Rode Dynamic Behavior 1

Req. 4 and 5 were studied in the static behavior chapter. We focus here on Req. 6.

As we already pointed out, rigid devices (e.g. a steel bar) do not meet requirements 4 and 5, so we must confine to flexible devices. With flexible materials (e.g. chain, textile or elastomers), unfortunately, the boat will move back and forth when the wind pressure changes. This motion is called surging. Due to vessel's inertia, this motion induces dynamic overtensions that can be much higher than the pulling forces that generate them, depending mainly on the rode material(s) and the pulling force variations vs. time.

Before studying various types of real rodes, it is interesting to know what would be the behavior of a "perfect spring" tying the boat to a fixed point e.g. a quay. Such a spring stretches proportionately to the tension T. If L₀ is its length for T = 0 and

is its stiffness, then its length L varies linearly vs. T :

For example, a spring with stiffness 1000 daN/m (686 lb/ft) will stretch for 1 m under a 1000 daN tension (or 1 ft under a 686 lb tension). Let's tie a 5 tonne boat (i.e. mass M = 5000 kg) to a quay with this spring. We start from the static equilibrium position: L = L₀ , spring tension T = 0, no wind (F = 0).

What happens if a gust suddenly steps F up to F_g = 400 daN (900 lb)? Figure 2.1.1 shows the variations of the spring tension, the velocity and the position of the boat relative to the starting point:

The boat begins to drift astern according to Newton's law, i.e. with an acceleration

. As the spring stretches, T increases until it becomes equal to F_g, which results in a null acceleration. At this moment, the boat is located at its static equilibrium position for the pulling force F_g, i.e.

(0.4 m) behind the starting point. But since its backward velocity is maximum

(0,18 m/s = 0.34 knot), the boat continues moving astern while decelerating. It reaches the apex position

(0.8 m) with a null velocity and a maximum spring tension

(800 daN - 1800 lb).

Then the movement reverses: the boat accelerates forward, crosses the static equilibrium point, stops at the starting point, and the above sequence is repeated cyclically (surging). The variations of all the parameters (position, velocity, acceleration, tension) are sinusoidal with period

(14 s). In practice, the friction of the water on the hull will gradually damp this oscillation, but very slowly because the velocity is very low.

Contrary to what could be expected intuitively, neither the maximum tension T_max (twice the pulling force F_g) nor the apex position (twice further the static position from the starting point) depend on the mass of the boat! Thus, high displacement boats are not penalized in this situation.

An even more important fact - although not visible in the above equations - is that a perfect spring is better than any other elastic device at limiting the dynamic overtension. In other words, non-linear elastic or pseudo-elastic devices used as anchoring rodes (e.g. chains or nylon lines) will always suffer overtensions higher than twice the pulling force of the gust - more on that later.

If the pulling force starts from a non-zero value F₀ , the general behavior is the same, but the maximum overtension is reduced by F₀ , i.e.

For example, if the settled wind applies a permanent 100 daN (225 lb) pulling force, the 400 daN (900 lb) gust will induce a 700 daN (1575 lb) maximum overtension.

In the real world, a gust cannot settle at its maximum level instantaneously; in addition, it does not remain at this level indefinitely - otherwise it would not be a gust! A more realistic profile is a trapezoid: we can define the rise time, the duration at maximum value and the decay time. But since we are mainly concerned about the maximum overtensions, we can neglect what happens beyond the first one.

In fig. 2.1.2, the gust rises from 0 to 400 daN (900 lb) in 5 seconds. In this case, the maximum overtension is reduced by 10 % compared with the step-profiled gust. Contrary to the step case, the boat's displacement has some influence: overtensions are higher for heavier boats, but the variations remain within a 20 % range.

Now the same 5 tonne boat is anchored in 5 m (16 ft) of water with 55 m (180 ft) of 8 mm (5/16 in.) chain. The settled wind applies a permanent 100 daN (225 lb) force, which is already high, but gusts at twice its velocity are expected, which means forces approximately 4 times higher - hence the very long scope! The critical tension that lifts the whole rode is 393 daN (884 lb) (see the static behavior chapter), so a 400 daN (900 lb) force could statically be withstood while maintaining a near zero angulation.

First, we can see the variations of the parameters are no longer sinusoidal, due to the high non-linearity of the position vs. force law specific to the chain. Second, for the same reason, the maximum overtensions are much higher than with a linear device (perfect spring): in the present example, they reach almost 1600 daN (3600 lb), i.e. 4 times the static force that generates them. Incidentally, 1600 daN (3600 lb) is the maximum working load of a typical 8 mm steel chain: beyond that point, the chain would not recover its shape when the gust is over! In addition, the anchor will likely drag under such a tension and with the associated angulation (4 degrees)! And veering more chain out won't help much: almost 100 m (330 ft) would be necessary to keep the anchor flat on the bottom, with tension peaks still at 1100 daN (2500 lb)!

As in the perfect spring case, under a step-gust, the boat displacement has no influence.

Conversely, if the gust were trapezoidal with a 5 s rise time, the tension would still peak at 1350 daN (3000 lb) and the angulation would not decrease significantly. A 10 tonne boat would get a 10 % overtension increase.

Note: In the above simulations, the natural (small) elasticity of steel is taken into account, (as discussed previously in the static - heterogeneous rode chapter) otherwise the tension peaks would be infinite!!

Now let us try the opposite solution: we replace the chain with a 18 mm (3/4 in.) nylon line the same 55 m (180 ft) length. Results are shown on fig. 2.1.4:

We can see the behavior is much like that of a perfect spring with moderate stiffness. The problem is, despite the very long scope (11:1) the angulation remains around 4.5 degrees whatever the tension: the line is almost completely tight. Nevertheless, in good bottoms, anchors that are designed for this type of rode should hold correctly.

When stretching, an elastic device, either real (e.g. a spring) or virtual (e.g. a chain, which uses the gravity) stores energy in a potential form. When it shrinks back, it restores this energy to the tied system, in a kinetic form but in the reverse direction – hence the oscillations. To counteract those oscillations, it is necessary to use a dampening device, which transforms the mechanical energy into any other form, e.g. heat as in friction dampers used in automotive suspensions. One could imagine dragging chains on the seabed, or using water parachutes... Let's be serious: the relative speeds between the boat and its environment (air, water, bottom) are much to low for such devices to be effective while keeping manageable!

Thus, unfortunately, the cyclic astern and forward motion (surging) looks unavoidable!

Let's check both technologies against the criteria defined at the top of this page (Req. 4, 5 and 6):

Criterion	All-chain	All-nylon
Can pull the anchor parallel to the bottom?	Yes	No, unless veering out a very long line
Easy to stow?	Yes, but very heavy	Yes
Easy to wind and unwind?	Yes (with a motorized windlass)	Yes
Reduce the tensile stresses?	No	Yes

So, an all-chain rode is both dangerous for the anchoring tackle and prone to dragging. On the other hand, an all-nylon rode is safe, but it needs very high scopes that can be incompatible with tight anchorages. Anyway, even with a chain rode, strong gusts always require a very high scope to maintain the anchor (almost) flat on the bottom.