The Physics of Quadcopter Flight

1.3.1 Steering

While ﬂying your multirotor, it is important to understand how the multirotor moves and how we control it. All of the movements of the multirotor are achieved by varying the rotational speed of the motors. By adjusting the relative speeds of the motors in just the right ways, keeping in mind that the rotational speed of the motors determines how much lift each prop produces, the ﬂight controller is able to cause the multirotor to rotate around any of the directional axes (roll, pitch, and yaw), or make the multirotor gain or lose altitude.

Roll and Pitch

To make the multirotor rotate about the roll or pitch axes, the ﬂight controller makes the motors on one side of the multirotor spin faster than the motors on the other side. This means that one side of the multirotor will have more lift than the other side, causing the multirotor to tilt.

So, for example, to make a quadcopter roll right (clockwise about the roll axis), the ﬂight controller will make the two motors on the left side of the multirotor spin faster than the two motors on the right side. The left side of the craft will then have more lift than the right side, which causes the multirotor to tilt, shown in Figure 1.4.

Similarly, to make a quadcopter pitch down (rotate about the pitch axis clockwise) the ﬂight controller will make the two motors on the back of the craft spin faster than the two motors on the front, shown in Figure 1.5. The same principles apply for multirotor with more than four motors as well.

Figure 1.4: With faster spinning motors on the left side, relative to the right, the multirotor rolls right.

Yaw

Controlling the multirotor’s rotation about the yaw axis is a bit more complex than controlling its rotation about the roll or pitch axes.
When a propeller spins, it encounters friction with the air, also known as aerodynamic drag. Friction generates a force that opposes motion. So, when a prop spins clockwise, its friction with the air generates a counter-clockwise force, which tends to make the craft spin counter-clockwise.

This is described by Newton’s Third Law: as a torque is applied to the propeller in a clockwise direction, the propeller exerts an equal and opposite reaction torque on the copter, causing it to want to spin anticlockwise.

In order to prevent our aircraft from spinning uncontrollably, we set up the motors so that each motor spins in the opposite direction to its neighbours, seen in Figure1.6.In other words, using a quadcopter

Figure 1.5: With faster spinning motors on the backside, relative to the front, the multirotor pitches down.

As an example again, starting from the front-left motor and moving around the multirotor clockwise, the motors’ rotational directions alternate: CW, CCW, CW, CCW.

Figure 1.6: Each motor spins in the opposite direction to its neighbours.

Each of the quadcopter’s four rotors tends to make the multirotor rotate in the opposite direction to their spin. So by using pairs of rotors spinning in opposite directions, we are able to cancel out this effect and the multirotor does not spin about the yaw axis.

Therefore, when we actually want the multirotor to rotate about the yaw axis, the ﬂight controller will slow down opposite pairs of motors relative to the other pair. This means the frictional forces between the props and the air are no longer in balance, and the craft rotates. We can make the multirotor rotate in either direction by slowing down different pairs of motors. For example, in Figure 1.7 the clockwise-spinning motors are faster than the counter-clockwise-spinning motors, so the craft yaws counter-clockwise.

1.3.2 Controlling Altitude (Thrust)
Everything on Earth is subject to a gravitational force pulling it towards the centre of the planet. In order to ﬂy, we must generate a suÿcient force in an upwards direction to overcome the downward force of gravity (or weight). In an aircraft, this force is called lift.

In a rotary-wing aircraft, the rotors are responsible for all lift. The blades are shaped similarly to an aeroplane wing and produce lift in the same way, except that the necessary airﬂow is achieved by the motors rotating the blades directly, and not by the motion of the entire aircraft through the air.

Figure 1.7: By making diametrically opposite motors (that spin in the same direction) spin at different rates, the craft can be made to yaw.

Thrust is the reaction force produced by a propeller pushing a ﬂuid (usually air). In a multirotor, the propellers push the air down, so the thrust force is in an upwards direction. When the multirotor is hovering and is not pitched or rolled, thrust is equivalent to lift. The vertical motion of the multirotor can be controlled by controlling the amount of thrust produced.

To be in a stable hover at a constant altitude, the upwards and downwards forces must be balanced — that is, the lift produced by the aircraft must be equal to its weight, such as in Figure 1.8. If the lift produced by the multirotor is greater than its weight, it will ascend. Conversely, if the lift is less than the weight, the aircraft will descend.

Weight

The force of weight can be assumed to act from a single point on the aircraft known as the centre of gravity (COG).
Imagine an aircraft placed on a pole. If the aircraft was placed on the centre of gravity it would be perfectly balanced. It’s important to note that an aircraft will move/pivot around it’s COG.

Also as weight is moved around an aircraft, the position of the centre of gravity will also change. For this reason, it’s important to always keep any additional weight to your RPA as close to the centre as possible.

The more the RPA banks, the more thrust is going to the horizontal component and less to the vertical component.
As discussed earlier,iftheRPAistoremainataconstantheight, the vertical component of thrust must be strong enough to counteract the weight. This means while the RPA is banking, the total thrust must be increased (throttling up on controls) in order to keep the aircraft level throughout the turn. The steeper the angle of roll/pitch of the RPA, the more the pilot will have to increase the throttle.

It should be noted that for Rotor RPAs if Angle of Bank is increased too far, the RPA will no longer be able to produce the required lift from thrust to stay in the air and will begin to slip out of the sky. This is a common error when reverting to manual control mode.

Figure 1.9: Centre of Gravity for a Quad-rotor.

1.3.3 Drag
Drag is the force opposing the aircraft’s motion through the air. There are two distinct types of drag that act on an RPA.

The ﬁrst of these is what we call ‘Parasite’ drag. Parasite drag is like the drag you feel on your hand when you hold it out of your car window. That force acting on your hand pushing it back is called parasite drag. If you put your foot down and accelerate, that force on your hand gets stronger. Just the same way as it gets weaker if you reduce speed.
Parasite drag is made up of three components:

• Form drag (Proportional to how much surface is presented to the airﬂow)
• Skin friction (Caused by friction on the surface, smoother surfaces = less skin friction)
• Interference drag (drag created by the airﬂow changing direction suddenly)

The second type of drag is known as ‘induced’ drag.

Induced drag is a by-product of the pressure differences during the production of lift in a ﬁxed-wing aircraft, but it is not relevant for a multi-rotor.

1.3.4 Helicopter Translational Lift

As the rotor RPA picks up speed the airﬂow hits the rotors at a different angle, resulting in additional lift/thrust being produced. This occurs up to a certain speed when the increased airﬂow no longer assists.
As a result, there will be a most eÿcient speed for any rotor RPA. This will generally be detected by the motors running quietest.

1.3.5 Ground effect

Ground Effect for any aircraft is caused by an increase in air pressure as the aircraft is ﬂying close to the ground or obstacle. This increased air pressure is caused by the downwash from the rotors. Since the aircraft is close to the ground, the downwash has no place to go, so air pressure builds under the aircraft. This high-pressure area under the rotor blades causes an interesting decrease in overall drag with an increase in the total lift from the rotor. Ground effect must be taken into consideration during landing and take-off.

Figure 1.11: Increased reaction to downwash when close to the ground.

Multirotor RPAs have a tendency to be a little bit unstable when ﬂying within about 30cm (generally, but it depends on the size of the RPA) of the ground or an object. They can also resist touching down inside this proximity.

1.3.6 Vortex Ring State

When the multirotor descends vertically at a fast rate, air ﬂows through the centre of the props and as a result there is a reduction in thrust. The drone will tend to wobble as it descends. If too much thrust is lost the drone will become very diÿcult to control and will fall to the ground.

This condition is called ”Vortex Ring State” or VRS.

To exit this state roll the drone sideways as it descends so it is not descending vertically through its own air. It should be noted that VRS is not so likely on drones which limit decent rate (such as DJI drones).

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