Göttingen 387 coordinate normalization

Göttingen 387 coordinate normalization converts published coordinates of the Göttingen 387 section into a reproducible airfoil geometry with declared length, origin and orientation. The primary experiment tabulates specified and measured upper and lower ordinates separately, with all dimensions expressed as percentages of chord.^[ref] A digitized outline should retain that distinction instead of silently mixing the designed and manufactured profiles.

If a station has tabulated coordinates $(X,Y)$ in percent of the stated reference chord, its dimensionless reference coordinates are $(X/100,Y/100)$. At reference chord $c_{\mathrm{ref}}$, its dimensional coordinates areFor the reported $5$-inch model chord, $c_{\mathrm{ref}}=127\mathrm{mm}$. A station at $X=30$ is therefore $38.1\mathrm{mm}$ along the table's horizontal reference, and one percentage point of ordinate is $1.27\mathrm{mm}$. These conversions preserve the table's coordinate frame; they do not establish that its leading-edge ordinate is zero.^[ref]

If a new convention requires the geometric chord to lie on the horizontal axis, perform a rigid motion before scaling. Choose a leading-edge point $P_L$ and a stated trailing-edge reference $P_T$, such as the midpoint of a finite-thickness trailing edge. DefineThen any point $P$ has chord-aligned coordinatesThis sends $P_L$ to $(0,0)$ and $P_T$ to $(1,0)$. The reference-chord scale $c_{\mathrm{ref}}$ and recomputed geometric length $c_g$ need not be numerically identical under every historical convention. Chord-line rotation of historical airfoil coordinates also changes the reference from which an angle of attack is measured.

For an original example unrelated to the actual tabulated profile, take $P_L=(0,0.03)$, $P_T=(1,0.01)$ and $P=(0.3,0.10)$ in one common length unit. Here $c_g=\sqrt{1.0004}$ andMerely dividing the original coordinates by a nominal chord would leave the ordinate at $0.10$, a different quantity from the chord-normal ordinate $\eta$.

A proposed reconstruction keeps an immutable transcription of each chosen table column, records the transformation, checks leading and trailing points, and overlays the transformed upper and lower surfaces. Check point ordering and intersections before interpolating. A finite trailing-edge gap should remain finite unless an explicit geometry modification is intended; closing it changes the profile.

Uniform scaling and rotation preserve shape up to similarity, but they do not preserve every flow condition in a physical model. With fluid properties and flow speed fixed, changing chord changes Reynolds number. A geometry normalization therefore prepares a specified test article or numerical boundary; it does not transfer a historical aerodynamic polar to an arbitrary size and operating condition.