Rode Forces

In order to correctly choose and use anchoring gear, we should have a realistic idea of the forces that act on an anchored boat. These forces are generated by 3 elements: the wind, the sea and the bottom.

1. Wind

Except submerged submarines ;-) all boats have windage, i.e. some surface area offered to the wind. Aerodynamic theory says that the windage force F_w varies proportionately to the cross-section S and to the square of wind velocity V. Assuming the air has density :

    (3.1)

The drag coefficient C_s depends on the object shape: its value is about 1.17 for a flat plate perpendicular to the wind direction, smaller than 0.5 for a streamlined object (e.g. an airplane or a car)... but unknown for a given boat with all its deck structures, rigging and appendices, from a specified direction! There's much worse: C_s actually varies with the wind velocity and the size of the object!! In other words, F_w is not exactly proportional to the square of V. In addition, the effective boat global area S is not simply the sum of areas of its components (hull, rigging etc.), because there are aerodynamic interactions between elements (e.g. the mast may be in the wake of a furled genoa). Thus, an accurate aerodynamic model of your sailboat is practically out of reach - unless you enjoy an America's Cup budget!

Figure 3.3 - Gusts and goats in Playa Real (Los Testigos, Venezuela)

1.1. Windage Models

Empirical models exist, though. If we analize the table published by the ABYC (American Boat and Yacht Council), which gives the windage force as a function of the boat length and the wind velocity, we discover it can be summarized, with less than 5% error, in one simple formula:

    (3.2)

where p = 1.66, V in knots; K = 0.0089 for L in meters and F_w in daN (or K = 0.0028 for L in ft and F_w in lb).

Note: The official metric unit for forces is the Newton (N). DecaNewton (daN) is more generally used, as 1 daN approximately equals 1 kgf (about 2 lb).

You can use the following form to compute the ABYC windage force, given the boat length and wind speed:

Units

Metric

Imperial

Boat length Wind Speed     Force

Computing the windage area with the boat length as a unique parameter looks dubious, doesn't it? To check this point, I analyzed the geometric cross-section of a dozen models in Jeanneau's Sun Odyssey® range, from 8 to 16 m (26 to 53 ft). I found it is roughly proportional to the power 1.7 of the boat length, which is remarkably consistent with the value of p derived from ABYC's data!

However, if we compare them with experimental data published in various sailing magazines, those theoretical values seem largely overestimated - about 3 times the forces measured on headwind modern monohulls.

One possible reason is the ABYC included a wide safety margin to take into account off the wind situations,which commonly occur when the direction of the wind changes. Let's elaborate this point.

Obviously, boats that have the same length may have very different windages. Fig. 3.1 shows the outlines of 4 types of 40 ft yachts as seen from 0 degree (head-on) and 30 degrees offset respectively:

Figure 3.1 - 40 ft yacht outlines

The windage of each boat is roughly estimated by adding the weighted areas of hull(s), roof, rigging and appendices. We choose the weighting coefficients C_s as follows:

By measuring the areas on the drawing or calculating them from real dimensions (furled gib, rigging), we get the following areas (in square meters):

We can notice that the rigging of a sailboat has a considerable influence, so that, contrary to a popular belief, a powerboat is not at a disadvantage!

Within these hypotheses, for a 40 ft yacht, equation (3.1) yields the following forces (in daN - to convert into lb, please multiply by 2.2):

We see ABYC's data match our results for a catamaran 30 degrees off the wind. Thus, using equation (3.2) or the associated form gives ample safety margin for most yachts. It is the skipper's responsibility to decide wether these values may be reduced or not, for a specific boat and the actual anchoring situation.

1.2. Wind Velocity Gradient

Another reason for a difference between theoretical estimations and actual measurements is that the velocity and the direction of the wind vary according to the height. The mean velocity gradient is maximum in an approximately 10 m (30 ft) thick layer above the surface, where friction vortices take place, but it varies according to the flow regime as shown in fig. 3.2 (10 m is the standard height for measuring wind, hence the velocity in percents of the standard value).

Figure 3.2 - Wind Velocity vs. Height and Flow

Since most windage of a 8 to 15 m (25 to 50 ft) boat is concentrated below a 3 m height, we deduce it is affected by a wind velocity equal to 40 to 80% of the standard velocity.

Note: Most sailboats have masthead wind transducers located about 15 to 20 m (50 to 65 ft) above the sea level, the reduction relative to the displayed speed is even higher!

In strong winds - the case we are interested on - the flow regime is highly instable (blue curve above), so we can only expect a moderate reduction coefficient, say 25%. But even so, it would result in overestimating the windage force by a factor 3!

This can explain why measurements always give much lower forces than predicted by the above models when using the standard wind velocity. Also, from a practical point of view, any attempt to forecast accurate values would be illusory!

2. Sea

2.1. Waves

Archimedes' buoyancy is the main force that acts on a boat afloat. If the boat and the sea are totally still, this upward force is constant and equal to the boat displacement. If the sea surface is not flat and/or the boat moves, the overall buoyancy varies only slightly, but the buoyancy of some parts of the hull(s) may appreciably change. This occurs mainly at bow, when the waves cause the boat to pitch while the anchor rode is too tight, which exerts dangerous jerks on the anchor.

Computing the local buoyancy variations and resulting torques is only possible with a complete mathematical model of both the boat (hull shape, masses distribution etc) and the waves. Anyway, since nobody can forecast the maximum height of the waves the boat will suffer when the wind rises from the open sea, a wise skipper will go and find a better shelter!

To withstand the pitching induced by moderate waves that can occur in a leeward anchorage, veering out more rode is the solution (preferably with an elastic line - see the Dynamic Behavior chapter).

2.2. Current

We won't even skim the application of hydrodynamics theory to a vessel - it would need an entire book! Let us just give one example. Fig. 3.2 shows the force exerted by the current on a typical 10 m (33 ft) waterline sailboat.

Figure 3.3 - Current Force vs. Speed

We can see a 6 kt current - which is unlikely in most anchoring situations - has about the same effect as a 20 kt wind. So we may generally neglect the current when tuning an anchor rode, except if we suffer a strong current and a strong wind, coming from different directions, at the same time

2.3. Moving Boat

If the anchored boat moves because some forces are changing, we must take into account the hydrodynamic resistance of the hull, the keel and other appendices below the waterline. More on that in the Dynamic Behavior chapter.

3. Bottom

The seabed acts on the boat via the anchor and the rode. If the anchor is not dragging, the bottom force is a reaction force, vectorially equal to the rode tension at the anchor pulling eye ((hopefully horizontal - see the static behavior chapter) + the anchor weight (vertical). If the anchor drags, the horizontal resistance decreases somewhat. Since dragging is the consequence of a rode overtension, this means dragging will continue unless the overtension stops or the anchor hooks something firmer!

By the way, do not rely on the friction of the chain on the bottom to hold your yacht: it never exceeds a few dozens of kg or lb, except if it meets rocks, coral patches etc.! Otherwise, we would never need an anchor, would we? As we'll see in the next chapters, having a fair length of chain lying on the bottom is not intended to increase the holding power via the chain friction, but instead to keep the tension on the anchor horizontal when the rode tightens.

4. Boat motions

Theory says a vessel, like any solid object, has 6 degrees of freedom: 3 translations (e.g. longitudinal, lateral, vertical) and 3 rotations (e.g. roll, pitch and yaw). For a boat at anchor, 4 motions are important regarding the dragging risks:

• Pitching, which we mentioned above.
• Surging, which is a forward and astern motion relative to the anchor, caused by the wind force variations.
• Yawing, which is a rotation around a vertical axis, caused by the wind direction variations.
• Swinging, which is a nearly circular movement around the anchor, caused by yawing.

5. Conclusions

To get a realistic idea of the total loading on the anchoring gear, we must first consider the pure (i.e. static) wind force as estimated with formula (3.2) above, then add the various forces for acceleration and/or momentum due to current, pitching, surging, yawing and swinging. It is important to realize that those additional forces can rise to several times the wind force alone!

We shall focus on surging, yawing and swinging later, in the Dynamic Behavior chapter.