Jul 4, 2018 7:00 AM

The Physics of Launching Fireworks From a Drone

Not that you’d ever do such a thing. Please keep drones and fireworks far away from each other.

Can you launch fireworks from your drone? Before I answer that question, I have one of my own: Why? People, why would you want to do this? I mean, I get it: Fireworks are cool. Drones are cool. Therefore, I guess, fireworks on drones are cool to the power of two.

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

On the other hand, the physics of pulling off something like this are definitely worth a look. For the sake of science, I'm going to point out two considerations you would need to sort out for a firework-drone combo.

Would It Have Enough Lift?

The first thing is lift. If you put fireworks on a 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 how a drone flies. (By "drone" I mean something like a quadcopter, but it's the same for real single-rotor helicopters.) In short, a rotor creates lift by taking air above the rotor and throwing it down below. (Here's a whole post on the physics of drones.) 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; second, you could throw down more air. It turns out that most rotors sort of max out at an air speed of around 30 meters per second, so really the only option is to throw more air. That means bigger rotors (i.e., with a larger radius) give more thrust. So your tiny drone can't lift a giant load of fireworks.

But wait! It gets worse. If you want to take a small rotor and lift more stuff, you have to increase the velocity of the air (v). Increasing the speed of air increases its kinetic energy, and kinetic energy is proportional to 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 velocity of air to the third power (v³). That's bad. Fast air uses up batteries fast.

But maybe that doesn't matter, because the drone is probably going to blow up from the fireworks—I mean, if you really did this, which you should not.

Would the Recoil Wreck It?

But speaking purely hypothetically, what kind of fireworks would you have in mind? Maybe something like a roman candle that shoots balls of fire? Actually, the physics involved in this are similar to the lift from the rotor—only 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 probably can shoot a roman candle from a drone. But you probably shouldn't.

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