Effect of anchor chain elasticity

[BjarneK]

I have done some calculations regarding energy absorption in anchoring equipment in dynamic situations (wind and/or waves). This can be done in several ways, but I have chosen a generic route where a given amount of kinetic energy is added to the boat, moving it away from the anchor. This energy must be absorbed by the chain and snubber.

Let us consider the example from my previous post on catenary: Anchor chain catenary is real - Cruisers & Sailing Forums

To recap, the boat is 42', the wind is 60 knots, 8 mm chain is used along with a 5 meter long 5/8" nylon snubber. The boat is anchored in 6 meters of water and has a 1.2 meter freeboard. The total (horizontal) force exerted on the boat in these conditions is 681 kg. Let us assume that half of this is the static load from the wind and that the rest is dynamic load from wind and/or waves.

If the boat is in a steady state of 340.5 kg of wind force, it turns out that adding 363 Joules (J) of kinetic energy to the boat will push it to a peak horizontal force of 681 kg when it comes to rest. So we will assume a static force of 340.5 kg and an additional 363 J of kinetic energy being added.

For a ten ton boat, the 363 J corresponds to just over half a knot of speed. Remember that this speed applies at the steady state point from the wind force, so speeds may be higher when the loads on the rode are smaller (i.e. the boat is closer to the anchor). Also, the speed is directly away from the anchor, creating maximal tension.

It turns out that the energy will be absorbed as the boat moves 23.3 cm away from the anchor. It should be noted that the anchoring system not only absorbs the 363 J of kinetic energy, but an additional 778 J from the wind pushing the boat along the 23.3 cm (0.233 m * 9.81 N/kg * 340.5 kg = 778 J).

The energy absorbed is distributed as 69.7% from the rope elasticity, 17.9% from gravity (chain being lifted) and 12.4% from chain elasticity.

Now, what if the snubber parted? Then the boat comes to a stop in only 13.0 cm since the elasticity of the nylon is gone. The peak force is 1,095 kg instead of the 681 kg with the snubber. This is a bit over the working load of the (Maggi Aqua4) chain, but should still be OK (though a good chain stopper is needed). The energy absorbed by the chain is now 38.4% due to gravity and 61.6% due to the elasticity of the chain.

What if we use a hypothetical non-elastic chain? In this case, the only possible place to store energy is by lifting the chain. In the case described here, only about 220 J is available be lifting the chain, even if it got totally straight. So with a non-elastic chain, something else would have to give (probably the anchor dragging or the chain stopper breaking).

What if we only added half the energy (181.5 J), again without a snubber? In this case, energy will be absorbed 50.6% by gravity and 49.4% by chain elasticity. Gravity plays a bigger role at lower forces. The peak force with the elastic chain model will be 823 kg. Using an inelastic chain in this case would give a peak force of 3,466 kg!

In conclusion: With a snubber, chain elasticity plays a role, but a small one. If the snubber parts, chain elasticity can become important.

[Dsanduril]

I'd be interested to see spreadsheet/program/website with which to play with the numbers. For instance, in your example, I'd probably use a heavier chain (10mm) and a smaller nylon snubber (1/2"). Would love to play around with various numbers, could lead to an actual informed decision about rode selection and design.

[BjarneK]

Originally Posted by Dsanduril

I'd be interested to see spreadsheet/program/website with which to play with the numbers. For instance, in your example, I'd probably use a heavier chain (10mm) and a smaller nylon snubber (1/2"). Would love to play around with various numbers, could lead to an actual informed decision about rode selection and design.

Thanks. Informed decisions is why I started doing this. At this moment, the program is a command line program written in C to run on Linux. Not exactly all that user friendly... I hope to make a web version of the program, so everybody can try it.

While you wait for that, I put in a 5 meter 1/2" snubber and 10 mm chain for you. It reduces the horizontal peak load from 681 kg to 607 kg. The rode load is little higher at 621 kg since there also is some downward force at the bow. With a 1/2" snubber, you are getting close to the working load of the Yale Double Brait (750 kg), but of course the breaking load is much higher. If high winds are expected, a longer snubber would probably be in order. Using a 10 meter 1/2" snubber with 10 mm chain reduces the peak horizontal load to 547 kg (remember that the base wind load represents 340.5 kg of this, so the reduction is quite significant).

[Dsanduril]

Thanks for running one other scenario. Fun to see the results. I have sometimes thought about a "variable elasticity" snubber, for instance a length of 1/2" and then another length of say 5/8" that is secured with some slack. Under normal conditions the smaller unit carries the load, but as it stretches the heavier line starts to pick up some of the task. Would want to play around with what are the loads (maybe the smaller snubber simply isn't needed because at the lower loads catenary is sufficient?) and what gets transmitted to the boat. Anyway, it has been quite interesting, so thanks for taking the time.

[Dave_S]

There is also the combination of the rate of horizontal and vertical alignment of the boat to consider as the loads increase, this could both add and reduce peak loads.

[thinwater]

In fact, if you had my book (Rigging Modern Anchors) this is discussed in Appendix V. I got the info from chain manufacturers. Shameless plug.


In fact, stretch does vary with the grade of steel, not because the elasticity of steel changes (not really), but because higher grade steels are used at higher stress at their WLL.


Elongation at the WLL:
grade 30 1%
grade 43 1.5%
grade 70 1.8%


Or at least, those are the numbers I was given.


And in fact, this is an important factor at high load. 1.5% of 300 feet of chain is 4 feet. You will only see this in a SEVERE storm, and it's not enough (remember that you are only cycling about 1 foot of this), but it helps.


If chain did not stretch, chain binders on trucks could not stay tight. This is why they don't use grade 30 chain.

[BjarneK]

Originally Posted by thinwater

In fact, if you had my book (Rigging Modern Anchors) this is discussed in Appendix V. I got the info from chain manufacturers. Shameless plug.


In fact, stretch does vary with the grade of steel, not because the elasticity of steel changes (not really), but because higher grade steels are used at higher stress at their WLL.


Elongation at the WLL:
grade 30 1%
grade 43 1.5%
grade 70 1.8%


Or at least, those are the numbers I was given.


And in fact, this is an important factor at high load. 1.5% of 300 feet of chain is 4 feet. You will only see this in a SEVERE storm, and it's not enough (remember that you are only cycling about 1 foot of this), but it helps.


If chain did not stretch, chain binders on trucks could not stay tight. This is why they don't use grade 30 chain.

I also came to the conclusion that higher grade chain has more elastic stretch at working load for the reason you describe. The numbers I have are somewhat lower, though. For Maggi chain which has conservatively rated working loads of 20% of the breaking loads, I get 0.14% stretch at working load for Aqua4 (like G40) and 0.25% for Aqua7 (like G70). Two sources give the effective modulus of chain around 60 GPa. The above numbers are for 54.4 GPa which is my best guess for this type of chain. This thread gives the details: http://www.cruisersforum.com/forums/...ch-225738.html

[thinwater]

Originally Posted by BjarneK

I also came to the conclusion that higher grade chain has more elastic stretch at working load for the reason you describe. The numbers I have are somewhat lower, though. For Maggi chain which has conservatively rated working loads of 20% of the breaking loads, I get 0.14% stretch at working load for Aqua4 (like G40) and 0.25% for Aqua7 (like G70). Two sources give the effective modulus of chain around 60 GPa. The above numbers are for 54.4 GPa which is my best guess for this type of chain. This thread gives the details: http://www.cruisersforum.com/forums/...ch-225738.html

Correct. I dropped a decimal. Thanks for catching it!


Corrected, my numbers were:


Elongation at the WLL:
grade 30 0.1%
grade 43 0.15%
grade 70 0.18%


Which is as close as it gets, allowing for minor brand differences.

[a64pilot]

Originally Posted by thinwater

If chain did not stretch, chain binders on trucks could not stay tight. This is why they don't use grade 30 chain.

I don’t think that’s why they use transport chain, because as you said electricity is close to constant. I used cheap chain all the time hauling tractors and bulldozers, but never Commercially so I wasn’t subject to the same rules commercial hauler was.
However the amount of stretch is very little, for example the reason your cylinder head stays firmly clamped to the block is due to bolt stretch, in fact some of the better torquing systems use the wrench arc method, which actually measures the amount of stretch and not just how much force is applied to the bolt.
However the actual amount of stretch is quite small, but present of course.
You rigging stretches to, likely why when sailing one side is much looser than the other, the tight side stretches some. How much? Not much would be my answer, but that’s not very scientific is it.

[thinwater]

Originally Posted by a64pilot

I don’t think that’s why they use transport chain, because as you said electricity is close to constant. I used cheap chain all the time hauling tractors and bulldozers, but never Commercially so I wasn’t subject to the same rules commercial hauler was.
However the amount of stretch is very little, for example the reason your cylinder head stays firmly clamped to the block is due to bolt stretch, in fact some of the better torquing systems use the wrench arc method, which actually measures the amount of stretch and not just how much force is applied to the bolt.
However the actual amount of stretch is quite small, but present of course.
You rigging stretches to, likely why when sailing one side is much looser than the other, the tight side stretches some. How much? Not much would be my answer, but that’s not very scientific is it.

In fact, the stretch of rigging is well known and can actually be used to tune it, in place of a gauge. Seldon says so (see page 32).
http://www.seldenmast.com/files/595-540-E.pdf

[tarian]

I believe you calculations will be wrong , as the energy stored in the cleat and the bow roller and the windlass take up what is potential energy , which will also flow through the bolts to the bulkheads, energy used, and in better words the total load is not shared by the chain , the snubber and the anchor alone. there are many factors to consider to fully get a true number , way beyond my limited physics.

In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself,
Also Hookes law could be an interesting law to follow although used for springs the way the chain will move can be like a spring

https://en.wikipedia.org/wiki/Hooke%27s_law
https://en.wikipedia.org/wiki/Potential_energy

[thinwater]

When the load comes on hard, the bow dips.


If the boat is yawing when the rode comes tight (probably is) the boat will start to straighten out.



If a wave lifts the bow as the rode comes tight (probably is, since that pulls the chain), that is another, common mechanism, perhaps the most important in shallow, exposed water.


The math is horrible. It's simpler, in many ways, to just measure it. The actual tortured motion of the boat in waves is complex.

[guyrj33]

Originally Posted by a64pilot

I don’t think that’s why they use transport chain, because as you said electricity is close to constant. I used cheap chain all the time hauling tractors and bulldozers, but never Commercially so I wasn’t subject to the same rules commercial hauler was.
However the amount of stretch is very little, for example the reason your cylinder head stays firmly clamped to the block is due to bolt stretch, in fact some of the better torquing systems use the wrench arc method, which actually measures the amount of stretch and not just how much force is applied to the bolt.
However the actual amount of stretch is quite small, but present of course.
You rigging stretches to, likely why when sailing one side is much looser than the other, the tight side stretches some. How much? Not much would be my answer, but that’s not very scientific is it.

if one side of your rigging is much looser than the other, your rigging wasn't tight enough before you started sailing.

[dick sargent]

My 30 proof coil chain stretched when it hung up under a ledge when I was hauling it in. 3 ft swells but what a jolt. Replaced wildcat too. I used 30 proof because it was available world wide at the time. Replaced 300' in Panama.

[Taipe]

Most of the energy is absorbed by two factors: lifting of the chain from a state of rest and motion of the vessel from it's relative state of rest. Why are you interested in physical formulas to gauge stretch of chain links? You must already know that the vulnerability of a chain to stretch is when it remains stiff at a 180 degree plane. And, the proof (hee, hee, unconscious pun I suppose) is in the pudding when identified from cumulative physical stresses after which the chain links no longer fit onto or release from the gypsy.