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The A/B Ratio Is Largely Meaningless
By Lou Codega
Naval Architect
Sooner or later potential trawler buyers will come across a term called the A/B ratio, as a measure of a yacht’s seaworthiness. Forget about it. The A/B ratio is, for all practical purposes, baloney.
Since its first publication in 1975, Robert Beebe’s Voyaging Under Power has been almost universally accepted as the authoritative source for information on long-distance cruising under power. This was undoubtedly a pioneering effort and, although dated, remains a wealth of practical considerations on many aspects of cruising boat mechanics. But it is not, and was never intended to be, a text on naval architecture as it applies to power craft. It is extremely weak in its treatment of many technical subjects in that it relies far too heavily on overly simplistic rules of thumb and comparisons made between a limited number of mostly similar boats.
I have tremendous respect for much of Beebe’s work, but I have a large ax to grind with his treatment of stability. There has probably never been an overused and yet so fundamentally useless a term as the A/B ratio. But it’s concept and calculation is easy for the layman to grasp, and its use has been perpetuated to some extent by those builders whose designs appear “good” by its measure. That’s too bad, as in this case a little knowledge is a terrible thing; I want to do my part to help it along a path to extinction.
Beebe proposed the A/B ratio as a measure of transverse stability, calculated simply as follows:
Projected profile area above the waterline
Projected profile area below the waterline
He then goes on to discuss ranges of this ratio that are found in then current trawler yachts, and those that he considers acceptable in boats that are, in his opinion, “qualified as ocean-crossers.” That’s it in a nutshell, and the discussion in the original text is only about twice as long as my summary. And there is no other mention of stability in the rest of the book, except to say how individual designs stack up to the A/B criteria.
This analysis is simplistic beyond credulity. The ratio is not now, and so far as I’m aware, has never been used by naval architects. It has a bit of utility when used to compare similarly proportioned and sized boats. But it neglects everything that is important to stability. The height of the boat’s center of gravity, its beam, weight, shape of the watertight boundaries, hull form, tankage and watertight integrity are all vital to an intelligent discussion of stability, but all are completely ignored. Take any boat that you want as an example. It has the same A/B ratio whether it is two feet wide or 25, whether hard chine or round bilge, if it has engine room air inlets on the side of the hull or amidships, or if it weights 100,000 pounds or 10,000.
The direct calculation of static stability has been done for 80 or 90 years, and, with the widespread use of computers, there is just no reason to simplify something so fundamentally important to the safety of the boat and its passengers into a rule of thumb ratio, and a half baked one at that.
A designer routinely models a boat’s form, calculates the weight and center of gravity, and in a matter of seconds mathematically rolls it while calculating it’s tendency to either roll upright or continue rolling to a greater angle. (In the “old days” the same calculation was done by hand, using an instrument of torture known as an integrating planimeter while seconds turned into days, but that’s another story for another time.) The complete watertight boundary, location of the center of gravity, weight, in short, all of the factors that affect intact stability are modeled exactly. The result is the so-called righting moment curve that you’ve all seen.
The example below, by the way, is not for the Navigator/Great Harbour boats and shows righting and heeling arms rather than moments. The moment is simply the arm multiplied by the boat’s displacement. The roll angle, usually zero through 180, is plotted on the horizontal axis. The vertical axis depicts the righting moment, which is the tendency of the boat to roll back upright or roll further. These typically depict a sine-like curve that starts a zero moment and zero degrees, increases to a maximum at say 50 degrees and then returns to zero at say 120 degrees. Up to 120 degrees, the so-called range of positive stability, the craft tends to return upright. Beyond that, the craft will tend to increase in roll, usually to 180 degrees or completely inverted.
I guess that I wouldn’t be so upset if the A/B ratio was backed up by some science. I could live with it if, for example, Beebe had done some true stability calculations and came to the conclusion that the A/B ratio was a good indicator of the stability characteristics proven by the more involved calculations. But there is no evidence that he, or anyone else, ever did such a thing. I haven’t either, and frankly I’d be shocked if it were the case.
By the way, an outstanding and very accessible discussion on stability, as well as most every other aspect of boat design can be found in Preliminary Design of Ships and Boats by Cyrus Hamlin. I can heartily recommend this book to anyone wanting to further his knowledge of boat design, intended as it is for the engaged amateur or beginning professional. It is remarkably well written and goes beyond simplistic ratios and rules of thumb to give a true understanding of underlying design principles.
One more point while we’re at it. Stability calculations and criteria are intended to be comparative, not predictive. This seems perhaps to be a minor point, but it is crucial to your understanding. The righting moment curve that results from the calculations I just described result from an artificial condition that the boat will never encounter. Remember, the designer mathematically rolls the boat in still water. This same calculation, by the way, is made for most any ship around, including warships and cruise liners. This is clearly not an accurate representation of what happens when the boat is at sea.
What most folks don’t realize is that this curve is only the first step in the process. Overlaid on the righting moment curve is a curve of wind heeling moment, (as shown in the example above) or the effects of off center loading, or high-speed turns, or the firing of guns broadside, as is appropriate to the service of the ship. The two graphs are then compared against each other as well as accepted, and in many cases mandated, standards on a pass or fail basis. These standards are based on past experience for similar types of craft. What is implied by this approach is that other craft having similar stability characteristics have proven sufficiently safe in service and that by extension, so should the new craft. There is no expectation, much less a guarantee, that a boat that has a positive righting arm up a stated angle will survive a roll to that angle in a fully arisen sea. It may, it may not. But stability calculations and criteria do not claim to offer an answer.
Which returns us to the A/B ratio. It’s a rule of thumb, and like all rules of thumb it is easy to grasp and understand. But it is a gross simplification of a vitally important issue, and to my mind one that does far more harm than good. Its time, if it ever existed, has long since past. Any builder or designer worthy of your consideration will be more than happy to discuss their boat’s stability characteristics and how they relate to your anticipated cruises. But please, leave A/B ratios out of the discussion.
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