マルチコプターエアロダイナミクス:ヘキサコプター上の推力の特徴付け

Multicopters are small aerial vehicles with multiple rotors, as opposed to traditional helicopters with one main rotor. A traditional helicopter rotor has variable pitch, which enables the pilot to control lift and steering. However, multicopters rely on fixed pitch rotors. Some rotate clockwise, and some rotate counterclockwise. Flight is controlled by varying the speed of one or more rotors. For example, in this hexacopter, all of the propellers operate at the same speed. This produces the same thrust for it to hover.

Like fixed wing aircraft, hexacopter attitude is described about three axes: the pitch axis, the roll axis, and the yaw axis. The hexacopter can be controlled about the pitch axis by increasing the speed of the propellers on one side of the pitch axis and decreasing the speeds of the ones on the other side. This creates a thrust differential between the two sides. If thrust is increased in the rear propellers and decreased in the forward propellers, the hexacopter pitches forward.

Similarly, the hexacopter can be controlled about the roll axis in the same way. This causes side-to-side movement. This is done by increasing the speed of the propellers on one side and decreasing the speed of the propellers on the other side.

Yaw control, which changes the heading angle, is achieved by balancing the clockwise propeller rotational torques with the counterclockwise propeller rotational torques. By spinning the counterclockwise propellers faster than the clockwise propellers, the opposite net reaction induces a clockwise rotation about the yaw axis.

We can calculate the thrust and torque of each propeller unit using the equations shown. where T is the thrust generated, CT is the thrust coefficient, tau is the torque, CQ is the torque coefficient, and omega is the rotational speed in RPM. Both the electrical power input and the mechanical power output can be calculated using the following equations. The electrical and mechanical power are then used to determine the efficiency of the propeller motor. The two coefficients, along with the electrical and mechanical power, are calculated using data acquired from experiments.

In this lab, we will demonstrate how to calculate aerodynamic and thrust forces on a hexacopter using a load cell mounted on a test stand. Then, we will characterize and analyze lift and drag over a range of air speeds using a wind tunnel.

To begin this experiment, we’ll use a dynamometer to measure and calculate parameters of one propeller. First, obtain a dynamometer with an onboard data acquisition system. Run the graphical user interface provided with the dynamometer system. Mount the motor on the dynamometer test stand and connect all device wires. Then, calibrate the system by following the onscreen instructions, using weights and the known lever arm when prompted.

Once calibration is complete, attach the propeller in a ‘puller’ configuration. Before running the experiments, make sure the dynamometer is firmly secured to the workbench using C-clamps, and that it is placed behind a plexiglass protection wall.

Now connect the battery to the dynamometer. Run the step input program, which powers the DC motors using a pulsed signal. The program will record the measured thrust, torque, motor RPM, motor current, and pulse with modulation throttle command.

For this part of the experiment, we will measure thrust from the hexacopter using a load cell outside of the wind tunnel to avoid disturbances from the wind tunnel walls.

First, fasten the hexacopter onto the load cell test stand using mounting screws. Then, open the data acquisition system and run the load cell strain gauge bias program to remove all of the bias load cell values. Connect the hexacopter flight controller to the computer using a micro USB cable, and connect the power supply to the hexacopter.

Then, open the ground controller station program. Under the configuration tab, link all motors by clicking the tick mark on the right side. Move the output channel slider to the desired throttle command at 1,300 microseconds. Let the system stabilize for a few seconds and then run the program to collect data from the load cell.

When the program is complete, stop the motors by moving the output channel sliders to the left on the ground controller station. Repeat the test with throttle commands of 1,500 and 1,700 microseconds. Then stop the motors, and transfer all of the data to a flash drive to use as a baseline for the wind tunnel measurements in the next test.

For the next part of the experiment, we will conduct the same test, except it will be done inside of the wind tunnel with airflow. To begin, mount the hexacopter on the load cell test stand. Then, connect the load cell to the data acquisition computer, and connect the hexacopter to the ground control station. Secure the test stand to the base of the wind tunnel using C-clamps, making sure that the hexacopter is free of the wind tunnel walls, floor, and ceiling to minimize free stream flow disturbances.

Then, mount two pitot tubes inside of the wind tunnel using industrial tape, making sure to place them a few feet away from the hexacopter to sample the undisturbed airflow. Now, set the pitch angle of the hexacopter to 0° by adjusting the hinge joint of the test stand. Then, close the wind tunnel.

Connect the pitot tube sensors to the data acquisition system. Next, run the bias program to establish the load cell voltage biases. Then, initialize the wind tunnel and set the wind speed to about 430 ft/min, or 2. 2 m/s. Once the free stream flow speed settles to the desired value, collect the baseline lift and drag readings from the load cell with the hexacopter motors off.

Now, turn the hexacopter motors on by initializing the throttle command to 1,300 microseconds. Let the air speed in the wind tunnel settle and then collect the readings from the load cell and from the pitot tubes. Then, repeat the test again for the three throttle command settings at varied hexacopter pitch angles and wind tunnel air speeds. To reduce complexity, a zero-yaw angle was maintained at all times.

Now let’s interpret the results. First, plot the thrust versus RPM and torque versus RPM data collected from the dynamometer experiment.

Here, we show the data for one motor. The plots illustrate that an increase in motor RPM results in an increase in torque and thrust. Now, fit a quadratic curve to the data in the form of the following equations. Using the quadratic relation, we can then determine the thrust coefficient, CT, and the torque coefficient, CQ.

Next, plot input motor RPM, electrical power, and throttle command on a 3-D plot. Since there is no direct RPM sensor feedback on our hexacopter, we have fit a polynomial surface to the data to obtain the actual RPM as a function of electrical power and throttle command.

Now that we’ve looked at the dynamometer results, let’s take a look at the wind tunnel experiments conducted using the parameters listed here. The variation of drag and lift are plotted against the different pitch angles tested. Both plots show that increasing the throttle command results in significant increase in lift, or motor thrust, as well as an increase in drag. An increase in wind tunnel air speed does not significantly increase lift. However, higher air speed did result in a significant increase in the drag force acting on the hexacopter.

In summary, we learned how aerodynamic forces control the flight of multicopters. We then tested a hexacopter in a wind tunnel and analyzed the lift and drag forces produced over a range of air speeds.