Trapezoidal wing

Last updated April 26, 2024

In aeronautics, a trapezoidal wing is a straight-edged and tapered wing planform. It may have any aspect ratio and may or may not be swept.^[1]^[2]^[3]

The thin, unswept, short-span, low-aspect-ratio trapezoidal configuration offers some advantages for high-speed flight and has been used on a small number of aircraft types. In this wing configuration, the leading edge sweeps back and the trailing edge sweeps forward.^[4] It can provide low aerodynamic drag at high speeds, while maintaining high strength and stiffness, and was used successfully during the early days of supersonic aircraft.

Design principles

Any wing with straight leading and trailing edges and with differing root and tip chords is a trapezoid, whether or not it is swept.^[5]

The area A of such a trapezoidal wing may be calculated from the span s, root chord c_r and tip chord c_t:

A=s{\frac {c_{r}+c_{t}}{2}}

The wing loading w is then given by the lift L divided by the area:

w={\frac {L}{A}}

In level flight, the amount of lift is equal to the gross weight.

In a straight trapezoidal wing, such as on the Bell X-1, the thickest part of the wing along its span, the line of maximum chord, runs straight out sideways from root to tip. The leading edge then sweeps backwards and the trailing edge sweeps forward.^[3] In a swept trapezoidal wing, the line of maximum chord is swept at an angle, usually forward. This increases the sweep of the leading edge and decreases the sweep of the trailing edge, and in the extreme case both edges sweep backwards by different amounts.^[5] The transition form, where the trailing edge is straight, is equivalent to a cropped delta planform.

High-speed trapezoidal wing

At supersonic speeds a thin, small and highly loaded wing offers substantially lower drag than other configurations. Low span and an unswept, tapered planform reduce structural stresses, allowing the wing to be made thin. For minimum drag, wing loading can be in excess of 400 kilograms per square metre (82 lb/sq ft).^{[ citation needed ]}

Early examples provided a solution to the problem of supersonic flight when engine power was limited. They were made so thin that they had to be machined from a thick, solid sheet of metal.^[6] Even with this low-drag wing the Douglas X-3 Stiletto was too underpowered to reach its design flight speed of Mach 2, but the design of its simple hexagonal-airfoil wing was developed for various other X-planes and for Lockheed's widely produced F-104 Starfighter Mach 2.2 high-altitude interceptor.

The small wing of the Starfighter was found to have good gust response at low level, providing a smooth ride at high subsonic speeds. Consequently, the type was adopted for the ground-attack role, notably by the German Luftwaffe. However, the high loading of the wing resulted in a high stalling speed with marginal take-off and landing characteristics and a corresponding high level of takeoff and landing accidents.

A variant with a curved airfoil, blunt trailing edge and conventional internal structure was developed for the North American X-15 rocket plane.^[6]

Lockheed continued to use the basic design on many of its aircraft proposals in the 1950s, including the Lockheed CL-400 Suntan and early versions of their supersonic transport designs.^{[ citation needed ]}

High-speed examples

X-planes

Military planes

Lockheed F-104 Starfighter

Related Research Articles

In aeronautics, the chord is an imaginary straight line joining the leading edge and trailing edge of an aerofoil. The chord length is the distance between the trailing edge and the point where the chord intersects the leading edge. The point on the leading edge used to define the chord may be the surface point of minimum radius. For a turbine aerofoil the chord may be defined by the line between points where the front and rear of a 2-dimensional blade section would touch a flat surface when laid convex-side up.

A delta wing is a wing shaped in the form of a triangle. It is named for its similarity in shape to the Greek uppercase letter delta (Δ).

A flying wing is a tailless fixed-wing aircraft that has no definite fuselage, with its crew, payload, fuel, and equipment housed inside the main wing structure. A flying wing may have various small protuberances such as pods, nacelles, blisters, booms, or vertical stabilizers.

A swept wing is a wing angled either backward or occasionally forward from its root rather than perpendicular to the fuselage.

The Lockheed L-2000 was Lockheed Corporation's entry in a government-funded competition to build the United States' first supersonic airliner in the 1960s. The L-2000 lost the contract to the Boeing 2707, but that competing design was ultimately canceled for political, environmental and economic reasons.

In aeronautics, the aspect ratio of a wing is the ratio of its span to its mean chord. It is equal to the square of the wingspan divided by the wing area. Thus, a long, narrow wing has a high aspect ratio, whereas a short, wide wing has a low aspect ratio.

A variable-sweep wing, colloquially known as a "swing wing", is an airplane wing, or set of wings, that may be swept back and then returned to its original straight position during flight. It allows the aircraft's shape to be modified in flight, and is therefore an example of a variable-geometry aircraft.

The Douglas X-3 Stiletto is a 1950s United States experimental jet aircraft with a slender fuselage and a long tapered nose, manufactured by the Douglas Aircraft Company. Its primary mission was to investigate the design features of an aircraft suitable for sustained supersonic speeds, which included the first use of titanium in major airframe components. Douglas designed the X-3 with the goal of a maximum speed of approximately 2,000 mph (3,200 km/h), but it was seriously underpowered for this purpose and could not even exceed Mach 1 in level flight. Although the research aircraft was a disappointment, Lockheed designers used data from the X-3 tests for the Lockheed F-104 Starfighter which used a similar trapezoidal wing design in a successful Mach 2 fighter.

An airplane or aeroplane, informally plane, is a fixed-wing aircraft that is propelled forward by thrust from a jet engine, propeller, or rocket engine. Airplanes come in a variety of sizes, shapes, and wing configurations. The broad spectrum of uses for airplanes includes recreation, transportation of goods and people, military, and research. Worldwide, commercial aviation transports more than four billion passengers annually on airliners and transports more than 200 billion tonne-kilometers of cargo annually, which is less than 1% of the world's cargo movement. Most airplanes are flown by a pilot on board the aircraft, but some are designed to be remotely or computer-controlled such as drones.

A supersonic aircraft is an aircraft capable of supersonic flight, that is, flying faster than the speed of sound. Supersonic aircraft were developed in the second half of the twentieth century. Supersonic aircraft have been used for research and military purposes, but only two supersonic aircraft, the Tupolev Tu-144 and the Concorde, ever entered service for civil use as airliners. Fighter jets are the most common example of supersonic aircraft.

A forward-swept wing or reverse-swept wing is an aircraft wing configuration in which the quarter-chord line of the wing has a forward sweep. Typically, the leading edge also sweeps forward.

<span class="mw-page-title-main">Elliptical wing</span> Airplane wing with an elliptical shape

An elliptical wing is a wing planform whose leading and trailing edges each approximate two segments of an ellipse. It is not to be confused with annular wings, which may be elliptically shaped.

The Avro 730 was a planned Mach 3 reconnaissance aircraft and strategic bomber that was being developed by Avro Aircraft for the Royal Air Force (RAF). It had been originally envisioned as a very high-speed aircraft to perform aerial reconnaissance missions, conforming with the requirements of Air Ministry Specification OR.330. Avro subsequently decided to modify the design of the proposed 730 in order to accommodate its arming with nuclear weapons; this change therefore meant that the type would be able to perform the nuclear weapons delivery mission as well, which had been called for under Air Ministry Specification RB.156T which sought a high speed reconnaissance-bomber aircraft.

The Handley Page HP.115 was an experimental delta wing aircraft designed and produced by the British aircraft manufacturer Handley Page. It was built to test the low-speed handling characteristics to be expected from the slender delta configuration anticipated for a future supersonic airliner.

A subsonic aircraft is an aircraft with a maximum speed less than the speed of sound. The term technically describes an aircraft that flies below its critical Mach number, typically around Mach 0.8. All current civil aircraft, including airliners, helicopters, future passenger drones, personal air vehicles and airships, as well as many military types, are subsonic.

In aeronautics, a tailless aircraft is an aircraft with no other horizontal aerodynamic surface besides its main wing. It may still have a fuselage, vertical tail fin, and/or vertical rudder.

The Lockheed XF-104 Starfighter was a single-engine, high-performance, supersonic interceptor prototype for a United States Air Force (USAF) series of lightweight and simple fighters. Only two aircraft were built; one aircraft was used primarily for aerodynamic research and the other served as an armament testbed, both aircraft being destroyed in accidents during testing. The XF-104s were forerunners of over 2,500 production Lockheed F-104 Starfighters.

<span class="mw-page-title-main">Wing configuration</span> Describes the general shape and layout of an aircraft wing

The wing configuration of a fixed-wing aircraft is its arrangement of lifting and related surfaces.

A supersonic airfoil is a cross-section geometry designed to generate lift efficiently at supersonic speeds. The need for such a design arises when an aircraft is required to operate consistently in the supersonic flight regime.

The crescent wing is a fixed-wing aircraft configuration in which a swept wing has a greater sweep angle on the inboard section than the outboard, giving the wing a crescent shape.

References

Notes

↑ Application #43. Trapezoidal High-Lift Wing, FUN3D (Fully Unstructured Navier-Stokes), NASA (retrieved 30 November 2015)
↑ Ilan Kroo ; AA241 Aircraft Design: Synthesis and Analysis Wing Geometry Definitions Archived 2015-10-13 at the Wayback Machine , Stanford University. (retrieved 30 November 2015)
1 2 G. Dimitriadis; Aircraft Design Lecture 2: Aerodynamics, Université de Liège. (retrieved 30 November 2015)
↑ Gunston, Bill. Jane's Aerospace Dictionary. London, England. Jane's Publishing Company Ltd, 1980. ISBN 0 531 03702 9, Page 436.
1 2 Tom Benson; Wing Area, NASA (retrieved 30 November 2015)
1 2 3 Miller, J.; The X-Planes, Speciality Press, 1983.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[1] Application #43. Trapezoidal High-Lift Wing, FUN3D (Fully Unstructured Navier-Stokes), NASA (retrieved 30 November 2015)

[2] Ilan Kroo ; AA241 Aircraft Design: Synthesis and Analysis Wing Geometry Definitions Archived 2015-10-13 at the Wayback Machine , Stanford University. (retrieved 30 November 2015)

[dimitriadis-3] 1 2 G. Dimitriadis; Aircraft Design Lecture 2: Aerodynamics, Université de Liège. (retrieved 30 November 2015)

[4] Gunston, Bill. Jane's Aerospace Dictionary. London, England. Jane's Publishing Company Ltd, 1980. ISBN 0 531 03702 9, Page 436.

[benson-5] 1 2 Tom Benson; Wing Area, NASA (retrieved 30 November 2015)

[miller-6] 1 2 3 Miller, J.; The X-Planes, Speciality Press, 1983.

[1]

[2]

[3]

[4]

[5]

[6]