 Airfoil leading-edge radius

The airfoil leading-edge radius is the local radius of curvature of the nose of an airfoil. It describes a local shape feature, unlike the airfoil chord or maximum airfoil thickness-to-chord ratio. A single maximum-thickness value does not determine nose sharpness.

For a regular planar curve $(x(u),y(u))$, the curvature magnitude and its reciprocal arewhere $r$ is finite when the numerator is nonzero. Near a symmetric nose, choose the foremost point as origin and write $x=a{y}^2+O(y^4)$. At the nose $\kappa =2|a|$, so $r=1/(2|a|)$. The expression is geometric; a badly scaled drawing changes an apparent visual radius without changing the actual coordinates.

Leading-edge radius estimation from sampled coordinates has a resolution tradeoff. In the exact model $x=200y^2$ with metre units, the true radius is $2.5\mathrm{mm}$. At $y=1\mathrm{mm}$ the horizontal displacement is $0.20\mathrm{mm}$. With the vertical coordinate treated as exact and the horizontal displacement error bounded by $10\mu \mathrm{m}$, the estimate $\hat{r}=y^2/(2\hat{x})$ ranges approximately over $[2.381,2.632]\mathrm{mm}$.

Moving the sampled height to $0.5\mathrm{mm}$ reduces the exact horizontal displacement to $0.05\mathrm{mm}$; the same coordinate error widens the inferred interval to $[2.083,3.125]\mathrm{mm}$. Sampling closer to the nose is therefore not automatically more informative. In a real curve with a quartic term, smaller offsets reduce truncation error but amplify fixed coordinate noise in the quotient.

For the symmetric four-digit thickness envelope, the familiar relation $r_{\mathrm{LE}}/c\simeq 1.1019{\eta }^2$ supplies another model-specific check.^[ref] The example NACA 0012 with $c=0.20\mathrm{m}$ has nominal radius about $3.1735\mathrm{mm}$. That family relation should not replace a local curvature calculation for an unrelated profile.