I saw this video on digg or reddit. I can't remember which.
I was in awe. Then I started thinking. I wonder how fast that water was moving up right after the explosion. Too bad the video doesn't have a scale. Well, it kind of does - there is that ship. I am terrible at ship identification though. Maybe I can use my favorite scaling trick - assume the stuff is on the surface of the Earth. This means that free falling objects would have an acceleration of -9.8 m/s2. Let me try this on the water as it falls. Oh, trust me. I know it is not really free falling, but it is in this big glop of water so maybe that will act like a falling object. It's the best I have.
Time for Tracker Video Analysis. I set the scale as 1 ship (the length of the ship). Then, I found some recognizable glob of water to track falling. Here is the y-position of that water as a function of time with a quadratic fit.
From this, the falling water has an acceleration of -0.03 ships/s2. If I assume this is the same as -9.8 m/s2, then 1 ship = 327 meters (about 1,000 feet). That just doesn't seem right. Ok, I searched and I think I found that ship. I assumed it was a left over from World War II or something. Does it look like this?
A liberty ship. I found that image at www.acepilots.com/ships/auxiliaries.html. Wikipedia says that the liberty ship is 135 meters long. That seems more realistic. And with that change, my water glob is accelerating at about -4 m/s2. So, maybe that plan wasn't so great.
There could also be a perspective problem here. The glob of water is farther away than the ship. However, I suspect that the camera location is extremely far from both the center of the explosion and the ship. This would mean that, from the perspective of the camera, the explosion, water glob and ship are all about the same distance away.
I think I have the distance to the camera. After the explosion, there is one point where the camera makes a little jump. It seems like this camera is mounted so maybe this is due to the shockwave hitting the camera. I don't know much about shock waves, but I am going to assume that they travel at the speed of sound. The explosion is first visible at frame 134 and the camera jolt is at 201. The video says that each frame is 0.041 seconds, this means that the time between the explosion and the shockwave is 2.7 seconds. If I use the speed of sound as 340 m/s, then 2.7 seconds would make the camera about a 1 km away. That still seems close. However, the point is that it may be far enough away.
Now back to the exploding water. If my assumptions are ok, then what would be the speed of the exploding water? Tracker Video gives this:
So, this gives a water speed of 270 m/s.
I was going to also estimate the energy needed to lift that much water, but I could really see all the water.
