Wednesday, August 8, 2012

The Physics of Total Recall

Total Recall, which I just watched last night, has a lot of problems, but I'm going to ignore most of them. As with the first film, there's a central ambiguity about reality and which side of the looking glass most of the action takes place on. I'll ignore that. I just want to focus on the central plot device in the movie: the shaft and transport vehicle that goes through the center of the Earth. It's introduced in the very beginning of the movie, so there won't be any real spoilers here. I will mention a scene later on that involves the same shaft/vehicle. but I won't introduce enough context to be interesting.
The movie introduces us to a future Earth, ravaged by toxic chemicals in a global chemical warfare apocalypse. Only two regions are habitable: a chunk of northwestern Europe and Australia. Workers commute from "The Colony" (Australia) to the other side of the planet through the core of the Earth via The Fall, a skyscraper-sized shuttle that drops into the Earth and comes out on the other side.

I'm going to ignore some obvious questions like, "how did we construct a stable tube through the center of the Earth's molten core." I'll arm-wave the really crazy stuff away as "magic". I'll also ignore the obvious implication that a society capable of such "magic" could get rid of the chemical agents that make the rest of the world uninhabitable.

What I want to focus on is velocity. The trip takes 17 minutes, we're told. The Earth is very roughly 8,000 miles wide. Making that trip in that time means that your average velocity is 470.6 miles per minute or, again very roughly, 28k miles per hour. I'll round down quite a lot and call that mach 36 or roughly 36 times the speed of sound.

To give you a frame of comparison, velocities that are greater than about mach 8 are referred to as "hypervelocity". This is where materials start to liquify or vaporize when they experience collision. Late in the movie someone sticks their head out of the shuttle as it moves. I just want to point out that this scene is so far into crazy land that everyone involved should be required to take Physics 101 over again. Seriously, that's kind of like showing someone roasting hot dogs over a nuclear mushroom cloud. Their heads would immediately vaporize and I suspect the fluid stresses caused by opening the hatch would rip the entire shuttle apart.

OK, the hatch thing is just silly. So, how do the people who stay inside fare?

We don't know how much time was spent accelerating or what the actual maximum velocity was (only that the average velocity was mach 36). But let's assume that they reach the average velocity over the course of the first third of the trip. That seems safe enough. Thanks to a handy acceleration calculator I found on the Web that converts back into metric, that means that they accelerated at 2207.6 m/sec^2. Since one g is defined as 9.8 m/sec^2, that means that the acceleration experienced in this scenario would be 225 gs. To give you a sense of what that means, humans rarely survive 10 gs unless they're trained fighter pilots in acceleration suits. So, the workers in this vehicle would have been turned to a puddle of goo by the acceleration forces.

Granted, they might have had some kind of magical gravity tech, but if they had that, then why didn't they just fly, effortlessly, in a ballistic trajectory around the world, spending most of the time in the partial vacuum of low Earth orbit where movement is a lot cheaper than trying to build a tunnel through the Earth?!

Oddly enough, I liked the film. Mostly, I just thought it was a fun action romp. Yes, it was written by someone who flunked high school physics and apparently couldn't find someone at NASA that was bored enough to moonlight as a consultant, but that doesn't really matter. Things blow up perfectly well to pass the time while I much down some popcorn...

Update: I have to learn not to talk to my co-workers. They're far too willing to delve into this sort of thing... Anyway, 225 gs might not be as accurate as I'd hoped, because the density of the Earth is not uniform. Given that, you might experience increased acceleration due to gravity as you descend through the tube. If someone wants to work out how much of an increase it would be, I'd be interested, but intuitively, I don't think it will be enough to save the poor, hapless people in the shuttle.