# CRUNCHING NUMBERS: Brewer Comfort Ratio

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It’s time to think a bit more about how we can use numbers and math to evaluate different sailboats. I’ve already explained the two most popular performance parameters–the displacement/length and sail-area/displacement ratios. These numbers, which estimate a boat’s speed potential and available sailpower, are the ones most commonly used to quantify how a sailboat behaves. They are often referred to in magazine articles and are often included by builders in a boat’s published specifications. But speed, as any cruiser will tell you, isn’t the only attractive quality in a sailboat. A boat’s motion, how it moves through the water while underway, is also very important. It is particularly important when seas get rough and stomachs start feeling queasy.

Most racing sailors aren’t very concerned about this. Indeed, if you read some accounts of modern long-distance races and record attempts, it seems they pride themselves on sailing aboard the most uncomfortable boats imaginable. The motion aboard some extreme sailboats can be so violent that crew members must wear helmets while sleeping in case their heads are smashed against bulkheads or ceilings while they lie in their berths.

Smart cruisers, on the other hand, are very interested in a boat’s motion and how it affects comfort aboard. Cruisers, like all sailors, are happy when sailing fast. But they are happiest when they are physically comfortable. Even short of getting seasick, this is the one factor that normally has the biggest influence on a cruiser’s sense of psychological well-being.

It isn’t really possible to quantify all aspects of a boat’s motion in a single numerical parameter. But there is a relatively simple so-called “comfort ratio,” developed by designer Ted Brewer, that does provide a reasonable indication of what a boat’s motion will be like in certain conditions. Though originally developed by Brewer somewhat in jest, it is now accepted by many as the best way to evaluate motion comfort using commonly published boat specifications. Unfortunately, the comfort ratio is rarely mentioned in magazine boat tests and is never published by boatbuilders. It’s easy, however, to figure it out on your own, and I urge you to use it when analyzing cruising boats, particularly bluewater cruising boats. It provides a much needed third dimension to complement the simplistic two-dimensional picture painted by the D/L and SA/D ratios.

To calculate Brewer’s comfort ratio, you need to run the following formula: Comfort ratio = D ÷ (.65 x (.7 LWL + .3 LOA) x Beam↑1.33), where displacement is expressed in pounds, and length is expressed in feet.

As an example, let’s again consider a hypothetical 12,000-pound boat with a load waterline length of 28 feet. Let’s assume it also has a length overall of 35 feet, and a beam of 11 feet. Therefore, to find its comfort factor, we first need to multiply its LWL by .7 (.7 x 28 = 19.6) and its LOA by .3 (.3 x 35 = 10.5) and should then add these two results together, which gives us 30.1 (19.6 + 10.5 = 30.1). Next take the boat’s beam to the 1.33 power, which gives us 24.27 (11↑1.33 = 24.27), and multiply this result and the previous result by .65, which gives us 474.84 (.65 x 30.1 x 24.27 = 474.84). Finally, divide this result into the boat’s displacement, which yields a comfort ratio of 25.27 (12,000 ÷ 474.84 = 25.27).

What the formula purports to assess is how quickly and abruptly a boat’s hull reacts to waves in a significant seaway, these being the elements of a boat’s motion most likely to cause seasickness. The formula favors heavier boats over lighter boats, as more weight always helps to dampen a boat’s motion, and also favors boats with smaller waterplanes. This refers to the horizontal plane on a boat’s waterline and is generally a function of length and beam. Boats that weigh less and have more waterplane tend to have a quicker motion, because more waterplane means there’s more area for waves to push up against and less weight means there’s less resistance to the pushing.

Longer boats obviously have larger waterplanes than shorter boats, but the exponential increase in their displacement always negates this. As a result, the comfort-ratio formula also favors length, though it penalizes beam. Generally, it favors heavy boats with overhangs and narrow beam, but longer boats may have considerably lower D/L ratios than shorter ones and still fare much better by comparison.

You can use the following guidelines to interpret comfort ratio results: numbers below 20 indicate a lightweight racing boat; 20 to 30 indicates a coastal cruiser; 30 to 40 indicates a moderate bluewater cruising boat; 50 to 60 indicates a heavy bluewater boat; and over 60 indicates an extremely heavy bluewater boat. If evaluating a larger boat, say 45 feet or longer, expect your results to be skewed a bit higher on this scale; if the boat is quite small, say 25 feet or less, they will be skewed slightly downwards.

Once again, increasing displacement to account for loads carried seriously affects results. Our hypothetical 12,000-pound boat, with its comfort ratio of 25.27, becomes decidedly more comfortable as we load it to cruise. Add on another 2,500 pounds for light coastal cruising, and the ratio rises to 30.5; make that an extra 3,750 pounds for bluewater cruising, and it becomes 33.16.

Limitations/Multihulls

What the comfort ratio does not assess is how comfortable a boat seems in relatively flat water. In these conditions it is normally a boat’s heeling that makes folks feel uncomfortable.  The best way to make a boat stiffer and decrease heeling is to increase its beam, which, ironically, is one the things that will make it less comfortable in a strong seaway.  Conversely, a narrow boat that heels easily may seem more comfortable in a seaway, but less comfortable, compared to a beamier boat, when sailing well in flat water.

Another factor the comfort ratio does not account for is ballast location. This is not often remarked upon, but I’ve found the closer you are to a boat’s ballast the more comfortable you tend to be. Presumably this is because ballast normally represents the greatest concentration of weight on a boat, so has a dampening effect on motion. Also, the heaviest part of the boat tends to be the fulcrum around which it revolves in rough conditions. The less distance there is between you and the fulcrum, the less motion you will experience.

On most modern boats with ballast keels this effect won’t really come into play. It will be noticeable, however, on some older wooden boats that carry some ballast in their bilges; even more so on certain modern centerboard boats that have no keels at all and carry all their ballast in their bilges. Boats like this, in my experience, are much more comfortable than their comfort ratios suggest.

The comfort ratio also does not pertain to multihulls. Because these boats carry no ballast at all and rely entirely on beam for their stability, their motion is entirely different from monohulls. Many cruisers are attracted to catamarans for precisely this reason. Because cruising catamarans normally do not heel, they are perceived by many as being more comfortable than monohulls.

This is true as far as it goes, but don’t assume that a catamaran’s motion in large seas is ever negligible. A monohull may experience more total motion in a strong seaway than a catamaran, primarily because it rolls more from side to side. Like the cat it will also be heaving up and down. But the motion of the monohull will usually have a distinct rhythm to it. If the seas are not absolutely confused and have some pattern to them, that pattern will be reflected in the motion of the boat. Those onboard can learn the pattern and anticipate it. The motion, because it is not random, is easier to adapt to.

This is not the case with catamarans. Catamarans not only have two hulls in the water, each reacting to separate sets of waves, they also have a bridgedeck connecting the hulls, which is struck by the irregular waves that heap up between the hulls at irregular intervals.  A catamaran thus receives input from three different sets of waves. Its aggregate motion, as a result, often has no rhythm to it.

Because it has no ballast and is light for its size, a cat’s motion is also fast and abrupt. The total effect in a seaway is quick, quirky, random, and harder to anticipate and adapt to. Some sailors aren’t bothered by this and are happy to live with it in exchange for not heeling. Others, however, prefer to deal with the slower, more predictable, albeit somewhat more exaggerated motion of a monohull, and will take their heeling as they find it.

### JAMES WHARRAM: His New Autobiography

14 Responses
1. Charlie

Response to Ken below: Thanks! What a cool resource. I see they have calculators for the various other formulae I’ve discussed in these Crunching Numbers posts. I’ll have to add several links! charlie

1. Doug Sage

I little late to when you posted but even more important now with lots of fat bottom boats being pushed. I laugh at the boats being advertised ocean boats. Can you speak to the reverse now ( negative bouyancy rate on dropping bow), wide sterns pushing down the bows on any heal angle encouraging slipping and plowing. I’d love to see a comparison of rocking motion, acceleration of boats about their rotation point. Rotation point being center of bouyancy and CG. Rocking motion then plotting angle vs volume. Add in wave shape and that wide stern prevents the bow from rising in a gradual motion. And small volume bows have very little restoring volume until the boat is immersed half way to the mast…..

2. Ken Heaton

Response to Ken below: Thanks!

You’re welcome. And thank you for the interesting and informative articles. And yes, I have your book… I bought it last year while we were trying to make up our minds about what boat we were going to purchase. It helped the process.

3. vic

Hi,
For people living on the SI-side of the universe, formula can be used with SI units too, just replace the 0.65 by 4.697 … enter length and beam in m, displacement in kg.
best rgds, vic

4. Tom

Great post, I am copying it, placing in my research.

5. Fredrick Roswold

On factor overlooked is the effect of heavy displacement, particularly in the ends of the vessel, when encountering waves from ahead of the beam. A light boat will more quickly and abruptly react to the waves, and will ride over them and this is thought to be a less comfortable motion than that of a heavier boat. On the other hand, and not acknowledged by this formula, is what happens to that heavier yacht which does NOT ride over the waves but plows directly into them. Given a bigger wave the heavier yacht, (with weight in the ends it is worse) plunges deep into the wave, throwing tons of water to each side, and it’s forward progress is dramatically slowed.
Next buoyancy comes into play and this boat, with it’s bow deep into the wave face, and nearly stopped, begins to rise, quickly. As the crest passes under the hull the bow will arch skyward, then plunge dramatically into the next wave. Two waves in a row like the and the boat can be totally stopped.

I’ve sailed on both types of boats and without a doubt, I prefer the jarring, jerky ride of a boat going over the waves, (BUT GOING), over the hobby horsing heavyweight which plunges deeply into each wave and cannot maintain headway in a seaway.

Ted Brewer’s comfort index is great for the armchair sailor but does not hold up when you got to sea and you encounter big waves coming from the direction you want to go.

6. Gary Langrock

Thank you for breaking this down in a way that even a beginning cruiser-to-be can understand, yet retaining the level of sophistication necessary to explain some important maritime concepts.

7. WKW

Clear and well written. I can see the variables of the comment above. A heavier boat digging in creating a stop and go motion compared to a boat that has a lower comfort ratio floating like a cork over the waves continuing forward … this is another scenario which is impacted by how big and closely spaced the waves are…it’s not as clear as the armchair formula that gives a general rating for a particular model boat. The formula makes sense and I can see how it compares to my previous boats. What brought me to this article is comparing numbers on 3 sailboats and this comfort ratio makes sense to me.

8. Mark Wyatt

Bethwaite’s books explain it perfectly. A deep keel boat’s motion in a seaway is more solidly hooked in underwater while a multihull, is skittering over the waves in general.

I’ve been on both in a seaway and it’s a tossup, lots of water on deck and a labored movement with a deep keeled monohull, vs. flying over the water on a multihull at speed ’till you hit the wrong wave set & risk capsizing the boat. Modern fin keeled monohulls are stiff & uncomfortable but always keep the mast pointing upward. The same cannot be said about performance multihulls where an “oops we’re capsizing” event is always possible.

9. Tony Solgard

The 40-50 range is missing. “…numbers below 20 indicate a lightweight racing boat; 20 to 30 indicates a coastal cruiser; 30 to 40 indicates a moderate bluewater cruising boat; 50 to 60 indicates a heavy bluewater boat; and over 60 indicates an extremely heavy bluewater boat.”

10. Joey Schueler

Thank you for this informative article! I wonder how this concept plays into the concept of heaving to in rough seas, as explained really well by Lin and Larry Pardis in their book, “The Capable Cruiser”. In this regard, they strongly endorse more heavier displaced boats with heavy full keel hulls to heave to in heavy weather, thereby creating a slick behind the boat that breaks the waves in advance of reaching the hull.

They maintain that as opposed to running before a storm, you should heave to and let it pass over while safe behind your slick, losing about 1.5-2 knots as the storm rolls over. Those who try to outrun a storm often elongate their being in the mess, versus those who ride it out. Of course, being highly skilled at it is essential, as failing to properly hove to leaves one vulnerable to building and sometimes very dangerous sea conditions.

They suggest that being able to hove to in bad weather is necessary in elongated lee shores, so I’m curious if this comfort ratio is pertinent if a sailor knows these tactics, and/or if the ratio is descriptive of the vessel’s capability in this regard. I’d enjoy hearing your thoughts on it. Certain keels cannot heave to very well and cats certainly are unable to create a slick without ample displacement.

11. Cloroxbottle

In general, modern monohulls with fin keels and spade rudders have significant yawing moments around those keels and don’t heave-to particularly well. Theoretically they should either lie to a sea anchor, or run +/- a drouge.

12. Per Landeback

Hi!
As an engineer of automobiles, I kind of thinking on the comfort ratio and heeling as effect of mass inertia. For example if you put a lot of loads at front/rear you will get a considerably high Iy mass inertia (Iz is about the same as Iy). For heeling it about Ix which can be affected by make the boat wider or with a person on side.

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