Thanks for a a well thought-through answer!
It seems I forgot to mention a couple of important factors that will simplify the problem. The coordinate system is attached to the vessel, and the origin is at the vessels centre of mass. Furthermore, you are correct in that the different frequencies will induce different movements, and that there are different functions for the different degrees of freedom. In the attached pic, you can see how this data looks, for one specific wave heading (0 deg., i.e. hitting directly on the stern in "B)" in previous pic).
For example in the data for a heading of 180deg (opposite direction) the phases will be negative for the surge motion, and it is this I am trying to figure out.
Hope this was of some help, and thanks again.
Thanks for your answers, however I am still a bit stuck. I'll try to give a more thorough description of the problem. In the attached picture two vessels, A and B, are illustrated. The blue vectors illustrate the waves and how their angles of attack are measured. When the waves hit the vessel, there will be motions in 6 degrees of freedom; surge, sway, heave, roll, pitch and yaw.
Surge=motion along x-axis
Sway=motion along y-axis
Heave=motion along z-axis
Roll=rotation about x-axis
Pitch=rotation about y-axis
Yaw=rotation about z-axis
The data I have is called RAO (response amplitude operator) data and is equal to the amplitude of the vessel motion (in meters or radians) divided with the amplitude of the waves. As mentioned, it is between these two amplitudes the phase shift will occur. My problem is that I can't seem to figure out how the phase shifts will change for the different degrees of freedom when the data is converted from B) to A).
Any clever minds have a clue?
I have been trying to figure out something that should be quite basic. I have some data that describes the motion of an object when exposed to waves. Between the wave amplitude and the amplitude of the object's motion there will be a phase shift. This phase shift is defined as lead phase, i.e. lag phase when negative. When I try to convert the data to another coordinate system, the phase shift will be different. Does anyone know any rules that relates phase shifts to a coordinate system? It can also be noted that the data in the coordinate system that I have, is defined with a positive wave direction opposte of the other coordinate system.
Any help is appreciated!
Well, here is the complete, static, problem:
An oilrig is floating on the surface. One of the mooring lines keeping the rig in place has an attached buoy at some point, in order to move the touchdown point (where the line meets the seabed) further away from the rig.
The curve will look something like this: http://www.globalmaritime.com/navalarch/mooring1.png where the discontinouation is the point where the upwards buoyancy force from the buoy is acting.
M in the equation is the weight of the line in N/m, and D and R is the horizontal and vertical distances from the rig (fairlead) to the buoy. However, I belive there must be a simpler approach than what I have attempted. (e.g. by using line distance S, instead of D and R)
Basically, I need to find an expression for the slope of the line, given that i know the line tension at the rig (fairlead), the buoyancy force of the buoy, the line weight M, the point on the line where the buoy is attached, and the total length of the line.
Think that's it
Cheers for ur time guys. MD/H and MR/H are not the same, and I guess Im still stuck trying to solve for C1. It has been a while since I used the taylor expression, so I can't see how it would simplify in providing an expression for C1...
Also, if anyone has derived an expression for a catenary with an applied force (like e.g. a mooring line with an attached buoy) this would also be helpful
I'm stuck with this equation at work, which im trying to solve in order to do some mooring calculations. I have a mooring line, with an attached buoy. When deriving one of the catenary equations, I end up with this:
Basically M, D, H and C1 are all constants and I need to find a symbolic expression for C1, i.e. C1=????
Any bright minds out there who can help me??