Over on Wired, Rhett Allain from Southeastern Louisiana University (who has previously analysed the length of the Balrog’s whip) has turned his number-crunching ability to another thorny problem if Middle-earth physics — could the Black Arrow of the movie actually exert enough force to slay Smaug?
(Of course, it does so because it does so … no additional explanation is needed. But I love that Rhett is using it as a starting point to teach folks about maths and physics.)
Could the Black Arrow actually kill a dragon?
In both the movie version and book version of The Hobbit, the dragon (Smaug) is defeated by an arrow – the Black Arrow. There are some differences between the book and movie versions of this arrow so I will just be using the movie version from now on.
You can see in this clip from The Hobbit: The Desolation of Smaug trailer, there is some machine like a ballista that shoots the black arrow (in the book version, it was shot with a normal bow). How fast would this arrow have to shoot? What kind of force would this ballista need to exert on the arrow? Let’s get started.
Dimensions of the Black Arrow
Clearly this isn’t a normal arrow. It’s much bigger and maybe it’s made of iron or steel (can’t tell for sure). The first thing I need to do is to estimate the size. In one scene, Bard (the defender of Lake Town) takes the last remaining Black Arrow in an attempt to hide it. This shot shows the full length of the arrow.