Amidships Chain Storage

A nylon rode is a shock absorber not a damper, ditto for a chain catenary.
There's a confusion between shock absorption and energy dissipation, ( removed from the system) that is required for what is termed "damping" .

Also an all chain rode is not a spring mass system, it's actually a mass mass system with a natural frequency that has far less harmonic or phase problems.

Consider that nylon needs around twice the scope of chain and 3 strand lay will stretch around 20% at half it's load rating . That stretched spring accelerates the boat fwd again and it will often veer as well as overshooting it's original position and often ends up well off to one side or the other. You now have substantial slack in the system that means the boat will accumulate more energy before it's brought to a halt, and the cycle keeps repeating. That's why nylon gives such a miserable ride in strong gusty conditions, to the point of making the crew motion sick. It can also actually yank an anchor around far more than a chain rode and produce higher loads at times.

I have a lot of issues with all the popularist analysis of boat anchoring systems. None of them consider that it's a complex dynamic system, they all presume a simple scenario and neglect anchor drag, energy return, phase and harmonic effects. The governing equations are at least 2nd order differential equations and few people apparently even understand the terminology let alone the system analysis.

Also shouldn't the first practical question for any cruiser choosing their rode material be the intended operational area !

 

I said it is a damped system. All vibratory systems consist of at least two elements: a mass and a spring. The mass is the boat and the spring the rode. However, the system is damped by friction between the fibers as the rode stretches and by the catenary of the rode as it moves through the water when the tension changes. This are basic vibrations concepts. An all chain rode is also a damped spring/mass system. Otherwise, it wouldn't have a natural frequency as you claim. Only spring mass systems can vibrate. By the way, there are millions of people that understand the equations; they are not that complex. Introductory college courses cover them.

 

We are probably not on the same page as to what constitutes a system of differential equations.

It's quite a complex dynamic system. As I said that few people apparently even understand the terminology let alone the system analysis. I'd be incredulous to find any introductory college course or basic under degree that covers anything like higher order systems of DE's and PDE's ? You can't even solve these equations in the time domain. Who's studied the transforms in introductory college courses let alone system modelling !

That's the problem with populist attempts to analyze subjects like this, they try and use basic college physics and it doesn't cut it.

What do you think the damping factor is of fiber friction when stretching a rope as a % of the energy in the system? I wouldn't considered it significant. I said before the only effective damping is hydrodynamic as the boat surges and yaws around.

And again you are having a bit of a problem with this: A chain catenary is a mass, the restoring force is due to its mass and the effect of gravity, the energy stored is gravitational. A stretched length of nylon is a spring with a restoring spring constant where the energy is stored in the material as strain energy. You cannot call a chain catenary a spring .

 

Those courses are required for engineering. They make use of Laplace transforms among other methods. Complex systems are solved by breaking them into simple ones. I don't know what you mean by populist though. However, there is no such thing as gravitational energy. Gravity is a force.
Definition of a spring: Something that fulfills the behavior explained by F = kx

 

You might consider a Drum Winch, Lonestar has them in Texas as well as EZanchor puller out of Florida. They are electric and spool the rope and chain or all chain on a drum.
The chain will dissipate some energy from its vertical ie no load as it drags through the water to say an almost straight line from the anchor to the bow. The chain mass acts as a
kellet which increases dampening. The comment about the anchor holding the full reverse thrust of the engine is interesting. But in high winds the wind, wave, current, surge could easily
surpass the several hundred pounds of thrust that many boats could exhibit in reverse. Not to be forgotten is the fact that if you are not stern tied the anchor will often release with the tide change and re hook itself without an opportunity to reset the anchor with your engine(s). I have found this to be a 2 am, occurrence so when choosing your anchor spend some serious internet time looking at the myriad of tests done of the various anchors for reset length. Some of the test comparisons that I have read, will show an anchor with superior holding ability but with
a longer time to reset itself with a pull back against it original direction of lie.
If you go with a drum winch, you can upsize the anchor for an increased factor of safety.

So, the chain will provide some dampening, due to the movement of the chain from vertical to the slope, and a bigger anchor will offer a better factor of safety, the drum winch can be located wherever you have room if you are considering an anchor windlass anyway, focus on the reset distance when looking at anchors as they vary, holding power is only one of the criteria.

(the other criteria is the type of bottom. We often anchor in areas of kelp/weeds and or small gravel and had an oversize Danforth get some junk caught in between the flukes and the
shank which would not allow the anchor to dig in on reset and almost ended up on the shore twice. Anchor types have their corresponding bottoms and many cruising boats that we see will often have a couple of types on their deck. A mud/sand anchor and something for rock or coral

 

Popularist, as in simplifying a complex subject for the layman to get a basic understanding of concepts.

Transforms of high order DE's and pDE's, no way are they learning that. An introduction to the Laplace is not what I'm talking about.

Complex dynamic systems are not broken down to simpler ones, they cant be for any meaningful solution. It occurs to me that without actually studying this it's going to be very hard to understand just why such statements are so far off the mark.

Gravitational energy is a very important concept, it's very basic physics to learn the relationship between force work and energy.

F=kx Precisely, k is a spring constant, with chain force is going to be a trig function of m.g

 

The problem with drums on a small lighter boat is that if you do use chain then the weight on deck and the detriment to stability is significant. They are used with wire rope a lot in some parts of the world and chain leader with wire cable are the only sensible alternative in many cruising areas where synthetic line would not be sensible.

There are several what are termed "high holding power anchors" that can be a size lighter and set in good bottom first pull which saves a bit of mucking about and as you say reset quickly. The Sarca Excel is proving itself a good replacement for a plow in this part of the world. Easier to handle too without the hinged shank. Danforths really are just sand anchors, you could try the similar but heavier dreadnaught type in kelp and rock or coral. I find they are surprisingly good and they hold in mud too. I carry an oversize plow for lee shore conditions, and I'm happy to reset an anchor once at night the odd time, usually when we are getting a combination of blustery offshore gale and a big swell wrapping into the anchorage, that makes every anchor drag. Modern electronics makes the more challenging anchorages a lot safer these days.

For most anchoring you don't want the heaviest anchor, you want a "working anchor" something easier to handle, you wear out your anchor winch too and I've seen deep anchorages where anchor winches couldn't lift the full length of chain with a big heavy anchor . Keep the heavy one for the bad forecast or the more demanding anchorage. Some boats have this one stowed below.
Another point is to use lighter high tensile chain which allows more scope for the same chain weight and less retrieval load on your gear.

 

Potential energy - Wikipedia https://en.wikipedia.org/wiki/Potential_energy

Gravitational energy - Wikipedia https://en.wikipedia.org/wiki/Gravitational_energy

 

What do you expect from Wikipedia? This is a reliable source:
Newton's Law of Universal Gravitation http://www.physicsclassroom.com/class/circles/Lesson-3/Newton-s-Law-of-Universal-Gravitation

 

Ok then:
Potential Energy http://www.physicsclassroom.com/class/energy/Lesson-1/Potential-Energy

 

Gonzo this may help you (it's quite basic high school level physics).

 

Sweet

Reminds me of my O-Level physics teacher...

 

Yep high school basics : Gonzo ( stalwart forum member ) is exhibiting the classic cognitive bias "whereby people who are incompetent at something are unable to recognize their own incompetence. And not only do they fail to recognize their incompetence, they’re also likely to feel confident that they actually are competent".
It's called the Dunning Kruger effect.

That's why I said to him before:

"It occurs to me that without actually studying this it's going to be very hard to understand just why such statements are so far off the mark."

 

I think you should open a new thread rather than keep on hijacking this one. Then we can discuss vibrations.