out at the base, rather than cylindrical, to prevent the rope (anchor warp or sail sheet) from sliding down. The rope wound several times around the winch can slip upwards gradually, with little risk of a riding turn, provided it is tailed (loose end is pulled clear), by hand or a self-tailer." The rope (sheet) will never SLIDE down. It's rather that with the next turn on the winch the next round turn of rope will end up underneeth where the coil of rope is at present had it been cylindrical. And it's not that the rope CAN slip upwards. By design it's forced upwards. — Preceding unsigned comment added by Laelele (talk • contribs) 12:23, 3 September 2012 (UTC)

I added a picture from "real life".Laelele (talk) —Preceding undated comment added 13:36, 19 October 2012 (UTC)
 * I made a slight change to your caption; I changed "better" to "more efficient". There are considerations in good design beyond whether it works efficiently. If the curved design *works* and also fulfills some other criteria that the straight design would fail to meet, then the curved design might well be "better" overall. Applejuicefool (talk) 13:37, 8 January 2015 (UTC)

The derivation seems unnecessarily complex. It is easy to show that the normal force (newtons/radian) is the same as the rope tension (newtons). Then the increase in tension dT over a small angle dphi is just the friction over dphi, that is dT = mu dphi T which is equation 15. Eqs 1-14 are superfluous and confusing. EE483597 (talk) 01:25, 3 March 2015 (UTC)

Added a photo but the link in the article can't seem to find it. I know it is there because when I try to repeat the upload I get a filename in use error with a thumb of my uploaded file. What am I doing wrong. EE483597 (talk) 00:21, 10 March 2015 (UTC)

The equation given in the main article has T_hold and T_load switched from what is given in the derivation. I'm too lazy to look at it more carefully right now, but I suspect the derivation has the correct formula. If someone else can confirm, I suggest the formula given earlier is modified, and the definition of the terms T_hold and T_load updated to the correct meanings. Also, in the "baby" example, you're mixing weight (force) with kilogram (mass, though in everyday practice, people also use it as weight, hence the confusion.) Itsnotmyfault1 (talk) 18:19, 4 January 2016 (UTC)

You are correct. The exponent in the capstan equation is lacking a minus sign. John G Hasler (talk) 20:52, 8 February 2021 (UTC)