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 <math display="inline">D_\text{i}</math>, and the lift-induced drag coefficient as <math display="inline">C_{D,i}</math>.
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,]]
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.
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.
:<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,
:<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. The drag characteristics of a wing with infinite span can be simulated using an airfoil section the width of a wind tunnel.
An increase in wingspan or a solution with a similar effect is one way to reduce induced drag. Winglets also provide some benefit by increasing the vertical height of the wing system. for a planar wing of a given span. A small number of aircraft have a planform approaching the elliptical — the most famous examples being the World War II Spitfire and Thunderbolt. For modern wings with winglets, the ideal lift distribution is not elliptical. While induced drag is inversely proportional to the square of the wingspan, not necessarily inversely proportional to aspect ratio, if the wing area is held constant, then induced drag will be inversely proportional to aspect ratio. However, since wingspan can be increased while decreasing aspect ratio, or vice versa, the apparent relationship between aspect ratio and induced drag does not always hold. Reducing induced drag can therefore significantly reduce cost and environmental impact. He observed that, at these low airspeeds, increasing speed required reducing power. (At higher airspeeds, parasitic drag came to dominate, causing the power required to increase with increasing airspeed.)
Induced drag must be added to the parasitic drag to find the total drag. Since induced drag is inversely proportional to the square of the airspeed (at a given lift) whereas parasitic drag is proportional to the square of the airspeed, the combined overall drag curve shows a minimum at some airspeed - the minimum drag speed (V<sub>MD</sub>). An aircraft flying at this speed is operating at its optimal aerodynamic efficiency. According to the above equations, the speed for minimum drag occurs at the speed where the induced drag is equal to the parasitic drag.