Lift-induced drag, induced drag, vortex drag, or sometimes drag due to lift, in aerodynamics, is an aerodynamic drag force that occurs whenever a moving object redirects the airflow coming at it. This drag force occurs in airplanes due to wings or a lifting body redirecting air to cause lift and also in cars with airfoil wings that redirect air to cause a downforce. It is symbolized as D i {\textstyle D_{\text{i}}} , and the lift-induced drag coefficient as C D , i {\textstyle C_{D,i}} . For a constant amount of lift, induced drag can be reduced by increasing airspeed. A counter-intuitive effect of this is that, up to the speed-for-minimum-drag, aircraft need less power to fly faster. Induced drag is also reduced when the wingspan is higher, or for wings with wingtip devices.
Explanation
The total aerodynamic force acting on a body is usually thought of as having two components, lift and drag. By definition, the component of force parallel to the oncoming flow is called drag, and the component perpendicular to the oncoming flow is called lift. At practical angles of attack the lift greatly exceeds the drag. Lift is produced by the changing direction of the flow around a wing. The change of direction results in a change of velocity (even if there is no speed change), which is an acceleration. To change the direction of the flow therefore requires that a force be applied to the fluid; the total aerodynamic force is simply the reaction force of the fluid acting on the wing. An aircraft in slow flight at a high angle of attack will generate an aerodynamic reaction force with a high drag component. By increasing the speed and reducing the angle of attack, the lift generated can be held constant while the drag component is reduced. At the optimum angle of attack, total drag is minimised. If speed is increased beyond this, total drag will increase again due to increased profile drag.
Vortices When producing lift, air below the wing is at a higher pressure than the air pressure above the wing. On a wing of finite span, this pressure difference causes air to flow from the lower surface, around the wingtip, towards the upper surface. This spanwise flow of air combines with chordwise flowing air, which twists the airflow and produces vortices along the wing trailing edge. The vortices reduce the wing's ability to generate lift, so that it requires a higher angle of attack for the same lift, which tilts the total aerodynamic force rearwards and increases the drag component of that force. The angular deflection is small and has little effect on the lift. However, there is an increase in the drag equal to the product of the lift force and the angle through which it is deflected. Since the deflection is itself a function of the lift, the additional drag is proportional to the square of the lift. The vortices created are unstable, and they quickly combine to produce wingtip vortices which trail behind the wingtip.
Calculation of induced drag For a planar wing with an elliptical lift distribution, induced drag Di can be calculated as follows:
D i = L 2 1 2 ρ 0 V E 2 π b 2 {\displaystyle D_{\text{i}}={\frac {L^{2}}{{\frac {1}{2}}\rho _{0}V_{E}^{2}\pi b^{2}}}} , where
L {\displaystyle L\,} is the lift,
ρ 0 {\displaystyle \rho _{0}\,} is the standard density of air at sea level,
V E {\displaystyle V_{E}\,} is the equivalent airspeed,
π {\displaystyle \pi \,} is the ratio of circumference to diameter of a circle, and
b {\displaystyle b\,} 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 efficiency factor e {\displaystyle e} . To compare with other sources of drag, it can be convenient to express this equation in terms of lift and drag coefficients:
C D , i = D i 1 2 ρ 0 V E 2 S = C L 2 π A R e {\displaystyle 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}}} , where
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