Whelp. Might as well pack it up now guys. Physics, the ever amazing scientific field that is also the occasional party-pooper of Pop culture, has found Bard's Black Arrow to be awfully lacking when it comes to killing Dragons. At least, so says Rhett Allain, Physics Lecturer and Wired Blogger!
Allain wrote an in depth post over at Wired looking at the science behind Bard's arrow and the Ballista he fires it out of in next month's final entry in the Hobbit saga. Looking at specifically the movie version of events (in the original novel, Bard shoots his arrow from his bow, rather than out of a Ballista), Allain made a rough calculation of both the mass and size of the Arrow we see Bard grab in Desolation of Smaug, and then the speed at which it flies out of the Ballista as show in the flashback to Smaug's first attack on Dale.
Using a few formulae and through some pretty graphs, he finds the Arrow... well, let's say wanting:
From these graphs I get an x-velocity of 12.4 m/s and a y-velocity of 6.66 m/s. The magnitude of this velocity is 14.08 m/s (31.5 mph) and at an angle of 28.2° above the horizontal. This is not very fast for an arrow. If I include the uncertainty from the length estimate, I get a launch speed of 14.08 +/- 1.48 m/s. Really, this is more like the speed of a nerf dart (yes, I measured the speed of a nerf dart) than a actual weapon that could kill an actual dragon. Maybe this is why Smaug destroyed the dwarves – their weapons sucked.
Allain comes to the conclusion that the Arrow speeds we're shown in the movie are so slow for the sake of us being able to see them fired on screen - firing it a decent speed would make it practically invisible normal framerates. And while okay, it's unsurprising that the physics of a fantasy epic movie based on a children's novel might not be the most accurate thing in the world, it's still pretty cool to see the science behind it. Head on over to Allain's blog and read the rest at the link below.
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