REST: what the comfort numbers can't tell you about a keel

A boat that measured well

Somebody buys a Morgan Out Island 41. It is a well-known boat, a lot of boat for the money, and it measures beautifully. Run it through the Comfort Ratio — the number sailors have used for fifty years to compare motion at sea — and it returns 34.9. In a fleet of twenty-six cruising boats spanning trailer-sailers to a Hallberg-Rassy 40, that is third place. Ahead of a Valiant 40. Ahead of a Pacific Seacraft 37. Ahead of the Hallberg-Rassy.

Then they take it to an anchorage and cannot sleep.

This is not a rare story, and it is not a story about a bad boat. The Morgan is a capable, roomy, seaworthy cruiser that has crossed oceans. It is a story about a number that had no way of seeing the thing that mattered.

The index described here — REST — puts the Morgan Out Island 41 twentieth of twenty-six, below a Catalina 34. It gets there from four numbers on the spec sheet, and it is not clever. It just has two fields the older number was never given.

What changed since 1970

The Comfort Ratio uses displacement, length and beam. Ted Brewer drew it up as a rough sketch — he has said as much himself, more than once — and it has outlasted almost everything else written about boat selection in its era because the trade it made was the right one. It gave up a little accuracy for total reproducibility. Anyone could compute it from any brochure, so everyone did.

Those three fields were also, in 1970, close to the only ones a buyer could reliably get. Draft was inconsistently published. Ballast weight, more so. If you were building a number that ordinary people could actually use, weight and beam were what you had, and in a fleet where nearly every cruising boat carried a keel of broadly similar depth, weight and beam carried most of the information.

That last part is what stopped being true. Today’s market puts hard-chined hulls with twin rudders next to shoal-draft centreboarders next to traditional full-keel voyagers, frequently at similar displacements. And draft and ballast are now two clicks away on any listing site.

So this is not a correction of anything. It is the same sketch, redrawn with two fields that exist now and did not exist then.

The Morgan, mechanically

The Morgan Out Island 41 displaces 27,000 lb. That is heavy, and weight is the dominant term in the older ratio, which is why it lands third.

It also carries 13.82 ft of beam on 4.17 ft of draft. That ratio — draft divided by beam — is 0.302. In this fleet of twenty-six, only the two swing-keel trailer-sailers are shallower relative to their width.

Heavy, wide and shallow is a specific combination, and it is the one that gets flattered. The weight is counted. The shallowness is invisible. What the buyer reads is the weight.

Why shallowness matters for motion is the whole argument, and it takes two paragraphs.

A hull resists heeling in two different ways. Some of the resistance comes from the shape of the waterplane — a wide flat hull has to lift a lot of water to roll, so it resists. Some comes from weight carried low, a heavy keel swinging out and pulling the boat back upright. Naval architects call these form stability and ballast stability. Both make a boat stiff. They do not feel remotely the same.

The reason is roll period. To a first approximation, a boat’s roll period goes as its radius of gyration divided by the square root of its metacentric height — that is, how far the mass sits from the roll axis, against how hard the boat is pushed back to level. Beam raises the restoring force and barely moves the mass distribution: the boat snaps upright. Ballast hung deep raises the restoring force too, but it also moves mass away from the axis, and that lengthens the period. At the same stiffness, a boat that got there through depth carries more inertia than one that got there through width. The two boats may be equally hard to heel. They will not be equally violent about coming back.

Stiff and comfortable are not the same property. A wide shallow hull is stable in the sense that it resists heeling, and unpleasant in the sense that it returns to level fast enough to throw the coffee off the table.

The index

L    = (Displacement / 64)^(1/3)

REST = 247.73 × (Ballast/Disp)^0.4 × (Draft/Beam)^0.9 × (L/Beam)^0.93 × (L/10)^1.33

Four inputs, all standard database fields:

L is a volumetric length — the cube root of the displaced volume, in feet. It is derived from displacement, not looked up, so it costs no additional field.

REST — Righting arm, Effective ballast, Scale, Total mass. The name is the input list: the righting arm is draft, the effective ballast is the lead, the scale term is size, and the total mass is displacement. Beam is the fourth number and is unnamed, because it is the quantity the other three are measured against.

Every term is a ratio, so the index is a pure dimensionless number. Multiply it out and it reduces to a single monomial, which is the form worth checking because it hides nothing:

REST = 0.505 × Disp^0.35333 × Ballast^0.4 × Draft^0.9 / Beam^1.83

Four exponents, visible at once, applied uniformly to every boat. Both forms agree to the last digit on every boat in the table below. The displacement exponent is 0.35333 rather than a rounder number because it is not free: it is what the size and ballast terms leave over, 2.26/3 − 0.4.

Units are imperial and not optional: pounds and feet. The reference lengths inside the formula are in feet, so metric inputs do not produce a converted score, they produce a meaningless one. Convert first — 1 kg = 2.20462 lb, 1 m = 3.28084 ft.

One rule.Swing-keel, centreboard and lifting-keel boats are scored board-up. That is the boat’s fixed ballasted body, and it is the configuration it lies in at anchor. This rule is a judgment call; see the limitations.

Worked example — Contessa 32. Disp 9,500 lb, ballast 4,500 lb, draft 5.5 ft, beam 9.5 ft.

L = (9500/64)^(1/3)  = 5.294 ft
Ballast/Disp         = 0.4737   ^0.4  = 0.7443
Draft/Beam           = 0.5789   ^0.9  = 0.6122
L/Beam               = 0.5573   ^0.93 = 0.5820
L/10                 = 0.5294   ^1.33 = 0.4278
REST = 247.73 × 0.7443 × 0.6122 × 0.5820 × 0.4278 = 28

What each term does

Draft is rewarded, with diminishing returns.It appears at a net exponent of 0.9, so depth buys comfort but not without limit — an extreme racing draft cannot purchase unbounded points.

Ballast ratio is rewarded at 0.4. Together with draft, this is the ballast-depth argument above: lead hung deep, in quantity.

Beam is penalised twice, deliberately— once in the draft-to-beam term and once in the slenderness term, for a net exponent of −1.83. That is harsher than the classic −1.33, and the harshness is the point. Beam is the principal source of form stability, and form stability is the kind that hurts.

Displacement enters at 0.35, which is much gentler than the older ratio’s linear treatment. This is deliberate and has a practical benefit: published displacements disagree. One boat in this fleet is listed at 13,900 lb by one source and 15,900 lb by another, a 14 percent spread. That moves REST by under 5 percent. An index computed across thousands of listings from databases that do not agree with each other should be built to survive exactly that.

Size is declared, not accidental. The final term carries an exponent of 1.33: a boat twice as long, all proportions equal, scores about 151 percent higher. Bigger boats are better in a seaway, and this is where that belief is written down and made arguable rather than left to emerge from the algebra. The evidence available permits anything from about 0.69 to about 2.16; 1.33 sits near the middle of that window. It is a judgment call, made once, published, and applied uniformly to every boat.

There is no keel-type lookup table, no hull-form coefficient, no clamp, and no special case. Earlier versions of this index had all of them. Each was removed when it proved impossible to fit against evidence rather than set by hand, and a number chosen by hand to produce a desired ranking cannot afterwards be evidence for that ranking.

What it changes

Here is the fleet sorted by how far each boat moves between the classic ratio’s ranking and REST’s.

Read the right-hand column. Almost everything that rises is deep for its beam; almost everything that falls is shallow for its beam. In practice REST is a shoal-draft detector, and the Morgan is the extreme case in both directions at once — heaviest of the shallow boats, shallowest of the heavy ones.

That is a claim any reader can test against their own experience, which is the point.

The controlled case

The movers table is suggestive but every row compares different boats, and someone can always say the boats differ in ways no formula sees. So here is the version where they don’t.

Catalina sold the 34 in two versions: a fin keel drawing 5 ft 7 in, and a wing keel drawing 4 ft 3 in. Same hull, same rig, same interior, displacement within 5 percent. The only meaningful difference is how deep the lead hangs. Ask sailors which lies quieter at anchor and the answer is not controversial: the deep one.

The classic ratio scores the wing keel higher, by 4.7 percent. It is not an error in the formula — draft is not one of its inputs, so the only difference it can detect between these two boats is that the deep-keel version is marginally lighter, and lighter scores lower. There is no mechanism available to it for getting this right.

REST separates them by 20.0 percent in favour of the fin, from measured draft and ballast alone, with no keel multiplier anywhere in the formula to put a thumb on the scale.

Catalina did the same thing with the 30. Same result: the classic ratio favours the wing by 1.2 percent, REST favours the fin by 31.1 percent.

Two production hulls, each sold in two configurations, where the answer is not a matter of opinion — and one number gets both backwards while the other gets both right, using nothing but two fields off the spec sheet.

Reading the score

All three boundaries fall on real gaps in the fleet distribution rather than round numbers chosen for neatness. Note that twenty-two of twenty-six boats sit between 16 and 37 — the index discriminates well in the middle of the market, where people actually shop, and less at the extremes.

The fleet

Twenty-six configurations, twenty-four boats, computed with no manual inputs. The inputs are published alongside the scores so that any reader can recompute a row by hand and check it. An index whose workings cannot be audited is worth no more than an opinion.

* Board-up draft, per the rule above.

What it gets wrong

The Contessa 26 scores 20.3, below a Catalina 34 wing keel. It is a proven small offshore boat; one has been sailed around the world. The Alberg 30 and the Westsail 32 also fall relative to the classic ratio. What these boats have that REST cannot see lives in their hull sections, and no spec sheet records hull sections. Adding a “traditional keel” bonus would fix the table and destroy the argument, because the fin-versus-wing result above is only worth reporting on the condition that nothing in the formula was set by hand to produce it.

The Catalina 22 lands at the bottom of the fleet, below a Pogo 36, which was registered in advance as a comparison the index should get the other way round. This has not been resolved and is stated rather than dropped. It may be a scope mismatch: a trailer-sailer board-up at anchor genuinely is a cork, while a Pogo is unpleasant under way but heavy and deep at rest. If the opinion was about sailing and the index is about lying at anchor, both may be right.

The board-up rule is the one judgment call in the pipeline that the evidence cannot settle. Scoring swing keels board-down changes no test result at all, but it puts a keel/centreboard 37-footer at the top of the fleet, which is clearly wrong. So board-up stands on plausibility, not on measurement.

REST is a monomial and therefore cannot saturate. Real comfort has diminishing returns that eventually flatten out; a monomial keeps extrapolating. That is part of why the extremes behave less well than the middle.

Limitations

• REST measures roll and behaviour at rest.It is not a pitching or pounding index — there is no length term for that, and adding one made no measurable difference when tested. Read it as a number about how a boat lies, not how it drives into a head sea.
• It is not a safety metric. It says nothing about capsize resistance, range of positive stability, downflooding or structural adequacy. The Capsize Screening Formula, angle of vanishing stability and ISO STIX exist for those. A high REST score is not an endorsement for offshore work: the Morgan Out Island 41 and the Contessa 26 sit two points apart in the table and are not equivalent boats for crossing an ocean.
• Ballasted monohulls only.Multihull motion is governed by different things — bridgedeck clearance and payload dominate, and clearance is not a standard database field.
• It cannot see where the ballast sits, only how much there is and how deep the boat draws. Lead in a shoal bilge is treated the same as lead in a deep fin of the same weight and draft.
• It does not model rig. Heavily-sparred ketches and schooners carry more roll inertia aloft than their score reflects.
• It assumes cruising trim. Ground tackle, water, fuel and stores change both displacement and its distribution, and none of that is on a spec sheet.
• Rolling at anchor is partly resonancebetween a hull’s roll period and the swell entering a particular bay. No static formula predicts that. Boats scoring 36 still roll in the wrong anchorage, which is why flopper stoppers exist.

How it was checked

Twenty-four comparisons of the form “boat A is more comfortable than boat B” were written down before the formula was computed, drawn from firsthand experience and from reputations settled enough that a reader would not dispute them. REST satisfies 22 of them. The Comfort Ratio satisfies 20.

Two comparisons is a thin margin, and the seven held back from fitting tell a blunter story: the Comfort Ratio got all seven, REST six. On this evidence REST is not measurably a better predictor of comfort in general, and it is not offered as one. What it does that the older number cannot do at all is see the keel, and that shows up in the only two places in this fleet where the keel is isolated as a variable. Two of the comparisons are the author’s own — a Saga 43 that lay remarkably quiet at anchor without a flopper stopper, and a Morgan Out Island 41 that did not. That is testimony, not a neutral field report, and readers with contradicting experience are invited to send it.

What it’s for

Not for reordering the cruising fleet. On most comparisons REST and the classic ratio agree, and where they agree you may as well use the number you already know.

It is for the moment when you are looking at one boat, offered with two keels, or at a shoal-draft version of something you liked, and you want to know what you are trading away. There the older number cannot help, and it was never given the data to. REST can, from four figures on the listing.

The Morgan buyer had a number that said third in the fleet. The two fields that would have told them otherwise are now published on every listing site there is. That is the entire contribution here, and the fleet table is there so you can check it.