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Static Behavior (2) - Heterogeneous Rode

1. General idea

Intuitively, the reason why an all-textile rode cannot get tangent to the bottom is that it lacks weight in its lower part. Conversely, the upper part of an all-chain rode looks ineffective, except to sink the front of the boat ;-) So, instead of spreading the weight evenly along the rode, putting more weight in its lower part and less weight in its upper part could be a good idea.

In practice, 2 technologies are commonly in use:

Both solutions are studied below.

2. Kellet

In the previous page, formula (1.2) gave the critical value Fc that lifts an homogeneous rode completely:

    (1.2)

If we add a weight K at distance Lk from the bow (fig. 1.6), what improvement can we expect beyond Fc?

Figure 1.6 - Kellet

There is no simple expression of the result, but if we assume the scope is greater than 3:1, an acceptable approximation (with less than 6% error) is given by:

    (1.6)

These expressions show the improvement equals the kellet weight K multiplied by the ratio Lk/H. Consequently, the best improvement is obtained by putting the kellet near the anchor, where it equals the kellet weight K multiplied by the scope N.

With the same kellet in the middle of the rode, the improvement would be halved.

An all-textile rode with a kellet close to the anchor has the same performance as an all-chain rode of same length, with only half the total rode weight. This confirms that concentrating the weight down the rode, if possible, would be much more effective than spreading it along the rode.

Unfortunately, handling capabilities limit the weight of actual kellets around 22 kg (50 lb), which is insufficient in severe wind conditions unless the scope is very large.

In addition, using a kellet does not significantly improve the swinging radius R.

3. Mixed Rode

Using some length of chain down a textile fibre rode is a better alternative, even though less effective than a kellet the same weight for a given rode length. For other reasons we'll study in the dynamic behavior chapter, polyamide (aka nylon) fibre lines are generally preferred. Since the weight of nylon in seawater is very small, the nylon part of a mixed rode looks like a straight line as soon as the pulling force exceeds a few pounds. In this sense, one can consider the additional line as a passive extension of a chain rode, used when the available chain length cannot keep the anchor flat on the bottom in the current depth and wind conditions.

It is interesting to estimate the height gain that can be achieved this way for a given pulling force F. Let's assume our chain-only rode (length Lch) gets completely lifted at height Hch. If we insert a nylon line (length Lny) between the chain and the bow, the allowable height is increased by Hny (fig 1.7).

Figure 1.7 - Mixed Rode

Hny is approximately given by the following formula:

    (1.7)

Thus, if a 25 m (82 ft) all-chain allows a 5 m (16 ft) height, adding a 12 m (39 ft) nylon line allows a 10 m (33 ft) extra height. To achieve the same improvement by increasing the length of the chain-only rode, we would need 11 m (36 ft) extra chain, with much weight penalty than 12 m (39 ft) nylon line, and a meager 1 m (3 ft) decrease of the swinging radius!

This confirms that an all-chain rode is unnecessarily heavy, and that it can be replaced by a slightly longer mixed rode for the same holding effectiveness.

The immediate question is: what is the best ratio chain length vs. nylon length? Well, there is no absolute answer, because it results from a compromise between many criteria that may vary according to boats and skippers. Anyway, since the chain must be chosen before going to sea, the right question should be: what chain size and length should I buy?

In some countries, administrative regulations specify minimum characteristics for anchor(s) and rode(s), given the length and/or the displacement of the boat. If minimizing the on-board weight is of prime importance, the legal minimum can be chosen. If more effectiveness takes priority, the size and/or length should be increased. (in case a motorized windlass is used, this helps handling the rode, too). However, whatever the available chain length, this does not mean putting some nylon in the actually veered rode is useless - more on that in the dynamic behavior chapter.

Although we cannot give a generic answer to the above fundamental question, specific answers are quite possible thanks to our spreadsheet - see below.

4. Elastic Rode

Up to now, we have assumed the rode material(s) had no stretch, which obviously is not true: all real materials have some intrinsic elasticity. From the present static point of view, the most notable effect is a slight increase of the swinging radius. On the other hand, in transient situations when the pulling force get high, the rode elasticity can have much significant effects - more on that in the dynamic behavior chapter.

Consequently, it is very important to know the rode extension as a function of the pulling force F.

For a metallic rod, as long as the tension T does not exceed the elastic limit of the material (beyond which the device does not recover its initial length when the tension gets back to zero), the extension is proportional to T. Let L0 be the length for T = 0, A the cross-section area of the rod and E the elasticity module of the material length. L has the following form:

    (1.8)

For ordinary steel, E is typically 21000 daN/mm2. Thus, we find a 1000 daN (2200 lb) tension applied to a 10 mm (3/8 ") diameter rod gives a 0.06 % extension, i.e. 0.6 mm/m only.

A chain the same size is slightly less stiff than a rod, so it will stretch approximately 20 % more for the same tension.

On the other hand, a nylon line is much more stretchable (about 200 times more), but the extension is not proportional to the tension at high values. We won't go into details here, but the spreadsheet we reference below includes an elasticity model that allows computing the net length of the simulated rode.

5. Pulling Force vs. Boat Drift

As we pointed out in the previous page, knowing the static relation between the pulling force and the horizontal coordinate of the boat is of prime importance to predict the movement of the boat and the strains that will affect the anchoring tackle under wind gusts (see the dynamic behavior chapter). Obviously, the elasticity of the rode must be taken into account. Let's compare the curves for the examples of paragraph 3 above:

.

Figure 1.8 - Boat Drift vs. Pulling Force

Thanks to the elasticity of its nylon part, the mixed rode has a more progressive behavior than the all-chain one at high pulling forces. This will help reducing constraints under severe wind gusts (see the dynamic behavior chapter).

6. Simulate Your Own Mixed Rode

You can make your own choices with the spreadsheet sta_mix.xls (requires Microsoft® Excel 2011 or +). It allows simulating a generic rode that includes a chain, a nylon line and a kellet. The kellet can be canceled out by choosing a null weight. Similarly, a null nylon length simulates an all-chain rode, and vice-versa. In addition, the intrinsic elasticity of chain and nylon can be taken into account.

Hint: To compare the performances of 2 rodes, you can duplicate the spreadsheet file under a different name (e.g. sta_hom2.xls), so you can open both files and display their windows side by side.

7. Conclusions

Let's check both technologies against the criteria defined at the top of the previous page (Req. 4 and 5):

Criterion
Kellet

Mixed (Chain + Textile)

Can pull the anchor parallel to the bottom?

Yes, but limited by kellet weight Yes
Easy to stow? No (kellet) Yes
Easy to wind and unwind? No (kellet setting-up and removing) Yes

Theoretically, the Textile + Kellet solution gives the best "effectiveness/weight" ratio, but only if the kellet is close to the anchor. Unfortunately, handling a heavy kellet is difficult and dangerous, so it turns out to be unsuitable in strong wind conditions unless the scope is very large. For the same on-board weight, a mixed rode is slightly less effective, but it suffers none of the drawbacks of the kellet solution. Of course, adding a kellet to any combination of chain and textile is not forbidden!

Now that we master the static behavior of an anchoring rode, we are ready to tackle the effects of wind gusts, which are responsible for most dragging situations.

Figure 1.9 - Cala Francesa (La Graciosa, Canary I.)

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