Vibratory System

There is no gravitational energy , the same as there is no tensional energy. Gravity is a force.
There is no "catenary action". The catenary is a hyperbolic curve caused by the force of gravity (or any other acceleration) and the tension on a chain, rope, etc. The nylon rode also forms a catenary curve. When the tension increases the catenary changes. There are several causes for damping (maybe that is what you call buffers). For example, the internal friction on the rode, the friction between the rode and the water, the force caused by turbulence. By the way, if a nylon rode did not form a catenary, it would be a straight line, which is easily proven to be a wrong statement. Simply get a piece of rope and hold it between your hands.
Finally, strain is the deformation of a body when a force is applied to it, not any kind of stored energy.

 

You can model the chain as a spring, since you need force to make the catenary more straight. That increases the potential energy. The behavior follows F=kx, therefore can be modeled as a spring.

 

Oh dear, throwing anything in the vain hope one of the throw away comments sticks!

I have no idea why you're even getting into chains/catenary (i've done more catenary calcs than i can shake a stick at) if you can't even understand the basics of strain.

What is strain?...well when work is done on a body is distorts. Ok...simple so far, but then what?...the distortion is termed "work", since work done is force x distance moved. With me so far?

So applying a force to a body, work is done on it. Work done is energy, and this energy is stored in the body, or material, and is recoverable once the applied force is removed. If the body or let's call it a material returns to its natural original state, it is an elastic material, if it doesn't it is a plastic material. However, I digress, so, ...work is being done from the applied force on the material and this is called "strain energy" as it is recoverable.

Energy, not force, strain energy, is the fundamental of structural mechanics!

You still have a lot more reading and understanding go before you start throwing around one liners to obfuscate the clearly obvious to everyone reading this thread. You keep throwing around 'forces' and 'energy' like it answers all your critics, yet gets you into more trouble!!??

 

So lets get this straight Gonzo you are now stating once again that:
There is no such thing as gravitational energy or to give it it's full name gravitational potential energy.
And adding :
There is no such thing as strain energy .

You certainly don't grasp the definition of energy.

 

For small changes you might correctly use simple linear methods. But the energy stored is a function of the work done to lift the chain.

That’s why single point moorings are not trivial. It’s actually possible for the vessel to be anywhere within a certain radius of the mooring when the vessel is under excitation and within a smaller radius when at rest.

Consider the model for the rest state for a start. The chain lies on the seabed often as bights or even heaped, from the vessel to the seabed is vertical.

Now for a simple example excite that model with a stepwise function. You should immediately comprehend that there’s no sensible f=kx except for small changes. And if you consider another small change later you need a different value of k. The chain response to the vessels surge function has it’s own function and it is not trivial.

Then energy absorption occurs initially as the chain is dragged across the seabed and secondly when the chain is pulled tight to the point where there is an equal horizontal force through each link of the chain ( but unequal vertical force) and forms a catenary. Energy absorption and return occurs as each link of the chain is lifted or dropped a different amount to a new position. The energy for that work comes from the vessels surge energy ( kinetic). Catenary action is then the action of the chain catenary in absorbing energy and in doing so producing a restoring function. In reducing acceleration it reduces the total force in the rode but returns the surge energy inverted. Comprehend ?

I’m not even sure why you are mentioning a nylon rodes catenary. It’s not significant.

 

Oh indeed. I'm no expert on this subject at all, but I do know it is very complex. Not unlike seakeeping!

But just looking at it from a layman's perspective.....you have links each link has a 'node'. At each node, when a chain, can have as as I see a minimum of 4 DoF, 3 translational and 1 rotational (Possibly 5 DoF). And that is just one link, and when joined together, it is an extremely complex mechanism to model. When the links are as you describe, they each behave differently and react differently to the an applied load where some maybe on the sea bed some closer to the surface etc.

However, when lets say a surge, the vessel moves fwd and the chain becomes fully taught, and then another surge I assume the extension is merely related to the E of the material,..or do you, in your analysis of this mechanisms, treat it differently?

 

Elasticity may or may not be included depending on the diameter and material of the rode. With chain strain energy wasn't usually considered in the analysis it's effective action was considered entirely gravitational (what I'm terming catenary action), and the chain is never straight, the anchor will drag well before that point ( also with a catenary force is heading for a limit where a denominator is approaching zero for a true straight line). With computer FE models for mooring design all the materials properties are used.

If we look at the sorts of craft this started off considering, say M&M Ovenden's classic and simplify this considerably for ballpark . They might have a Danforth with say 10kN holding force and Mark said they are using 1/2 inch chain, cross section 253mm2 so 39 MPa. Using E of 200E9 the total strain is 39/200E3 or .0002 if they had 50m of chain out it'll stretch 10mm before the anchor drags (ballpark simplified model) .

In comparison Nylon rode is selected to stretch around 20% at design load ( Anchor holding force) and it needs a longer rode than chain.

I have several good papers on mooring design but they are hard work unless you've studied advanced engineering maths. Some of the models have been refined more recently with the advent of computer FE models. Allowing cheaper investigation into various effects then verified by real world models. Not huge changes but it gets refined more and more.

 

Very simple when you put it like that...i was over thinking it
Cheers Mike

 

The dynamics of mooring systems are explained in the textbook "Sea Loads on Ships and Offshore Structures" by O.M. Faltinsen. It covers chain as well as elastic cables.
This book is always a valuable reference.
It is also helpful to google "Dynamics of Ship Anchor-Lines" or "anchor mooring line dynamics" which will show you a large number of relevant papers.
There are model tests at the Marin-wave tank, simulation in ANSYS AQWA, an MIT-lecture series etc...

There is exhaustive research on the subject, no need for heated arguments.
Uli

 

Uli
This started with a comparison of nylon and chain rodes on small craft. Numerous papers could have been posted but this isn't an argument about mooring dynamics it's just frustration with the continual denial of the existence of fundamental principles of work and energy from one person alone. Principally how energy is stored in simple mechanical systems.

It appears to me at least that Gonzo continually denies those first principles even exist. The papers that need posting are more likely to be Sir Isaac Newtons. Until there's some understanding of where energy is stored lifting a brick or stretching a rubber band there's no hope of any sensible discussion.

 

The part of the chain that is on the seabed and lift with tension is similar to the example of a balloon with a long string, with part of it laying on the floor. If the balloon is disturbed and starts moving up and down, the string becomes a spring. In that case x is the length of the spring and F is gravity.

 

In Newtonian physics gravity is not a force. The sought after Unified Theory may be able to treat is as a force. The latest discoveries, of which professor Woods at UW-Milwaukee took place of, indicate that gravity may have or be a wave. However, it may have no consequence for engineering since we use Newtonian physics. If a brick is lifted or a rubber band stretched, the energy is stored in the body, not in gravity.

 

Gonzo,
While Mikejohns rude comments to you, totally unprofessional and from his viewpoint, omniscient, your comment that in Newtonian physics gravity is not a force is not correct.

F = G m1m2/rr or the FORCE of gravity between two masses equals the universal gravity constant times the two masses divided by the square of the distance between
between the centers of the masses is in fact a Newtonian equation.
Gravity is a force, the attraction between bodies.

Mikejohns states in a post on this thread
"Well for a start gravitational force is the force component of gravitational energy (and Gravity is acceleration not force)"
This is quite incorrect that Gravity is an acceleration. The FORCE of gravity (on earth) is what the object weighs, and this force will accelerate the mass,
at the acceleration of 32 feet per second per second. (9.8m/ss)

While many years ago in engineering, we did not separate gravitation energy from any other type of POTENTIAL energy. Ie if an object was moved vertically upward a certain distance,
then work was done to make this happen and the object would have the ability to release this energy if it was able to fall.
As I read the posts, for clarity, the word Potential energy should always be included in the phrase and gravitational portion omitted or included.

The other issue regarding gravitational,( totally unrequired adjective) POTENTIAL ENERGY is the analysis that a 10 pound object held say 10 feet above the earths surface possesses a fixed amount of Potential Energy. What energy does it possess?

10 pounds times 10 feet???? An obvious answer??? Well not really, Potential Energy needs a boundary or distance of travel and this makes this potential energy different than strain
energy. If there is a table 5 feet under the 10 pound weight the potential energy is 5 feet times 10 feet. If the 10 pound weight can fall 10 feet, then that is 10 x 10 foot pounds of energy can be released and if
the 10 pound weight falls into a hole in the ground 10 feet below the earths surface, then the energy that can be released is 10 pounds x 20 feet.

So the same object, can produce different Potential Energy numbers due to the distance that it falls.

Whereas, potential energy stored in a spring will release the same energy anywhere, on earth, underwater, in space

I think Mike in the other thread you said that the boat could over shoot the original starting point with a nylon rode. With the dampening in place, ie hydrodynamic, pulling the rope through the water etc, I am wondering where the additional energy comes from to over come the dampening?
The papers that this thread has prompted me to read about mooring, it appears that most mooring system ropes are significantly damped so there should not be an ability for
other energy additives to the system?
Some comments here please

 

I wrote force for energy; too early in the morning;(. Thanks for the correction. I say it is a force and Mike says I am wrong, in all the previous posts.
As for potential energy, there is no difference in the energy stored by stretching a spring, or by lifting a body. Potential energy in a gravity field is not linear, since the force diminishes with increasing distance. However, for small distances like 10 or 20 feet, the difference is negligible.

 

Well I do feel that I owe an apology to you Gonzo. I looked at your bio on this site that says you are a technician with a handful of industry maintenance certificates. Apparently that's not the case and you have just graduated with a degree in this field ( congratulations). So I was quite wrong to say you lack the ability to see where you are wrong. But I still think you were being very stubborn if you wouldn't accept the terms Gravitational or strain energy in the context of a technical discussion. If you ever go on to study detailed structural analysis strain energy methods are very an important concept.