Anchoring in our waters has seldom been as attractive as it was in times of the pandemic, as you automatically meet all the requirements for hygiene and distance on your own ground iron. In addition, calm suddenly returns to a sheltered, in the best case lonely bay. Only the rustling of the wind and a slight lapping of the waves on the hull can be heard. In addition, there are often grandiose lighting moods at sunset and sunrise. For many, these are the moments that make sailing so valuable.

The right equipment is necessary so that an overnight stay at your own anchor becomes a relaxing experience. Opinions differ when it comes to the choice of base iron: some trust the inexpensive plate anchor, the next swears by its ploughshare version à lCQR, and the third is convinced that only the spade shape of the bracket anchor holds securely in the ground.

In fact, there is no one hundred percent answer to the question of the optimal basic iron. Because depending on the nature of the seabed, contradicting design features are sometimes advantageous, and there is no such thing as an all-round anchor that always works. However, our extensive tests, in which we have checked 27 different types over the past 16 years, clearly show which properties distinguish a good construction and what it is better to keep away from.

A decisive criterion is the size of the anchor, which is usually defined by its weight. The gradations according to ship displacement, as published by manufacturers or classification societies such as DNV GL, can only be approximate recommendations. In general, if you choose a lightweight, you automatically accept losses in terms of security. If in doubt, you should opt for the next higher weight class.

This is especially true for the second anchor. A lighter version is often recommended for this, which is incomprehensible. After all, it should not only complement the main harness, it must also replace it in the event of failure or loss. Therefore, the same criteria should apply when choosing.

## Math instead of a textbook

Even the best anchor is of little use if the connection to the boat is not right. Above all, the length of the chain or line inserted is decisive for the safe functioning of the anchor. The iron can only develop its full holding power if the anchor shaft remains on the ground under load.

Traditionally, the chain length is given as a multiple of the water depth. As a general rule, the recommendations are to put between three and five times as much chain as the depth sounder indicates. With ropes eight times the water depth should be lowered.

Even the range of the recommendation raises doubts as to its correctness; in addition, contrary to all practical experience, the wind force is not taken into account.

YACHT reader René Lattmann thought that too. The experienced skipper of the Cruising Club of Switzerland used the corona-related sailing-free time and dealt with the underlying mathematics. In the static case, i.e. when swings and swells are neglected, the course of the anchor chain or line follows the so-called chain line, which can be calculated with the help of hyperbolic functions.

Fivefold: too little in the flat, too much in the deep. Anchoring according to the textbook at 15 knots of wind. Five times the water depth was attached to a chain. The small markings indicate where the feed begins and from where the dishes move horizontally. Good to see: With 3 meters of water depth, 15 meters of chain is not enough, the anchor shaft is pulled up. From a depth of 8 meters, the chain is significantly longer than actually necessary

Safe minimum lengths: Mathematically correctly calculated from the chain curve, the result is a minimum chain length that depends on the water depth, the wind strength and the chain weight. The wind attack area of the boat is included in the wind dependency, so the diagram only applies to our example boat: a Hallberg-Rassy 340 with an eight millimeter chain

The exact course results from the difference in height between anchor and bow, the pull and the chain weight per meter. This can also be used to calculate the length that is necessary so that the anchor shaft is not lifted.

The exact derivation and solution of the equations would go beyond the scope of this article, but is not necessary to understand the results. It is sufficient to consider a simplified approximation. With the assumption that the wind speed is significantly greater than the water depth, the following formula results for the minimum chain length in meters:

"Depth" is the sum of the water depth and the freeboard and the wind in knots. "K" is a ship- and chain-specific constant:

"A" stands for the wind attack area of the yacht in square meters, "w" is the chain weight per meter in the water. The attack surface must be estimated. For the practical calculations, Lattmann used the information from the book "Richtig ankern" by Joachim Schult and adapted it for a Hallberg-Rassy 340.

Another possibility is the direct measurement of the chain hoist at different wind strengths. However, due to the expected forces of several 100 decanewtons, a massive tensile scale is necessary for this.

## Simulated anchoring

With the help of a program written by Lattmann, different anchor scenarios can be played through. For example, what course a chain has according to the fivefold rule and what length is actually necessary. It is noticeable that the rigid coupling to depth goes wrong both in shallow water and at great depths. With two meters of water and one meter of freeboard, the chain length is 15 meters. Even the pull generated by 15 knots of wind raises this chain so much that the anchor shaft is pulled upwards with two decanewtons, which corresponds to a weight of about two kilograms. With a little more wind, the configuration would definitely be overwhelmed, so more than five times the length is necessary in shallow water.

The opposite occurs at a deeper level. According to the rule of five, 40 meters of chain should be put on eight meters. In fact, with a wind of 15 knots, around 28 meters would be enough to keep the angle of attack of the chain on the anchor at zero.

The stronger the wind, the further the mismatching of the rule of five shifts to greater depths. If it refreshes to 6 Beaufort, a sufficient chain length can usually only be achieved from a water depth of ten meters.

When performing the calculations, it should be noted that an anchor shaft lying flat on the base is required, which undoubtedly provides the maximum holding force of the anchor. It is difficult to predict how much the holding power will decrease due to a slightly upward pulling angle.

If the chain is allowed to rise slightly, the possible anchor depths increase. This consideration is the origin of the simple chain length rules. They are based on the hope that a fully tensioned chain with a pitch of 1: 5 or 1: 8 does not lead to the breaking of the base iron.

## Chain or leash?

The program can also be used to simulate different chain-line combinations or lead anchor lines. The chain is clearly superior, while the differences between the chain feed and the lead line are comparatively small. With the 40-meter-long ballast line, you could just anchor at a depth of four meters in a 20-knot wind. With ropes and ten meters of chain, the maximum depth increases to six meters. A pure chain would be enough for almost ten meters of water, but at 56 kilograms it also weighs three times the chain-rope combination and around nine times as much as the lead line.

A word about the chain: The material and design do not play a role in the calculation - but in practice they do. If you want to be on the safe side, take a galvanized and calibrated version. You should have the breaking load assured. There are also chains in circulation that can only withstand a fraction of the normal forces. Stainless steel chains are not only much more expensive, they are also sometimes prone to corrosion. The problems usually occur on the welds and are not always easy to spot, so only branded goods should be used. The greatest advantages of the stainless steel chain are: it takes up less space in the anchor locker, its smooth surface allows it to slide better, and there is no large pile under the winch.

Chain or line: comparison with 20 knots of wind. The small markings indicate from where the dishes will lie parallel on the floor. With a chain between 25 and 35 meters are necessary. If you use a 10 meter long chain lead and line, you can get by with a 25 meter hawser at a depth of 4 meters. At 7 meters a riding weight is necessary even with a 30 meter hawser, the lead line is already overwhelmed at a depth of four meters, without a riding weight it no longer pulls horizontally.

The effect of a riding weight is also interesting. With a weight lowered right up to the anchor, for example a second anchor, the effective chain length can be increased and an overloaded harness can be stabilized.

The effect depends on the mass of the riding weight relative to the chain. The heavier the weight, the better. In our example with a weight weighing 13 kilograms in the water and an eight millimeter chain, the effective length can be increased by about eight meters or the wind range can be increased from 20 to 25 knots.

## The limits of the model

Due to the influence of the area exposed to the wind and the chain, these values, like the other diagrams, only apply to a Hallberg-Rassy 340 or comparable yachts equipped with an 8-chain. The assumed effective area of the hull and rig exposed to wind is around 13 square meters. Bigger yachts also need more chain, while more streamlined boats need less.

In addition, the calculations relate to stationary anchoring. In practice, however, the yacht will move with increasing wind; she begins to sail back and forth at anchor. Depending on the type of boat and the strength of the wind, considerable speeds can be achieved before the chain becomes stiff and the movement stops. At this moment, the kinetic energy is transferred to the anchor, and higher tensile forces occur. The situation is similar with Schwell, here too the dishes have to cope with additional loads.

Effect of the riding weight: Simulation of a riding weight weighing 13 kilograms in the water with a wind of 20 knots and the vertical forces acting on the anchor (lift). It can be clearly seen that the further it is lowered to the anchor, the greater the effect. With optimal placement, 17 meters of chain are sufficient; without a riding weight, 8 additional chain meters would be required. Conversely, the riding weight extends the wind range of the 25-meter chain to 25 knots

The individual chain links do not have a horizontal bar, so such load peaks can only be cushioned by lifting the chain and reducing the chain slack. However, this is only possible to a very limited extent in shallow water, as there is not enough chain weight. A chain and rope combination is then very advantageous. Mooring ropes can absorb a comparatively large amount of energy due to their stretching behavior of 5 to 15 percent (see test in YACHT 13/2010). Therefore, it cushions the indentation when swinging well. In addition, the swaying can be combated with an anchor sail. In our practical tests, the welding angle at 6 Beaufort could be reduced by around 25 degrees, which significantly reduced the indentation into the chain.

Even if the estimation of the effective wind attack area and the dynamic behavior involve uncertainties, one thing is clearly confirmed by the theoretical considerations and the example calculation: the fixed textbook factor does not result in the optimal chain length.

The shallow water area in particular is likely to be decisive in domestic waters. There should be more than five times the water depth in moderate winds. But the behavior of the chain at greater depths is also interesting. Because deeper water does not automatically mean that an endless amount of chain is necessary.

## Shallow water risk

When the yacht is at anchor, the harness has to cope with much higher loads than previously calculated. This can significantly increase the minimum chain length required

The calculations carried out above to determine the minimum required chain length have already shown that not only the water depth but also the wind pressure play a decisive role and that a simple multiple of the water depth can be dangerous.

Load increase with slight swaying: The example boat, an HR 340, drifts back and forth at the anchor with 0.1 knots. The forces acting on the anchor correspond almost to the static case. The extreme rise in the very shallow water already makes the essential aspect of dynamic anchoring clear

To simplify the mathematics, we limited ourselves to a stationary situation, i.e. only the forces generated directly by the wind were taken into account.

Long-distance sailor and YACHT reader Dr. Mathias Wagner made the same considerations, but also dealt with the forces caused by swell or swell and their consequences.

In addition to the static wind pressure, the kinetic energy of the boat is also considered because it has to be absorbed by the anchor gear. The energy depends on the displacement of the yacht and its speed and can be determined using the following formula:

Where "M" is the displacement of the yacht and "v" is the speed achieved by swiveling. The additional load on the anchor gear increases with the displacement. The speed of the sweat has an even greater influence, as it enters into the square. It can be estimated with the help of the log: If you look at the display in medium winds, you will see that a few tenths of a knot are reached quickly.

For a moment we ignore the dampening effect of a possible anchor drop; then the chain has to absorb the energy of the swell. As it has practically no horizontal bar, this can only be done as potential energy by lifting the chain. Under the condition that the chain does not lift the anchor shaft from the ground, the minimum required chain length can be determined from this. The detailed derivation of the formula can be found on the author's website; it would go beyond the scope of this article.

Therefore we limit ourselves to the result for the chain length in meters:

The first term of the formula describes the static anchoring, as it was already dealt with in YACHT 12/2020. The second term roughly describes the effect of dynamic anchoring. "Y" is the water depth at the anchor including the freeboard, "g" the acceleration due to gravity, "m" the weight of the chain per meter in the water. "∆E" denotes the kinetic energy of the boat, which must correspond to the change in the potential energy of the chain. The parameter "a" summarizes the influences of the chain weight, the area exposed to wind and the wind strength.

## Risky shallow water

What the formula means in practice is best illustrated with an example. As in the previous issue, we assume a Hallberg-Rassy 340 with an 8-millimeter chain. By calculating the wind pressure differently, the area exposed to the wind "Aeff" is 10 square meters this time.

Chain length with slight swaying: The ship hardly moves and the chain has to absorb little energy. Therefore, the effects of dynamic anchoring only have an effect in shallow water depths that cannot be reached anyway due to the draft

At a speed of 0.1 knots, the chain has to absorb an additional energy of only 8 joules. As a result, the load on the anchor largely corresponds to that of the static anchor. The dynamic component can be seen in shallow water. The force acting on the anchor increases sharply.

The consequences for the chain length can be read from the next diagrams. As long as little energy has to be absorbed, the dynamic effects only become apparent in water depths that cannot be reached due to the depth of the water without digging through the mud with the keel.

It becomes critical when the chain has to absorb more energy, for example because the boat is sweating with a knot. As can be seen in the diagram on the left, dynamic anchoring becomes relevant in a large depth range. It is hardly possible to anchor in less than seven meters of water without overwhelming the anchor.

What happens when there is a lot of vibration: The longer it is and the further it is lifted, the more energy the chain can absorb. If it is shallow, it runs at a shallow angle, so more chain has to be moved for the same amount of energy. Safe anchoring is only possible from a depth of about seven meters

The black curves indicate the maximum load on the anchor. For example, if you do not want it to exceed 500 decanewtons, only chain lengths below this curve are permissible. As a result, it may be necessary to move to greater anchor depths in order to reduce the load. The escape into shallow water with a lot of wind and swell is not always the right way!

## Long and thin or short and thick?

It is interesting to compare different chains. 80 meters of an eight-millimeter chain weighs as much as 35 meters of a twelve-inch version. The diagrams show the maximum possible depth for the chain length and wind strength.

What the chain weight brings: If you compare the curves with the diagram for a chain of eight (left), it becomes clear that the heavier chain of twelve can be significantly shorter. In return, a lighter, longer chain can be used to anchor safely at greater depths

For example, with an 80-meter chain of eight in 45 knots of wind, you can anchor at a depth of eleven meters - with a 35-meter chain of twelve, on the other hand, you can only anchor at a depth of up to five meters. Since the distance to the bow roller still has to be calculated for the water depth, there is hardly any room for tidal fluctuations in the water level.

In areas with great water depths or strong tides, you are better served with a thin and long chain. If the Schwoikreis is to be kept small because the bays are overcrowded, but the tides and water depths do not play a major role, then a heavier and shorter chain is the better choice.

Whether the dynamic effects have to be taken into account depends on the conditions and the anchor depth. The shallower the water, the sooner the anchor chain reaches its limits. This makes it clear once again how useful it is to use a rope sling with a shock absorber to relieve the chain. The much greater stretching of the sling can absorb a large part of the energy.