 Parabolic drag polar

A parabolic drag polar models drag coefficient as
The zero-lift drag coefficient supplies the intercept. In a simple finite-wing approximation, $k$ can represent lift-induced drag; fitted whole-aircraft values can include additional lift-dependent losses. The model is conditioned on a configuration and operating regime, rather than universally valid through aerodynamic stall.

Its dimensional form explains a useful speed tradeoff. In steady level flight let lift equal gravitational weight $W$, with fixed mass density $\rho$ and wing area $S$. Substitution of $C_L=W/(qS)$ and $q=\rho V^2/2$ yields
The first contribution grows with speed; the second decreases as the required lift coefficient falls. Differentiation gives the minimum-drag speed $V_{\mathrm{MD}}=(b/a{)}^{1/4}$.

Minimizing required propulsive power instead gives
The minimum-power speed is therefore different from the minimum-drag speed in this model. For stipulated $\rho =1.2kg/{\mathrm{m}}^3$, $S=20{\mathrm{m}}^2$, $W=10000\mathrm{N}$, $C_{D0}=0.020$ and $k=0.050$, the speeds are about $36.30$ and $27.58m/s$, respectively.

These are idealized level-flight comparisons of required propulsive power. Engine efficiency, allowable lift coefficients and a speed-dependent polar can move an operational optimum. Relating the result to minimum sink speed in unpowered flight requires the additional shallow-glide approximation; it does not identify minimum fuel flow for an arbitrary engine.