Wednesday, April 10, 2013

GI Joe and Physics - yup, still got it

My friend Janeth and I have been trying to see Oz Great and Powerful together for over a month, but one of us has always been busy, so we haven't had the chance.  Thinking that this past Sunday might be just perfect for both of us, I called Janeth up, asked if she wanted to go watch it ... and promptly learned that eventually she got exasperated and just went and saw it herself.  Hmph. 

-But!-, Janeth asked, would I be interested in seeing GI Joe 2 Cobra Strikes instead?  Turns out she really REALLY wanted to go see it.  Now, usually action movies don't exactly set me atwitter with anticipation, but this one does feature Channing Tatum and DJ Cotrona, men known for their absolutely fantastic, um, acting abilities. That, plus the fact that it's been a crappy 2 weeks
Fine Acting Abilities
and I was really looking forward to just being entertained for 2 hours, meant GI Joe 2 was in order.  (Side note - did you know that after Magic Mike debuted, Channing Tatum was so popular that GI Joe 2 was rewritten to give Tatum a bigger part?  Now you do.)
Anyway, off we went to see guys blow each other up.  And really, it was about as you expected: lots of explosions, lots of guys duking it out, the hot girl who's a better fighter than any of them, futuristic space weapons, disasters averted at the last possible second, and plot holes galore.  (Someone should explain to their script writers that it is not possible for it to be daytime in the US, Britain, France, Russia, Israel, India, and North Korea all at the same time.  Nor is it likely that you would design a control pad for your space weapon where the biggest button on the pad is the self-destruct.  But I digress)  Janeth walked out of the theater and promptly declared herself disappointed, in that it wasn't very realistic, an expectation that still perplexes me to this day.

BUT, (spoiler alert) I have to admit, there was an idea for a pretty cool weapon in there, one that at least seems semi-plausible in terms of the physics involved.  Basically, you haul a moderate-sized, pure heavy-metal rod into orbit (one that can withstand the heat of reentry), position it over a major city, then let it drop.  Gravity takes over and accelerates it downward, until it smashes into the Earth with enough kinetic energy to demolish said city.  Sound in principle (go look at some impact craters from meteors if you don't believe me) ... but do the numbers work?  The fact that nobody's done it yet makes me suspect no, but what's the real answer?  It's .... PHYSICS TIME!!

First, let's assume that the engineers took care of any pesky problems about angular momentum and keeping the rod on target.  (That's what she said! -Zing!)  Second, let's assume that the rode has a small enough cross-section that it can zip through the atmosphere with practically no drag, and not bleed off any energy in the form of heat and reduced speed.  Both of those just increase the destructive potential, so if we're looking at feasibility, that's a good bet.

Now, for some more grounded assumptions.  Judging by the scenes in the movie when it's still under construction, the satellite carrying the rods is about 10 meters tall.  The rods look like they're about half that, so let's say 5 meters tall, and half a meter in diameter.  That gives it a volume of about 10*pi*(.25)^2 ~= 2 cubic meters.  The movie specifically says this rod is Tungsten (a popular metal for military use given its hardness and high melting point), which at 19.25 g/cm^3, makes this Tungsten rod mass out at about 38500 kilograms.

Now, for the speed.  Let's assume a standard solar orbit, which is about 700 kilometers, and still close enough to Earth that gravity will accelerate anything towards earth at a constant 9.8 m/sec^2.  Integrating twice, that's 4.9t^2 = 700000, were t is the time it takes for the rod to fall the 700,000 meters, and solves to 378 seconds, or just over 6 minutes (again, assuming no drag and falling straight down).  Derivating to get back to velocity ... you get 378 * 9.8 = 3,700 meters per second.  (If you're having trouble thinking in metric, that's about 8200 miles per hour, or about 11x the speed of sound.  Zippy rod!

Ok.  Kinetic energy is 1/2*m*v^2, so 1/2*38500*(3700)^2 = 2.6*10^11 Joules.  That is a LOT of Joules, but just how big is it, really?  Well, a giga Joule is 10^9 Joules, so that's about 260 giga Joules ... or roughly 40-45 barrels of oil.  Destructive?  To any given building, definitely.  But to an entire city?  Hardly.  This weapon would really only be good at destroying individual buildings, and it's a LOT cheaper to do that by flying a plane over said building than it is by launching a complicated weapon system into space.  In other words ... COBRA FAIL.  Just as well, really.  If it were that easy to destroy entire cities, I'd be walking around a bit more cautiously.  You never know when a Tungsten rod will fall out of the sky and hit you on the head.

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