= Drag polar
A \b[drag polar] relates <drag coefficient> $C_D$ to <lift coefficient> $C_L$ for specified geometry, configuration and flow conditions. It is commonly displayed with $C_D$ horizontally and $C_L$ vertically. The slope of a ray from the origin to a measured point is then $C_L/C_D$, the <lift-to-drag ratio> when common references are used.
A <wind tunnel> can obtain a polar by varying <angle of attack> while recording both forces and the reference <dynamic pressure>. <Reynolds number>, <Mach number>, surface condition and deployed devices must also be recorded; changing one of those can change the curve. A polar is not a geometry-only fingerprint.
For an original illustrative dataset, the pairs $(C_L,C_D)=(-0.2,0.024),(0,0.020),(0.4,0.028),(0.8,0.052)$ lie on $C_D=0.020+0.050C_L^2$. Their positive-lift ratios at $C_L=0.4$ and $0.8$ are about $14.29$ and $15.38$. The larger ratio among those samples does not establish the continuous <maximum lift-to-drag ratio>; the unsampled neighborhood near $C_L=0.63$ performs better in this assumed model.
A <parabolic drag polar> summarizes such data with a small number of parameters. A <shifted parabolic drag polar> allows minimum <drag> to occur at nonzero <lift coefficient>. <Flow separation> and changes of flow state can also produce branches or hysteresis that one parabola does not describe. A fit supplies a model whose residuals need inspection, rather than evidence that every unmeasured state lies exactly on the fitted curve.
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