Yacht Stability: Considerations for Safety and Sea Worthiness
By: Bill Bolin, CPYB, YBAA Board Member, S&J Yachts
A yacht’s stability is defined, by boat designers, as both the ability of a yacht to resist capsize and once capsized, the ability of that yacht to recover to an upright position. The first part of this equation, resistance to capsize, arises primarily from two different sources: the yacht's form stability and the yacht's displacement. Picture a Jon boat (flat bottomed, beamy) and a canoe (round bottom, narrow). The Jon boat has more form stability than the canoe and is less likely to capsize. One can also understand that a heavier displacement yacht will be less likely to capsize than a lighter one. Imagine a large ocean-going container ship and a small fishing runabout. It's going to be much harder (take much more energy) for the heavier ship to capsize. There are, of course, other factors to take into account, as I will point out later.
So how does one gauge the actual differences in stability between various yachts? Most of you have probably seen a stability curve in sailing magazines or product brochures (stability concerns are rarely brought up with powerboats). These graphs illustrate the overall stability characteristics of a yacht, its sail-carrying power (stiffness), and how it is able to resist and recover from a capsize. Let's see how these curves are generated and what they mean.
At rest, a yacht has two equal and opposing forces acting on it: gravity, holding the yacht down in the water, and buoyancy, keeping the yacht afloat. A naval architect locates the geometric center of these forces (with the center of gravity labeled as "G" and the center of buoyancy as "Z') and will picture them as shown in Figure 1.
When a yacht heels over, the center of gravity remains fixed (moveable ballast boats aside for the moment), but the center of buoyancy moves as the shape of the submerged hull changes (Figure 2). The horizontal distance between the moving center of buoyancy and the fixed center of gravity, referred to as distance “G-Z”, is called the “righting arm” and can be plotted on a graph for various angles of heel (Figure 3). As the yacht heels at increasing angles, at some point the two centers are again directly above one another and a heel angle beyond this point will result in the yacht going to a fully inverted position where it will remain until there some outside force allows it to recover (e.g. waves or wind). This point, where the G-Z distance is again at zero, is the yacht’s “limit of positive stability” (LPS).
A stability curve can also supply you with the “righting moment” of a yacht, or the force (torque) trying to push the yacht back into an upright and static position. In Figure 4, I have taken the displacement of a typical 46 foot modern full-keeled yacht (Island Packet 460) and multiplied this number by the righting arm (in feet) to get “foot pounds of righting moment (torque)” at various angles of heel. This curve is laid against a similar-sized fin keel boat, the Tartan 4600. The resulting curves shows the amount of torque each yacht exerts throughout the stability range. Note that at just 15 degrees of heel (a typical sailing angle) the Island Packet is exerting over 20,000 “foot pounds” of torque that balances the heeling force of the sails. Let the sheets go and the yacht comes back upright quickly! The heavier the displacement, and/or the longer the “righting arm”, the more righting moment is increased and thus more sail carrying capacity, and/or, less heel angle for a given sail configuration.
One more very important observation to glean from the stability curve: the shaded areas “under” the curve above and below the horizontal axis relate to the amount of energy needed to capsize a yacht, and how much energy is required to right it once again. You want a large area above the line (lots of energy to capsize) and/or a small area below the line (easy to recover from a capsize) for best ocean-going seaworthiness. Note figure 5 showing a 35’ catamaran vs. a 35’ monohull. A catamaran takes a huge amount of energy to capsize it but takes an equally large number to recover from a capsize.
I mentioned earlier that there are more factors in stability calculations and as the EU set up to merge its collective standards back in the mid 1990’s, several committees were set up to study yacht standards and, more specifically, yacht stability. After three years of efforts, the sub-committee on stability recommended to the ISO a four-tier rating system for yachts deemed worthy of everything from “unlimited offshore work” to “safe for protected inland waters”. Their proposal (which was accepted) defines a yacht’s STIX value (for Stability Index), derived from a complicated calculation taking into account the aforementioned dimensions and displacement (length, beam and weight), but also data from the stability curve (knockdown recovery, inversion recovery and down-flooding angles), plus wind moment and dynamic stability figures. The curves we looked at earlier are all generated in “flat water” (a swimming pool calculation). Imagine a fast, lightweight racing sailboat nearing maximum hull speed and you can picture the bow and stern waves moving further apart, leaving the beam unsupported by water. Anyone who has raced a boat like this knows that stability is greatly decreased in these conditions! So important are STIX values that in the EU, a manufacturer must publish them as part of the yacht’s data, right alongside length, beam, etc.
A few quick and easy takeaways:
Fin keel boats have a righting arm of around two feet (maximum righting moment equals displacement times two) and an LPS (limit of positive stability) of about 120-125.
Full keel cruisers often develop upwards of three feet of righting arm (maximum righting moment equals displacement times three) and an LPS of closer to 140-145 degrees.
Catamarans develop a righting arm measuring roughly ½ the beam (a 20-foot-wide boat develops about a 10-foot righting arm) and a righting moment of: beam times 0.5 times displacement, with an LPS of roughly 70 degrees.
A STIX value of 32 or above is required to meet the highest Category “A” standards for “Offshore” use.
Finally, I can’t leave a discussion of a yacht’s stability without bringing up the “Capsize Screen Value”, proposed in the wake of the 1979 Fastnet race disaster (multiple capsized boats and deaths) by SNAME and USYRU. It was a very simple formula using just beam and displacement to “screen” racing boats into two categories: acceptable for offshore racing, and “needs further review”. Because it was simple to apply, many journalists and authors incorporated this calculation into literature as they endeavored to “grade” boats for suitability for offshore safety. Suffice it to say that you can move a yacht’s keel onto the top of a mast (instead of under the hull) and the Capsize Screen Value would not change, although the stability characteristics certainly would! Both SNAME and USYRU dropped the proposal after harsh criticism, yet we still hear (and read) of reference to this worthless number today. Feel free to correct anyone who attempts to use this arcane and useless number.
I hope this helps shed some light on these important considerations to seaworthiness and safety.