BASIC THEORY OF ANCHORING.
This is covered in more detail in two articles by J H Knox (1) Anchoring by Numbers, Yachting Monthly, August 1997 (2) Snatching at Anchors, Practical BoatOwner, February 1999. The main conclusions are summarised below.

DIVING ANCHORS!

Modern plough and spade type anchors are designed to bury themselves completely. The way the work is shown in Figure 2. When pulled very hard by a horizontal cable, they first of all dive into the seabed. As they bury themselves, the cable bends down into the seabed and eventually a stable state is reached when the cable leaves the buried anchor at an angle above the horizontal. The diving force is now


balanced by the upward force of the seabed on the partially buried cable. When the anchor is pulled so hard that it drags, it ploughs horizontally under the surface while still remaining buried. When pulled with a cable which leaves the sea bed at an small angle above the horizontal, the anchor will remain buried but not so deeply as before, and the ploughing-force will be lower. But if the angle of pull is above a critical value, the anchor will pull out completely. This critical angle appears to be around 15-20° for most anchors. This corresponds to a scope (Chain length to Depth ratio) in the range THREE to FOUR with a taut anchor cable. It is therefore wise to regard FIVE as the minimum scope for safe anchoring.

THE ALL-CHAIN CATENARY

If your anchor cable is all-chain, it will hang from the bow in a curve called a "catenary". The chain performs two functions. It exerts a horizontal force on the yacht which resists the force produced by wind and waves, and it absorbs energy when the yacht surges backwards in response to gusts and waves. A completely slack chain it exerts no horizontal force, and hangs vertically from the bow of the yacht, while a bar-taut chain exerts an enormous force. A crucially important state between these extremes is the borderline state, when the last links of the chain are just about to lift from the bottom. The borderline state is the limit for safe anchoring with an all-chain cable. This is because a chain tensioned beyond this point can absorb very little energy even though the tension becomes enormous. Snatching is the physical manifestation of this failure.
The force exerted by a catenary in the borderline state is given to a good approximation by the formula:

Catenary Force in kg = Specific chain weight x (chain length)²/(2 x Depth)

F(catenary) = w x S²/2D (units: kilograms, metres) Formula 1

Force is measured in Kilograms; specific chain weight in Kilograms/metre; Chain length and depth in metres.

When at anchor the catenary force is balanced by the wind force. Thus to understand more fully how one can achieve safe anchoring it is necessary to know about the wind forces experienced by yachts.

WIND FORCES
The main force which is experienced by a yacht at anchor comes from wind resistance. It is proportional to the wind speed squared and to the frontal area presented by the yacht. Broadly speaking the frontal area will be proportional to the square of the length. Experience with our own yacht MYFANWY (a Hustler 35) shows that the cable tension in a wind varies widely over time. But, provided snatching does not occur, the maximum force on the anchor cable is given by the approximate formula:

Maximum force in kg = (yacht length in metres)² x (wind speed in knots)²/500

F(wind) = L²xV²/500 (units kilograms,metres and knots) Formula 2

Again force is measured in kilograms; wind speed in knots, yacht length in metres.
So with a 10 metre yacht anchored in a 30 knot wind, the maximum force on the anchor cable is expected to be about 180 kg if the chain is not tensioned beyond the borderline state. The force will be much larger if snatching occurs.

CHAIN LENGTH REQUIRED FOR BORDERLINE STATE
For safe anchoring with chain, the wind force should be no larger than the force required to lift the last links of the chain off the bottom at the anchor. Equating the forces given by Formulae 1 and 2 gives the expression:

Chain length = (1/16) x (Yacht length ) x (wind speed ) x Square root of (Depth /specific chain weight)
S = (1/16) x L x V x (D/w) ^0.5 Formula 3

Formula 3 can readily be made specific to one's own yacht, since the yacht length, L, and specific chain weight, w, are fixed. Thus, the formula for a 10 metre yacht with 3/8" chain (L = 10 metres, w = 2.0 kg per metre) becomes:

Chain length in metres = (wind speed x [depth/5]^0.5
s = v x (D/5)^0.5 (units in metres and knots) Formula 3A

If this yacht is anchored in 5 metres of water, the chain length required equals the wind speed. For other depths a correction has to be made according to the square root of the depth. However most yachtsmen will have a preferred depth for anchoring, around which they make only small variations. If for example the preferred depth is 8 metres, the Formula 3A reduces to a still simpler form:

Chain Length = (5/4) x Wind Speed Formula 3B

The factor 5/4 will of course be different for different yachts and preferred depths, but the multiplication factor is readily evaluated. Once this is done, it is easily committed to memory. Of course a scope of FIVE should still be regarded as a safe minimum except under the mildest conditions.

ANCHORING IN SEVERE CONDITIONS

For an all-chain rode, Formula 3 states that the length of chain required for safe anchoring is proportional to the wind speed.Typically one will need a length of chain at least equal to this. Indeed the Formula 3 may well call for more chain than one can deploy. You may not have that amount of chain, or your swinging room may be restricted. But if too little chain is deployed snatching is bound to occur, since the chain will straighten beyond the borderline state: it will lift from the bottom at the anchor, and it will not be able to absorb the energy of the surging yacht. For a well buried anchor, snatching will cause the anchor to "walk" downwind in small steps under the seabed and it is very likely ultimately to pull out due to obstruction or weed. Snatching spells grave danger to a yacht at anchor.

If one cannot let out enough chain to satisfy Formula 3, what is the solution? The first point to note is that a modern anchor will hold even if the cable leaves the anchor at a small angle above the horizontal although this must be less than about 15°. It may not hold to such a high force but it will still hold. To avoid snatching, which would occur with an all-chain rode, an energy absorbing spring must be introduced. The best spring is undoubtedly nylon rope. Experience shows that 10 or 20 metres of nylon Anchorplait, 14 to 20 mm diameter can absorb many times the energy which can be absorbed by chain. But it is still more important now to ensure that the scope exceeds FIVE as ones anchor cable is likely to run straight from the anchor to the bow roller in the stronger gusts.

QUANTITATIVE ANCHORING WITH ANCHORWATCH
The theory of anchoring shows that measurement of the actual tension on the anchor cable by a device such as ANCHORWATCH can give valuable information about the state of the anchor and its cable when it is hidden below the water. Before anchoring, a skipper should make an assessment of the likely wind force from Formula 2, and also calculate from his own version of Formula 3 the amount of chain which he would need for safety. If this proves to be too large due say to limited swinging room or limited availability of chain, then addition of a nylon spring will be necessary to take up the snatching loads which would otherwise be inevitable. Having calculated the anticipated loading, the holding should then be tested up to that level using ANCHORWATCH when one first anchors and the alarm set to some load below the test load. Subsequently ANCHORWATCH monitors the actual load and records the peak load. Clearly if the alarm goes off, the skipper has to take some action. However, if his anchor has been well dug in initially, it may well have held to something higher than the original alarm load: this can readily be checked using the peak load facility. The alarm load can then be reset to a higher value.
So the answer to anchoring in strong winds is:
(1) Before anchoring, make a realistic assessment of the maximum loading you are likely to experience using Formula 2,
(2) Let out the maximum possible length of chain,
(3) If necessary, back this up with at least 10 metres of nylon Anchorplait, 14 to 20 mm diameter,
(4) Make sure that the scope, measured from the stemhead, is at least FIVE,
(5) When anchoring use ANCHORWATCH to test holding to at least the value calculated in (1), above.
(6) Set the ALARM LOAD somewhere below the test load,
(7) Use ANCHORWATCH to monitor the current load and record the peak load thereafter.
(8) If the alarm goes off, you are in danger of dragging and action must be taken.