Induced drag (idea)

Induced drag is the component of the drag force that is caused by lift. It is a consequence of the way in which a wing provides lift. A (symmetric) wing only provides lift at a positive angle of attack. Since the lift force vector of a wing is perpendicular to the effective flow direction in the plane of the wing's cross section, the lift vector is not pointing straight up. Instead, it has an upward component and an aft component. The aft component opposes the thrust (or the freestream velocity), and thus is a drag force. Since this force was caused by lift, it is referred to as the drag due to lift or drag induced by lift, shortened to induced drag.

                           ^     ^
                           |    /
                   Lift = L|   /"Effective Lift" (lift + induced drag)
                           |  /
                           | /
               ________    |/----> induced drag = D_i
             _-        ---------__________
            (___________________          ---------________
                                -------------------

It can be shown that the coefficient of induced drag C_Di is proportional to the square of the lift coefficient C_L:

C_Di = C_L² / (π*AR*e)

Note: e is not Euler's number, but is instead the airplane efficiency factor.

Note that as AR→∞, the coefficient of induced drag, and thus the induced drag, tend to zero. This is why gliders have very long, slender wings, to improve their aerodynamic efficiency. Also, an airfoil has no induced drag, since it is two dimensional.