Editing Lift-induced drag (section)

==Reducing induced drag==
According to the equations above, for wings generating the same lift, the induced drag is inversely proportional to the square of the [[wingspan]]. A wing of infinite span and uniform [[airfoil]] section (or a 2D wing) would experience no induced drag.<ref name="Houghton">{{cite book |last1=Houghton |first1=E. L. |title=Aerodynamics for engineering students |date=2012 |publisher=Elsevier Science |location=Waltham, MA |isbn=978-0-08-096632-8 |page=61 |edition=Sixth |chapter=1.6 |quote=For a two-dimensional wing at low Mach numbers, the drag contains no induced or wave drag}}</ref> The drag characteristics of a wing with infinite span can be simulated using an airfoil section the width of a [[wind tunnel]].<ref name="Molland">{{cite book |last1=Molland |first1=Anthony F. |title=Marine rudders and control surfaces : principles, data, design and applications |date=2007 |publisher=Elsevier/Butterworth-Heinemann |location=Amsterdam |isbn=9780750669443 |page=41 |edition=1st |chapter=Physics of control surface operation |quote=With infinite span, fluid motion is 2-D and in the direction of flow perpendicular to the span. Infinite span can, for example, be simulated using a foil completely spanning a wind tunnel.}}</ref>

An increase in wingspan or a solution with a similar effect is one way to reduce induced drag.<ref name="McLean"/>{{rp|4.10|quote=Based on our general appreciation of the physics, we can anticipate that drag-reduction devices need to be fairly large as viewed in the Trefftz plane, since any significant reduction in induced drag requires changing the global flowfield associated with the lift, so as to reduce its total kinetic energy. We know that we can’t do this just by tinkering with the "tip vortex" and thus that having a significant effect on the drag requires a significant change in the way the lift is distributed spatially. If our starting point is a wing on which the lift is already advantageously distributed, the only way to improve will be to provide a significant increase in the horizontal span or to introduce a nonplanar element that has a similar effect.}} The [[Wright brothers]] used curved trailing edges on their rectangular wings.<ref name="NASA Induced Drag Coefficient"/> Some early aircraft had fins mounted on the tips. More recent aircraft have wingtip-mounted [[Wingtip device|winglets]] to reduce the induced drag.<ref>{{cite tech report |author=Richard T. Whitcomb |title=A design approach and selected wind-tunnel results at high subsonic speeds for wing-tip mounted winglets |publisher=NASA |date=July 1976 |id=19760019075 |url=https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19760019075.pdf |quote-page=1 |quote=Winglets, which are small, nearly vertical, winglike surfaces mounted at the tips of a wing, are intended to provide, for lifting conditions and subsonic Mach numbers, reductions in drag coefficient greater than those achieved by a simple wing-tip extension with the same structural weight penalty.}}</ref> Winglets also provide some benefit by increasing the vertical height of the wing system.<ref name="McLean"/>{{rp|4.10|quote=Trefftz-plane theory tells us that we can reduce the ideal induced drag by increasing the vertical height of the lifting system, as well as by increasing the horizontal span. A vertical fin or winglet that adds vertical height to the system will reduce the ideal induced drag if it is placed anywhere along the span of the wing off of the airplane center plane, but it is most effective by far when it is placed at the station of maximum span; that is, at the tip.}} Wingtip mounted fuel tanks and wing [[Washout (aviation)|washout]] may also provide some benefit.{{cn|date=January 2022}}

Typically, [[elliptical wing|the elliptical spanwise distribution of lift]] produces the minimum induced drag<ref>Glauert, H. ''The Elements of Aerofoil and Airscrew Theory'' (1926); referenced in Fig. 5.4 of ''Airplane Aerodynamics'' by Daniel O. Dommasch, Sydney S. Sherby, Thomas F. Connolly, 3rd ed. (1961)</ref> for a [[Wing configuration|planar]] wing of a given span. A small number of aircraft have a planform approaching the elliptical — the most famous examples being the [[World War II]] [[Supermarine Spitfire|Spitfire]]<ref name="NASA Induced Drag Coefficient">{{cite web |title=Induced Drag Coefficient |url=https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/induced-drag-coefficient/ |website=www.grc.nasa.gov |access-date=9 February 2023}}</ref> and [[P-47 Thunderbolt|Thunderbolt]]. For modern wings with winglets, the ideal lift distribution is not elliptical.<ref name="McLean"/>{{rp|4.9|quote=The well-known elliptic spanload is "ideal" for a planar (flat) wing. For nonplanar configurations, the ideal spanload is not generally elliptic, but it is easily calculated for a given geometry. With a vertical winglet added, for example, the ideal spanload shows less lift inboard and more lift outboard, relative to elliptic, with a certain, optimum distribution on the winglet itself, as shown in Figure 3.5... Relative to these "ideal" spanloads, the spanloads used on real wings are usually modified somewhat to reduce bending loads and allow a lighter wing structure, at the expense of a slight increase in drag. The presence a fuselage and wing-mounted engines also tends to alter the spanload on real wings.}}

For a given wing area, a high [[wing aspect ratio|aspect ratio]] wing will produce less induced drag than a wing of low aspect ratio.<ref>{{cite web |url=http://www.skybrary.aero/index.php/Induced_Drag |title=Skybrary: Induced Drag|access-date=5 May 2015}}</ref> While induced drag is inversely proportional to the square of the wingspan, not necessarily inversely proportional to aspect ratio, ''if'' the wing area is held constant, then induced drag will be inversely proportional to aspect ratio. However, since wingspan can be increased while decreasing aspect ratio, or vice versa, the apparent relationship between aspect ratio and induced drag does not always hold.<ref name="Illsley">{{cite web |last1=Illsley |first1=Michael |title=Why Aspect Ratio doesn't Matter – Understanding Aerospace |url=https://bigsynthesis.com/understandingaerospace/index.php/21-why-aspect-ratio-doesn-t-matter/ |website=Understanding Aerospace |date=4 July 2017 |access-date=25 March 2022}}</ref><ref name="Understanding Aerodynamics"/>{{rp|489}}

For a typical twin-engine [[wide-body aircraft]] at [[Cruise (aeronautics)|cruise]] speed, induced drag is the second-largest component of total drag, accounting for approximately 37% of total drag. [[Skin friction drag]] is the largest component of total drag, at almost 48%.<ref name="AGARD">{{cite journal |last1=Robert |first1=JP |editor1-last=Cousteix |editor1-first=J |title=Drag reduction: an industrial challenge |journal=Special Course on Skin Friction Drag Reduction |volume=AGARD Report 786 |page=2-13 |date=March 1992 |publisher=[[AGARD]] |url=https://www.sto.nato.int/publications/_layouts/mobile/view.aspx?List=03e8ea21%2D64e6%2D4d37%2D8235%2D04fb61e122e9&View=7e9c814c%2D056a%2D4d31%2D8392%2D7c6752b2af2b&RootFolder=%2Fpublications%2FAGARD%2FAGARD%2DR%2D786&ViewMode=Detail }}</ref><ref name="Coustols">{{cite journal |last1=Coustols |first1=Eric |editor1-last=Meier |editor1-first=GEA |editor2-last=Schnerr |editor2-first=GH |title=Control of Turbulent Flows for Skin Friction Drag Reduction |journal=Control of Flow Instabilities and Unsteady Flows |date=1996 |page=156 |isbn=9783709126882 |url=https://books.google.com/books?id=w1ruCAAAQBAJ&pg=PA156 |access-date=24 March 2022}}</ref><ref name="Marec">{{cite conference |last1=Marec |first1=J.-P. |title=Aerodynamic Drag Reduction Technologies. Proceedings of the Ceas/Dragnet European Drag Reduction |chapter=Drag Reduction: A Major Task for Research |date=2001 |pages=17–27 |doi=10.1007/978-3-540-45359-8_3 |chapter-url=https://link.springer.com/chapter/10.1007/978-3-540-45359-8_3 |access-date=22 March 2022 |editor=Peter Thiede |isbn=978-3-642-07541-4 |issn=0179-9614 |publisher=Springer |bibcode=2001adrt.conf...17M |language=en}}</ref>{{rp|20}} Reducing induced drag can therefore significantly reduce cost and environmental impact.<ref name="Marec"/>{{rp|18}}