Editing Wing loading (section)

==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]] ''v'' is given by
<math display="block">
 L = \tfrac{1}{2} \rho v^2 A C_L,
</math>
where ''ρ'' is the density of air, and ''C''<sub>L</sub> is the [[lift coefficient]]. The lift coefficient is a dimensionless number that depends on the wing cross-sectional profile and the [[angle of attack]].<ref>Anderson, 1999, p. 58.</ref> At steady flight, neither climbing nor diving, the lift force and the weight are equal. With ''L''/''A'' = ''Mg''/''A'' = ''W''<sub>S</sub>''g'', where ''M'' is the aircraft mass, ''W''<sub>S</sub> = ''M''/''A'' the wing loading (in mass/area units, i.e. lb/ft<sup>2</sup> or kg/m<sup>2</sup>, not force/area) and ''g'' the acceleration due to gravity, this equation gives the speed ''v'' through<ref>Anderson, 1999, pp. 201–203.</ref>
<math display="block">
 v^2 = \frac{2gW_S}{\rho C_L}.
</math>
As a consequence, aircraft with the same ''C''<sub>L</sub> at takeoff under the same atmospheric conditions will have takeoff speeds proportional to <math>\sqrt{W_S}</math>. 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&nbsp;mph grows in weight during development by 40%, its takeoff speed increases to <math>150 \sqrt{1.4}</math> ≈ 177&nbsp;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''<sub>S</sub> is critical, whereas [[passerine]]s and cliff-dwelling birds can get airborne with higher wing loadings.

===Effect on turning performance===
To turn, an aircraft must [[Flight dynamics (aircraft)|roll]] in the direction of the turn, increasing the aircraft's [[Banked turn#Aviation|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 (aircraft)|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 [[Pitch (flight)|pitching]] maneuvers.<ref>Spick, 1986, p. 24.</ref>

[[File:P334a(1).jpg|thumb|Load factor varying with altitude at 50 or 100&nbsp;lb/ft<sup>2</sup>]]
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 (aeronautics)|load factor]].<!--<ref name=NASA-Maneuverability/>-->
At Mach 0.85 and 0.7 lift coefficient, a wing loading of {{cvt|50|lb/sqft|kg/m2}} can reach a structural limit of 7.33''g'' up to {{convert|15000|ft|m}} and then decreases to 2.3''g'' at {{convert|40000|ft|m}}. With a wing loading of {{cvt|100|lb/sqft|kg/m2}} the load factor is twice smaller and barely reaches 1''g'' at {{cvt|40000|ft|m}}.<ref name=NASA-Maneuverability>{{cite book |url= https://history.nasa.gov/SP-468/ch11-6.htm |title= Quest for Performance – The Evolution of Modern Aircraft |author= Laurence K. Loftin Jr. |publisher= NASA Scientific and Technical Information Branch |date= 1985 |section= Chapter 11. Aircraft Maneuverability}}</ref>

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 {{cvt|{{#expr:13166/18.22round0}}|kg/m2|lb/sqft}} wing loading.

At the opposite end of the spectrum was the large [[Convair B-36]]: its large wings resulted in a low {{cvt|{{#expr:119318/443.5round0}}|kg/m2|lb/sqft}} wing loading that could make it sustain tighter turns at high altitude than contemporary jet fighters, while the slightly later [[Hawker Hunter]] had a similar wing loading of {{cvt|{{#expr:11158/32.42round0}}|kg/m2|lb/sqft}}. The [[Boeing 367-80]] airliner prototype could be rolled at low altitudes with a wing loading of {{cvt|{{#expr:86360/223round0}}|kg/m2|lb/sqft}} at maximum weight.

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 center at <math>v^2/R</math>. This acceleration is caused by the inward horizontal component of the lift, <math>L sin\theta</math>, where <math>\theta</math> is the banking angle. Then from [[Newton's second law]],
<math display="block">
 \frac{Mv^2}{R} = L \sin\theta = \frac{1}{2} v^2\rho C_L A \sin\theta.
</math>
Solving for ''R'' gives
<math display="block">
 R = \frac{2Ws}{\rho C_L \sin\theta}.
</math>
The lower the wing loading, the tighter the turn.

Gliders designed to exploit [[thermal]]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]]), 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 {{cvt|650|kg/m2}} (excluding fuselage contributions to the effective area), whereas most [[delta-wing]] aircraft (such as the [[Dassault Mirage&nbsp;III]], for which ''W''<sub>S</sub> = 387&nbsp;kg/m<sup>2</sup>) tend to have large wings and low wing loadings.{{Citation needed|date=March 2011}}

Quantitatively, if a gust produces an upward pressure of ''G'' (in N/m<sup>2</sup>, say) on an aircraft of mass ''M'', the upward acceleration ''a'' will, by [[Newton's second law]] be given by
<math display="block">
 a = \frac{GA}{M} = \frac{G}{W_S},
</math>
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 [[Glider (sailplane)|gliders]] often use water ballast carried in the wings to increase wing loading when [[Lift (soaring)|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 or prior to landing.