How does induced drag vary with an increase in velocity?

Induced drag is associated with the generation of lift and is a crucial component in the aerodynamics of an aircraft. As the velocity of the aircraft increases, the induced drag decreases, and this relationship can be understood through the principles of lift and drag.

When an aircraft generates lift, it also creates induced drag, which is a byproduct of the lift-generation process. The formula for induced drag can be expressed in relation to lift and the square of the velocity. Specifically, induced drag decreases with an increase in the square of the velocity because the lift required to maintain altitude can be achieved more efficiently at higher speeds.

In essence, as the velocity increases, the required angle of attack to maintain a constant lift decreases, leading to reduced induced drag. Hence, this inverse relationship between induced drag and the square of velocity gives us a clear understanding of how improving speed can reduce this specific type of drag.

This foundational concept is critical for pilots and those studying aerodynamics, as it explains why aircraft tend to perform more efficiently at higher speeds, where induced drag becomes less significant compared to other forms of drag, such as parasitic drag.