= Pressure-tap position calibration
\b[Pressure-tap position calibration] determines the locations assigned to <pressure tappings> relative to a specified model coordinate system, with corrections and uncertainties. It is a geometrical <measurement calibration>, distinct from calibrating the <pressure transducer>. A correct pressure reading cannot compensate for assigning it to the wrong point on a steep <pressure coefficient> profile.
A proposed practical procedure measures each hole center against visible reference marks, establishes the <leading edge> and <airfoil chord> used for normalization, and records the coordinate transformation. A calibrated imaging scale or translation stage can provide the comparison. Record repeated readings and shared datum errors separately, and check that the measured view represents the intended surface coordinates rather than an oblique projection. This is a proposed metrological procedure, not an assertion that a particular historical airfoil experiment performed it.
An <affine pressure-tap coordinate calibration> has the simple form
$$
x=a+br,\qquad \xi=\frac{x-x_{\rm LE}}c,
$$
where $r$ is the instrument coordinate, $a$ an offset and $b$ a scale. With an independently established $x_{\rm LE}=0$, $c=200\,\mathrm{mm}$, $a=0.20\,\mathrm{mm}$ and $b=1.001$, a nominal reading $r=100\,\mathrm{mm}$ gives $x=100.30\,\mathrm{mm}$ and \b[$\xi=0.5015$], rather than $0.5000$. For a locally linear <pressure coefficient> slope of $10$, that coordinate discrepancy corresponds to $\delta C_p=0.015$.
Reference sharing matters. If the same affine map determines the tap, leading-edge and trailing-edge coordinates, its common offset and scale cancel in
$$
\xi=\frac{(a+br)-(a+br_{\rm LE})}{(a+br_{\rm TE})-(a+br_{\rm LE})}
=\frac{r-r_{\rm LE}}{r_{\rm TE}-r_{\rm LE}}.
$$
This cancellation does not remove distortion, uncertain feature identification or non-affine errors. It shows why the references and their <covariances> must be part of the <measurement model>, rather than independently attached after normalization.<Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results by Barry N. Taylor and Chris E. Kuyatt>[Appendix A.1 and equation A-3, complete measurement model and correlated inputs]{ref}
<Robert M. Pinkerton>'s 54-orifice <airfoil> experiment illustrates why spatially distributed pressure data matter: the experiment compared measured distributions with <potential flow> predictions.<Calculated and Measured Pressure Distributions over the Midspan Section of the NACA 4412 Airfoil by Robert M. Pinkerton>[Author abstract, pressure orifices and measured/theoretical comparison]{ref} A position check tests the coordinate assignment, whereas additional taps address <quadrature ambiguity of pressure-tap data>; neither task substitutes for the other.
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