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. ThenThe 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 $\varphi$, the reading is $g|\cos \varphi |$.

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.^[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.