MODERN SAILBOAT DESIGN: Quantifying Stability

Capsized sailboat

We have previously discussed both form stability and ballast stability as concepts, and these certainly are useful when thinking about sailboat design in the abstract. They are less useful, however, when you are trying to evaluate individual boats that you might be interested in actually buying. Certainly you can look at any given boat, ponder its shape, beam, draft, and ballast, and make an intuitive guess as to how stable it is, but what’s really wanted is a simple reductive factor–similar to the displacement/length ratio, sail-area/displacement ratio, or Brewer comfort ratio–that allows you to effectively compare one boat to another.

Unfortunately, it is impossible to thoroughly analyze the stability of any particular sailboat using commonly published specifications. Indeed, stability is so complex and is influenced by so many factors that even professional yacht designers find it hard to quantify. Until the advent of computers, the calculations involved were so overwhelming that certain aspects of stability were only estimated rather than precisely determined. Even today, with computers doing all the heavy number crunching, stability calculations remain the most tedious part of a naval architect’s job.

There are, however, some tools available that you can use to make a sophisticated appraisal of a boat’s stability characteristics. If you dig and scratch a bit–on the Internet, or by pestering a builder or designer–you should be able to unearth one or more of them.

Stability Curves and Ratios

The most common tool used to assess a boat’s form and ballast stability is a stability curve. This is a graphic representation of a boat’s self-righting ability as it is rotated from right side up to upside down. Stability curves are sometimes published or otherwise made available by designers and builders, but to interpret them correctly, you first need to understand the physics of a heeling sailboat.

When perfectly upright, a boat’s center of gravity (CG)–which is a function of its total weight distribution (i.e., its ballast stability)–and its center of buoyancy (CB)–which is a function of its hull shape (i.e., its form stability)–are vertically aligned on the boat’s centerline. CG presses downward on the boat’s hull while CB presses upward with equal force. The two are in perfect equilibrium, and the boat is motionless. If some force heels the boat, however, CB shifts outboard of CG and the equilibrium is disturbed. The horizontal distance created between CG and CB as the boat heels is called the righting arm (GZ). This is a lever arm, with CG pushing down on one end and CB pushing up on the other, and their combined force, known as the righting moment (RM), works to rotate the hull back to an upright position. The point around which the hull rotates is known as the metacenter (M) and is always directly above CB.

The longer the righting arm (i.e., the larger the value for GZ), the greater the righting moment and the harder the hull tries to swing upright again. Up to a point, as a hull heels more, its righting arm just gets longer. The righting moment, consequently, gets larger and larger. This is initial stability. A wider hull has greater initial stability simply because its greater beam allows CB to move farther away from CG as it heels. Shifting ballast to windward also moves CG farther away from CB, and this too lengthens the righting arm and increases initial stability. The angle of maximum stability (AMS) is the angle at which the righting arm for any given hull is as long as it can be. This is where a hull is trying its hardest to turn upright again and is most resistant to further heeling.

Once a hull is pushed past its AMS, its righting arm gets progressively shorter and its ability to resist further heeling decreases. Now we are moving into the realm of ultimate, or reserve, stability. Eventually, if the hull is pushed over far enough, the righting arm disappears and CG and CB are again vertically aligned. Now, however, the metacenter and CG are in the same place, and the hull is metastable, meanings it is in a state of anti-equilibrium. Its fate hangs in the balance, and the least disturbance will cause it to turn one way or the other. This point of no return is the angle of vanishing stability (AVS). If the hull fails to right itself at this point, it must capsize. Any greater angle of heel will cause CG and CB to separate again, except now the horizontal distance between them will be a capsizing arm, not a righting arm. Gravity and buoyancy will be working together to invert the hull.

GZ stability illustration

Stability at work. The righting arm (GZ) gets longer as the center of gravity (CG) and the center of buoyancy (CB) get farther apart, and the boat works harder to right itself. Past the angle of vanishing stability, however, the righting arm is negative and CG and CB are working to capsize the boat

A stability curve is simply a plot of GZ–including both the positive righting arm and the negative capsizing arm–as it relates to angle of heel from 0 to 180 degrees. Alternatively, RM (that is, both the positive righting moment and the negative capsizing moment) can be the basis of the plot, as it derives directly from GZ. (To find RM in foot-pounds, simply multiply GZ in feet by the boat’s displacement in pounds.) In either case, an S-curve plot is typical, with one hump in positive territory and another hopefully smaller hump (assuming the boat in question is a monohull) in negative territory.

The AMS is the highest point on the positive side of the curve; the AVS is the point at which the curve moves from positive to negative territory. The area under the positive hump represents all the energy that must be expended by wind and waves to capsize the boat; the area under the negative hump is the energy (usually only waves come into play here) required to right the boat again. To put it another way: the larger the positive hump, the more likely a boat is to remain right side up; the smaller the negative hump, the less likely it is to remain upside down.

GZ stability curve

Righting arm (GZ) stability curve for a typical 35-foot cruising boat. The angle of maximum stability (AMS) in this case is 55 degrees with a maximum GZ of 2.6 feet; the angle of vanishing stability (AVS) is 120 degrees; the minimum GZ is -0.8 feet

The relationship between the sizes of the two humps is known as the stability ratio. If you have a stability curve to work from, there are some simple calculations developed by designer Dave Gerr that allow you to estimate the area under each portion of the curve. To calculate the positive energy area (PEA), simply multiply the AVS by the maximum righting arm and then by 0.63: PEA = AVS x max. GZ x 0.63. To calculate the negative energy area (NEA), first subtract the AVS from 180, then multiply the result by the maximum capsizing arm (i.e., the minimum GZ) and then by 0.66: NEA = (180 – AVS) x min. GZ x 0.66. To find the stability ratio divide the positive area by the negative area.

Working from the curve shown in the graph above for a typical 35-foot cruising boat, we get the following values to plug into our equations: AVS = 120 degrees; max. GZ = 2.6 feet; min. GZ = -0.8 feet. The boat’s PEA therefore is 196.56 degree-feet: 120 x 2.6 x 0.63 = 196.56. Its NE is 31.68 degree-feet: (180 – 120) x -0.8 x 0.66 = 31.68. Its stability ratio is thus 6.2: 196.56 ÷ 31.68 = 6.2. As a general rule, a stability ratio of at least 3 is considered adequate for coastal cruising boats; 4 or greater is considered adequate for a bluewater boat. The boat in our example has a very healthy ratio, though some boats exhibit ratios as high as 10 or greater.

You can run these same equations regardless of whether you are working from a curve keyed to the righting arm or the righting moment. The curve in our example is a GZ curve, but if it were an RM curve, we only have to substitute the values for maximum and minimum RM for maximum and minimum GZ. Otherwise the equations run exactly the same way. The results for positive and negative area, assuming RM is expressed in foot-pounds, will be in degree-foot-pounds rather than degree-feet, but the final ratio will be unaffected.

GZ and RM curves are not, however, interchangeable in all respects. When evaluating just one boat it makes little difference which you use, but when comparing different boats you should always use an RM curve. Because righting moment is a function of both a boat’s displacement and the length of its righting arm, RM is the appropriate standard for comparing boats of different displacements. It is possible for different boats to have the same righting arm at any angle of heel, but they are unlikely to have the same stability characteristics. It always takes more energy to capsize a larger, heavier boat, which is why bigger boats are inherently more stable than smaller ones.

RM stability curve comparison

Righting moment (RM) stability curves for a 19,200-pound boat and a 28,900-pound boat with identical GZ values. Because heavier boats are inherently more stable, RM is the standard to use when comparing different boats (Data courtesy of Dave Gerr)

Another thing to bear in mind when comparing boats is that not all stability curves are created equal. There are various methods for constructing the curves, each based on different assumptions. The two most commonly used methodologies are based on standards promulgated by the International Measurement System (IMS), a once popular rating rule used in international yacht racing, and by the International Organization for Standardization (ISO). Many yacht designers have developed their own methods. When comparing different boats, you must therefore be sure their curves were constructed according to the same method.

Perfect Curves and Vanishing Angles

To get a better idea of how form and ballast relate to each another, it is useful to compare curves for hypothetical ideal vessels that depend exclusively on one type of stability or the other. A vessel with perfect form stability, for example, would be shaped very much like a wide flat board, and its stability curve would be perfectly symmetrical. Its AVS would be 90 degrees, and it would be just as stable upside down as right side up. A vessel with perfect ballast stability, on the other hand, would be much like a ballasted buoy–that is, a round, nearly weightless flotation ball with a long stick on one side to which a heavy weight is attached, like a pick-up buoy for a mooring or a man-overboard pole. The curve for this vessel would have no AVS at all; there would be just one perfectly symmetric hump with an angle of maximum stability of 90 degrees. The vessel will not become metastable until it reaches the ultimate heeling angle of 180 degrees, and no matter which way it turns at this point, it must right itself.

Ideal stability curves

Ideal righting arm (GZ) stability curves: vessel A, a flat board, is as stable upside down as it is right side up; vessel B, a ballasted buoy, must right itself if turned upside down (Data courtesy of Danny Greene)

Beyond the fact that one curve has no AVS at all and the other has a very poor one, the most obvious difference between the two is that the board (vessel A) reaches its point of no return at precisely the point that the buoy (vessel B) achieves maximum stability. A subtler but critical difference is seen in the shape of the two curves between 0 and 30 degrees of heel, which is the range within which sailboats routinely operate. Vessel A achieves its maximum stability precisely at 30 degrees, and the climb of its curve to that point is extremely steep, indicating high initial stability. Vessel B, on the other hand, exhibits poor initial stability, as the trajectory of its curve to 30 degrees is gentle. Indeed, heeling A to just 30 degrees requires as much energy as is needed to knock B down flat to 90 degrees.

Catamaran and monohull stability curves

Righting arm (GZ) stability curves for a typical catamaran and a typical narrow, deep-draft, heavily ballasted monohull. Note similarities to the ideal curves in the last figure

To translate this into real-world terms, we need only compare the curves for two real-life vessels at opposite extremes of the stability spectrum. The curve for a typical catamaran, for example, looks similar to that of our board since its two humps are symmetrical. If anything, however, it is even more exaggerated. The initial portion of the curve is extremely steep, and maximum stability is achieved at just 10 degrees of heel. The AVS is actually less than 90 degrees, meaning that the cat, due to the weight of its superstructure and rig, will reach its point of no return even before it is knocked down to a horizontal position. The curve for a narrow, deep-draft, heavily ballasted monohull, by comparison, is similar to that of the ballasted buoy. The only significant difference is that the monohull has an AVS, though it is quite high (about 150 degrees), and its range of instability (that is, the angles at which it is trying to capsize rather than right itself) is very small, especially when compared to that of the catamaran.

The catamaran, due to its light displacement and great initial stability, will likely perform well in moderate conditions and will heel very little, but it has essentially no reserve stability to rely on when conditions get extreme. The monohull because of its heavy displacement (much of it ballast) and great reserve stability, will perform less well in moderate conditions but will be nearly impossible to overturn in severe weather.

What Is An Adequate AVS?

In the real world you will rarely come across stability curves for catamarans. If you do find one, you should probably be most interested in the AMS and the steepness of the curve leading up to it. Monohull sailors, on the other hand, should be most interested in the AVS, and as a general rule the bigger this is the better.

Coastal cruisers sailing in protected waters should theoretically be perfectly safe in a boat with an AVS of just 90 degrees. Assuming you never encounter huge waves, the worst that could happen is you will be knocked flat by the wind, and so as long as you can recover from a 90-degree knockdown, you should be fine. It’s nice to have a safety margin, however, so most experts advise that average-size coastal cruising boats should have an AVS of at least 110 degrees. Some believe the minimum should 115 degrees.

For offshore sailing you want a larger margin of safety. Recovering from a knockdown in high winds is one thing, but in a survival storm, with both high winds and large breaking waves, there will be large amounts of extra energy available to help roll your boat past horizontal. There is near-universal consensus that bluewater boats less than 75 feet long should have an AVS of at least 120 degrees. Because larger boats are inherently more stable, the standard for boats longer than 75 feet is 110 degrees.

The reason 120 degrees is considered the minimum AVS standard for most bluewater boats is quite simple. Naval architects figure that any sea state rough enough to roll a boat past 120 degrees and totally invert it will also be rough enough to right it again in no more than 2 minutes. This, it is assumed, is the longest time most people can hold their breaths while waiting for their boats to right themselves. If you don’t ever want to hold your breath that long, you want to sail offshore in a boat with a higher AVS.

AVS table

Estimated times of inversion for different AVS values (Data courtesy of Dave Gerr)

As this graph illustrates, an AVS of 150 degrees is pretty much the Holy Grail. A boat with this much reserve stability can expect to meet a wave large enough to turn it right side up again almost the instant it’s turned over.

Other Factors To Consider

Stability curves may look dynamic and sophisticated, but in fact they are based on relatively simple formulas that can’t account for everything that might make a particular boat more or less stable in the real world. For one thing, as with regular performance ratios, the displacement values used in calculating stability curves are normally light-ship figures and do not include the weight that is inevitably added when a boat is equipped and loaded for cruising. Even worse, much of this extra weight–in the form of roller-furling units, mast-mounted radomes, and other heavy gear–will be well above the waterline and thus will erode a boat’s inherent stability. The effect can be quite large. For example, installing an in-mast furling system may reduce your boat’s AVS by as much as 20 degrees. In most cases, you should assume that a loaded cruising boat will have an AVS at least 10 degrees lower than that indicated on a stability curve calculated with a light-ship displacement number.

Another important factor to consider is downflooding. Stability curves normally assume that a boat will take on no water when knocked down past 90 degrees, but this is unlikely in the real world. The companionway hatch will probably be at least partway open, and if the knockdown is unexpected, other hatches may be open as well. Water entering a boat that is heeled to an extreme angle will further destabilize the boat by shifting weight to its low side. If the water sloshes about, as is likely, this free-surface effect will make it even harder for the boat to come upright again.

This may seem irrelevant if you are a coastal cruiser, but if you are a bluewater cruiser you should be aware of the location of your companionway. A centerline companionway will rarely start downflooding until a boat is heeled to 110 degrees or more. An offset companionway, however, if it is on the low side of the boat as it heels, may yield downflood angles of 100 degrees or lower. A super AVS of 150 degrees won’t do much good if your boat starts flooding well before that. To my knowledge, no commonly published stability curve accounts for this factor.

Another issue is the cockpit. An open-transom cockpit, or a relatively small one with large effective drains, will drain quickly if flooded in a knockdown. A large cockpit that drains poorly, however, may retain water for several minutes, and this, too, can destabilize a boat that is struggling to right itself.

Sailboat on land

This boat has features that can both degrade and improve its stability. The severely offset companionway makes downflooding a big risk during a port tack knockdown or capsize, but the high rounded cabintop and small cockpit footwell will help the boat to right itself

Fortunately, not all unaccounted for stability factors are negative. IMS-based stability curves, for example, assume that all boats have flush decks and ignore the potentially positive effect of a cabin house. This is important, as a raised house, particularly one with a rounded top, provides a lot of extra buoyancy as it is submerged and can significantly increase a boat’s stability at severe heel angles. Lifeboats and other self-righting vessels have high round cabintops for precisely this reason.

ISO-based stability curves do account for a raised cabin house, but not all designers believe this is a good thing. A cabin house only increases reserve stability if it is impervious to flooding when submerged. If it has open hatches or has large windows and apertures that may break under pressure, it will only help a boat capsize and sink that much faster. The ISO formulas fail to take this into account and instead may award high stability ratings to motorsailers and deck-saloon boats with large houses and windows that may be vulnerable in extreme conditions.

Simplified Measures of Stability

In addition to developing stability curves, which obviously are fairly complex, designers and rating and regulatory authorities have also worked to quantify a boat’s stability with a single number. The simplest of these, the capsize screening value (CSV), was developed in the aftermath of the 1979 Fastnet Race. Over a third of the more than 300 boats entered in that race, most of them beamy, lightweight IOR designs, were capsized (rolled to 180 degrees) by large breaking waves, and this prompted a great deal of research on yacht stability. The capsize screening value, which relies only on published specifications and was intended to be accessible to laypeople, indicates whether a given boat might be too wide and light to readily right itself after being overturned in extreme conditions.

To figure out a boat’s CSV divide the cube root of its displacement in cubic feet into its maximum beam in feet: CSV = beam ÷ ³√DCF. You’ll recall that a boat’s weight and the volume of water it displaces are directly related, and that displacement in cubic feet is simply displacement in pounds divided by 64 (which is the weight in pounds of a cubic foot of salt water). To run an example of the equation, let’s assume we have a hypothetical 35-foot boat that displaces 12,000 pounds and has 11 feet of beam. To find its CSV, first calculate DCF–12,000 ÷ 64 = 187.5–then find the cube root of that result: ³√187.5 = 5.72; note that if your calculator cannot do cube roots, you can instead take 187.5 to the 1/3 power and get the same result. Divide that result into 11, and you get a CSV of 1.92: 11 ÷ 5.72 = 1.92.

Interpreting the number is also simple. Any result of 2 or less indicates a boat that is sufficiently self-righting to go offshore. The further below 2 you go, the more self-righting the boat is; extremely stable boats have values on the order of 1.7. Results above 2 indicate a boat may be prone to remain inverted when capsized and that a more detailed analysis is needed to determine its suitability for offshore sailing.

As handy as it is, the CSV has limited utility. It accounts for only two factors–displacement and beam–and fails to consider how weight is distributed aboard a boat. For example, if we load our hypothetical 12,000-pound boat with an extra 2,250 pounds for light coastal cruising, its CSV declines to 1.8. Load it with an extra 3,750 pounds for heavy coastal or moderate bluewater use, and the CSV declines still further, to 1.71. This suggests that the boat is becoming more stable, when in fact it may become less stable if much of the extra weight is distributed high in the boat.

Note too that a boat with unusually high ballast–including, most obviously, a boat with ballast in its bilges rather than its keel–will also earn a deceptively low screening value. Two empty boats of identical displacement and beam will have identical screening values even though the boat with deeper ballast will necessarily be more resistant to capsize.

Another single-value stability rating still frequently encountered is the IMS stability index number. This was developed under the IMS rating system to compare stability characteristics of race boats of various sizes. The formula essentially restates a boat’s AVS so as to account for its overall size, awarding higher values to longer boats, which are inherently more stable. IMS index numbers normally range from a little below 100 to over 140. For what are termed Category 0 races, which are transoceanic events, 120 is usually the required minimum. In Category 1 events, which are long-distances races sailed “well offshore,” 115 is the common minimum standard, and for Category 2 events, races of extended duration not far from shore, 110 is normally the minimum standard. Conservative designers and pundits often posit 120 as the acceptable minimum for an offshore cruising boat.

Since many popular cruising boats were never measured or rated under the IMS rule, you shouldn’t be surprised if you cannot find an IMS-based stability curve or stability index number for a cruising boat you are interested in. You may find one if the boat in question is a cruiser-racer, as IMS was once a prevalent rating system. Bear in mind, though, that the IMS index number does not take into account cabin structures (or cockpits, for that matter), and assumes a flush deck from gunwale to gunwale. Neither does it account for downflooding.

Another single-value stability rating that casts itself as an “index” is promulgated by the ISO. This is known as STIX, which is simply a trendy acronym for stability index. Because STIX values must be calculated for any new boat sold inside the European Union (EU), and because STIX is, in fact, the only government-imposed stability standard in use anywhere in the world, it is likely to become the predominant standard in years to come.

A STIX number is the result of many complex calculations accounting for a boat’s length, displacement, beam, ability to shed water after a knockdown, angle of vanishing stability, downflooding, cabin superstructure, and freeboard in breaking seas, among others. STIX values range from the low single digits to about 50. A minimum of 38 is required by the European Union for Category A boats, which are certified for use on extended passages more than 500 miles offshore where waves with a maximum height of 46 feet may be encountered. A value of at least 23 is required for Category B boats, which are certified for coastal use within 500 miles of shore where maximum wave heights of 26 feet may be encountered, and the minimum values for categories C and D (inshore and sheltered waters, respectively) are 14 and 5. These standards do not restrict an owner’s use of his boat, but merely dictate how boats may be marketed to the public.

The STIX standard has many critics, including many yacht designers who do not enjoy having to make the many calculations involved, but the STIX number is the most comprehensive single measure of stability now available. As such, it can hardly be ignored. Many critics assert that the standards are too low and that a number of 40 or greater is more appropriate for Category A boats and 30 or more is best for Category B boats. Others believe that in trying to account for and quantify so many factors in a single value, the STIX number oversimplifies a complex subject. To properly evaluate stability, they suggest, it is necessary to evaluate the various factors independently and make an informed judgment leavened by a good dose of common sense.

As useful as they may or may not be, STIX numbers are generally unavailable for boats that predate the EU’s adoption of the STIX standard in 1998. Even if you can find a number for a boat you are interested in, bear in mind that STIX numbers do not account for large, potentially vulnerable windows and ports in cabin superstructures, nor do they take into account a boat’s negative stability. In other words, boats that are nearly as stable upside down as right side up may still receive high STIX numbers.

The bottom line when evaluating stability is that no single factor or rating should be considered to the exclusion of all others. It is probably best, as the STIX critics suggest, to gather as much information from as many sources as you can, and to bear in mind all we have discussed here when pondering it.

5 Responses
  1. Extremely good analysis of the issue. Did you do an engineering degree before law school Charlie?
    One more thought on stability that is outwith the scope of the indices.
    In the classic broach, as the vessel rounds up th keel bites the water and makes the turn worse, increasing the apparent wind and angle of heel, making the rudder progressively less effective,until it is powerless at 90 degrees heel.
    In a centreboarder with the board up, the bow skids off, avoiding a real broach, and hence danger of being forced to the spreaders hitting the water.
    We were caught in a 25 knot gust with our somewhat oversize spi up, the helmsman fell and let go, yet we never heeled past about 50 degrees.
    You had some fun on the cboard Che Vive in strong wind from aft.
    To some extent, this phenomenon mitigates the poorer AVS of the centreboarder. Is it enough?
    I hope to avoid checking it out in practice

  2. Charlie

    @Neil: You’re right. I think centerboard boats are more stable in some situations, less stable in others, and the situations in which they are more stable are not represented in stability curves. It is an imperfect science, to say the least. For example, a point I probably should have emphasized a bit more strongly in the text is that the capsize screening value was never ever intended to be dispositive. It was only intended to identify boats that should be subjected to a more rigorous analysis. Thus the word “screening.” charlie

  3. john kretschmer

    Charlie just came across this post while preparing for my next workshop this weekend. It’s flat out great, the best real world explanation of stability I’ve read.

  4. tony craggs

    A bit late in the day given the date of the article. Anyway here goes.
    The boat properties in this article are obtained under static equilibrium conditions.
    Thus the moment resistance curve is obtained by calculating the relative positions of the weight of the vessel and the buoyancy force as the hull is caused to rotate or heel- the resistance due to the moment produced by the misalignment of the two forces at various angles of heel. Because the movement takes place extremely slow no account is allowed for the effect of inertia.
    I would like to make my point my considering the example of a bag of sugar :
    In the first example (a) the sugar is gently poured from the bag onto the pan of a weigh scale until the required weight is reached , say one pound: thus an oz at a time until the scale pointer is at one pound !
    In case (b) the sugar is placed in a bag, and the bag is placed in contact with the scale but then suddenly released. At which point the scale pointer will swing well past the 1 pound mark reaching 2 pounds , and the pointer will oscillate about the one pound mark, eventually coming to rest about this value!
    In case (c) the bag , instead of being placed in contact with pan is released from a height of one foot before being released. This will cause likely cause the pointer to be bent and a broken weigh scale.

    It is a apparent that the properties used to measure a boats stability are derived from the conditions similar to case (a), while in reality they should be deduced from case (c) INERTIA IS IMPORTANT.

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