How is propeller thrust vector accurately expressed for airplanes and multirotors? For propellers, as the airspeed increases thrust decreases. Is the airspeed component taken as a vector quantity perpendicular to the propeller? If that's true, then it's quite easy to visualize in the case of airplanes.

However, for quadcopters can the forward component of the thrust vector of a quadcopter type rotor be expressed as:

$$
V_q\cdot{sin}\theta_t
$$

Where:  


$V_q$ is the forward airspeed of the quadcopter, and
$\theta_t$ is the angle of rotor tilt


Is this an accurate expression of the thrust vector?
The term 
$$V_q\cdot{sin}\theta_t$$
is a speed, not a force, so it cannot be an accurate expression of the thrust vector.

Propellers accelerate the air flowing through the propeller disc in the direction of the propeller axis (or perpendicular to the propeller disc), so the force is only parallel to the propeller axis when the airspeed is aligned with the propeller axis. If the airspeed is at an angle to the propeller axis, the thrust vector is tilted towards the airspeed vector. The magnitude of this tilt depends on the speed increase of the propeller stream relative to airspeed.