I own a drone. Maybe you do, too. I use mine to make simple videos and annoy my dog. Drones are quite popular these days, and you can without spending too much money.
WIRED's latest Dot Physics video explains the physics behind drone. Cameras and interchangeable lens models with expensive lenses,. A quadcopter, also called a quadrotor helicopter or quadrotor, is a multirotor helicopter that is. Convertawings Model A Quadrotor (1956): This unique helicopter was intended to be the prototype for a line of much larger civil and military.
Oh, I'm talking about the remotely controlled flying vehicles with four rotors, not the bigger drones scientists use to and stuff. Those cost a lot of money.Small drones like mine are easy to fly—a skilled pilot can hover and fly in just about any direction, which makes them great for recording video. But how does a drone actually fly? Ah, this is an excellent opportunity to look at some physics.
Vertical MotionDrones use rotors for propulsion and control. You can think of a rotor as a fan, because they work pretty much the same. Spinning blades push air down. Of course, all forces come in pairs, which means that as the rotor pushes down on the air, the air pushes up on the rotor. This is the basic idea behind lift, which comes down to controlling the upward and downward force. The faster the rotors spin, the greater the lift, and vice-versa. Now, a drone can do three things in the vertical plane: hover, climb, or descend.
To hover, the net thrust of the four rotors pushing the drone up must be equal to the gravitational force pulling it down. So what about moving up, which pilots call climbing? Just (speed) of the four rotors so that there is a non-zero upward force that is greater than the weight. After that, you could decrease the thrust a little bit—but there are now three forces on the drone: weight, thrust, and air drag. So, you will still need for the thrusters to be greater than for just a hover. Descending requires doing the exact opposite: Simply decrease the rotor thrust (speed) so the net force is downward.
Turning (Rotating)Let's say you have a hovering drone pointed north and you want to rotate it to face east. How do you accomplish this by changing the power to the four rotors? Before answering, I will draw a diagram of the rotors (viewed from above) labeled 1 through 4.In this configuration, the red rotors are rotating counterclockwise and the green ones are rotating clockwise. With the two sets of rotors rotating in opposite directions, the total angular momentum is zero.
Is a lot like linear momentum, and you calculate it by multiplying the angular velocity by the moment of inertia. What is the moment of inertia? It is similar to the mass, except it deals with rotation. Yes, it gets rather complicated, but all you need to know is that the angular momentum depends on how fast the rotors spin.
Fun With Physics.If there is no torque on the system (the system here being the drone), then the total angular momentum must remain constant (zero in this case). Just to make things easier to understand, I will say the red counterclockwise rotors have a positive angular momentum and the green clockwise rotors have a negative angular momentum. I'll assign each rotor a value of +2, +2, -2, -2, which adds up to zero (I left off the units).Let's say you want to rotate the drone to the right.
Suppose I decrease the angular velocity of rotor 1 such that now it has an angular momentum of -1 instead of -2. If nothing else happened, the total angular momentum of the drone would now be +1. Of course, that can't happen. So the drone rotates clockwise so that the body of the drone has an angular momentum of -1.
Rotation.But wait! Decreasing the spin of rotor 1 did indeed cause the drone to rotate, but it also decreased the thrust from rotor 1. Now the net upward force does not equal the gravitational force, and the drone descends. Worse, the thrust forces aren't balanced, so the drone tips downward in the direction of rotor 1.
I can fix this.To rotate the drone without creating all those other problems, decrease the spin of rotor 1 and 3 and increase the spin for rotors 2 and 4. The angular momentum of the rotors still doesn't add up to zero, so the drone body must rotate. But the total force remains equal to the gravitational force and the drone continues to hover. Since the lower thrust rotors are diagonally opposite from each other, the drone can still stay balanced.
How do you get the drone into this position? You could increase the rotation rate of rotors 3 and 4 (the rear ones) and decrease the rate of rotors 1 and 2. The total thrust force will remain equal to the weight, so the drone will stay at the same vertical level. Also, since one of the rear rotors is spinning counterclockwise and the other clockwise, the increased rotation of those rotors will still produce zero angular momentum.
The same holds true for the front rotors, and so the drone does not rotate. However, the greater force in the back of the drone means it will tilt forward. Now a slight increase in thrust for all rotors will produce a net thrust force that has a component to balance the weight along with a forward motion component.
Using a ComputerBy now, you've surely noticed that every movement is accomplished by changing the spin rate of one or more rotors. Doing that simply requires a controller that can increase or decrease the.
That's not too difficult to set up. But just imagine this—you have a drone with 4 controllers. You'd need one controller for each motor power level.
It would be crazy difficult to manually adjust each motor power to achieve the desired motion.However, if you have some type of computer control system, you can simply push a joystick with your thumb and let a computer handle all of that. An accelerometer and gyroscope in the drone can further increase the ease and stability of flight by making minute adjustments in the power to each rotor. Add a GPS system and you can pretty much get rid of the human entirely. So you can see that flying a drone is pretty easy if you let the computer do all the work. But it's still nice to understand the physics behind it.
If you want to take a deep look at the physics of drones, you can read how. I also looked at the power needed to hover using —a question that actually started with my estimation of the power needed for the.Let's recap how I can estimate the power need to hover a drone. Imagine you have a drone with spinning rotors. It actually doesn't matter if you have just one rotor (like a helicopter) or four like a quadcopter or even eight like an octocopter.
What really matters is that the rotors take stationary air above the vehicle and push this air down. By increasing the momentum of the air, the rotor exerts a force on the air and the air pushes back on the rotor. If this air force is equal to the weight of the vehicle, the drone will hover.
This leads to the following expression for the air speed of a hovering drone. If the energy is measured in Joules and the time interval in seconds, then the power would be in units of Watts. So a drone with a large power will need a bigger battery in order to fly for a reasonable amount of time.Now for the fun stuff. Let's look at the battery size and power for two drones. I am going to randomly pick the Syma X20 and the DJI Phantom 4. I'll start with the Phantom.
It has a and the rotor radius is about 12 cm. This gives it a rotor area of about 0.18 m 2. Using the equations above, I get a hovering power of around 150 Watts. In order to reach its listed flight time of 28 minutes, the battery would need to have a total energy of 2.5 x 10 5 Joules (compared to a listed power of 2.9 x 10 5 Joules). OK, two quick notes.
![Aerodynamic Aerodynamic](http://qdrone.schloesser.li/wp-content/uploads/2014/04/physics_angle.png)
First, the DJI battery is listed at 15.2 volts with a capacity of 5350 mAh (milli-amp hours). There is a small trick to convert this to Joules, but it's not too hard. Second, I should point out that my energy estimation is super close to the listed energy even though I derived that based on basic assumptions.But what about the tiny drone (the Syma X20)? It has a rotor area of 0.0043 m 2 and I'm going to guess a mass of 100 grams (the specs list it at 250 grams, but I think that is for the remote as well). Using these values, I get a hover power of just 19 Watts.
That's not much power, but if it were to have the same runtime as the Phantom (28 minutes) it would need a battery that would have 3.2 x 10 4 Joules—just about 1/10 th the energy of the bigger drone. This seems like it would be OK since the mass of the smaller drone is also about 1/10 th the mass of the larger drone.
![Drone Drone](http://wordlesstech.com/wp-content/uploads/2013/08/The-Hybrid-Quadrotor-drone.jpg)
However, there is one big difference—the mass of a battery itself.Most of the drones have a lithium ion battery. These have a specific energy (the energy per mass) of around 5 x 10 5 Joules per kilogram.
So, to have a battery with 3.2 x 10 4 Joules of energy it would have a mass of 60 grams. That would leave just about 40 grams for other stuff that might be important—like a camera, a controller, a radio, oh—and motors and stuff. And that is the problem. These small drones have to save mass for other important stuff that just can't get any smaller. The sacrifice for small drones is a short flight time—at least for now.