Wing aspect ratio ($AR=b^2/S$)

The wing aspect ratio is the dimensionless measurewhere $b$ is wingspan and $S$ is projected wing area. For a rectangular wing planform, $S=bc$ and therefore $AR=b/c$, where $c$ is airfoil chord. For other wing planforms, dividing the span by a chosen root chord need not give the wing aspect ratio.^[ref]

Its aerodynamic importance comes from lift-induced drag. The wingtip vortices of a finite aircraft wing change the local flow direction; maintaining lift then entails an additional rearward force. A standard model writesHere $e$ is a span efficiency factor, $q$ is dynamic pressure and $C_L=L/(qS)$ is lift coefficient. The model compares a specified spanwise loading in a regime where this finite-wing approximation is appropriate; $e$ need not stay unchanged when the design changes.^[ref]

For an original example, take $S=16{\mathrm{m}}^2$, $q=500\mathrm{Pa}$, $C_L=0.6$ and $e=0.8$. Both wings then supply $L=4800\mathrm{N}$. Spans of 8 and 12 metres give $AR=4$ and $9$, respectively, and lift-induced drag approximately $286.48$ and $127.32\mathrm{N}$. Under those stipulated conditions, increasing span by 50% reduces that drag component by $1-(8/12{)}^2=5/9$, about 55.6%.

The boxed expression also exposes a common comparison error. At fixed $L$, $q$, $e$ and $b$, changing only the reference wing area changes both wing aspect ratio and lift coefficient; their effects cancel in this model's dimensional lift-induced drag. A larger numerical $AR$ is therefore not, by itself, a promise of smaller total drag. Structural loads, wing loading, surface losses and aerodynamic stall impose further design constraints.