= Factorial contrast for aerodynamic interference
{title2=$D_{11}-D_{10}-D_{01}+D_{00}$}
A \b[factorial contrast for aerodynamic interference] compares four configurations formed by independently including or excluding two components. Write their matched-condition mean <drag> readings as $D_{ij}$, where $i,j\in\{0,1\}$. The interaction contrast is
$$
\Delta=D_{11}-D_{10}-D_{01}+D_{00}.
$$
It measures nonadditivity between the specified configurations, not a universal attribute of either part alone.
The two-factor representation
$$
D_{ij}=\beta_0+\beta_A i+\beta_B j+\beta_{AB}ij
$$
reproduces any four means. Substitution gives \b[$\Delta=\beta_{AB}$]. In the original illustrative dataset $(D_{00},D_{10},D_{01},D_{11})=(2,22,7,32)\,\mathrm N$, the baseline is $2$, the separate increments are $20$ and $5$, and the interaction is $5\,\mathrm N$. The four-parameter representation does not by itself explain the responsible <fluid flow>.
With repeated measurements, retain the <factorial design> and run order. A change in <dynamic pressure>, orientation, mounting system or balance zero can otherwise enter the contrast. <Common-zero cancellation in a drag interaction contrast> handles a truly common additive offset, while <drift rejection by contrast orthogonality> determines which time-varying offsets a chosen run order removes.
<Kenneth E. Ward>'s strut experiments motivate the physical comparison: separate strut drag was compared with changes measured when struts were attached to a wing, revealing <aerodynamic interference> beyond a sum of isolated loads.<Interference Effects and Drag of Struts on a Monoplane Wing by Kenneth E. Ward>[Discussion of Results, attached and isolated strut comparisons]{ref} The algebra supplies a controlled comparison; pressure and wake observations are needed to test a mechanism.
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