Editing Lift-induced drag (section)

==Calculation of induced drag==
For a ''planar'' wing with an elliptical lift distribution, induced drag D<sub>i</sub> can be calculated as follows:

:<math>D_\text{i} = \frac{L^2}{\frac{1}{2}\rho_0 V_E^2 \pi b^2}</math>,
where
:<math>L \, </math> is the lift,
:<math>\rho_0 \, </math> is the standard [[density of air]] at sea level,
:<math>V_E \, </math> is the [[equivalent airspeed]], 
:<math>\pi \,</math> is the ratio of circumference to diameter of a circle, and
:<math>b \, </math> is the wingspan.
From this equation it is clear that the induced drag varies with the square of the lift; and inversely with the square of the equivalent airspeed; and inversely with the square of the wingspan. Deviation from the non-planar wing with elliptical lift distribution are taken into account by dividing the induced drag by the span [[Oswald efficiency number|efficiency factor <math>e</math>]].

To compare with other sources of drag, it can be convenient to express this equation in terms of lift and drag coefficients:<ref>Anderson, John D. (2005), ''Introduction to Flight'', McGraw-Hill. {{ISBN|0-07-123818-2}}. p318</ref>

:<math>C_{D,i} = \frac{D_\text{i}}{\frac{1}{2}\rho_0 V_E^2 S} = \frac{C_L^2}{\pi A\!\!\text{R} e}</math>,   where
:<math>C_L = \frac{L}{ \frac{1}{2} \rho_0 V_E^2 S} </math>
and
:<math>A\!\!\text{R}=\frac{b^2}{S} \, </math> is the [[Aspect ratio (wing)|aspect ratio]],
:<math>S \, </math> is a reference wing area,
:<math>e \, </math> is the span efficiency factor.
This indicates how, for a given wing area, high aspect ratio wings are beneficial to flight efficiency. With <math>C_L</math> being a function of angle of attack, induced drag increases as the [[angle of attack]] increases.<ref name="Clancy"/>{{rp|Section 5.17}}

The above equation can be derived using [[Lifting-line theory|Prandtl's lifting-line theory]].{{cn|date=April 2022}} Similar methods can also be used to compute the minimum induced drag for non-planar wings or for arbitrary lift distributions.{{cn|date=April 2022}}