## Thursday, August 04, 2016

### Jumping without a parachute

You've probably seen this video of Luke Aikins jumping out of a plane from 25,000 feet without a parachute. Knowing the physics behind it doesn't make it any less impressive:

There are several videos online but I like this one with the height gauge at the side. This video shows his top speed at 150 mph but this LiveScience post and a few other sources quote a human's terminal velocity around 120 mph or 53 m/s. Aikins says both 150 mph and 120 mph in this NPR interview about how they prepared for the jump. Wired also discussed some of the physics behind Aikins' jump, focusing on air resistance and terminal velocity. The net is 100 feet by 100 feet and held 200 feet above the ground by four cranes at each corner. In the interview Aikins refers to the giant net as his parachute, its just below him instead of above him.

Remind students it Aikins were to go from 120 mph to 0 mph by hitting the ground he (probably) isn't surviving. So how can he go through the same change of speed in the net and survive? Hopefully you hear a chorus of students saying that time is a factor and it has been its extended by the net. If you bring up this example in your motion unit your students will probably refer to the acceleration equation. A smaller time value means a larger acceleration (and a larger force); an extended time will produce a smaller acceleration. Students can practice their unit conversions to find Aikins terminal velocity in kilometers per hour or meters per second.

Aikins flips on to his back, so that he can land without snapping his neck, at 2:30 in the video above. I downloaded the video and edited it down to his landing in the net. In this edited version the first contact with the next is seen at 2:24 seconds. As Aikins falls into the net the edges don't stay taught (another talking point) so its tough to call when he comes to a full stop and when the lowering of the net starts. I called it at 4:00 seconds making the time it takes him to stop in the net 1.76 seconds. If students use 53 m/s they will find a decceleration for Aikins of about -30 m/s^2 or about 3g.

With the same information students can calculate Aikins kinetic energy just before he hits the net. All of that kinetic energy is converted to work done on the net and to elastic potential energy of the net. You will have to make some assumptions about Aikins mass and the stretch of the net. The NPR article includes these two pictures of the net before and after Aikins jumps into it, he's the speck in the top of the left side. I set them side by side and drew a line over to show 200 feet about the ground. The perspective will make it difficult to exactly determine the height of Aikins when he stops completely, you can discuss with students how best to do so.
What else can you discuss? Momentum! This is just like a car traveling at high speed that has to be stopped. It can hit a wall in a short time and be destroyed or it can be stopped over a (relatively) long time and suffer minor damage. Again students can calculate Aikins' change in momentum based on the information they find and making a few simple assumptions.

Obviously the experts that helped build it went into a little more detail but its an interesting piece of Physics not beyond basic mechanics principles we teach our students.

#### 1 comment:

Jessica Downing said...

Additional point of discussion--he almost had to wear a parachute (http://www.nytimes.com/2016/07/31/us/skydiver-luke-aikins-without-parachute.html?_r=0) which he said would make the jump more dangerous due to the increased weight. When I first heard about it, I wondered if it would make landing more dangerous due to focusing more of the impact on his back. Having now seen the give in the net, I think that less likely, but it still could be considered by students who can distinguish between pressure and force.