Angle of Attack with Relative Velocities

The angle of attack is the angle between the oncoming airflow and the chord line of the wing or airfoil.

Generally, we can see the angle of attack as shown in Image 1 if we assume the flight path is perpendicular to the direction of gravity. But, for modeling such as Computational Fluid Dynamics, it is easier to change the angle of attack instead of rotating the geometry (as shown in Image 2), by converting the velocity components:

u = U*cos(AoA)

v = U*sin(AoA)

With the u and v are the velocity components in the x and y directions respectively, and U is the magnitude of the velocity.

so we must calculate the Lift and Drag based on the calculated forces (for example Fx and Fy) with the equations:

Lift = Fy*cos(AoA) – Fx*sin(AoA)

Drag = Fx.cos(A0A) + Fy*sin(A0A)