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Lundi, 02 Janvier 2012 14:30

## The Speed of a Nerf Vortex Disk

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Around Christmas time I have a tradition. I like to “borrow” some of my kids’ toys and use them for blog posts. So, here we go.

This is the Nerf Vortex Nitron Blaster. The Nerf vortex guns are different from regular Nerf in that they shoot spinning disks instead of dart-like objects. Essentially, they are like tiny frisbees. I guess the advantage is that they sort of fly rather than having a projectile-like motion.

## How Fast?

But how do you determine the speed of these little disks? Yes, you already know the answer: video analysis. It gets even better. I have borrowed a Casio Exilim camera from school. Let me just say something nice about these cameras for no particular reason. These cameras can record videos up to 1000 frames per second and they aren’t too expensive. Yes, the 1000 fps comes at a price and that price is resolution. The higher the frame rate, the lower the video resolution. But still, quite useful.

Here is a video showing a couple of shots at 480 fps. The yellow stick on the ground (in case you want to repeat my measurements) is a yard stick. Yes, I couldn’t find a meter stick at home.

Now that I have a video, it is time for analysis with Tracker Video (free). One quick tip regarding the Exilim and Tracker Video. The Casio Exilim video that is 480 fps. However, it changes the meta data so that it looks like a 30 fps video. This way it plays back in slow motion. So, when you load the video into Tracker, you will need to manually change the frame rate to 480 fps.

Here is a plot of the horizontal position of the vortex projectile.

From this, the slope of the position-time graph will give the horizontal speed of the object. In this case, that value is 15.7 m/s. This seems a bit faster than a Nerf bullet. Previously, I found the bullets shoot at about 10 m/s.

Oh, and just to be sure I looked at another disk shot. This second shot has a horizontal speed of 14.8 m/s.

If this were a Nerf-bullet projectile, it would have a vertical acceleration just like a dropped rock. What about the vortex disks? Here is a plot of the vertical motion for one of the shots.

If there were no air resistance or lift forces on the disk, then this object should have a vertical acceleration of -9.8 m/s2. Instead, this object has an acceleration of about -8.3 m/s2 (you can get this from the parabolic fit to the data). Let me go ahead and draw a force diagram for the flying vortex disk.

So, this is good for the plot above. The vertical acceleration has a smaller magnitude than -9.8 m/s2. This means that there could be a lift force, but the lift force is smaller (in magnitude) than the gravitational force. If I had the mass of a disk, I could find the value of this lift force.

## Air Drag

There must be a drag force on these disks. If there is, it is probably small in magnitude. One way to look for this air drag force would be to fit a second order polynomial to the position data. Perhaps I could get a better estimate of the air drag if I looked at the motion of the flying disk over a larger range. Unfortunately, I don’t have the Nerf gun with me. Perhaps that post will have to wait for another day.

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