Tuesday, April 16, 2013

Boston Marathon Bombing: Deriving some Physics and other info from video analysis

While the official investigations proceed, there is a ridiculous amount of speculation about the bombing, who did it, what it was, etc. Very little of this speculation is evidence based. Almost all of it is just blathering based on the beliefs or prejudices of the posters.
Instead, let's take a quick look at what we can know with certainty from the evidence we have.
The first thing we have to do is determine where the bombs went off. Fortunately, the New York Times provides an excellent infographic for that purpose:

AP has a photo of the exact position of the bomb taken from above as it is being viewed by a bomb squad member:
It seems likely that the exact location of the bomb was the scorch-mark on the right hand side of this image. This comes from both the pattern of the debris on the sidewalk, and the fact that the right-hand window over the Lenscrafters is gone while the left-hand second story window is apparently damaged only by debris penetrating in the lower right corner. Additionally, there is no damage to the glass doors on the left, and appears to be a debris shadow from the right hand side of the door's alcove.
We can visit Google Maps to get a sense of the place.

 Here's a 45 degree view of that sidewalk:
We can use the measure tool in gimp to get the width of the sidewalk:
The 20 ft bar is approximately 220 px wide. The sidewalk is approximately 410 px wide, and thus 37 feet wide.

Edit: 2017: The Times video is long gone, but you can get the same frames from ABC News' youtube channel.  The equivalent to the views below is linked in at time=49 seconds...


Now, let's look at two frames from the Times live video at the finish line:
In the first picture, you can just see the first capture of the flame front of the explosion. The globe of flame is visible just to the right of the Brazilian flag.
In the second, 0.021 seconds later, the people have not yet begun to react (duh, the sound hasn't even reached them) but the flame front has grown but has not yet reached the top of the flags, nor reached the barricades. You can tell because the flags have not moved at all from the blast.

Here's a closeup of the two images:

 In the first closeup, the flame front from the bomb appears to have not quite reached head-height of the person in the black jacket between the two right-most flags. Let's call it five feet tall.

In the second, the flame front has reached approximately the height of the flagpoles. Using Gimp's measuring tools, that seems to be about 15 feet.

So, in 0.02 seconds, the flame front expanded about 10 feet, or about 500 feet per second (340 MPH). The speed of sound in air is about 1100 feet per second, so this is a sub-sonic deflagration not a detonation. (It's still a bomb, and still an explosion but the stuff making the bomb BURNED and the wave-front of the burning moved out through the explosive at less than the speed of sound. It was very fast, but it didn't go off all at once.)

So, this is the result of a “low explosive.” High explosives detonate at 3 to 9 kilometers per second and produce sonic or super-sonic wave fronts.

In terms of being an “IED” and being a “terrorist improvised explosive” the bomb was probably -not- TATP for two reasons: TATP is a high-explosive, so it would have gone off all at once, rather than burning for many hundredths of seconds. In the New York Times You-tube video cited above, flame can still be seen in the cloud from the explosion until timestamp 70.5. – the combustion continued from 69.7 to 70.5, almost eight tenths of a second. That's burning, not detonation.

Additionally, the explosion left a large white cloud of dust in the air, and a black scorch mark at the presumed site of the explosion.

Take a look at this You-tube video to see the difference between open burning of black powder and smokeless gun powder:

Based on the big white cloud, the speed of the flame-front, the color of the burning cloud, and the black-mark left on the sidewalk, I think it is almost certain that this was a black-powder explosion.

In addition, we can make a few other conclusions.

The container holding the black powder was not nearly strong enough with much of the force of the deflagration being wasted in the cloud rather than in rupturing the vessel and making the explosion more violent. The person who made this hadn't done much experimenting, nor did they have good designs. This could have been MUCH more deadly.

In addition, the circle of damage was limited to less than the 37 feet to the line of flags and barricades. The flag poles were not knocked over, nor were the barricades as is apparent in the Boston Globe video. Flags blew flying out from the explosion for almost 28 seconds, but not one flag was torn off, nor were any flagpoles broken, nor any of the yellow-clad security people knocked off their feet at no more than 40 feet from the bomb. One runner is clearly visible who fell, apparently by being struck by a fragment from the explosion, but there's no “bang” effect. Bystanders have to tear the barricades away to get at the injured.

Recall also that the second story window, not more than 20 feet from the bomb was not broken by the explosion. Apparently, the circle of damage sufficient to break plate glass windows was less than 20 feet. The bomb was far less effective than Eric Rudolf's Atlanta Centennial Olympic Park bombing in 1986 altho the two Boston bombs killed more people, presumably because the victims were closer to the explosion.

The conclusion then is that this is a pretty typical black-powder pipe bomb. Those typically have a blast radius of 15 to 20 feet, which is consistent with the damage seen above. Fragments of ruptured and torn metal of course, can travel much further and injure more, but the people who were in the ghastly photos of folks with their legs torn off would have had to have been standing within about 15 feet of the trash can the bomb was placed in.

Oh. Right. One last conclusion. At least the finish line bomb was in a trash can. Watch the sky between the buildings between 8 and 10 seconds in this video and you can see the trash can arc up and then fall.

Sorry, that video's disappeared from Youtube. Link rot happens.
It's too bad, because the soaring trash can was a neat thing to see and
proved that the bomb had to have been IN the trash can in order 
to launch it straight up rather than sideways. 

It's not as good as the previous video, but if you watch closely between 4 and 6 seconds into this AP video, you can see the trash can disappear behind the red brick building.  At first, it looks like it's a small piece of debris falling close to you, but then, as it falls, it disappears when it crosses the line of the top of the building, so it must be further away.


dudley stump said...

Nice work. What do you make of the fact that most of the shrapnel stayed near or at ground level?

dudley stump said...

Nice work. What do you make of the fact that most of the shrapnel stayed near or at ground level?

That Guy said...

very good analysis. Thanks.

Rick Boatright said...

The released photos of the pressure cookers used indicate that they failed by tearing open rather than fragmenting, which is common in this kind of thing... and so the result was a "spray" of the nails and bbs rather than a true omni-directional explosion.

Peter said...

Maybe a spray would be deadlier than an omni directional explosion. Not that it was intentional of the bombers to have the device tear open.