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The Physics of Launching Fireworks From a Drone – ANITH
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# The Physics of Launching Fireworks From a Drone

## The Physics of Launching Fireworks From a Drone

Can you launch fireworks from your drone? OK, before I answer this question I have my own question: Why? Guys, why would you want to put fireworks on your drone? I mean, I get it. Fireworks are cool and drones are cool. Therefore fireworks on drones are cool to the power of two, I guess.

But really, it’s probably not a good idea to manifest your American pride with this particular version of pyrotechnics. As a PSA, let’s say that my official stance is that drones should just be drones and fireworks should just be fireworks.

The physics of pulling off something like this is an entirely different thing, though. For the sake of science, I’m going to point out two considerations you would need to have for a firework-drone combo.

### Lift

The first thing is lift. If you put fireworks on your drone, chances are those fireworks will have mass. The more massive the fireworks, the more massive the boom. But more mass also means more of a potential problem. It turns out that drones can’t just fly and carry whatever they want. Yes, it is possible for a large drone to lift some heavy stuff but a small and cheap drone can barely lift anything.

The reason has to do with the way that a drone flies. (By “drone” I mean something like a quadcopter, but this physics also applies to real single rotor helicopters.) In short, a rotor creates lift by taking air above the rotor and throwing it down below. Since air has mass, moving air has momentum (the product of mass and velocity). How do you change the momentum of something? You push on it with a force. So the rotors push the air down and increase the air-momentum. Since forces are an interaction between objects, pushing down on the air means the air pushes up on the rotors.

So indeed the lift force on a spinning rotor is equal to the change in momentum of the air that it throws down. There are two ways to increase the thrust. First, you could increase the speed of the air as it moves down and second, you could throw down more air. It turns out that most rotors sort of max out at an air speed of around 30 m/s—so really the only option is to throw more air. That means bigger rotors (those with a larger radius) give more thrust. So your tiny drone can’t lift a giant load of fireworks.

But wait! It gets even worse. If you want to take a small rotor and lift more stuff, you have to increase the speed of the air. Increasing the speed of air increases its kinetic energy and kinetic energy is proportional the square of the velocity. By increasing the velocity, you go through more air—so in the end, the rate a drone uses energy (from the battery) depends on the 3velocity of air to the third power (v3). That’s bad. Fast air uses batteries fast.

I guess it doesn’t matter much that your battery won’t last long, because the drone is probably going to blow up from the fireworks. Probably.

### Recoil

If you are going to put fireworks on your drone (and you probably shouldn’t), I bet you are going to use something like a roman candle that shoots balls of fire or something. Actually, shooting balls of fire is very similar to the lift from the rotor—just instead of throwing down air, it’s balls of fire.

The goal of shooting a fireball is to take that ball of fire and increase its speed. Increasing speed means increasing the momentum, and yes—changing the momentum requires a force. In the case of a roman candle, the fireball’s momentum is increased by an expanding gas in the barrel of the candle (an explosion). This expanding gas pushes on the drone with the same force for the same time such that the drone will have the same change in momentum as the fireball, but in the opposite direction.

What happens when a drone has a recoil momentum equal to the momentum of a fireball? Probably not very much. A fireball has a very low mass and a speed of just “meh.” Come on—we know these fireballs aren’t really that fast. So low mass and “meh” speed means a fairly low momentum. The drone will have a much higher mass so in order to have an equal momentum, it really doesn’t have to have a very high recoil speed.

So yes, you can probably shoot a roman candle from a drone. But you probably shouldn’t.