Last night, a fertilizer plant in Waco, Texas caught fire and exploded. The energetic rupture shook the earth for miles around (the explosion was picked up by seismographs in Oklahoma), set fire to the surroundings, and collapsed nearby buildings.
Tragically, as you might suspect with an explosion this size, there are many suspected fatalities.
As chilling pictures like these rolled in, the comparison to an atomic mushroom cloud by the media was immediate. The Waco explosion was no hydrogen bomb, but the visual evidence does suggest a connection to a nuclear cloud. Looking at nuclear clouds might even be a good way to figure out how big the explosion in Waco was.
Over the decades, countries around the world have conducted nuclear explosion tests and recorded the effects. We’ve gathered so much data this way that researchers have discovered relationships between many of the bomb’s deadly variables. For example, when talking about atomic explosions, we know a general relationship between the height of the explosion’s cloud and the size—the explosive yield—of the event.
The graph above shows the relationship between the energy of a nuclear blast and the size of the cloud it produces. The first orange line you see represents the explosion of the Fat Man nuclear device over Nagasaki, Japan, during World War II. The second shows the cloud produced by the Castle Bravo thermonuclear hydrogen bomb, itself over 20 miles high.
When something so terrible happens, we clamor for answers. Using graphs like the one above and pictures from the scene, we could guess at how large the explosion in Waco was, if for nothing else than to learn from the devastation and move safely forward.
Like many of the nuclear tests of the 1950s, the Waco explosion occurred on the ground and produced a huge mushroom cloud afterwards. Looking at more pictures of the Waco explosion, the cloud is towering over the countryside. In many pictures, you can see the top of the blast cloud seemingly tickling the bottom of the atmosphere’s less ominous clouds.
The lowest clouds in our atmosphere can appear anywhere from ground level up to 6,500 feet, putting the Waco blast cloud in some kind of context. This range means that the explosion cloud could be anywhere from a few hundred to a few thousand feet high. Comparing this range with the graph above, this means that the Waco explosion could have been a nearly one-kiloton blast. A one-kiloton detonation carries four trillion joules of energy with it—comparable to all the energy stored in all the jet fuel of a fully gassed Boeing 747.
And reports do seem to support this link between the size of the cloud and the blast. One report claims that the fertilizer factory could have contained as much as 54,000 pounds of anhydrous ammonia—a potentially explosive gas. To find out how big an explosion it would produce, we have to look at the material’s energy density—how much energy you get per kilogram or pound. I have seen estimates that put the energy density of ammonia at 50% greater than liquid hydrogen, which is the same fuel used in rockets. Therefore, knowing the energy density of the liquid hydrogen and the amount of the ammonia gas, the calculation yields a 1.2-kiloton blast. Keep in mind this is the size of the explosion only if all the ammonia were to go off. It’s more likely that much of that 54,000 pounds remained unexploded in tanks, exacerbated another explosion, or escaped into the air. However, given this uncertainty, a nearly full explosion does support the earlier mushroom cloud-based estimation of the explosion size.
Another report of the explosion size claims that 100 tons of solid ammonium nitrate, the same chemical used in the Oklahoma City bombings, was the cause of the explosion. The energy density of this chemical, commonly referred to as ANFO (ammonium nitrate/fuel oil), multiplied by the reported amount gives an explosive yield about 10 times less, or about 100 tons of TNT—comparable to the total energy released in the nuclear fission of one gram of uranium-235. This too is within the range suggested by mushroom cloud comparisons.
Of course, because reports are still coming in and numbers can always be fuzzy right after a disaster, the Waco explosion was probably somewhere between both estimates. And the blast most likely wasn’t caused by just one factor. We will probably never quite know how much of what chemical compound combusted. It could have been a combination of leaky gas tanks, open chemical containers, and a raging fire. Only time and forensic science will tell.
Estimations like these will eventually be superseded by better numbers as experts study the scene. It may even take up to half a year to fully determine the cause of the explosion. The reason we would want this kind of information is clear: to learn about potential risks and act accordingly. Gauging the sizes of possible explosions could lead to better zoning laws or even stricter safety regulations for factories like the one in Waco.
And maybe comparisons like these will help us understand what the people of Waco are going through, help us tell their story.
In the wake of another explosion-related tragedy, everyone is reeling, including myself. I don’t mean to seem uncaring or cold or callous to the tremendous suffering of those in Waco, but calculations are all I can do from here. It’s how I cope; it’s the only thing I can control. I grapple with the numbers and the science so I don’t have to grapple with the emotion…maybe.
My thoughts are with you Waco.
[Please know that I am not an expert in the field of explosives and these are back-of-the-envelop estimations on my part. If you have any details or corrections, please share them in the comments.]