Calculating the Sail Area-Displacement Ratio
For those of us fortunate (or perhaps unfortunate) enough to have had to memorize the concept of a ratio in the 5th grade, calculating the sail area-displacement ratio is a relatively straightforward endeavor. You need to take a measurement of the sail area, which is generally given in square feet, and a measurement of displacement and divide them. There are, however, light complications with both measurements. Here is the formula, and you can read on in this section if you want to understand the various nuances in the calculation and derivation of it, or skip to the next section if you just want to understand what it means for your boat.
When calculating the sail area, there are different points of view on how to accurately measure effective sail area. As the interactions between mainsail, overlapping or non-overlapping headsails, and off-the-breeze sails are not always the same depending on the point of sail. Because the different setups utilize these areas differently, relative sail plan measurements do not always represent how much sail area is directly being used to power the boat. Comparing the sail area-displacement ratio on a plan with a 150% overlapping genoa or a non-overlapping jib by simple square footage will favor the former, even if they have the same effective power. This doesn’t mean that you can’t use the SA/D to compare boats, but you just want to make sure that both boats are using the same method of measurement and that you account for such sail plan differences. Regardless, the sail area component, which will be the numerator in our ratio, is generally just equal to SailArea(ft2), indicating that it is measured in square feet.
The fundamental value of the denominator is a little bit more mathematically confusing, as it requires some conversions in order to return the final ratio. The displacement of a boat is simply equal to its weight, which can be given in pounds. We want our ratio, however, to be unitless, so we have to do some transformations. First, we realize that a displacement in pounds causes the boat to displace a certain volume of water, which we can measure in cubic feet. A single cubic foot of water weighs approximately 64 pounds, i.e. it has a density of 64 lbs/ft3. Therefore, if we want to determine the cubic footage that a boat of a certain weight displaces, we would have to divide its weight by that density. This gives us a converted value for displacement in cubic feet. Finally, we convert cubic feet to square feet by raising the measurement to the power of 2/3, which leaves us with a ratio of square feet over square feet. With this, we can finally perform our SA/D calculation.
Performance Implications and Categorization
The point of the SA/D is to give you an intuitive sense of how a boat will perform under sail. Sail area is one of the best sailing analogues for horsepower. Still, boats are much more dependent on the costs of these larger sail plans--longer, heavier, wider--and so sail area does not tell you as much about a boat as horepower does about a car. This is why we need to incorporate displacement as a shorthand for how big the boat is, and then use the ratio between the two to discuss performance.
Boat Categories
In general, sail area-displacement ratios float around the high teens. Heavy, casual cruising boats tend to be in the range of 15-16, while high performance racing boats can push over 20. A SA/D of 20 is generally accepted as a cutoff for modern performance cruising and racing hulls.
There are helpful niche-types within this larger range, however, so we will discuss the breakdown of what each ratio range should tell you about a boat in which you might be interested.
<15: Motorsailors and Auxiliary Sailboats
Boats in this range are never meant to operate purely on sail power, and cannot really be expected to make much headway under sail alone. With a good breeze, you can certainly save a little on gas, but you will not be cutting through the harbor with any particular excitement.
15-16: Average offshore cruiser
These boats, while a little bulky, need that bulk to handle the rigors and strains of offshore sailing. This is your first level of acceptable performance for making way under sail power alone.
16-17: Coastal cruiser
Sleeker and with more aggressive sail plans than their offshore counterparts, cruising hills SA/D range starts pushing you into the sporty range. You can expect decent maneuverability and fresh speeds, but you won’t be breaking and sea-speed records, and you may well want to stay within sight of land.
17-19: Racing yachts
Once you get into the high teens, SA/D figures tend to point towards racing hulls with minimal capabilities for cruising and distance sails. These boats are engineered to go fast, shave off every bit of weight possible, and do everything they can to cut through the water. This means getting slimmer and lighter, both to reduce the displacement, in terms of weight, and the sheer amount of ‘wetted surface’ in the water, which introduces drag. It will be hard to say much about a boat’s relative performance within this range, however, as racing boats tend to have more factors effecting their performance at the slimmest of margins, but this range is, nonetheless, a good indicator that you should not expect to be taking such a boat for a long cruise.
20+: Performance racers, Dinghies, One-Design Sailboats
Once you get into the 20s, you may be presented with one of two options. Either you have made it into high-performance racing mono- and multi-hulls tuned for racing, or you have found your average sail around dinghy. The Laser, the Olympic Class singlehanded sailboat and also one of the most common sailboats in the world, has a SA/D of 47.3 by a quick calculation, but this certainly does not mean that it is the highest performance boat in the world: it just means that it is very light! A J-70, a widely competitive racing monohull has a more reasonable SA/D of 24.7, and is a good example of demonstrating a fast, light, and snappy boat that at least resembles the others on this list.
Shortcomings and Alternatives
As with any attempt to compactify an incredibly complex problem into one or two numbers, the SA/D has its share of shortcomings. In particular, it can tell you very little about how a boat will perform on the racing front and is unlikely to help you truly distinguish between the performance of boats within a small range. A boat with an SA/D of 17.2 may just be a fast cruiser, and the foiling boats used in the America’s Cup may well be so far off the charts that it is not even relevant to measure the SA/D for them (in fact, the AC72’s, by a quick calculation, have an SA/D of 81, which is not even on the charts).
Other measurements of performance have come to prominence in an effort to replace the SA/D. Yacht designers use velocity prediction programs to model the hydrodynamics of hull shapes, weights and sizes against sail plans across various windspeeds. Performance Handicap Racing Fleet (PHRF) ratings are tabulated based on years of empirical data from racing times to give an appropriate handicap for timed races, which does a good job of leveling the playing field across boats and giving you a sense of how fast or slow a boat is in a vacuum. Most boat outside the racing field, however, are not tabulated in such systems. Polars demonstrate the expected speeds for a boat at different wind angles and velocities, though they are dense and hard to read graphics.
So there is no single metric that can be used to determine a boat’s performance. Critics of the sail area-displacement ratio will claim that it is a number that does not tell you anything, especially as it can be manipulated by boatbuilders to sell their newest line even if it is not representative of a boat’s true performance. Still, even if it is not useful at the edges of the competitive racing field or can be subject to questionable sail area accounting, the rough categorization bands are useful for a quick summary of a boat’s fundamental characteristics. You would never buy a car just by reading its horsepower, but it is still good to know it in a pinch.
Happy sailing!
