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induced drag

The increase in drag due to the finite length of the wing. The finite wing and the tip and starting vertices constitute a large vortex ring inside which there is a downward velocity (usually referred to as downwash velocity) induced by the vortices. Prandtl showed that this induced velocity is constant if the distribution of lift is elliptical over the wing. This induced velocity component caused the effective angle of attack of the wing to decrease. One effect of this reduction is that the lift vector, which must be perpendicular to the effective approach velocity, must be rotated. Consequently, the lift vector has two components, one of which is the true lift, which is perpendicular to the velocity vector without the induced velocity component, and the other is parallel to the velocity vector. The parallel component is in the direction of drag and is accordingly called induced drag. The induced drag is related to the lift as

<center>

<math>

C_{Di} = rac{C_L^2}{pi B^2/A} = rac{C_L^2C}{pi B}

</math>

</center>

where <math>B</math> is the span of the airfoil and <math>C</math> is the mean chord length. The ratio <math>B/C</math> is the aspect ratio. Induced drag is critical during takeoff and landing when the lift coefficient is especially large.

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