Göttingen 387

Göttingen 387 is a named cambered airfoil profile defined by tabulated upper- and lower-surface coordinates. The number identifies a particular section; it is not a general formula from which arbitrary airfoil camber or thickness can be read as decimal digits. A primary NACA investigation reproduces specified and measured ordinates for this section, making the geometry used in that experiment explicit.^[ref]

A practical reconstruction begins with Göttingen 387 coordinate normalization. Coordinates stated in percent of the reference chord become lengths by multiplying by $c/100$. Preserve the table's origin and reference line: a vertical coordinate offset is not automatically an airfoil camber measured from a newly chosen chord line. Distinguish the specified design coordinates from measured model coordinates rather than mixing their columns.

The section provides a concrete example of why a profile name alone does not specify a wing experiment. Ward's 1931 apparatus used a rectangular duralumin model $5$ inches in chord and $30$ inches in span, tested at an average Reynolds number of $3.4\times 10^6$ in the variable-density tunnel at a working pressure of $20$ atmospheres. The model was tested alone and with struts mounted at different upper- and lower-surface positions.^[ref]

From those dimensions, the model's span is $0.762\mathrm{m}$, chord $0.127\mathrm{m}$, area $0.096774{\mathrm{m}}^2$ and aspect ratio $b^2/S=6$. An original coefficient conversion illustrates the reporting convention: if a test of that geometry at stipulated dynamic pressure $q=1000\mathrm{Pa}$ gave $C_L=0.8$, then $L=qS{C}_L=77.4192\mathrm{N}$. This coefficient and dynamic pressure are illustrative inputs, not values transcribed from Ward's tables.

The reported comparison found that attaching struts changed the aerodynamic behavior, with larger effects for the tested upper-surface arrangements. The strut-interference drag could be comparable with the isolated-strut contribution.^[ref] That observation concerns the complete tested arrangements, not an intrinsic drag coefficient of every object carrying the same airfoil profile.

A proposed reproduction records the coordinate source, manufactured surface, span, end conditions, Reynolds number, angle of attack and support arrangement. Measure the wing alone before and after adding a support, and keep reference area and tunnel corrections consistent. A finite-wing result, even after a wall correction, should not be silently treated as an isolated two-dimensional section polar.

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.