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The Lockheed F-104 Starfighter has a high wing loading (723 kg/m2 at maximum weight.)
A very low wing loading on a flexible-wing hang glider

In aerodynamics, wing loading is the total mass of an aircraft divided by the area of its wing.[1] The stalling speed of an aircraft in straight, level flight is partly determined by its wing loading. An aircraft with a low wing loading has a larger wing area relative to its mass, as compared to an aircraft with a high wing loading.

The faster an aircraft flies, the more lift can be produced by each unit of wing area, so a smaller wing can carry the same mass in level flight. Consequently, faster aircraft generally have higher wing loadings than slower aircraft. This increased wing loading also increases takeoff and landing distances. A higher wing loading also decreases maneuverability. The same constraints apply to winged biological organisms.

Contents

Range of wing loadingsEdit

Wing loading examples[2]
Aircraft Type Introduction MTOW Wing area kg/m² lb/sqft
Monarch Butterfly Animal Cenozoic 0.168 0.034
birds[a] Animal Cretaceous 1–20 0.20–4.10[3]
bird flight upper critical limit 25 5.1[4]
Ozone Buzz Z3 MS Paraglider 2010 75–95 kg (165–209 lb) 25.8 m2 (278 sq ft) 2.9–3.7 0.59–0.76[5]
Wills Wing Sport 2 155 Hang glider 2004 94.8–139.8 kg (209–308 lb) 14.4 m2 (155 sq ft) 6.6–9.7 1.4–2.0[6]
upper limit Microlift glider 2008 220 kg (490 lb) max. 12.2 m2 (131 sq ft) min.[b] 18 3.7[7]
UK CAA microlight wing loading limit 450 kg (990 lb) max. [c] 18 m2 (190 sq ft) min.[d] 25 5.1[8]
Schleicher ASW 22 sailplane 1981 1,023 kg (2,255 lb) 16.7 m2 (180 sq ft) 61.3 12.6
Piper Warrior General aviation 1960 1,055 kg (2,326 lb) 15.14 m2 (163.0 sq ft) 69.7 14.3
Beech Baron General aviation twin 1960 2,313 kg (5,099 lb) 18.5 m2 (199 sq ft) 125 26
Supermarine Spitfire WWII Fighter 1938 3,039 kg (6,700 lb) 22.48 m2 (242.0 sq ft) 135 28
Beechcraft Airliner Regional airliner 1968 4,727 kg (10,421 lb) 25.99 m2 (279.8 sq ft) 182 37
Learjet 31 Business jet 1990 7,031 kg (15,501 lb) 24.57 m2 (264.5 sq ft) 286 59
Mig-23 Variable-geometry fighter 1970 17,800 kg (39,200 lb) 34.16–37.35 m2 (367.7–402.0 sq ft) 477–521 98–107
General Dynamics F-16 Multirole fighter 1978 19,200 kg (42,300 lb) 27.87 m2 (300.0 sq ft) 688.9 141.1
Fokker F27 turboprop airliner 1958 19,773 kg (43,592 lb) 70 m2 (750 sq ft) 282 58
McDonnell Douglas F-15 Air superiority fighter 1976 30,845 kg (68,002 lb) 56.5 m2 (608 sq ft) 546 112
Fokker F28 Regional Jet 1969 33,000 kg (73,000 lb) 78.97 m2 (850.0 sq ft) 418 86
Boeing 737-300 Narrow-body airliner 1984 62,820 kg (138,490 lb) 91.04 m2 (979.9 sq ft) 690 140
Boeing 737-900 Narrow-body airliner 2001 84,139 kg (185,495 lb) 124.6 m2 (1,341 sq ft) 675 138
Boeing 767 Wide-body airliner 1982 142,882 kg (315,001 lb) 283.3 m2 (3,049 sq ft) 504 103
Concorde Supersonic transport 1976 187,000 kg (412,000 lb) 358.2 m2 (3,856 sq ft) 522 107
Boeing 777 Wide-body airliner 1995 247,200 kg (545,000 lb) 427.8 m2 (4,605 sq ft) 578 118
Boeing 747 Large aircraft 1977 333,000 kg (734,000 lb) 511 m2 (5,500 sq ft) 652 134
Airbus A380 Large aircraft 2007 575,000 kg (1,268,000 lb) 845 m2 (9,100 sq ft) 680 140

Effect on performanceEdit

Wing loading is a useful measure of the general maneuvering performance of an aircraft. Wings generate lift owing to the motion of air over the wing surface. Larger wings move more air, so an aircraft with a large wing area relative to its mass (i.e., low wing loading) will have more lift available at any given 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 higher speed.

Effect on takeoff and landing speedsEdit

Quantitatively, the lift force L on a wing of area A, traveling at speed v is given by

 ,

where ρ is the density of air and CL is the lift coefficient. The latter is a dimensionless number of order unity which depends on the wing cross-sectional profile and the angle of attack.[9] At take-off or in steady flight, neither climbing nor diving, the lift force and the weight are equal. With L/A = Mg/A =WSg, where M is the aircraft mass, WS = 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, that equation gives the speed v through[10]

  .

As a consequence, aircraft with the same CL at takeoff under the same atmospheric conditions will have takeoff speeds proportional to  . So if an aircraft's wing area is increased by 10% and nothing else 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   = 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 and the same is so for a hang glider pilot, though he or she may get an assist from a downhill run. For all these a low WS is critical, whereas passerines and cliff dwelling birds can get airborne with higher wing loadings.

Effect on climb rate and cruise performanceEdit

Wing loading has an effect on an aircraft's climb rate. A lighter loaded wing will have a superior rate of climb compared to a heavier loaded wing as less airspeed is required to generate the additional lift to increase altitude. A lightly loaded wing has a more efficient cruising performance because less thrust is required to maintain lift for level flight. However, a heavily loaded wing is more suited for higher speed flight because smaller wings offer less drag.

The second equation given above applies again to the cruise in level flight, though   and particularly CL will be smaller than at take-off, CL because of a lower angle of incidence and the retraction of flaps or slats; the speed needed for level flight is lower for smaller WS.

The wing loading is important in determining how rapidly the climb is established. If the pilot increases the speed to vc the aircraft will begin to rise with vertical acceleration ac because the lift force is now greater than the weight. Newton's second law tells us this acceleration is given by

 

or

 

so the initial upward acceleration is inversely proportional (reciprocal) to WS. Once the climb is established the acceleration falls to zero as the sum of the upward components of lift plus engine thrust minus drag becomes numerically equal to the weight.

Effect on turning performanceEdit

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 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 creates even more drag. The tighter the turn radius 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 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.[11]

 
Load factor varying with altitude at 50 or 100 lb/sq ft

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 50 lb/sq ft (240 kg/m2) can reach a structural limit of 7.33 g up to 15,000 feet and then decreases to 2.3 g at 40,000 feet while with a wing loading of 100 lb/sq ft (490 kg/m2) the load factor is twice smaller and barely reach 1g at 40,000 feet.[12]

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 723 kg/m2 (148 lb/sq ft) wing loading.

At the opposite end of the spectrum was the large Convair B-36: its large wings resulted in a low 269 kg/m2 (55 lb/sq ft) wing loading that could made it sustain tighter turns at high altitude than contemporary jet fighters, while the slightly later Hawker Hunter had a similar wing loading of 344 kg/m2 (70 lb/sq ft). The Boeing 367-80 airliner prototype could be rolled at low altitudes with a wing loading of 387 kg/m2 (79 lb/sq ft).

Like any body in circular motion, an aircraft that is fast and strong enough to maintain level flight at speed v in a circle of radius R accelerates towards the centre at  . That acceleration is caused by the inward horizontal component of the lift,  , where   is the banking angle. Then from Newton's second law,

 

Solving for R gives

 

The smaller the wing loading, the tighter the turn.

Gliders designed to exploit thermals 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 stabilityEdit

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), 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 has a wing loading of 650 kg/m2 (excluding fuselage contributions to the effective area), whereas most delta wing aircraft (such as the Dassault Mirage III, for which WS = 387 kg/m2) tend to have large wings and low wing loadings.[citation needed]

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 be given by

 ,

decreasing with wing loading.

Effect of developmentEdit

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 glidersEdit

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 is achieved at a higher airspeed than with a lower wing loading, and this allows a faster average speed across country. The ballast can be ejected overboard when conditions weaken to maximize glider cross-country speed in gliding competitions.

Design considerationsEdit

Fuselage liftEdit

 
The F-15E Strike Eagle has a large relatively lightly loaded wing

A blended wing-fuselage design such as that found on the F-16 Fighting Falcon or 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 wingEdit

Aircraft like the F-14 Tomcat and the Panavia Tornado employ variable-sweep wings. 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.[13]

Fowler flapsEdit

Like all aircraft flaps, Fowler flaps increase the camber and hence CL, lowering the landing speed. They also increase wing area, decreasing the wing loading, which further lowers the landing speed.[14]

See alsoEdit

ReferencesEdit

NotesEdit

  1. ^ Thom, Trevor. The Air Pilot's Manual 4-The Aeroplane-Technical. 1988. Shrewsbury, Shropshire, England. Airlife Publishing Ltd. ISBN 1-85310-017-X, p. 6.
  2. ^ Henk Tennekes (2009). The simple science of Flight: From Insects to Jumbo Jets. MIT Press. ISBN 9780262513135. , "Figure 2: The great flight diagram". 
  3. ^ Thomas Alerstam , Mikael Rosén, Johan Bäckman, Per G. P Ericson, Olof Hellgren (July 17, 2007). "Flight Speeds among Bird Species: Allometric and Phylogenetic Effects". PLoS Biology. 
  4. ^ Meunier, K. Korrelation und Umkonstruktionen in den Größenbeziehungen zwischen Vogelflügel und Vogelkörper-Biologia Generalis 1951: p403-443. [Article in German]
  5. ^ Gérard Florit (23 Jan 2016). "Ozone Buzz Z3". P@r@2000. 
  6. ^ "Sport 2 / 2C". Wills Wing. 
  7. ^ "Sporting Code Section 3: Gliding". Fédération Aéronautique Internationale. 12 October 2016. 
  8. ^ "Microlights". UK CAA. 
  9. ^ Anderson, 1999 p.58
  10. ^ Anderson, 1999 pp. 201-3
  11. ^ Spick, 1986. p.24.
  12. ^ Laurence K. Loftin, Jr. (1985). "Chapter 11 - Aircraft Maneuverability". Quest for Performance - The Evolution of Modern Aircraft. NASA Scientific and Technical Information Branch. 
  13. ^ Spick, 1986. p.84-87.
  14. ^ Anderson 1999, pp.30-1

BibliographyEdit

  • Anderson, John D. Jnr. (1999). Aircraft Performance and Design. Cambridge: WCB/McGraw-Hill. ISBN 0-07-116010-8. 
  • Spick, Mike. Jet Fighter Performance-Korea to Vietnam. 1986. Osceola, Wisconsin. Motorbooks International. ISBN 0-7110-1582-1

NotesEdit

  1. ^ 138 species from 10 g to 10 kg, from small passerines to swans and cranes
  2. ^ at max weight
  3. ^ for a two seat landplane
  4. ^ at max weight

External linksEdit