trimaran length to beam ratio

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In comparison with Moore's Law , the nonsilicon world's progress can seem rather glacial. Indeed, some designs made of wood or metal came up against their functional limits generations ago

The length-to-beam ratio (LBR) of large oceangoing vessels offers an excellent example of such technological maturity. This ratio is simply the quotient of a ship's length and breadth, both measured at the waterline; you can think of it simply as the expression of a vessel's sleekness. A high LBR favors speed but restricts maneuverability as well as cargo hold and cabin design. These considerations, together with the properties of shipbuilders' materials, have limited the LBR ratio of large vessels to single digits.

If all you have is a rough wickerwork over which you stretch thick animal skins, you get a man-size, circular or slightly oval coracle —a riverboat or lake boat that has been used since antiquity from Wales to Tibet. Such a craft has an LBR close to 1, so it's no vessel for crossing an ocean, but in 1974 an adventurer did paddle one across the English Channel.

Building with wood allows for sleeker designs, but only up to a point. The LBR of ancient and medieval commercial wooden sailing ships increased slowly. Roman vessels transporting wheat from Egypt to Italy had an LBR of about 3; ratios of 3.4 to 4.5 were typical for Viking ships , whose lower freeboard—the distance between the waterline and the main deck of a ship—and much smaller carrying capacity made them even less comfortable

The Santa María , a small carrack captained by Christopher Columbus in 1492, had an LBR of 3.45. With high prows and poops, some small carracks had a nearly semicircular profile. Caravels , used on the European voyages of discovery during the following two centuries, had similar dimensions, but multidecked galleons were sleeker: The Golden Hind , which Francis Drake used to circumnavigate Earth between 1577 and 1580, had an LBR of 5.1.

Little changed over the following 250 years. Packet sailing ships, the mainstays of European emigration to the United States before the Civil War, had an LBR of less than 4. In 1851, Donald McKay crowned his career designing sleek clippers by launching the Flying Cloud , whose LBR of 5.4 had reached the practical limit of nonreinforced wood; beyond that ratio, the hulls would simply break.

A high LBR favors speed but restricts maneuverability as well as cargo hold and cabin design. These considerations, together with the properties of shipbuilders' materials, have limited the ratio of large vessels to single digits.

But by that time wooden hulls were on the way out. In 1845 the SS Great Britain (designed by Isambard Kingdom Brunel , at that time the country's most famous engineer) was the first iron vessel to cross the Atlantic—it had an LBR of 6.4. Then inexpensive steel became available (thanks to Bessemer process converters), inducing Lloyd's of London to accept its use as an insurable material in 1877. In 1881, the Concord Line's SS Servia , the first large trans-Atlantic steel-hulled liner, had an LBR of 9.9. Dimensions of future steel liners clustered close around that ratio: 9.6, for the RMS Titanic (launched in 1912); 9.3, for the SS United States (1951); and 8.9 for the SS France (1960, two years after the Boeing 707 began the rapid elimination of trans-Atlantic passenger ships).

Huge container ships , today's most important commercial vessels, have relatively low LBRs in order to accommodate packed rows of standard steel container units. The MSC Gülsün (launched in 2019) the world's largest, with a capacity of 23,756 container units, is 1,312 feet (399.9 meters) long and 202 feet (61.5 meters) wide; hence its LBR is only 6.5. The Symphony of the Seas (2018) , the world's largest cruise ship, is only about 10 percent shorter, but its narrower beam gives it an LBR of 7.6.

Of course, there are much sleeker vessels around, but they are designed for speed, not to carry massive loads of goods or passengers. Each demi-hull of a catamaran has an LBR of about 10 to 12, and in a trimaran, whose center hull has no inherent stability (that feature is supplied by the outriggers), the LBR can exceed 17.

This article appears in the August 2021 print issue as "A Boat Can Indeed Be Too Long and Too Skinny."

Vaclav Smil writes Numbers Don’t Lie, IEEE Spectrum 's column devoted to the quantitative analysis of the material world. Smil does interdisciplinary research focused primarily on energy, technical innovation, environmental and population change, food and nutrition, and on historical aspects of these developments. He has published 40 books and nearly 500 papers on these topics. He is a distinguished professor emeritus at the University of Manitoba and a Fellow of the Royal Society of Canada (Science Academy). In 2010 he was named by Foreign Policy as one of the top 100 global thinkers , in 2013 he was appointed as a Member of the Order of Canada , and in 2015 he received an OPEC Award for research on energy. He has also worked as a consultant for many U.S., EU and international institutions, has been an invited speaker in more than 400 conferences and workshops and has lectured at many universities in North America, Europe, and Asia (particularly in Japan).

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Comparing trimarans & catamarans.

Trimarans tend to be more performance oriented than catamarans. In part, this is because it’s easier to design a folding trimaran, and as a result Farrier, Corsair, and Dragonfly trimarans had a disproportionate share of the market.

In spite of this and in spite of the fact that many are raced aggressively in windy conditions, capsizes are few, certainly fewer than in equivalent performance catamaran classes.  But when they do go over, they do so in different ways.

Trimarans have greater beam than catamarans, making them considerably more resistant to capsize by wind alone, whether gusts or sustained wind. They heel sooner and more than catamaran, giving more warning that they are over powered. 

Waves are a different matter. The amas are generally much finer, designed for low resistance when sailing deeply immersed to windward. As a result, trimarans are more susceptible to broach and capsize when broad reaching at high speed or when caught on the beam by a large breaking wave.

In the first case, the boat is sailing fast and overtaking waves. You surf down a nice steep one, into the backside of the next one, the ama buries up to the beam and the boat slows down. The apparent wind increases, the following wave lifts the transom, and the boat slews into a broach. If all sail is instantly eased, the boat will generally come back down, even from scary levels of heel, but not always.

In the second case a large wave breaks under the boat, pulling the leeward ama down and rolling the boat. Catamarans, on the other hand, are more likely to slide sideways when hit by a breaking wave, particularly if the keels are shallow (or raised in the case of daggerboards), because the hulls are too big to be forced under. They simply get dragged to leeward, alerting the crew that it is time to start bearing off the wind.

Another place the numbers leave us short is ama design. In the 70s and 80s, most catamarans were designed with considerable flare in the bow, like other boats of the period. This will keep the bow from burying, right? Nope. When a hull is skinny it can always be driven through a wave, and wide flare causes a rapid increase in drag once submerged, causing the boat to slow and possibly pitchpole.

Hobie Cat sailors know this well. More modern designs either eliminate or minimize this flare, making for more predictable behavior in rough conditions. A classic case is the evolution of Ian Farrier’s designs from bows that flare above the waterline to a wave-piercing shape with little flare, no deck flange, increased forward volume, and reduced rocker (see photos page 18). After more than two decades of designing multihulls, Farrier saw clear advantages of the new bow form. The F-22 is a little faster, but more importantly, it is less prone to broach or pitchpole, allowing it to be driven harder.

Beam and Stability

The stability index goes up with beam. Why isn’t more beam always better? Because as beam increases, a pitchpole off the wind becomes more likely, both under sail and under bare poles. (The optimum length-to-beam ratios is 1.7:1 – 2.2:1 for cats and 1.2:1-1.8:1 for trimarans.) Again, hull shape and buoyancy also play critical roles in averting a pitchpole, so beam alone shouldn’t be regarded as a determining factor.

Drogues and Chutes

While monohull sailors circle the globe without ever needing their drogues and sea anchors, multihulls are more likely to use them. In part, this is because strategies such as heaving to and lying a hull don’t work for multihulls. Moderate beam seas cause an uncomfortable snap-roll, and sailing or laying ahull in a multihull is poor seamanship in beam seas.

Fortunately, drogues work better with multihulls. The boats are lighter, reducing loads. They rise over the waves, like a raft. Dangerous surfing, and the risk of pitchpole and broach that comes with it, is eliminated.  There’s no deep keel to trip over to the side and the broad beam increases the lever arm, reducing yawing to a bare minimum. 

Speed-limiting drogues are often used by delivery skippers simply to ease the motion and take some work off the autopilot. By keeping her head down, a wind-only capsize becomes extremely unlikely, and rolling stops, making for an easy ride. A properly sized drogue will keep her moving at 4-6 knots, but will not allow surfing, and by extension, pitch poling. 

For more information on speed limiting drogues, see “ How Much Drag is a Drogue? ” PS , September 2016.

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On board the world's largest trimaran White Rabbit

She’s blissfully quiet, impressively efficient and comfortably cavernous. Oh, and she’s an 84 metre trimaran. Stewart Campbell follows the White Rabbit ...

The obvious question, really, is: why bother building a trimaran when the rest of the world is cruising around in monohulls? Why go so radically against the grain?

Vindication can be sweet – in January 2019 the team behind White Rabbit picked up the Best Naval Architecture Award for Displacement Motor Yachts at the Boat International Design & Innovation Awards . It turns out that trimarans, done right, are quieter, leaner and more environmentally sound than monohulls. The owner of White Rabbit has known this for some time; he has never been anything but evangelical about their benefits. He has almost single-handedly proven the concept in big boats and now owns the world’s two biggest trimaran superyachts: the original three-hulled 61-metre White Rabbit from 2005 and now this 84-metre version, delivered just in time for Christmas. There’s also a large catamaran in the fleet, a 51-metre support vessel called Charley .

Let’s tick off some of those other benefits. You might think that a trimaran platform limits interior space, but you’d be wrong. White Rabbit carries 2,940 gross tonnes, so roughly the same as a 90-metre monohull. Sunrays , the 85-metre 2010 Oceanco , has an internal volume of 2,867GT. Solandge , the 85-metre Lurssen from 2013, has a gross tonnage of 2,899. The 90-metre DAR from Oceanco has an interior measured at 2,999GT, so only a snip more than 84-metre White Rabbit . All this volume is generated by the trimaran’s 20-metre beam, which makes it around five metres wider than equivalent-length monohulls. And she could be a lot more voluminous – the top deck, for instance, is fairly modest, while a bluff bow would generate even more GTs.

Such novel naval architecture surely adds to the cost, though? Not according to Mark Stothard, founder and owner of Echo Yachts , the Australian yard responsible for  White Rabbit , who estimates the yacht was "significantly cheaper" to build than an equivalent-size monohull at a Northern European yard. You sometimes hear complaints about the ride of trimarans, and here, they have a little work to do. A comparison study by the Maritime Research Institute Netherlands (MARIN) in 2000 showed that when bow-on to the weather, at speed or rest, trimarans are more comfortable than monohulls with equivalent displacements.

But in some conditions, particularly stern-quartering seas, the motion of a trimaran can be worse. To counter this,  White Rabbit’s  naval architects drew on the experience gained from the 61-metre boat, installing four enormous Naiad fins totalling 45 square metres that jut out from the centre hull. These have a limited range of movement and essentially act as aircraft wings under the water, planting the hulls and evening out the ride. Each of the three hulls also carries significant flare, generating buoyancy to dampen roll. The brains behind  White Rabbit  claim that trimarans, unlike monohulls, are far easier to fine-tune to find a ride motion the owner is comfortable with, simply by increasing or decreasing buoyancy in the outer hulls – "so the negatives are really not negatives", says exterior and interior designer Sam Sorgiovanni .

The very same MARIN study points out the obvious, and massive advantage of trimarans: "When the same speed is required, the installed propulsion power [in the trimaran] can be reduced by some 40 per cent, leading to lower operational costs, a reduction in weight and less environmental contamination." And there you have it – three slender hulls are better than a single fat one. Or, as Sorgiovanni puts it: "What would you rather be paddling in? A bathtub or a kayak?" In an age when all superyacht owners, regardless of bank balances, are casting a lingering eye over fuel bills and environmental impact, comes a concept that offers you better space, value and a cleaner conscience. So naval architects’ phones should be ringing off the hook with billionaires demanding multihulls, right? Right...? Not quite.

The problem is one of perception, says Stothard. Not necessarily on the part of owners, he says, but from an occasionally reactionary superyacht industry inexperienced with the multihull form. Sorgiovanni agrees. "Why would I build three hulls instead of one?" was one shipyard’s response to a trimaran design he presented. "Meanwhile, you’ve got big-name naval architects who in their whole career have never done anything like it, so why would they endorse it? Why would they endorse something they’re fearful or ignorant of?" Whatever the reasons for the inertia, it doesn’t look like the needle will be twitching in favour of trimarans any time soon. Which is a shame, because for all the above reasons and more, this platform makes all kinds of sense – as  White Rabbit  capably proves.

As a rough guide, the length-to-beam ratio of a monohull superyacht in this size range is around 6:1. By comparison, the length-to-beam ratio of  White Rabbit’s  centre hull is 13.7:1. You don’t need a degree in naval architecture to know which one will use less fuel, but the truly impressive thing about  White Rabbit  is the engineering underpinning her natural slipperiness. One key demand of the owner was that Echo Yachts limit noise – and therefore engineering – in the centre hull, where he has a cabin, so designers had to rethink the arrangement seen on the 61-metre, where the main engines are located on the centreline. "The owner sat us down and said, ‘Boys, with this thing I want some engineering boldness.’ He said what was important to him was smoothness and quietness," says Stothard. "And he gave us the latitude to go out and explore solutions."

The team quickly decided to go diesel-electric, with generators in the outer hulls powering STADT electric motors in the centre hull, in turn spinning two Rolls-Royce variable pitch props. Other ideas were discussed and thrown out: waterjets because the boat would be sitting idle in Singapore for lengths of time, so divers would be required to go down to pump out the jet tunnels and then plug them; Voith thrusters because the yard felt it a "bit early for them to be able to gear up to such a project"; and azimuthing pods because they would have required too much volume in the centre hull. They also looked at putting everything – engines, motors, shafts – in the outer hulls, but studies revealed the ultimate solution to be the most efficient. Just how efficient is best exemplified, again, by way of comparison: according to White Rabbit’s naval architect, the Sydney studio One2Three , it requires 91.5-metre Equanimity (now Tranquility ), which has an equivalent gross tonnage to White Rabbit , 7.2MW of power to reach its top speed of 19.5 knots; White Rabbit requires just 4.2MW of power to reach its top speed of 18.7 knots – some 40 per cent less.

There are six generators on board – four Caterpillar C32s outputting 940ekW and two C18s outputting 550ekW, each brought online and off by a Kongsberg power management system. The engineers should get plenty of life out of these units because the boat can run at a 12-knot cruise with just two gensets engaged. "I’ve been on sea trials up the coast using just two C32s – and that will be cruising at 12.8 knots, with 75 per cent power to the drive system and 25 per cent, or 500kW, to run the house," says Stothard. "That’s with four generators offline and a burn of about 320 litres an hour for everything. The crew even think they could do 12 knots on one C32 and one C18." The boat’s eco-cred doesn’t end there: she barely creates a wake. Sea trial images included in this feature show the yacht running at around 15 knots, but she might as well be idling for all the wash she generates. The owner does a lot of coastal cruising and wanted the "ability to operate without detrimental wash impact on surrounding vessels and foreshores", says Steve Quigley, One2Three’s managing director.

All this has resulted in a very quiet boat. In the lower deck master cabin Echo Yachts recorded sound levels of just 40db at 13 knots. Up on the main deck those levels dipped below 40db. "The owner was walking around with his own sound meter," says Stothard. "He didn’t even bother going up top." The diesel-electric set-up on  White Rabbit  has the added benefit that you can carry less fuel. The trimaran’s fuel capacity is 166,200 litres, for a range of 5,000 nautical miles.  Solandge ? 222,000 litres.  Sunrays ? 285,000 litres.  Equanimity ? 271,000 litres. That’s a lot of weight she’s not lugging around.

Smaller fuel tanks free up space, of course, but the designers weren’t fighting for volume here: there’s plenty of it. On the main deck, the boat gets very beamy, for a length-to-beam ratio of 4.3:1. Fat, but without looking it. That’s down to the skill of Sorgiovanni, whose office is not far from the Echo Yachts facility in Henderson, Western Australia. He’s the first to admit that the layout of White Rabbit is very idiosyncratic and has developed more "conventional" versions with beach clubs, gyms and bigger master cabins. But his brief from this client, with whom he worked on the 61-metre  White Rabbit , was very clear: this is a multigenerational yacht, built for family use, but with a necessary corporate function. Translation: lots of cabins – two masters, three VIPs and six guest – for a total guest capacity of 30 and a wide open main deck to host upwards of 200 people when alongside in her hometown of Singapore.

"You’re spanning three generations in terms of functionality as well as style," says Sorgiovanni, who travelled to Singapore to spend time with family members and hear each of their wants. "The overwhelming comment was, ‘We love what we’ve got, we just want it bigger.’ The words were: ‘We want [61-metre]  White Rabbit  on steroids.’ They literally meant it. As we started to develop the boat we realised that whatever we presented kept coming back to what they loved, which was their current boat. In a way it’s flattering to think they enjoy and love that boat so much, but it has evolved. The bigger boat has a far more sophisticated approach, both inside and out, but nevertheless there is that link there to something that is familiar." The art deco edge on the smaller yacht has been rounded off a little on the 84-metre, but there are still references throughout – in the light column at the huge bar in the main saloon, for instance, and wall sconces.

The colours used are rich enough to keep you interested, but not so much that the spaces feel stuffy or overly formal; you’re never afraid to put your glass down. The tactile, chequer-style wall panelling used all over the yacht, made of brushed Tasmanian oak, helps with this, and brings a bit of nature to the saloons. All the cabinetry and furniture was custom made by Alia Yachts in Turkey, who Sorgiovanni worked with on 41.3-metre  Ruya .

He was so impressed by their furniture skills he asked them to pitch for  White Rabbit’s  interior, which was fully assembled in Turkey, allowing Sorgiovanni and Echo’s project manager, Chris Blackwell, to walk through it making changes before it was disassembled and shipped to Australia for installation. This was a considerable undertaking considering the 1,200 square metres of guest area on board. The amount of space proved one of the designer’s biggest challenges – just what do you do with it all?

The main deck is the main event – and where the boat’s 20-metre beam is most evident. "And it could have been even wider," says Sorgiovanni. "But I was very conscious about keeping it human scale. It’s just a massive area." The designer has split the space into zones, according to generations. Upon entry, and beyond the spectacular staircase leading to the upper deck, the saloon splits – to port is a more informal lounge for younger members of the family, and to starboard a slightly stiffer seating area for elder generations. "The saloons are separated but not completely separated, because the owner didn’t want the generations split up," he says.

Beyond, all ages come together around that attention-grabbing bar and games area and dining space. The owner dictated that there be no televisions in any of the cabins (except his), forcing kids into the light and demanding that they spend time with the rest of the family. If they want a screen, they’ll find one only in a communal area. In direct contravention of the modern vogue for massive, floor-to-ceiling windows, meanwhile, the owner was deliberately modest with his glazing choices, but the windows still usher plenty of light across the 20-metre expanse.

The upper deck saloon is tiny by comparison and used as a media lounge and karaoke hangout by the family, complete with baby grand piano. The focus of this deck is really accommodation, for both guests and crew. Strangely, the guest cabins on this level either have very little or no cupboard space, but they do have benches, "so guests can put their stuff out", says Sorgiovanni. "They said they didn’t want any wardrobe space as guests are expected to live out of their suitcases," which suits the kind of cruising guests are expected to join for – weekends and overnights. Up again is the sundeck, with another games area and forward-facing cinema with seats that shake to mirror the action on screen. "From a sound point of view, it’s in the right spot," says the designer. "You can really crank it up and you’re not disturbing anyone." The deck spaces up here are ample – and the site of the only spa pool on board – but they are under-exploited. Sitting in the sun is clearly not a priority for this family, nor is charter a fixation. This is, and will remain, a private yacht.

The real master cabin is on the main deck, close to the family action, but there is an alternative on the lower deck of the centre hull for passages. It’s a strange feeling walking down to this level – almost like going underwater. Hull windows reveal the tunnel between the centre hull and the starboard outrigger. It’s an unusual view, but also quite an exciting one as water rushes between the hulls at 18 knots. "We decided to make a feature of it," says Blackwell. "All the underwater lights are deliberately in this centre hull so they shine under the outer hulls as well, so you get the benefit of glow here. It creates a different ambience and shows off the trimaran concept." The art subtly plays on this underwater sensation. "On the lower decks the artwork is all scenes from below the water; on the main deck it’s all on the water and then it’s above the water on the upper deck," says Sorgiovanni.

The 30 guests are served by a crew of 32, who get plum real estate forward on the main deck in the shape of a huge cafeteria-like mess and crew lounge. "The boat is on call 24/7, so the owner wanted very specifically to have the crew in a very comfortable space on the main deck, with large windows," says Sorgiovanni. In an alternative universe, this might be reserved for a vast, full-beam owner’s cabin, with crew moved to the lower deck, or voluminous guest cabins. In the same universe, those rear VIP cabins in the centre hull would become a wellness and spa area, with direct access to the water through a folding transom door. Maybe in that universe, trimarans are the norm and everyone’s cruising the world using a lot less fuel than in this one. I’m not saying trimarans are the answer for everyone – obviously berthing is a key factor and some people just might not like the look of them – but the benefits definitely deserve closer attention.

It’s something the owner of  White Rabbit  has learned through long experience. He started out in a monohull Feadship in 1989, built another in 1995 before experimenting with a catamaran in 2001. Then came the first trimaran in 2005, and, finally, the 84-metre  White Rabbit . He’s a true convert. As is Mark Stothard, the Echo Yachts boss: "If anyone is serious about building a yacht this size and they didn’t make the time to come and have a look at this boat, they’d be mad. I’ve been in this game since the early 1980s and I’ve been on some really impressive yachts in that time and this thing blows my mind. Regardless of whether we build it or not, it is unequivocally doing everything that we said it was going to do... and then some."

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Length-beam ratio

L/B = length divided by beam.

Units: Dimensionless.

Usually, the waterline dimensions L WL and B WL are used for monohulls, or for a single hull of a multihull.

What it's used for

Performance.

Larger L/B indicates a slimmer hull. This usually implies less wave-making resistance, and thus more efficient high-speed performance, but also suggests reduced load-carrying ability for a given length.

If a boat can plane, smaller L/B often suggests more efficient performance at low planing speeds. The balance generally tilts in favour of high L/B for fast boats.

Typical ranges of L/B are:

2 to 4 - Small to mid-size planing powerboats.

3 to 4 - Most small to mid-size sailboats and motor yachts, the longer ones generally having higher L/B. Some "skimming dish" racing sailboats also have L/B in this range; their wide beam gives them more initial stability so that they can fly larger sails.

4 to 6 - Fairly long and lean for a monohull. Some large, efficient long-range cruisers fall in this range, along with many racing monohulls.

6 to 10 - Large freighters; main hulls of cruising trimarans; a few very portly cruising catamarans; the lightest and slimmest of large sailing monohulls.

10 to 16 - Fast cruising cats and tris; a few racing multihulls.

Over 16 - Racing multihulls. Such high L/B is conducive to very light, low-drag hulls for race boats, but makes it very hard to get enough room inside the hulls for equipment or living space.

Living Space

If a boat is going to spend most of its time in a marina or at anchor, relatively low L/B implies a larger, more spacious interior and increased carrying capacity when compared to slimmer competitors of the same length. For a boat that must entertain guests at the dock but will rarely be used in rough weather or at high speeds, this may be a significant advantage. The slimmer boat, though, will generally have the advantage when fuel is expensive or when the weather picks up.

Topic: 

• Boat Design

• The Displacement to Length Ratio

THE DISPLACEMENT TO LENGTH RATIO (DLR)

A measure of your ease of motion through the water … how low can you go?

We struggle to find ways to reduce our footprint as we travel. Striving to save the planet is hard work when you're designing, building and voyaging in modern high performance yachts. But there are steps we can take in the right direction without building our boats out of biodegradable materials or figuring out how to turn our old boats into compost for orange orchards.

For a start we need to stop thinking about our boats simply in terms of length and how much stuff we can carry in that length. We need to be mindful of how much air and water we are  pushing around as we travel. Whatever it is we need to bring along; sleeping cabins, bathrooms, sun decks and water toys; the answer is to use efficient hull forms and spread the superstructure lengthwise rather than stacking it wedding cake style. Thoughtful design is part of the solution.

There's a pretty basic formula that measures this ease of motion through the water. It's the displacement to length ratio (DLR). It compares hull length against the vessel's weight and it's a reliable measure of how much resistance we are pushing against in the water as we travel.  It can be a reasonable indication of air resistance as well because if you're heavy and you're not that long it's a fair indication that you have a lot of superstructure above the waterline.  More weight drives the number up. Longer hulls bring it down. The lower the number the better.  

A low DLR comes with a host of benefits. Lower fuel costs, extended range from a given fuel capacity, less sail area to drive the boat if it's a sailing boat. Longer hulls provide a more comfortable ride. And if your profile above the water is modest you have a lower centre of gravity which means less roll, less pitch and less energy needed for forward motion.

The displacement to length ratio is a little but more complex than just the length or the weight measurement but if we have that figure handy and we're talking to someone who understands its relevance it tells us more about the performance characteristics of any particular design that any other number.

Consider the vessel as a given mass, that is; the total weight of the boat and everything it carries. The longer the hulls for a given mass (displacement), the lower the displacement to length ratio, the more easily driven the hulls are and the more sea kindly the motion of the vessel in a seaway.

 Determining the Displacement to Length (D/L) Ratio:

You don't often see  the D/L ratio published in a brochure or even in the designer's specifications, but it's not hard to figure out if know the sailing weight of the boat with reasonable accuracy.

1. Calculate its displacement in long tons. One long ton equals 2,240 pounds or 1018kg.

2. Multiply the length of waterline in feet (LWL) by 0.01 

[To convert metres to feet multiply by 3.2808}

3. Cube the result.

4. Divide the result of 1 by the result of  3.

The formula can be written like this: D/L = DLT (disp. long tons) ÷ (0.01 x LWL)³.

Even easier; you can do a search online and find a calculator that will do the sums for you, and some of them will convert your metric measurements in the process.

This online calculator makes it easy:

https://calculator.academy/displacement-to-length-ratio-calculator/

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Catamaran Beam to Length Ratios Explained: For Beginners

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Starting my sailing career something that struck me was the wast number of weird words and strange terminology, no longer was a rope just a rope, it’s a halyard or a sheet. In this article, I will explain one concept that is important to understand for anyone trying to buy a boat or for someone who wants to better understand the limitations of the vessel they already have.

Catamaran beam-to-length ratios are mathematical representations of the difference between the length of a sailing vessel and its width. There are multiple beam to length ratios, some impacts stability (Bcl/Lwl), and the amount of sail the vessel is able to carry. Others are used to calculate exterior space (B/L). In general, a narrow boat will be less stable but weigh less and cheaper to build.

Most modern catamarans have a beam to length ratio of >50%. You can easily calculate this on your own by following the steps below. But first, let’s check out some more terminology to make sure we really understand this ratio.

Table of Contents

Nautical Terminology

No matter how much you love the ocean, you will have limited success if you are unfamiliar with the words that go with adventuring out on it. I need to clarify some nomenclature before we delve into the ins and outs of ratios and catamarans (and monohulls).

• Beam overall (Boa): is the width of a boat at its widest point. The wider a ship’s beam, the more interior and exterior space. this allows for more gear and and better living accomodations.
• Draft: sometimes spelled “draught,” is the measure of how deep your vessel “sits” in the water. Catamarans have shallower drafts than monohulls, meaning they can sail in shallower waters and some can even be sail all the way up onto the beach, called beaching a cat .
• Catamaran: is a boat with twin hulls positioned parallel to each other. This design lends stability to the craft, and since there are two hulls, each can be narrower than a monohull without giving up stability. 
• Monohulls: boats with one hull. They derive their stability from a heavy keel and a wide hull, in comparison to a catamaran with two thin hulls separated far apart.
• Length over all (Loa): is measured from the aft to the bows including all gear such as bowsprits etc. To be compared with Length on waterline LWL.
• Length on waterline (Lwl) is the boats length measured on the surface of the water.

If you want to better understand catamaran construction and the impact of hull shape on performance and safety I suggest you read the book Catamarans; The complete guide for cruisers . It has helped me to better understand multihull dynamics in a more structured way than just googling. Gabo

Different Beam to Length Ratios

Hull centerline beam to waterline length (bcl/lwl) :.

The distance between the centerlines of the hulls divided by the waterline length on one hull is a good indicator of performance. It measures the points of the boat that interacts with the water. A higher ratio will give a higher resistance to capsizing and a lower ratio will increase drag due to wave interactions under the bridge deck.

Compared to the beam overall to length overall (Boa/Loa) that more or less only gives you an understanding of whether or not the boat will fit in a certain slip or what you will pay for a canal passage.

Hull Fineness Ratio (HFR)

Hull Fineness Ratio (HFR) is another name for Hull length-to-beam ratio . This is basically the same as the ratio mentioned above but only measures one of the hulls instead of the entire boat. And “fineness,” essentially, means “thinness.” Most cats have a ratio between 8:8 and 10:1 .

Boat Overall Beam (Boa) to Length Overall (Loa)

These are the exterior measurements of the boat. This ratio will not offer much other information than estimating marina fees and general boat size. To understand catamaran stability the two above ratios are much better since they show how the boat interacts with the water. It is in theory possible to have a very high Boa/Loa ratio but still have a boat that is very unstable due to having a low Bcl/Lwl ratio.

General Rules When Calculating Ratios

Ratios are exercises in long division. Since you remember your rules from math in school, you know that the order of the numbers in the equation makes a difference. 

Make sure you divide Beam by Length (B/L) and not the opposite!

If you mix them up you will get the wrong result and you might assess the stability of the boat incorrectly. And remember to stick to either meter or feet.

The formula looks like this:

B/L = Beam (in ft or meter) to length (in ft or meter) ratio

But how do you measure and from where to where? With those questions in mind, we add even more terminology to all this ciphering.

If, for instance, you have a bowsprit (the railing at the bow that extends past the deck), including this in your length measurement will skew your ratio. The extra length added by the largely cosmetic feature will not contribute to the stability or lack thereof of the craft, mainly because it does not touch the water.

So we look, then, at the measurements at the waterline .

Why Ratios Matters

If your Bcl/Lwl is too low, you will have an unstable craft. Adding a sail to the mix makes it even more so – if you have a ridiculous ratio of something like 1:18, wind in the sails at the correct angle will very likely capsize it. A wave of moderate size could do it, too.

If you want to know why catamarans capsize i suggest you read my other article ! Gabo

But a 1:1 Bcl/Lwl will make for a floating square with the maneuvering ability of a brick. A floating brick, sure, but it’s still a brick. This ratio is something you only see on really fast racing trimarans, since trimarans lift the windward hull the actual ratio when turning is half of that.

The fineness of a hull determines its speed and stability, which means that with every increase to one of those factors comes a decrease in the other. 3:1 seems to be the Goldilocks Zone for most monohulls. But since catamarans have two hulls separated wide apart the cat will be able to have thinner hulls while still maintaining high stability, a ratio around 8-12:1 is common on catamaran cruisers.

Final Thoughts

Casual sailors may never calculate Bcl/Lwl, B/L, or hull fineness ratio. But if you’re looking to buy a boat and want to better understand its sailing capabilities then these numbers will give you the ability to objectively compare different boats.

Speed and stability are the main factors governed by these ratios, and a change in one of them changes the other in the opposite direction. Generally speaking, the wider the beam, the more stable a ship is.

• Boat Building: Catamaran Design Guide – Catamarans Guide
• Marine Link: What Hull Shape Is Best?
• MB Marsh Marine Design: Length-beam ratio
• Multihull Dynamics: Six Kinds of Cats and Two Kinds of Trisi
• Ocean Navigator: Beam and Draft

Owner of CatamaranFreedom.com. A minimalist that has lived in a caravan in Sweden, 35ft Monohull in the Bahamas, and right now in his self-built Van. He just started the next adventure, to circumnavigate the world on a Catamaran!

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Catamaran Design Formulas

• Post author By Rick
• Post date June 29, 2010
• 10 Comments on Catamaran Design Formulas

Part 2: W ith permission from Terho Halme – Naval Architect

While Part 1 showcased design comments from Richard Woods , this second webpage on catamaran design is from a paper on “How to dimension a sailing catamaran”, written by the Finnish boat designer, Terho Halme. I found his paper easy to follow and all the Catamaran hull design equations were in one place.  Terho was kind enough to grant permission to reproduce his work here.

Below are basic equations and parameters of catamaran design, courtesy of Terho Halme. There are also a few references from ISO boat standards. The first step of catamaran design is to decide the length of the boat and her purpose. Then we’ll try to optimize other dimensions, to give her decent performance. All dimensions on this page are metric, linear dimensions are in meters (m), areas are in square meters (m2), displacement volumes in cubic meters (m3), masses (displacement, weight) are in kilograms (kg), forces in Newton’s (N), powers in kilowatts (kW) and speeds in knots. 

Please see our catamarans for sale by owner page if you are looking for great deals on affordable catamarans sold directly by their owners.

Length, Draft and Beam

There are two major dimensions of a boat hull: The length of the hull L H  and length of waterline L WL  . The following consist of arbitrary values to illustrate a calculated example. 

L H  = 12.20      L WL  = 12.00

After deciding how big a boat we want we next enter the length/beam ratio of each hull, L BR . Heavy boats have low value and light racers high value. L BR  below “8” leads to increased wave making and this should be avoided. Lower values increase loading capacity. Normal L BR  for a cruiser is somewhere between 9 and 12. L BR  has a definitive effect on boat displacement estimate.  

• Tags Buying Advice , Catamaran Designers

Owner of a Catalac 8M and Catamaransite webmaster.

10 replies on “Catamaran Design Formulas”

Im working though these formuals to help in the conversion of a cat from diesel to electric. Range, Speed, effect of extra weight on the boat….. Im having a bit of trouble with the B_TR. First off what is it? You don’t call it out as to what it is anywhere that i could find. Second its listed as B TR = B WL / T c but then directly after that you have T c = B WL / B TR. these two equasion are circular….

Yes, I noted the same thing. I guess that TR means resistance.

I am new here and very intetested to continue the discussion! I believe that TR had to be looked at as in Btr (small letter = underscore). B = beam, t= draft and r (I believe) = ratio! As in Lbr, here it is Btr = Beam to draft ratio! This goes along with the further elaboration on the subject! Let me know if I am wrong! Regards PETER

I posted the author’s contact info. You have to contact him as he’s not going to answer here. – Rick

Thank you these formulas as I am planning a catamaran hull/ house boat. The planned length will be about thirty six ft. In length. This will help me in this new venture.

You have to ask the author. His link was above. https://www.facebook.com/terho.halme

I understood everything, accept nothing makes sense from Cm=Am/Tc*Bwl. Almost all equations from here on after is basically the answer to the dividend being divided into itself, which gives a constant answer of “1”. What am I missing? I contacted the original author on Facebook, but due to Facebook regulations, he’s bound never to receive it.

Hi Brian, B WL is the maximum hull breadth at the waterline and Tc is the maximum draft.

The equation B TW = B WL/Tc can be rearranged by multiplying both sides of the equation by Tc:

B TW * Tc = Tc * B WL / Tc

On the right hand side the Tc on the top is divided by the Tc on the bottom so the equal 1 and can both be crossed out.

Then divide both sides by B TW:

Cross out that B TW when it is on the top and the bottom and you get the new equation:

Tc = B WL/ B TW

Thank you all for this very useful article

Parfait j aimerais participer à une formation en ligne (perfect I would like to participate in an online training)

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Trimaran Performance vs Hull Form

QUESTION: If I build a multihull with straight sides of plywood to make construction easier, how much performance would I lose compared to a more ideal shape?

Now let's compare that to the shape with a semi-circular bottom that has the least wetted surface. Superimposed, the two might look like this (picture on right). Although I might refer to this simple shape as 'a Vee-hull', the shape I prefer actually has a little wider flat bottom in order to provide useful buoyancy lower down - see later. See also the article on relative virtues of flat panel shapes .

Right away, for the same displacement, one can see that the boxy hull has more draft, is narrower at the waterline but will have more underwater (wetted) surface. In practice, the Vee hull is likely to be 10% heavier in construction, but that might only mean say 5% required increase in overall displacement as the deadweight (crews, supplies etc.) could double the dry weight.

Now we need to look at how a boat's resistance varies with its speed and this is much related to its length. About 140 years ago, a William Froude discovered that up to a Speed/Length ratio (SLR)* of about 1, resistance is mostly made up of frictional resistance and in such a case, would be directly proportional to the wetted surface. From a SLR of 1 to about 2 (for a typical multihull), there's an increase in hull resistance due to waves made by the hull through the water, and the wetted surface resistance, although still there, takes a more minor role.

Once over a SLR of about 3.0, the wetted surface is again on the increase (although wave resistance is still significant).  So for different boat lengths, here are the speeds we are talking about.

*SLR = speed (in knots) divided by the square root of Waterline Length (ft)

So, below the speed given for SLR=1 and above the speed given for SLR=3.0, the majority of resistance would be directly affected by the roughly 20% increase in the wetted surface for the Vee (or 15% for the Box shape) and if we add in the 5% weight penalty, this could go to about 24%. ( While these percentages might also apply for speeds well under SLR of 0.5 or over 3.5, they would in fact be somewhat less than that at the SLRs listed, as not all the resistance would be due to surface friction )

But between the two values listed, wave resistance grows to a peak at around SLR=2 (for the average multihull) and at this point, the narrower beam of the Vee hulls could lower wave resistance enough to offset the frictional resistance and therefore be quite efficient in the range between the two speeds listed above for each length.   The box or Vee'd shape would also offer less leeway and that will also help to compensate.

If we widen the hull at the bottom, the sides can become more vertical and this more box-like section can further lower the wave-making compared to the Vee-section we started out with, as it disturbs the passing waves even less.

Of course, there are other aspects to consider too—like having less interior space at the waterline with the V-hull and also, that the V-hull would initially sink about 15% more for each 100 lbs of extra weight loaded on. The extra draft of a Vee hull is sometimes used as a longitudinal keel to resist lateral drift and that 'might' annul the need for a dagger board or centerboard, although deep fins are clearly more efficient for sailing upwind.

But if you're content to sail in the speed range indicated by the table, which is surprisingly broad, and can accept the other compromises, there's definitely a case for using the box hulls and keeping it simple. Outside of that, expect speeds at around 10% slower at the low end and similar at the much higher end beyond SLR of 3.5.

Of course, even 'ideal hulls' are seldom perfectly semi-circular and the total resistance also depends on many other things, such as the hull ends and even air resistance etc., but this gives a general idea of speed performance for such differing hull shapes, assuming all other factors are alike and comparable. On another aspect, the deeper V-hulls will also have more directional stability but in turn, be harder to tack—helpful for long trips but not for short tacking.

True V-hulls are seldom used for the center hull of a trimaran as they offer so little space. However, they have been used for easy-to-build catamarans and trimaran amas, for owners ready to accept the performance sacrifices noted above. However, the more box-hull can be justified for the sake of easy building. and at least offers more foot space than the narrow Vee'd for a main hull.   [Deep, near vertical flat-sided hulls are also drier than Vee'd hulls and have more recently proven to have less wave drag].

Recent tests (2009) on a small prototype trimaran with this Box-hull form and flat bottom, demonstrated that performance can be surprisingly good and some of what is lost through increased wetted surface is indeed made up by the slimmer form. While this may not be true at low speeds (below say 4 kt), the flat of bottom may give enough dynamic lift over at least part of the hull length to offset the theoretically greater surface, and show that the higher speeds of a light trimaran will not be as adversely affected by this box form as one might first think.

Editors Note: For this reason, this simple-to-build form was chosen for the new W17 that has since proven to perform very well indeed. The added resistance at the very low end (say under 4 k) will still be there and will need some imaginative boat trimming and added light-wind sail area to overcome. But for a significant speed range above that, this boat, especially when built to design weight, is proving that the flat underbody surface can indeed offer a very clean running hull with some dynamic lift at higher speeds that some W17 owners are calling 'oiling', as it reportedly feels 'like the boat is running on oil'. Even with the very moderate cruising rig, a speed of 14.9 k has already been recorded (by GPS) in this mode, so this is impressive and promises to offer lots of fun. So for this particular design at least, the high end restriction of a boxy hard chine hull has been overcome by the relatively narrow hull, the flat of bottom and its low-rocker design profile. Compared to a round bilge, the box-hull also offers additional lateral resistance, so the dagger board wetted surface can be slightly reduced for another small speed gain.

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Catamaran vs Trimaran beam question

Discussion in ' Multihulls ' started by Red Dwarf , Jun 28, 2012 .

Red Dwarf Senior Member

Why are most catamarans, length divided by beam, near 50% while trimarans appear to be closer to 66%? Is there any reason you couldn't make a catamaran just as wide as a trimaran of the same length?  

Ad Hoc Naval Architect

You obviously mean beam overall, rather than demihull. The width apart of the hulls dictates the stability (for driving force v sail area) but also structural strength. Thus if you make the hulls further apart, the biggest influence will be the strength of the beams and being aluminium or mostly composite, the deflection is the driver. To minimise the deflection becomes harder with hulls which are further and further apart. Not impossible, but the compromises required can lead to a design that is not satisfactory. A tri-has hull spacing much closer, thus the structural loading is different and easier to control deflections. In a nut shell.  

Doug Lord Flight Ready

Beam A post by me from another thread-actual beam of a number of racing catamarans. Trimarans vary from less than square to over square. For instance Hydroptere is 1.36 times as wide as it is long. The Rave, Osprey and Hobie trifoiler are over square as well. There is a conviction among some that nearly square or over square cats don't tack well. Thats not my experience in RC models. Oversquare trimarans can tack very well. Doug Lord said: ↑ ================= 1) Hydroptere.ch- a. LOA 10.85m ( 35.58' ) b. Beam 10.4m (34.11 ) Beam 96% of length - 2) Decision 35 a. LOA 10.81 m ( 35.46' ) b. Beam 6.89 m ( 22.59' ) Beam 64% of length - 3) Alinghi AC cat a. LOA 33.5m ( 110' ) b. Beam 25.3m (83' ) Beam 75% of length - 4) AC 72 a. LOA 22m ( 72' ) b. Beam 14m ( 46' ) Beam 64% of length - In contrast, the new AC 45's are more conventional( beam wise)- 5) AC 45 a. LOA 13.45m ( 44' ) b. Beam 6.9m ( 22.6' ) Beam 51% of length - 6) Extreme 40's a. LOA 12.19m ( 40' ) b. Beam 7.92m (26' ) Beam 65% of length - 7) Whites Dragon(full flying foiler cat) http://www.boatdesign.net/forums/multihulls/whites-dragons-mini-hydroptere-esq-35062.html a. LOA 7m ( 22.96' ) b. Beam 4m ( 13.12' ) Beam is 57% of length ----- - Click to expand...

ChrisSR Junior Member

Hi Red Dwarf, Having built multihulls since the mid sixties, I remember the problems cat designers had in overcoming the stresses trying to tear the hulls apart. It was overcome much later in cats than in tris. So we have the stresses over a wider span in cats, and the compression load from the mast in the middle of the longer crossbeam, and the tension involved in trying to keep the forestay tight and straight,(absorbed by the main hull of the tri), and the underwing impacts with the waves. All easier to overcome in tris than cats by the limited knowledge of the time and most important, by trial and error by amateurs such as myself who were prepared to build ocean going boats that nobody had built before. Hey, the joy of youth! Cheers, ChrisSR  

TANSL Senior Member

Probably there are some parameters that I do not know because I have only projected 5 or 6 cats, passenger, cargo and fishing. I have always used the rules of Lloy's Register for "Special Service Craft." In them, torques supported by deck beams depend on several factors, displacement, waterline length and greatest breadth of the hulls at water line. I have seen nothing to suggest that these depend on the ratio LWL / Total Breath of the ship. I would be interested if someone knows, tell me where I'm wrong, for I am sure I have some error.  

Hi Tansl, I would see is as abeam with mast load in the middle(compression) and get it engineered by a Nav. Arch. familiar with multihulls,(not all Nav. Archs are)to handle the boat being droped off waves. Cheers ChrisSR  

Silver Raven Senior Member

ChrisSR said: ↑ Hi Red Dwarf, Having built multihulls since the mid sixties, I remember the problems cat designers had in overcoming the stresses trying to tear the hulls apart. It was overcome much later in cats than in tris. So we have the stresses over a wider span in cats, and the compression load from the mast in the middle of the longer crossbeam, and the tension involved in trying to keep the forestay tight and straight,(absorbed by the main hull of the tri), and the underwing impacts with the waves. All easier to overcome in tris than cats by the limited knowledge of the time and most important, by trial and error by amateurs such as myself who were prepared to build ocean going boats that nobody had built before. Hey, the joy of youth! Cheers, ChrisSR Click to expand...

ChrisSR said: ↑ I would see is as abeam with mast load in the middle(compression) and get it engineered by a Nav. Arch. familiar with multihulls,(not all Nav. Archs are)to handle the boat being droped off waves. ChrisSR Click to expand...

teamvmg Senior Member

most trimarans only use 2 hulls at a time  

Richard Woods Woods Designs

Ad Hoc has it pretty much in a nutshell, as he says. But also: Boat designers are conservative. If you draw a wide beam catamaran it looks very strange on paper. Looks a bit weird being built, but very "right" on the water. So early designs were narrow because it looked right on paper Then many early boatyards were building in sheds that usually launched monohulls. So doorways and slipways were narrow. One major reason why the Iroquois, for example, was the beam it was was because the Sailcraft door was 14ft wide. When I worked with Derek Kelsall his shed door was 20ft wide so we tried to keep boats narrower than that, if they were wider (like the 38ft wide GB4) they had to be assembled outside. The Gemini 105 was designed to suit a standard 14ft wide slip. Many European boats are less than 5m wide so they can fit in the French canals and so get to the Med without going out to sea. Wide bridgedeck cabinned catamarans are very heavy as there is so much extra deck area. And heavy means more expensive to build as all the weight has to go through the builders hands. On a monohull at least 30% of the weight is in a bolt on keel. So generally it is open deck boats that are wide. And then you have the beam strength problem. More width adds weight. Many racing boats are deliberately narrow so they can hull fly in lower winds. A trimaran has shorter cantilever beams than a catamaran The widest catamaran I have designed was 17ft wide on a 22ft waterline. It sailed really well. But as I said at the beginning, it looked very strange on paper, especially when I first drew it 25 years ago and compared it to its competitors. It was wider than the 26ft Telstar trimaran for example. Richard Woods of Woods Designs www.sailingcatamarans.com  

Thank you Richard that is very interesting. It also gives me more incentive to go ahead with my ideas for a catamaran. It is very much in the pipe dream phase but all ideas start somewhere.  

hump101 Senior Member

My Irens F40 cat is 11.7m long and 7.75m wide, open bridgedeck, all kevlar/carbon/epoxy. It was designed for offshore use originally, so not to fly a hull routinely, though with a 19m wing mast it will do so. It spins around the daggerboards easily, very maneuverable compared to a typical beach cat, but of course has a lot more inertia which helps. Width/length should be a balance of transverse/longitudinal stability requirements, as well as other considerations. On a fast multihull the longitudinal stability is only required when accelerating, as the wind is always forward, but if you only have transverse you are risking a pitchpole when accelerating/decelerating. So a race boat can be wider than a cruising boat, for example, but a race boat for use in light winds would want to be narrower to limit stability and fly a hull earlier. As such, decide how you intend to use the boat, and adjust the width accordingly.  

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hump101 said: ↑ My Irens F40 cat is 11.7m long and 7.75m wide, open bridgedeck, all kevlar/carbon/epoxy. It was designed for offshore use originally, so not to fly a hull routinely, though with a 19m wing mast it will do so. It spins around the daggerboards easily, very maneuverable compared to a typical beach cat, but of course has a lot more inertia which helps. Width/length should be a balance of transverse/longitudinal stability requirements, as well as other considerations. On a fast multihull the longitudinal stability is only required when accelerating, as the wind is always forward, but if you only have transverse you are risking a pitchpole when accelerating/decelerating. So a race boat can be wider than a cruising boat, for example, but a race boat for use in light winds would want to be narrower to limit stability and fly a hull earlier. As such, decide how you intend to use the boat, and adjust the width accordingly. Click to expand...

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