Could You Bungee-Jump Using Only Magnets?

Bungee jumping has been around for ages. The land divers of Vanuatu tied vines around their ankles. The first modern-style jump with elastic cords was undertaken in Bristol, England, in 1979 by the Oxford University Dangerous Sports Club. The idea, of course, is that—if all goes well—the cord stretches and exerts an upward force to keep you from hitting the ground.

But how’s this for a new way to tempt fate: What if you replaced the elastic cord with two magnets? You could put a magnet on the jumper with another magnet on the ground, aligned in such a way that their poles repel. As the person gets close to the ground, magnetic levitation would hopefully buoy them back up. Bungee jumping without a bungee!

That’s the premise behind this video of the supposed “first wireless bungee jump.” Let me be real clear: It’s a fake. It’s really an Ikea commercial. Do NOT try this at home. Don’t even think about trying it.

OK, but … could the concept actually work? We could use trial and error to find out. I suggest we analyze the physics instead. Ready? Let’s jump in.

The Physics of Bungee Jumping

First we need to be clear on why it’s bad to hit the ground. So, here’s the deal. It’s all about acceleration. Suppose a person foolishly jumps off a 10-meter-high ledge. As they fall, the gravitational force pulls down to cause an increase in velocity. Ignoring the air resistance force, this would produce an acceleration of 9.8 m/s2.

Starting from rest, this would put their speed at 14 meters per second just before impact. Now let’s say the jumper stops on the ground over a distance of 5 centimeters. (It’s probably much less than that.) This would produce a stopping acceleration of about 1,960 m/s2. That is 200 g’s. That’s the problem. A human can survive an acceleration of only around 30 to 40 g’s.

So how does the bungee fix the acceleration problem? As the cord stretches, it exerts an upward force on the jumper in the same direction that the ground would push. However, it pushes over a much larger distance, so it produces a much lower acceleration.

Here is a quick numerical model for a bungee jumper starting 10 meters high and just barely touching the ground. (Follow the link to see the animation.) I made the bungee 5 meters long, so it doesn’t start stretching until after that. This gives the following acceleration curve:

Illustration: Rhett Allain

Notice that this has a maximum acceleration of just 2 g’s—easily survivable. The key to this bungee jump is the springlike nature of the bungee. Here, let me make one more plot. This is the same bungee jump except that I am plotting the spring force as a function of vertical position:

Illustration: Rhett Allain

Don’t confuse this with a force vs. time graph. The horizontal axis is the vertical position. So the jumper actually starts way over on the right side of the graph at 10 meters. Once the fall starts, the graph moves along to the left until the bungee stretches. Notice that there’s a linear relationship between the position and the spring force. If you double the bungee stretch, you will double the force it produces. This linear relationship is what makes springs (like a bungee) so nice to work with in physics. It also means you can have this spring act over a large distance to slow the jumper down.

Why Magnets Won’t Work

Now, what about magnets? Yes, it’s similar to a bungee cord. If the jumper has a magnet with the south pole facing down toward a south pole mounted on the ground, there will again be an upward-pushing force as these two magnets get closer together. But for magnetic repulsion, this force is not linear with distance like the bungee. What does it look like?

Here’s a quick experiment that I ran. I put a cart on a track with two magnets—one mounted on a structure on the track, the other on a force sensor attached to the cart. Then I measured both the position of the cart and the magnetic force. Note that I shifted the x position (and called it xprime) so the two magnets would be together at x = 0 meters. Here’s what I got:

Illustration: Rhett Allain

You can see the problem. When the magnets are separated by even a moderate distance, the repulsive force is very close to zero newtons. Then, as they get close together, it rapidly increases to some crazy high magnitude. In fact, the magnetic force between two magnets isn’t simple to calculate—but it’s clearly not a great force for a wireless bungee jump. This kind of magnetic force would slow down a human jumper in a very short distance and cause a super high acceleration. You might be better off hitting the ground.

OK, let’s do this anyway. Here’s a quick test. I have a magnet that I’m dropping onto another (repelling) magnet. I put the falling magnet in a clear tube so it would stay right in line with the mounted magnet. (Yes, this is another problem with magnetic bungee jumping.) Here’s what that looks like:

Photograph: Rhett Allain

Now, using video analysis I can get a plot of the position as a function of time for the dropped magnet. It looks like this:

Illustration: Rhett Allain

I’m going to get a very rough estimate of the acceleration at the bottom. Right before the bottom of the motion, the magnet is moving with a speed of about –1.9 m/s (the negative sign means down). Right after the repulsion, the magnet is moving up with a speed of around 1.2 m/s. This change in velocity occurs over a time interval of 0.025 seconds. Now I can calculate the average acceleration:

Illustration: Rhett Allain

That’s only 12.7 g’s, but that magnet was only dropped from a height of about 20 cm. If you used this with a greater starting height, it would be bad. Real bad.

But wait! It’s even worse. Repelling magnets don’t just repel. If they aren’t perfectly lined up (and they never are), there is also a torque on both the magnets. Even a slight torque will cause the falling magnet to rotate, which produces an even greater torque. Eventually, the falling magnet will flip over, turning repelling magnets into attracting magnets. Good luck stopping your fall with the two magnets attracting each other.

This is why I dropped the magnet in a tube—it prevents it from twisting. Oh, sure, we could try using four magnets on the base (like in the fake video). It still wouldn’t work. Trust me on this.

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