= Directional measurement of trailing-edge thickness
<Directional measurement of trailing-edge thickness> specifies which component of the gap between two terminal surface points is reported. A full endpoint separation, a chord-normal projection and a mean-line-normal thickness can be different quantities. The convention is part of the geometric measurement, not an adjustment to an aerodynamic result.
For selected endpoints $\mathbf r_u,\mathbf r_l$, write $\Delta\mathbf r=\mathbf r_u-\mathbf r_l$ and choose a <unit vector> $\mathbf n$ in the measurement direction. Then
$$
t_{\mathbf n}=|\Delta\mathbf r\cdot\mathbf n|,\qquad
g=\lVert\Delta\mathbf r\rVert,\qquad 0\le t_{\mathbf n}\le g.
$$
The last inequality is the <Cauchy-Schwarz inequality>. Equality requires the measurement direction to align with the endpoint gap, apart from its sign. If that alignment is off by an <angle> $\phi$, the reading is $g|\cos\phi|$.
For an original coordinate example, let $\Delta\mathbf r=(0.30,0.40)\,\mathrm{mm}$. The full gap is $0.50\,\mathrm{mm}$; a vertical measurement gives $0.40\,\mathrm{mm}$ and a horizontal one gives $0.30\,\mathrm{mm}$. The direction $(3/5,4/5)$ recovers the full $0.50\,\mathrm{mm}$. A separate one-millimetre gap measured with $20\,{}^{\circ}$ misalignment gives $0.939693\,\mathrm{mm}$, about six percent low.
Changing coordinate frames is harmless when both the endpoints and direction are transformed consistently. For a <rotation matrix> $Q$, $(Q\Delta\mathbf r)\cdot(Q\mathbf n)=\Delta\mathbf r\cdot\mathbf n$. Using the page's vertical direction after rotating the profile, however, changes the measurement direction.
The <NACA four-digit airfoil> equations place the two terminal points on opposite sides of the <airfoil mean camber line> along its normal. When that mean line slopes at the endpoint, the gap has both chordwise and transverse components.<Applied Computational Aerodynamics by W. H. Mason>[Appendix A, equations (A-1)–(A-3)]{ref} A profile-image or coordinate comparison should therefore identify the terminal-point pairing, the chord reference and the unit measurement direction. Interpolating both surfaces at the same horizontal coordinate is not automatically the same endpoint measurement.
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