Aspect ratio (aeronautics)

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In
aeronautics Aeronautics is the science or art involved with the study, design, and manufacturing of air flight–capable machines, and the techniques of operating aircraft and rockets within the atmosphere. The British Royal Aeronautical Society identifies ...
, the aspect ratio of a
wing A wing is a type of fin that produces lift while moving through air or some other fluid. Accordingly, wings have streamlined cross-sections that are subject to aerodynamic forces and act as airfoils. A wing's aerodynamic efficiency is expres ...
is the ratio of its
span Span may refer to: Science, technology and engineering * Span (unit), the width of a human hand * Span (engineering), a section between two intermediate supports * Wingspan, the distance between the wingtips of a bird or aircraft * Sorbitan ester ...
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.Kermode, A.C. (1972), ''Mechanics of Flight'', Chapter 3, (p.103, eighth edition), Pitman Publishing Limited, London Aspect ratio and other features of the
planform In technical drawing and computer graphics, a multiview projection is a technique of illustration by which a standardized series of orthographic two-dimensional pictures are constructed to represent the form of a three-dimensional object. Up to ...
are often used to predict the aerodynamic efficiency of a wing because the
lift-to-drag ratio In aerodynamics, the lift-to-drag ratio (or L/D ratio) is the lift generated by an aerodynamic body such as an aerofoil or aircraft, divided by the aerodynamic drag caused by moving through air. It describes the aerodynamic efficiency under gi ...
increases with aspect ratio, improving the fuel economy in powered airplanes and the gliding angle of sailplanes.

# Definition

The aspect ratio $\text$ is the ratio of the square of the wingspan $b$ to the projected wing area $S$, which is equal to the ratio of the wingspan $b$ to the standard mean chord $\text$: $\text \equiv \frac = \frac$

# Mechanism

As a useful simplification, an airplane in flight can be imagined to affect a circular cylinder of air with a diameter equal to the wingspan. A large wingspan affects a large cylinder of air, and a small wingspan affects a small cylinder of air. A small air cylinder must be pushed down with a greater power (energy change per unit time) than a large cylinder in order to produce an equal upward force (momentum change per unit time). This is because giving the same momentum change to a smaller mass of air requires giving it a greater velocity change, and a much greater energy change because energy is proportional to the square of the velocity while momentum is only linearly proportional to the velocity. The aft-leaning component of this change in velocity is proportional to the
induced drag In aerodynamics, lift-induced drag, induced drag, vortex drag, or sometimes drag due to lift, is an aerodynamic drag force that occurs whenever a moving object redirects the airflow coming at it. This drag force occurs in airplanes due to wings or ...
, which is the force needed to take up that power at that airspeed. The interaction between undisturbed air outside the cylinder of air, and the downward-moving cylinder of air occurs at the wingtips and can be seen as
wingtip vortices Wingtip vortices are circular patterns of rotating air left behind a wing as it generates lift.Clancy, L.J., ''Aerodynamics'', section 5.14 One wingtip vortex trails from the tip of each wing. Wingtip vortices are sometimes named ''trailing ...
. It is important to keep in mind that this is a drastic oversimplification, and an airplane wing affects a very large area around itself.

# In aircraft

Although a long, narrow wing with a high aspect ratio has aerodynamic advantages like better lift-to-drag-ratio (see also details below), there are several reasons why not ''all'' aircraft have high aspect-ratio wings: * Structural: A long wing has higher bending stress for a given load than a short one and therefore requires higher structural-design (architectural and/or material) specifications. Also, longer wings may have some torsion for a given load, and in some applications this torsion is undesirable (e.g. if the warped wing interferes with
aileron An aileron (French for "little wing" or "fin") is a hinged flight control surface usually forming part of the trailing edge of each wing of a fixed-wing aircraft. Ailerons are used in pairs to control the aircraft in roll (or movement around ...
effect). * Maneuverability: a low aspect-ratio wing will have a higher
roll Roll or Rolls may refer to: Movement about the longitudinal axis * Roll angle (or roll rotation), one of the 3 angular degrees of freedom of any stiff body (for example a vehicle), describing motion about the longitudinal axis ** Roll (aviation), ...
angular acceleration than one with high aspect ratio, because a high aspect-ratio wing has a higher moment of inertia to overcome. In a steady roll, the longer wing gives a higher roll moment because of the longer moment arm of the aileron. Low aspect-ratio wings are usually used on
fighter aircraft Fighter aircraft are fixed-wing military aircraft designed primarily for air-to-air combat. In military conflict, the role of fighter aircraft is to establish air superiority of the battlespace. Domination of the airspace above a battlefield ...
, not only for the higher roll rates, but especially for longer chord and thinner airfoils involved in supersonic flight. * Parasitic drag: While high aspect wings create less induced drag, they have greater
parasitic drag Parasitic drag, also known as profile drag, is a type of aerodynamic drag that acts on any object when the object is moving through a fluid. Parasitic drag is a combination of form drag and skin friction drag. It affects all objects regardless of ...
(drag due to shape, frontal area, and surface friction). This is because, for an equal wing ''area'', the average chord (length in the direction of wind travel over the wing) is smaller. Due to the effects of
Reynolds number In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be domi ...
, the value of the section drag coefficient is an inverse logarithmic function of the characteristic length of the surface, which means that, even if two wings of the same area are flying at equal speeds and equal angles of attack, the section drag coefficient is slightly higher on the wing with the smaller chord. However, this variation is very small when compared to the variation in induced drag with changing wingspan.
For example, the section drag coefficient $c_d\;$ of a
NACA The National Advisory Committee for Aeronautics (NACA) was a United States federal agency founded on March 3, 1915, to undertake, promote, and institutionalize aeronautical research. On October 1, 1958, the agency was dissolved and its assets ...
23012 airfoil (at typical lift coefficients) is inversely proportional to chord length to the power 0.129:
$c_d \varpropto \frac.$ :A 20% increase in chord length would decrease the section drag coefficient by 2.38%. * Practicality: low aspect ratios have a greater useful internal volume, since the maximum thickness is greater, which can be used to house the fuel tanks, retractable
landing gear Landing gear is the undercarriage of an aircraft or spacecraft that is used for takeoff or landing. For aircraft it is generally needed for both. It was also formerly called ''alighting gear'' by some manufacturers, such as the Glenn L. Martin ...
and other systems. * Airfield size: Airfields, hangars, and other ground equipment define a maximum wingspan, which cannot be exceeded. To generate enough lift at a given wingspan, the aircraft designer must increase wing area by lengthening the chord, thus lowering the aspect ratio. This limits the
Airbus A380 The Airbus A380 is a large wide-body airliner that was developed and produced by Airbus. It is the world's largest passenger airliner and only full-length double-deck jet airliner. Airbus studies started in 1988, and the project was annou ...
to 80m wide with an aspect ratio of 7.8, while the
Boeing 787 The Boeing 787 Dreamliner is an American wide-body jet airliner developed and manufactured by Boeing Commercial Airplanes. After dropping its unconventional Sonic Cruiser project, Boeing announced the conventional 7E7 on January 29, 2003, ...
or
Airbus A350 The Airbus A350 is a long-range, wide-body twin-engine jet airliner developed and produced by Airbus. The first A350 design proposed by Airbus in 2004, in response to the Boeing 787 Dreamliner, would have been a development of the A330 ...
have an aspect ratio of 9.5, influencing flight economy.Hamilton, Scott.
Updating the A380: the prospect of a neo version and what’s involved
Leehamnews.com, 3 February 2014. Accessed: 21 June 2014
Archived
on 8 April 2014.

## Variable aspect ratio

Aircraft which approach or exceed the speed of sound sometimes incorporate
variable-sweep wing 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 fli ...
s. These wings give a high aspect ratio when unswept and a low aspect ratio at maximum sweep. In subsonic flow, steeply swept and narrow wings are inefficient compared to a high-aspect-ratio wing. However, as the flow becomes transonic and then supersonic, the
shock wave In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a med ...
first generated along the wing's upper surface causes
wave drag In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (r ...
on the aircraft, and this drag is proportional to the span of the wing. Thus a long span, valuable at low speeds, causes excessive drag at transonic and supersonic speeds. By varying the sweep the wing can be optimised for the current flight speed. However, the extra weight and complexity of a moveable wing mean that such a system is not included in many designs.

# Birds and bats

The aspect ratios of birds' and bats' wings vary considerably. Birds that fly long distances or spend long periods soaring such as
albatross Albatrosses, of the biological family Diomedeidae, are large seabirds related to the procellariids, storm petrels, and diving petrels in the order Procellariiformes (the tubenoses). They range widely in the Southern Ocean and the North Pacifi ...
es and
eagle Eagle is the common name for many large birds of prey of the family Accipitridae. Eagles belong to several groups of genera, some of which are closely related. Most of the 68 species of eagle are from Eurasia and Africa. Outside this area, just ...
s often have wings of high aspect ratio. By contrast, birds which require good maneuverability, such as the
Eurasian sparrowhawk The Eurasian sparrowhawk (''Accipiter nisus''), also known as the northern sparrowhawk or simply the sparrowhawk, is a small bird of prey in the family Accipitridae. Adult male Eurasian sparrowhawks have bluish grey upperparts and orange-barred ...
, have wings of low aspect ratio.

# Details

For a constant-chord wing of chord ''c'' and span ''b'', the aspect ratio is given by: :$AR =$ If the wing is swept, ''c'' is measured parallel to the direction of forward flight. For most wings 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 The wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip. For example, the Boeing 777–200 has a wingspan of , and a wandering albatross (''Diomedea exulans'') caught in 1965 had a wingspan of ...
''b'' divided by the wing area ''S''. In symbols, :$AR =$. For such a wing with varying chord, the standard mean chord ''SMC'' is defined as :$SMC = =$ The performance of aspect ratio AR related to the lift-to-drag-ratio and wingtip vortices is illustrated in the formula used to calculate the drag coefficient of an aircraft $C_d\;$ :$C_D =C_ + \frac$ where :

## Wetted aspect ratio

The wetted aspect ratio considers the whole wetted surface area of the airframe, $S_w$, rather than just the wing. It is a better measure of the aerodynamic efficiency of an aircraft than the
wing aspect ratio 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 a ...
. It is defined as: :$\mathit_ =$ where $b$ is span and $S_w$ is the
wetted surface The surface area that interacts with the working fluid or gas. In maritime use, the wetted area is the area of the hull (watercraft) which is immersed in water. This has a direct relationship on the overall hydrodynamic drag of the ship or submar ...
. Illustrative examples are provided by the
Boeing B-47 The Boeing B-47 Stratojet (Boeing company designation Model 450) is a retired American long- range, six-engined, turbojet-powered strategic bomber designed to fly at high subsonic speed and at high altitude to avoid enemy interceptor aircraft ...
and
Avro Vulcan The Avro Vulcan (later Hawker Siddeley Vulcan from July 1963) is a jet-powered, tailless, delta-wing, high-altitude, strategic bomber, which was operated by the Royal Air Force (RAF) from 1956 until 1984. Aircraft manufacturer A.V. Roe and ...
. Both aircraft have very similar performance although they are radically different. The B-47 has a high aspect ratio wing, while the Avro Vulcan has a low aspect ratio wing. They have, however, a very similar wetted aspect ratio.

# See also

* Centerboard *
Wing configuration The wing configuration of a fixed-wing aircraft (including both glider (aircraft), gliders and powered aeroplanes) is its arrangement of lifting and related surfaces. Aircraft designs are often classified by their wing configuration. For examp ...

# References

* Anderson, John D. Jr, ''Introduction to Flight'', 5th edition, McGraw-Hill. New York, NY. * Anderson, John D. Jr, ''Fundamentals of Aerodynamics'', Section 5.3 (4th edition), McGraw-Hill. New York, NY. *
L. J. Clancy Laurence Joseph Clancy (15 March 1929 - 16 October 2014) was an Education Officer in aerodynamics at Royal Air Force College Cranwell whose textbook ''Aerodynamics'' became standard. He was born in Egypt to Alfred Joseph Clancy and Agnes Hunter. I ...
(1975), ''Aerodynamics'', Pitman Publishing Limited, London * John P. Fielding. ''Introduction to Aircraft Design'', Cambridge University Press, * Daniel P. Raymer (1989). ''Aircraft Design: A Conceptual Approach'', American Institute of Aeronautics and Astronautics, Inc., Washington, DC. * McLean, Doug, ''Understanding Aerodynamics: Arguing from the Real Physics'', Section 3.3.5 (1st Edition), Wiley. {{DEFAULTSORT:Aspect Ratio (Wing) Engineering ratios Aircraft wing design Wing configurations