= Airfoil trailing-edge thickness
{title2=$t_{\rm TE}$}
<Airfoil trailing-edge thickness> measures the separation of the upper and lower surfaces at a specified terminal reference. A sharp ideal <trailing edge> has zero thickness. A finite-edge model needs both the endpoint convention and the measurement direction; these choices matter when comparing coordinates or manufacturing tolerances.
For <directional measurement of trailing-edge thickness>, choose terminal points $\mathbf r_u,\mathbf r_l$ and a <unit normal vector> $\mathbf n$. The reported projected gap is
$$
t_{\mathbf n}=|(\mathbf r_u-\mathbf r_l)\cdot\mathbf n|.
$$
For a <NACA four-digit airfoil> built with normal offsets, the full endpoint separation has <length> $2y_t(1)$. Its component normal to the <airfoil chord> is $2y_t(1)|\cos\theta_{\rm TE}|$, while their chordwise separation is $2y_t(1)|\sin\theta_{\rm TE}|$. Comparing a full normal gap to a projected gap silently changes the quantity being measured.<Applied Computational Aerodynamics by W. H. Mason>[Appendix A, equations (A-1)–(A-4), thickness placed normal to the mean line]{ref}
For a symmetric section with $c=0.20\,\mathrm m$ and $\eta=0.12$, the standard polynomial gives $t_{\rm TE}=0.504\,\mathrm{mm}$ and $t_{\rm TE}/c=0.00252$. The same absolute $0.504\,\mathrm{mm}$ gap on a $0.40\,\mathrm m$ section would have only half that normalized thickness. Absolute and normalized tolerances answer different questions.
<Measurement uncertainty> also depends on shared coordinate errors. If signed endpoint heights give $t=y_u-y_l$, then
$$
u_t^2=u_u^2+u_l^2-2\operatorname{Cov}(y_u,y_l).
$$
An identical coordinate-origin shift cancels from the difference, whereas independent endpoint errors do not. Stipulated independent $10\,\mathrm{\mu m}$ standard uncertainties give $u_t=14.14\,\mathrm{\mu m}$. A common translation alone contributes zero. This is a <covariance> calculation, not evidence that every instrument error is common.
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