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==Aerodynamic design== ===Subsonic and transonic flight=== [[File:Jak 25.svg|thumb|[[Yakovlev Yak-25]] swept wing ]] [[File:swept wing w transonic shock.svg|thumb|Shows a swept wing in transonic flow with the position of a shock wave(red line). This line is a line of constant pressure (isobar) since shock waves cannot exist across isobars and for a well-designed wing coincides with a constant percent chord<ref>Fundamentals Of Flight, Second Edition, Richard S.Shevell{{ISBN|0 13 339060 8}}, p.200</ref> as shown. The triangles show that only part of the streamwise incident airflow is responsible for producing lift or causing shock waves (i.e. that part shown by the arrow perpendicular to the red isobar). Its length behind the shock is shorter signifying that the flow has slowed down in going through the shock.]] Shock waves can form on some parts of an aircraft moving at less than the speed of sound. Low-pressure regions around an aircraft cause the flow to accelerate, and at transonic speeds this local acceleration can exceed Mach 1. Localized supersonic flow must return to the freestream conditions around the rest of the aircraft, and as the flow enters an adverse pressure gradient in the aft section of the wing, a discontinuity emerges in the form of a shock wave as the air is forced to rapidly slow and return to ambient pressure. At the point where the density drops, the local speed of sound correspondingly drops and a shock wave can form. This is why in conventional wings, shock waves form first ''after'' the maximum Thickness/Chord and why all airliners designed for cruising in the transonic range (above M0.8) have supercritical wings that are flatter on top, resulting in minimized angular change of flow to upper surface air. The angular change to the air that is normally part of lift generation is decreased and this lift reduction is compensated for by deeper curved lower surfaces accompanied by a reflex curve at the trailing edge. This results in a much weaker shock wave towards the rear of the upper wing surface and a corresponding ''increase'' in critical mach number. Shock waves require energy to form. This energy is taken out of the aircraft, which has to supply extra [[thrust]] to make up for this energy loss. Thus the shocks are seen as a form of [[drag (physics)|drag]]. Since the shocks form when the local air velocity reaches supersonic speeds, there is a certain "[[critical mach]]" speed where sonic flow first appears on the wing. There is a following point called the [[drag divergence mach number]] where the effect of the drag from the shocks becomes noticeable. This is normally when the shocks start generating over the wing, which on most aircraft is the largest continually curved surface, and therefore the largest contributor to this effect. Sweeping the wing has the effect of reducing the curvature of the body as seen from the airflow, by the cosine of the angle of sweep. For instance, a wing with a 45 degree sweep will see a reduction in effective curvature to about 70% of its straight-wing value. This has the effect of increasing the critical Mach by 30%. When applied to large areas of the aircraft, like the wings and [[empennage]], this allows the aircraft to reach speeds closer to Mach 1. One limiting factor in swept wing design is the so-called "middle effect". If a swept wing is continuous - an [[Oblique wing|oblique swept wing]] - the pressure isobars will be swept at a continuous angle from tip to tip. However, if the left and right halves are swept back equally, as is common practice, the pressure isobars on the left wing in theory will meet the pressure isobars of the right wing on the centerline at a large angle. As the isobars cannot meet in such a fashion,{{why|date=July 2022}} they will tend to curve on each side as they near the centerline, so that the isobars cross the centerline at right angles to the centerline. This causes an "unsweeping" of the isobars in the wing root region. To combat this unsweeping, German aerodynamicist [[Dietrich Küchemann]] proposed and had tested a local indentation of the fuselage above and below the wing root. This proved to not be very effective.<ref name="GerDev">Meier, Hans-Ulrich, editor ''German Development of the Swept Wing 1935–1945'', AIAA Library of Flight, 2010. Originally published in German as ''Die deutsche Luftahrt Die Pfeilflügelentwicklung in Deutschland bis 1945'', Bernard & Graefe Verlag, 2006.</ref> During the development of the [[Douglas DC-8]] airliner, uncambered airfoils were used in the wing root area to combat the unsweeping.<ref>Shevell, Richard, "Aerodynamic Design Features", DC-8 design summary, February 22, 1957.</ref><ref>Dunn, Orville R., "Flight Characteristics of the DC-8", SAE paper 237A, presented at the SAE National Aeronautic Meeting, Los Angeles California, October 1960.</ref> ===Supersonic flight=== Swept wings on supersonic aircraft usually lie within the cone-shaped shock wave produced at the nose of the aircraft so they will "see" subsonic airflow and work as subsonic wings. The angle needed to lie behind the cone increases with increasing speed, at Mach 1.3 the angle is about 45 degrees, at Mach 2.0 it is 60 degrees.<ref>[http://www.centennialofflight.gov/essay/Theories_of_Flight/supersonic_flow/TH22G2.htm "Supersonic Wing design: The Mach cone becomes increasingly swept back with increasing Mach numbers."] {{webarchive|url=https://web.archive.org/web/20070930032627/http://www.centennialofflight.gov/essay/Theories_of_Flight/supersonic_flow/TH22G2.htm |date=30 September 2007 }} ''Centennial of Flight Commission,'' 2003. Retrieved: 1 August 2011.</ref> The angle of the [[Mach cone]] formed off the body of the aircraft will be at about sin μ = 1/M (μ is the sweep angle of the Mach cone).<ref>Haack, Wolfgang. [http://www.bwl.tu-darmstadt.de/bwl2/akl/downloads/kolloquien/%5bakl09%5d%20-%20heinzerling%20BILDER.pdf "Heinzerling, Supersonic Area Rule" (in German), p. 39.] {{webarchive|url=https://web.archive.org/web/20090327095031/http://www.bwl.tu-darmstadt.de/bwl2/akl/downloads/kolloquien/%5bakl09%5d%20-%20heinzerling%20BILDER.pdf |date=27 March 2009 }} ''bwl.tu-darmstadt.de.''</ref> === Disadvantages === {{More citations needed section|date = November 2021}} When a swept wing travels at high speed, the airflow has little time to react and simply flows over the wing almost straight from front to back. At lower speeds the air ''does'' have time to react, and is pushed spanwise by the angled leading edge, towards the wing tip. At the wing root, by the fuselage, this has little noticeable effect, but as one moves towards the wingtip the airflow is pushed spanwise not only by the leading edge, but the spanwise moving air beside it. At the tip the airflow is moving along the wing instead of over it, a problem known as ''spanwise flow''. The lift from a wing is generated by the airflow over it from front to rear. With increasing span-wise flow the boundary layers on the surface of the wing have longer to travel, and so are thicker and more susceptible to transition to turbulence or flow separation, also the effective aspect ratio of the wing is less and so air "leaks" around the wing tips reducing their effectiveness. The spanwise flow on swept wings produces airflow that moves the stagnation point on the leading edge of any individual wing segment further beneath the leading edge, increasing effective [[angle of attack]] of wing segments relative to its neighbouring forward segment. The result is that wing segments farther towards the rear operate at increasingly higher angles of attack promoting early stall of those segments. This promotes tip stall on back-swept wings, as the tips are most rearward, while delaying tip stall for forward-swept wings, where the tips are forward. With both forward and back-swept wings, the rear of the wing will stall first creating a nose-up moment on the aircraft. If not corrected by the pilot the plane will pitch up, leading to more of the wing stalling and more pitch up in a divergent manner. This uncontrollable instability came to be known as the ''[[Sabre dance (pitch-up)|Sabre dance]]'' in reference to the number of North American [[F-100 Super Sabre]]s that crashed on landing as a result.<ref name="historynet.com">{{cite web |url = http://www.historynet.com/deadly-sabre-dance.htm |title = Deadly Sabre Dance |date = 11 July 2011 |publisher = historynet.com |access-date = 11 November 2020}}</ref><ref>Ives, Burl. "Burl Ives Song Book." Ballantine Books, Inc., New York, November 1953, page 240.</ref> Reducing pitch-up to an acceptable level has been done in different ways such as the addition of a fin known as a ''[[wing fence]]'' on the upper surface of the wing to redirect the flow to a streamwise direction. The [[MiG-15]] was one example of an aircraft fitted with wing fences.<ref name="Gunston Russian p188">Gunston 1995, p. 188.</ref> Another closely related design was the addition of a [[dogtooth extension|dogtooth notch]] to the leading edge, used on the [[Avro Arrow]] interceptor.<ref>Whitcomb 2002, pp. 89–91.</ref> Other designs took a more radical approach, including the [[Republic XF-91 Thunderceptor]]'s wing that grew wider towards the tip to provide more lift at the tip. The [[Handley Page Victor]] was equipped with a [[crescent wing]], with three values of sweep, about 48 degrees near the wing root where the wing was thickest, a 38 degree transition length and 27 degrees for the remainder to the tip.<ref>Brookes 2011, pp. 6–7.</ref><ref>Lee, G.H. [http://www.flightglobal.com/pdfarchive/view/1954/1954%20-%201386.html "Aerodynamics of the Crescent Wing."] ''[[Flight International|Flight]]'', 14 May 1954, pp. 611–612.</ref> Modern solutions to the problem no longer require "custom" designs such as these. The addition of [[leading-edge slat]]s and large compound [[flap (aircraft)|flaps]] to the wings has largely resolved the issue.<ref name="Smith1975">[http://www.arvelgentry.com/amo/High-Lift_Aerodynamics.pdf High-Lift Aerodynamics, by A. M. O. Smith, McDonnell Douglas Corporation, Long Beach, June 1975] {{webarchive|url=https://web.archive.org/web/20110707172637/http://www.arvelgentry.com/amo/High-Lift_Aerodynamics.pdf |date=7 July 2011 }}</ref><ref>{{citation |first=F.|last= Handley Page |url=https://www.flightglobal.com/pdfarchive/view/1921/1921%20-%200844.html |title= Developments In Aircraft Design By The Use Of Slotted Wings | archive-url=https://web.archive.org/web/20121103181345/http://www.flightglobal.com/pdfarchive/view/1921/1921%20-%200844.html |archive-date=3 November 2012 |work=Flight |date= 22 December 1921 | page= 844 |via=Flightglobal Archive |volume= XIII |number=678 |url-status=live }}</ref><ref name=perkins-hage>Perkins, Courtland; Hage, Robert (1949). ''Airplane performance, stability and control'', Chapter 2, John Wiley and Sons. {{ISBN|0-471-68046-X}}.</ref> On fighter designs, the addition of [[leading-edge extension]]s, which are typically included to achieve a high level of maneuverability, also serve to add lift during landing and reduce the problem.<ref>{{cite web |last1=Lee |first1=Gwo-Bin |title=Leading-edge Vortices Control on a Delta Wing by Micromachined Sensors and Actuators |url=http://www.las.inpe.br/~jrsenna/AerospaceMEMS/Contr-Ensaios-voo/caltech1.pdf |publisher= American Institute of Aeronautics and Astronautics |access-date=18 October 2018}}</ref><ref>''Effects of Wing-Leading-Edge Modifications on a Full-Scale, Low-Wing General Aviation Airplane.'' Nasa TP, 2011.</ref> In addition to pitch-up there are other complications inherent in a swept-wing configuration. For any given length of wing, the actual span from tip-to-tip is shorter than the same wing that is not swept. There is a strong correlation between low-speed drag and [[aspect ratio (wing)|aspect ratio]], the span compared to chord, so a swept wing always has more drag at lower speeds. In addition, there is extra torque applied by the wing to the fuselage which has to be allowed for when establishing the transfer of wing-box loads to the fuselage. This results from the significant part of the wing lift which lies behind the attachment length where the wing meets the fuselage. ===Sweep theory=== [[Sweep theory]] is an [[aeronautical engineering]] description of the behavior of airflow over a [[wing]] when the wing's leading edge encounters the airflow at an oblique angle. The development of sweep theory resulted in the swept wing design used by most modern jet aircraft, as this design performs more effectively at transonic and [[supersonic]] speeds. In its advanced form, sweep theory led to the experimental [[oblique wing]] concept. [[Adolf Busemann]] introduced the concept of the swept wing and presented this in 1935 at the Fifth [[Volta Conference]] in Rome.<ref>{{cite web | url=https://scholar.google.com/scholar?cluster=11348315140095133548 | title=Google Scholar }}</ref> Sweep theory in general was a subject of development and investigation throughout the 1930s and 1940s, but the breakthrough mathematical definition of sweep theory is generally credited to [[NACA]]'s [[Robert Thomas Jones (engineer)|Robert T. Jones]] in 1945. Sweep theory builds on other wing lift theories. Lifting line theory describes lift generated by a straight wing (a wing in which the leading edge is perpendicular to the airflow). Weissinger theory describes the distribution of lift for a swept wing, but does not have the capability to include chordwise pressure distribution. There are other methods that do describe chordwise distributions, but they have other limitations. Jones' sweep theory provides a simple, comprehensive analysis of swept wing performance. An explanation of how the swept wing works was offered by [[Robert Thomas Jones (engineer)|Robert T. Jones]]: "Assume a wing is a cylinder of uniform airfoil cross-section, chord and thickness and is placed in an airstream at an angle of yaw – i.e., it is swept back. Now, even if the local speed of the air on the upper surface of the wing becomes supersonic, a shock wave cannot form there because it would have to be a sweptback shock – swept at the same angle as the wing – i.e., it would be an oblique shock. Such an oblique shock cannot form until the velocity component normal to it becomes supersonic."<ref>Sears, William Rees, ''Stories form a 20th-Century Life'', Parabolic Press, Inc., Stanford California, 1994</ref> To visualize the basic concept of simple sweep theory, consider a straight, non-swept wing of infinite length, which meets the airflow at a perpendicular angle. The resulting air pressure distribution is equivalent to the length of the wing's [[chord (aircraft)|chord]] (the distance from the leading edge to the trailing edge). If we were to begin to slide the wing sideways ([[spanwise]]), the sideways motion of the wing relative to the air would be added to the previously perpendicular airflow, resulting in an airflow over the wing at an angle to the leading edge. This angle results in airflow traveling a greater distance from leading edge to trailing edge, and thus the air pressure is distributed over a greater distance (and consequently lessened at any particular point on the surface). This scenario is identical to the airflow experienced by a swept wing as it travels through the air. The airflow over a swept wing encounters the wing at an angle. That angle can be broken down into two vectors, one perpendicular to the wing, and one parallel to the wing. The flow parallel to the wing has no effect on it, and since the perpendicular vector is shorter (meaning slower) than the actual airflow, it consequently exerts less pressure on the wing. In other words, the wing experiences airflow that is slower - and at lower pressures - than the actual speed of the aircraft. One of the factors that must be taken into account when designing a high-speed wing is [[compressibility]], which is the effect that acts upon a wing as it approaches and passes through the [[speed of sound]]. The significant negative effects of compressibility made it a prime issue with aeronautical engineers. Sweep theory helps mitigate the effects of compressibility in transonic and supersonic aircraft because of the reduced pressures. This allows the [[mach number]] of an aircraft to be higher than that actually experienced by the wing. There is also a negative aspect to sweep theory. The lift produced by a wing is directly related to the speed of the air over the wing. Since the airflow speed experienced by a swept wing is lower than what the actual aircraft speed is, this becomes a problem during slow-flight phases, such as takeoff and landing. There have been various ways of addressing the problem, including the [[variable-incidence wing]] design on the [[Vought F-8 Crusader]],<ref name="Bjorkman, Eileen 2015, p.62">Bjorkman, Eileen. Gunfighters. Air & Space, November 2015. p. 62.</ref> and [[Variable-sweep wing|swing wings]] on aircraft such as the [[Grumman F-14 Tomcat|F-14]], [[General Dynamics F-111|F-111]], and the [[Panavia Tornado]].<ref name="Woolridge">Woolridge, Capt. E.T., ed. ''Into the Jet Age: Conflict and Change in Naval Aviation 1945–1975, an Oral History''. Annapolis, Maryland: Naval Institute Press, 1995. {{ISBN|1-55750-932-8}}.</ref><ref name = "spickgreenswan 33">Spick, Green and Swanborough 2001, p. 33.</ref>
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