Editing Wing loading (section)

===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.