How Anchoring works it out

Every figure Rainbow’s End Anchoring gives you, and where it comes from. Each section shows the formula, what it means, what it rests on, and the numbers for Rainbow, the ketch the app starts with, so you can check them in the app yourself.

Rainbow: 46.7 ft long, 13.7 ft beam, 5.5 ft draft, 36,500 lb, bow roller 6 ft above the water, a 65 lb scoop anchor on 200 ft of 3/8″ G43 chain. The night: 10 ft on the sounder, 12 kt of wind, a short chop, firm mud, overnight in settled weather, one anchor down.

What each figure rests on

Physics

Standard physics: the drag equation, the catenary, the friction of water.

Geometry

Arithmetic on lengths and angles. Nothing is assumed.

Published

A published figure, and whose. We name a source only when we have read it.

Our estimate

A figure we chose. The app treats it as an estimate, and so should you.

Contents

• Depth
• Scope
• The load
• Current
• The chain’s curve
• Holding and the margin
• Strength of the gear
• The swing
• Mooring balls
• Held and two-anchor moors
• The anchor watch’s fence
• The alarm and the early warning
• Marking the anchor after the drop

Depth

How deep the rode has to reach

Scope is measured from the bow roller to the seabed at the worst of the night, not from the surface. In shallow water the height of the roller is a large share of it.

Scope

How much rode to pay out

A base ratio for the kind of rode, raised for wind, for a stop you will leave the boat on, for doubtful ground and for boats that range at anchor, and lowered for a short stop with someone aboard.

On a chain-and-rope rode the app works from what is paid out. If the chain alone covers the all-chain scope, it pays out chain only. If rope must go out too, it moves the base from 4:1 toward 7:1 by the share of rope out. The two ends are published; the straight line between them is our estimate.

Pay out = scope × depth to reach. The chain’s curve is checked separately below; it adds advice, never a longer pay-out.

The load

How hard the wind pulls

The wind pushes on everything the boat shows it from ahead: the hull above the water, the rig, and the canvas. The pull grows with the square of the wind, so twice the wind is four times the pull.

The frontal area is estimated from what you enter: the hull from beam and bow height, the rig from length and rig type, the canvas from how much you carry. A boat with a hard dodger, davits and a dinghy can show half again what the estimate gives.

From steady wind to the design load

Wind alone is not what breaks ground tackle. Waves surge the boat back on her rode, and a boat that sails about at anchor snatches at it. The app multiplies the wind’s pull for both.

The yaw allowance assumes a boat that lies fairly quietly. One that sails back and forth through 60° or more pulls harder, and her anchor holds less: in Practical Sailor’s tests a 60° yaw took a fifth to two-thirds off the margin. From 20 knots, with no riding sail or bridle set, the app says so under What to watch. The style factors for a boat held across the wind (Med moored, lines ashore) are our judgment from her side-on area, which is more than twice what she shows bow-on, not a measured figure.

The four surge factors are our estimate, chosen when the app was built; no published source stands behind them. Against the one published table they bracket it: for Rainbow at 30 knots the design load is 0.6 of the ABYC working load for her length when flat, 0.84 in a chop, 1.1 in a moderate swell and 1.47 when rough. Practical Sailor puts snatch loads at up to five times the average, and found the worst of them on all chain with no snubber in shallow water. The app warns when an all-chain rode has no snubber.

The surge allowance is the same whatever the rode is made of. Nylon stretches and takes up some of each surge, so on a rode with rope beyond the chain, or with a snubber, the real load is likely lower than this figure. The app does not count that stretch, or a rubber absorber’s: no published test measures it on a boat at anchor well enough to count. So its figures err on the high side for a nylon rode.

Current

How hard the stream pulls

Water is about 836 times denser than air. Head-on, a hull is streamlined and meets little of it. Lying at an angle to the stream, her whole underwater profile meets it. So the pull has two parts, and the angle matters more than the speed.

We take the waterline as 0.85 of her length and the profile from abeam as 0.65 of waterline × draft, keel included. A current is steady, so surge and yaw multiply the wind only.

How the current raises the scope

The scope rule sizes on wind. In a current it sizes on the wind that would pull as hard as the wind and the current together, through the same table, so the same limits hold.

A current’s pull is steady, so on all chain it can lift the whole chain off the bottom by itself, leaving nothing to soften a surge or to let the anchor pivot when the tide turns. Then the app pays out what keeps chain on the bottom at the steady pull, up to 7:1 and no more, and past 7:1 it says the chain still lifts.

This rule is ours: no published test measures the benefit of chain on the bottom in a current. The current’s pull it works from is our estimate too, not yet checked against a test, which is why the rule stops at 7:1. Where it lands, about 5 to 7:1, is within published advice for a night at anchor: Practical Sailor recommends 7:1 or more overnight in shallow to moderate depths, and finds no practical gain from less than 6:1.

The chain’s curve

When the chain pulls straight

Chain hangs in a curve under its own weight, so the pull at the anchor stays along the bottom. Pull hard enough and the curve comes out; above that load the chain no longer cushions anything, and a snubber does, or on a rode with rope beyond the chain, the nylon’s stretch.

Steel in water weighs 0.87 of its weight in air (the water it displaces). The weight in air is the chain maker’s figure for your size and grade. The app offers more chain only when it is cheap: never more than 1.3 times what is out.

The two formulas above are for a rode that is all chain, like the worked example. With rope beyond the chain, the rope runs nearly straight from where the chain ends, so the app works both figures, and the angle the rode makes at the anchor, from the rode’s true shape: the chain’s curve, then the rope. The drawing on the Anchor tab is the same shape.

Holding and the margin

How hard the anchor holds, and how much to spare

Once set, an anchor holds by its weight times a factor that depends on its design and the bottom. A bigger anchor gains a little less than its weight: tested across sizes, tripling the weight about doubled the hold. So past the size the factors were measured at, the app counts the weight at a lower rate. Small claws hold far less per pound than big ones, and are cut further. Whether an anchor sets at all is a separate question, which the app asks separately.

The margin is figured on the steady pull, with waves and yawing allowed for. The gusts are checked separately: if their peak load could exceed what the anchor holds, the app warns under What to watch.

An adjustable aluminum fluke anchor, the Fortress FX, ships with its flukes at 32°, the setting for most bottoms; Fortress advises 45° for soft mud only. In Practical Sailor’s 2014 Chesapeake test the 21 lb FX-37 held 47.4 lb per pound of anchor at 32° and 88.6 at 45°. An earlier Practical Sailor test, in soft mud over a firmer bottom, found the reverse: two FX anchors held 350 to 450 lb at 32° and 100 to 200 lb at 45°, or would not set. Fortress answered that the mud was not deep enough for the flukes to open. So 45° pays only in deep soft mud. The app counts 32°, a factor of 50 in soft mud, unless the bottom is soft mud or silt and you have said the flukes are reset to 45°; then it counts 88.6. In any other bottom it counts 32°, because at 45° the anchor will not set there.

The angle at the anchor

An anchor holds best when the rode pulls it along the bottom. When the rode lifts and pulls it upward, it holds less. The holding factors above were measured with the rode meeting the anchor at about 7°, so the app counts them in full up to that angle and reduces them past it. A flatter pull is not credited above the tests.

The angle is the rode’s own angle where it meets the anchor, worked from its curve at tonight’s steady pull (see The chain’s curve), the same angle the rode drawing shows. Chain lies flat far longer than rope, so a short scope costs an all-chain rode little and a mostly-rope rode more. It is the rode actually out: the app’s figure, what you paid out, or all of a rode that runs out. The gusts are checked at the steeper angle the gusts lift the rode to.

In the tests, the Danforth-style anchor (a Fortress Guardian) kept about nine tenths of its holding at 18°, where the scoops and the claw kept about half, so fluke anchors (Danforth pattern and Fortress) have their own column. The tests also found that waves and gusts jerking a short rode loosen the bottom’s grip. The app allows for gusts in the load, not here, so as not to count them twice.

Big enough for the boat

A light night makes any anchor’s margin look large, so the app also sizes the anchor against the boat. For a night aboard, a storm or a boat left unattended, the pick must hold, in good sand, the load ABYC gives for a boat of her length in 30 knots of wind. A smaller anchor is never the pick while a bigger one aboard holds as much tonight; it is marked as fine for a lunch stop. If it holds more than every bigger anchor in tonight’s bottom, it can still be the pick, marked as small for her. Good sand is the bottom makers size their anchors for; a poorer bottom tonight is the margin’s business, above.

This is a minimum, not a recommended size: makers’ charts, which allow for poorer bottoms and harder weather, usually call for a bigger anchor.

Strength of the gear

What breaks first

The system is as strong as its weakest part. Chain size sets the curve; chain grade sets the strength. The app keeps the two apart and checks the peak load against the weaker of the chain and the rope. Shackles and swivels are not counted: each should be rated at least as high as the chain.

Makers publish chain working load limits at different margins: in the US, G30 at a quarter of the breaking load and G43 at a third. So the app puts every chain on one footing, a quarter of its breaking load. European G40 is its own grade: it breaks lower than US G43. Rope gets five to one because anchor rode is rarely new and rarely inspected end to end.

The swing

How far she can range

She can lie anywhere on a circle around the anchor. Its radius is how far the rode reaches across the bottom, plus the boat herself.

Taking the rode as straight is the safe side: the sag of the chain only ever shortens its reach. The depth is tonight’s highest water; at low water the same rode reaches a little further (on Rainbow’s 70 ft, about 1.6 ft with an 8 ft fall), which the fence’s GPS margin covers.

Mooring balls

How far a ball lets her range

The ball floats on a riser from the mooring’s anchor. Laid for high water, the riser is slackest at low water, which is when the ball can range furthest.

A long riser ranges further, so the app takes the top of the usual range for chain. It does not rank your own anchors on a ball; none of them is in the water.

Held and two-anchor moors

Med mooring, lines ashore, the Bahamian moor

The anchor watch’s fence

The line the alarm watches

The fence is the swing circle with room for GPS scatter. It allows for the phone anywhere aboard, since the swing already includes the boat’s length.

You can move the fence in steps of 5%. It cannot be tightened inside the swing, which she reaches by doing nothing wrong, or widened past 200%.

The alarm and the early warning

When the alarm sounds

One stray GPS fix must not wake you. The alarm sounds after 3 fixes in a row clearly outside the fence: outside by more than 15 ft, or half the fix’s own accuracy if that is more. It stands down by itself when she comes back inside.

The early warning is a band inside the fence, 50 ft wide (a held boat’s 25). It chimes once as she enters it, and not again until she has come 15 ft back inside. When you widen the fence, the plan’s own line warns too. A band narrower than 10 ft is no band, and the screen says so.

Marking the anchor after the drop

When the alarm was not set at the drop

From the bow, backing down gently with the rode straight, the anchor lies the rode’s reach ahead, along the rode. The direction is the weak point, so the fence is widened by how far the mark may be off.