Wing loading

In aerodynamics, wing loading is the total weight of an aircraft or flying animal divided by the area of its wing. The stalling speed, takeoff speed and landing speed of an aircraft are partly determined by its wing loading.

The faster an aircraft flies, the more its lift is changed by a change in angle of attack, so a smaller wing is less adversely affected by vertical gusts. Consequently, faster aircraft generally have higher wing loadings than slower aircraft in order to avoid excessive response to vertical gusts.

A higher wing loading also decreases maneuverability. The same constraints apply to winged biological organisms.

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.

The lift force L on a wing of area A, traveling at true airspeed v is given by $${\displaystyle L={\tfrac {1}{2}}\rho v^{2}AC_{L},}$$ where ρ is the density of air, and C_L is the lift coefficient. The lift coefficient is a dimensionless number that depends on the wing cross-sectional profile and the angle of attack. At 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, this equation gives the speed v through $${\displaystyle v^{2}={\frac {2gW_{S}}{\rho C_{L}}}.}$$ As a consequence, aircraft with the same C_L at takeoff under the same atmospheric conditions will have takeoff speeds proportional to ${\displaystyle {\sqrt {W_{S}}}}$. 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 mph grows in weight during development by 40%, its takeoff speed increases to ${\displaystyle 150{\sqrt {1.4}}}$ ≈ 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 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_S is critical, whereas passerines and cliff-dwelling birds can get airborne with higher wing loadings.

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.

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 7.33g up to 15,000 feet (4,600 m) and then decreases to 2.3g at 40,000 feet (12,000 m). With a wing loading of 100 lb/sq ft (490 kg/m²) the load factor is twice smaller and barely reaches 1g at 40,000 ft (12,000 m).