Rhett Allain is an Associate Professor of Physics at Southeastern Louisiana University. He
enjoys teaching and talking about physics. Sometimes he takes things apart and can't
put them back together.I saw this video posted on Physics and Physicists:
It reminded me that I had at one point tried to analyze this. I had actually posted something about this on the first generation of my blog (which no longer exists). I have found the analysis, and here it is from the archives. Thanks ZZ for reminding me.
Could this be true, or is it fake? I started to do an analysis of the trajectory, but I found the following frames:
Look at the guy's back. His back starts moving before the water bottle rockets. It must be some type of cable pulling him. If the rockets were propelling him, the rockets would move first.
Energy Storage
What about the energy? Is there enough energy stored in these water bottles to get this guy this high? First, how much energy? I know this isn't exactly correct, but the best I could find is that there are 17 Wh per liter of compressed air. (yes, it would depend on the pressure - but let me proceed anyway since I don't even know the pressure anyway). So, how much compressed air?
From this picture, it looks like there are maybe 10 bottles. They look bigger than a 3 liter bottle, so I will guess they are 4 liter bottles (do they make those)? The bottles look like they have maybe 1 liter of water in them. That would give 30 liters of compressed air (probably not more than 60 psi or the bottles might explode). The energy stored in compressed air can be calculated with the following:
110 
kJ/m3 at 25 °C (298 K), per mole. This would give:
Where I assumed the bottles were compressed to 60 psi (about 4 atmospheres) using 6 moles of air. So, now the guy has some energy (even though I made tons of approximations). So, if all this energy just went to increasing the gravitational potential energy of a small Japanese guy, how high would it go?
Wow, that is pretty high. But the water has to also be lifted. Suppose there are 10 liters of water and half of it has to be lifted, that would make this it go 51 meters high. This doesn't seem to be correct, let me move on.
Trajectory
How about I analyze the trajectory of the guy? This is a little difficult because the motion is not at a right angle to the camera, but I will proceed anyway (that's what I do).
Here is a plot of the vertical position (not adjusted for the angle) versus time. I scaled the video assuming the people were about 1.7 meters.
A few things to look at. First, the speed on the way up is about 3.9 m/s. On the way down, I would assume a near free-fall speed. This should be near 9.8 m/s2 but from the quadratic fit, the acceleration on the way down is around 1.4 m/s2. Wait, this is totally messed up. I need to work on my video analysis techniques.
Comments
4 liters is about a gallon(living in the metric challenged US), so I would say they're 5 liters(Canadian by birth). From my experience with bottle rockets the pressure could easily be 100 psi and there are at least 15 bottles. The problem is they contain far to little water to maximize the thrust. The trajectory would be a somersault, judging from the weight distribution, possibly a 2.5 gainer and then splash. Even a single 2 liter bottle will lose half it's elevation do to the smallest increase in drag and this guy is a real drag. He's not worth the effort to calculate, but some experimentation might be interesting. I wonder if the local indoor driving range will let me launch at they're device?
Posted by: Weldon MacDonald | January 8, 2009 8:16 AM
I love it when people use math to bust things like this! :-) I think you can bust this just by looking at the forces involved. There is no way that he would get that linear trajectory right after take of with the only force lifting him strapped on the back (law of inertia). He would need the same amount of bottles strapped to his front to archive such an trajectory.
Posted by: Kim | January 8, 2009 7:59 PM
Hi Rhett,
Here's one that appears real. In the end, 100 water bottle rockets lift a man (and platform) several feet off the ground.
http://www.youtube.com/watch?v=cOagszQgTl8
The same Japanese TV show also did this one (great for vector addition of velocities):
http://www.youtube.com/watch?v=yPHoUbCNPX8
I'd love to see what else these guys have done, but I don't know the name of the show. :(
Anyway, thanks again Rhett for your great work!
Posted by: Frank Noschese | January 8, 2009 8:40 PM
Frank,
Great links. That first one with the water bottle rockets was great. The other was good also, I had seen it before but never got around to posting anything. Thanks!
Posted by: Rhett | January 8, 2009 9:16 PM
Your max height calculation ignores the considerable energy that will be in the expelled water, which is why you get such a large value for h.
Posted by: Tom | January 11, 2009 9:57 AM
Tom, Good point. Sorry I missed that. I will try to update this post to take that into account sometimes. Thanks!
Posted by: Rhett | January 11, 2009 9:27 PM
Frank Noschese... checked out your link. 100 bottles.. one chinese man.. He is holding onto two ropes that dont slack when the bottles are released. Bringing me to suspect they are helping pull the man up... yes I do mean helping. Quite possibly the 100 bottles on their own might have not revealed such a wonderful performance on their own?
Posted by: einstein | March 31, 2009 2:50 PM
This is a really weird website!!! XD
Posted by: Erin | May 14, 2009 1:37 PM
Interesting! Nice to see some worthwhile analysis on this, I was terribly disappointed by the Mythbuster's shoddy approach - as usual. Still don't know why I watch that show, it drives the scientist in me crazy, though I guess the tinkering kid in me still loves it. Which brings up the following tidbit of info: According to the translation MBs got of the Japanese show, the Japanese show used 15 bottles. Unfortunately, it didn't say what type or size. MBs didn't even address that point, and just used 2L bottles for lack-of-detail's sake I suppose, though from the still you have above they very clearly aren't. Also, I guess as corroboration on the number 15, I didn't notice this before but a 15 is visible between all the kanji characters on that same still picture.
From a theoretical standpoint, it seems to be plausible, though because there are so many practical considerations that would need to be addressed to make it work, it leads the game show's very simple kit to seem fake, bolstered by the evidence of the moving hidden harness underneath the jetpack's straps.
Posted by: jack | September 8, 2009 3:04 AM