stumbling into aerodynamics
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When testing in a wind tunnel, engineers need to achieve
dimensional similarity. This means that all results can be scaled from a smaller model to a larger object. Because wind tunnels can be expensive, they are not generally full size. If we couldn't scale the results of a test, we'd be stuck building planes for cats.
The lift and drag coefficients are non-dimensional numbers which are used in analyzing systems which are dimensionally similar. The coefficients are as given:
$$\displaystyle C_ L \equiv \frac{L}{\frac{1}{2}\rho _{\infty }V_{\! \scriptscriptstyle \infty }^2 S_{\rm ref}}$$
$$\displaystyle C_ D \equiv \frac{D}{\frac{1}{2}\rho _{\infty }V_{\! \scriptscriptstyle \infty }^2 S_{\rm ref}}$$
\(L\) represents the total of all lift forces, \(D\) represents the total of all drag forces, \(\rho _{\infty }\) represents the density of the air before the aircraft disturbs it, \(V_{\! \scriptscriptstyle \infty }\) represents the freestream velocity, and \(S_{\rm ref}\) represents the reference area, usually the planform area.
In order to scale the model, we must maintain these coefficients by adjusting our . If testing conditions stay the same, shouldn't all non-dimensional coefficients, numbers that by nature bear no relation to the size or dimension
of the subject, remain constant? It is in this manner that we can test small models in wind tunnels and achieve results that are useful to us for full scale aircraft.
-Aryn Harmon