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)"?

• What is your question? Where are you getting copter_airspeed from? Why would this not be the velocity of the quadcopter normal to the plane of the propeller? – Chuck Mar 30 '16 at 19:33
• advance ratio of propeller is a function of velocity of air speed in the propeller. According to my understanding in case of airplane it is perpendicular to the surface area of the propeller and equal to speed of aircraft assuming surrounding air velocity is zero. But in case of quadcopters horizontal speed of quadcopter is at angle to propeller so what component of velocity sholud be used to calculate advance ratio? – nik0987 Mar 31 '16 at 2:38
• Same as this question (though Robotics is probably the best place for it): aviation.stackexchange.com/questions/26547/propeller-physics – Andy Mar 31 '16 at 13:38
• You may find the following helpful (older question here, covering some of the material you need): robotics.stackexchange.com/questions/2704/… – Andy Mar 31 '16 at 13:42

Have a look at investigating flight with toy helicopter

• So to summarize: when quadcopter is moving forward Thrust of propeller is used for 1) balancing the weight and 2) moving forward. "sine" component of forward velocity will be used for calculating the advance ratio of the propeller. Is this correct? – nik0987 Mar 31 '16 at 2:34
• Yes, that's right. The model I passed you is only valid for toy quadrotor, which means that rotors are not formed by deformable blades. You cannot make the same assumption with real scale helicopters – galtor Apr 2 '16 at 9:01

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 an airplane, horizontal motion is (for the most part) normal to the [geometric!] plane of the prop:

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.

• As you mentioned in the post for quadcopter "horizontal motion is (again, for the most part) parallel to the plane of the prop" is incorrect. You need to provide tilt to quadcopter to move in horizontal direction. In above diagram there is no horizontal component to push quadcopter forward. So you need to tilt quadcopter to make horizontal motion. – nik0987 Apr 12 '16 at 17:21
• @nik0987 - You need to tilt to apply force in the horizontal direction. That is, to accelerate and then to overcome air resistance. If it takes 10g of thrust to move horizontally at 10mph, and the quadcopter's motors make 100g of thrust (numbers totally made up), then the quadcopter is tilted at asin (0.1) ~ 6 degrees. Assuming the quadcopter is maintaining altitude in still air, the air speed is largely parallel to the plane of the props, and the advance ratio calculations don't really apply. – Chuck Apr 13 '16 at 0:24