Wing loading

In aerodynamics, wing loading is the loaded weight of the aircraft divided by the area of the wing.Thom, 1988. p. 6. The faster an aircraft flies, the more lift is produced by each unit area of wing, so a smaller wing can carry the same weight in level flight, operating at a higher wing loading. Correspondingly, the landing and take-off speeds will be higher. The high wing loading also decreases maneuverability. The same constraints apply to birds and bats.
==Units==
Aircraft "weights" are always given as masses, i.e. in units like kilograms or pounds. Wing loadings are nearly always given in either lb/ft2 or kg/m2. Occasionally force units replace mass, so then the wing loading is in N/m2. To get from lb/ft2 to kg/m2, multiply by 4.88; to get from kg/m2 to N/m2, multiply by 9.81. This last number is the standard value of the gravitational field in m/s2; the real field, g varies slightly with place and altitude but by less than about 1%.
==Range of wing loadings==
Aircraft 	Fun 160Airborne Fun 160: http://www.airborne.com.au/pages/hg_fun.html	ASK 21	Nieuport 17	Ikarus C42	Cessna 152	Vans RV-4	Spitfire V	DC-3 	B-17 	Bf 109 	B-36 	Eurofighter	F-104 	A380 	B747
Wing Loading(kg/m2)	6.3 	33 	38 	38 	51 	67 	120 	123 	190 	210 	272 	311 	514 	663 	740
Role 	hang glider 	glider	fighter 	microlight	private 	sports 	fighter 	airliner	bomber	fighter	bomber	fighter 	fighter	airliner	airliner
Date 	2007 	1990 	1916 	1997 	1978 	1980 	1940 	1936 	1938 	1937 	1949 	1998 	1958 	2007 	1970
The table, which shows wing loadings is intended to give a feeling for the range of wing loadings used by fixed wing aircraft. Maximum weights have been used. There will be variations amongst variants of any particular type. The dates are approximate, indicating period of introduction.
The critical limit for bird flight is about 5 lb/ft2 (25 kg/m2)Meunier, 1951. An analysis of bird flight which looked at 138 species ranging in mass from 1x10-2 to 10 kg, from small passerines to swans and cranes found wing loadings from about 1 to 20 kg/m2http://www.biology-online.org/articles/flight-speeds-among-bird-species.html. The wing loadings of some of the lightest aircraft fall comfortably within this range. One typical hang-glider (see table) has a maximum wing loading of 6.3 kg/m2, and an ultralight rigid gliderBUG4 http://home.att.net/~m--sandlin/bug.htm 8.3 kg/m2.
 
==Effect on performance==
Wing loading is a useful measure of the general maneuvring 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 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 faster.
===Effect on take-off and landing speeds===
Quantitatively, the lift force L on a wing of area A, travelling at speed v is given by
\textstyle\frac{L}{A}=\tfrac{1}{2}v^2\rho C_L ,
where \rho 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. At take-off or in steady flight, neither climbing or 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 and g the acceleration due to gravity, that equation gives the speed v through
\textstyle v^2=\frac {2gW_S} {\rho C_L} .
As a consequence, aircraft with the same CL at take-off under the same atmospheric conditions will have take off speeds proportional to \scriptstyle\sqrt {W_S}. So if an aircraft's wing area is increased by 10% and nothing else changed, the take-off 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 take-off speed increases to \scriptstyle150 \sqrt{1.4} = 177 mph.
Some flyers rely on their muscle power to gain speed for take-off over land or water. Ground nesting and water birds have to be able to run or paddle at their take-off 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 performance===
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.
The second equation given above applies again to the cruise in level flight, though \rho and particularly CL will be smaller than at take-off, CL because of a lower angle of incidence and the retraction of flaps or slots; 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\textstyle Ma_c=\tfrac{1}{2}v_c^2\rho C_LA -Mg
or
 \textstyle a_c=\frac{1}{2W_S}v_c^2\rho C_L -g,so the initial upward acceleration is inversely proportional 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 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 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 has the effect of increasing the wing loading and also the stalling speed. This effect is also experienced during level pitching manouevers. Spick, 1986. p.24. 
 
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 gigantic Convair B-36. Its large wings resulted in a low wing loading, and there are disputed claims that this made the bomber more agile than contemporary jet fighters (the slightly later Hawker Hunter had a similar wing loading of 250 kg/m2) at high altitude. Whatever the truth of that, the delta winged Avro Vulcan bomber, with a wing loading of 260 kg/m2 could certainly be rolled at low altitudeshttp://uk.youtube.com/watch?v=X4r0Kk-xX4o.
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 \scriptstyle\frac{v^2} {R}. That acceleration is caused by the inward horizontal component of the lift, \scriptstyle L sin\theta, where \theta is the banking angle. Then from Newton's second law ,\textstyle\frac{Mv^2}{R}=L\sin\theta=\frac{1}{2}v^2\rho C_L A\sin\theta. Tidying up gives \textstyle R=\frac{2W_s}{\rho C_L\sin\theta}. 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 manouevrability. 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), 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 been criticized for its ride quality, despite its wing loading of 650 kg/m2 (excluding fuselage contributions to the effective area), as have most delta wing aircraft (such as the Dassault Mirage III, for which WS = 387 kg/m2) which 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 be given by \textstyle a=\frac {GA} {M}=\frac {G} {W_S} ,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 take-off 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 lift-to-drag ratio is increased at higher airspeeds. The ballast can be dumped overboard when conditions weaken Maximizing glider cross-country speed. (see Gliding competitions)
==Design considerations==
===Fuselage lift===
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 wing===
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). In the forward position takeoff and landing performance is greatly improved.Spick, 1986. p.84-87. 
===Fowler flaps===
The use of Fowler flaps increases the wing area, decreasing the wing loading which allows slower landing approach speeds.
==See also==
*Disk loading
*Lift coefficient
==References==
===Notes===
===Bibliography===
* Meunier, K. Korrelation und Umkonstruktionen in den Größenbeziehungen zwischen Vogelflügel und Vogelkörper-Biologia Generalis 1951: p403-443. [Article in German]
* Thom, Trevor. The Air Pilot's Manual 4-The Aeroplane-Technical. 1988. Shrewsbury, Shropshire, England. Airlife Publishing Ltd. ISBN 1-85310-017-X
* Spick, Mike. Jet Fighter Performance-Korea to Vietnam. 1986. Osceola, Wisconsin. Motorbooks International. ISBN 0-7110-1582-1
==External links==
*NASA article on wing loading Retrieved 8 February 2008
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