March 18, 2010
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Understanding Performance Ratios
Some Simple Calculations Can Help You Compare One Boat Against Another

If there's one thing all boaters have in common, it's thinking about boats we'd like to own. Whether you're a powerboater or a sailor, the shopping list you create probably contains a handful of boats, and perhaps even different lengths.

If you're in the market for a new boat, you might have wondered if there's any way of comparing two or more models without actually taking them out. You may have even wondered whether there's a way to fairly evaluate boats of different sizes.

The good news is, not only are there great measurement tools, but you can use them from the comfort of your desk. They take the form of ratios, and they're not hard to figure out. You may need a good calculator for some, and others might be more easily obtained from the manufacturer. But they do allow buyers to compare different boats with relative ease.

Here are some of the most commonly used calculations.

Sail area is a fine figure, but Sail Area/Displacement ratio is more helpful.Sail area is a fine figure, but Sail Area/Displacement ratio is more helpful.STABILITY RATIOS

The beam of sailboats, relative to their length, varies within certain limits. This can be expressed as the Beam/Length ratio (B/L). Catboats are traditionally half as wide as they are long, for a B/L of .50. Most other sailboats have a B/L of about .33, or one-third as wide as they are long.

Even with these rules of thumb, however, there are variations. These variations will give you some sense of a boat's "form stability," which is the degree of resistance to heeling provided by the shape of the hull. Basically, the wider a hull is in proportion to its length, the greater its form stability; as the boat heels, its center of buoyancy moves to leeward to compensate. With a wider beam, the center of buoyancy can move farther. Thus it would seem that the beamier the boat, the more stable.

The downside is that increasing the beam increases drag. So designers of most monohull sailboats stay close to a B/L of about .33. Catboats are at one extreme, and multihulls solve the problem by mounting two or three very narrow (B/L of .15 or lower) hulls wide apart, giving a much more effective B/L for the boat as a whole.

Unballasted boats, like catboats, multihulls and dinghies depend on form stability. With less form stability, you can increase stability by adding ballast (the ballast in dinghies is called "crew").

The Ballast to Displacement ratio (B/D), for example, indicates how much of the boat's weight is composed of ballast. You can derive this figure by dividing the weight of the ballast by the boat's total displacement.

For example, the J/30 has a B/D of 0.3, a Catalina 30 has a B/D of 0.41, the Pearson 28-1 measures in at 0.45. For similar boats, the higher this number, the stiffer the boat will be. By comparing the B/D of two or more vessels, you can get some sense of how well a particular boat will stand up to its canvas or whether it will tend to sail on its ear.

But don't ignore the other factors. The catboat Herreshoff America has a B/D of just 0.22, but with a B/L of 0.45, it gets most of its stability from its beam and does not heel excessively. And multihulls, which don't carry any ballast, are very stiff due to their extreme beam and the buoyancy of the leeward hull.

PERFORMANCE RATIOS

Ratios can also be helpful in predicting performance. The Displacement to Length ratio (D/L) allows you to compare the displacement of boats of different sizes. Why is this important? It tells you something about the wave-making resistance of two or more boats you're considering.

The PHRF number, typically used for racing, provides the performance potential of different boats.The PHRF number, typically used for racing, provides the performance potential of different boats.

To push water aside, a sailboat depends partially on the "horsepower" developed by the sails, but it also depends on the boat's relative weight. A lower number usually indicates a faster boat (more horsepower per unit weight). D/L ratio is computed by dividing the displacement in tons (1 ton equals 2,240 pounds) by .01 of the Load Water Line (also known as the length at the waterline) cubed:

D/L = Dt / (.01 LWL)3

For comparison: light racing multihulls will have a D/L ratio around 40 to 50, light ocean racing sailboats are 150 to 200, the average cruising auxiliary is about 250 to 300, and a heavy cruising auxiliary is in the 350 to 400 range.

Once you know the relative weight of a boat, you can examine the other factor mentioned above: the sails. The measurement is referred to as sail-area ratio. But sail area by itself can be meaningless if you are comparing dissimilar boats. So what do you do in this case? Use the Sail Area/Displacement (SA/D) ratio. This is a non-dimensional ratio that compares the amount of drive per unit of displacement. The ratio is:

SA / D cubic feet 2/3

That means the sail area in square feet is divided by the displacement in cubic feet of water to the two-thirds power. Seawater is 64 pounds to the cubic foot, while fresh water is lighter, at 62.4 pounds. You may need to dig out your scientific calculator, though sail-area ratios are sometimes already worked out by the manufacturers and readily available.

Anything less than 15 requires large, light-air sails. The average sail-area ratio is 16 to 17 for coastal cruisers, and anything higher than 20 indicates a pure racing boat. A higher number is better if you are concerned with light-air performance. For example, someone who sails on Long Island Sound, with its light winds, would look for a boat with a SA/D ratio of 17 or higher, while someone who sails on San Francisco Bay would be fine with a lower SA/D.

Another important ratio is the Speed/Length ratio, represented as VvL. This is the speed in knots divided by the square root of the Load Water Line in feet. A typical displacement monohull cannot sail much faster than a Speed/Length ratio of about 1.34. This is not a figure that is generally published, but you can apply the formula in reverse – multiply the LWL by 1.34 – to find what is usually referred to as "hull speed." This is the fastest you can normally expect a typical sailboat to go.

Trying to exceed that Speed/Length ratio on a traditional monohull requires a significant increase in applied power, but it also results in stern "squatting," where the boat tries to climb out of the hole made by the wave it creates in going through the water. Multihulls can overcome this, however, because of reduced drag due to considerably higher waterline B/L ratios. Some ultra-light monohulls can achieve a Speed/Length ratio of as much as 2.0; but most boats need to plane to achieve higher speeds than that, and that gets you into a different area of physics.

Even though it's not a ratio, there is another number that's useful in comparing boats: the PHRF number. PHRF stands for the Performance Handicap Racing Fleet, and it's a system for handicapping different boats – not of a one-design fleet – so that they can race together.

The handicaps are created locally, so they may vary slightly from region to region, but they are reasonably consistent. They represent the handicapper's judgment on the speed potential of each type of boat that races in that area. Each kind of boat (typically make and model) is given a number that represents the speed, in seconds per mile, it should attain in typical conditions.

So if Boat A has a PHRF rating of 125, you could expect it to sail a mile in 125 seconds (2:05); Boat B might have a PHRF of 180, meaning it would normally take 180 seconds (3:00) to sail a mile. Thus the lower the PHRF rating, the faster the boat. Even if you don't expect to race, PHRF gives you a good comparison of the performance potential of different boats.

Having a good sense of a boat's potential involves more than just checking out standard gear and accommodations. Ratios are key for you to compare two or more vessels for such things as stiffness and speed. And you can do it all without having to leave the dock.


Gene Bjerke, whose work has appeared in Cruising World, Chesapeake Bay, Good Old Boat and Multihulls magazines, regularly crews on square riggers near his home in Virginia. He has been boating for 45 years.

 
 
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