In propellers as the airspeed increases thrust decreases. Is the air speed component taken as a vector quantity perpendicular to the propeller? If thats true the its quiet easy to visualize in case of airplanes but for quadcopters will it be "copter_airspeed * sin(copter tilt)"?
Have a look at investigating flight with toy helicopter
Can you draw a picture of what you're asking for? I think you may be thinking about the problem wrong (no offense). The big problem (I think) is that quadcopter's propellers are not oriented the same as an aircraft's, which means that the velocity direction for calculating advance ratio is not the same for the two types of aircraft.
In a quadcopter, horizontal motion is (again, for the most part) parallel to the plane of the prop.
As I understand it, the advance ratio is calculated with the ratio of fluid speed across the blades relative to the tip speed of the blade. In an airplane, this is equal to the horizontal speed of the airplane because the plane of the blades is normal to the horizontal motion.
In a quadcopter, horizontal motion causes air to pass along the blades because horizontal motion is in the same plane as the face of the blade. That is, I don't think you use horizontal speed to calculate the advance ratio of a quadcopter.
Instead, I would use (generally) the vertical speed of the quadcopter because the vertical direction is normal to a quadcopter's propellers.