Spar Bouy - Thin Cylinder

Hi there. We are designing a floating spar buoy hooked up to a three catenary anchors as a floating base for a vertical axis wind turbine. Being a thin cylinder, where would be a pivotal point, (center of rotation) of the buoy, Center of Flotation, or Center of Buoyancy? Would those points differ in a thin cylinder?
Thanks a lot for a help.
Eugene

 

The center of flotation is at the center of gravity of the water line.
The center of buoyancy is the center of gravity of the submerged volume and, therefore, is always below the waterline.
Both points can never match.
Any floating body revolves around the c. of g. of its water line.

 

Thank you very much sir.
Just to confirm, the thin cylinder would pitch / heel about the centroid of water-plane area, located in the center of the disk that is cut by the waterline?

 

That's correct

 

I can't stop thinking about the ball of chain that thing's going to make.

What is resisting the generator's torque load on the mast?

 

The turbine will consist of two parts which would counter rotate.

 

Get a copy of Buoy Engineering by Berteaux from Woods Hole. This exact problem is worked in that book.

The dynamics of a moored system is not the same as a floating system so the moored buoy does not rotate about its waterplane CG, and FWIW, neither does a free floating body. A free floating body rotates about it CG...it just also happens to surge,sway, and heave at the same time due to cross coupling.

 

Do you have access to FEA? This problem is relatively easy to solve using a linear transient solver. You set up your geometry, chains etc and you set it at about the right floating height. You set a hydrostatic table that changes the surface pressure relative to water depth and run the solver. You can start the geometry in any attitude you want and the solver will find its stabilty configuration. It can be done by hand as well, you'll ned to find some good reference books to handle the maths. The chains require catenary calcs which can get tedious. FE is simple to do if you have it. Cheers Peter s

 

Thank you very much sir. I actually have this book. I found the maths a bit heavy. Would you point at the page where the similar problem is worked out?

I am not sure I understand how the free floating body rotates about its CoG? Would this point be mentioned in the book as well?

 

A floating body does not rotate about its CoG. There may be something you have not interpreted correctly.

 

It does seems to be logical that the pivotal point is the CoFlt. Why then spar buoys are being hooked up to the catenary anchors at the point located typically 2/3 down of the underwater length of the buoy? One would think the logical place of hooking up would be a pivotal point (which is located on the surface, but obviously nobody has seen the anchor points at this level)?

 

I do apologise here, I am new here, I don’t know yet how to answer to the individual recipient. My reply

"Thank you very much sir. I actually have this book. I found the maths a bit heavy. Would you point at the page where the similar problem is worked out?
I am not sure I understand how the free floating body rotates about its CoG? Would this point be mentioned in the book as well? “

Was intended for Mr. jehardiman, since he indicates that the system does not rotate about its waterplane CG. Granted, he could have had in mind effect of heavy chains 2/3 down the underwater length, but in my particular case I am trying to strip the system down to the bare spar buoy, without it being attached to any thing for now. Once I understand it I would consider attachments. On the other hand I am considering a light weight fiber ropes instead of chains.
Eugene

 

Eugene, an object floating freely, rotates around an axis through the CoG of its flotation. But when there are forces such as the transmited by chains, that statement may no longer be correct. Not least because the tension transmitted by chains disturbs the balance weight-buoyancy. We have to know exactly what we are talking about and even knowing it, I'm not sure I can give you the solution.
Cheers.

 

Does FEA means "Finite Element Analysis"? I always was under impression that this is a very generic term. Is there is any user friendly software for stability calculations of thin cylinders?

 

Hi Eugene,
I think tansl means "CoG of floatation" means the bouy rotates about its centre of bouyancy not the centre of gravity of the bouy. The CoG is the centroid of the mass. The CoB is the centroid of the immersed volume of water. Yes FEA means finite element analysis. I use Strand7, but any FE software with transient capability can calculate this easily. The centre of floatation is the centroid of the waterplane area. If you place a vertical plane through the CoF this is the plane that the bouy trims around. I have attached an avi of a coke can being dropped into water to show what an FE solution would look like. In your case you would have the cables etc attached and these would settle to their correct places due to gravity, bouyancy and the hydrostatic forces. You have to play with a damping factor a bit to get it to settle reasonably. Peter