A finite wing is described geometrically by how its chord varies across the span. That planform geometry is distinct from the aerodynamic loading the wing eventually carries.

Choose spanwise coordinate $y$ with

$$-\frac b2\le y\le\frac b2,$$

where $b$ is the full wing span. Let

$$\boxed{c(y)}$$

be the local chord length.

Planform area

The wing planform area is the integral of local chord across the span:

$$\boxed{S=\int_{-b/2}^{b/2}c(y),dy}.$$

For a symmetric wing,

$$\boxed{S=2\int_0^{b/2}c(y),dy}.$$

A rectangular wing with constant chord $c$ has

$$S=bc.$$

Aspect ratio

The aspect ratio compares span squared with area:

$$\boxed{AR=\frac{b^2}{S}}.$$

It is dimensionless.

For a rectangular wing,

$$AR=\frac bc.$$

A high-aspect-ratio wing is long and slender relative to its area; a low-aspect-ratio wing is comparatively short and broad.

Aspect ratio is a global geometric property. Two wings can have the same $AR$ while having very different chord distributions.

Taper ratio

For a straight-tapered wing whose chord changes linearly from root chord $c_r$ to tip chord $c_t$, define the taper ratio

$$\boxed{\lambda=\frac{c_t}{c_r}}.$$

A rectangular wing has

$$\lambda=1,$$

while stronger taper corresponds to smaller positive $\lambda$.

For a symmetric linearly tapered wing, the average chord is

$$\frac{c_r+c_t}{2},$$

so

$$\boxed{S=\frac b2(c_r+c_t)}.$$

Using $c_t=\lambda c_r$,

$$\boxed{c_r=\frac{2S}{b(1+\lambda)}},$$

$$\boxed{c_t=\lambda c_r}.$$

Thus span, area, and taper ratio determine the root and tip chords of a trapezoidal planform.

Elliptic planform

An ideal elliptic chord distribution can be written

$$\boxed{ c(y)=c_0\sqrt{1-\left(\frac{2y}{b}\right)^2} },$$

where $c_0$ is the centerline chord.

Its area is

$$\boxed{S=\frac{\pi b c_0}{4}},$$

so

$$\boxed{AR=\frac{4b}{\pi c_0}}.$$

An elliptic planform should not be confused with elliptic loading. The first describes chord geometry; the second describes the spanwise aerodynamic force or circulation distribution. Planform, twist, and section properties together determine the loading.

Worked example: a tapered wing

A wing has

$$b=10,\mathrm m,$$

$$S=15,\mathrm{m^2},$$

and taper ratio

$$\lambda=0.50.$$

Its root chord is

$$c_r =\frac{2(15)}{10(1+0.50)} =\frac{30}{15} =\boxed{2.0,\mathrm m}.$$

The tip chord is

$$c_t=(0.50)(2.0) =\boxed{1.0,\mathrm m}.$$

The aspect ratio is

$$AR=\frac{10^2}{15} =\boxed{6.67}.$$

Changing taper while keeping the same $b$ and $S$ changes how chord is distributed spanwise but leaves this aspect ratio unchanged.

Geometry does not determine loading by itself

Two wings with the same planform can carry different spanwise loads because section camber, twist, angle of attack, and the wing's own induced flow can differ.

Conversely, different combinations of chord distribution and section operating condition can be designed to produce the same target loading.

Planform geometry therefore describes where wing area is placed. Finite-wing aerodynamics determines how that geometry combines with section properties and induced flow to produce force.