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{{Short description|none}} <!-- "none" is a legitimate description when the title is already adequate; see [[WP:SDNONE]] -->
{{Main|Sail}}
[[File:Points of sail--close-hauled (right) and down wind (left).jpg|thumb|right|300px|Aerodynamic force components for two points of sail. <br />''Left-hand boat'': Down wind with stalled
to heel.]]
[[File:Points of sail--English.jpg|thumb|right|300px|Points of sail (and ''predominant sail force component'' for a displacement sailboat).<br />A. Luffing (''no propulsive force'')
'''Forces on sails''' result from movement of air that interacts with [[sail]]s and gives them motive power for sailing craft, including [[sailing ship]]s, [[sailboat]]s, [[Windsurfing|windsurfers]], [[ice boat]]s, and [[Land sailing|sail-powered land vehicles]]. Similar principles in a rotating frame of reference apply to [[
Forces on sails depend on wind speed and direction and the speed and direction of the craft. The direction that the craft is traveling with respect to the "true wind" (the wind direction and speed over the surface) is called the [[point of sail]]. The speed of the craft at a given point of sail contributes to the "[[apparent wind]]"—the wind speed and direction as measured on the moving craft. The apparent wind on the sail creates a total aerodynamic force, which may be resolved into [[Drag (physics)|drag]]—the force component in the direction of the apparent wind—and [[Lift (force)|lift]]—the force component [[normal (geometry)|normal]] (90°) to the apparent wind. Depending on the alignment of the sail with the apparent wind, lift or drag may be the predominant propulsive component. Total aerodynamic force also resolves into a forward, propulsive, driving force—resisted by the medium through or over which the craft is passing (e.g. through water, air, or over ice, sand)—and a lateral force, resisted by the underwater foils, ice runners, or wheels of the sailing craft.
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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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{{Main|Apparent wind|Point of sail|High-performance sailing}}
Apparent wind ('''V<sub>A</sub>''') is the air velocity acting upon the leading edge of the most forward sail or as experienced by instrumentation or crew on a moving sailing craft. It is the [[Euclidean vector#Addition and subtraction|vector sum]] of true wind velocity and the apparent wind component resulting from boat velocity ('''V<sub>A</sub>''' = '''
<div class="center">
;Effect of apparent wind on sailing craft at three points of sail
Boat velocity (in black) generates an equal and opposite apparent wind component (not shown), which adds to the true wind to become apparent wind.
</
<gallery mode="packed" heights="300px">
File:Forces on sails for three points of sail.jpg|'''Apparent wind and forces on a ''sailboat''.'''<br />As the boat sails further from the wind, the apparent wind becomes smaller and the lateral component becomes less; boat speed is highest on the beam reach.
File:Ice boat apparent wind on different points of sail.jpg|'''Apparent wind on an ''iceboat''.'''<br />As the iceboat sails further from the wind, the apparent wind increases slightly and the boat speed is highest on the broad reach. The sail is sheeted in for all three points of sail.<ref name = Kimball/>
</gallery>
<div class="center">
Sailing craft '''A''' is close-hauled. Sailing craft '''B''' is on a beam reach. Sailing craft '''C''' is on a broad reach.
</
A sailboat's speed through the water is limited by the resistance that results from hull drag in the water. Sail boats on foils are much less limited. Ice boats typically have the least resistance to forward motion of any sailing craft. Craft with the higher forward resistance achieve lower forward velocities for a given wind velocity than ice boats, which can travel at speeds several multiples of the true wind speed.<ref name = Kimball/> Consequently, a sailboat experiences a wider range of apparent wind angles than does an ice boat, whose speed is typically great enough to have the apparent wind coming from a few degrees to one side of its course, necessitating sailing with the sail sheeted in for most points of sail. On conventional sail boats, the sails are set to create lift for those points of sail where it's possible to align the leading edge of the sail with the apparent wind.<ref name=Jobson/>
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| publisher = CRC Press
| date = 2009
| pages = 296
| url = https://books.google.com/books?id=Xe_i23UL4sAC
| isbn = 978-1466502666 }}</ref>
<div class="center">
;Aerodynamic forces in balance with hydrodynamic forces on a close-hauled sailboat
</
<gallery mode="packed" heights="350px">
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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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The values of driving force (''F<sub>R</sub>'' ) and lateral force (''F<sub>LAT</sub>'' ) with apparent wind angle (α), assuming no heeling, relate to the values of lift (''L'' ) and drag (''D'' ), as follows:<ref name=Fabio/>
:<math>
:<math>\ F_{LAT} = L \cdot \cos(\alpha) + D \cdot \sin(\alpha) </math>
===Reactive forces on sailing craft===
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| first=G.K.
| last=Batchelor
|
| title=An Introduction to Fluid Dynamics
| year=1967
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| last = Committee for the National Tire Efficiency Study
| url = http://onlinepubs.trb.org/onlinepubs/sr/sr286.pdf
| title = Tires and Passenger Vehicle Fuel Economy: Informing Consumers, Improving Performance
|
</ref> but on ice may become reduced with speed as it transitions to [[Friction#Lubricated friction|lubricated friction]] with melting.<ref name = Kimball/>
Ways to reduce [[Wave-making resistance#Ways of reducing wave-making resistance|wave-making resistance]] used on sailing vessels include ''reduced displacement''—through [[Planing (boat)|planing]] or (as with a windsurfer) offsetting vessel weight with a lifting sail—and ''fine entry'', as with catamarans, where a narrow hull minimizes the water displaced into a bow wave.<ref>
{{Citation
|
|
| last2 = Löhner
| first2 = R.
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| date = Aug 22, 2001
| pages = 1422
{{Citation
|
|
| last2 = Grogono
| first2 = James
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| place = London
| publisher = Juanita Kalerghi
| year = 1972
| pages = 96
| isbn = 978-0903238007 }}</ref>
<div class="center">
;Sailing craft with low forward resistance and high lateral resistance.
</
<gallery mode="packed" heights="200px">
File:Bladerider-8.jpg|[[Moth (dinghy)|International Moth class sailboat]] on [[Sailing hydrofoil|foils]].
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| title = Higher Performance Sailing: Faster Handling Techniques
| date = 2013
| pages = 448
|
| url = https://books.google.com/books?id=WTRLAAAAQBAJ&
| 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
|
|
}}</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=
*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
| access-date = 2017-01-29 | archive-date = 2020-09-19 | archive-url = https://web.archive.org/web/20200919123639/https://www.sname.org/chesapeakesailingyachtsymposiumcsys/pastpapers/16thcsys | url-status = dead }}</ref><ref>{{cite web '''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
|
|url-status = dead
|
|
}}</ref>
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<ref>
{{Citation
|
|
| last2 = Meindl
| first2 = E. A.
| 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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| year = 1994
| doi=10.1175/1520-0450(1994)033<0757:dtplwp>2.0.co;2| bibcode = 1994JApMe..33..757H
| url = https://zenodo.org/record/1234685
| doi-access = free
}}
</ref><ref>
{{Citation
|
|
| last2 = Sheppard
| first2 = P. A.
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|date = January 2006
|url = http://www.nwas.org/ej/pdf/2006-EJ2.pdf
|
|url-status = dead
|
|
}}
</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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Additionally, apparent wind direction moves aft with height above water, which may necessitate a corresponding [[Sail twist|twist in the shape of the sail]] to achieve attached flow with height.<ref>
{{Citation
|
|
| first2 = F.
| last2 = Fossati
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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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}}</ref>
This formulation allows determination of ''C<sub>L</sub>'' and ''C<sub>D</sub>'' experimentally for a given sail shape by varying angle of attack at an experimental wind velocity and measuring force on the sail in the direction of the incident wind (''D''—drag) and perpendicular to it (''L''—lift). As the angle of attack grows larger, the lift reaches a maximum at some angle; increasing the angle of attack beyond this [[Angle of attack#Critical angle of attack|critical angle of attack]] causes the upper-surface flow to separate from the convex surface of the sail; there is less deflection of air to windward, so the sail as airfoil generates less lift. The sail is said to be [[Stall (flight)|stalled]].<ref name=Weitner/> At the same time, induced drag increases with angle of attack (for the headsail: ''α<sub>j</sub>'' ).
<div class="center">
;Determination of coefficients of lift (''C<sub>L</sub>'' ) and drag (''C<sub>D</sub>'' ) for angle of attack and aspect ratio
</
<gallery mode="packed" heights="250px">
File:Coefficients of Lift and Drag for a Hypothetical Sail.png|'''Angle of attack''': Coefficient of lift (''C<sub>L</sub>'') and coefficient of drag (''C<sub>D</sub>'') and their ratio as a function of angle of attack (α) for a hypothetical sail.
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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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url=http://www.aerospaceweb.org/question/aerodynamics/q0156.shtml|
date=2003-12-28|
}}</ref>
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| publisher = Sheridan House, Inc.
| date = January 1, 1996
| pages = 268
| url = https://books.google.com/books?id=0VLXORumEF4C&
▲ | url = https://books.google.com/?id=0VLXORumEF4C&pg=PA61&lpg=PA61&dq=sail+lift+to+drag+ratio#v=onepage&q=sail%20lift%20to%20drag%20ratio&f=false
| isbn = 9781574090000}}</ref>
<div class="center">
;Polar diagrams, showing lift ('''L'''), drag ('''D'''), total aerodynamic force ('''F<sub>T</sub>'''), forward driving force ('''F<sub>R</sub>'''), and lateral force ('''F<sub>LAT</sub>''') for upwind points of sail
</
<gallery mode="packed" heights="300px">
File:Total aerodynamic force and components--Close-hauled.jpg|'''Close-hauled''': The lateral force is highest and driving force is lowest close to the wind.
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===Drag predominant (separated flow)===
When sailing craft are on a course where the angle of attack between the sail and the apparent wind (''α'' ) exceeds the point of maximum lift on the ''C<sub>L</sub>''–''C<sub>D</sub>'' polar diagram, separation of flow occurs.<ref>{{Citation
| last1 = Collie
|
| 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
|
| archive-date = 2010-07-28
</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>▼
| archive-url = https://web.archive.org/web/20100728123723/http://syr.stanford.edu/RINA_Steve.pdf
| url-status = dead
▲ }}</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
| last = Textor
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| publisher = Sheridan House, Inc.
| date = 1995
| url = https://books.google.com/books?id=2JIbS0c1XPwC&
| pages = 228
| isbn = 978-0924486814 }}
</ref>
<div class="center">
;Polar diagrams, showing lift ('''L'''), drag ('''D'''), total aerodynamic force ('''F<sub>T</sub>'''), forward driving force ('''F<sub>R</sub>'''), and lateral force ('''F<sub>LAT</sub>''') for downwind points of sail
</
<gallery mode="packed" heights="300px">
File:Total aerodynamic force and components--Broad reach.jpg|'''Broad Reach''': With apparent wind behind the sail (''α'' = 45°), the sail has stalled and lift has diminished.
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</gallery>
Again, in these diagrams the direction of travel changes with respect to the apparent wind ('''V<sub>A</sub>'''), which is constant for the sake of illustration, but would in reality vary with point of sail for a constant true wind. In the left-hand diagram (broad reach), the boat is on a point of sail, where the sail can no longer be aligned into the apparent wind to create an optimum angle of attack. Instead, the sail is in a stalled condition, creating about 80% of the lift as in the upwind examples and drag has doubled. Total aerodynamic force ('''F<sub>T</sub>''') has moved away from the maximum lift value. In the right-hand diagram (running before the wind), lift is one-fifth of the upwind cases (for the same strength apparent wind) and drag has almost quadrupled.<ref name=Garrett/>
<div class="center">
;Downwind sailing with a spinnaker
</
<gallery mode="packed" heights="200px">
File:Sailboat on broad reach with spinnaker.jpg|Spinnaker set for a broad reach, generating both lift with separated flow and drag.
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===Sail interactions===
Sailboats often have a jib that overlaps the mainsail—called a [[Genoa (sail)|genoa]]. Arvel Gentry demonstrated in his series of articles published in "Best of sail trim" published in 1977 (and later reported and republished in summary in 1981) that the genoa and the mainsail interact in a symbiotic manner, owing to the circulation of air between them slowing down in the gap between the two sails (contrary to traditional explanations), which prevents separation of flow along the mainsail. The presence of a jib causes the stagnation line on the mainsail to move forward, which reduces the suction velocities on the main and reduces the potential for boundary layer separation and stalling. This allows higher angles of attack. Likewise, the presence of the mainsail causes the stagnation line on the jib to be shifted
<ref name=Garrett/><ref>
{{Citation
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| journal = Proceedings of the Eleventh AIAA Symposium on the Aero/Hydronautics of Sailing
| date = September 12, 1981
| url = http://ljjensen.net/Maritimt/A%20Review%20of%20Modern%20Sail%20Theory.pdf
| archive-url = https://web.archive.org/web/20140422225628/http://ljjensen.net/Maritimt/A%20Review%20of%20Modern%20Sail%20Theory.pdf
| accessdate = 2015-04-11 }}</ref>▼
| url-status = usurped
| archive-date = April 22, 2014
The two sails cause an overall larger displacement of air perpendicular to the direction of flow when compared to one sail. They act to form a larger wing, or airfoil, around which the wind must pass. The total length around the outside has also increased and the difference in air speed between windward and leeward sides of the two sails is greater, resulting in more lift. The jib experiences a greater increase in lift with the two sail combination.<ref>{{Cite book|last=Anderson|first=Bryon D.|title=The physics of sailing explained|date=2003|publisher=Sheridan House|isbn=1-57409-170-0|___location=Dobbs Ferry, NY|oclc=52542601}}</ref>
==Sail performance design variables==
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===Sail terminology===
{{Main|Sail components}}
Sails are classified as [[Parts of a sail#Triangular
|
|
| editor-last2 = Kemp
| editor-first2 = Peter
| title = The Pocket Oxford Guide to Sailing Terms
| place = Oxford
| 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
*For medium air (
*For heavy (greater than15 knots), the sail is flattened and allowed to twist in a manner that dumps lift with a depth of draft set between 9
Plots by Larsson ''et al'' show that draft is a much more significant factor affecting sail propulsive force than the position of maximum draft.<ref name=Principles>
{{Citation
|
|
| last2 = Eliasson
| 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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</ref>
<div class="center">
;Coefficients of propulsive forces and heeling forces as a function of draft (camber) depth or position.
</
<gallery mode="packed" heights="300px">
File:Sail Camber Aerodynamic coef.png|Draft depth.
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===Drag variables===
Spinnakers have traditionally been optimized to mobilize drag as a more important propulsive component than lift. As sailing craft are able to achieve higher speeds, whether on water, ice or land, the velocity made good (VMG) at a given course off the wind occurs at apparent wind angles that are increasingly further forward with speed. This suggests that the optimum VMG for a given course may be in a regime where a spinnaker may be providing significant lift.<ref>
▲ | title = Downwind Sails - Design thinking
| publisher = Australian Sailing & Yachting
| 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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===Measurement of pressure on the sail===
Modern [[Sail#
{{Citation
| last = Marchaj
| 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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