When I first looked at jumping off a building with bubble wrap, I wasn't aware that the question was based on a video. It wasn't until I saw the preview of an upcoming episode of Mythbusters that I realized such a video existed. Here it is.
Of course I am going to look at a video analysis of this. It's not the best video. The camera isn't on a tripod and there are clearly some perspective issues. However, that has never stopped me before. Here is my first plot from Tracker Video Analysis showing the vertical position of the jumper.
Clearly the scale is wrong. I used the height of one level in the building -- so this plot is not in meters. The posted YouTube video states the building is 35 feet high. It also appears that it has four levels (stories). This would put each level at a height of 2.67 meters (which seems rather low -- but what do I know). Now using the conversion of 1 level = 2.67 meters, I get a vertical acceleration of the jumper at 24 m/s2. Yes, that doesn't seem quite right. And yes, I excluded the first part of the data since it appears the jumper isn't even moving down during this time.
Is there any way to check this crazy acceleration? Well, if I assume the jumper is in free fall (such that air resistance is negligible) then I can calculate the time to fall (from rest) a height of 35 feet (10.67 meters). I can then compare this time to the time from video -- which gives a free fall time of 1.4 seconds. For an object with a constant accleration, I can write:
Putting in a height of 10.67 meters, I get a falling time of 1.47 seconds. So, the time isn't a problem. What about the final velocity? If I fit a linear function to just the last part of the vertical position data, I get a speed of 18.34 m/s. How fast should the jumper be moving? Using the work-energy principle, I can write:
Again, putting in a height of 10.67 meters, I get a final speed of 14.5 m/s. OK -- that isn't so bad either. What about the stopping acceleration? Let me just say that the jumper is moving at 14.5 m/s right before colliding with the ground. Let me also assume that the jumper stops over a distance of 0.4 meters (a generous estimate). I can get the acceleration during this interval as:
This 262 m/s2 is an acceleration of 26.8 g's. Here is the official NASA human g-tolerance table.
If the person lands on his back, the acceleration would be "eyeballs in" with a maximum acceleration of 35 g's. OK -- let me be honest here. I think this video is fake. The problem is that none of my calculations are showing me convincingly that it is fake. Fine.
Data From the MythBusters
Looking back at my first calculations for jumping off a building with bubble wrap, I think I over-estimated the effect of contact area for the bubble wrap. I attempted to collect data with actual bubble wrap, but it was just statically compressing sheets of wrap and not an actual collision with bubble wrap.
Of course, the MythBusters spent a little more time on this than I did. Here is a shot from the data they collected.
Notice how much nicer the video from MythBusters is compared to the viral bubbleboy video:
- Tripod? Check.
- Clear video? Check.
- High Speed? Check.
- Clearly marked distances for scale? Check. (even if the distances are in feet instead of meters)
- Comparison with non-bubble wrap jumper? Check.
The really have this covered. Assuming the frame rate is 1,000 frames per second (I am pretty sure they said that in the video), then this is the plot of the bubblewrap dummy as it falls.
This seems to perfectly agree with the calculation for final falling speed of 14.5 m/s. Also, I fit a linear function instead of a parabola to this data since it is only covering a time period of 0.15 seconds. The change in velocity during this time is only 1.5 m/s.
What about the acceleration during the collision? This is a little difficult to measure since the dummy isn't exactly a rigid body. Different parts move differently. Just look at the dummy's head. Since there is no bubble wrap on it, the head acceleration must be huge. OK, so to estimate the acceleration I will just look at the change in velocity divided by the length of the time interval. This is actually the definition for average acceleration:
The initial y-velocity is -14.4 m/s and the final velocity is about 4 m/s (upward). The time interval for this collision is around 0.03 seconds. This puts the acceleration (average acceleration) at 613 m/s2 or 62 g's. This is quite a bit smaller than the value from the MythBusters. They claim 260 g's. Well, there could be any number of reasons for the difference. The MythBusters obtained their value from acceleration sensors on the body. Since the body is not rigid, parts could have greater accelerations than other parts. Also, I calculated the average acceleration and I assume they have the maximum value.
Back to the Question
Really, there are two questions. Can you survive a jump from a building by wrapping yourself in bubble wrap? I think the answer to this is "yes." I mean, look at it this way: What if you are covered in bubble wrap that makes a thickness of 40 feet? When you jump off the building, you wouldn't even fall that far. This would clearly be survivable.
The other question: How much would you have to wrap around you? I think this one is tougher. My previous calculation was much too theoretical. More experimental data is needed to answer this question. So, I will wait. I will wait for the upcoming episode of MythBusters and see what data they show. It should be an interesting show.
