= Airfoil thickness-to-chord ratio
{title2=$\eta=t_{\max}/c$}
The <airfoil thickness-to-chord ratio> is the dimensionless maximum section thickness divided by the <airfoil chord>:
$$
\eta=\frac{t_{\max}}{c}.
$$
Its percentage form is $100\eta$. The <airfoil thickness convention> must specify how upper and lower surface points are paired and in which direction their separation is measured. For the standard <NACA four-digit airfoil> construction, the prescribed thickness envelope is placed normal to the <airfoil mean camber line>, not simply added vertically everywhere.<Applied Computational Aerodynamics by W. H. Mason>[Appendix A, equations (A-1)–(A-4)]{ref}
For an original scale example, $t_{\max}=24\,\mathrm{mm}$ and $c=200\,\mathrm{mm}$ give $\eta=0.12$, or twelve percent. Scaling every coordinate by three gives $72\,\mathrm{mm}$ thickness and $600\,\mathrm{mm}$ chord, with the same <ratio>. Holding the chord fixed while adding $0.2\,\mathrm{mm}$ thickness instead gives $\eta=0.121$: the percentage thickness rises by $0.1$ percentage point.
The differential relation
$$
\delta\eta\simeq\frac{\delta t_{\max}}c-\frac{t_{\max}}{c^2}\,\delta c
$$
shows why an identical fractional scale error in both lengths cancels to first order, while an independent thickness error survives. Exact common scaling cancels in the quotient itself. This is the geometric counterpart of a <ratiometric measurement>.
The scalar $\eta$ does not specify where the thickest station lies, the <airfoil leading-edge radius>, or the <airfoil camber>. Two sections can therefore share $\eta$ while having different pressure distributions and structural envelopes. The early NACA investigation varied thickness and mean-line form independently in a <variable-density wind tunnel>, making those distinctions experimentally useful.<The Characteristics of 78 Related Airfoil Sections from Tests in the Variable-Density Wind Tunnel by Eastman N. Jacobs and others>[Summary and derivation of the related section family]{ref}
A geometric check of a manufactured section should report the chord reference, the thickness direction and the coordinate scale. Measuring a projected thickness in a tilted image without correcting its direction can change the reported <ratio> even when the physical section is unchanged.
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