= Wing taper ratio
{title2=$\lambda=c_t/c_r$}
The \b[wing taper ratio] $\lambda$ is the tip <airfoil chord> $c_t$ divided by the root <airfoil chord> $c_r$:
$$
\lambda=\frac{c_t}{c_r},\qquad c_r>0.
$$
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.<Applied Computational Aerodynamics by W. H. Mason>[Appendix A, pp. A-27–A-29: trapezoidal-planform definitions]{ref}
For a symmetric trapezoidal <wing planform> with <wingspan> $b$, the chord varies linearly on each half-wing:
$$
c(y)=c_r\left[1-(1-\lambda)\frac{2|y|}{b}\right],\qquad |y|\le b/2.
$$
Integrating this expression gives <wing area>
$$
S=\frac{bc_r(1+\lambda)}{2}.
$$
For a prescribed <wing area> and <wingspan>, the required chords are therefore
$$
c_r=\frac{2S}{b(1+\lambda)},\qquad
c_t=\frac{2S\lambda}{b(1+\lambda)}.
$$
For 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>.
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