= Downwash
<Downwash> is a downward component of fluid <velocity>, commonly the induced flow associated with a lifting wing and its trailing <vortices>. For positive upward <lift>, this flow changes the direction of the local relative wind and contributes to <lift-induced drag>. NASA's primary explanation connects the trailing vortex system, reduced effective incidence and rearward component of the aerodynamic <force>.<Induced Drag Coefficient by NASA Glenn Research Center>[Air Pressure of a Wing]{ref}
Choose streamwise <velocity> $U>0$ and let $w>0$ denote downward induced <speed> at a section. The induced angle and effective <angle of attack> are
$$
\alpha_i=\arctan(w/U),\qquad \alpha_{\rm eff}=\alpha-\alpha_i.
$$
An ideal local lifting <force> normal to that relative flow is tilted rearward. Its vertical and downstream projections obey $D_i/L=\tan\alpha_i=w/U$; hence $D_i\approx L\alpha_i$ for small induced angles. This projection isolates the induced contribution in the stated model; it does not include skin friction or every source of total <drag>.
For an original uniform-downwash example, take $U=50\,\mathrm{m/s}$, $w=2\,\mathrm{m/s}$ and total <lift> $L=10\,000\,\mathrm N$. Then $\alpha_i\approx2.291^\circ$ and $D_i=400\,\mathrm N$ in the projection model. The <power> required to overcome this contribution is $UD_i=20\,\mathrm{kW}$. At geometric incidence $6^\circ$, the effective incidence is about $3.709^\circ$.
A real finite wing generally has span-dependent loading and induced <speed>. In small-angle <lifting-line theory>,
$$
D_i\simeq\frac1U\int_{-b/2}^{b/2}L'(y)w(y)\,dy.
$$
Using an unweighted arithmetic mean of measured $w$ need not reproduce that integral. For <elliptic span loading>, the ideal lifting-line downwash is constant across the span and $\alpha_i\simeq C_L/(\pi AR)$, consistent with $C_{D_i}=C_L^2/(\pi AR)$. These statements concern the ideal planar model rather than arbitrary wakes or separated flow.
A proposed observation measures flow direction and <speed> at a specified plane around a loaded wing, using calibrated directional probes or timed tracer images. Repeat with zero and reversed <lift>, and compare the sign and spatial distribution of the induced flow. Record the freestream reference and wing incidence as well as the probe positions. <Wake-plane dependence of a downwash measurement> matters: a <velocity> measured well downstream cannot simply be inserted as the wing-section induced <speed> without a model connecting the two planes. Visible tracer deflection demonstrates flow direction only to the extent that the tracer follows the fluid; it is not by itself a quantitative <lift> or <drag> measurement.
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