Boats & Gear

CRUNCHING NUMBERS: Sail-Area/Displacement Ratio

Hallberg Rassy under sail

We've discussed how to evaluate a boat’s speed potential, but this really only tells you half the story. A fast hull won’t actually go fast unless there is enough power available to drive it at or near its potential. Aboard sailboats, of course, the source of this power is the boat’s sail plan. The parameter designers normally use to evaluate a boat’s sail-power relative to its weight is called the sail-area/displacement ratio (SA/D ratio).  Like the D/L ratio, this is a “non-dimensional” value that facilitates comparisons between vessels of different types and sizes.

To calculate a boat’s SA/D ratio you must first quantify its sail area in square feet. In that boats normally have an inventory of different-sized sails so their sail area can be varied, sometimes very significantly, to accommodate different wind conditions, it’s important to use a uniform standard when comparing different boats to one another. The accepted convention is to add the mainsail area to 100 percent of the foretriangle area, where the foretriangle is defined as all the lateral area above the deck between the mast and the forestay. If the boat is a ketch or a yawl, the most common practice is to also add in half the area of the mizzen sail. For schooners, the practice is to add all the area of the main and foresail to 100 percent of the foretriangle.

When publishing specifications, boatbuilders often have a tendency to overstate sail area, just as they understate displacement, so that their boats look faster on paper. Many publish sail-area numbers that add in all the area of a large overlapping 130- or even 150-percent genoa. Fortunately, it is easy to correct for these overstatements.

Calculating Sail Area

To figure out the size of a boat’s foretriangle area for yourself, you need only collect the I and J dimensions of its sail plan. These are often published in more detailed spec sheets; if not, they are relatively easy to come by, as sailmakers always need them to cut sails for a boat. The I dimension is defined as the vertical height in feet of the foretriangle (from the deck, not the cabin top), and J is the horizontal distance in feet from the mast to the root of the forestay.

Sail area dimensions

To find the area of the triangle in square feet, just multiply the two together and divide by 2 (100% foretriangle = (I x J) ÷ 2). As for the mainsail area, technically you are supposed to find it in the same way, by using the P and E dimensions (P = mainsail luff length; E = mainsail foot length) to solve for the area of the main’s triangle (main triangle = (P x E) ÷ 2).  This, however, ignores extra area outside the triangle if the main has full battens and a large roach. It also ignores the negative area inside the triangle if the main is on a roller-furler and has a hollow leech and no battens. Since boats don’t carry different size mainsails the way they do headsails, I reckon it’s perfectly fair (and certainly more accurate) to use the actual mainsail area when calculating SA/D ratios for comparison purposes.

Calculating the SA/D Ratio

Having found a boat’s sail area, you next need to calculate its displacement in cubic feet (DCF) in order to ultimately find its SA/D ratio. This is very easy, as you’ll recall that a boat’s weight and the volume of water it displaces are directly related. All you need do is decide what sort of water you’re talking about. Assuming it's salt water (which weighs 64 pounds per cubic foot, while fresh water weighs 62.4 pounds), you need only divide the boat’s displacement in pounds by 64 to find its displacement in cubic feet (DCF = D ÷ 64).

To then find the boat’s SA/D ratio, just divide its sail-area in square feet (SA) by its displacement in cubic feet taken to the two-thirds power (SA/D ratio = SA ÷ DCF↑.667). Assuming as an example a hypothetical 12,000-pound boat with a sail area of 650 square feet, you would calculate its SA/D ratio by first dividing 12,000 by 64 to find its displacement in cubic feet (12,000 ÷ 64 = 187.5). Then take that number to the two-thirds power (187.5↑.667 = 32.8) and divide the boat’s sail area by the result (650 ÷ 32.8 = 19.8), and you’ll get an SA/D ratio of just under 20.

Interpreting the SA/D Ratio

The basic guidelines for interpreting an SA/D ratio are as follows: below 16 indicates a slow underpowered boat; 16 to 19 indicates reasonably good performance; 20 to 22 indicates high performance; and anything over 22 indicates super-high performance.

The hypothetical boat described above, with an SA/D ratio of 20, therefore is on the cusp between good performance and high performance and should do a better than average job of living up to its speed potential. Note, however, how adjustments in the displacement value can skew the final result. If you load your 12,000-pound boat for light coastal cruising and make it a 14,500-pound boat (per the formula in Nigel Calder’s Cruising Handbook, which we discussed earlier), its SA/D ratio becomes 17.4. Loaded for heavy coastal or moderate bluewater use at 15,750 pounds, its SA/D ratio is 16.5, which puts it decidedly on the low side of the good-performance range.

What sort of SA/D ratio you should look for in a good cruising boat? This depends largely on how much you really like to sail your boat. My own preference, all other things being equal, is to sail my boat as much as possible and to use my engine only as a last resort. So I like to maximize sail area. Subject only to the important proviso that a boat should not carry a larger rig than it can stand up to, the only downside to having the largest possible sail plan, even aboard a heavyweight cruising boat, is that you’ll spend more time taking in reefs and letting them out again and/or changing sails as conditions fluctuate.

Indeed, I believe the heavier your boat is, the more sail area you will want to drive it. A heavy boat driven hard can often sail nearly as fast, and sometimes even faster, than a lighter boat that is undercanvased or driven conservatively. And when the wind is light, a heavy boat will always want as much canvas as can possibly be spread. Thus, the ideal SA/D ratio for cruisers like me is always as high as possible, which normally translates to ratios of 17 or better.

Many cruisers, however, are not so obsessed about sailing their boats all the time. They are happy to be sailing if the wind is moderate to strong, but if it starts to get a bit light, they prefer to motor to keep their boat moving at a more respectable speed. Some will also almost always motor to windward, no matter how strong or light the wind is, in order to save time. There are even a few I’ve met who rarely put their sails up and normally motor unless conditions are absolutely optimal. For cruisers such as these a high SA/D ratio is much less important.

You must also always consider a boat’s SA/D ratio in relation to its corresponding D/L ratio. If you want the benefits of a heavier hull--more comfort and stowage capacity--but also want decent performance, you need a higher SA/D ratio to compensate for the weight and must be prepared to do more sailhandling. If you want decent performance, but don’t want to do an awful lot of sailhandling, look for a light boat with a relatively low SA/D ratio and be prepared to carry less stuff with you. If you want the best performance possible, look for a light boat with a very high SA/D ratio. If you want a heavy boat and don’t want to handle sails too much (a common prejudice among shorthanded bluewater sailors), you need a boat with a lower SA/D ratio, but must be prepared to take your time getting from place to place.

Light-Air Performance

One thing to keep in mind if you do prefer to keep sailing when the wind is weak is that the SA/D ratio is technically not the best indicator of light-air performance. Because displacement relates to the amount of resistance a moving boat encounters due to its own wave-making ability (i.e., heavier boats make bigger waves because they displace more water as they move), and because this is the sort of resistance that most affects a boat’s performance in moderate to strong conditions, the SA/D ratio is most accurate in these situations.

The same is true of other displacement-based parameters. The D/L ratio, for example, describes how easily (or not) a boat can be driven to its top speed potential, but is not necessarily indicative of a boat’s speed potential in low-power situations. Likewise, Dave Gerr’s speed-prediction formula can project a top speed for any given boat, but says nothing about how easily a boat will move when the wind is light.

The sort of resistance that most affects performance in low-power or light-air conditions is the amount of friction between a hull and the water. This in turn is most directly related to the hull’s wetted surface area. The larger the area, the more friction there is, and the more effort it takes to overcome that friction and get the boat moving.

There is a performance ratio--the sail-area/wetted-surface ratio (SA/WS ratio)--that quantifies this relationship and thus more accurately predicts performance in light air. Ironically, it is, in terms of the mathematics involved, by far the easiest of all performance ratios to calculate: just divide a boat’s sail area in square feet by its wetted surface area in square feet (SA/WS = SA ÷ WS), and you’ve got it. Unfortunately, it is of no use to lay people, because a boat’s wetted surface area is never included in its published specifications, and you pretty much have to be a naval architect to figure it out.

De-rigged ketch under sail

This is not quite as tragic as it seems. Though you should theoretically always use wetted surface area instead of displacement as the base factor in evaluating light-air performance, in the real world lighter boats almost always have less wetted surface area than heavier boats. After all, having less hull below the waterline is usually a big part of what makes one boat lighter than another in the first place. And while you may not be able to precisely calculate a boat’s wetted surface area, you can get a general sense of it by simply eyeballing a boat or a drawing of it.

As a general rule, then, you can expect light boats to perform better in light air than heavy boats, and you should be able spot any exceptions, those few unusual boats that are light in spite of having a lot of hull underwater, by eye. And regardless of whether you use displacement or wetted surface as your basis of comparison, remember the other half of the formula in both cases is sail area. And in both cases more sail always means better performance.

 

 

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