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Old 06-11-2016, 03:08 PM   #101
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Yep, that's it.


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Old 06-11-2016, 03:54 PM   #102
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Originally Posted by Nomad Willy View Post
wadden,
I don't need to calculate anything.
Just wondering what catenary force is.

Eric,
Don't know either. A catenary is given by
- the horizontal force in the rode which is constant throughout its length and
- the vertical force in the rode which is at any point equal to the weight of rode that point is carrying.
These are the two components of the only force a flexible rode can transfer, the tensile force. So which one should be the "catenary force" ?


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Old 06-11-2016, 11:12 PM   #103
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wadden,
Disagree ...
The tension on a rode would be the same along it's length if the rode weighed nothing. But the weight of the chain should vary because w catenary the angle of pull or tension will be different all along the rode and the water density deeper would make the chain lighter ect.

Also I would think the rode would need to be straight for the tension to be equal along it's length.

The link says;
"The weight of the mooring lines activly contributes to the ultimate holding capacity"
It contributes to the tension but not the capacity IMO.
Don't know if I can buy that. The weight of a chain rode pulls on each end. If the rode were level (both ends being at the same height) the tension would be the same at both ends. But on an anchor rode w catenary more pull will be on the boat. But the rode applies pull to both ends because of the rodes weight and that pull would IMO decrease the holding power of the system. The anchor is preloaded by the pull from the rodes weight decreasing the amount of windage that would be necessary to break the anchor out.

Just say'in
Not being an engineer the link is probably true but it seems to me it would'nt be.

So the catenary force is that tension in the rode that is a result of the rodes weight?
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Old 06-11-2016, 11:31 PM   #104
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Bill,
Now I see the link most meaningful .. I think.
The math is beyond me
On page 13 the author shows a catenary curve and I question it's shape. Each half should'nt be reversable. That is if you fliped the catenary line end to end it would be the same ... in the cat curve shown. I don't think so. The catenary should'nt be a liniar line. It should be more curved near the anchor and straighter near the boat. Like most of a fish hook or one quarter of an elipse. The catenary in the drawing lackes this feature. Perhaps it's excluded only to simplify the drawing?
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Old 06-12-2016, 12:04 AM   #105
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My experience: lower an anchor with a short chain and rope rode or with an all-chain rode, and the anchor holds. Have good holding ground here.
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Old 06-12-2016, 01:04 AM   #106
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Quote:
Originally Posted by Nomad Willy View Post
wadden,
I don't need to calculate anything.
Just wondering what catenary force is.
Ok, I think this is another one of those, 'knots per hour' type of semantic arguments. A knot is a combination term that means, nautical mile per hour. So, if you say knots per hour, you are in effect saying knots per hour per hour...

In the case of catenary, it is a function of weight in the rode and its downwards force, counteracting the horizontal pulling force, or words to that effect, I think. So catenary, is by definition a 'force', so if one says 'catenary force' you are in effect saying catenary force force...
How you calculate it?..well, it's in those formulae, which I will leave to better mathematicians than me...I just know it's there, and I love it.
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Old 06-12-2016, 12:03 PM   #107
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[QUOTE=Nomad Willy;

What on earth is "catenary force"?[/QUOTE]

Well it would be less on the moon and less on Mars, due to their smaller masses thus having less gravitational force. But the cool thing about catenary is it works the same as hydraulics, it's all about leverage. It's how my 90 pound wife can apply 4000 pounds of force to a spring line just by standing on it, in order to reposition our boat in a slip on a windy day. It's why suspension bridges can support more weight than the cables suspending them can actually lift without breaking.

I wish you could see the animated gif I posted previously in action as the boat is literally leaping 8 footers while securely anchored in place. If it was a nylon rode the boat would be slingshotting fore and aft until the rode fatigued internally and possibly failed without warning.

I admire Steve Dashew and have read his thoughts on anchoring as well as the stuff Peter Smith posts on the rocna site but I disagree with much of it. Steve Dashew designs and constructs boats that are extremely light and perform very well as long as they stay light, much like Colin Chapman did with lotus years ago. Dashew needs to save weight and likes using ultra light, ultra strong, 1 size down chain and 6:1 scope . There is no doubt that 50 knots of wind would certainly cause that catenary to disappear. But if he had just let out at least 86 meters of chain in the in the first place you wouldn't see the famous almost bar taught chain in the photo he uses to justify his methods. If your willing to put on a mask and do some experimenting or perhaps crunch a few numbers you might be surprised at what you find out about anchors rodes and anchoring.


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Old 06-12-2016, 12:16 PM   #108
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Originally Posted by cafesport View Post
Well it would be less on the moon and less on Mars, due to their smaller masses thus having less gravitational force. But the cool thing about catenary is it works the same as hydraulics, it's all about leverage. It's how my 90 pound wife can apply 4000 pounds of force to a spring line just by standing on it, in order to reposition our boat in a slip on a windy day. It's why suspension bridges can support more weight than the cables suspending them can actually lift without breaking. ......

cut for space......

catenary to disappear. But if he had just let out at least 86 meters of chain in the in the first place you wouldn't see the famous almost bar taught chain in the photo he uses to justify his methods. If your willing to put on a mask and do some experimenting or perhaps crunch a few numbers you might be surprised at what you find out about anchors rodes and anchoring.


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I beach anchored the other day and the pros of ever inch of chain and catenary were evident....

Interesting work


Sure there are limitations on ground tackle and preferences for all sorts of reasons...but usually not the backyard guessing that abounds here and even some pros seem to do based on their point of view.
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Old 06-12-2016, 12:32 PM   #109
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Ok, I think this is another one of those, 'knots per hour' type of semantic arguments. A knot is a combination term that means, nautical mile per hour. So, if you say knots per hour, you are in effect saying knots per hour per hour...

In the case of catenary, it is a function of weight in the rode and its downwards force, counteracting the horizontal pulling force, or words to that effect, I think. So catenary, is by definition a 'force', so if one says 'catenary force' you are in effect saying catenary force force...
How you calculate it?..well, it's in those formulae, which I will leave to better mathematicians than me...I just know it's there, and I love it.
It seems to me (not an engineer) that the total force on the chain (ie, its tension) can be completely described by two components -- horizontal and vertical (net downward only), and that (at least if friction is ignored) the tension on the chain is constant along its length and that it is equal to the vector sum of those two forces. I suspect (at the risk of stating the obvious) that the ratio of those two forces is equal to the tangent at any particular point along the chain.

So, if tangent is important, being able to precisely describe the shape of the rode (which is a parabola in any event) is important, since that shape defines the tangent at every point. Knowing length and weight of the chain rode and its tension, should be the only variables necessary to mathematically describe the shape of the rode.

With that information, and if the strength of the chain is also known, it becomes trivial to calculate, the force necessary to lift the anchor end of the chain off the sea floor, and similarly, the scope beyond which the force necessary to lift the anchor end of the chain off the sea floor exceeds the chain's breaking strength.

It is also then possible to demonstrate that the chain can never be pulled upon hard enough (even disregarding its breaking strength) become "straight". As arbitrarily close to straight as one might want but not perfectly straight. Moreover, when the chain's breaking strength is regarded, not even close to straight, at least not for any typical anchor chain for a decent sized boat.
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Old 06-12-2016, 04:27 PM   #110
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How Much Chain Rode

Please let me try to convince you of the laws of mechanics.
A flexible rode can transmit only a tensile force which is at any point tangential to its curve shape. No forces perpendicular to its shape and no moments can be transferred via the flexible rode (as long as there is no friction between the chain links).
This tensile force T can be divided in one vertical component V and one horizontal component H. Thus
T^2 = H^2 + V^2 (law of Pythagoras)
while obviously
tan(alpha) = V / H
with alpha as the local slope angle measured against the horizontal plane.

For the time being we don't need more formulas and we will make instead two experiments. Let's imagine we are sitting vis-a-vis at a table. Between us lies a chain on the table, 6 ft long with a specific weight of 1 lb/ft (weight obviously 6 lbf). On both ends we have mounted identical spiral springs which will later indicate the force in the chain.

First experiment:
I'm holding my end tight on the table and ask you to pull at your end of the chain without lifting it. Since the chain lies on the table which is taking the weight of the chain the only force in the chain is your pulling force, let's say 4.5 lbf. Obviously on both ends we have only a horizontal component of the tensile force. The spiral springs on both ends will be elongated by the same amount according the spring constant, let's assume your pull has caused 10 inch on both springs indicating that the force at both ends has the same magnitude.
I will mark now the length of the spring on my end on the table in order to prepare our set up for the next experiment.

Second experiment:
I will ask you now to lift your end 3 ft above the table and to pull so at the chain that only one last chain link on my side touches the table while the rest is completely lifted. The chain will establish its catenary curve and the horizontal pull on my end will be again exactly 10 inch, thus the tensile force on my end which is a truly horizontal force is again 4.5 lbf (I picked the numbers accordingly). But the spring on your end will now be elongated by 16.7 inch indicating that the tensile force on your end has increased to 7.5 lbf.
Why? Because you hold in addition to the horizontal component of 4.5 lbf the complete weight of 6.0 lbf in your hand:
4.5^2 + 6.0^2 = 7.5^2
Second observation: the slope angle alpha of the chain is 0 degrees on my end and increases continuously to 53 degrees on your end. This corresponds to
tan(0) = V / H = 0 / 4.5 on my end and tan(53) = 6.0 / 4.5 on your end.
The increasing slope angle from my end to your end indicates that the vertical component V of the tensile force and therefore the tensile force itself increases along the chain because every chain link has to carry the weight of all chain links below.

To summarize: H constant along the chain length while V and consequently the resulting tensile force T increases from chain link to chain link with the weight each link has to carry.



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Old 06-12-2016, 04:48 PM   #111
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How Much Chain Rode

Quote:
Originally Posted by Nomad Willy View Post
The anchor is preloaded by the pull from the rodes weight decreasing the amount of windage that would be necessary to break the anchor out.
?

Eric,
Definitely not. The weight of the lifted chain gives the vertical component V and contributes via
H = V / tan(alpha)
to the horizontal holding force H at the bow. No preload on the anchor, it rather pulls our bow back towards the anchor. And H is constant throughout the applied chain ...


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Old 06-12-2016, 05:11 PM   #112
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Wadden,
Remember cafesports wife on the spring line? Every bit of weight on a rode above the seafloor is pushing down on the rode like cafesports wife on the spring line and pull is exerted on the line. Either the boat moves or the anchor .. or both. But when the boat is held in a specific place as by the wind the pull on the line will be felt down the rode to the anchor. And the weight of the rode develops pull on both ends of the rode. The boat is usually pulled closer to the anchor but if you could instantly change the rode from all chain to all nylon the pull from the weight of the rode would be far less and the rode would rise up and the pull that was exerted by the chain weight would all but disapear.

All that would mean is that the boat would drift upwind and the tension on the rode would be the same .. so I was wrong. The thing that would be different is that the rode would assume more catenary .. more droop in the rode. So w an anchor rode the boat would just be pulled closser.

Only if the rode was attached to a dock (fixed point) and a set anchor would the weight of the chain increase the tension on the rode. Yes I was wrong.
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Old 06-12-2016, 05:17 PM   #113
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wadden,
Disagree ...
The tension on a rode would be the same along it's length if the rode weighed nothing. But the weight of the chain should vary because w catenary the angle of pull or tension will be different all along the rode and the water density deeper would make the chain lighter ect.
I believe you are correct. i must rethink.
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Old 06-12-2016, 05:27 PM   #114
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MYTraveler,
I agree the chain can never be pulled straight.
But can it be for all practical purposes? More or less straight at the anchor end?

I think so. But w the rode at low pulling forces like when you're setting your anchor there is usually lots of catenary and the anchor sets more readily and probably deeper. But in a gale and w a reasonable amount of chain weight the chain rode would become more or less straight and therefore have no advantage over nylon line. I think that this is true to the degree that just as Chapman states "a few feet of chain" is all that can reasonably be used to any significant advantage.

So if it's going to blow one should depoly "a few feet of chain" to insure good setting and a big anchor to hold the boat.
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Old 06-12-2016, 06:02 PM   #115
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If the horizontally pulling force H exceeds significantly the weight of the chain the ratio
V(x) / H
with V(x) the vertical component of the tensile force T in the chain at the horizontal distance from the anchor x will become more or less independent from the position x. Thus with
tan(alpha(x)) = V(x) / H
the slope angle alpha of the chain will become independent from the local distance x to the anchor. Meaning the chain has become stiff!
We will not be able to recognize this excessive load situation by a significantly increased distance to the anchor e.g. by monitoring our anchor alarm since the difference between (ultimate) catenary and stiff chain will be in the range of 2-3 feet only under typical anchor situations.
Indication could be the significant change of the slope angle at the bow. But is there anybody monitoring this? Me not.


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