You probably know the rules of thumb. Something like 7:1 scope if you’re staying overnight, 5:1 if you’re just there for a few hours. But where do these rules come from, and what if you can’t lay that much scope – say you’re up against the shore line, or the swing radius is too big. I took an engineering approach to calculate what scope you actually need, depending on the relevant variables.
Scope, Pull Angle, and Holding Power
So what are we trying to do with scope anyway? Fundamentally, we’re trying to achieve maximum holding power for our anchor. Since anchors are designed to grab onto the see floor, they function best when they are pulled sideways. The more scope you lay, the shallower the angle of pull on the anchor. If we assume the anchor rode is pulling in a straight line between the boat and the anchor the pull angle can be calculated by simple trigonometry – the pull angle equals cosine of 1/scope. The chart below illustrates how the pull angle increases when scope is reduced.
As it turns out, a rough “rule of thumb” estimate for pull angle is 60/scope. For example, for a 3:1 scope, the pull angle is 60/3 = 20. The “exact” calculation using trigonometry is 19.5 degrees.
So the pull angle is related to holding power – a shallower pull angle improves holding power. The figure below illustrates pull angle and holding power (as a percentage of maximum holding power) for two common anchors, the Fortress and the Mantus.
You can see that the curves flatten out around 5 to 6 and there are diminishing returns to adding more scope. Holding power precipitously drops off as scope is reduced below 4:1, and full holding power on the Fortress is achieved at 10:1. From this chart, it’s easy to see the origin of common rules of thumb came from (the following is excerpted from Happy Hooking):
The rule of thumb for a rope rode is that the minimum scope (using a good anchor) should be:
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5:1 at normal conditions below Force 6
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7:1 is a highly acceptable ratio for conditions up to Force 9
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10:1 and two anchors are desired for strong storm conditions.
What about the real world?
But the charts above assume a rope rode that is straight as an arrow. In reality, most cruising boats have at least partial chain which benefit from catenary – more on that in a bit. And unless you’ve chosen a very poor anchorage, or have somehow found yourself in a storm (shame on you), you will need much less holding power than what your anchor is sized for.
In reality, the total amount of scope needed to keep your boat secure depends on a number for factors: The size of your boat, the expected wind speed, the length and weight of chain, and whether or know you’re deploying a kellet anchor.
A simple model
The primary input into any calculation of anchor holding power is the horizontal loading that is experience by the boat. This is the load the anchor ultimately needs to offset. The horizontal loading on a boat at anchor is a function of the environment (wind speed, current, swell) and the boat (length, beam, windage). Fortunately, the American Boat and Yacht Council (ABYC) has published a conservative estimate of the expected horizontal loads that can be expected.
Note that horizontal load goes as the square of the wind speed in knots. So the horizontal load for any wind speed can be calculated using the formula:
For example, the horizontal load on a 30 ft boat in 15 knots of wind is 700 x (15/30)2 = 175 lb.
With this load estimate, and details about the boat configuration, the curvature of the anchor rode can be calculated. Any line (rope or chain) under tension will follow a catenary curve – not a straight line. This is due to the fact that the line is reacting both tension and gravity. Even a line that is under extremely high tension – although it may be very close to straight – is actually curved.
To calculate the catenary curve under any given condition, I built a finite difference model – fancy way of saying excel spreadsheet (I’ll send it to you if you like – just reach out). It essentially divides the rode up into many short straight sections. Each finite section of rode must carry both the horizontal load defined by the ABYC estimates, as well as a vertical load equal to the total weight of all the rode below it.
With this model, we can get a better idea of the shape of the rode – and in turn holding power – under the specific conditions we’re interested in.
Chain Matters
Using the model, I took a look at some different scenarios to see how much scope is actually needed to maintain a zero-degree pull angle. For a 35-foot sailboat anchored in 20 knots of wind, almost 15:1 scope is needed if a bare minimum of 10 feet of chain is used. Yes, 15:1 is totally impractical, but that’s what the physics says. With a more reasonable 50 feet of chain, roughly 6:1 scope achieves a zero-degree pull angle. This still less than the 7:1 rule of thumb, but keep in mind this is for 20 knots of wind. If the wind picks up, more scope will be needed. Adding chain rode helps too. With 100 feet of chain, only 4.5:1 of total scope is needed.
Let’s say you’re ok with an 8-degree pull angle on the anchor. This would still achieve 75-85% of the anchor’s maximum holding power according to the figure above, and would allow a much reduced scope of 3:1 to 5:1, depending on the length of chain. Very good information to have if you find yourself in a crowded anchorage.
The Kellet Anchor
A kellet anchor (a weight that is slipped down the rope rode via a separate line called a sentinel) is another technique that can be employed to achieve a shallower anchor pull angle with reduced scope. On a recent cruise, I heard a fellow skipper claim that adding a 20 lb kellet was “like having another 50 ft of chain.” I tested this theory using the model.
It turns out, adding a 20 lb kellet with a sentinel of 40 ft doesn’t have much of an effect. Even if the kellet is slid all the way down to the point where it’s weight matches an equivalent length of chain (107 ft down the rode), it doesn’t act like having “another 50 ft of chain.”
But what if you’re already in a marginal situation, with reduced scope of 4:1. What is the effect of adding the kellet? It turns out the kellet will reduce the anchor pull angle slightly and add a bit of additional holding power. But it still doesn’t come close to behaving like another 50 ft of chain. In fact, it’s equivalent to another 11 ft of chain.
The Nomograph
As you can see, the scope needed to keep you’re anchor secure depends on a lot of variables specific to your configuration: boat length, chain length, chain weight, depth, wind. There is no simple generalizable formula. Enter the nomograph.
A nomograph is just a fancy word for a chart that can be used to make complicated calculations. It’s basically a slide rule for a specific application. The example below is from the Naval Ship’s Technical Manual.
Using the finite difference model, I created a similar set of charts that can be used for quick reference on the water. These aren’t nomographs per-se, but can be used to select the proper scope for a given set of conditions, and see how susceptible you might be if the situation changes due to tidal range or wind gusts.
For example, If I’m anchoring in 35 feet and expect less than 15 knots of wind, I would be very comfortable laying 140 ft of rode (4:1), knowing that even if the wind unexpectedly kicks up to 25 knots, my anchor pull angle would be around 5 degrees. These charts are handy if you don’t feel like carrying a laptop computer with you on your cruise.
The Bottom Line
As it turns out, in most conditions, you probably need a lot less scope than what the rules of thumb dictate. By all means, when the wind picks up and you’re feeling insecure, let out more scope. If you start dragging anchor, let out more scope. But if your swing radius is more of a concern than storm conditions, doing some calculations in advance an help you understand just what you need, and sleep better when you can’t get the 7:1 scope you were hoping for.
