Stability involves a complex set of factors. As a boat moves through the water and as conditions of wave and weather interact with the physical characteristics of the vessel, a particular design will demonstrate its ability to stay within accepted parameters of stability.
The stability of any vessel can be broken down into two types: static stability and dynamic stability. A look at static stability may help to explain basic stability concepts.
Fortunately there is primarily one rule that must be understood: Instability of the sort we want to avoid will ensue when an object’s center of gravity (CG) moves laterally out beyond the margins of its base. To illustrate this, let’s start with a box resting on a flat floor. Because it is a homogenous object, the CG is right in the middle. Tip it so that the CG goes just beyond a line drawn vertically from the edge below, and it will “capsize.” Adding weight will make it harder to lift and overturn, but as long as the center of gravity remains in place it will always become unstable at the same angle. By experiment, we can learn that the object will tip over sooner when weight is added on top (raising the CG) or, later, if added at the bottom. The diagram shows why: Raising the CG makes it pass beyond the fixed “base” point earlier, and lowering retards that passage. All this is made simple by the fact that the base remains at the same place – the hard edge of box that rests on the floor.
Remove the box from the floor and place it in water. All that changes is that our “base” becomes a more fluid entity. Instead of being the outside bottom edge, the upward force of the “base” becomes the geometric center of whatever part of the box immerses as we incline it – this is called the “center of buoyancy.”
As we begin to incline the floating box, some volume of our changing immersed hull moves quickly over to “leeward.” The block is only so wide, so the center of buoyancy can only move laterally a limited amount. The CG eventually moves beyond the changing center of buoyancy and the box capsizes. When, as in this simple case, the center of gravity of a floating object is at the geometric center of the object, every bit of stability derives from the shape of the object alone and is called “form” stability.
Let’s try this experiment with another shape – a hollow cylinder. Put in the water, it remains as placed. Rotated and launched again, it will come to rest at an unpredictable and wholly arbitrary position. It has no stability due to form, so it stays put solely due to friction and/or inertia. Now place some metal inside the hollow cylinder. It need not be much. In fact, it can be anything that moves the center of gravity the slightest bit away from dead center. The “form” of the cylinder remains unchanged as it is inclined, but the metal rotates the whole so that it’s weight is always at the bottom. This is “pendulum” or “ballast” stability.
Now let’s go back to the floating box. As we have done to the cylinder, we insert some metal on the bottom. The ballasted box is found to be more stable than the original empty one. It has the original’s initial stability due to form, and added to that is the pendulum stability provided by the ballast. The metal has moved the CG away from geometric center (downwards). It is clear that the two forms of stability acting together are what will resist the block’s tipping – up to a point.
Whether a cylinder, block, or a yacht with a complex sectional shape, it’s useful to be able to calculate how much force is needed to tip the object a given amount. Just as was the case with the box on the hard floor, the force needed to incline always equals the weight of the object times the lateral distance from CG to the base, or, in the case of the yacht, to the center of buoyancy. The lateral distance is called the righting arm, and the product of the distance in feet times the weight of the boat in pounds is called the righting moment and is expressed in foot/pounds. Any floating object with stability will become harder and harder to tip as we push on it for a time, then, as the “side” of the object creates a limit to outboard movement of the CB and “ballast” passes beyond it’s furthest lateral position, the force reaches a maximum and declines. A continuous plot of the righting arms (or righting moments) will produce a sinusoidal curve of stability. For sailboats, this curve is instructive. Let’s look at two extreme examples.Ballast vs. form stability
The first yacht is a British channel cutter of the 1900s (see accompanying diagram). She is extremely narrow and deep, but, being a racer, has outside lead ballast. Initial stability is minimal, because the center of buoyancy hardly moves aside as she heels. (In other words, she has minimal form stability.) Even out beyond a 45 degree angle, the center of buoyancy never moves enough to become a significant righting factor. It is the keel, or more rightly, the center of gravity, moving out to the side, that stabilizes the boat. Even when the keel is high in the air, the CG remains within the “base”, that is, to left of the CB. This boat can even go fully upside down and retain some positive stability. In fact, the situation when a boat has been fully turtled is extremely important, and this “plank-on-edge” model has nothing to fear: at 180 degree heel the slightest push causes her to re-right. In general, this type of stability was used by designers of ocean racers in the past. In addition to an almost assured confidence against capsize, such a yacht has an easy motion. The lack of hull volume, and especially of beam which accentuates roominess, makes for cramped quarters below, however. And because of its low ratio of volume to mass, such a hull tended to be driven through the sea rather than rise buoyantly over it. On the other hand, such pendulum stability represents the best insurance against inversion.
The second yacht is the opposite case, a wide centerboarder (see accompanying diagram). The beamy shape pushes her wide bilge into the water as soon as the sails begin to heel her, immediately lengthening the athwartships righting arm. On our stability curve, the slope of rising stability is very steep because the hull becomes very asymmetrical at first. This condition provides stiffness just when it’s wanted, during the first 30 degree of heel – the angles at which one is sailing the vast majority of the time. The downside is that eventually, at high heel angles, the higher center of gravity of a flat, shoal boat becomes problematical. Even before the wind begins to glance over the sails, thus reducing heeling pressure, the CB might reach its outer limit while CG is headed towards the dangerous position overhead.
To be accurate, we must be sure to consider the rapid alteration in hull shape that occurs when the rail goes under, and even the extra weight of the lead keel once it is no longer in saltwater. Such factors will produce slight wobbles on our plotted curve of moments. Even the camber arc of the deck, the volume of the cabin trunk, or a solid sitka spruce mast could be important, since these factors might move the CB out a bit beyond CG, thus saving the day. (This is why modern boats’ point of vanishing stability, or what I call capsize angle, must consider the architecture of superstructures and mast if complete accuracy is desired.) Smaller boats of this general shape, if extreme (catboats and such) can capsize, although this usually is compounded by downflooding as water rushes over the cockpit coamings.
Even heavier ocean cruisers with this geometry can overturn given the added push provided by wave action. Unlike the channel cutter, this boat can exhibit stability even when upside down—the stability represented by the right half of the sine curve below the abscissa. (This is often termed “negative” stability, but I feel that terminology can be confusing. It is stability, per se, but the object is upside down—the same laws apply in terms of what has to happen between CG and CB before all is well.)
Without getting into the intricacies of metacentric height – which are useful in quantifying these principles – it must be understood that once inverted, some outside action is needed that will provide enough of a push to put the (inverted) CG back past one side’s (inverted) CB. Given that, the boat will flop back to her more normal stable position.
A close look at the stability curve is appropriate now, because this boat represents the trend that boat designers have increasingly favored over the past half century. When upright stability appears early, as is common in modern boats, it is usually due to form rather than a low CG. Most of the Fastnet boats that had stability problems shared a stability curve that favored form stability. Inverted stability
Whenever the possibility exists that a yacht can turn turtle, the naval architect must address inverted stability. As boats and ships get larger relative to the waves they’ll encounter, there is less need for a reserve of righting ability. For instance, an aircraft carrier might capsize at a “stability index” of 75 degrees – but few forces on earth are likely to tip it that far! However, small ocean sailors suffer a real threat of inversion. In general, a low center of gravity will always be a strong assist in re-righting a vessel, but as beam increases, the actual shape of overturned flotation becomes critical.
The Joint Committee on Safety from Capsizing, formed by the Society of Naval Architects and Marine Engineers and the United States Yacht Racing Union (now U.S. Sailing) actually formulated a means of predicting how long various boats were likely to remain turtled based upon their curves, but here is an example of where averages can give a false sense of security. It is best to avoid any yacht that has high inverted stability. One of the best ways to do so is to measure the ratio of total positive stability (represented by the area beneath the left-hand curve before capsize) and the total “negative” stability (represented by the area above the right-hand curve beyond capsize.) This is the gauge the U. S. Coast Guard uses for passenger-carrying auxiliaries, for instance (in addition to other considerations). There isn’t a consensus among experts regarding the proper minimum ratio of moment areas, but a ratio of not more than 20% is at the high end of expert opinion.
Readers should be aware that nearly all stability curves they see published are spurious. It takes a substantial measurement and computation to create an accurate stability curve. Many designers do a fine job for their needs – between 0 dgrees and 40 degrees. Many will go on to “guesstimate” righting moments beyond that angle, and often the inverted state is pure fiction. Any boat that isn’t shaped like an ellipse with inside ballast will have a bumpy curve, often with a clear deflection at the capsize angle. If a curve looks anything like a perfectly smooth sine wave, it is probably bogus. It should be intuitive by this point that one can gauge a lot about the critical upright/inverted stability ratio simply by inspection. Boats that will readily re-right will have features such as voluminous, rounded, and rather high cabins, rolled deck edges, or, very rarely, a foam-filled or float-tipped mast. Quite a few French designs are moving in the right direction, because that nation has begun to legislate in favor of self-righting yachts.
The ultimate case of form stability is the multihull. In a catamaran the stability is entirely that of form. The base is wide because the hulls are widely separated. But once a cat is tipped to around 90 degrees, there is no keel bringing the CG of the whole down in such a way that the CGs passage outside the base is delayed. Therefore it will overturn at a shallower angle than any ballasted boat, and once capsized the geometry is so similar to the upright condition that it is just as stable inverted. (The experience of those aboard Northern Light, a catamaran capsized and subsequently re-righted by rogue waves, was a once-in-a-lifetime stroke of fortune.) Before we condemn outright the multihull on the basis of stability alone, we should consider that capsize is infrequent in larger modern multihulls that are properly built. Even if it does happen, the lack of a heavy ballast keel becomes an asset, there being far too little deadweight to actually sink the overturned craft. Multihull capsize almost always requires outside assistance, but survival of the occupants is the rule, not the exception. A discussion of yacht stability must never lose sight of the fact that human survival is really the primary need.Dynamic stability
It’s been common knowledge for centuries that larger vessels fared better at sea than small ones. The 1979 Fastnet Race, with 300 starters, proved an excellent sample case. While only three boats larger than 40 feet were fully inverted, most of the smaller ones were, and the severity of circumstances increased as the size diminished. This data was so obvious that it inspired researchers to study the influence of both the yachts’ sizes and shapes in the Annapolis and Wolfson Unit wave tanks.
All who took part in the studies—the best naval architects then drawing racing boats in the U.S. and Britain—knew that wind alone could not have capsized even the smallest participant in the race. Small IOR raters had routinely beam-reached across heavy seaways before. However, it was the conditions of that Fastnet, where survivors uniformly described confused, breaking seas, that resulted in boats being flipped over. The smaller boats that were able to steer, trail warps, or motorsail into the seas – those that presented bow or stern to the sea – were generally more successful. It was clear from the statistics that rollovers primarily occurred as a result of boats being caught beam-to the breaking seas.
For the tank tests, models were prepared that were properly scaled and weighted to represent a cross section of full-sized yachts in distress. No one was surprised that larger models were more difficult to capsize in equal sized breakers. Nor were the scientists caught aback by the importance of the mast in preventing capsize. But many were astounded by the degree of importance of the mast. We now know that even the largest voyaging boat can be capsized by a breaking wave of unusual height, but that this is especially likely if she has a lightweight or missing mast. Very quickly, scientists realized the dominant factor in yacht capsize: the transverse moment of inertia. (The key clue being that the weight of the mast, however light, is centered far from the roll axis. In the rules of inertial moments, the effect of mass is multiplied by the square of the distance off axis.)
Racing sailors are familiar with the concept of weight distribution, especially as it masses in the ends of the boat. Often called “polar moment,” the existence of greater weight at greater distance from a yacht’s center can slow down the boat’s motion as it reacts to head seas, usually cutting boat speed. The same principle works athwartships. Greater weight distributed outboard will retard the boat’s reaction to forces of wind and water that would rapidly heel her.
The fact that transverse inertia and not actual length or even actual weight (the distribution of the weight being the greater factor) was the cause for most capsizes compelled American designers to try and combine inertial and static stability factors in order to evaluate yachts. A formula was devised that did this, but although it has proven empirically accurate, it is so complex that few outside naval architecture are familiar with it.
Still, the concept—establishing “capsize length” for a boat – is far more pertinent than the current media focus on capsize angle. The product of the capsize length formula is a theoretical boat length. If a small boat has a very low CG, narrow beam, and high roll inertia, then it would yield an extended capsize length rating. A 30-footer, for instance, might “rate” as susceptible to capsize as a 55-footer – and boats of that length hardly ever flip over, except perhaps in the Southern Ocean. Probably the best example of the inappropriateness of the current emphasis on stability index rather than “capsize length” is evidenced by the observed capabilities of American keel-centerboarders.Capsize length vs. stability index
Consider, for example, the Hinckley Bermuda 40. Although her wide beam and her shoal draft are negative factors in the formula, this boat’s roll inertia (and low freeboard) play such a major part that there is a huge discrepancy between her “stability index” and her “capsize length.” There are IMS certificates on file for B-40s with stability indexes between 106 degrees and 122 degrees. (By the way, this shows the great variation in static stability that can occur in a given hull model based upon loading and the type of mast.) I have often captained Bermuda 40s in storms; by virtue of actual experience I’d say that this would be near the top of a list of boats I’d want to take across an ocean. Plugged into the “capsize length” formula, B-40s can achieve as high a “capsize length” rating as 76 feet! Actual experience bears this out. Despite their lower stability indexes and a history of numerous circumnavigations, not one B-40 has ever been fully rolled.
Findings of the Joint Committee on Safety from Capsizing recommended that yachts be deemed unsuitable for ocean service if their capsize length fell below 30 feet. Overall length is unimportant. Most of the Fastnet victims were boats between 30 and 40 feet, but their calculated capsize length was often below 30 feet!
Unfortunately, in order to plug into the formula for capsize length, it is necessary to calculate the complete transverse mass moment of inertia of a vessel, which means multiplying the centers of each individual piece aboard a boat times the squares of their distances off-center. If this were a normal procedure in the regimen of calculations for yacht designers, then we could easily achieve the ideal: a published capsize length for each type of boat. But it isn’t. Thus, the only boats that might have done a “capsize length” are those studied by designers after a demonstrated instability problem, boats whose salesmen have been put on the defensive due to market uneasiness about them, or a rare few whose owners have sufficient curiosity and money to commission the difficult task. (The formula is available on page 62 of Desirable and Undesirable Characteristics of Offshore Boats.)
The Capsize Project coordinators soon recognized that their formula was too cumbersome for practical use. They created a simpler, admittedly less accurate, yardstick for evaluating a dynamic capsize index. It is called the capsize screening formula:Step 1: X = Sailing weight of boat (pounds) ÷ 64Step 2: Boat’s maximum beam (feet) ÷ cube root of X
The result will fall in the low single numbers. If the number is below two then total stability is similar to a boat with a capsize length above 30—deemed competent for sea. The lower the number below two, the more certain will be the boat’s resistance to the inertial forces that cause capsize.
I suspect that the capsize screening formula suffers from oversimplification as much as the very accurate capsize length formula is diminished by it’s complexity. The screening formula considers only beam and weight, and thus ignores the very latest trend in yacht design, where designers have finally begun to ignore the rating formulas’ emphasis on the inclining experiment and push center of gravity as low as they can get it. Such boats will be far better all-round sea boats than the screening formula would indicate.Evaluating for capsize
With our better understanding of the many factors involved in the capsize of an oceangoing sailboat, how would one go about assessing stability? Certainly the most prevalent clue, the one that has brought so much attention to the issue, is IMS measurement.
At the outset, sailors must understand that this rating rule was never devised as a way to provide data relating to capsize. It did set out to evaluate stability among manifold other factors that impact upon boat speed under normal racing conditions. Because boats customarily sail between dead-level and rail down, no measurements in the formula are taken above a yacht’s sheer. So much data was attainable through the IMS measurement procedure that the rule numerically extrapolated righting moments for all measured boats. When yacht owners (and yacht brokers trying to sell wide, shoal, comfortable cruising boats) were aghast at some of the low estimates of vanishing stability, the IMS rule makers were quick to admit that their figures ignored effects above the sheer that would normally increase the range of positive stability. Their subsequent statements proved insufficient to calm the waters, so a “fudge factor” was formulated which, added to the hull measurements, would give a more accurate guess at the critical capsize angle.
This is the “stability index” number that is so often quoted in the sailing press. Needless to say, it is only an approximation of ultimate stability. An IOR type boat that has essentially a flat deck with just enough cabin to meet the headroom minimums of the rule (virtually all the Fastnet victims, for instance) might be less stable than the index and certainly runs the risk of lingering upside-down. Most real voyaging boats have a nice amount of shedwater deck arc and a roomy trunk cabin, along with a diminutive cockpit well. These boats would often be more secure than their “stability index.”
Because the IMS rule was devised to allow real voyaging sailboats to be rated for occasional races, there’s a good likelihood that a certificate will be on file for sister ships of one’s boat. With a clear recognition of the “ball-park” nature of the figures, and knowing that they might vary by 10 or more degrees depending on how one’s boat is loaded and particularly by the weight and height of the mast, furler(s) and rolled-up sails, one will have a starting point in evaluating the range of positive static stability.
Older or unusual designs and non-production boats will probably not have a certificate available (from U. S. Sailing, Box 209, Newport, R.I. 02840). One can, however, find the measurement certificates of very similar boats and make some educated guesses. In so doing, one is actually using the same tactics yacht designers employ when they are zeroing in on a prospective boat’s parameters. Weight calculations
Assuming that one can estimate the weight of one’s boat or were clever enough to ask for it from the gauges on a Travelift last fall (end-of-season readings are often much higher than in the spring, before you’ve hauled all that gear aboard), one will be close in terms of displacement. It may be possible to measure, or determine from a sales brochure, a boat’s maximum beam, length, waterline length, and draft. But then comes the hard part: One must get a good idea of the center of gravity, and that isn’t easy. If one is only after “ball-park” figure, one can select near sister hulls with similar keels and ballast-displacement figures. Just as important, one should try and assess the weight and height of a near sister’s mast and rig, ideally through actual measurement. Comparison with very similar IMS certificates will be sufficient to either mollify one’s concerns or scare one into action.
Far more accuracy can be gotten through doing an inclining experiment. (See accompanying story.) It is easier than one might guess – the hardest part is finding an absolutely quiet nook in which to accomplish it. Once one knows how much weight at what distance inclines one’s boat a given number of degrees, there are several options. Inputting waterplane, one can simply compute righting moments (as explained), and fit them to the most similar IMS rating certificate. Particularly if one is aware that the midship section of the comparison boat is similar to one’s own, the other’s stability curve can be considered comparable.
More accuracy can be had by taking the inclining experiment figures and a lines plan to a naval architect who has a “fit” lines program amongst his or her software disks. The designer can then apply the commonly known IMS “fudge factor” and thus achieve a very accurate “stability index.” A fair warning: busy design offices would only do this task in a slack period. It’s much more fun – and more lucrative – to design boats.
There are specialized naval architectural firms who don’t design boats but are set up to calculate such things as static stability and even the complex “capsize length.” They won’t go down to the marina with a tape rule, though. The job would be made much simpler if one could gain access to the weight study for one’s boat that was done by the original design firm (along with the blueprints of not only the hull but everything above the sheer). Designers should have the weight of every item on the boat – they needed that data for longitudinal moments stability measurements that insured proper fore-and-aft trim. Lacking that, if one really wishes to achieve the ultimate in stability assessment – a capsize length – one will have to somehow determine the weight and distance off center of every constituent part of the boat. One now begins to realize the primary limitation of the capsize length formula. (A second limitation is that, unlike IMS figures, which are produced by a disinterested body, any capsize length assessment or stability figures one gets from a vendor are going to have to be swallowed with some amount of salt.)
A useful option might be the easiest one. Have one’s boat measured for an IMS rating. It may cost between $700 and $1,500 depending upon the size of the boat, travel and accommodation expenses for the measurer, etc. But when it comes time to sell a boat, an owner can usually recover some of the measurement cost, particularly if the buyer wants to race.
The IMS stability index angle is helpful, but it fails as a meaningful index to capsize susceptibility in many ways. First, it ignores entirely the dominant inertial factor; second, it emphasizes capsize angle at the expense of total righting force; and third, it is extremely inapplicable to the critical factor of inverted stability which is enormously influenced by an individual boat’s superstructure and spars. A comparison
As an example, we’ll take a worst-case Bermuda 40. Because it is an older Mk-1 model with a lighter keel and has a heavy sail-stowing mast, its CG is high, yielding an unnerving stability index of 105 degrees. Clever naval architects that we are, we can even find an IMS race-rocket whose stability curve is a close fit to the B-40’s, all the way from zero heel to capsize. However, although both boats are shaped so that the maximum length of the righting arm goes out to, say, 1 1/2 feet from centerline, the Bermuda 40 weighs twice what the hot racer weighs. That means that the B-40 has twice the righting moment.
Now, both boats are subjected to a breaking wave. The racer’s righting resistance to the punch on its windward topsides isn’t enough, and over she goes. The B-40 would be twice as resilient in terms of its righting moment, perhaps enough to prevent her from heeling to the critical angle of 105°. However, that is only part of the scenario.
Because the Bermuda 40 is twice as heavy, she will have at least two times the total transverse inertial moments. In actual fact, she is a cruiser and, as such, the designer made little attempt to pull all weight in towards the center. No Bermuda 40 in history has ever lost a mast—which certainly indicates that her spar is stronger and much heavier than the engineering marvel adorning the racer; and we’ve learned that a spar is an important dynamic factor due to its height. In truth, the cruiser might even have triple the other’s transverse mass moment of inertia. Taken together, twice the righting moment and nearly three times the athwart ships mass inertia has always been sufficient to save the day for Bermuda 40s. And remember, both boats had the same stability index—meaning both would capsize at the same heel angle. One is simply far less likely to ever get there than the other!
A look at midship section is next. Citing the same two yachts as we used above, any modern racing boat, including the IMS racer, will have a midship section that masses volume amidships and pares away at the bilges. It will heel quickly at first; it’s intended to do just that when the measurer hangs some jugs out on the end of the spinnaker pole for the inclining test. We can discern the effect of the midships section on the righting arm curve. It has less of a bulge at first, although it may even reach a greater maximum at the top of the parabola. Unfortunately, the top of the parabola is too late. The drama of capsize doesn’t begin at dead-level. The crux of the situation takes place when the boat is already heeled relative to the sea and on the face of a wave that is steeply inclined. Both racer and cruiser may be a mere 20 to 30 degrees away from the point where CG passes beyond CB. Thus, in addition to inertia, initial stability will be a factor. The B-40, in addition to her other advantages, will be a bit more stable during those critical 20 to 30 degrees. The modern voyaging yacht designer will cite this final factor in support of the current trend towards immediate stiffness (form stability).
Finally, a look at freeboard, which is another input in the “capsize length” formula. Virtually all the Fastnet racers were light-displacement. In order to get interior space and headroom, as well as to gain one more advantage from that rating rule, their freeboards were high. This gives a higher center of impact for the breaking wave, thus a more powerful overturning force. Even without bothering with the intricacies of the formula, anyone evaluating capsize stability should have a predilection towards a lower point of wave impact.
Incidentally, I’ve already made a point that two boats with identical deck plan outer margins will re-right at markedly different rates depending upon their masts and coachroofs. Here too, most voyaging sailboats have a roomy cabin house and tidy cockpit well – another point in their favor in the unlikely event they overturn.
It must be clear at this point that there isn’t a single convenient formula to use in evaluating a boat against the possibility of capsize. For smaller boats, which face a greater statistical risk, a combination of a higher capsize angle and a lower ratio between negative and positive moment areas would work best. Beamy boats with higher centers of gravity won’t be saved by their range of positive stability, so they would be better evaluated by computing a capsize length but it’s simply too difficult.
The best analysis will, therefore, have to revert to experience and judgment. There are a few racing sailors, delivery skippers, boat surveyors, and designers, or, better yet, individuals who combine a few of those vocations, whose advice might be worth far more that the price asked.
