Angels, Demons and antimatter
On Saturday I went to see Angels & demons. It was entertaining to watch, although it was apparent at times that whoever wrote the script was more at home in medieval myths than physics. I guess I got used to weird things characters tend to say in Hollywood movies whenever the topic of conversation shifts to science.
One thing that did made me curious is a scene towards the end when they had to get rid of an anti-matter explosive device in the middle of Rome with 5 minutes to spare. So a guy jumps into a helicopter and flies straight up. When the time is up, the helicopter is high enough that the explosion only causes a spectacular fireworks display and shatters some frescoes.
At the first thought, that seemed like a really bad idea to me. They say that the explosion had an equivalent yield of 5 kT of TNT, which is comparable to a small nuclear bomb. This kind of devices do the greatest damage when they're exploded at some height above the target, so is it really feasible to save a city in the way shown in the movie?
First question is how high can you get in an average helicopter in 5 minutes? After sampling some random technical specs on Wikipedia it appears that the rate of climb of a helicopter varies from 6 m/s in civilian to 13 m/s in military craft. In the movie they use a police or a medical helicopter. It's also empty, so take an average, say 8 m/s, to get a nice rounded figure of 500 m/min.
Second question: How dangerous is a 5 kT explosion at 2500 m if you're standing right below it (like the crowds does in the movie)?
Unfortunately the Strangelove Slide Rule doesn't provide this kind of calculation. I did some more searching and found a couple of old DOS programs from the US Defense Nuclear Agency that answer exactly this kind of questions (they're complete with warnings to reset the computer after entering classified data - I guess they haven't yet come to shredding hard disks at that stage).
The result shows that 5 kT explosion will cause a shock-wave with 10 kPa of maximum pressure on the ground zero directly below. That's a little under 1.5 PSI, which is, according to the previously mentioned slide rule, not so bad for any by-standers. Such a shock will shatter windows, but won't knock down houses or even damage most people's hearing.
Surprisingly, that's exactly what you see in the movie. So this may be one case where they actually got it right.
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I loved the pretty fireworks :3. Anyway it's interesting that, for one time, they not only centered on the reaction that would cause a blast like that, but also on the realistic simulation of it.