= Pressure-tap spatial footprint
A \b[pressure-tap spatial footprint] describes the finite region of a <surface pressure> field that contributes to a tap's response, rather than treating the reading as an exact point value. A <pressure-footprint response kernel> can represent spatial averaging in a simplified linear model. A real opening can also disturb the flow, so averaging is not a complete physical correction model.
For an ideal one-dimensional strip of width $w$, suppose the reading at $x_0$ is
$$
p_m(x_0)=\frac1w\int_{-w/2}^{w/2}p(x_0+s)\,ds.
$$
For a smooth field, a Taylor expansion gives $p_m=p(x_0)+p''(x_0)w^2/24+O(w^4)$. Symmetry cancels the first-order gradient term, but not curvature. For an exactly quadratic field this expression through $w^2$ is exact. It shows why a footprint cannot in general be summarized by a displaced point location.
If $p(x)=A\sin(kx)$, direct integration instead gives
$$
p_m(x)=A\frac{\sin(kw/2)}{kw/2}\sin(kx).
$$
The multiplier is a <sinc function>. For wavelength $\lambda=2\pi/k$, a half-wavelength strip retains $2/\pi\approx0.637$ of the amplitude, while a full-wavelength strip gives zero. These results concern an ideal strip <spatial averaging filter>, not an asserted weighting law for a circular pressure hole.
\Image[/pressure-footprint-spatial-filter.png]
{title=Ideal strip averaging attenuates a sinusoidal pressure field; one-wavelength averaging gives zero}
An actual <wind tunnel> experiment by <E. B. Plentovich> and <Blair B. Gloss> used interchangeable orifices in a flat plate. Increasing opening size increased the observed pressure error; a flush porous-metal plug reduced it under the tested conditions.<Orifice-Induced Pressure Error Studies in Langley 7- by 10-Foot High-Speed Tunnel by E. B. Plentovich and Blair B. Gloss>[NASA-TP-2545, Summary and printed pp. 3–4: model, interchangeable orifices and apparatus]{ref} This is direct evidence that opening geometry affects the measurement, including through local flow disturbance.
Footprint characterization and tap spacing address separate limitations. Closely spaced readings from broad footprints may still suppress short spatial variations, while narrow footprints sampled too sparsely can suffer <spatial aliasing>. Neither problem is removed merely by improving the precision of the <pressure transducer>.
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