In the previous article, we provided an overview of ESCs. To design an ESC, it is essential to understand the BLDC motor itself, which is the component being controlled. In this article, we will explain the physical mechanisms behind how a BLDC motor generates torque and what determines its rotational speed. Grasping these concepts is crucial for establishing criteria for motor selection.
The Physics of Torque Generation
Torque in a BLDC motor is generated by the interaction between the magnetic field created by the stator coils and the magnetic field of the rotor magnets. According to the fundamentals of electromagnetism, a conductor carrying current within a magnetic field experiences a Lorentz force, which is the source of torque.
When current I flows through the stator coils, a magnetic field is generated around the coils. When this magnetic field and the rotor magnet's magnetic field have a certain angle, a force acts on the rotor to align the magnetic fields (restoring torque). Maximum torque is generated when the two magnetic fields are orthogonal (a 90-degree phase difference), and the torque becomes zero when they are parallel.
For this reason, the direction of the current on the stator side must be switched every time the rotor rotates and the phase relationship of the magnetic fields changes. This is the role of 'commutation' explained in the previous article, and it is the reason why the ESC switches the three-phase energization pattern according to the rotor position.
Mathematically, torque T can be expressed as follows:
T = Kt × I
Kt is the torque constant, an inherent value determined by the motor's structure (magnet strength, number of coil turns, rotor diameter, etc.). The relationship where torque increases in proportion to current I is the most fundamental characteristic of a BLDC motor.
Back Electromotive Force (BEMF) and Rotational Speed
As the motor rotates, the magnetic field of the rotor magnets crosses the stator coils. This induces a voltage in the coils according to Faraday's law. This is the Back Electromotive Force (Back EMF or BEMF).
BEMF is proportional to the rotational speed and is expressed by the following formula:
Vbemf = Ke × ω
Ke is the back EMF constant, and ω is the angular velocity (rad/s). In fact, the torque constant Kt and the BEMF constant Ke have the same value in the SI unit system, which is a consequence of the law of conservation of energy (the relationship where mechanical output equals electrical input).
This BEMF is extremely important in motor control. The voltage obtained by subtracting this BEMF from the voltage V applied to the coils becomes the driving force that pushes current through the coil resistance and inductance. Written as an equivalent circuit:
V = R × I + L × dI/dt + Vbemf
In a steady state (dI/dt = 0):
I = (V - Vbemf) / R
In short, the structure is such that the difference between the applied voltage V and the BEMF determines the current, and that current generates torque.
Meaning of the KV value
The KV value is always listed in the catalogs for drone motors. This represents the "rotational speed (RPM/V) when 1V is applied under no-load conditions."
For example, a "2300KV" motor rotates at 2300 RPM at 1V, which means it will spin up to approximately 55,200 RPM under no-load conditions when connected to a 24V battery (the nominal value for a 6S LiPo battery).
The KV value corresponds to the reciprocal of the aforementioned BEMF constant Ke. A motor with a high KV value has a smaller Ke and rotates faster at the same voltage, but in exchange, the torque constant Kt also becomes smaller (since Kt and Ke are equal). In other words, there is always a trade-off: "high KV = high speed, low torque" and "low KV = low speed, high torque."
In drone design, the optimal KV value is determined by the airframe size, propeller diameter, and battery voltage. High KV (around 2000–3000) is chosen for small aircraft and small propellers, while low KV (around several hundred to 1000) is chosen for large aircraft and large propellers.
Electrical Rotation and Mechanical Rotation
When discussing the "rotational speed" of a BLDC motor, it is necessary to distinguish between two different speeds.
Mechanical rotational speed is how many times the rotor physically rotates, which is directly linked to the propeller's rotational speed.
Electrical rotational speed is the number of magnetic pole switching cycles, which determines the ESC's control frequency. For a motor with P poles (the total number of N and S poles), it rotates electrically P/2 times for every one mechanical rotation.
For a 14-pole drone motor, it rotates electrically 7 times for every one mechanical rotation. If the mechanical rotation is 10,000 RPM (166.7 Hz), the electrical rotation is 70,000 RPM (1167 Hz). The ESC must generate 6-step (trapezoidal wave) or continuous sine/FOC waveforms in synchronization with this electrical rotation, and the upper limit of the drive frequency constrains the maximum motor rotational speed.
Relationship Between Torque and Current: Why Does Current Flow During Hovering?
There is a misconception that "rotating means producing torque," but in reality, torque is zero when rotating at a constant speed. Torque is the quantity that produces acceleration, and a large amount of torque is only required when accelerating, decelerating, or changing the attitude of the aircraft.
So why does a large current flow to the motor during hovering? This is because it is generating torque against the reaction force (= air resistance) of the propeller pushing air downward. A load torque is applied to the propeller, and current continues to flow to continuously produce a torque that balances this load.
When rapidly accelerating the aircraft or performing sudden attitude changes, acceleration torque is required in addition to this base torque, causing the current to increase further momentarily. The current capacity of the ESC and battery wires must be designed to match this peak current, not the steady-state current during hovering.
Motor Efficiency and Heat Generation
A motor's input power is divided into mechanical output and losses. The main losses are the following three:
Copper loss is heat generated by coil resistance, determined by I²×R. Because it is proportional to the square of the current, it increases rapidly in the high-current range. This is the main reason efficiency drops when the throttle is increased.
Iron loss is the eddy current and hysteresis loss generated in the stator core, which depends on the rotational speed. It increases in the high-speed rotation range.
Windage loss is the loss due to mechanical air resistance and friction, which becomes impossible to ignore, especially in the high-rotation range.
All of these losses accumulate in the motor as heat. Because drone motors prioritize small size and light weight, they struggle with heat dissipation and have a structure where the temperature easily rises during continuous use. To avoid irreversible demagnetization of the magnets (which progresses gradually even at temperatures lower than the Curie temperature), it is a general guideline to keep the surface temperature below 70–80°C during operation.
Matching Motors, Propellers, and Battery Voltage
Aircraft performance is determined not by the motor alone, but by the combination of the motor, propeller, and battery voltage.
The larger the propeller diameter and pitch, the greater the thrust generated at the same rotational speed, and the greater the required torque. If a motor with a KV value that is too high (i.e., a low torque constant Kt) is paired with this, the required current becomes excessive, causing the motor or ESC to be destroyed by heat.
Conversely, if the KV value is too low, the motor will not reach a sufficient rotational speed at the given battery voltage, resulting in insufficient thrust.
It is standard practice to utilize the motor thrust tables published by manufacturers (data on thrust, current, and efficiency for each propeller, voltage, and throttle setting) to select an operating point that maximizes efficiency for the aircraft's design weight and required thrust.
Summary
BLDC motor torque is generated by the interaction between the stator magnetic field and the rotor magnetic field, and is proportional to the current. The rotational speed is determined by the equilibrium with the BEMF, and the catalog metric known as the KV value expresses this characteristic. Understanding these basic principles—electrical versus mechanical rotation, the relationship between torque and current, and efficiency versus heat generation—is a prerequisite for appropriate motor selection and ESC design. Next time, we will explain specific drive methods—the differences between trapezoidal wave, sine wave, and FOC—in detail from the perspective of current waveforms and torque characteristics.