Aerodynamic forces are forces between air and solid objects caused by relative motion between solid objects and air.

We focus on two important aerodynamic forces: lift and drag. Lift is the component of aerodynamic force perpendicular to the relative direction of motion; drag is the component of aerodynamic force parallel to the relative direction of motion.

In this video, aerodynamic lift on the grid fin is used to steer the rocket toward landing.

SpaceX booster cam captures amazing launch and landing footage (time-lapse) - YouTube

In this video, aerodynamic lift on the wing is used not only to lift the airplane upwards, but also "lift" the airplane downwards and sideways to provide centripetal force.

Top Gun: Maverick (2022) - Maverick's Test Run Scene | Movieclips - YouTube

From the video, as the airplane flys by, a column of air around the airplane is set to motion in a direction opposite to the direction of the lift force. Suppose the airplane is flying with a speed LaTeX: V . Over each second, the column of air lengthens by $LaTeX: V\times 1s$ . Suppose the column of air has a width and height proportional to the wing span LaTeX: b , then the air volume set in motion every second is equal to LaTeX: b^2 V . Denoting air density as $LaTeX: \rho$ , the airplane set to motion $LaTeX: \rho b^2 V$ mass of air per second. If the initially stationary air is set to flow downward at a speed of $LaTeX: c\, V$ , where is a non-dimensional constant that depends on the airplane geometry, control surface deflection, etc., then the aerodynamic lift force exerted on the airplane can be calculated via momentum balance as $LaTeX: c\,\rho\,V^2\,b^2$ .

All aerodynamic forces are proportional to air density $LaTeX: \rho$ , the square of relative speed LaTeX: V , and some geometric area (in this case LaTeX: b^2 .) Therefore, we define the nondimensional lift coefficient as

$LaTeX: C_L := \frac{L}{\frac12 \rho V^2 S_{ref}}$

where LaTeX: L is the lift force; $LaTeX: S_{ref}$ is a scenario-dependent reference area. We also define the drag coefficient as

$LaTeX: C_D := \frac{D}{\frac12 \rho V^2 S_{ref}}$

This video explains the aerodynamic lift force on a racecar:

BBC: Downforce explained by Martin Brundle - YouTube

This video shows from the perspective of a helicopter blade the relative motion between blade and air:

Helicopter Main Rotor Blade In Flight Slow Motion - YouTube

This video shows a slow motion of a propeller blade -- what is the direction of lift force on the propeller blades?

Airplane propeller in slow motion - YouTube