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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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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Dear Readers

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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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

Small Trimarans are Taking Off!

By bob gleason.

The daysailing trimaran market has grown tremendously in the last few years. This is largely because the three-hull platform certainly makes more sense for the way many people want to sail.

Compared to either a monohull or a catamaran, a trimaran is amazingly stable. This can be attributed to its length to beam ratio. Compared to other small boats, a trimaran will heel less and have more deck space. There are some trimarans that are as beamy as they are long and, of course there are trade-offs to consider. The added beam does add more stability and deck space, but how much is too much? The added beam does add weight, and may make a boat less maneuverable. The stability makes for a less athletic boat to sail, which allows for lounging around comfortably. Additionally, there is no need for a trapeze wire or hiking off the rail. Here is a very brief explanation of each of the small trimarans handled by The Multihull Source in Wareham, MA.

© WindRider.com

WindRider 17 WindRider  trimarans have been around since 1996. They are great recreational boats that are extremely durable, thanks to the rotomolded polyethylene construction. They are a little unusual to sail in that all the models have helm seats facing forward and you steer with foot pedals. The WindRider 17 is perhaps the most versatile in that it can take more weight and therefore more people, and it has a rotating rig with both main and roller furling jib. It is hard to hurt a boat that is almost impossible to capsize and can be sailed in knee-deep water. The smaller Tango (W10) and original WindRider 16 have simple freestanding masts with only a mainsail. Visit  WindRider.com .

Weta 4.4 Perhaps the fastest growing class of trimarans is the  Weta 4.4  (14’ 5”). The first ever Weta National Championships was held in Ft. Walton Beach, FL in March 2013 and it attracted a fleet of 16 boats. This class is great fun! The Weta sports all-carbon components (mast, beams, sprit, daggerboard, rudder and rudderhead; the rig is boomless) and a sail plan that is powerful yet easy to manage. The nylon reacher is roller furling and the jib and main are fully battened. At 220 pounds all up, this is an easy boat to rig and push around the beach singlehanded. The Weta was originally designed as a kids’ training boat but is now mostly used as a single or doublehanded daysailer. Wetas are primarily raced singlehanded, but the winning boat at this year’s Nationals was doublehanded. Visit  WetaMarine.com .

© Peter McGowan

SeaRail 19 New for 2014 is the  SeaRail 19 . Designed by Nigel Irens, it’s a pretty, graceful, daysailer that has enough room in the cabin that you could sleep there, although the space will be primarily used for sails and gear for either trailering or in-water storage. The cabin can be locked to keep gear safe. This boat is fun for singlehanding or with a group of three or four. The tiller is in front of the mainsheet and traveler, and the roller furling jib is self-tacking. This combination makes the SeaRail 19 a pleasure for relaxed sailing, and to it’s very easy to sail because you can tack and jibe without touching the sheets. The roller furling reacher adds the power many will like for screaming reaches. Visit  SeaRail19.com .

© smalltrimarans.com

UltraLight 20 The  UltraLight 20  from Warren Light Craft is pure sailing joy! Lightweight, state-of-the-art construction combined with a modern design allows for a fast yet stable ride. Each boat is built to order, allowing you to create a boat tailored to your preferences. The UltraLight 20 comes completely apart in minutes and can be car-topped or trailered. This boat is the brainchild of Ted Warren, who has made a name for himself in both kayaks and performance trimarans. Visit WarrenLightCraft.com .

© CorsairMarine.com

Corsair 750 The  Corsair 750  comes in both a daysailer version called the SPRINT and a cabin cruiser version called the DASH. These 750s (7.5 meters; 24’ 5” LOA) are a recent update from the earlier Corsair 24s. The added mast height and higher volume floats have made this a rocketship for a boat its size. The 750 rates closer to the Corsair 28 than either the Corsair 27 or 24. It is so much faster than the earlier 24s that it owes them over a minute a mile on the racecourse! As with all Corsair boats, the 750s are easy to trailer and easy to launch. Visit  CorsairMarine.com .

© MotiveTrimarans.com

Motive 25R Of all the smaller trimarans on the market today, the  Motive 25R  is truly a unique daysailer that can go much faster than the wind while seating a bunch of friends comfortably. If you have the money to spend on the latest, greatest, sexiest, all-carbon rocketship, the Motive 25R has to be considered. It may not be quite as quick at the launching ramp (the boat is actually easy to trailer and launch, but with only one built to date the systems are not refined yet), but on the water…watch out! Visit  MotiveTrimarans.com . Bob Gleason is the President of The Multihull Source in Wareham, MA. For more information, visit themultihullsource.com.

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Adastra - The Search for a Seakindly Fuel Efficient Vessel

By john shuttleworth - march 2012.

In recent years there have been a few attempts to find a new solution to achieving low fuel consumption in large ocean going yachts. In this article we will look at the design considerations and compare performances of some of the types of vessel in commission today. We will review aspects of the design of various vessels, not with a view to criticising them, but to show how our thinking has been guided by what has gone before, and then to give our ideas and design concepts on how we have taken up the challenge to reduce fuel consumption and still retain sea kindliness. Finally we will endeavour to demonstrate how successful our solution has been and to explain why the concept has worked so well.

Length to Beam Ratio

Most vessels in the superyacht category cross oceans at about 13 knots. At these relatively low speeds it has long been known that a thinner hull will be more efficient. This is because frictional drag dominates the resistance of the hull at low speed. In fact research conducted by the US Navy many years ago indicated that efficiency would continue to improve past length to beam ratios of 13.5.

Currently it appears that the limiting length to beam ratio of a monohull in the 40m range is about 7. Increasing the L/B ratio above 7 starts to become problematic for two reasons. Firstly the boat will have an increasing tendency to roll uncomfortably at sea and at anchor, and secondly in order to meet current safety standards the Vertical Centre of Gravity (VCG) will have to be kept low in order to increase the stationary stability to required levels. Keeping the VCG low increases the tendency to roll and limits the accommodation space. Most monohulls have to have some form of added stabiliser, usually using hydraulic fins, gyroscopes, or both. Palmer Johnson have recently introduced a new type of stabilisation for a monohull with a length to beam ratio of 7. They have added small outer hulls aft to increase the righting moment of the hull and further reduce rolling. The first vessel is due to launch in a year or so.

Catamarans in this size and accommodation range, on the other hand, have length to beam ratios of around 10 which is an improvement on 7 as seen on monohulls, however having two hulls in the water increases wetted surface for the same weight carrying ability. Thus a catamaran and a monohull of similar length with length to beam ratios of 10 and 7 respectively have similar fuel efficiency. The catamaran gains by having much more accommodation and is inherently very stable.

In the case of a trimaran the centre hull has no inherent stability of its own and all the stability is created by the outriggers. These vessels can achieve length to beam ratios in excess of 17 which has been shown to significantly increase fuel efficiency and has been proven by boats like Earthrace and Cable & Wireless which were stripped out record breaking machines, and now by the sea trial results of Adastra, which is a fully fitted out superyacht, with space for 6 crew and 9 guests. The comparisons in Table 1 and Fig. 1 show the differences in the length to beam ratios of a number of vessels in the 40m range.

Table 1. Length to beam ratio for various 40m vessels.

Fig. 1. length to beam ratio for five 40 m vessels.

The other key factor in achieving fuel efficiency is weight. The lighter the boat, the easier it will be to propel through the water. Composite materials and modern analysis methods allow us to design much lighter structures. The easily driven hull of the trimaran which needs much smaller engine/s can be significantly lighter than other types of vessel. This is shown in Fig. 2.

Fig 2. Displacement in tonnes of four 40m vessels.

Displacement to length ratio.

Naval architects use a formula (see appendix) to calculate the displacement to length ratio of a vessel. The lower the displacement to length ratio, the more efficient the vessel.

Table 2. Displacement to length ratio for four 40m vessels.

In a catamaran the displacement to length ratio of each hull will be less than a monohull, but the fact that there are two hulls in the water means that the catamaran performs like a monohull with displacement to length ratios of approximately 50 % higher than the displacement to length ratio of each hull. Hence the 40 m Catamaran will have similar performance to the Outrigger stabilised LDL 42m monohull and the 41,2 m LDL monohull. All of these vessels will use about half the fuel of the 40 m semi-displacement monohull.

Fig 3. Displacement to length ratio of four 40 m vessels.

Earthrace trimming bow up at speed..

The picture of Earthrace shows how some vessels trim bow up at speed. As the length to beam and the displacement to length ratios are critical in creating low drag, it is essential that the vessel remains trimmed flat throughout the speed range. The above image shows that the waterline of Earthrace has reduced to about 80% of the stationary waterline. By tank testing we have been able to develop a hull shape for Adastra that has near zero change in trim up to 30 knots, thereby using the full waterline length for maximum efficiency through the whole speed range.

Adastra at 23 knots trims level. Using the full waterline length.

Speed and powering.

Adastra could have a top speed of over 32 knots, but on balance we calculated that by keeping the top speed at a maximum of 23.2 knots, we could keep the engine weight on Adastra to a very reasonable 1.2 tonnes compared to the two engines on the Outrigger stabilised LDL monohull weighing 15.6 tonnes. This approach increases the efficiency considerably throughout the speed range because the boat is not carrying the extra weight of large engines. 23 knots is still a very respectable speed for a 40 m superyacht as shown in Table 3 and Fig. 3.

It is clear that the trimaran Adastra will be orders of magnitude more efficient than other solutions, on the basis of the light weight, the displacement to length ratio and the length to beam ratio.

Table 3. Six current versions of Power Yachts in the 40m range, showing published figures for top speed and HP. Arranged in order of top speed.

Shuttleworth designs "adastra" 42.5 m - top speed 23.2 knots - 1150 hp, fig. 4. top speed (red) in knots vs maximum hp/200 (blue) for six vessels. shows how efficient adastra is compared to other 40 m vessels., comparing fuel consumption for the same weight.

Accurate figures for fuel consumption for most yachts are very difficult to obtain, however using our own data we find that Adastra uses one third of the fuel of a semi displacement monohull of the same weight over most of the speed range. Table 4 shows how Adastra compares speed and fuel consumption for an equal weight semi-displacement monohull.

Table 4. Litres per hour for Adastra vs. same weight monohull

Fig. 5. speed in knots vs litres per hour for trimaran adastra and a semi displacement monohull of the same weight., comparing fuel consumption for the same length.

A semi displacement 40m monohull power yacht will use approximately 250 to 300 litres per hour at 12 to 14 knots. Published figures do not state whether they are for full fuel or empty lightship.

A 40m LDL monohull or as predicted the outrigger stabilised monohull, and a catamaran, will use half that at 120 to 150 litres per hour. The outrigger stabilised monohull is predicted to use 112 litres per hour at 13.5 knots. We assume that this is at light load.

At 12 knots Adastra uses a measured 38 litres per hour with 19 tonnes of fuel, and 29 litres per hour at light load (10% fuel)

At 13.5 knots Adastra uses a measured 65 litres per hour with 19 tonnes of fuel and 43 litres per hour at light load (10% fuel)

Comparing fuel consumption on a length for length basis, Adastra uses less than a seventh of the fuel at 12 knots of a similar length semi displacement monohull, and a third of an LDL monohull.

For maximum range Adastra has extremely low fuel burn at 10.5 knots. 23 litres per hour with 19 tonnes fuel and 17 litres per hour at 10% fuel load. So if time is not an issue the range could be 10,000 miles starting with 30,000 litres of fuel.

It is clear from these figures and the actual measured fuel consumption of Adastra, that if all the factors that improve fuel consumption are achieved in one vessel the gains that can be made are huge.

Fig 6. Fuel consumption at 12 knots with minimum and maximum fuel for four 40m vessels.

Accommodation.

At 40m LOA it is clear that the trimaran does not have as much accommodation as a 40m Semi displacement or planing monohull, however compared to the Hang Tuah or other similar LDL vessels the accommodation space is similar to Adastra. The outrigger stabilised monohull is an improvement because they have been able to widen the vessel at deck level, but they still do not achieve the same accommodation as the heavier wider designs.

If fuel economy is the aim, we suggest that LOA has to be much higher for the same interior volume. Due to the fact length and weight reduction are the key factors in achieving displacement to length ratios in the region of 20 and below, and length to beam ratios of 17 and above. In a superyacht like Adastra increasing the length of the main hull does not significantly increase the cost of the vessel, compared to the other costs of systems and accommodation, as long as the added length is in the bow, which is very low volume and low surface area compared to a conventional yacht.

In developing the Adastra concept we have found that when the LOA increases to 65 m and above, the same concept as Adastra can be retained, but with full standing headroom inside the wings enabling us to significantly increase the accommodation space in relation to the LOA.

Further Increasing the LOA to 75 metres and keeping a length to beam ratio of 17 it is possible to fit two double cabins side by side with a corridor between on the lower deck, and very large cabins on the mid deck extending into the wings. The additional length also enables us to maintain the displacement to length ratio required for maximum fuel efficiency.

Formulae referred to in the text.

The Displacement/Length ratio is determined by the following formula:

Displacement to Length ratio = Displ. / (0.01 x WL)3

Where: Displ. is the displacement in long tons (2240 lbs)

WL is the waterline length in feet.

The Length/beam ratio is determined by the following formula:

L/B ratio = WL / B

WL is the waterline length. B is maximum beam at the waterline.

Part 2 - Motion at Sea

General principles of motion, fig. 1. six degrees of movement.

Fig. 1 shows the 6 ways in which a vessel can move in a seaway. Comfort at sea will depend on how large these movements are, the frequency of movement and the accelerations. Slow movements can be less disturbing to crew than fast movements and high acceleration will cause discomfort and sometimes injury.

Safety is connected to sea kindliness, since a vessel that is easy on the crew will result in less fatigue and hence leave the crew more alert and energetic should a difficult situation arise.

The primary considerations are - how does the vessel get induced to move and how is that movement damped or controlled.

The main design aims for easy motion at sea are:

1. Reduce accelerations. 2. Increase inertia or resistance to movement, both fore and aft to resist pitching, and sideways to reduce roll. 3. Increase damping. 4. Increase the period of roll or pitch. i.e slow the movement down.

The study of these effects in the following discussion shows that with careful attention to the relationship between weight distribution and hull form, we can achieve a vessel that is seakindly and fuel efficient. The trimaran configuration has exceptionally good damping of movement thereby creating a vessel that is very seakindly, both at rest and powering through waves.

Roll accelerations are well documented as being the primary culprit that induces seasickness. All vessels are partly or only stabilised by the shape of the hull. In order to achieve fuel efficiency the trend is towards longer narrower hulls. In a monohull as the hull is narrowed the vessel becomes more prone to rolling and in all cases some means of roll damping is added to reduce this effect. A mathematical analysis of the hull forms in Fig. 2 shows that the LDL hull shape will have the least resistance to roll of the five hull forms. The catamaran and the trimaran have the highest, and although the trimaran has less of the outer hulls in the water than the catamaran, the wide beam gives the same or higher righting moment and hence the same or higher resistance to roll as the catamaran.

Fig 2. Underwater hull forms for five different vessels.

Conventional monohull yacht design theory states that ...." in general we observe that while greater beam will provide less roll angle, greater beam will also provide much more harsh, rapid, aggressive roll accelerations. Other factors being equal, stiffness (initial stability) varies as the cube of the beam. In other words, small changes in beam have a dramatic effect. We conclude from this that widening the water plane (increasing beam) will increase stiffness, but will at the same time reduce comfort and degrade seakindliness. " Michael Kasten 2012.

In a monohull this is true, but in a trimaran provided the outriggers are immersed to the correct depth, the wider beam does decrease roll angle but does not create worse roll accelerations. In fact the opposite is true. The very high initial righting moment in a catamaran and trimaran of the Adastra type has a huge effect in damping roll. This has been proven by many sea miles covered in large catamarans, and in the case of Adastra in radio controlled model testing in waves and now in the full sized vessel. The owner of Adastra describes the motion as stately, and "like an old transcontinental steam train". Basically a small slow easy movement from side to side.

This is caused by the hulls of a catamaran and a trimaran reacting to waves in a completely different way to a monohull.

Monohulls in Roll

Wind warrior at sea. ldl monohull in waves..

The reason that a vessel will roll is that a varying force is being applied to the hull side by the passing waves. Fig. 3 shows three different positions of a LDL monohull in relation to the wave fronts. If the pressure from the waves was fixed then the boat would roll to a fixed angle of heel and stop there. However the diagram shows that the pressure changes constantly. Therefore the boat will roll back and forth in an attempt to stabilise itself in relation to the changing force on the side of the hull. This causes the vessel to roll.

Fig. 3. Waves passing along hull of LDL monohull. Long thin monohull length/beam = 7. LDL type. Wavelength 12.5 m. wave height 1.5 m.

Ldl monohull and pj 42m supersport, bow on..

The photographs above show a typical low displacement to length ratio (LDL) monohull shape and the Palmer Johnson outrigger stabilised monohull (PJ 42m Supersport) side by side. Both vessels have a main hull length to beam ratio of 7, and it is clear that the outriggers on the PJ Supersport will reduce rolling, as the LDL hull on its own has very low resistance to rolling. In the standard LDL underwater hydraulic wing stabilisers have to be added, or a Gyroscopic system is required. These boats will still roll to some extent depending on the added damping system.

Catamarans in Roll

Catamarans have very high roll moment of inertia because most of the weight is concentrated in the hull. The theory behind why this reduces roll will be discussed later in this chapter. The high volume of the hulls and the high inertia prevent any significant roll. However, the varying loads on the two hulls does create sway. There can also be a sense of dipping the bow as the overall buoyancy of the platform changes. So the boat does not go through the water as if there are no waves, but the effect is different and rolling is virtually eliminated.

Moving diagonally to the direction of the waves, the catamarans two hulls are crossing the wave face at different times. This means that the motion of the catamaran can be more complex due to the period of the lifting force varying in an irregular manner.

Fig. 4. Waves passing along the hulls of a catamaran

Catamaran in big waves., sunreef 40 m catamaran..

Trimarans in Roll In earlier versions of the power trimaran concept like Earthrace and Cable & Wireless, the outriggers were designed to skim the water. This reduced drag by about 8% compared to the position of the outriggers on Adastra. However the problem with having very low initial stability is that when a wave lifts the windward outrigger the downwind one has to sink to the depth required to counteract the lift on the opposite side of the vessel. If the outrigger is just touching the water it will sink very rapidly and then slow very suddenly as it picks up buoyancy. The image below shows how the outriggers of Cable & Wireless skim the surface, and hence how easily the boat will roll with high accelerations.

Cable & Wireless trimaran.

Adastra on the other hand has both outriggers firmly in the water. As a wave lifts the windward hull, the opposite outrigger picks up buoyancy immediately and damps the roll. This is the same roll damping effect that is used in the PJ Supersport, except in Adastra the outriggers are 14 meters apart as opposed to 7.5 m, and are higher volume and more deeply immersed.

Fig. 5. Adastra (blue) with Cable & Wireless type outrigger in red.

Another difference between Cable & Wireless and Adastra is that Adastra's outriggers are longer and have more overall volume lower to the water which has a further damping effect on rolling.

PJ 42 m Supersport and Adastra - bow on view.

Comparing the PJ Supersport to Adastra in the above picture, with both boats at similar scale, it is obvious that the outriggers placed at 7 metres from the centre will have a massive effect in roll damping. Note that the main hull of Adastra with a length/beam ratio of 17 has no inherent stability. Not having to design the main hull with the constraints of creating stability from the hull form, allows us to design a hull that is optimised to reduce pitching, heave and yaw.

Fig. 6. Waves passing along the hull of Trimaran Adastra.

Fig. 6 shows how the wave pressures affect the main hull and the outriggers. Although there is a varying force on the three hulls, the forces on the outriggers are much lower than the main hull. The larger lateral pressure on the main hull is not enough to cause the boat to roll provided the outriggers are immersed to the correct depth and have the correct volume. It can also be seen from the diagram that the effect of varying force on the hulls will be virtually eliminated compared to a catamaran. With the long thin hull, directional stability is excellent and the boat will not have the same uneven motion that can occur in a catamaran.

Effect of Inertia on Roll

The next important element is inertia. This is the vessel's inherent ability to resist movement and, rather like a flywheel, it is dependent on the weight relative to the centre of rotation. If the weight is concentrated at the perimeter it will be hard to get moving and then equally can be hard to stop once it is going. The rate at which a vessel begins to roll and then stops rolling is therefore highly dependent on the vessel's weight distribution and beam. While the hull form dominates the reaction of the vessel to the waves, the distribution of the vessel's mass has a very significant effect on the momentum and accelerations as the boat responds to the effect of the interaction between the hull/s and the waves. The roll moment of inertia is a measure of the vessel's resistance to rolling. The higher the roll moment of inertia, the more the vessel will resist rolling and the more slowly it will return from movement to a neutral state. Moment of inertia is calculated using the square of the distance between the resisting mass and the centre of rotation (C of R.). The effect of the square rule is that weights far from the centre of rotation have significantly more effect in increasing the moment of inertia than those close to the C of R.

One way of increasing the inertia in a monohull is to raise the Vertical Centre of Gravity (VCG), but as previously explained this can only be done to a limited degree in an LDL because the vessel will not pass the required stability requirements of the classification societies if the VCG is too high. On a trimaran we prefer to keep the VCG low as it means a smaller and lower volume outrigger is required to achieve stability in waves. The total volume of the outer hull is determined by the lift required when the hull is following the face of a steep breaking wave. It can be reduced as the VCG is lowered and the beam is increased. The smaller the outriggers the less they will drive the pitching or yawing motion of the vessel which is discussed later in this article.

In a trimaran like Adastra we placed generators and engines for back up propulsion, and for maneuvering in the outer hulls. These weights are 7 m from the centerline and therefore create very high roll moments of inertia. A further benefit is that the generators are kept separate from the main hull and living areas. A weight positioned 7 metres from the centre of rotation has a roll moment of inertia of 49/14 = 3.5 times the roll moment of inertia of the same mass at 3.75 metres from the centre of rotation, as in the PJ 42m Supersport LDL monohull. It is not surprising then that we find that Adastra extremely stable at anchor.

In a catamaran most of the weight is in the two hulls, and so this type of vessel has a very high roll moment of inertia and is very resistant to roll accelerations. The effect of this is that the catamaran is very stable in long wavelengths where the hull will follow the wave face in a gentle manner while the monohull will always roll to some degree. Adastra will also follow the wave face in a similar manner to the catamaran without the complex swaying movement as described in the section above on catamarans in roll.

The next most important movement in causing uncomfortable motion is pitching. This is where the vessel is rocking in the fore and aft direction. High accelerations and large movements in this direction can be very disturbing and in extreme cases can cause injury due to the high G forces that can be generated.

In a similar way to the factors that cause and control roll, in pitching the hull form reacting to the wave movement along the hull or hulls is the primary factor inducing the motion. The displacement of the vessel and the distance of the centre of gravity from the centre of rotation (C of R) will be the main factor in creating damping. The volume of the forward part of the vessel and its relationship to the volume aft will also pay a part in damping pitching.

Effect of Inertia on Pitching

The pitch moment of inertia is the sum of the moments of inertia of all the weights in the vessel x the square of the distance of each weight from the C of R.

It is a common misconception that a vessel will pitch either around the centre of Gravity (C of G) or the centre of the waterplane area. A fairly simple calculation of the relationship of forward momentum and rotational momentum as a vessel accelerates shows that the centre of rotation moves aft from the centre of the waterplane area, and eventually ends up about a quarter of the waterline length forward of the stern.

It is clear then from the diagram in Fig.7 that concentrating some weight in the vessel further forward will increase the lever arm of the pitch moment of inertia, and since that effect is proportional to the square of the distance between the C of R and each weight, the effect of pitch damping can be quite dramatic. This approach has been proven on the sea trials of Adastra at full size. It is possible sometimes to create a resonant pitching frequency in the vessel that can match the frequency of the wave fronts, and then the boat will pitch more. This can be controlled by moving weight if necessary. In the case of Adastra we have fuel tanks distributed along the bottom of the hull with a capacity of about twice the normal full fuel load. This means that weight (fuel) can be moved along the hull fore and aft to create optimum trim and/or pitching control.

Fig. 7. Adastra - Distance of Centre of Gravity (C of G) from centre of rotation (C of R) at speed.

The effect of hull shape and position on pitching.

In the case of a trimaran it might seem sensible to put the outriggers right at the aft end of the vessel so that the effect of the two outer hulls pitching forces are completely damped by the inertia of the main hull. The picture below shows the approach taken in the Earthrace design of pulling all the weight aft, including the engines. We believe that this will cause the boat to pitch more than it would if the outriggers, accommodation, wing beams and engines were further forward.

We have found that the correct size outriggers do not have the power to make the vessel pitch even if placed further forward. This means that the outriggers can be placed to create maximum stability, and further away from the C of R thereby increasing the pitch moment of inertia of the vessel.

The image below shows the bow of Adastra"s outrigger and it is visibly obvious that the upward lift of the bow will have little effect on the pitching of the main hull. This can also be shown mathematically.

Catamaran and Adastra outrigger bow on view.

The catamaran on the other hand has two bows which are more buoyant than the single bow of the trimaran as the length to beam ratio of the trimaran is in the range of 17 to 20 as opposed to 10 for both of the catamaran hulls.

In the image below it is again visibly clear that the very long thin main hull bow of Adastra will cut through the waves rather than lift upwards. The amount of lift induced by the bows will be significantly less than any of the vessels shown.

LDL monohull, PJ supersport, and Adastra bow on views.

The other factor of induced motion in pitching is the way the wave will lift the stern. So even if the bows of the vessel are lengthened and made narrow, the stern could have too much volume and hence lift the aft end of the vessel and dip the bow. Therefore it is essential to keep the centre of gravity far enough forward to allow the stern to work with the bow to reduce rather than increase pitching.

The long thin main hull of Adastra has the least tendency to lift in a wave of any vessel because of the relatively thin sections forward and aft. In seas with a wavelength up to approximately 70% of the waterline length and a typical maximum height 3 metres she will slice straight through the waves with very little pitching. The outrigger volume is balanced so that they are just large enough to create sufficient roll stability but slender enough to cut through the waves and thereby induce very little pitching motion into the boat. As the wavelengths get longer she will start to follow the wave surface, but with an easy motion which can be further controlled by choosing the best speed and angle to the waves for the conditions.

The image below shows how large the bows of a semi displacement vessel are compared to the LDL, the catamaran and the trimaran. The reason that this does not cause as much pitching as would appear to be the case from the hull form, is because the pitching moment of inertia is high, and the large weight of the vessel damps the movement.

Semi displacement yacht shows volume of bow.

If we refer to the bow on views of the vessels in the previous sections, it will be visually apparent that the hull of Adastra, with the near vertical hull sides and very narrow long thin shape will be lifted by the waves the least of any hull shown. This can be shown mathematically by calculating the rate of increase of volume with hull immersion, and comparing that for different vessels. But the mathematics only shows what the images reveal.

The narrow beam of the main hull will allow waves to rise further up the hull sides without lifting the vessel. Wider hull vessels will heave much more than thin hulls. In heavier wider hulls some of the effect of heave will be counteracted by the forward momentum and this will reduce heave, but in a relatively light vessel like Adastra the long thin hull and the forward momentum combined will control heave.

Surging is the tendency of the vessel to accelerate and decelerate fore and aft. In order to achieve fuel efficiency the vessel needs to be as light as possible. As the boat becomes lighter its ability to drive through waves without decelerating decreases. By making the hull very long and thin, this effect is reduced. Thereby reducing surge to a minimum.

A long thin hull with a skeg aft has very good directional stability. This will reduce yawing to a minimum. The most serious form of yawing is broaching. Broaching is caused by the pressure on the bow slowing the boat, while at the same time the overtaking wave pushes the stern around from aft. The long thin bow of the trimaran cuts more easily through the water reducing this breaking effect on the bow. The lower drag of the hull allows it to move more easily forwards as the wave pushes from aft, and the long hull will track in a straight line down the wave face. This effect has been proven many times in large racing multihulls.

The movement of Adastra sideways in waves will be similar to a long narrow monohull vessel. In normal conditions swaying will not be a significant cause of discomfort in either of these types of vessel. In large breaking waves the ability of the vessel to drift sideways when struck by a breaking crest can be an important factor in dissipating the energy of the wave impact.

Inertia of forward movement

With all vessels the effect of forward movement has a gyroscopic effect (like riding a bicycle), and that creates more inertia and reduces sudden accelerations. Due to all of the points discussed so far Adastra is more easily driven than the other vessels considered in this article, so she can move faster through waves than vessels with a wider hull. This enables her to use inertia created by forward momentum to dampen induced accelerations still further, and gives the captain of the vessel a wider range of speeds to choose in order to achieve minimum pitching.

The search for greater fuel efficiency appears to be limited in the monohull form by the difficulty of creating a seakindly vessel with narrow beam. The solution to use small outriggers to reduce roll on a LDL monohull, still does not make the vessel as efficient as a power trimaran.

Power trimarans can be made to be very seakindly, provided the full benefits inherent in the three hull configuration are taken into account at the design stage, and careful attention is paid to the effect of mass distribution and hull shape on the inertias and driving forces induced by waves.

Very different hull forms are possible in a trimaran compared to monohulls which creates new possibilities for efficiency and comfort at sea.

Adastra has proven to be extraordinarily fuel efficient and in the words of her owners is also proving to be "a good sea boat, and a joy to be aboard".

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length/beam ratio of around 20

Discussion in ' Multihulls ' started by PetterM , Apr 21, 2015 .

PetterM Senior Member

I am looking for resistance data/prediction methods for very slender hulls, with length/beam ratio of around 20 and Froude number of up to 0.8-1.0. Anyone?  

daiquiri Engineering and Design

Use Michlet, it seem to be pretty reliable in that L/B range: http://www.boatdesign.net/forums/design-software/michlet-9-32-released-50211.html  

hump101 Senior Member

For such slender hulls you wouldn't be far out with just using ITTC curve and allowances, wavemaking will be minimal provided you aren't dragging a transom.  

That is true. The resistance will be almost entirely frictional. So the easiest method is to just calculate the wetted surface of the hull and the friction coefficient, and get the resistance. It will be given by the formula: R = 0.5 rho V^2 Awet Cf.  

Mr Efficiency Senior Member

I assume, (maybe shouldn't !) these could be hulls of a catamaran ? If so, the issue of wave interference comes into play.  

Ad Hoc Naval Architect

Mr Efficiency said: ↑ I assume, (maybe shouldn't !) these could be hulls of a catamaran ? If so, the issue of wave interference comes into play. Click to expand...

oldsailor7 Senior Member

The late Edmond Bruce extensively researched L/B ratios in non heeling situations. He showed that form drag only increases as the displacement increases. Skin friction drag increases as both displacement and waterline length increase. Wave induced drag is bad At low L/B ratios , but improves very greatly from about 7/1, to 12/1 where, it practically disappears. Improvement continues until it reaches it's limit of diminishing returns at about 20/1 providing the displacement, (weight) is kept light. The super light Tornado Cat, at 20/1 is a case in point. A compromise is reached by designers of cruising Cats and Tris, usually between 8/1 to 12/1, and performance multis from 13/1 to 20/1. Interference drag between the hulls of multis is not usually a problem these days as modern cats and tris have much wider overall beams than in the early years of multihull design.  

oldsailor7 said: ↑ Interference drag between the hulls of multis is not usually a problem these days as modern cats and tris have much wider overall beams than in the early years of multihull design. Click to expand...

Gary Baigent Senior Member

On square and oversquare sailing multihulls (modern and also advanced for their time "old" designs) of fine hull beam/length ratios. like above 12/1, wave interferance is a non issue - as OS7 writes - and with lifting foils, you can say it doesn't exist.  

Leo Lazauskas Senior Member

Try Michlet 9.33 for a start. http://www.boatdesign.net/forums/design-software/michlet-9-33-released-52865.html It can handle monos and cats. If you want near-field effects (for a monohull) try Flotilla 6.2 http://www.boatdesign.net/forums/design-software/flotilla-6-2-released-50116.html  

Gary Baigent said: ↑ .... of fine hull beam/length ratios. like above 12/1, wave interferance is a non issue .... Click to expand...

Now Ad Hoc, kindly explain that graph a little, are the 4 dotted lines the resistance of each hull of a catamaran, and S/L is what ?  

Mr Efficiency said: ↑ .. kindly explain that graph a little, are the 4 dotted lines the resistance of each hull of a catamaran, and S/L is what ? Click to expand...

Alright, but Gary Baigent specified "square or oversquare" catamarans, so the S/L could be 1.0, how does that look on the graph ? Seeing the others are very convergent at the higher Fn, is it similar there too ?  

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Mr Efficiency said: ↑ Alright, but Gary Baigent specified "square or oversquare" catamarans, so the S/L could be 1.0, how does that look on the graph ? Seeing the others are very convergent at the higher Fn, is it similar there too ? Click to expand...

Length vs Beam - will this cause any problems?

Lengthen beachcat beams.

What’s formula for estimating catamaran speed? Speed from length better than from design?

F-18 genny halyard length?

add length to rudder shaft or shorter blade?

Tris and Proas - realtive lengths of vaka and ama

Small cat crossbeam questions

Limits to the beam of a catamaran ratio ?

Design of wood epoxy trimaran beams

Cross Beam thoughts for small Tri

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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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