Aerodynamics of a Quadcopter
Quadcopter structure and x-mode and +-mode
The four motors of the quadcopter are arranged in a cross shape, driving the four propellers to rotate to generate upward thrust. The distance between the four motors’ wheel and the geometric center is equal. When the lift generated by the two diagonal axes is the same, the torque balance can be ensured, and the four axes will not tilt in any direction. The way of reversal balances the anti-torque rotating around the vertical axis, ensuring the stability of the four-axis heading.
Compared with traditional helicopters, quadrotors have the following advantages: The counter torque applied by each rotor to the fuselage is opposite to the direction of rotation of the rotor, so when motor 1 and motor 3 rotate counterclockwise, motor 2 and motor 4 are clockwise. Clockwise rotation balances the counter-torque of the rotor to the fuselage.
According to the different positions of the user-defined nose, the quadcopter can be divided into x mode and + mode. The head direction of the x mode is between the two motors, while the head direction of the + mode is on one of the motors. The x and + are the shape of the aircraft when facing the direction of the nose. As shown below. The x-mode is a little harder to fly, but more flexible. The + mode is better to fly, and the movements are less flexible, so it is suitable for beginners. Note that the flight controller installations for x-mode and +-mode are different. If the flight control board is installed incorrectly, it will shake violently and cannot fly at all.
Aerodynamic Principles
The quadrotor has a total of 6 degrees of freedom in space (translation and rotation along the 3 coordinate axes respectively), and the control of these 6 degrees of freedom can be realized by adjusting the speed of different motors. The basic motion states are:
- vertical movement;
- pitching motion;
- rolling motion;
- yaw movement;
- forward and backward movement;
- Lateral movement.
In the figure, motor 1 and motor 3 rotate counterclockwise, and motor 2 and motor 4 rotate clockwise. It is stipulated that the movement along the positive direction of the x-axis is called forward movement. The arrow above the movement plane of the rotor indicates that the motor speed is increased. At the bottom is indicated that this motor speed drops.
Vertical Movement: Vertical movement is relatively easy. In the figure, because there are two pairs of motors with opposite directions, the counter torque to the fuselage can be balanced. When the output power of the four motors is increased at the same time, the rotor speed increases and the total pulling force increases. When the total pulling force is enough to overcome the overall pulling force When the weight is high, the quadrotor will rise vertically from the ground; on the contrary, if the output power of the four motors is reduced at the same time, the quadrotor will descend vertically until it lands in a balanced manner, realizing vertical movement along the z-axis. When the external disturbance is zero, when the lift generated by the rotor is equal to the weight of the aircraft, the aircraft will remain in a hovering state. The key to vertical motion is to ensure that the rotational speed of the four rotors increases or decreases synchronously.
Pitching motion: In Figure (b), the rotational speed of motor 1 increases, the rotational speed of motor 3 decreases, and the rotational speeds of motor 2 and motor 4 remain unchanged. In order not to change the overall torque and total pulling force of the quadrotor aircraft due to the change of the rotor speed, the variable of the speed of the rotor 1 and the rotor 3 should be equal. As the lift of rotor 1 rises and the lift of rotor 3 falls, the resulting unbalanced moment causes the fuselage to rotate around the y-axis (the direction is shown in the figure). Similarly, when the speed of motor 1 decreases, the speed of motor 3 increases, and the motor The body rotates in the other direction around the y-axis to realize the pitching motion of the aircraft.
Rolling motion: the same principle as in Figure b, in Figure c, changing the speed of motor 2 and motor 4, keeping the speed of motor 1 and motor 3 unchanged, the body can be rotated around the x-axis (forward and reverse). direction) to realize the rolling motion of the aircraft.
Yaw motion: The yaw motion of the quadrotor can be achieved by the anti-torque generated by the rotor. During the rotation of the rotor, due to the effect of air resistance, a counter-torque opposite to the rotation direction will be formed. In order to overcome the influence of the counter-torque, two of the four rotors can be rotated forward and two reversed, and each rotor on the diagonal line can be rotated. same direction. The magnitude of the counter-torque is related to the rotational speed of the rotors. When the rotational speeds of the four motors are the same, the counter-torques generated by the four rotors are balanced with each other, and the quadcopter does not rotate; when the rotational speeds of the four motors are not exactly the same, the unbalanced counter-torque will Causes the quadrotor to turn. In Figure d, when the rotational speed of motor 1 and motor 3 increases, and the rotational speed of motor 2 and motor 4 decreases, the reaction torque of rotor 1 and rotor 3 to the fuselage is greater than the reaction torque of rotor 2 and rotor 4 to the fuselage. The body rotates around the z-axis under the action of the surplus anti-torque to realize the yaw motion of the aircraft, and the steering is opposite to the steering of the motor 1 and the motor 3.
Front and rear movement: In order to realize the movement of the aircraft in the horizontal plane, front and rear, left and right, a certain force must be applied to the aircraft in the horizontal plane. In Figure e, increase the speed of motor 3 to increase the pulling force, correspondingly reduce the speed of motor 1 to reduce the pulling force, while keeping the speed of the other two motors unchanged, the counter torque still needs to be balanced. According to the theory in Figure b, the aircraft first tilts to a certain degree, so that the rotor pull produces a horizontal component, so the forward flight motion of the aircraft can be realized. Flying backward is the exact opposite of flying forward. Of course, in Figures b and c, the aircraft also produces horizontal movements along the x and y axes while generating pitch and roll motions.
Inclination motion: In Figure f, due to the symmetry of the structure, inclination flight works exactly the same as fore and aft motion.
All in all, it controls the speed of the four motors. Then increase the speed and slow down accordingly to make the four axes move.