Aircraft Drag Polar
Aircraft parabolic drag polar
\[C_D = C_{D0} + K\,C_L^2 \label{eq:Drag:Polar:Parabolic:A}\] \[K = \frac{1}{\pi\, \mathrm{A\!R} \, e} \label{eq:K:Drag:Polar:Parabolic}\]- $C_{D0}$, parasite drag coefficient at zero lift.
- \(C_{D\mathrm{i}} = C_L^2/\big(\pi \mathrm{A\!R} \, e\big)\), drag coefficient due to lift (induced drag).
- $e$, Oswald efficiency factor, includes all effects from airplane.
- \(\mathrm{A\!R}_\mathrm{e}=\mathrm{A\!R}\,e\), effective aspect ratio.
- $b_\mathrm{e}=b\sqrt{e}$, effective wing span.
Parabolic polar:
Actual polar:
Generalized parabolic polar
\[C_D = C_{D\mspace{2mu}\mathrm{min}} + K\,\left( C_L - C_{L\mspace{2mu}\mathrm{ideal}} \right)^2 \label{eq:Drag:Polar:Parabolic:B}\]- $C_{L\mspace{2mu}\mathrm{ideal}} = C_L @ C_{D\mspace{2mu} \mathrm{min}}$, ideal lift coefficient, i.e. $C_L$ at the angle of attack of minimum $C_D$.
Equation (\ref{eq:Drag:Polar:Parabolic:B}) is unnecessarily too complicated. An acceptable approximation is given by the simple parabolic drag polar (\ref{eq:Drag:Polar:Parabolic:A}).
Equivalent parassite area
\[f = C_{D0} \, S \label{eq:f:Parassite:Equivalent:Area}\] \[f = C_{f\mspace{2mu}\mathrm{e}} \, S_\mathrm{wet} \label{eq:f:Parassite:Equivalent:Area:Swet}\] \[f = C_{f\mspace{2mu}\mathrm{e}} \, S_\mathrm{wet} \quad \Rightarrow \quad C_{D0} = \frac{f}{S} \quad \Rightarrow \quad C_{D0} = C_{f\mathrm{e}} \, \frac{S_\mathrm{wet}}{S} \label{eq:CD0:f:Swet}\] \[C_{f\mspace{2mu}\mathrm{e}} = 1.5 \cdot C_{f\mspace{2mu}\mathrm{turb}} \label{eq:Cfe:Cfturb}\]- $C_{f\mspace{2mu}\mathrm{turb}}$, friction coefficient of a flat plate aligned with the flow, calculated in turbulent regime at the aircraft flight Reynolds number $\mathrm{Re} = \rho V \bar{c}/\mu$.
Oswald efficiency factor
\[e = f \left( M, \mathrm{A\!R}, \Lambda_\mathrm{le} \right) \label{eq:e:Drag:Polar}\](various calculation methods in literature)