Yacht Stability

Prerequisites

• Day Skipper level knowledge of yacht construction, keel types, and sail trim, and Coastal Skipper course entry experience (15 days, 2 as skipper, 300 miles, 8 night hours).
• Basic arithmetic: multiplying and dividing, and the idea of a moment (a weight multiplied by its distance from a pivot).
• Some experience of how your boat heels and recovers in a breeze.

The Yachtmaster Coastal syllabus expects a skipper to understand stability qualitatively and use it in practical decisions: how to load and stow the boat, how to manage tanks, when to reduce sail, and which sea conditions threaten a knockdown or capsize. You will not be asked to do naval architecture, but you should be able to explain GM, GZ, the stability curve and the angle of vanishing stability.

Learning Objectives

This lesson covers the RYA Yachtmaster Coastal shorebased syllabus topic "Stability and Loading" (weight distribution, stability awareness, loading calculations), at the practical level the syllabus asks for. By the end you will be able to:

• Define the centre of gravity (G), centre of buoyancy (B) and metacentre (M), and explain how they produce a righting moment (syllabus: stability awareness).
• Explain metacentric height (GM) and the righting lever (GZ), and the difference between a stiff and a tender yacht (syllabus: GM and initial stability).
• Read a GZ curve and identify maximum righting lever, angle of vanishing stability (AVS) and range of positive stability.
• Explain the downflooding angle and why it can limit safe heel before the AVS.
• Describe the effects of loading, tank management, free surface and deck loads on stability, and calculate a simple KG (syllabus: weight distribution and loading calculations).
• Describe the effect of flooding on stability, and the idea of cross-flooding (syllabus: damage stability).
• Monitor displacement, draught and trim as fuel, water and stores are used (syllabus: loading calculations, draft and trim).
• Relate stability to sea state, especially beam and breaking seas, and to RCD design categories and the stability information in the owner's manual.

The Basic Forces: G and B

A floating yacht is acted on by two forces:

• Weight, acting straight down through the centre of gravity, G: the average position of all the boat's mass, including keel, hull, rig, engine, stores and crew.
• Buoyancy, acting straight up through the centre of buoyancy, B: the centre of the volume of water displaced by the hull. Buoyancy equals weight when the boat is floating freely.

When the boat is upright and at rest, G and B are on the same vertical line, as the diagram shows.

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G stays fixed relative to the hull unless weights move (crew, water in the bilge, loose stores, liquids in tanks). B is not fixed: when the boat heels, the immersed shape changes and B moves towards the lower side.

The Righting Lever (GZ)

When the yacht heels, B moves out to leeward while G stays put. The weight down through G and buoyancy up through B are now offset horizontally. The horizontal distance between the two lines of action is the righting lever, GZ. The two forces form a couple that tries to bring the boat upright.

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The righting moment is displacement multiplied by GZ. For example, a yacht displacing 8 tonnes with a GZ of 0.35 m at 30 degrees of heel has a righting moment of 8 x 0.35 = 2.8 tonne-metres. To heel her further, the wind must produce a greater heeling moment, through the sails, than that.

This explains why:

• A heavy, deep-keeled boat stands up to her canvas: large displacement and a low G give large righting moments.
• Crew sitting on the windward rail adds to righting moment by moving G to windward.
• A wide, light, flat boat has great initial stiffness from form (B moves a long way out as she heels) but may lose stability rapidly at large angles.

The Metacentre and Metacentric Height (GM)

At small angles of heel (up to roughly 10 to 15 degrees), the vertical line up through the new position of B crosses the boat's centreline at a nearly fixed point, the metacentre, M. The distance from G up to M is the metacentric height, GM.

At small angles, GZ is approximately GM multiplied by the sine of the heel angle. So GM tells you how strongly the boat resists the first few degrees of heel:

Typical cruising yachts have a GM of around 0.5 to 1.5 m, depending on design. The roll period gives a practical clue: a quick snappy roll suggests a large GM, a long lazy roll a smaller GM. If a boat that normally rolls briskly starts rolling slowly and hanging at the end of each roll, something has raised G or reduced the waterplane: water in the boat, a heavy deck load, or ice on the rig in high latitudes.

GM is only an indicator of initial stability. A boat can be very stiff at small angles and still have a poor range of stability, which is why you need the full GZ curve.

The GZ Curve and Angle of Vanishing Stability

Plotting GZ against heel angle from 0 to 180 degrees gives the stability curve.

Reading the curve:

• The slope at the origin reflects GM: the steeper the initial slope, the stiffer the boat.
• Maximum GZ typically occurs at about 30 to 40 degrees of heel for a modern cruiser (more for narrow, heavy, deep-ballasted boats). Beyond that angle, the righting moment decreases as she heels further, so a gust that pushes her past maximum GZ meets less resistance.
• The angle of vanishing stability (AVS) is where GZ returns to zero. Beyond the AVS the righting lever becomes negative: the boat will continue to capsize and settle inverted.
• The range of positive stability is 0 degrees to the AVS.
• The area under the positive part of the curve represents the energy needed to capsize the boat; the area under the negative part represents the energy needed to capsize her back from inverted. The ratio of the two is a measure of how quickly she will right after an inversion.

Typical AVS values: many modern production cruisers around 110 to 130 degrees; heavy, narrow traditional yachts can exceed 140 degrees. A boat with an AVS below about 120 degrees can stay inverted for a significant time if rolled by a breaking wave; an AVS below 90 degrees is inadequate for open-water sailing.

RCD design categories and STIX

Boats sold in the UK and EU since 1998 are assessed under the Recreational Craft Directive (now the UK Recreational Craft Regulations). Each boat is given a design category linked to the conditions it is designed for:

For sailing monohulls, the category depends partly on a Stability Index (STIX) calculated under ISO 12217-2, combining range of stability, righting energy, length, displacement, and downflooding and knockdown recovery factors. A STIX of at least 32 is required for Category A and 23 for Category B. The builder's documentation (the owner's manual) shows the category and often the GZ curve: read it for the boat you skipper.

Downflooding Angle

The downflooding angle is the angle of heel at which water can pour into the hull through an opening: an open companionway hatch, a cockpit locker without a seal, a dorade vent, an open forehatch, or the engine air intake.

If the boat heels past this angle, water enters, adds weight (often high and to leeward) and creates a large free surface: stability collapses long before the theoretical AVS. With the main hatch open and washboards out, a typical yacht's downflooding angle may be only 35 to 60 degrees, well within the range of a knockdown.

Practical consequences:

• Fit washboards and close the main hatch when the sea is rough or at night, and secure the washboards so they cannot fall out in a knockdown.
• Close the forehatch and portlights before going to sea.
• Ensure cockpit lockers have latches and good seals; a cockpit full of water should drain through the cockpit drains, not into the boat.
• Treat the downflooding angle, not the AVS, as the real limit.

Loading and Weight Distribution

G is the balance point of everything in the boat. Every weight you add, remove or move changes it. Adding weight low (below the existing G) lowers G and increases GM; adding weight high raises G and reduces GM.

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Practical rules:

• Stow heavy items low and near the centre of the boat: tinned food, water containers, tools, spare anchor and chain.
• Weight aloft is particularly bad because it has a long lever arm. A radar scanner, in-mast furling with sail, a heavy masthead instrument cluster, a second halyard left at the masthead, or a person up the mast all raise G. One kilogram at the masthead of a 14 m rig has the same effect on KG as several kilograms on deck.
• Ends of the boat: weight in the bow and stern (anchor chain in a forward locker, dinghy on davits, an outboard on the pushpit) does not much affect transverse stability, but it increases pitching and can make her bury her bow. Many owners move chain aft (to a locker near the mast foot) for passages.
• Deck loads: jerry cans lashed to the guardrails, a dinghy on the foredeck, bikes on deck. They raise G, increase windage, can shift, and absorb water (a soaked sail bag or sprayhood cover weighs much more than when dry).
• Secure everything. In a knockdown, the batteries, anchor, toolbox and tins of food become missiles, and a weight that moves to leeward reduces stability at exactly the wrong time. Battery boxes and floorboards should be fixed.

Calculating KG

Naval architects locate G by taking moments. KG is the height of G above the keel reference (K). Multiply each weight by its height above the keel to get its moment; add up the weights and the moments; KG equals total moment divided by total weight. Then GM = KM minus KG, where KM is the height of the metacentre above the keel, which comes from the hull form (the designer's data).

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In the example above, a light displacement 3.6 tonne boat has a KG of 0.81 m. With KM of 1.8 m, GM is 0.99 m. Now see what happens when the owner adds weight on deck.

Extension: adding deck cargo. The owner lashes four 20-litre jerry cans of diesel (about 17 kg each, 68 kg total) to the guardrail stanchions, 2.5 m above the keel, and carries a 40 kg inflatable dinghy on the coachroof at 2.4 m.

New KG = 3186 divided by 3708 = 0.86 m. If KM stays about 1.8 m (it changes slightly with displacement), new GM = 1.8 minus 0.86 = 0.94 m. GM has fallen by 5 cm, about 5 percent, from just over 100 kg of deck cargo. On a light boat in a seaway, combined with crew on deck and wet sails, these effects add up. Stowing the jerry cans in a cockpit locker at 1.2 m instead would give a moment of 82 kg m instead of 170, almost halving their effect.

Free Surface Effect

A tank that is completely full behaves like a solid weight. A tank that is partly full allows the liquid to slosh to the low side as the boat heels. The shifted weight acts to leeward, reducing GZ just as if G had been raised. This is the free surface effect, and the effective (virtual) rise in G depends mainly on the width of the free surface (it varies with the cube of the breadth of the tank), not the amount of liquid.

Practical rules:

• Keep tanks full or empty where possible. Use one tank at a time rather than drawing from all of them together, so only one tank has a free surface.
• Baffles in tanks reduce sloshing and dynamic loads but do not eliminate the effect.
• Bilge water is the worst free surface because it extends across the full width of the hull. Keep bilges dry; a few hundred litres of water sloshing across the cabin sole can reduce stability dramatically, and is one way a boat that is taking water can capsize before it sinks.
• Damage stability: if the boat is holed, the flooded compartment adds weight and free surface. Watertight bulkheads (common on larger yachts with a crash box forward) limit the flooded volume.

Consumables and the End-of-Voyage Condition

As you burn fuel, drink water and eat stores, weight comes out of the boat. If those weights were low (tanks under the cabin sole), G rises as they are used. Plan for the worst condition, usually near the end of the passage when tanks are low and partly filled (free surface) and the crew are tired. On longer passages this is why some skippers refill an empty water tank with seawater ballast, or carry fuel in jerry cans low rather than on deck.

Stability and the Sea

Static stability tells you how the boat resists a steady heeling force. At sea, wind gusts and waves add dynamic loads.

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• Gusts: a gust can be around 1.5 times the mean wind speed, and since wind force increases with the square of speed, a 1.5 times gust exerts over twice the heeling force. Reef for the gusts, not the mean.
• Breaking beam seas are the main capsize threat to yachts. Studies after the 1979 Fastnet race found that a breaking wave with a height of around 30 percent of the boat's length could knock a typical yacht down to the horizontal, and one of around 55 percent could roll many boats through 180 degrees. For a 10 m yacht that is a breaking wave of only 3 m and 5.5 m respectively, sizes found in a gale over a tide race or in shallow water.
• Following seas can cause a broach (the boat slews beam-on and is knocked flat) or, in extreme conditions, a pitchpole. Speed control and holding the stern to the seas matter.
• Wind against tide, shoaling water and headlands steepen waves and make them break. These are the places a Coastal Skipper must plan around.

Reducing risk: reduce sail early, keep the boat moving under control, avoid being beam-on to breaking seas (take them on the quarter or bow), avoid tide races and overfalls in strong winds, keep weight low, hatches closed and washboards in, and crew clipped on.

Multihulls

Catamarans and trimarans have very large initial stability from their beam, but their GZ curve peaks at a small angle (often 10 to 15 degrees) and then falls away; once a hull flies high enough to pass that point, capsize can happen quickly, and a capsized multihull is stable upside down. Their sails must be reefed according to wind strength rather than heel angle, because they give little warning by heeling.

Damage Stability and Flooding

The syllabus asks you to understand what flooding does to a yacht. Three things happen together when water enters the hull.

1. Added weight. Every litre of water is a kilogram. A hundred litres in the bilge of a 6 tonne yacht is only about 1.7 percent of her displacement, but it sits low, so the effect on KG is small; the boat floats lower and her freeboard shrinks.
2. Free surface. Water free to move across the cabin sole behaves like the part-full tank described above, but with the widest possible surface. This is usually the dominant effect, and it reduces GM sharply and often invisibly.
3. Reduced reserve buoyancy. As she sinks lower, the downflooding angle falls, and the deck edge goes under at a smaller angle of heel. The more she floods, the easier it is to flood further.

A flooded yacht can capsize before she sinks. If a boat is taking water, the order of priorities is: stop or reduce the inflow (close a seacock, bung or plug a failed hose, put a collision mat over a hole), start pumping (electric pump, then the manual pump, then buckets), and keep the water from running to one side by trimming the boat upright and keeping the crew central. Reduce sail and reduce speed to lessen the load on a damaged bow.

Cross-flooding and watertight subdivision

Larger yachts and many motor sailers have watertight bulkheads, such as a collision bulkhead forward, that limit the volume which can flood. Where a flooded compartment is on one side only, the boat will list. Naval architects use cross-flooding (an opening that lets water reach the other side deliberately) to limit list. On a small yacht the practical point is simpler: know where your bulkheads are, whether they are genuinely watertight (a door with a gap is not), and which spaces will flood first through a damaged skin fitting or a broken window.

Practical checks

• Know the position of every seacock and keep a tapered softwood bung tied beside each one.
• Check hoses and clips at the start of the season. A failed cockpit drain hose or engine intake hose is the commonest cause of serious flooding.
• Test the bilge pumps and know their capacity in litres per minute. A manual pump moves perhaps 20 to 30 litres per minute for a fit person; a bucket is often faster.
• Fit a high-water alarm in the bilge so that you learn about flooding before the water reaches the batteries.

Displacement, Draught and Trim

Loading calculations in the syllabus cover tracking the weight in the boat over a passage and keeping her in trim.

Displacement monitoring

Displacement is the total weight of boat, equipment, fuel, water, stores and crew. Makers quote a light displacement and often a loaded one; a cruising yacht usually floats 10 to 20 percent above her brochure figure once she is fitted out with a liferaft, anchor, chain, dinghy, outboard, batteries and a month of gear. You can estimate the effect with this rule: the extra weight (in tonnes) divided by the tonnes-per-centimetre immersion (TPC) of the waterplane gives the extra sinkage in centimetres. For a typical 10 m cruiser, TPC is about 0.15 tonne per centimetre, so 300 kg of stores sinks her by 2 cm. That is a small number, but the same 300 kg sitting aft raises the stern and changes her trim, and it is at the end of the boat that the worst effects appear.

Weights come out of the boat as well. On a long passage, 100 litres of diesel (about 85 kg) and 200 litres of water (200 kg) may be used. If those tanks were at the stern, the bow will now sit lower, and if they were low in the keel the effect on G is to raise it slightly. Check the trim after a few days and move gear to correct it.

Draught and trim

Read the waterline against the boot top, or against draft marks if fitted. A yacht trimmed by the stern drags a wide wake, slams less but steers less well downwind; one trimmed by the bow pitches deeper, buries her bow in a head sea and is wetter. Aim for the designer's waterline: the bow and stern boot-top lines at about the same height above the water. The simplest corrections are moving heavy items (anchor chain, water jerry cans, spares) fore and aft until she floats right.

Load lines

The syllabus also mentions load line awareness. Commercial vessels carry a load line (Plimsoll mark) showing the maximum draught allowed in different waters and seasons. A leisure yacht does not carry one, but a vessel coded under the MCA Small Commercial Vessel Code does need a freeboard mark, and the principle is the same: do not overload the boat and keep her well above her minimum freeboard.

Reading the Owner's Manual and Builder's Plate

Every recreational craft sold in the UK or EU since 1998 has a builder's plate showing the design category, the maximum recommended load (including crew) and the maximum number of people. Check three things for any yacht you skipper:

1. The design category (A, B, C or D) matches the passage. A category C boat is not designed for a crossing of the North Sea in a gale, however well she is equipped.
2. The maximum load has not been exceeded. This figure covers stores, fuel, water, equipment and crew; it is easy to exceed on a charter yacht with a full crew and full tanks.
3. The stability information: a published GZ curve or an AVS figure. Some manufacturers publish the STIX number; many give only the category. If you charter, ask.

A useful field test: the roll period

You cannot measure GM directly aboard, but you can get a feel for change. With the boat at a mooring in light wind, push the boom or the shrouds to start a roll, then count how long one complete roll (side to side and back) takes. Note it in the ship's records. A noticeably longer roll period after loading means G has risen and GM has fallen; a shorter period means the reverse. The formula used by naval architects is that GM is proportional to one over the roll period squared, so a roll period that lengthens by 20 percent means GM has fallen by roughly 30 percent.

Stability and the Crew

The crew are a weight, and they move. Four or five adults on the windward rail of a 10 m yacht can add a considerable righting moment, but the same people standing on the leeward side deck on a roll, or all together in the cockpit, raise G and add weight at the stern. Keep a minimum number of people on deck in rough weather, clipped on, and keep the rest low in the boat. In an emergency, move crew to the high side of a heeled boat to help righting.

Another factor is fatigue. A tired crew make poor sail decisions, and late reefing is the commonest preventable cause of a knockdown. Stability is a property of the boat, but the decision to reef is the crew's. The practical rule is: reef when you first think of it.

Second Worked Example: Righting Moment and Sail Area

A 9 tonne yacht has a GZ of 0.40 m at 25 degrees of heel. What heeling moment from the wind balances her at that angle?

• Righting moment = 9 tonnes x 0.40 m = 3.6 tonne-metres.
• At equilibrium, heeling moment = righting moment = 3.6 tonne-metres.

Now a gust raises the wind speed from 20 to 30 knots. Wind force is proportional to the square of the speed, so the heeling force rises by (30/20) squared = 2.25 times. The heeling moment becomes about 3.6 x 2.25 = 8.1 tonne-metres if the sails stay set the same way. At 25 degrees the boat can only produce 3.6, so she must heel much further. Perhaps maximum GZ is 0.55 m at 35 degrees, a maximum righting moment of 9 x 0.55 = 4.95 tonne-metres: still far less than 8.1. She will be laid on her side, the sails will spill and the helmsman must bear away or the sheets be eased immediately. This is why reefing for the gust, not the mean, matters: a reefed main in the same gust halves the area and the heeling moment, bringing it back under 4.95.

This simplified model ignores the fact that the sails depower as the boat heels and the rig moves lower. Even so, it shows the principle that the examiner wants to hear: a doubling of wind speed quadruples the force, and a boat has a hard limit to the righting moment she can produce.

Exam and Practical Tips

• Examiners and instructors expect you to explain G, B, M, GM and GZ with a sketch, and to say what happens to each when weight is added high or low.
• Be ready to answer a loading question: "Where would you stow 200 kg of tinned food, and why?" (Low, in the centreline lockers near the middle of the boat, strapped down.)
• Be able to say why you keep tanks full or empty and why you pump the bilge dry before a passage.
• Know the RCD category of the boat you are using and what it implies.
• State that the downflooding angle, not the AVS, is the practical limit, and say what you do to raise it (close hatches, fit washboards, close vents).

Worked Example: Preparing a Yacht for a Windy Passage

You are skipper of a 10.5 m cruiser, Category B, AVS 118 degrees according to the owner's manual. The forecast for tomorrow's 35-mile passage is southwest 5 to 6, occasionally 7 later, sea moderate to rough. The boat has just returned from a fortnight's cruise.

Inventory: the anchor chain (60 m of 8 mm, about 85 kg) is in the bow locker; four full jerry cans are lashed on deck; the dinghy is inflated on the foredeck; the main water tank is half full; the bilge has 20 litres of water in it.

Actions:

1. Move the jerry cans to the cockpit locker and lash them; deflate and stow the dinghy below or in a locker.
2. Flake about 30 m of chain into the bilge near the mast foot to reduce weight in the bow.
3. Pump the bilge dry and find the source of the water.
4. Fill the water tank (or empty it completely if a second tank is full).
5. Secure batteries, floorboards and heavy lockers. Close and dog the forehatch and all portlights.
6. Fit the washboards in rough weather and keep the lower washboard in at all times on passage.

Sail plan: with gusts possibly reaching force 7 (28 to 33 knots), plan to sail with two reefs and a partly furled genoa from the start of the exposed leg, rather than reefing on the foredeck in rising seas.

Route: the planned route passes a headland race at a time when the stream will run against the wind. Re-time the departure so you pass at slack water, or route 3 miles offshore of the race.

These actions lower G, eliminate free surface, raise the downflooding angle and keep the boat out of the waves most likely to break. Nothing in the list needs a calculator; it needs understanding of the principles.

Further Detail from the Stability Literature

STIX values and design category thresholds

The Stability Index is a single number that summarises several stability properties under ISO 12217-2. The minimum STIX for each design category is A 32, B 23, C 14 and D 5. STIX is not the whole story: ISO 12217-2 also sets minimum values for the angle of vanishing stability (roughly 130 degrees or more for Category A and B boats of typical size, with lower figures for smaller or less exposed categories), for the downflooding height and angle, and for the knockdown recovery. A high STIX on a boat with a low downflooding angle is a poor safety margin, so always read the number alongside the other data in the builder's documentation.

Wind heeling moment and why gusts matter

Wind force on a sail is proportional to the square of the apparent wind speed. Doubling the wind speed from 20 to 40 knots therefore quadruples the heeling force; going from 15 to 30 knots does the same. The heeling moment is that force multiplied by the height of the centre of effort of the sails above the centre of lateral resistance, so reducing sail area and lowering the centre of effort (reefing the mainsail, changing to a smaller headsail) reduces the heeling moment far more than the loss of area alone suggests. A boat that sails comfortably at 18 knots with full sail needs roughly a quarter of the area at 36 knots to carry the same heeling moment.

The boat settles at the heel angle where righting moment equals heeling moment. If the gust is strong enough that the heeling moment exceeds the maximum righting moment, there is no equilibrium angle and the boat goes over until the sails spill the wind or the mast hits the water. This is why a knockdown can happen in a squall long before the AVS is relevant, and why you reef early rather than relying on the boat's reserves.

Capsize screening formula

A simple rule of thumb from the Offshore Racing Congress is the Capsize Screening Formula (CSF):

CSF = maximum beam (m) divided by the cube root of displacement volume (m3)

A value of 2.0 or less is considered acceptable for an offshore yacht; higher values indicate a wide, light boat more vulnerable to being inverted by a breaking wave.

Example: a yacht of 8000 kg with a maximum beam of 3.8 m. Displacement volume in sea water = 8000 / 1025 = 7.8 m3. The cube root of 7.8 is 1.98. CSF = 3.8 / 1.98 = 1.92, which is under 2.0, so acceptable. A lighter yacht of 5000 kg (4.9 m3, cube root 1.70) with the same beam gives 3.8 / 1.70 = 2.24, which is above the guideline.

Inclining test and measuring stability

Builders and surveyors determine the real position of G by an inclining test: a known weight is moved a measured distance athwartships and the resulting angle of heel (measured with a long pendulum or inclinometer) gives GM. The relationship is GM = (w x d) / (W x tan of the heel angle), where w is the moved weight, d the distance moved and W the displacement. The result is the starting point for the GZ curve. If you have made major modifications (a heavy new radar arch, a liferaft on the coachroof, a furling mast, extra batteries), the published figures no longer apply exactly, so treat the modification as a loss of stability margin.

Dynamic stability and the effect of a wave

A boat resists capsize by absorbing energy, represented by the area under the GZ curve. A breaking wave delivers energy suddenly, and the heel and roll angle reached depends on how much energy there is relative to the area available. A boat with a larger area under its curve (higher GM, greater range) needs a bigger wave to invert it. A sea state in which waves break with a height of more than about half the boat's length is a recognised capsize threat, which is why the 1979 Fastnet and later research focused on breaking wave height relative to boat size.

Worked example: hanging loads and the effect on KG

A yacht displaces 6000 kg with KG 1.00 m and KM 2.30 m, so GM = 1.30 m. The crew fit a 40 kg outboard on the pushpit at 2.5 m above the keel and fill two 25-litre jerrycans of fuel (50 kg total) lashed on the side deck at 1.5 m.

1. Moments: 6000 x 1.00 = 6000; 40 x 2.5 = 100; 50 x 1.5 = 75. Total = 6175 kg m.
2. New displacement = 6090 kg.
3. New KG = 6175 / 6090 = 1.014 m.
4. New GM (assuming KM unchanged) = 2.30 - 1.014 = 1.286 m, a loss of about 1 percent.

The effect of one item is small, which is the danger: ten small additions over a refit can reduce GM by 10 percent or more without anyone noticing. Stowing the outboard in the cockpit locker and the fuel low in the cockpit locker would have kept most of that margin.

Common Mistakes

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• Stowing heavy gear on deck or high in lockers. Keep heavy items low and central.
• Running with half-full tanks and a wet bilge. Free surface effectively raises G; use one tank at a time, keep bilges dry.
• Ignoring the burn-off of consumables. Plan for the end-of-passage condition.
• Treating the AVS as the limit. Downflooding usually happens first. Keep hatches and washboards closed.
• Unsecured deck loads. They shift, absorb water and add windage.
• Lying beam-on to breaking seas. It is the most dangerous orientation for capsize.
• Assuming a stiff boat is a seaworthy boat. High initial stability (GM) does not guarantee a good range of stability.

Summary

• G is the centre of all weight; B is the centre of the underwater volume and moves to the low side when the boat heels.
• The righting lever GZ is the horizontal distance between the weight and buoyancy forces; righting moment equals displacement times GZ.
• GM, the height of M above G, governs initial stability: large GM is stiff, small GM is tender, negative GM is unstable.
• The GZ curve shows maximum GZ (typically 30 to 40 degrees) and the AVS (often 110 to 130 degrees for modern yachts). Beyond the AVS the boat capsizes.
• The downflooding angle is often much less than the AVS and is the practical limit.
• Keep weight low and central, avoid weight aloft and on deck, keep tanks full or empty, keep bilges dry and secure everything.
• Breaking beam seas around 30 to 55 percent of the boat's length can knock down or roll a yacht. Avoid tide races and overfalls in strong winds.

Check Your Understanding

1. What is the righting lever GZ, and how is righting moment calculated?

Answer: GZ is the horizontal distance between the line of action of weight through G and the line of action of buoyancy through B when the boat is heeled. Righting moment equals displacement multiplied by GZ.

1. Your boat has started rolling slowly and hanging at the end of each roll. What might have happened?

Answer: GM has reduced: G has risen or the effective G has risen, for example from water in the bilge (free surface), a heavy deck load or weight aloft. Investigate immediately.

1. Define the angle of vanishing stability.

Answer: The angle of heel at which the righting lever GZ falls to zero. Beyond it the boat will continue to capsize.

1. Why might a boat be in danger at an angle of heel well below its AVS?

Answer: It may reach its downflooding angle first, where water enters through open hatches, vents or lockers, reducing stability rapidly.

1. A 4000 kg yacht has a KG of 0.9 m. You add 100 kg at 2.9 m above the keel. What is the new KG?

Answer: Total moment = 4000 x 0.9 + 100 x 2.9 = 3600 + 290 = 3890 kg m. Total weight 4100 kg. New KG = 3890 / 4100 = 0.95 m, a rise of 5 cm.

1. Why should you draw water from one tank at a time?

Answer: So that only one tank has a free surface at any time; partly filled tanks allow liquid to shift and effectively raise G.

1. What size of breaking wave can knock down or roll a 12 m yacht, according to research after the 1979 Fastnet race?

Answer: Around 30 percent of length (about 3.6 m) could knock her down to the horizontal; around 55 percent (about 6.6 m) could roll many yachts through 180 degrees.

1. What does RCD design category C indicate?

Answer: Inshore: designed for coastal waters, large bays, estuaries and lakes, in winds up to force 6 and significant wave heights up to 2 m.

1. Why is weight at the masthead so much more harmful than the same weight on deck?

Answer: The rise in G caused by an added weight is proportional to the weight multiplied by its height above the existing G. A masthead weight may be ten or more times further above G than one on deck, so it raises G many times as much.

1. A yacht's roll period lengthens by about 20 percent after the owner stows extra gear in the aft lockers and on deck. What does this tell you, and what would you do?

Answer: GM has fallen (roughly 30 percent for a 20 percent longer roll) because G has risen, so stability has reduced. Find the heavy or high weight, move it low and central or remove it, and re-check the roll period.

1. A flooded cabin sole is more dangerous to stability than the same weight of water in a narrow tank. Why?

Answer: Water across the whole width of the cabin sole has a very wide free surface. The free surface effect depends on the width of the surface, so the shifting water reduces GM far more than its weight alone would suggest.

1. A wind gust takes the wind from 20 to 30 knots. By what factor does the heeling force rise, and what is the practical lesson?

Answer: Force rises with the square of the speed: 2.25 times. Reef for the gusts, not the mean wind, and ease sheets or bear away at once if overpowered.