I have a boat which is supporting an umbilical (cable) - which is supplying the electrical power and communications to an ROV (remote operated vehicle) which is several hundred metres below the surface of the water. There is a bit of a twist to the problem - because the ROV operator wants to attach weights to the umbilical (at location number A - over maybe 50m of umbilical length) - and he also wants to add small buoyancy modules (at location number B - over maybe 50m of umbilical length). The ROV operator wants to do this - in order to isolate the ships motion from the ROV - so the shape of the umbilical will be an "S" shape (rotated through 90 degrees) - when looked on side ways.
I decided to approach this problem as a "chain" - with a series of links (with each link having its own individual weight to allow for the situation where the umbilical has additional weight - location A (lead weights) - or buoyancy blocks - at location B). I then sought to get equilibrium at each end of each link. I then set out the equations for 16 links - and used the Find function to solve for the 50 unknowns. The equations are non linear as they have sin and cos functions - so using the Find function appeared the only option. So apart from the spreadsheet being - not very slick - I noticed that if I had more than 16 elements - which generated 50 unknowns - the Find function would not work with more than 50 unknowns.
As you can perhaps appreciate - if the umbilical is 2000m long - dividing this up into 16 links - is very rough indeed. Additionally, I would like to input the drag forces on the umbilical - but that is just going to add more unknowns - as this varies with the inclination of each link.
So I am looking for any ideas on how I could
- add more links to get a more "accurate" representation of the "S" shape (rotated through 90 degrees) - when looked on side ways
- how to resolve the 50 unknown apparent limit on the Find function
Many thanks in advance - to positive contributors.
Jan Kowalski wrote:
I do not see it. Share us a solution please
See please http://communities.ptc.com/videos/3787 and the attach.
Thanks Valery for sharing
Walery you say: "We solve numerically (see the vibrations of the chain) "
the cause of the vibration is bad chosen calculation method.
- Nonlinear: Levenberg-Marquardt ->bad (bug)
- Nonlinear: Conjugate Gradient -> good -"Advanced option I'm change to(Variable estimation to quadratic)" -> more time to calculate
- Nonlinear: Quasi-Newton -> a little better (bug)
Perhaps it is the fault of the software bug
I'm calculated the integral of the equation and abandoned see worksheet. I'm added video symulation NO vibration.
Just in your file Chain-0-1-2-3-4.xmcd.zip just change the Nonlinear: Conjugate Gradient and TOL=10^-12 and work fine.
Sorry, this system has infinite number of solutions - between two curves on the plot. The task will have one solution if we will take into account not only the kinetics but also the dynamics, forces. And Levenberg-Marquardt method (with vibration) is best, more honest
Gordon Durward wrote:
Hi Valery,
Thanks for your recent posts - and the efforts of your students to solve the problem - and yes I can see it is even more challenging for them - because their number system is different in Burma.
Gordon.
Gordon, sorry, I understand your irony, but without experiments (in one pool with moving water and with my students ), your problem can not be solved. I think.
Valery Ochkov wrote:
Valery Ochkov wrote:
I will give to my students tomorrow this problem:
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The first step of my students:
We have checked how Mathcad accurately calculate
The problem is in contraction!
I hope tomorrow we can see the solution with animation.And we can check the solution by help with real catenary! How!?
I like to collect a wall pictures with mathematical meaning.
One of them is so - a virtual and real catenary. It is a print of this Web-Sheet - http://twt.mpei.ac.ru/MCS/Worksheets/chain-eng.xmcd
with real silver catenary
Richard Jackson wrote:
See the attached worksheet.
Looked through the file and it all is a little improved , work fine to me
You got it to work for one equation, but actually it cannot work for all the variables. There are more then 50 of them, and that is not allowed. The solution vector on the right has fewer values then the number of variables being solved for, and is therefore incomplete. The vector of variable names on the left also has fewer elements than the number of solve variables, which is probably the source of the "pattern error" when the evaluation on the right is deleted.
There were some mistakes in my previous worksheet. I threw it together in a real hurry, and didn't even look at the results. The angles of the segments are not realistic. Here's a new version with the mistakes fixed. The solve block needs to have the angles constrained to get a realistic answer. I also added a function to plot the catenary, which makes it easier to check the solution is realistic (so you have your plot Valery ). New stuff is highlighted in cyan.
Looked through the file and it all is a little improved , work fine to me.
The FIND function should be the same variables as vertical an horizontal vector.And it has just a mistake.
Sorry English bad
I'm surprised you took te time to type in the extra variable names. Since that version of the solve block wasn't very useful I couldn't be bothered 
I guess more than 50 variables are allowed.
Looks can be deceptive. The solution is not realistic (the solve block needs the same constraints I added).
It's generally not a good idea to set TOL and CTOL to very small numbers. The floating point precision is only about 10^-15, so if you set them this low (setting them lower than the precision is the same as setting them at the precision) all sorts of things start to fail, including Find, numerical integration and differentiation, etc. If you get rid of those settings you can put Find back instead of minerr, and it will give you the same answers.
I would just like to say thank you for all the effort you have put into showing me how to solve this problem using vectors - which is a method I haven't seen before in the solution of multiple unknowns - and I have been on the Mathcad courses and it wasn't discussed in those courses - and I bought a book on Mathcad - and it was not in that either. It is definetely the way to solve this type of problem - it is a very good way of doing it.
Apart from being easily extensible to more variables, it saves typing out dozens of variable names at every step. Since I'm lazy that's a big plus for me
There is a lot you can do in Mathcad, and books and courses can only cover so much. If in doubt, the best thing to do is exactly what you did: ask here.
I feel it would be good if Mathcad could maybe have some "real world examples" in its "database" of what Mathcad can do - then I am sure others like me would learn from these examples.
There are many examples on these forums. Also look here at the old Mathsoft library:
http://web.archive.org/web/20040804121505/http://www.mathcad.com/Library/
I am sure that there are other engineers out there - like me - who just want to solve lots of equations with lots of unknowns
Bear in mind that with a very large number of variables it might become unstable. You are trying to find the minimum of a very complicated multi-dimensional error surface, and how easy that will be depends on the shape of that surface.
Also, the time taken will scale as the square of the number of variables, so it may become impractical beyond a certain number. In this case you can avoid this problem by using the recursive method I added to the final version of the worksheet. The time taken for that will scale linearly with the number of variables.
I don't have Mathematica, so I can't look at it, but it's nice to know the answers are the same
