Underwater explosion analysis

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 http://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.

1. #1 Joseph Smidt
August 23, 2009

270 m/s! This is ~80% the speed of sound! That’s incredible.

Dugg for more great analysis. ðŸ™‚

2. #2 Rob
August 23, 2009

I’m not sure. I haven’t even finished the post yet but I think the shock wave travels faster than sound for part of its journey. Maybe not for long enough to mess you up though. I found the following quote at the Federation of American Scientists web page at http://www.fas.org/nuke/intro/nuke/blast.htm.

“During the time the blast wave is passing through the superheated atmosphere in the fireball, it travels at supersonic velocities. After it leaves the vicinity of the fireball, it slows down to the normal speed of sound in the atmosphere.” Maybe for an underwater explosion, there is no superheated atmosphere.

Thanks for another good and thought provoking post though.

3. #3 Crasty
August 24, 2009

In truth, immediately i didn’t understand the essence. But after re-reading all at once became clear.

4. #4 Dave
August 24, 2009

You’re WAY low for the speed of sound in water. In air, the speed of sound is about
1100 feet per second, depending upon conditions. In water, the speed of sound is closer
to 1560 meters per second (note the units change). Wikipedia has a reasonably good
writeup:

http://en.wikipedia.org/wiki/Speed_of_sound#Water

Also, the DOE has a rather extensive archive of nuclear testing:

http://www.nv.doe.gov/library/photos/complete.aspx

There were several underwater tests, mostly in Bikini Atoll. I think you’re flawed in your
guess that the camera is located quite far away from the ship, at least with regards to the
distance between the ship and the column.

Wikipedia has some decent articles about nuclear testing:

http://en.wikipedia.org/wiki/Nuclear_testing

The shot you’re witnessing very well may be the Operation Crossroads Baker shot:

although photographic evidence indicates it’s more likely the Hardtack Umbrella shot:

Dave

5. #5 Rhett
August 24, 2009

@Dave,

Good point. I was only thinking about sound and shock wave in the air. I guess the shockwave through the water could have also made the ship with the camera on it move. I guess I was (for some unknown reason) thinking the camera was on land. A camera on a boat would make more sense.

6. #6 C. Chu
August 25, 2009

I’d like to mention that moving shockwaves do not necessarily move at the speed of sound. They can move at any Mach number higher than 1. Also as mentioned before, the speed of sound in water is much higher than for that in air.

7. #7 Ron
August 25, 2009

Hey Rob

Just discovered your blog today and this is a keeper. Anyway, you said :

“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.”

2.7 seconds seem a little too big to me. The video is only 0.40secs long! I have 0.7 seconds just from observation (Am I wrong?). Speed of sound in seawater is 1560 m/s (well, it depends on salinity). So distance from simple equation is 4.2km or 2.6 miles. If this was indeed Hardtack Umbrella, it was an 8 kiloton bomb exploded 150 ft below the surface.

8. #8 Ron
August 25, 2009

That video analysis software is cool. How do you use it?

9. #9 Ron
August 25, 2009

“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.”

Cool blog. Rob, its more like 2 miles away, I think, from calculation putting the right speed of sound in seawater. If this was Hartack Umbrella, it was an 8kt bomb exploded 150 ft below water.

10. #10 Rhett
August 25, 2009

@Ron,

this might help – http://blog.dotphys.net/2009/06/another-video-analysis-tutorial/

You can find some more stuff under the ‘tools’ tag