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An aircraft wing is an aerodynamic lifting structure of an aircraft. Its three-dimensional shape combines airfoil sections with a spanwise arrangement described by the wing planform. The airfoil specifies a local profile; the wing planform specifies the shape seen from above. Wingspan, wing area, wing taper ratio and wing sweep describe different aspects of that geometry.^[ref]

The surrounding fluid flow exerts pressure and viscous stress on the wing's surface. Integrating these surface forces gives a resultant whose component perpendicular to the incoming flow is lift and whose parallel component is drag. A useful whole-wing relation iswhere $\rho$ is air density, $V$ is flight speed relative to the air, $S$ is wing area and $C_L$ is lift coefficient. The lift coefficient packages the effects of shape and operating conditions, including angle of attack; it is not determined by wing area alone.

For a stipulated example, $\rho =1.2kg/{\mathrm{m}}^3$, $V=30m/s$, $S=10{\mathrm{m}}^2$ and $C_L=0.8$ give dynamic pressure $540\mathrm{Pa}$ and lift $4320\mathrm{N}$. Halving the speed at unchanged lift coefficient reduces lift to one quarter. Maintaining the original lift would require $C_L=3.2$, which the actual wing might be unable to achieve before aerodynamic stall.

A wind tunnel makes the shape–force connection measurable: hold a model at controlled angle of attack, measure its lift and drag with a balance, and vary the model or flow conditions. Such measurements distinguish a geometrical description from an aerodynamic prediction. Two wings with equal wingspan and wing area can still have different lift coefficients, drag and stall behavior.

For a symmetric trapezoidal wing planform, let root chord be $c_r$, tip chord $c_t=\lambda c_r$, and wingspan $b$. The wing taper ratio $\lambda$ describes the linear local chord $c(y)=c_r[1-2(1-\lambda )y/b]$ on one half-wing. Direct integration givesA rectangular planform has $\lambda =1$ and $\overline{c}=c_r$; the triangular limit $\lambda =0$ gives $\overline{c}=2c_r/3$. These are lengths, not aerodynamic-center locations.

The mean aerodynamic chord reference position requires a placement convention. On the positive half-span, define the area-weighted stationFor a straight leading edge with $x_{\mathrm{LE}}(y)=x_0+y\tan {\Lambda }_{\mathrm{LE}}$, its corresponding chord reference starts at $x_{\mathrm{LE},\mathrm{MAC}}=x_0+y_{\mathrm{MAC}}\tan {\Lambda }_{\mathrm{LE}}$. A geometric quarter-chord reference is then $x_{1/4}=x_{\mathrm{LE},\mathrm{MAC}}+\overline{c}/4$. These are the standard planform integrals, not a guarantee about the aerodynamic center of every finite wing.^[ref]

For the stipulated $b=10\mathrm{m}$, $c_r=2\mathrm{m}$, $c_t=1\mathrm{m}$, the values are $\overline{c}=14/9\mathrm{m}$ and $y_{\mathrm{MAC}}=20/9\mathrm{m}$. With $x_0=0.10\mathrm{m}$ and ${\Lambda }_{\mathrm{LE}}=20{}^{\circ }$, the leading-edge reference is $0.908823\mathrm{m}$ aft of the chosen origin, and the quarter-chord reference is $1.297712\mathrm{m}$. Changing the wing sweep moves these reference positions without changing $\overline{c}$ when the same spanwise chords are retained.

The displayed $y_{\mathrm{MAC}}$ belongs to one half-wing; the spanwise centroid of the whole symmetric planform is instead zero. A half-wing placement convention and a whole-wing centroid are different quantities.

The mean geometric chord, also called the standard mean chord, is the span-average airfoil chord of an aircraft wing:where $S$ is the wing area and $b$ the wingspan. The area is the projected wing planform, not the sum of the upper and lower skin areas.^[ref]

A useful exact identity explains its difference from the mean aerodynamic chord. Represent uniform spanwise averaging by a coordinate $Y$ with a continuous uniform distribution on $[-b/2,b/2]$, and put $C=c(Y)$. This is a mathematical averaging device, not a claim that the wing geometry is random. With $\mu =\mathbb{E}[C]=S/b>0$,Thus the relative excess is the squared coefficient of variation of the local chords. The mean aerodynamic chord can also be interpreted as the expected value under the corresponding size-biased distribution, since larger chords receive proportionally larger weights.

For the original linear taper from $2$ to $1\mathrm{m}$, uniform spanwise sampling makes $C$ uniform on $[1,2]\mathrm{m}$. Its expected value is $1.5\mathrm{m}$ and variance is $1/12{\mathrm{m}}^2$. Hence ${\overline{c}}_a=1.5+(1/12)/1.5=1.5556\mathrm{m}$, a relative excess of $1/27\simeq 3.70\%$. A constant-chord wing has zero variance, so its two averages coincide.

Equal $S/b$ does not determine how local chord varies or where the wing lies relative to a reference axis. Those additional data enter wing sweep and the mean aerodynamic chord reference position.

The 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.^[ref]

If the projected airfoil chord at spanwise position $y$ is $c(y)$, thenFor a symmetric trapezoidal wing planform this becomes twice the area under a linear half-wing chord distribution: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.^[ref]

The choice of reference area also affects reported coefficients. From $L=qS{C}_L$, 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.

A wing planform is the two-dimensional outline of an aircraft wing viewed from above. It is bounded by the projected leading edge, trailing edge and wing tips. A rectangular, tapered or swept wing planform can be combined with many different airfoil profiles; the outline alone does not specify the wing's thickness or airfoil camber.^[ref]

Let $x$ point aft and $y$ run along the wingspan. Describe the two edges by $x_{\mathrm{LE}}(y)$ and $x_{\mathrm{TE}}(y)$. Their separation is the projected local airfoil chord,The second equation computes wing area. The first retains information lost by that single area value: where the chord lies along the fore-and-aft direction.

For an original comparison, a rectangular wing with $b=10\mathrm{m}$ and $c=2\mathrm{m}$ has $S=20{\mathrm{m}}^2$. A symmetric trapezoidal wing of the same wingspan, root chord $3\mathrm{m}$ and tip chord $1\mathrm{m}$ also has $S=20{\mathrm{m}}^2$. Now shift both edges of each spanwise strip aft by $k|y|$: the local airfoil chord and wing area stay unchanged, while the wing sweep changes. This explains geometrically why even specifying wingspan, wing area and wing taper ratio does not uniquely determine a wing planform.

The construction compares geometry, not aerodynamic equivalence. The airfoil, angle of attack and three-dimensional fluid flow still matter when predicting lift and drag.

The wing taper ratio $\lambda$ is the tip airfoil chord $c_t$ divided by the root airfoil chord $c_r$:It describes the relative narrowing of a wing planform toward its tips. A rectangular wing has $\lambda =1$; a straight-edged triangular wing has $\lambda =0$. The ratio specifies two chord values, not the entire spanwise chord distribution.^[ref]

For a symmetric trapezoidal wing planform with wingspan $b$, the chord varies linearly on each half-wing:Integrating this expression gives wing areaFor a prescribed wing area and wingspan, the required chords are thereforeFor example, $S=20{\mathrm{m}}^2$, $b=10\mathrm{m}$ and $\lambda =1/3$ give $c_r=3\mathrm{m}$ and $c_t=1\mathrm{m}$. At $y=2.5\mathrm{m}$ the chord is $2\mathrm{m}$. A rectangular wing with the same wing area and wingspan instead has $2\mathrm{m}$ chord everywhere.

Changing wing sweep while preserving these chord lengths leaves the wing taper ratio unchanged. Curved or compound edges can also share the same root and tip chords while enclosing different wing areas. Consequently the trapezoidal area formula requires the stated straight-edge assumption; a taper ratio alone cannot supply a general area or a prediction of lift.