= Wing area
{title2=$S$}
The \b[wing area] $S$ is the area of an <aircraft wing>'s projected <wing planform>. It is a reference area for such quantities as <lift coefficient> and <wing aspect ratio>. It is not the sum of the upper and lower curved surface areas.<Wing Geometry by NASA Glenn Research Center>[Top View: projected planform area versus total surface area]{ref}
If the projected <airfoil chord> at spanwise position $y$ is $c(y)$, then
$$
S=\int_{-b/2}^{b/2}c(y)\,dy.
$$
For a symmetric trapezoidal <wing planform> this becomes twice the area under a linear half-wing chord distribution:
$$
S=2\frac b2\frac{c_r+c_t}{2}=\frac b2(c_r+c_t).
$$
With <wingspan> $b=10\,\mathrm{m}$, root chord $3\,\mathrm{m}$ and tip chord $1\,\mathrm{m}$, the result is $20\,\mathrm{m^2}$ for both halves together. Each half has area $10\,\mathrm{m^2}$. This factor of two matters when converting a half-wing drawing into a whole-wing reference area.<Applied Computational Aerodynamics by W. H. Mason>[Appendix A, pp. A-27–A-29, planform integration and trapezoidal wings]{ref}
The choice of reference area also affects reported coefficients. From $L=qSC_L$, where $q$ is <dynamic pressure>, a measured <lift> of $4000\,\mathrm{N}$ at $q=500\,\mathrm{Pa}$ and $S=20\,\mathrm{m^2}$ gives $C_L=0.4$. Using the half-wing area in that same whole-wing equation would incorrectly produce $C_L=0.8$. When comparing experiments or calculations, preserve the reference-area convention along with the measured force.
A <wing sweep> construction that shifts both projected edges aft by the same amount at each $y$ preserves $c(y)$ and therefore preserves <wing area>. The original comparison in <wing planform> illustrates this invariance. Changes to <airfoil camber> or thickness can likewise alter the three-dimensional surface and aerodynamic behavior without changing the projected outline.
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