resistance of 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. 

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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

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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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Numerical analysis of the interference effects on resistance, sinkage and trim of a fast catamaran

• Original article
• Published: 16 September 2014
• Volume 20 , pages 292–308, ( 2015 )

Cite this article

• Wei He 1 , 3 ,
• Teresa Castiglione 2 ,
• Manivannan Kandasamy 1 &
• Frederick Stern 1  

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The purpose of the present paper is the numerical investigation of the interference phenomena between the waves generated by the individual hulls of a catamaran. The study focuses on the effects of both Froude number and demi-hull separation distance on resistance and on sinkage and trim. The numerical simulations are carried out by the URANS solver CFDShip-Iowa V.4 and, to assess the capability for prediction of resistance, sinkage and trim of the URANS code for twin-hull configuration vessels, a verification and validation study is performed for global as well as for local variables. A very good agreement between the numerical results and the experimental data is obtained, and the validation study demonstrates the high level of accuracy of the current predictions, which are used to have a better insight into the interference phenomena. In accordance with the experiments, within Fr  = 0.45–0.65, the catamaran has a significantly higher resistance coefficient compared to the mono-hull; furthermore, the C T value increases with decreasing the separation distance between the twin hulls. On the contrary, at Fr lower than 0.45 and at Fr higher than 0.65, the effects of hull spacing on resistance as well as on sinkage and trim can be neglected. The flow field characteristics, wave pattern, wave cuts and pressure distributions are analyzed through the CFD analysis. Finally, the effects of the Reynolds number on resistance are also investigated and results show a small decrease in interference with increasing the Reynolds number.

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Parametric investigation of the effects of deadrise angle and demi-hull separation on impact forces and spray characteristics of catamaran water entry.

Roya Shademani & Parviz Ghadimi

Hydrodynamic Analysis and Propulsive Arrangement of Two Corvette Hulls with Different Operational Profiles

CFD Investigation into the Wave Added Resistance of Two Ships

Abbreviations.

Beam of the demi-hull (–)

Frictional resistance coefficient (–)

Pressure resistance coefficient (–)

Residuary resistance coefficient (–)

Total resistance coefficient (–)

Catamaran total resistance coefficient (–)

Mono-hull total resistance coefficient (–)

Experimental data value

Comparison error

Froude number \(\left( { = {U \mathord{\left/ {\vphantom {U {\sqrt {gL_{\text{pp}} } }}} \right. \kern-0pt} {\sqrt {gL_{\text{pp}} } }}} \right)\)

Acceleration of gravity (= 9.81 m/s 2 )

Water depth (m)

Interference coefficient (–)

Turbulent kinetic energy (J/kg)

Model length (m)

Normal direction

Order of accuracy, pressure (N/m 2 )

Estimated order of accuracy

Richardson extrapolation order of accuracy

Estimated order of accuracy \(\left( { = \frac{p}{{p_{\text{th}} }}} \right)\)

Grid refinement ratio

Ratio between solution changes

Reynolds number \(\left( { = {{\rho UL} \mathord{\left/ {\vphantom {{\rho UL} \mu }} \right. \kern-0pt} \mu }} \right)\)

Total resistance (N)

Catamaran total resistance (N)

Mono-hull total resistance (N)

Separation distance between the hulls [m], wet surface area (m 2 )

Simulation value with grid j

Non-dimensional separation distance (=  S / L PP )

Model draft (m)

Model velocity components (m/s)

Data uncertainty

Facility bias uncertainty

Grid uncertainty

Iterative uncertainty

Numerical simulations uncertainty

Validation uncertainty

Absolute earth-fixed coordinates

Non-dimensional coordinates

Turbulence model constant (–)

Numerical error computed by Richardson extrapolation

Turbulence dissipation rate (J/kgs)

Difference between solutions i and j

Free surface level-set function

Wavelength (m)

Water density (kg/m 3 )

Non-dimensional sinkage

Highest wave elevation (m)

Specific turbulence dissipation (1/s)

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Acknowledgments

This work was supported by Office of Naval Research (ONR), grant of N000141010017, under the administration of Dr. Patrick Purtell. The authors appreciate INSEAN who provides the EFD data for this study.

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IIHR-Hydroscience and Engineering, The University of Iowa, Iowa, IA, USA

Wei He, Manivannan Kandasamy & Frederick Stern

Department of Mechanical Energy and Management Engineering, University of Calabria, Arcavacata di Rende, Cosenza, Italy

Teresa Castiglione

School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, China

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Correspondence to Frederick Stern .

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W. He and T. Castiglione contributed equally to the present work.

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He, W., Castiglione, T., Kandasamy, M. et al. Numerical analysis of the interference effects on resistance, sinkage and trim of a fast catamaran. J Mar Sci Technol 20 , 292–308 (2015). https://doi.org/10.1007/s00773-014-0283-0

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Received : 28 April 2014

Accepted : 24 August 2014

Published : 16 September 2014

Issue Date : June 2015

DOI : https://doi.org/10.1007/s00773-014-0283-0

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Shape & Resistance

A boat's hull shape and the distribution of volume are key factors in determining how it will behave in varying wind and load conditions. The underwater characteristics of a vessel are responsible for allowing a multihull and its cargo to travel through the water. The faster and more effortlessly the twin hulls can displace the surrounding fluid, the less resistance and more efficient a catamaran will be.

Typically modern catamaran designs have sharp bows to drive the vessel through the seas with as little wave making as possible. High freeboard assures a dry ride. Ample buoyancy helps keep the stems out of the water and spray to a minimum. Elliptical sections make up the first third of the hull, providing an easy entry in the water and some means to resist leeway. Towards the middle of the boat, gradually flattening out towards the stern, the sections become semicircular to help distribute buoyancy. These portions help carry payload and facilitate the hull lifting at speed. Basically, the majority of all cruising catamarans share these same underwater features.

Decades ago very seakindly, double-ended hull shapes were the norm as found in the thousands of Wharram catamarans. They were easy to construct, relatively slippery, and provided ample freeboard. Unfortunately they could not carry a lot of cruising gear, had cramped accommodations and were not the best windward performers. Their sharp V-sectioned hulls and rudders were their only means of resisting leeway as they had no leeway preventing devices. Similarly, the narrow asymmetrical type hull, such as found in the Hobie 16 beach catamaran, is hardly used in today's cruising multihull. The idea was to keep the underwater appendage to a minimum and eliminate any keels or daggerboards.

In contrast, the modern catamaran benefits from tank testing and computer-aided design. Composite molding technology allows for infinite shapes and each designer or manufacturer can now realize his idea of the perfect hull shape. Today's mini keels and daggerboards keep the cat hard on the wind and rival the weatherliness of monohull racers.

Drag on the hulls is the main deterrent to speed and has many components. We have to distinguish between water and air drag. Water-induced resistance can be further broken down into drag caused by wetted surface and wave making. Wetted surface, which is the frictional resistance the hulls experience when they are passing through the water, is the main cause of resistance at low speed. Wave making becomes more important as boat speed exceeds hull speed , or 1.34 x square root of the waterline length. Wave making resistance is not as easy to analyze and is more complex than drag caused by wetted surface; it is primarily a function of weight and, secondarily, of hull shape.

Pitch is another form of drag which can slow the boat down. This unwanted phenomenon is directly related to the buoyancy of the extremities and weight distribution. Wave-making resistance caused by the boat's constant plunging will slow a multihull, especially since it has less momentum to drive it through waves as compared to a single-hulled vessel. In addition the airflow over the sails will be disturbed by a constant change of attitude, further hindering efficient progress. Pitching can also be caused by placing items that are too heavy into the extreme ends of the multihull. In addition, various design- and construction-related issues can cause this problem, such as bridge decks extending too far forward of the mast and a high, heavy rig. Solid decking instead of trampoline nets, and/or large protrusions, which strangely some manufacturers claim break up waves, can also cause a hobby-horsing effect. Not only can this result in more wave-making drag than desired, but can seriously tire the crew. Any structure ahead of the mast can cause major slamming when having to face steep seas. Although many cruising catamarans, such as the Prouts, have been built with large bridgedeck structures extending forward to the bows, it is my opinion that an open trampoline, which poses no resistance to wind and seas, is imperative on a good cruising cat.

above High freeboard and angled-out hulls are trademark features of this capable Catana 521. Much thinking has gone into the hull shape of this catamaran, yet the pronounced step running along the inside of the vessel might create some wave slap in some conditions, a typical example of a compromise between space and performance.

Resistance & Performance

Resistance vs. Speed of four different vessel configurations

A. Traditional, heavy displacement monohull cruiser

B. ULD (Ultra Light Displacement) monohull

C. Typical performance catamaran cruiser

D. Racing multihull, with almost no wave making resistance below A popular French catamaran, as photographed out of the water at the Paris Boat Show . Note that there are barely several inches of clearance between the bridgedeck and waterline. The pronounced forward knuckle of the nacelle is claimed to break up waves. In my mind however, there is very little that can resist the continued impact of seas, and any conflict between the wingdeck and waves should be avoided.

Continue reading here: Catamaran Sailboat Wide Bodied Hulls

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Readers' Questions

What is a characteristic of a catamaran hull?

A characteristic of a catamaran hull is that it has two parallel hulls, which provide greater stability than a monohull vessel and help reduce roll, pitch and yaw. Catamarans also generally require less power to achieve a given speed than a monohull and provide improved handling characteristics in open water.

What may cause hull on catamaran to bend?

Hull flexing on catamarans may be caused by several factors, such as high winds, strong waves, heavy loads, and improper loading. Poorly designed or constructed hulls can also be more vulnerable to flexing.

How to construct catermaran hull show pictures?

Unfortunately, it is not possible to construct a catamaran hull with pictures alone. A catamaran hull is a complex structure that requires precise measurements and calculations in order to ensure that it is structurally sound and performs optimally when in the water. If you would like to learn more about constructing a catamaran hull, you should refer to resources such as books, websites, and experienced boat builders who can provide you with detailed instructions.

How far should a catamaran bridge be of the water?

The height of a catamaran bridge will depend on the size and type of the catamaran. Generally, a bridge should be slightly above the water line, typically between 6 and 12 inches.

How to get catamaran hull resistance?

Catamaran hull resistance is determined by a number of factors, such as the shape of the hull, length and beam dimensions, wetted surface area, type of appendages, and underwater profile. To determine the resistance, the hull needs to be tested in a towing tank or in the open water. The resistance coefficients obtained by testing can then be used to calculate the total resistance of the catamaran hull.

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Numerical hull resistance calculation of a catamarán using OpenFOAM

2017, Ciencia y tecnología de buques

In the present study, numerical resistance predictions using OpenFOAM were performed considering the Cormorant Evolution Catamaran, which provides travel services in the Galapagos Islands. These predictions were compared with experimental data published by Chávez and Lucín [1] and with systematic series [2].Simulations were made at model scale of 2 [m] in two load conditions, considering demi and twin hull (s=0.56 [m]) configurations. A mesh convergence study was performed with 3 different meshes for V=1.05 [m/s] at Light Condition (T=0.086 [m]). The converged mesh, with 1 million of cells approximately, has the lower standard deviation and a 5% error when compared to its experimental value of 1.79 [N]. The errors between the experimental data and the numerical simulations for demi hull configuration were 43% and 36% for Light and Full conditions, respectively. Besides, for twin hull configuration the errors were around 14% and 32% for Light and Full conditions, respectively.

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Taiwan commissions 2 new navy ships as safeguards against rising threat from China

T AIPEI, Taiwan (AP) — Taiwan has commissioned two new navy ships as a safeguard against the rising threat from China, which has been ratcheting up its naval and air force missions around the island that it claims as its own territory to be annexed by force if necessary.

The pair of Tuo Chiang class corvettes completes the first order of six of the domestically produced catamarans with stealth capabilities. The ships are relatively small, capable of carrying just 41 sailors and officers, but are fast and highly maneuverable and carry a range of missiles and deck guns aimed at countering larger Chinese vessels and rocketry.

Outgoing President Tsai Ing-wen oversaw the commissioning on Tuesday at the northern port of Suao, emphasizing her push to revitalize Taiwan’s defense industries, alongside extensive arms purchases and support from key ally the United States .

Tsai has also fast-tracked the production of trainer jets and the island's first homebuilt submarines, sometimes pushing budgets for such purchases through the legislature against resistance from representatives of the opposition Nationalist Party, which favors eventual unification with China.

Ma Ying-jeou, the last president from the Nationalists, also known as the KMT, is reportedly planning a visit to China next month that could include a meeting with Communist Party leader Xi Jinping.

Taiwan was colonized by China in the 1600s but later taken over by Japan, before reverting to the Republic of China at the end of World War II. The sides then split again amid the Chinese Civil War in 1949. Xi has been building his military with an eye to consolidating China's territorial claims throughout the Pacific, the South China Sea and along the contested high-mountain border with India.

China boasts the world's largest standing military and biggest navy — with three aircraft carriers — but has not fought in a major conflict since its brief 1979 invasion of Vietnam. Since then, its military budget has ballooned to the world's second largest behind the U.S., alongside a huge expansion of its economy, which is now showing signs of losing steam.

Most recently, frictions between patrol vessels from the sides near Taiwan-controlled islands just off the Chinese coast have renewed concerns about a conflict that could draw in the U.S., which is legally bound to ensure Taiwan can defend itself and considers all threats to the island as matters of “grave concern.”

While vastly outgunned, Taiwan's military has been bolstered by new weaponry and an extension of the universal period of national service for men from four months to one year. Its air force, navy and missile corps also respond to near-daily incursions by Chinese ships and planes .

Taiwan's Defense Ministry says it is on alert for a Chinese sneak attack, possibly targeting Tsai or Vice President William Lai, who will take over the top office in May . Both are despised as separatists by Beijing. Recent Taiwanese media reports have shown satellite photos of Chinese People's Liberation Army training grounds including mock-ups of the neighborhood surrounding Taipei's Presidential Office Building.

Taiwan's Defense Ministry said it detected nine Chinese planes and six ships operating around the island between Tuesday afternoon and Wednesday morning.

In Beijing on Wednesday, a spokesperson for the Cabinet's Taiwan Affairs Office criticized live-firing exercises by the Taiwanese military planned for next month near the Taiwan-held island group of Kinmen just off the Chinese coast.

“Any provocative move Taiwan's military takes is doomed to fail,” Chen Binhua said at a biweekly news conference.