The Physics of VTOL UAV Flight – Force, Acceleration, and Velocity Explained

UAVs are complicated machines, and it’s a true feat of engineering to be able to design and build them feasibly. To do so, however, requires an in-depth understanding of the underlying physics. A UAV has to be able to sense it’s position, velocity, acceleration, and many of the other variables that describe it’s motion. All of these ideas are clearly defined and described in the laws of physics, and understanding them can answer many questions about UAV flight characteristics. In this article, we’ll focus on VTOL (Vertical Takeoff and Landing) UAVs like our Draganflyer X6, but the same concepts apply to all other air vehicles and UAVs.

Some Basic Concepts Explained

Before we can explain more complicated ideas (like how airfoils and accelerometers work), an understanding of a few basic physical principles is needed.  These include force, mass, and acceleration. We’re going to skip a more thorough explanation (which would require calculus), and instead use a purely algebraic approach.

Mass

Mass is a quantity that defines how an object interacts with a gravitational field, and how acceleration, momentum, energy and similar concepts work. Mass is commonly associated with weight, and it’s true that an increase in mass results in an increase in weight, but they are two separate concepts. Weight is a force – a push or pull on an object, while mass is a quantity intrinsic to a particular object. The SI (International System) unit of mass is the Kilogram, equal to a weight of 1000 grams. Kilograms are different from pounds – a pound is a unit of force, which we will describe shortly.

Velocity

Velocity is often used as a synonym for speed, but as with mass and weight, they are two separate ideas. Speed measures how fast something is moving, without reference to the direction that it’s travelling. Velocity keeps track of both speed and direction, giving a more complete picture of the behaviour of an object. The direction is given as an angle, measured with respect to some reference. Angle usually has units of degrees, of which there are 360 in a complete circle.

Acceleration

Acceleration describes the rate at which velocity changes. You can find the average acceleration of an object by dividing the change in velocity (delta V) by the time interval in which that change takes place (delta T). The result becomes more precise as you let delta T and delta V get smaller, and as they become infinately small, the calculation becomes precise. Acceleration is measured by an electronic device called an accelerometer. Our Draganflyer X6 UAV has 3 accelerometers, which measure acceleration in the X, Y, and Z directions respectively.

Acceleration takes into account both the change in speed and the change in direction, making it a vector quantity as well.

Force

Now that acceleration and mass are understood, we can define force. Loosely, force is a “push” or “pull” on an object. Mathematically, force is the product of mass and acceleration (also known as Newton’s Second Law). This makes sense intuitively: the force required to move an object gets larger as the object gets heavier, and it also increases if you want to accelerate it faster.

From this, we can see that applying a force to an object with mass will result in an acceleration, and in order to accelerate an object, a force must be applied.

It may be hard to believe, but these few concepts are actually all you need to understand the basic physics of aircraft and UAV flight. New concepts are built upon them, but these same principals are fundamental.

UAV Flight Equilibrium

Equilibrium is a state of motion where all forces balance, cancelling each other out exactly. Because any force on an object causes an acceleration, so if an aircraft is to remain in one place all the forces acting on it must add to 0. So how does this happen?

Let’s start by imagining a generic aircraft, that is currently hovering in one place. The forces acting on it are:

• Gravity, pulling downwards
• Thrust from the motors, pushing upwards

We will neglect airflow, torque from the propellers, or any other force that acts sideways.

In order to hover without gaining or losing altitude, the thrust from the motors must equal the force of gravity. This is shown graphically on the right. The gravitational force is represented by the green arrow, and the lift force provided by the motors is shown by the orange arrow.

This concept becomes immediately useful. For example: the Draganflyer X6 weighs 1000 grams, so the motors and propellers need to provide exactly 1000 grams of thrust downwards to keep the UAV in a hover.

Obviously, the forces don’t always have to balance. If we wanted the UAV to turn, that imbalance has to be created. On the Draganflyer X6, this is done by spinning one of the propeller sets faster than the other two. This creates an excess force on one side of the aircraft, resulting in an acceleration. It’s this acceleration of one side of the aircraft that allows the turn. Once the aircraft is banked, all the thrust from the motors is directed away from the downward direction, allowing it to move relative to the ground. When we desire the motion to stop, the UAV banks in the opposite direction.

Error Measurements

Every measurement has an error of uncertainty associated with it. It’s theoretically impossible to measure something with absolute precision. Because of this, all of the instruments built in to the Draganflyer X6 have an error tolerance associated with them. This error can be estimated as the smallest graduation on the measuring device. The magnetometer, for example, is capable of measuring to the nearest degree. This error may increase due to external influences, such as electric equipment operating nearby.

Because every instrument in the IMU has an error bar, the flight computer can’t be 100% sure of the UAVs position at any given time. This means that if you let go of the controls, the UAV will drift off of the position that you left it in. It’s simply a consequence of the physics involved – no amount of engineering precision can change the fact that there will always be an error in the instrument measurments.

In a well designed aircraft, errors are handled well so that their effect on flight performance is minimal. In the Draganflyer X6, for example, the uncertainty in GPS position is always displayed on the handset, and trim tabs are provided to cancel out any unwanted movement. We’ve taken every possible step to minimize the effect of errors, and display them to the user.

Applications to UAV and Aircraft Design

All these concepts are important, but how are they applied to UAV design? Well, we know from Newtons Second Law that any force results in an acceleration, which is just a change in velocity. UAVs need to control their position and velocity, so there must be some means of obtaining and processing this information. Our Draganflyer X6 UAV does this by using the following:

• A magnetometer to measure heading
• 3 accelerometers to measure acceleration
• A GPS to find position and velocity
• A barometric pressure sensor to measure altitude

Combined, all these sensors can be considered an “inertial measurement unit”, or IMU. Data from each of these sensors is processed by the flight computer and used to make altitude, heading, and speed corrections.

The physics behind how the Draganflyer X6 UAV works are complicated, but these simple ideas should help you to understand why it behaves the way it does, and the degree of understanding required to build such a complicated machine.