Wing loading

In aerodynamics, wing loading is the loaded weight of the aircraft divided by the area of the wing.^[1] An aircraft with a low wing loading has a larger wing area relative to its weight (i.e. a glider), as compared to an aircraft with a high wing loading (i.e. fighter jet, or modern airliner).

The faster an aircraft flies, the more lift is produced by each unit of wing area, so a smaller wing can carry the same weight in level flight, therefore increasing the wing loading. This increased wing load also increases takeoff and landing distances and speeds. A high wing loading also decreases maneuverability. The same constraints apply to winged biological organisms.

A highly loaded wing on a Lockheed F-104 Starfighter

A very low wing loading on a flexible-wing hang glider

Range of wing loadings

Aircraft	Buzz Z3[2][3]	Fun 160[4]	ASK 21	Nieuport 17	Ikarus C42	Cessna 152	Vans RV-4	DC-3	Spitfire	Bf-109	B-17	B-36	Eurofighter Typhoon	F-104	A380	B747	MD-11F
Role	paraglider	hang glider	glider	World War I fighter	microlight	trainer	sports	airliner	World War II fighter	World War II fighter	World War II bomber	intercontinental bomber	multi-role fighter	jet interceptor	large airliner	large airliner	medium-long range airliner
Year introduced	2010	2007	1979	1916	1997	1978	1980	1936	1938	1937	1938	1949	2003	1958	2007	1970	1990
Wing loading (kg/m^2)	3.9	6.3	33	38	38	49	67	123	158	173	190	272	311	514	663	740	844
Wing loading (lb/ft^2)	0.8	1.3	6.8	7.8	7.8	10	14	27	32	35	39	56	64	105	136	152	173

The table, which shows wing loadings, is intended to give an idea of the range of wing loadings used by 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 upper critical limit for bird flight is about 25 kg/m² (5.1 lb/sq ft).^[5] An analysis of bird flight which looked at 138 species ranging in mass from 10 g to 10 kg, from small passerines to swans and cranes found wing loadings from about 1 to 20 kg/m².^[6] 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 glider^[7] 8.3 kg/m².

Effect on performance

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 speeds

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

$\textstyle {\frac {L}{A}}={\tfrac {1}{2}}v^{2}\rho C_{L}$,

where ρ is the density of air and C_L 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.^[8] At take-off or in steady flight, neither climbing nor diving, the lift force and the weight are equal. With L/A = Mg/A =W_Sg, 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, that equation gives the speed v through^[9]

$\textstyle v^{2}={\frac {2gW_{S}}{\rho C_{L}}}$ .

As a consequence, aircraft with the same C_L at takeoff under the same atmospheric conditions will have takeoff speeds proportional to $\scriptstyle {\sqrt {W_{S}}}$. 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 ${\displaystyle \scriptstyle 150{\sqrt {1.4}}}$ = 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 W_S 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. 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 $\rho$ and particularly C_L will be smaller than at take-off, C_L because of a lower angle of incidence and the retraction of flaps or slats; the speed needed for level flight is lower for smaller W_S.

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

$\textstyle Ma_{c}={\tfrac {1}{2}}v_{c}^{2}\rho C_{L}A-Mg$

or

$\textstyle a_{c}={\frac {1}{2W_{S}}}v_{c}^{2}\rho C_{L}-g,$

so the initial upward acceleration is inversely proportional (reciprocal) to W_S. 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 having the effect of increasing the wing loading and also the stalling speed. This effect is also experienced during level pitching maneuvers.^[10]

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 in that, the delta winged Avro Vulcan bomber, with a wing loading of 260 kg/m² could certainly be rolled at low altitudes.^[11]

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, $\scriptstyle Lsin\theta$, where $\theta$ is the banking angle. Then from Newton's second law,

$\textstyle {\frac {Mv^{2}}{R}}=L\sin \theta ={\frac {1}{2}}v^{2}\rho C_{L}A\sin \theta .$

Solving for R 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 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), 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 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 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 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 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.^[12] (See Gliding competitions)

Design considerations

Fuselage lift

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 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). When the wing is in the forward position takeoff and landing performance is greatly improved.^[13]

Fowler flaps

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

See also

• Disk loading
• Lift coefficient

References

Notes

1. Thom, 1988. p. 6.
2. Ozone Buzz Z3: http://www.para2000.org/wings/ozone/buzzz3.html
3. Ozone Buzz Z3: http://www.flyozone.com/paragliders/en/products/gliders/buzz-z3/info/
4. Airborne Fun 160: http://www.airborne.com.au/pages/hg_fun.html
5. Meunier, 1951
6. http://www.biology-online.org/articles/flight-speeds-among-bird-species.html
7. BUG4 http://home.att.net/~m--sandlin/bug.htm
8. Anderson, 1999 p.58
9. Anderson, 1999 pp. 201-3
10. Spick, 1986. p.24.
11. https://www.youtube.com/watch?v=X4r0Kk-xX4o
12. Maximizing glider cross-country speed
13. Spick, 1986. p.84-87.
14. Anderson 1999, pp.30-1

Bibliography

• Anderson, John D. Jnr. (1999). Aircraft Performance and Design. Cambridge: WCB/McGraw-Hill. ISBN 0-07-116010-8.
• 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