Aircraft component drag interaction

An aircraft component drag interaction is the part of a combined drag measurement that is not accounted for by an additive model of the specified separate components. It is one measurable consequence of aerodynamic interference; its sign and magnitude depend on operating conditions and on what counts as the common baseline.

Use the factorial contrast for aerodynamic interference, $\Delta =D_{11}-D_{10}-D_{01}+D_{00}$. With readings ordered as $\mathbf{d}=(D_{00},D_{10},D_{01},D_{11}{)}^T$, put $\mathbf{a}=(1,-1,-1,1{)}^T$. If $\Sigma$ is their covariance matrix, thenThe second expression propagates the standard uncertainty of the linear contrast; it requires the actual covariance model, not an assumption that every reading is independent.

For a stipulated instrument model, let $\mathbf{d}=\mathbf{\mu }+Z1+\mathbf{ϵ}$, with a shared zero error $Z$ independent of four independent residual errors of standard deviation $0.5\mathrm{N}$. Because ${\mathbf{a}}^{T}1=0$, the shared zero cancels exactly and $u_{\Delta }=1.0\mathrm{N}$, regardless of its variance. This common-zero cancellation in a drag interaction contrast fails for a changing zero or for a shared gain error. At the illustrative contrast $5\mathrm{N}$, a common relative gain error $g$ leaves the factor $(1+g)5\mathrm{N}$.

Kenneth E. Ward distinguished attached-component measurements from isolated-strut measurements in his wind tunnel study, rather than attributing the entire assembly drag increase to the struts alone.^[ref] In a modern repetition, interleave baseline and assembly runs, retain all raw balance channels, and compare after consistent measurement calibration. Repeatability alone does not bound a systematic support interaction shared by every run.

Common-zero cancellation in a drag interaction contrast follows from the coefficients summing to zero. Order the readings as $\mathbf{d}=(D_{00},D_{10},D_{01},D_{11}{)}^T$ and put $\mathbf{a}=(1,-1,-1,1{)}^T$. If
then
because ${\mathbf{a}}^{T}1=0$. The cancellation is pointwise and does not require $Z$ to be independent of the residual errors. It requires the same additive offset to enter all four readings on the same scale.

For finite covariance, the residual contribution to the contrast's variance is ${\mathbf{a}}^T{\Sigma }_{ϵ}\mathbf{a}$. Four independent residual errors with standard deviation $0.5\mathrm{N}$ give contrast standard deviation $1.0\mathrm{N}$, however large the exactly common zero error is. A shared gain error instead multiplies a nonzero true contrast and generally survives.

Run order can also reject some changing zeros. With equally spaced run times $\mathbf{t}=(0,1,2,3{)}^T$ in the displayed configuration order, ${\mathbf{a}}^T\mathbf{t}=0$. An additive linear drift $r\mathbf{t}$ therefore cancels. A quadratic drift $c{\mathbf{t}}^{\circ 2}$ does not: ${\mathbf{a}}^T{\mathbf{t}}^{\circ 2}=4$, leaving $4c$. This drift rejection by contrast orthogonality concerns the actual time assignments; a different order can change it.

Normalization can defeat the common-scale assumption. If every dimensional reading has offset $Z$ but coefficients divide the last reading by twice the dynamic pressure used for the others, the scaled offset no longer has the form $Z1$. Keeping raw loads and reference readings allows the factorial contrast for aerodynamic interference and its measurement uncertainty to be reconstructed consistently.