How the Boat Calculator works it out

Every figure Rainbow’s End Boat Calculator gives you, and where it comes from. Each section shows the formula, what it means, what it rests on, whose it is, and the numbers for Rainbow, the ketch the calculator opens on, so you can check them yourself.

Rainbow, a Perry 47 ketch: 46′ 7″ long, 36.8 ft on the waterline, 13′ 6″ beam, 30,400 lb empty, with 12,000 lb of encapsulated lead ballast in a shoal-draft keel. Sail area 973 ft²: main, 100% fore triangle and mizzen. As she sails: 250 gal of diesel, 125 gal of water, and 2,000 lb of people, stores and gear.

What each figure rests on

Physics

Standard physics: the weight of water and fuel.

Geometry

Arithmetic on lengths, areas and weights. Nothing is assumed.

Published

A published figure, and whose. We name a source only when we have read it.

Our estimate

A figure we chose. The calculator treats it as an estimate, and so should you.

Contents

• The load
• Pounds per inch
• Sail area to displacement
• Displacement to length
• Ballast ratio
• Comfort ratio
• Capsize screening
• Hull speed and top speed
• Multihulls
• Sheet and halyard loads
• Range under power

The load

What she carries that the brochure left out

A builder’s displacement is usually the boat empty. Every ratio below is worked twice: on the published figure, and on the boat as she sails. Compare boats in the same state of load.

Brochure figures and comparing in the same trim: Ralph Naranjo, “Measuring Performance,” Practical Sailor, 2020.

Pounds per inch

How far the load sinks her

The weight that sinks her one inch, from the area of her waterplane. The waterplane is estimated from her waterline length and beam.

Her published sheet gives 1,770 lb/in. The calculator’s figure is within 0.3% of it.

Sail area to displacement

How much sail she carries for her weight

A sailor’s power-to-weight ratio. It says nothing about how well the hull uses the power.

Empty, she is in the good-performance band. Loaded, she drops just under 15. Her published sheet gives 16.

Ralph Naranjo, “Measuring Performance,” Practical Sailor, 2020.

With the sails she sets

The standard figure counts the 100% fore triangle, so every boat is measured the same way and the bands apply. Few sailors carry a 100% jib. The calculator also works SA/D on the sails you set: the headsail at its LP, the main (the sailmaker’s area if you have it), the mizzen or foresail, and any staysail. That figure has no bands, because the bands were drawn for the standard one; the calculator says how much more sail it is instead.

With her 135% genoa she carries 19% more sail than the standard figure. Most of the extra is light-air power, and it’s the first sail you reef.

Displacement to length

How heavy she is for her waterline

Ralph Naranjo, “Measuring Performance,” Practical Sailor, 2020.

Ballast ratio

How much of her weight is ballast

How much the ballast helps her stand up depends on how deep it sits. Two boats with the same ratio can stand up very differently. Hers is encapsulated lead in a shoal-draft keel.

Depth of ballast: Ralph Naranjo, “Measuring Performance,” Practical Sailor, 2020.

Comfort ratio

How quickly she moves upward in a seaway

Ted Brewer devised it as a measure of motion comfort: how fast a boat moves upward in waves. Lower is quicker and less comfortable; higher is calmer. Brewer put moderate, successful ocean cruisers in the low to mid 30s.

It ignores wave direction, hull shape, bow buoyancy, ballast depth and speed. It does not measure safety. Use it to compare boats of a similar size and style.

Jamie Gifford, “Hands-on Sailor: Comfort Ratio,” Cruising World, 2026, quoting Ted Brewer. The exponent 1.333 reproduces Rainbow’s published 36.6; the article prints 1.33, which gives 36.9.

Capsize screening

Beam against weight

A first look, not a stability test. It ignores hull shape and where the ballast sits.

Ray Ville, Freedom 45 CC review, Practical Sailor, 2025. The calculator reproduces that review’s 1.90.

Hull speed and top speed

How fast a displacement hull goes

The traditional rule ignores weight. Dave Gerr’s formula allows for it: light boats can be driven past 1.34 × √LWL without planing; heavy ones hold at it. It ignores sail area, and long overhangs make a boat’s D/L read high and her top speed low.

Hull speed: Darrell Nicholson, “Determining a Fuel-efficient Engine RPM,” Practical Sailor, 2025. Top speed: Dave Gerr, “What Efficiency Means, How It Can Save Money and How It Makes for Better Boats,” Part 1, 2011 (gerrmarine.com). The calculator reproduces the worked example in Charles Doane, “Crunching Numbers: A Better Way to Estimate Hull Speed,” Wave Train, 2010: 7.9 kt for 12,000 lb on a 28 ft waterline.

Multihulls

Power, and the wind that lifts a hull

A multihull stands up on her beam, not her keel, so the ballast ratio, comfort ratio and capsize screening are left out. Three figures take their place. The worked figures are for a Lagoon 42, from the table in the source.

An offshore cruising multihull should not need a reef below 22 to 25 kt apparent. Waves, and the wind getting under the bridgedeck once she heels, lower the real figure.

“Multihull Capsize Risk Check,” Practical Sailor, 2021. The calculator reproduces all seven boats in its table.

Sheet and halyard loads

What the sheet is holding

The load climbs with the square of the wind: twice the wind, four times the load. The halyard carries about the same. The mainsheet depends on where it meets the boom, so its figure is rough.

Load: Win Fowler, “Ask Sail,” SAIL, 2014. Line: the Cordage Institute puts a line’s safe working load at 1/5 to 1/12 of its breaking strength, as reported in Practical Sailor, November 2010. Five is the low end.

Range under power

How far the tanks take her

The power a displacement hull needs climbs steeply with speed. An efficient cruising speed is 60 to 70% of hull speed; past 75%, the fuel per mile climbs fast.

As she sails, 80 hp, 250 gal, a third kept in reserve. Her efficient speed is 4.9 to 5.7 kt. These figures assume calm water and a clean bottom.

The speed-from-power formula is widely attributed to Gerr, but we have not read it at its source, so it is our estimate here. Practical Sailor’s worked example uses Gerr’s propeller table, which needs the engine’s RPM. The formula here needs only horsepower and asks for about a third more power at cruising speed, so its ranges are on the short side.

Fuel, efficient speed and the rule of thirds: Darrell Nicholson, “Determining a Fuel-efficient Engine RPM,” Practical Sailor, 2025, quoting Dave Gerr. Shaft power: Dave Gerr, “What Efficiency Means,” Part 1, 2011: a direct shaft delivers 95 to 96% of the engine’s horsepower to the propeller.