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# Lift-induced drag

In aerodynamics, lift-induced drag, or more simply, induced drag, is a drag force arising from the generation of lift during high-level flight. It is a small, but proportionate component directly arising from lift - the greater the lift, the greater the induced drag.

A wing of finite length adds downwards momentum to the air it encounters, and this is the primary source of induced drag. An aircraft produces a descending wake or net "downwash" as it travels forwards. Gravity adds downward momentum to the aircraft, and the wing must perform work upon the air in order to shed the downward momentum into the air. The energy it expends in order to produce the descending wake will appear as a friction-like force which opposes the aircraft's forward motion. This force is inversely proportional to aircraft speed because at a higher speed, the wing visits a greater mass of air per unit time, so it performs less work in injecting the same downwards momentum into a greater mass. Induced drag is also inversely proportional to wingspan. As with increased speed, a wider span also allows the wing to visit a greater mass of oncoming air per unit time.

A secondary source of drag arises at the wingtips. The higher pressure below the wing and lower pressure above it will cause the air to "roll around" the wingtip, creating a vortex which is shed behind the aircraft. Each wingtip produces one vortex, and the pair of vortices rotate in opposite directions. The energy expended in causing the oncoming air to rotate will lead to a friction-like force which slows the aircraft. The strength of the vortex is directly proportional to the lift force generated by the wing. Various devices have been tried to combat this effect, the most successful of which are winglets, as seen on a number of modern airliners such as the Airbus A340. Winglets do not prevent the vortex, but they control its formation such that the vortex energy actually adds to the aircraft's thrust, rather than to its drag. Winglets can yield very worthwhile economy improvements on long distance flights.

Induced drag must be added to the form drag to find the total drag. In a practical aircraft, induced drag becomes less of a factor the faster the aircraft flies. The opposite occurs with form drag (the drag caused simply by pushing the aircraft through the air), which increases with speed. The combined overall drag curve therefore shows a minimum at some airspeed - an aircraft flying at this speed will be at or close to its optimal efficiency. Pilots will use this speed to maximise endurance (minimum fuel consumption), or maximise gliding range in the event of an engine failure.

Induced drag is insignificant in two-dimensional airfoil simulations and in "infinite wing" wind tunnel testing where the effect of wingtips is removed. In these situations no net downwards momentum is injected into the air. The "upwash" equals the "downwash," the airfoil does not generate a constantly-descending wake as it travels, and so with no the energy expenditure to produce a spinning and descending wake, the induced opposing forward flight is zero.

When a real-world aircraft flys at an altitude less than approximately two wingspans, it enters "Ground-effect" mode of flight. In Ground-effect mode the aircraft interacts directly with the Earth's surface, the momentum injected into the descending wake approaches zero, and the induced drag approaches zero. The lack of induced drag has been harnessed in order to produce fuel-efficient flight by "Wing In Ground-effect" or WIG vehicles.