Finding a Nerf Gun's Muzzle Velocity Using a GoPro

Written by Josh on November 27, 2014

One of the many Nerf guns in our collection is the Triad EX-3. This is a tiny gun, but it stings more than any other Nerf gun I’ve used when it hits you. I started to wonder how quickly it shot.

The Mythbusters frequently use the combination of a high-speed camera and a board with painted stripes of a known width to determine the speed of a bullet or other projectile. I figured I would use a similar method. I took a sheet of printer paper and marked lines an inch wide across the paper. I mounted my GoPro on a tripod and adjusted it so the paper would fill most of the image. The camera I used can shoot at 240 frames per second at 480p resolution, which I used. (I previously tried 120 frames per second at 720p, but the bullet shot so fast that it was difficult to tell where it was.

I took two different videos of the gun firing: 1 and 2. (Your web browser probably won’t like 240fps video, though. Try using VLC instead.) VLC can only slow video down to quarter speed, so I executed ffmpeg -i GOPR4216.MP4 -filter:v "setpts=8.0*PTS" 4216-8th.mp4 to slow the video down to 8th speed. (ffmpeg is a command-line tool that can manipulate about any video format you throw at it.) This didn’t adjust the audio, but that was not a concern. The slowed-down video files can be found here and here. (These files are also 240fps.) While the slow-motion video is nice to watch, it is not overly helpful when finding the speed of the bullet. I used ffmpeg -i GOPR4216.MP4 -r 240 -s 848x480 -f image2 4216-frames/4216-%03d.jpg to split the video into one JPEG per frame, resulting in a mere 634 images between both videos. Curiously, the combined size of the pictures was less than the size of the original video.

I narrowed both folders down to just the frames where the bullet is travelling, leaving only 26 images, 8 for the first video and 18 for the second. Let’s focus on the first one. The image quality is terrible, but that is the result of going from a low resolution video to a JPEG. It does not really matter in this case as even in the original video you could not tell exactly where the bullet was.

Between these two frames (frames 50 and 53, respectively), the bullet moves from a half inch or so off the left of the paper to around the right edge. It is difficult to see where exactly the bullet is, but we know that it traveled between 11 and 12 inches in 3 frames ($\frac3{240}$ or $\frac1{80}$ seconds).

\text{rate} = \frac{\text{distance}}{\text{time}} \Rightarrow \frac{\approx11.5\text{ inches}}{\frac3{240} = 0.0125\text{ seconds}} = 920 \frac{\text{inches}}{\text{second}} \bullet \frac{1\text{ foot}}{12\text{ inches}} = 76{\frac23} \text{ feet per second}

Therefore, the bullet was travelling at around 76.7 feet per second in the first video. For such a small package, it certainly packs a punch. I may analyze the “muzzle velocity” of other guns in the future, but this is the fastest Nerf gun we own.


The second video captured a far weaker shot. A full eight frames passed while the bullet travelled over the paper. (The first shot only took three.) This works out to only 30 feet per second, less than a third of the first. My guess is that the plunger of the gun was caught on the desk or my hand, or the bullet was not seated firmly in the gun. Any way, this shows that the gun is not perfect.

\frac{\approx12\text{ inches}}{\frac{8}{240} = 0.0\overline{3}\text{ seconds}} = 360 \frac{\text{inches}}{\text{second}} = 30 \text{ feet per second}
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