Scope vs catenary

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50-60 knots of wind at Deception Island, Antarctica. With 6:1 scope in 8 meters of water, no effective catenary remains in this all-chain rode. (Click picture to enlarge)
PeterSmith-icon.png The topic of this section is supplemented by an article at the Rocna designer's personal website.

To read this article, click here: Catenary & Scope In Anchor Rode: Anchor Systems For Small Boats

Catenary is a word which appears frequently in articles and books on the topic of anchoring. It is a mathematical term which describes the shape of a flexible line (like chain) hung between two points (like the bow of your boat and the seabed, or the anchor). Heavier chain means that it takes more force to straighten the rode, so the catenary curve remains more pronounced which in turn keeps the angle of pull on the anchor lower than otherwise (which is beneficial to the ultimate performance of the anchor).

Scope on the other hand is the ratio between the length of rode deployed and the distance the boat is from the seabed (the height from the seabed to the bow-roller or hawse-pipe, not just depth). By way of simple trigonometry, it is obvious that for a constant depth, a longer rode (greater scope) will present a lower angle of pull on the anchor.

Scope and catenary are accordingly the only two methods by which a skipper can assist the anchor by providing it with a pull which is as close as possible to horizontal. The lower this angle, the better. Traditionally, heavy chain has been recommended to provide the 'all important' catenary. In the past of big ships and their anchors, this had a good basis. Modern anchors and small boats however change this picture.

Limits of catenary

The problem with catenary is that it does not really provide that much assistance. While the force required to pull a length of chain bar tight is extremely high, the force required to straighten out most of its curve is actually relatively low. We can easily demonstrate this by using a static computer simulation.

Simulating moderate winds of 20 knots, the catenary curve is obvious and the angle of pull on the anchor is clearly lowered. 20 knots of wind however is unlikely to trouble an adequately sized anchor in most sea-beds.
Simulating more testing winds of 50 knots, the catenary curve has all but disappeared. The chain is nearly straight and the angle of pull on the anchor is not being improved by the weight of the chain.

We must examine the anchor's requirements, what it is capable of handling at any given angle of pull and for any given seabed, and how this compares to the forces that can be expected to eliminate most of the catenary curve from the rode.

In the West Marine testing in 2006, anchors around the 15 kg (33 lb) size were tested, with a rode consisting of 1" (25mm) nylon rope with a 20' (6m) leader of 5/16" (8mm) chain. The Rocna was the top performing anchor – Yachting Monthly reported "The Rocna was a powerful, impressive performer in our tests, recording instant sets at multiple 5,000 lb maximum (or near max) pulls at 5:1 scope." The behavior of the rode at these limits of performance were described by SAIL magazine, who commented that "the anchor's resistance produces whirlpools of turbulence [from the test vessel's propellers]... and a bar-tight cable."

So, it is clear that modern anchors are very efficient. Some, particularly the Rocna, also endure high pull angles fairly well, even in poor holding sea-beds. This means that the range of force vectors that the anchor can handle is quite wide, and it turns out that the majority of rode make-ups (at least those that are practical) lose most of their catenary curve well before the anchor is likely to be troubled. Beyond this point (once the rode is effectively straightened), the weight of the chain makes absolutely no difference to what the anchor will do, and the sole factor of import is the geometrical scope.

What does this mean?

The practical consequence of this is that it is not necessary to carry heavy chain merely for the sake of it. Rather, chain can and should be as light as possible, subject to strength requirements. Many boats could lose a large amount of weight by swapping to a lighter but stronger chain, and then investing part of that weight back into a larger anchor. Performance (holding power) of the system is thus substantially improved, while total weight is actually lowered. Find more, including recommendations for chain sizes, in the chain section.

Scope ratios

A 3:1 ratio of rode-length to water-depth should be considered minimal ("1" being the vertical distance from the seabed to the bow roller, not the waterline, at high tide). Generally speaking about 5:1 is appropriate. Typically you should set the anchor at the same scope it will be left at, in order to be sure the anchor can re-set itself again should it pull out. However, it may be necessary to set it at a higher scope and then pull in some of the rode.

In bad conditions, the ratio can be increased up to around 8:1. There is little benefit in going beyond this point, and boaters using scopes of 10:1 and higher are gaining almost nothing from their efforts and huge swinging circles. At 8:1, the maximum angle of pull on the anchor is already capped at just over 7°, and of course the scope must be doubled in order to halve the angle (i.e, even very large increases in the scope result in angle reductions of only several degrees). Considering the desire to lower the angle against the practical problem of longer rodes and increased swinging circles, 8:1 is roughly the 'sweet spot'.

Practical matters

Scope is calculated from the length of rode deployed (forward of the roller or fairlead) and the distance from the sea-bed to the roller or fairlead. For the latter measurement, it is important to consider the possible scenarios the vessel may encounter while anchored. The water depth at high tide should be considered, particularly in shallow water where the tide could easily double the depth.

In adverse conditions, swell or waves will cause the vessel to pitch. The vessel will place the highest loads on the anchor system when it is pitching upward, and the effective scope ratio is reduced at this point because the bow is higher.

It is necessary to be able to measure the length of rode deployed. Exact accuracy is not critical, but an idea within 5 meters or so is important. For techniques on keeping track of chain and rope deployed, refer to counting chain.

Catenary in deeper water

The rode's catenary effect on holding power is determined by the amount of chain and/or rope suspended between the boat and the seabed, so the need for a high ratio decreases with increasing depth, as shown in the graph below. In other words, in deep water, catenary does start to have a practical impact.

How the situation changes with varying depth: 8mm (5/16") chain with 500 daN (1,124 lb-force) in the system, which equates to approximately 40 knots wind on a 10m / 33' vessel. A constant angle of pull on the anchor of 6.6° is maintained for the same force.

This chart is intended to illustrate an example scenario, in order to show how this relationship between depth and scope works because of catenary. It is not supposed to recommend a particular scope for a particular depth – there is no such simple conclusion, and rules of thumb are generally overly simplistic. A scope of 3:1 should normally remain the minimum. In very shallow water this minimum may be too low. Then again, if your boat is in shallow water, it is probably well sheltered. There are many variables to consider.