The Physics of Why the Drones Can Fly More

Jan 31, 2018 AT 10:03 AM | BY LifeBanter


YOU CAN GET a drone in a wide range of sizes. Some of them fit in the palm of your hand (like the Syma X20) while others are quite large. But have you noticed something about the flight time? A lot of super-small drones have flight times that are less than five minutes. The largest of the drones (like the DJI Phantom 4) have a maximum time-of-flight closer to a half-hour. Why is a bigger, probably heavier drone to be able to last longer in the air?

If you want to take a deep look at the physics of the drones, you can read how to vary the power to the four rotors allows the vehicle to fly in all directions. I also looked at the power required to hover using very basic models of physics—a question that actually started with my estimate of the power required for the SHIELD helicarrier to fly (this is huge).

Here’s a recap of how I can estimate the power required to hover a drone. Imagine that you have a drone with rotors. It does not matter if you have just one rotor (like a helicopter) or four as a quadcopter or even eight as an octocopter. What really matters is that the rotors take a stationary air above the vehicle and push the air down. By the increase of the momentum of the air, the rotor exerts a force on the air and the air pushes back on the rotor. If this army of the air is equal to the weight of the vehicle, the drone into stationary flight. This leads to the following expression for the air speed of a drone into stationary flight.

In this expression, ρ is the air density, m is the mass of the uav, g is the gravitational constant (9.8 N/kg) and A is the surface area of the rotor. You can see that the increase of the size of the rotors, you can decrease the speed of the air. It is important for the power, which can be written as follows (based on fundamental principles and actual data).

Here you can see why the larger rotors are better. If you increase the area of the rotor, you can reduce the speed of the air and the energy depends on the speed of the air to the third power. If you want to have a low-power drone, you need to keep that air speed as low as possible.

I just need one thing—the definition of power. The power is the speed to something that uses energy. This can be described by the following equation.

If the energy is measured in Joules and the time interval in seconds, and then the power would be in Watts. If a drone with a high power will need a bigger battery to fly for a reasonable amount of time.

Now for the fun stuff. Look at the size of the battery and the power for the two drones. I’ll randomly choose the Syma X20 and the DJI Phantom 4. I’ll start with the Ghost. He has a mass of 1.38 kg and the rotor radius is about 12 cm. Which gives a rotor area of about 0.18 m2. Using the equations above, I get a hover power of 150 Watts. In order to achieve its time-of-flight of 28 minutes, the battery will need to have a total energy of 2.5 x 105 Joules (in relation to a listed power of 2.9 x 105 Joules). OK, two quick notes. First of all, the DJI battery is displayed to 15.2 volts with a capacity of 5350 mAh (milli-ampere-hours). There is a small trick to convert this to Joules, but it is not too hard. Secondly, I would like to stress that my energy estimate is super close to the list of energy, even if I pulled that based on basic assumptions.

But what about the small drone (Syma X20)? It has a rotor area of 0.0043 m2, and I’m going to guess a mass of 100 grams (the spec of the list to 250 grams, but I think it is for the remote). Using these values, I get a hover power of only 19 Watts. This is not a lot of power, but if it were to have the same performance as the Phantom (28 minutes), it would need a battery that would be 3.2 x 104 Joules—only about 1/10th of the energy of the great bourdon. It also seems that it is OK, since the mass of the smallest drone is also about 1/10th of the mass of the larger drone. However, there is one major difference: the mass of the battery itself.

Most of the drones have a lithium-ion battery. They have a specific energy (energy per unit mass) of the order of 5 x 105 Joules per kilogram. So, to have a battery of 3.2 x 104 Joules of energy that it would have a mass of 60 grams. That would leave 40 grams for other stuff that might be important, such as a camera, a controller, a radio, oh—and engines and stuff. And that is the problem. These little drones have to save weight for other important things that just can’t be smaller. The sacrifice for small drones is a short-time of flight—at least for the moment.

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