How to Find the Thrust Force on Your Drone

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I’ll be honest: I love my drone. I mean, I always had remote-control vehicles back when I was a teenager. And of course the most impressive RC vehicle was the gas-powered helicopter. But it was expensive and hard to fly. Now, with a quadcopter, it’s a breeze. On top of that, it takes pictures and videos.

Since I have this fascination with drones, it’s only logical to take the next step and use it for some physics. How about an analysis of the aeronautics of this particular drone, the DJI Spark. Drones, physics—what could be better?

So I used my phone to record some slow-motion videos of the Spark moving first vertically and then horizontally. Here’s an example below. And then I used one of my favorite tools, the Tracker video-analysis app, to plot the position of the drone in each frame. Armed with that data, it’s just a hop, skip, and a jump to derive performance specs like acceleration and thrust.

Video: Rhett Allain

On the Ball

The video essentially gives me a series of time-stamped snapshots of the drone as it moves, but I need to know the frame rate to calibrate the time scale. My phone says it records slo-mo at 240 frames per second—or, in other words, at 4.17 millisecond intervals.

Just to double-check that, I’m going to run a test analysis on something I already know about: the acceleration of a ball tossed straight up into the air. An object in free fall, where gravity is the only force working on it, has a vertical acceleration of about –9.81 meters/second2.

So if I put a meter stick in the video frame (it’s that horizontal stick next to my hand), I will know both the distance scale and the vertical acceleration. From that, I can figure out the true frame rate. Here’s what the ball toss looks like:

Video: Rhett Allain

I ran the Tracker software on this clip and adjusted the listed frame rate until the fitting equation gives me a vertical acceleration of –9.81 m/s2. After playing around a bit, I got a time interval of 4.28 milliseconds—so actually about 234 frames per second. Here is the trajectory with the adjusted frame rate:


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