Editing Catamaran (section)

== Performance ==
[[File:Brady 45&#039; strip-built catamaran with fractional Bermuda rig.jpg|thumb|upright|A [[Brady catamarans|45' catamaran]] under sail, showing minimal bow wave and wake resulting from the hulls being [[Beam (nautical)|narrow]], [[Displacement (ship)|low displacement]] and [[Waterline length|long]]]]

Catamarans have two distinct primary performance characteristics that distinguish them from displacement monohull vessels: lower resistance to passage through the water and greater stability (initial resistance to capsize). Choosing between a monohull and catamaran configuration includes considerations of carrying capacity, speed, and efficiency.

=== Resistance ===

At low to moderate speeds, a lightweight catamaran hull experiences resistance to passage through water that is approximately proportional to its speed. A displacement monohull has the same relationship at low speed since resistance is almost entirely due to surface friction. When boat speed increases and waves are generated the resistance is dependent on several design factors, particularly hull displacement to length and hull separation to length ratio, it is a non trivial resistance curve with many small peaks as wave trains at various speeds combine and cancel<ref>Principals of Naval Architecture SNAME</ref><ref name=Garrett/> For powered catamarans, this implies smaller power plants (although two are typically required). For sailing catamarans, [[Forces on sails#Reactive forces on sailing craft|low forward resistance]]<ref>{{ cite book | last1 = Yang | first1 = C. | last2 = Löhner | first2 = R. | last3 = Soto | first3 = O. | title = Practical Design of Ships and Other Floating Structures: Eighth International Symposium | place = China | publisher = Elsevier | volume = 1 | editor-last = Wu | editor-first = You-Sheng | editor2 = Guo-Jun Zhou | editor3 = Wei-Cheng Cui | chapter = Optimization of a wave-cancellation multihull using CFD tools  | date = August 22, 2001 | isbn = 9780080539355}}</ref> allows the sails to [[Forces on sails#Lift predominant .28attached flow.29|derive power from attached flow]],<ref name=Weitner>{{ cite journal | last = Weltner | first = Klaus | title = A comparison of explanations of the aerodynamic lifting force | journal = American Journal of Physics | volume = 55 | issue = 1 | pages = 52 | date = January 1987 | doi = 10.1119/1.14960 | bibcode = 1987AmJPh..55...50W }}</ref> their most efficient mode—analogous to a wing—leading to the use of [[wingsail]]s in racing craft.<ref name=Sail>{{ cite magazine | last = Nielsen | first =  Peter  | title = Have Wingsails Gone Mainstream? | magazine = Sail Magazine | publisher = Interlink Media | date = May 14, 2014 | url = http://www.sailmagazine.com/boats/have-wingsails-gone-mainstream | access-date = 2015-01-24 }}</ref>

=== Stability ===

Catamarans rely primarily on form stability to resist heeling and capsize.<ref name=Garrett>{{cite book | last = Garrett | first = Ross | title = The Symmetry of Sailing: The Physics of Sailing for Yachtsmen | publisher = Sheridan House, Inc. | date = January 1, 1996  | page = 133 | url = https://books.google.com/books?id=0VLXORumEF4C&q=catamaran&pg=PA133 | isbn = 9781574090000}}</ref> Comparison of heeling stability of a rectangular-cross section [[monohull]] of beam, ''B'', compared with two catamaran hulls of width ''B''/2, separated by a distance, 2×''B'', determines that the catamaran has an initial resistance to heeling that is seven times that of the monohull.<ref>{{cite book | last1 = Biran | first1 = Adrian | last2 = Pulido | first2 = Ruben Lopez  | title = Ship Hydrostatics and Stability | publisher = Butterworth-Heinemann | edition = 2 | year = 2013 | page = 67 | url = https://books.google.com/books?id=LostoMz5ZpMC&q=catamaran+stability&pg=PA66 | isbn = 978-0080982908 }}</ref> Compared with a monohull, a cruising catamaran sailboat has a high initial resistance to heeling and capsize—a fifty-footer requires four times the force to initiate a capsize than an equivalent monohull.<ref name = Offshore>{{ cite book | last1 = Howard | first1 = Jim | last2 = Doane | first2 = Charles J. | title = Handbook of Offshore Cruising: The Dream and Reality of Modern Ocean Cruising | publisher = Sheridan House, Inc | date = 2000 | pages = 36–8 | url = https://books.google.com/books?id=NB4uFQuUlnEC&q=capsize&pg=PA38 | access-date = 2016-01-27 | isbn = 1574090933 }}<!-- This ref listed total pages instead of a specific page; the best support I could find for the assertion of four times the force is in figure 5.1 on p. 38, showing approx. 200,000 ft. pounds max stability for a 50 foot catamaran vs approx. 50,000 ft. pounds max stability for a 50 foot monohull. --></ref>

=== Tradeoffs ===

[[File:Catamaran at Straits Quay, Georgetown, Pulau Pinang, Malaysia..jpg|thumb|''Vangohh Seafarer'', a catamaran motor yacht berthed at Straits Quay, Georgetown, Pulau Pinang, Malaysia]]

One measure of the trade-off between speed and carrying capacity is the [[Froude number#Ship hydrodynamics|displacement Froude number (Fn<sub>V</sub>)]],<ref>{{Cite book | last=Newman | first=John Nicholas | author-link=John Nicholas Newman | title=Marine hydrodynamics | url=https://archive.org/details/marinehydrodynam00newm | url-access=limited | year=1977 | publisher=[[MIT Press]] | location=Cambridge, Massachusetts  | isbn=0-262-14026-8 |page=[https://archive.org/details/marinehydrodynam00newm/page/n43 28]}}.</ref> compared with ''calm water transportation efficiency''.<ref name = Watson/> Fn<sub>V</sub> applies when the [[waterline length]] is too speed-dependent to be meaningful—as with a planing hull.<ref>{{ cite journal | last1 = Wilson | first1 = F.W. | last2 = Vlars | first2 = P.R. | title = Operational Characteristics Comparisons | journal = AIAA 6th Marine Systems Conference | page = 11 | publisher = American Institute of Aeronautics and Astronautics | date = September 1981 | url = https://books.google.com/books?id=QboKAQAAMAAJ&q=%22displacement+Froude+number%22 | access-date = 2017-03-31 }}</ref> It uses a reference length,  the cubic root of the volumetric displacement of the hull, ''V'', where ''u'' is the relative flow velocity between the sea and ship, and ''g'' is [[Gravitational constant|acceleration due to gravity]]:
 
:<math>\mathrm{Fn_V} = \frac{u}{\sqrt{gV^{1/3}}}</math>

''Calm water transportation efficiency'' of a vessel is proportional to the full-load [[Displacement (ship)|displacement]] and the maximum calm-water speed, divided by the corresponding power required.<ref>{{cite journal | last = Eames | first = Michael C. | title = Advances is Naval Architecture for Surface Naval Ships | journal = Proceedings | pages = 31 | publisher = Royal Institution of Naval Architects | location = London | date = April 15, 1980 | url = http://cradpdf.drdc-rddc.gc.ca/PDFS/zbd89/p36271.pdf | access-date = 2016-01-31 | archive-date = February 1, 2016 | archive-url = https://web.archive.org/web/20160201081051/http://cradpdf.drdc-rddc.gc.ca/PDFS/zbd89/p36271.pdf | url-status = dead }}</ref>

Large merchant vessels have a Fn<sub>V</sub> between one and zero, whereas higher-performance powered catamarans may approach 2.5, denoting a higher speed per unit volume for catamarans. Each type of vessel has a corresponding calm water transportation efficiency, with large transport ships being in the range of 100–1,000, compared with 11-18 for transport catamarans, denoting a higher efficiency per unit of payload for monohulls.<ref name = Watson>{{ cite book | last = Watson | first = D. G. M. | title = Practical Ship Design | publisher = Gulf Professional Publishing | series = Elsevier Ocean Engineering Book Series | volume = 1 | edition = Revised | date = 2002 | pages = 47–48 | quote = See Fig. 2.1 'Slender' and 'Swath' figures. | url = https://books.google.com/books?id=L4W1XZ9Lf8cC&q=wave+piercing+catamaran+design&pg=PA48 | isbn = 0080440541 }}</ref><!--See chart on P. 47 for catamaran numbers. Look for SWATH: You'll be in the right neighborhood. The transport ship value is on P. 48.-->