How a quadcopter flies

TL;DR:

• A quadcopter has no moving control surfaces. It steers by changing the speed of each of its four propellers.

• Two propellers spin clockwise and two counterclockwise, so their reaction torques cancel when all spin at the same speed.

• Roll and pitch come from thrust differences between opposite sides, and yaw from a speed difference between the two spin directions.

A helicopter needs a tail rotor and a swashplate to control its motion. A quadcopter has four motors and four fixed propellers, and nothing else. All its control comes from changing how fast each propeller spins. That is why quadcopters became cheap, and also why they need a computer to fly at all.

Thrust and torque

A spinning propeller pushes air down and so is pushed up. The upward force is thrust, and it grows rapidly with speed: for a given propeller, thrust is roughly proportional to the square of its rotation speed.

A spinning propeller also feels a drag torque from the air. By Newton's third law, the propeller pushes the air around in one direction and the air pushes the aircraft around in the opposite direction. This reaction torque would spin the drone's body if it were not balanced.

Four propellers, two directions

The solution is to have two propellers spin clockwise and two counterclockwise. In the common X layout, the diagonal pairs match: the front-left and rear-right propellers spin one way, and the front-right and rear-left the other. When all four spin at the same speed, the four reaction torques cancel and the drone does not turn.

Roll, pitch and yaw

Define the three rotations of the aircraft:

• Roll: tilting about the front-to-back axis (left side down or right side down).

• Pitch: tilting about the left-to-right axis (nose down or nose up).

• Yaw: turning about the vertical axis (nose to the left or right).

Control each by changing the speeds of particular propellers:

• Roll right: speed up the two left propellers, slow down the two right propellers. More thrust on the left lifts the left side.

• Pitch forward: speed up the two rear propellers, slow down the two front ones, so the nose dips.

• Yaw: speed up one diagonal pair (one spin direction) and slow the other pair. The reaction torques no longer cancel, and the body turns, while the total thrust stays about the same.

• Climb or descend: speed up or slow down all four together.

To move sideways or forward, the drone tilts first, so part of the thrust points sideways. There is no other way: the thrust always points along the vertical axis of the body.

Worked example: roll, pitch and yaw from four propellers

A drone of mass 0.8 kg hovers. Its weight is 0.8 × 9.8 = 7.84 N, so each of the four propellers produces 7.84 / 4 = 1.96 N of thrust. The motors sit 0.12 m from the center, along the diagonals of the X.

Roll right. Raise each left propeller by 0.20 N, to 2.16 N, and lower each right propeller by 0.20 N, to 1.76 N.

1. Total thrust: 2 × 2.16 + 2 × 1.76 = 4.32 + 3.52 = 7.84 N. It is unchanged, so the drone neither climbs nor sinks.

2. The roll axis runs front to back. Because the motors are on the diagonals of an X, each one is at a perpendicular distance of 0.12 × cos 45° = 0.0849 m from that axis.

3. The thrust differences give a torque: the left side adds 2 × 0.20 × 0.0849 = 0.034 N·m and the right side removes 2 × 0.20 × 0.0849 = 0.034 N·m in the same rotation direction. Total: 0.0679 N·m of roll torque.

Yaw. Raise the two clockwise propellers a little and lower the two counterclockwise propellers by the same amount. Total thrust stays equal, so the drone holds its height. The reaction torque of the faster pair is bigger than that of the slower pair, so the net torque turns the body, in the direction opposite to the faster pair's spin.

Notice the design logic: thrust changes in pairs that sum to zero, so one command (roll, pitch or yaw) does not disturb the others or the height. The flight controller's job is to compute that mix of four motor commands from the pilot's requests and the sensors.

Why it needs a computer

A quadcopter is unstable. If it tilts a little, nothing in the airframe pushes it back, so the tilt tends to grow. A flight controller reads gyroscopes and accelerometers hundreds to thousands of times per second and adjusts the four motors to keep it level and on course. Without that loop it would flip within a second or two.

Where it goes wrong

• Motor failure. Lose one motor and the thrust and torque balance are gone. A basic quadcopter cannot recover and falls.

• Wrong propeller direction. A propeller fitted to the wrong motor, or a motor wired to spin the wrong way, makes the drone flip at take-off.

• Battery sag. As the battery drains, the voltage and the maximum thrust drop, so the controller has less margin.

• Vibration. An unbalanced propeller shakes the gyroscope readings and degrades control.

• Wind. A gust adds a torque and a force the controller must cancel.

Safety: Spinning propellers can cause deep cuts, and a drone can accelerate quickly and unexpectedly. Remove the propellers for any bench test, wiring change or first power-up. Fly only in an open area away from people, keep your distance, and never catch a drone in flight. Use batteries and chargers with care (LiPo packs can ignite when damaged) and check the local rules about flying drones.

How real drones use it

Photography drones, racing drones and delivery prototypes all use this arrangement, sometimes with six or eight propellers for redundancy and lifting power. The flight controller software mixes the four commands as above, and the details of how it stays level are in drone flight controllers and stabilization. The simpler question of how much thrust it takes just to hover is answered in why a drone hovers.

Try it yourself

On paper, draw a quadcopter from above with the four motors numbered and the spin direction of each marked with an arrow. Write down the thrust of each motor for a hover, then for each of roll, pitch, yaw and climb, change the numbers so the total stays the same where it should. Check each time that clockwise and counterclockwise totals match for the non-yaw moves.

Frequently asked questions

Why do two propellers spin the other way?

A propeller's drag makes a reaction torque on the body. Equal numbers of clockwise and counterclockwise propellers at the same speeds cancel that torque.

How does a quadcopter move forward?

It tilts forward by speeding up the rear propellers, so some thrust points forward while the rest holds it up, then it accelerates in that direction.