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{{Main|Lift (force)|Lift-induced drag}}
Lift on a sail ('''L'''), acting as an [[airfoil]], occurs in a direction perpendicular to the incident airstream (the apparent wind velocity, '''V<sub>A</sub>''', for the head sail) and is a result of pressure differences between the windward and leeward surfaces and depends on angle of attack, sail shape, air density, and speed of the apparent wind. [[Pressure]] differences result from the [[Stress (mechanics)#Normal and shear stresses|normal force]] per unit area on the sail from the air passing around it. The lift force results from the average pressure on the windward surface of the sail being higher than the average pressure on the leeward side.<ref>{{Citation |first=G.K. |last=Batchelor |
As the lift generated by a sail increases, so does [[lift-induced drag]], which together with [[parasitic drag]] constitutes total drag, ('''D'''). This occurs when the angle of attack increases with sail trim or change of course to cause the [[lift coefficient]] to increase up to the point of [[Stall (flight)|aerodynamic stall]], so does the lift-induced [[drag coefficient]]. At the onset of stall, lift is abruptly decreased, as is lift-induced drag, but viscous pressure drag, a component of parasitic drag, increases due to the formation of separated flow on the surface of the sail. Sails with the apparent wind behind them (especially going downwind) operate in a stalled condition.<ref name = Clancy>
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| publisher = CRC Press
| date = 2009
| pages = 296
| url = https://books.google.com/books?id=Xe_i23UL4sAC&q=iceboat
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| date = 2005
| url = http://www.star-board.com/images/2007/drake_chronicles/doc/PhysicsLecture.pdf
|
| archive-url = https://web.archive.org/web/20160304101621/http://www.star-board.com/images/2007/drake_chronicles/doc/PhysicsLecture.pdf
| archive-date = 2016-03-04
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| first=G.K.
| last=Batchelor
|
| title=An Introduction to Fluid Dynamics
| year=1967
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| url = http://onlinepubs.trb.org/onlinepubs/sr/sr286.pdf
| title = Tires and Passenger Vehicle Fuel Economy: Informing Consumers, Improving Performance -- Special Report 286. National Academy of Sciences, Transportation Research Board, 2006
|
</ref> but on ice may become reduced with speed as it transitions to [[Friction#Lubricated friction|lubricated friction]] with melting.<ref name = Kimball/>
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| date = Aug 22, 2001
| pages = 1422
{{Citation
| last1 = Alexander
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| place = London
| publisher = Juanita Kalerghi
| year = 1972
| pages = 96
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| title = Higher Performance Sailing: Faster Handling Techniques
| date = 2013
| pages = 448
| url = https://books.google.com/books?id=WTRLAAAAQBAJ&q=Faster+than+the+wind&pg=PA204
| isbn = 9781472901309 }}</ref>
*High-performance catamarans, including the [[Extreme 40]] catamaran and [[International C-class catamaran]] can sail at speeds up to twice the speed of the wind.<ref>{{cite web | author = Staff | date = September 2004 | url=http://www.sailmagazine.com/winged-world-c-cats| publisher = Sail Magazine | title = The Winged World of C Cats |
{{cite web
|last = Springer
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|date = November 2005
|url = http://www.sailmagazine.com/sailboat-reviews/volvo-extreme-40
|
|url-status = dead
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}}</ref>
*[[Sailing hydrofoil]]s achieve boat speeds up to twice the speed of the wind, as did the [[AC72]] catamarans used for the [[2013 America's Cup]].<ref name=2013first2>{{cite web|url=http://www.americascup.com/en/news/3/news/18009/emirates-team-new-zealand-gets-leg-up-on-oracle-team-usa |title=Emirates Team New Zealand gets leg up on ORACLE TEAM USA |publisher=2012-13 America's Cup Event Authority |date=7 September 2013 |
*Ice boats can sail up to five times the speed of the wind.<ref name=Boat_Speed>{{Citation
| first = Bob
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| title = The 16th Chesapeake Sailing Yacht Symposium
| date = March 2003
| place = Anapolis
| publisher = SNAME
| url = http://www.sname.org/chesapeakesailingyachtsymposiumcsys/pastpapers/16thcsys }}</ref><ref>{{cite web|last=Editors|title=Commonly Asked Questions|url=http://iceboat.org/faqiceboat.html|publisher=Four Lakes Ice Yacht Club|
'''Lateral force''' is a reaction supplied by the underwater shape of a sailboat, the blades of an ice boat and the wheels of a land sailing craft. Sailboats rely on [[keel]]s, [[centerboard]]s, and other underwater foils, including rudders, that provide [[Lift (force)|lift]] in the lateral direction, to provide hydrodynamic lateral force ('''P<sub>LAT</sub>''') to offset the lateral force component acting on the sail ('''F<sub>LAT</sub>''') and minimize leeway.<ref name=Fabio/> Such foils provide hydrodynamic lift and, for keels, ballast to offset heeling. They incorporate a wide variety of design considerations.<ref>
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|issue = June/July
|url = http://www.sponbergyachtdesign.com/keel%20and%20rudder%20design.pdf
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|url-status = dead
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}}</ref>
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| last3 = Gilhousen
| first3 = D. B.
| title = Determining the Power-Law Wind-Profile Exponent under Near-Neutral Stability Conditions at Sea
| journal = Journal of Applied Meteorology
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|date = January 2006
|url = http://www.nwas.org/ej/pdf/2006-EJ2.pdf
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|url-status = dead
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}}
</ref> This suggests that sails that reach higher above the surface can be subject to stronger wind forces that move the centre of effort (''CE'' ) higher above the surface and increase the heeling moment.
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| date = April 2008
| url = http://www.vos.noaa.gov/MWL/apr_08/overwater.shtml
|
</ref>
:<math>G = 1 + 2p </math>
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| publisher = Adlard Coles Nautical
| date = November 1, 2009
| pages = 352
| isbn = 978-1408113387 }}</ref> based on the work of [[Gustave Eiffel]], who pioneered [[wind tunnel]] experiments on airfoils, which he published in 1910. Among them were studies of cambered plates. The results shown are for plates of varying camber and aspect ratios, as shown.<ref name=Anderson/> They show that, as aspect ratio decreases, maximum lift shifts further towards increased drag (rightwards in the diagram). They also show that, for lower angles of attack, a higher aspect ratio generates more lift and less drag than for lower aspect ratios.
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| publisher = Sheridan House, Inc.
| date = January 1, 1996
| pages = 268
| url = https://books.google.com/books?id=0VLXORumEF4C&q=sail+lift+to+drag+ratio&pg=PA61
| isbn = 9781574090000}}</ref>
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| last1 = Collie
| first1 = S. J.
| last2 = Jackson
| first2 = P. S.
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| first5 = J.B.
| last5 = Fallow
| title = Two-dimensional CFD-based parametric analysis of down-wind sail designs
| journal = The University of Auckland
| date = 2006
| url = http://syr.stanford.edu/RINA_Steve.pdf
|
</ref> The separation becomes more pronounced until at ''α'' = 90° lift becomes small and drag predominates. In addition to the sails used upwind, [[spinnaker]]s provide area and curvature appropriate for sailing with separated flow on downwind points of sail.<ref name=Textor>
{{cite book
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| date = September 12, 1981
| url = http://ljjensen.net/Maritimt/A%20Review%20of%20Modern%20Sail%20Theory.pdf
|
==Sail performance design variables==
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| publisher = Oxford University Press
| series = Oxford Quick Reference
| date = March 1987
| pages = [https://archive.org/details/pocketoxfordguid00iand/page/220 220]
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| edition = 8
| chapter = 3
| page = 103
| isbn = 978-0-273-31623-7 }}</ref> For most sails, the length of the chord is not a constant but varies along the wing, so the aspect ratio ''AR'' is defined as the square of the [[wingspan|sail height]] ''b'' divided by the area ''A'' of the sail [[planform]]:<ref name=Clancy/><ref name=Anderson>
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| first = Rob
| title = RYA Sail Trim Handbook
| publisher = Royal Yachting Association
|
| year = 2015
| pages = 88
| isbn = 9781906435578 }}</ref> Staysails and sails attached to a mast (e.g. a mainsail) have different, but similar controls to achieve draft depth and position. On a staysail, tightening the luff with the halyard helps flatten the sail and adjusts the position of maximum draft. On a mainsail curving the mast to fit the curvature of the luff helps flatten the sail. Depending on wind strength, Dellenbaugh offers the following advice on setting the draft of a sailboat mainsail:<ref name= Dellenbaugh>{{Citation
| last = Dellenbaugh
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| publisher = Sailing Breezes Online Magazine
| date = February 2009
| url = http://www.sailingbreezes.com/Sailing_Breezes_Current/Articles/Feb09/Guidelines_for_Good_Mainsail_Shape.htm
|
*For light air (less than 8 knots), the sail is at its fullest with the depth of draft between 13-16% of the cord and maximum fullness 50% aft from the luff.
*For medium air (8-15 knots), the mainsail has minimal twist with a depth of draft set between 11-13% of the cord and maximum fullness 45% aft from the luff.
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| first2 = Rolf E
| title = Principles of yacht design
| publisher = International Marine/Ragged Mountain Press
|date=January 2014
| edition = 4
| pages = 352
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| date = January 2012
| url = http://www.mysailing.com.au/news/downwind-sails-design-thinking
|
''C<sub>D</sub>'' ≈ 4/3 for most sails with the apparent wind angle astern, so drag force on a downwind sail becomes substantially a function of area and wind speed, approximated as follows:<ref name = Kimball/>
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| first = C. A.
| title = Sail Performance: Techniques to Maximize Sail Power
| publisher = International Marine/Ragged Mountain Press
| year = 2002
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| isbn = 978-0071413107 }}</ref>
Instruments for measuring air pressure effects in wind tunnel studies of sails include [[pitot tube]]s, which measure air speed and [[manometer]]s, which measure [[static pressure]]s and [[atmospheric pressure]] (static pressure in undisturbed flow). Researchers plot pressure across the windward and leeward sides of test sails along the chord and calculate [[pressure coefficient]]s (static pressure difference over wind-induced [[dynamic pressure]]).<ref name=Marchaj1/><ref name=Fabio/><ref name=Crook2>{{cite web|last=Crook|first=A|title=An experimental investigation of high aspect-ratio rectangular sails|url=http://ctr.stanford.edu/ResBriefs02/crook2.pdf|work=see Figure 2|publisher=Center for Turbulence Research Annual Research Briefs|
Research results describe airflow around the sail and in the [[boundary layer]].<ref name=Marchaj1/> Wilkinson, modelling the boundary layer in two dimensions, described nine regions around the sail:<ref name=WilkinsonS>{{cite journal|last1=Wilkinson|first1=Stuart|title=Simple Multilayer Panel Method for Partially Separated Flows Around Two-Dimensional Masts and Sails|journal=AIAA Journal|volume=26|issue=4|pages=394–395|doi=10.2514/3.48766|date=April 1988|bibcode=1988AIAAJ..26..394W}}</ref>
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Sail design differs from wing design in several respects, especially since on a sail air flow varies with wind and boat motion and sails are usually deformable airfoils, sometimes with a mast for a leading edge. Often simplifying assumptions are employed when making design calculations, including: a flat travel surface—water, ice or land, constant wind velocity and unchanging sail adjustment.<ref name=WilkinsonS/>
The analysis of the forces on sails takes into account the [[Aerodynamic force|aerodynamic]] [[surface force]], its [[center of pressure (fluid mechanics)|centre of effort]] on a sail, its direction, and its variable distribution over the sail. Modern analysis employs [[fluid mechanics]] and [[aerodynamics]] airflow calculations for sail design and manufacture, using [[aeroelasticity]] models, which combine computational fluid dynamics and structural analysis.<ref name=Fabio/> Secondary effects pertaining to [[turbulence]] and separation of the [[boundary layer]] are secondary factors.<ref name=WilkinsonS/> Computational limitations persist.<ref name=LEFD1>{{cite web|title=Pressure PIV and Open Cavity Shear Layer Flow|url=http://www.me.jhu.edu/lefd/PPIV/index.html|publisher=Johns Hopkins U. Laboratory for Experimental Fluid Dynamics|
==See also==
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