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aerodynamics Aerodynamics () is the study of the motion of atmosphere of Earth, air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics, and is an ...
, wing loading is the total weight of an aircraft or flying animal divided by the area of its wing. The stalling speed, takeoff speed and landing speed of an aircraft are partly determined by its wing loading. The faster an aircraft flies, the more its
lift Lift or LIFT may refer to: Physical devices * Elevator, or lift, a device used for raising and lowering people or goods ** Paternoster lift, a type of lift using a continuous chain of cars which do not stop ** Patient lift, or Hoyer lift, mobile ...
is changed by a change in angle of attack, so a smaller wing is less adversely affected by vertical gusts. Consequently, faster aircraft generally have higher wing loadings than slower aircraft in order to avoid excessive response to vertical gusts. A higher wing loading also decreases maneuverability. The same constraints apply to winged biological organisms.


Range of wing loadings


Effect on performance

Wing loading is a useful measure of the stalling speed of an aircraft. Wings generate lift owing to the motion of air around the wing. Larger wings move more air, so an aircraft with a large wing area relative to its mass (i.e., low wing loading) will have a lower stalling speed. Therefore, an aircraft with lower wing loading will be able to take off and land at a lower speed (or be able to take off with a greater load). It will also be able to turn at a greater rate.


Effect on takeoff and landing speeds

The lift force ''L'' on a wing of area ''A'', traveling at
true airspeed The true airspeed (TAS; also KTAS, for ''knots true airspeed'') of an aircraft is the speed of the aircraft relative to the air mass through which it is flying. The true airspeed is important information for accurate navigation of an aircraft. Tra ...
''v'' is given by L = \tfrac \rho v^2 A C_L, where ''ρ'' is the density of air, and ''C''L is the
lift coefficient In fluid dynamics, the lift coefficient () is a dimensionless quantity that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area. A lifting body is a foil or a co ...
. The lift coefficient is a dimensionless number that depends on the wing cross-sectional profile and the
angle of attack In fluid dynamics, angle of attack (AOA, α, or \alpha) is the angle between a Airfoil#Airfoil terminology, reference line on a body (often the chord (aircraft), chord line of an airfoil) and the vector (geometry), vector representing the relat ...
. At steady flight, neither climbing nor diving, the lift force and the weight are equal. With ''L''/''A'' = ''Mg''/''A'' = ''W''S''g'', where ''M'' is the aircraft mass, ''W''S = ''M''/''A'' the wing loading (in mass/area units, i.e. lb/ft2 or kg/m2, not force/area) and ''g'' the acceleration due to gravity, this equation gives the speed ''v'' through v^2 = \frac. As a consequence, aircraft with the same ''C''L at takeoff under the same atmospheric conditions will have takeoff speeds proportional to \sqrt. So if an aircraft's wing area is increased by 10% and nothing else is changed, the takeoff speed will fall by about 5%. Likewise, if an aircraft designed to take off at 150 mph grows in weight during development by 40%, its takeoff speed increases to 150 \sqrt ≈ 177 mph. Some flyers rely on their muscle power to gain speed for takeoff over land or water. Ground nesting and water birds have to be able to run or paddle at their takeoff speed before they can take off. The same is true for a hang-glider pilot, though they may get assistance from a downhill run. For all these, a low ''W''S is critical, whereas
passerine A passerine () is any bird of the order Passeriformes (; from Latin 'sparrow' and '-shaped') which includes more than half of all bird species. Sometimes known as perching birds, passerines generally have an anisodactyl arrangement of their ...
s and cliff-dwelling birds can get airborne with higher wing loadings.


Effect on turning performance

To turn, an aircraft must roll in the direction of the turn, increasing the aircraft's bank angle. Turning flight lowers the wing's lift component against gravity and hence causes a descent. To compensate, the lift force must be increased by increasing the angle of attack by use of up
elevator An elevator (American English) or lift (Commonwealth English) is a machine that vertically transports people or freight between levels. They are typically powered by electric motors that drive traction cables and counterweight systems suc ...
deflection, which increases drag. Turning can be described as "climbing around a circle" (wing lift is diverted to turning the aircraft), so the increase in wing
angle of attack In fluid dynamics, angle of attack (AOA, α, or \alpha) is the angle between a Airfoil#Airfoil terminology, reference line on a body (often the chord (aircraft), chord line of an airfoil) and the vector (geometry), vector representing the relat ...
creates even more drag. The tighter the turn
radius In classical geometry, a radius (: radii or radiuses) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is th ...
attempted, the more drag induced; this requires that power (thrust) be added to overcome the drag. The maximum rate of turn possible for a given aircraft design is limited by its wing size and available engine power: the maximum turn the aircraft can achieve and hold is its ''sustained turn performance''. As the bank angle increases, so does the
g-force The g-force or gravitational force equivalent is a Specific force, mass-specific force (force per unit mass), expressed in Unit of measurement, units of standard gravity (symbol ''g'' or ''g''0, not to be confused with "g", the symbol for ...
applied to the aircraft, this having the effect of increasing the wing loading and also the stalling speed. This effect is also experienced during level pitching maneuvers. As stalling is due to wing loading and maximum lift coefficient at a given altitude and speed, this limits the turning radius due to maximum load factor. At Mach 0.85 and 0.7 lift coefficient, a wing loading of can reach a structural limit of 7.33''g'' up to and then decreases to 2.3''g'' at . With a wing loading of the load factor is twice smaller and barely reaches 1''g'' at . Aircraft with low wing loadings tend to have superior sustained turn performance because they can generate more lift for a given quantity of engine thrust. The immediate bank angle an aircraft can achieve before drag seriously bleeds off airspeed is known as its ''instantaneous turn performance''. An aircraft with a small, highly loaded wing may have superior instantaneous turn performance, but poor sustained turn performance: it reacts quickly to control input, but its ability to sustain a tight turn is limited. A classic example is the F-104 Starfighter, which has a very small wing and high wing loading. At the opposite end of the spectrum was the large
Convair B-36 The Convair B-36 "Peacemaker" is a strategic bomber built by Convair and operated by the United States Air Force (USAF) from 1949 to 1959. The B-36 is the largest mass-produced piston-engined aircraft ever built, although it was exceeded in span ...
: its large wings resulted in a low wing loading that could make it sustain tighter turns at high altitude than contemporary jet fighters, while the slightly later
Hawker Hunter The Hawker Hunter is a transonic British jet propulsion, jet-powered fighter aircraft that was developed by Hawker Aircraft for the Royal Air Force (RAF) during the late 1940s and early 1950s. It was designed to take advantage of the newly dev ...
had a similar wing loading of . The Boeing 367-80 airliner prototype could be rolled at low altitudes with a wing loading of at maximum weight. Like any body in
circular motion In physics, circular motion is movement of an object along the circumference of a circle or rotation along a circular arc. It can be uniform, with a constant rate of rotation and constant tangential speed, or non-uniform with a changing rate ...
, an aircraft that is fast and strong enough to maintain level flight at speed ''v'' in a circle of radius ''R'' accelerates towards the center at v^2/R. This acceleration is caused by the inward horizontal component of the lift, L sin\theta, where \theta is the banking angle. Then from
Newton's second law Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body re ...
, \frac = L \sin\theta = \frac v^2\rho C_L A \sin\theta. Solving for ''R'' gives R = \frac. The lower the wing loading, the tighter the turn. Gliders designed to exploit
thermal A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example ...
s need a small turning circle in order to stay within the rising air column, and the same is true for soaring birds. Other birds, for example, those that catch insects on the wing, also need high maneuverability. All need low wing loadings.


Effect on stability

Wing loading also affects ''gust response'', the degree to which the aircraft is affected by turbulence and variations in air density. A small wing has less area on which a gust can act, both of which serve to smooth the ride. For high-speed, low-level flight (such as a fast low-level bombing run in an
attack aircraft An attack aircraft, strike aircraft, or attack bomber is a tactical military aircraft that has a primary role of carrying out airstrikes with greater precision than bombers, and is prepared to encounter strong low-level air defenses while pr ...
), a small, thin, highly loaded wing is preferable: aircraft with a low wing loading are often subject to a rough, punishing ride in this flight regime. The
F-15E Strike Eagle The McDonnell Douglas (now Boeing) F-15E Strike Eagle is an American all-weather multirole strike fighter derived from the McDonnell Douglas F-15 Eagle. Intended for the Dual-Role Fighter (DRF) program (initially called Enhanced Tactical Fi ...
has a wing loading of (excluding fuselage contributions to the effective area), whereas most delta-wing aircraft (such as the Dassault Mirage III, for which ''W''S = 387 kg/m2) tend to have large wings and low wing loadings. Quantitatively, if a gust produces an upward pressure of ''G'' (in N/m2, say) on an aircraft of mass ''M'', the upward acceleration ''a'' will, by
Newton's second law Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body re ...
be given by a = \frac = \frac, decreasing with wing loading.


Effect of development

A further complication with wing loading is that it is difficult to substantially alter the wing area of an existing aircraft design (although modest improvements are possible). As aircraft are developed they are prone to "''weight growth''"—the addition of equipment and features that substantially increase the operating mass of the aircraft. An aircraft whose wing loading is moderate in its original design may end up with very high wing loading as new equipment is added. Although engines can be replaced or upgraded for additional thrust, the effects on turning and takeoff performance resulting from higher wing loading are not so easily reconciled.


Water ballast use in gliders

Modern gliders often use water ballast carried in the wings to increase wing loading when soaring conditions are strong. By increasing the ''wing loading'' the average speed achieved across country can be increased to take advantage of strong thermals. With a higher wing loading, a given
lift-to-drag ratio In aerodynamics, the lift-to-drag ratio (or L/D ratio) is the Lift (force), 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 efficie ...
is achieved at a higher
airspeed In aviation, airspeed is the speed of an aircraft relative to the air it is flying through (which itself is usually moving relative to the ground due to wind). In contrast, the ground speed is the speed of an aircraft with respect to the sur ...
than with a lower wing loading, and this allows a faster average speed across country. The ballast can be ejected overboard when conditions weaken or prior to landing.


Design considerations


Fuselage lift

A blended wing-fuselage design such as that found on the
General Dynamics F-16 Fighting Falcon The General Dynamics F-16 Fighting Falcon is an American single-engine supersonic Multirole combat aircraft, multirole fighter aircraft originally developed by General Dynamics for the United States Air Force (USAF). Designed as an air superio ...
or Mikoyan MiG-29 Fulcrum helps to reduce wing loading; in such a design the fuselage generates aerodynamic lift, thus improving wing loading while maintaining high performance.


Variable-sweep wing

Aircraft like the
Grumman F-14 Tomcat The Grumman F-14 Tomcat is an American carrier-capable supersonic aircraft, supersonic, twinjet, twin-engine, Tandem#Aviation, tandem two-seat, twin-tail, all-weather-capable variable-sweep wing fighter aircraft. The Tomcat was developed for t ...
and the
Panavia Tornado The Panavia Tornado is a family of twin-engine, variable-sweep wing multi-role combat aircraft, jointly developed and manufactured by Italy, the United Kingdom and Germany. There are three primary #Variants, Tornado variants: the Tornado IDS ...
employ
variable-sweep wing A variable-sweep wing, colloquially known as a "swing wing", is an airplane wing, or set of wings, that may be modified during flight, swept back and then returned to its previous straight position. Because it allows the aircraft's shape to ...
s. As their wing area varies in flight so does the wing loading (although this is not the only benefit). When the wing is in the forward position takeoff and landing performance is greatly improved.


Flaps

Like all aircraft flaps, Fowler flaps increase the camber and hence the maximum value of lift coefficient (''C''Lmax) lowering the landing speed. They also increase wing area, decreasing the wing loading, which further lowers the landing speed.Anderson 1999, pp. 30–1 High lift devices such as certain flaps allow the option of smaller wings to be used in a design in order to achieve similar landing speeds compared to an alternate design using a larger wing without a high lift device. Such options allow for higher wing loading in a design. This may result in beneficial features, such as higher cruise speeds or a reduction in bumpiness at high speed low altitude flight (the latter feature is very important for close air support aircraft roles). For instance, Lockheed's Starfighter uses internal Blown flaps to achieve a high wing loading design (723 kg/m²) which allows it a much smoother low altitude flight at full throttle speeds compared to low wing loading delta designs such as the Mirage 2000 or Mirage III (387 kg/m²). The F-16 which has a relatively high wing loading of 689 kg/m² uses leading-edge extensions to increase wing lift at high angles of attack.


See also

*
Disk loading In fluid dynamics, disk loading or disc loading is the average pressure change across an actuator disk, such as an airscrew. Airscrews with a relatively low disk loading are typically called rotors, including helicopter Helicopter rotor, main ro ...
*
Lift coefficient In fluid dynamics, the lift coefficient () is a dimensionless quantity that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area. A lifting body is a foil or a co ...
*
Wing warping Wing warping was an early system for lateral (roll) control of a fixed-wing aircraft or kite. The technique, used and patented by the Wright brothers, consisted of a system of pulleys and cables to twist the trailing edges of the wings in opposit ...


References


Notes


Bibliography

* *


Notes


External links

* * {{DEFAULTSORT:Wing Loading Aircraft aerodynamics Aircraft configurations Aircraft performance Gliding technology