How do multicopters differ from traditional helicopters in their control mechanisms?

Multicopters use fixed-pitch rotors and control flight by varying rotor speeds, whereas traditional helicopters employ variable-pitch rotors controlled by the pilot. In a hexacopter, some propellers rotate clockwise and others counterclockwise. Flight control is achieved by adjusting individual rotor speeds rather than changing blade pitch angles.

What are the three axes used to describe hexacopter attitude and movement?

Hexacopter attitude is described using the pitch axis, roll axis, and yaw axis, similar to fixed-wing aircraft. Pitch control involves increasing propeller speed on one side and decreasing it on the other. Roll control creates side-to-side movement using the same differential speed method, while yaw control changes heading by balancing clockwise and counterclockwise rotational torques.

How is yaw control achieved in a hexacopter?

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.

What equations are used to calculate thrust and torque in multicopter propellers?

Thrust is calculated using T = CT × ρ × n² × D⁴, where CT is the thrust coefficient, ρ is air density, n is rotational speed in RPM, and D is propeller diameter. Torque uses τ = CQ × ρ × n² × D⁵, where CQ is the torque coefficient. Both coefficients are determined experimentally from dynamometer data.

What role does a dynamometer play in characterizing hexacopter performance?

A dynamometer measures and calculates individual propeller parameters including thrust, torque, motor RPM, motor current, and throttle command using a step input program with pulsed signals. The system records these values to establish relationships between motor performance and control inputs, providing baseline data for propeller characterization and propeller characterization variations in pitch diameter and blade number performance analysis.

How does wind tunnel testing complement load cell measurements for hexacopter characterization?

Load cell testing outside the wind tunnel measures static thrust at various throttle commands. Wind tunnel testing then characterizes lift and drag forces under airflow conditions at different pitch angles and airspeeds. Results show that increasing throttle significantly increases lift and drag, while higher airspeed increases drag but not lift substantially.

What is the relationship between motor RPM, electrical power, and throttle command in a hexacopter?

Since hexacopters lack direct RPM feedback, a polynomial surface is fitted to dynamometer data relating motor RPM to electrical power and throttle command. This relationship enables calculation of actual RPM from control inputs and power measurements, allowing engineers to predict motor performance across different operating conditions without direct sensor feedback.

Multicopter Aerodynamics: Characterizing Thrust on a Hexacopter

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This protocol characterizes hexacopter thrust and aerodynamics. For this experiment, we used commercially available, off-the-shelf components for the hexacopter, and the details are provided in Table 2. For the flight controller, we selected an open-source autopilot, Librepilot,⁹ as it provided flexibility to control individual motor commands issued to the hexacopter.

The test stand for mounting the load cell and hexacopter was fabricated in-house using laminated plywood and is shown in Figure 2. When designing the test stand, note that it must allow accurate adjustment of the multicopter’s angle of attack and be sufficiently rigid to withstand bending forces and vibrations created while operating the motors.

A 6-axis load cell is mounted on the test stand and connected to the data acquisition board, as shown in Figure 3. Aerodynamic and thrust forces are sensed in the body frame of the hexacopter by the load cell. Strain gauge data passes through a signal conditioner. The data acquisition (DAQ) board then acquires the analog force and torque components using a calibration procedure provided by the load cell manufacturer. The DAQ board then stores these values in a high-speed buffer and later to permanent disk.

For this protocol, first, determine the forces generated by the individual motors. Then determine the forces acting on the bare airframe, followed by determining the forces generated by the whole hexacopter as a function of motor RPM commands. Issue the same RPM commands to all motors for each test.

1. Dynamometer Experiment

The dynamometer allows direct measurement of parameters, including thrust, torque, RPM, battery voltage, and current. Parameters such as electrical power, mechanical power, and motor efficiency can then be derived from Equations (3), (4), and (5).

Connect the dynamometer to the DAQ computer using a USB connector.
Run the graphical user interface (GUI) provided with the dynamometer.
Calibrate the dynamometer by following the on-screen instructions provided. Use weights and a known lever arm when prompted.
Mount the motor on the dynamometer test stand.
Attach the propeller in a puller (tractor) configuration, as shown in Figure 4.
Connect the battery to the dynamometer.
Firmly secure the dynamometer to the workbench using C-clamps.
Run the step input program and record the measured parameters, including thrust, torque, motor RPM, motor current, and pulse width modulation (PWM) “throttle” command.

2. Static Thrust Test

Fasten the hexacopter on the load cell test stand using mounting screws.
Open the Data Acquisition System (DAQ), and run the load cell strain gauge bias program.
Connect the hexacopter flight controller to the computer using a micro USB cable and open the Ground Controller Station (GCS) software.
Connect the power supply to the hexacopter.
Select the Configuration tab -> Output in GCS. Link all the motors, and check the Live testing of the outputs.
Set the desired throttle command to 1300 ms. Make sure you can operate all motors with the same throttle (PWM) command.
Let the system stabilize for several seconds, and then run the DAQ program to collect data from the load cell.
After data collection is complete, stop the motors.
Repeat steps 3. 6 to 3.8 for throttle commands 1500 ms and 1700 ms.
Transfer data stored in the DAQ system to a data processing computer and long-term storage.

3. Dynamic Thrust Test

Conduct a series of wind tunnel tests to characterize and analyze the hexacopter’s linear aerodynamic forces, primarily lift and drag, over a variety of airspeeds and incidence angles. During the wind tunnel experiments, the hexacopter is assumed to be in steady flight conditions. Therefore, the magnitude of the hexacopter velocity vector is the same as airspeed and assumed horizontal in the world frame. Lift and drag forces are primarily due to the flow of air around the hexacopter. Note that lift and drag forces are assumed to characterize the total lift and total drag on hexacopter; side forces are negligible.

The experimental procedure performed in this experiment is similar to those reported in Foster¹⁰and Russell¹¹. During wind tunnel testing, the hexacopter was driven by a power converter plugged into building (AC) power to assure consistent power and voltage levels throughout all tests. Note that motors at high RPMs can consume appreciable current; use low gauge and short length wire to prevent appreciable voltage drop across the wire during operation.

Mount the hexacopter on the load cell test stand
Connect the load cell to the DAQ computer, and connect the hexacopter to the GCS using the procedure described for the Static Thrust Test.
Secure the test stand to the base of the wind tunnel with C-clamps.
Make sure the multicopter is well clear of wind tunnel walls, floor, and ceiling to minimize free stream flow disturbance and reflection.
Mount pitot tubes several feet away from the hexacopter to sample undisturbed airflow. Connect the pitot pressure sensors to the DAQ system.
Set the pitch angle for the hexacopter to 0° by adjusting the hinge joint of the test stand. In the wind tunnel, hexacopter pitch angle and angle of attack are identical.
Run the bias program to establish load cell voltage biases.
Initialize the wind tunnel to the wind speed of 2.2 m/s.
Once the free stream flow speed settles to the desired value, collect baseline FT readings from the load cell with hexacopter motors off.
Initialize the throttle command to 1300 ms, let the airspeed in the wind tunnel settle before collecting FT and pitot data.
Repeat steps 3.7 - 3.9 for throttle commands of 1500 ms and 1700 ms.
Repeat Steps 3.5 - 3.10 for different hexacopter pitch angles and wind tunnel airspeed values, as stated in Table 1.