Yes, there are jet packs in the movie Tomorrowland. I don’t think that’s really a spoiler since you see jet packs in the trailer. Also, I’ll be honest—I think these might be rocket packs instead of jet packs (rocket packs don’t need external fuel like air).

But who really cares how these jet packs work since they might kill you. I’m not talking about crashing into the ground killing—I mean just plain turning too fast killing you. Yes, it’s true. If you have too large of an acceleration—even if you are still in the air, it could kill you.

In this case it would be the acceleration caused by the circular motion of these vertical loops.

When an object moves in a circle of radius *r* with a speed *v* (or you could use the angular velocity ω), then it will have an acceleration of:

Now I just need to look at the jet packs flying in circles and estimate both the speed and the radius of curvature. Clearly this calls for some basic video analysis (I’ll use Tracker Video Analysis). Of course there is one small problem—setting the scale. It’s difficult to see these flying people in the video clip, but I am just going to roughly approximate the length of a person at 2 meters. After that, I can get the following data for the position of a rocketeer (this is actually the trajectory).

You can see that human flies in a smaller circle as time goes on, but what about the angular speed? If I put the origin at the center of the circles, I can get the following plot for the angular position as a function of time.

Since angular velocity is defined as the derivative of the angle with respect to time, the slope of this line would be the angular velocity. That puts it at around ω = 6.87 rad/s. Actually, I’m surprised. I would think that as the radius of motion became smaller, the angular velocity would increase but the linear velocity would remain constant. Oh well.

Just to give the complete data, here is a plot of the radius of the jet pack’s motion as a function of time.

Let’s just break this into two parts. The first part has a radius of curvature of 13 meters and the second part is 7 meters. From this, I get two different acceleration. The 13 meter radius circle has an acceleration of 613.6 m/s^{2} (62.6 g’s) and the smaller radius has an acceleration of 330.4 m/s^{2} (33.7 g’s).

And now for the bad news. Even the lower acceleration would be bad. According to NASA research (top NASA engineers), accelerations over 20 g’s can be bad. Accelerations over 50 g’s *are* bad.

Those rocket packs (or jet packs) might look fun, but if you fly like that you will have a bad time.

### Homework

Yes, there is homework. Why? Because I didn’t answer all the questions this video brings up.

- Why do the jet packs fly at a constant angular velocity instead of a constant linear speed? I don’t know the answer—you get to make one up.
- Make a numerical model (I suggest using GlowScript.org) to show what a rocket pack loop with a constant linear velocity—and changing angular velocity—would look like).
- Why does the lower radius curve have a lower acceleration? Shouldn’t that be higher? Hint: It has to do with angular velocity.
- What if you take gravitational effects into account? Where is the maximum g-force?
- Suppose you wanted to stay at under 5 g’s in your rocket pack flight. If you keep a similar speed, how big of a circular loop could you fly in?
- There is something else wrong with this jet pack motion. How would you actually fly like this? The video shows the rockets pushing the human forward, but that’s not how it would work. Here is a hint—look at how R2-D2 flies incorrectly.

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