Spectacular sunsets in the Pacific turn the horizon into a brilliant spectrum of gold and orange colors.
Copyright © 2006, 2008 by Gregor Tarjan. Click here for terms of use.
performance, yet desire high daily averages and passage times, which should be as short as possible. When choosing a large multihull, sailors look, above all else, for safety and comfort, long before the consideration for flat-out speed comes into the discussion. Nevertheless, performance is a highly important design consideration. No catamaran sailor wants to sail slower than a same length ballasted keelboat. Below are some EVALUATION & COEFFICIENTS useful coefficients, which will help compare monohulls and multihulls objectively.
Bruce Number (BN)
below "Indigo," a magnificent Wormwood 70, sailing in sparkling Caribbean waters.
Various multihull characteristics and design features can be expressed in mathematical formulas. Their results are crucial and will give prospective owners a basis of comparison between different types of catamarans. These numbers are important, as they eliminate ambiguity and clearly display various advantages or concessions of a design, which would be hard to quantify any other way. Mathematical coefficients not only will provide insight into a boat's performance in varying conditions, they also reflect concerns about loads to be carried safely, speed and stability.
We have already mentioned the Displacement/Length and Sail Area/ Displacement ratio in our chapter on Multihull Advantages, illustrating the point of a multihull's efficiency. Let's look at some other coefficients that give us an indication of a boat's performance.
What is performance and how do we really measure it? Most people who buy a cruising catamaran are not really interested in racing
The Bruce Number is very similar to the Sail Area to Displacement ratio although the formula is slightly different. It is the square root of the sail area in feet, divided by the cube root of the boat's displacement in pounds:
SA = upwind sail area (mainsail and 100% jib)
Displ = weight of the boat in pounds
Similar to the Sail Area to Displacement ratio, the higher the coefficient the faster the boat and better is its performance in light air. Typically a BN of 1.1 will be the threshold between fast and more sluggish multihulls. A heavy displacement monohull might have a BN of .7, whereas a modern cruising catamaran shows a BN of 1.3. Offshore multihull racers can have BNs of 2.0 and higher. The BN will also tell us about a catamaran's ability to withstand stronger winds before reefing. A boat with a higher BN is usually overcanvassed in strong conditions and will have to be reefed earlier than one with a lower coefficient.
On the other hand, they will be able to produce more "power" than their counterparts in lighter winds and perform better.
Sail Area to Wetted Surface (SAWS)
SA/WS = Sail Area Wetted Surface Coefficient
SA = upwind sail area
WS = total underwater surface area (hull and appendages)
This formula simply divides the upwind sail area of the boat (mainsail and 100% jib) by the wetted surface. This coefficient will give us a statistical indication of the multihull's lightair performance since in low wind conditions skin friction becomes an important factor. Monohulls can have coefficients of at least 7% more than multihulls.
Hull Fineness Ratio (HFR)
The Hull Fineness Ratio, known as the hull's beam-to-length ratio, is an interesting number. It is derived by simply dividing the waterline length of the hull by the waterline beam of the hull.
Max. WL/Max. Beam WL = Hull Fineness Ratio Max. WL = length of the hull at waterline in ft. Max. Beam WL = beam of the hull at the waterline in feet.
Monohulls, when compared to multihulls, have low hull/fineness ratios. In Part 1 of this
On the other hand, they will be able to produce more "power" than their counterparts in lighter winds and perform better.
book, discussing "Efficiency," we saw that ballasted keelboats are limited to Archimedes' principle of hull speed (1.34 x VWL). Multihulls do not have these theoretical barriers, because their hulls are narrower.
The thinner the hull the faster it will be able to travel through the water. But, attention! It will also carry less unless you are on a mega cat. Typically, a 40' cruising catamaran's HFR will range from 8:1 to 10:1. Dennis Conner's above While sailing under spinnaker and experiencing virtually no roll at all, guests will always find a comfortable spot to relax on the foredeck, an impossibility on a monohull.
There are various methods of calculating the transverse stability of a catamaran. One of the simplest and most utilized techniques is establishing a relationship between the height of the Center of Effort (CE), displacement, beam and sail area. Multihull designer, James Wharram added safety factors of 20% to compensate for gusts and the dynamic environment of the ocean. Another method is described in the text below.
Multihull Stability & Capsizing Moment d - Displacement (kg) x half beam (m) max ~ Sail Area (sq m) x Height of Center of Effort (m)
P max = maximum pressure exerted onto sails
Multihull Stability & Capsizing Moment
P max = maximum pressure exerted onto sails
height of sailplan CE
half overall beam (half hull beam)
height of sailplan CE
half overall beam (half hull beam)
racing cat "Stars and Stripes" had a 16:1 HFR. Of course, the larger the boat, the narrower the hulls will become in comparison to its length. For example, the HFR of a 100' luxury catamaran may be 12:1, providing it with a high speed potential. However, monohulls can show HFRs of 3:1, though the comparison is complicated as their angle of heel affects the measurement.
One has to be very careful when analyzing the Hull Fineness Ratio of a cruising catamaran, because other factors such as the actual shape of the hull cross sections (Prismatic Coefficient, PC) can throw the analysis off balance. Go-fast sailors like to think that fine hulls are always fast. That is not necessarily true because a slim hull could have a large underwater volume, thus slowing it down. Consequently, a wide waterline-beam hull could have less drag than a narrower one. It could have a shallow underbody (low PC), which would be beneficial to load carrying (Pounds Per Inch Immersion Number, PPI) and early surfing characteristics at speed.
Stability Coefficient (SC)
This mathematical formula has been devised by the distinguished catamaran designer and sailor James Wharram and his team. This coefficient analyzes a multihull's ability (in a static environment) to resist capsizing due to wind.
( 0.682 VW x (.5 Boa) ) x .555 = CW .00178 x SA x h
W = Wind speed, apparent, in mph CW = Critical Wind Speed to capsize in mph SA = upwind sail area in sq ft. h = height of Center of Effort (CE) of total sail area
Boa = Beam overall
This formula will tell us how much wind it will take to overturn our multihull. By instinct we will know that a catamaran with a wide stance and a conservative sail plan will be very stable offshore. The SC formula will inevitably illustrate that a wider beamed catamaran with a tall sail plan will be as resistant to wind induced capsize as a short-rigged, narrower boat. This is not so if one considers the chaotic environment of waves and the real world of heavy weather sailing. It is interesting to note that a wide beamed boat (regardless of the SC) is more resistant to capsize in seas due to the effects of a higher moment of inertia. In an open-ocean environment, which is everything but static, the SC formula has little meaning. Nevertheless, it serves as a good basis to evaluate stability as a factor of wind force.
below When the wind suddenly comes up, all that is needed is a couple of turns on the jib furler to quickly reduce the headsail size. The catamaran will hardly sail any slower, but feel more comfortable.
Wide hulls and a large overall beam will increase the overall righting moment of a catamaran. A word of caution: Excessive beam will reduce the fore and aft stability. Designers strive to compromise hull fineness ratios, place heavy weights towards the CG (Center of Gravity), and engineer hull and overall beam to achieve a seaworthy balance, which is safe, yet provides ample liveaboard accommodations.
Catamaran Stability Considerations
Catamaran Stability Considerations
Diagonal Stability & Beam-to-Length Ratio (BLR)
Stability of a multihull, or the resistance to capsize, should be seen as three components. Athwartship Stability is one well-publicized type and the one often talked about. The other much more important types are Fore and Aft and Diagonal Stability. Fore and aft stability is established by the relationship between the boat's waterline length and the distance between the hull centerlines. It will reflect the catamaran's resistance to tripping. This relationship should be in the vicinity of 39% to 42%. For a seaworthy cruising multihull it is important maintain the proper ratio between length and beam, which, in turn, balances equal amounts of athwartship with diagonal stability. The goal should be to prevent the possibility of a sudden discrepancy of powers between fore and aft and sideways resistance. Most of today's multihulls keep these two component forces in equilibrium, making them extremely seakindly and safe.
Some early design multihulls were very narrow, partly due to the material limitations of that time. But things have changed. Contemporary composite construction allows designers to build wider boats without compromising stiffness. Production catamarans of today have a wide stance and have the benefit of greater safety margins in gusty wind conditions than their older cousins. Multihulls are sophisticated structures and true modern miracles. They provide a more comfortable ride and more interior room. Thanks to modern materials they weigh less and perform better than catamarans built only 10 years ago.
Some catamarans, especially production boats, which are very popular in the charter fleets, are growing wider by the year. The businesses who rent these beamy monsters adore them. Lots of room plus open decks are ideal for clients and the bigger (wider) the boat, the more paying guests can share the fees. But there certainly is a limit as to how wide is too wide. Extreme beam can be dangerous. It can lead to instability fore and aft and to excessive bridgedeck slamming, as the relative distance from the bridge deck to the water will decrease with an increase in width. A vessel with excessive beam might seem stable athwartships, but it will compromise overall stability.
We know that multihulls can, in extreme cases of seamanship error in wild storms, be thrown over from any side - front, back and beam-on. The best examples of this phenomenon are racing multihulls, especially Formula 1 trimarans, which have fine hulls for speed and huge sailplans to provide driving power. They are initially extremely stable athwartships (High Beam-to-Length Ratio), but have a tendency to become unstable fore and aft. They will surf down waves and reach a point where the power of the sails, and speed, will exceed the ability to keep the bows out of the water and the boat will pitchpole. This is the reason why catamaran designers usually draw their multihulls with a Beam-to-Length relationship of between 50% and 55%. The longer the vessel the lower that percentage becomes.
I am currently involved in the "Gemini" project, which presents an example. It very well might become the world's largest sailing catamaran. She will have an overall length of 145 feet, yet her beam will "only" be 54.4'.
Please, don't worry. "Gemini" will not be tender and tip over in the slightest breeze. On the contrary, this monster will be one of the most stable craft afloat, although the beam-to-length relationship is only 37%. The relatively low beam-to-length ratio also involves the fact that the boat would be too heavy and building costs would be prohibitive if she were to have a standard 52% BL relationship. Most importantly, could you imagine turning a 75-foot-wide boat?
above Asymmetric spinnakers on furlers are great inventions. They add instant sail area, yet can be doused in a matter of seconds when the wind picks up strength.
above Although this Edel 35 was a good-looking and popular catamaran, it suffered from excessive bridgedeck pounding, which was caused by only several inches of clearance between the saloon's underwing and the sea.
Obviously there is a sweet spot in the beam vs. stability question. Designing too beamy a boat will also necessitate more freeboard to preserve bridgedeck clearance which, in turn, will increase windage and complicate maneuvering. Unless sophisticated aramid construction methods are utilized, more beam will also add more weight and stress to the structure. Adding more mass will, to a certain point, help make the boat more stable, but where do we stop? Is it better to add weight or width to make a boat stiffer? Of course, both characteristics are interrelated as a beamier boat normally is also heavier. Just adding weight to a catamaran simply to make her more stable will not pay off. Consequently, making a boat too wide might increase living space yet it will also burden the structure, require a beefier manufacture, and yield an even heavier boat. Needless to say, a boat which is too wide will also create practical restrictions such as maneuvering, the ability to haul the vessel and much higher building costs.
Beam has a great effect on bridgedeck clearance, which is one of the most vital characteristics of a good cruising catamaran. As standard practice, the well-known rule of 1" of bridgedeck clearance for each foot of beam was a safe way to prevent excessive wave slap. The wider the beam the more the relationship changes and the necessary height of 1" per foot of beam needs to be increased to 1.3" or more. In the extreme case of overly square boats, that number will have to be closer to 1.8" per foot of beam. This will have a negative effect on any seaworthy multihull that has a bridgedeck saloon. The wide beam will necessitate a high cabin sole to remain a safe distance from the waterline. In order to provide standing headroom, the coachroof might be higher than practical, which could result in a boxy, high-windage multihull. Not only will this be unattractive, but also raise the Center of Gravity (CG) which really should be kept as low as possible.
More overall beam on the other hand (given that there is still sufficient bridgedeck height) has a less known benefit, as it reduces the possibility of hull-wave interference, which is particularly important for fast designs. The wave interaction between the hulls can lead to additional resistance, and especially in an agitated sea state, the formation of wave crests can pound the bridge deck. Most early narrow-beamed catamarans suffered from this phenomenon,
Ultimately, a boat's design has a major influence on its ability to stand against the forces of nature, and to keep occupants safe. Manufacturing excessively wide catamarans is like trying to market monohulls with super deep-draft keels. Both are totally impractical. We designers have to make sensible compromises and learn from past experiences of what has worked at sea by balancing the benefits of a wide boat with its disadvantages.
below This narrow-hulled Outremer 64 Light has completed her third circumnavigation with the same owners. Note the smooth underwing clearance, lacking any protrusions or steps.
"A great cape, for us, can't be expressed in latitude and longitude alone. A great cape has a soul, with very soft, very violent shadows and colors. A soul as smooth as a child's, and as hard as a criminal's. And that is why we go!"
~ Bernard Moitessier
Copyright © 2006, 2008 by Gregor Tarjan. Click here for terms of use.
Dinghies, windsurfers and every imaginable type of water toy can be stored conveniently on large catamarans and easily launched from the wide transom steps for shore-side pleasures. Note the twin life rafts located in special compartments on the massive aft crossbeam.
Copyright © 2006, 2008 by Gregor Tarjan. Click here for terms of use.
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