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.

12 comments:

  1. I did some rough calculations last night using estimations for the density of various different layers in the Earth (Crust, Mantle, Outer Core, Inner Core). All this data makes the assumption that 'The Fall' travels through the center of the earth. A direct route would actually miss the center by 1200 miles and would be less efficient, so I imagine the fall would travel to the center of the earth and changes course. I also assume a vacuum, frictionless environment. I know the movie showed Quaid leaving the train mid-transit, but as you said, this make absolutely no sense.

    Distance Vs Acceleration: http://i49.tinypic.com/ruwqoh.png
    Distance Vs Velocity:
    http://i46.tinypic.com/rwqxlk.png

    At a complete freefall, there would be NO apparent gravity in the cabin for the course of the fall (they're falling) UNLESS the train were accelerating at 1G+gravity acceleration. If this were the case, then the cabin would have to start upside-down, and not have to flip midway through. At a free-fall acceleration using only Earth's gravity, I estimate it would take 57 minutes to reach the opposite side of Earth.

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    1. Yep, sounds pretty reasonable. If they'd said it took an hour, I would have been fine with it (still silly, but it would only involve an insane level of tech, not a physical impossibility). The 17 minutes number means that the "gravity" they're experiencing has to be acceleration-based (or artificial, but see my above comments on that), so reversing half-way makes sense, but it should be at least 200 Gs.

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  2. Another big goof is the way gravity is represented. If the Fall device was free falling, people inside would be weightless, therefore floating in regards to the device. But given it was accelerating further than the earth's gravity, they would be thrown against the ceiling, not walking around. But lets consider the device was just free falling. As it approaches and reaches the earth's core, the gravity felt by the passengers would decrease continuously down to 0 in the core, due to mutual gravitational attraction from the whole mass of the earth which evens out in the center because the earth's body is almost symmetrical. And then as the device comes out on the other side people would start feeling a progressive gravity increase again, minus the vehicle's deceleration.

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  3. I think it is is pretty accurate how they did it! My calculations show they knew what they were doing in Total Recall.They have an acceleration of 1G+1G gravity, so the travellers experience 1G gravity during travel. Exactly at the center they swap accelleration to 1g+1G decelleration. The traveller "feel" 1G during the whole trip.
    The velocity at the center of the earth is 20KM/sec.
    The trip takes about 1000 sec thats pretty close to 17 minutes...

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    1. You realize that your suggestion is that they're moving at mach 59 when they reach the core, right? I'll buy your math (though I haven't checked it), but even I wasn't going to assume they were being that silly. At that velocity, I would expect the sonic boom (even if they manage to get the shaft down to near-vacuum) to cause earthquakes, and the amount of energy required to maintain a constant 1G acceleration the entire time... I can't believe that they wouldn't have the technology to simply replace the damaged chunks of atmosphere and repopulate the Earth!

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  4. Am I happy I'm not the only one who found things wrong with this. Apart from physics in high school and a fair amount of math I have little to base my claims on. But, watching this I remembered hearing in a discovery show about gravity trains, I also did some research and theory crafting as I used gravity trains in a short piece of fiction. Watching this, I remembered that the free fall through the planet would take just over 42 minutes, but this is faster, meaning that the shuttle accelerates and decelerates quicker than earth's gravity. This sets up an interesting scenario.

    1. Enter "The Fall" shuttle and ignore advice to strap in.
    2. The shuttle starts accelerating with more than 1G making the ceiling your new floor.
    3. Halfway through the planet you would have a brief moment of zero gravity, but it's not going to last.
    4. The shuttle begins artificial deceleration, stopping faster than any occupants inside. This effectively reverses gravity again, throwing you from the ceiling back onto the floor.
    5. The shuttle comes to a stop. The floor you had been crammed against for the last part of the journey is no longer the floor. Gravity crashes you into the ceiling as the cabin is now effectively upside down.
    6. Walk out beaten and battered out of the cabin and order time with a chiropractor and curse yourself for not strapping yourself in like they told you to.

    The cabin would have to turn 3 times, though I would suggest small grace periods with no artificial acceleration at the beginning of the journey, at the center, and before stopping, enabling the cabin to turn in zero G. In the end, 42 minutes wouldn't be bad travel time to get through the planet and having zero G all the way would probably be safer and easier. Also more fun. Though you would have to keep the tube a complete vacuum or friction from the air would prevent the shuttle from making it all the way to the other side, and it would keep rubber banding back and forth, until it would eventually come to a stop in the center of the tunnel. Probably not where you want to be with the heat and limited supplies.

    Just my five cents.

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  5. having thought things over myself the maximum acceleration they would experience would be at the surface and around 1g. How could the acceleration of the ship increase as they fall when the gravitational force between earth and ship is decreasing... acceleration falls linearly with distance to the centre of the earth a=(g/r)*x where a is acceleration r is earths radius and g is 9.81 ms^-2 the maximum x can be is r so if we insert r into our eqn for acceleration we get a=g
    hope this is all clear.

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  6. If gravity pulls to the center of the earth, how does it push the train from the core to the surface?

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  7. I disagree with your conclusions (apart from the fact the film is somewhat unbelievable) I wrote a blog here: http://alistaircunningham.com/the-physics-of-total-recalls-the-fall/

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  8. Some interesting comments BUT although your all correct that the film is unbelievably inaccurate with regards to physics, some wild assumptions and calculations seem to have been made for no particular reason.

    First it's shown several times (on a digital map) that the Fall doesn't travel in a straight line (marked by red dashes) but rather a semi-circle around the Earth's core and what seems to be partly through the outer core. So I expect this would change the travel distance greatly.

    Secondly at no point does the film suggest the fall is travelling through a vacuum but rather the complete opposite.

    Lastly in the first scene when we see the digital map, the speed it's travelling can be seen lower left part of the screen I can't recall the number but it might be interesting to use the above to formulate more accurate thoughts.

    Loved the film though.

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