'Pacific Rim' Vs. Real World Physics: Giant Robots, Galileo, And The Square Cube Law

Physics Pacific Rim

Pacific Rim looks awesome and all, but let's talk about science for a second. Specifically, let's talk about the science, or lack thereof, behind completely awesome giant robots.

Guillermo Del Toro's upcoming sci-fi action pic is probably going to be as awesome as the trailers make it look, unless you're the kind of person who hates the sight of huge mecha fighting against equally huge monsters, in which case please show yourself out. How could you not love enormous robots punching out enormous monsters who lay waste to entire cities? Giant robots represents 90 percent of what we want the future to be like (the other 10 percent: flying cars, and a male birth control pill.) They're extremely cool looking, they transform, and for sheer shock factor they're impossible to beat.

We want them so badly, but could we have them in real life? Unfortunately, hell no. Not because of budgetary constraints, frustratingly missing confirmation of alien life, or the lack of a decent fuel source. There's a bigger problem facing these robots than any alien invasion: Physics.

Yes, the terrible dictator that ruins everything from warp drive to immortality also has a bone to pick with Del Toro's supersized combatants. And unfortunately, as inherently awesome as it sounds, having giant robots brawling with giant monsters in regular ol' planet earth gravity runs right up against the twin problems of weight distribution and the nefarious square cube law.

The square cube law is a paradoxical-sounding mathematical concept, first identified by Galileo, which states that when a given object increases proportionally in size the new surface area is proportional to the square of the multiplier, but the new volume is proportional to the multiplier's cube. Or restated for those of us whose eyes begin to bleed when the subject of math comes up: When something increases in size, its volume increases faster than its area. If you double the size of an object for instance, surface area increases by four times, but the volume of that object, which is (duh) all the space inside it, increases eightfold.

This law has implications for numerous scientific disciplines, including construction and biology. To get an idea of how it works, let's say you take an average human woman, someone approximately 5 feet, 5 inches tall. Increase her size to 11 feet. You now have a woman whose heart is four times bigger, forced to pump a presumably proportional increase in blood through 8 times the amount of circulatory system her smaller incarnation had. That's a tremendous amount of stress and likely to kill anyone who grows beyond a certain height*.

Of course, animals which have evolved to be big, rather than having had a gene preventing abnormal growth turned off, have developed the respiratory and circulatory systems necessary to handle their needs. But before you break out the snacks for your 'Yay, monsters for everyone!' party, bear in mind that all that volume comes with a ton of additional weight. Mice, for example, don't look like miniature elephants for the very excellent reason that an elephant's bones have to be much bigger in proportion to its body size than a mouse's skeleton does, in order to support all that weight. In fact, if you zapped a mouse with magic to increase it to the size of an elephant, its bones would probably be crushed under the weight of its soft tissue within seconds. EEK! And even though the elephant's bones can support it, it still has to deal with the fact that it's far easier to break something heavy than something light, which is why a mouse could jump off a waist-high kitchen table with no ill-effect, but an elephant can break a leg simply tripping over something.

Complicating things further, all that weight needs musculature capable of dealing with it, and that's another way the square cube law totally screws over giant animals. It takes considerably more muscles to manipulate the animal's limbs and moving parts, but those muscles have to deal with a hell of a lot more weight. This means larger animals tend to be slower and less agile than smaller animals and beyond a certain point there's no amount of naturally evolved biomechanical components that can do the job. In fact, this is why earth's largest animals are water-dwelling, where buoyancy mitigates a lot of the stressors caused by huge mass and weight. Forget deftly sweeping cars off a bridge with the swipe of a taloned hand; a giant monster like the beasts in Pacific Rim might find it difficult to even stand up.

* Read Orson Scott Card's Shadow series for an excellent depiction of the problem. But ignore his reactionary politics which become insufferable as the series goes on.

NEXT: The square cube law and giant freaking robots

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Comments

  • BMN says:

    Interesting. Now you owe it to the dreamers to explain how our beloved monsters and mechs (or jaegers) can be made plausible.

    I’ll be watching, and waiting.

  • Krome says:

    Interesting article, but seeing as this films based around monsters that come through a dimensional rift, well that MacGuffin is all that's needed to explain their biology, as for the Jaegers, perhaps around the very same rift, some kind of ultra light and ultra durable alloy (that can be manipulated by hopes and dreams to create the bad a$$ machines we'll be hopefully enjoying when the movie comes out) will be found. Pacific Rim doesn't look to have the high science of Asimov, it looks like a less metaphysical version of Evangelion and as long as Zilla doesnt turn up to spoil the fun, I'm sure it'll be at its worst a solid fun beer and popcorn fest.

  • John says:

    SCREW EARTH THEN!! LETS GO TO SPACE!!!!! THEN WE CAN MAKE ALL THE EPIC MECH SUITS WE WANT!!!!

  • 2+2=4 says:

    The monsters are so large they adapted to the water and Earth's crust pressure when they lived under it. So once they are on the surface the gravity for them is much easier to bare, this is why they move fast. Their muscles feel stronger. You can ask how is that possible that they've developed at all, well... it's a mystery. Maybe they were born inside the magma of the earth, eating giant crystals. I don't know, maybe they have hot air chambers in their body to inhale air that makes them light, whatever.
    The robots have anti-gravity technology, making them lighter, like in zero gravity. But when they move or fight, the anti-gravity distributes the weight in such manner they can walk and punch very hard, and can defeat the monsters.

  • Ian Greene says:

    It's not supposed to be scientifically correct. It's a movie about giant monsters that come through a pandimensional portal in the ocean floor as well as a throwback to kaiju films.

  • Onix says:

    Giant robots aren't realistic?

    YOU DON'T SAY?

  • nugun says:

    Thoughts on physics...

    1. An Artic Cat tractor can go on ice thinner than we can, because its weight is more evenly distributed.

    Why is this relevant, well, what is the proportions being spoken of here? If it's a bipedal human form, it may sink into the earth, but is it sinking in any more than if we were to walk in mud? Probably not...

    2. The scale of square is not necessarily the relevant factor. The scale of mass is. For example, I could scale up a human to 80ft. It'd be bad. Humans are mostly water.

    But scale up a human form to 80ft. Use an advanced hitherto unknown alloy 100x stronger than steel for the skeletal structure. (Not as implausible as one might think.) Construct the exterior to function as an exo-skeleton. Providing double the structural support. And keep 90% of the internal area "empty" space. That's right. The unit should mostly be empty. (Actually, I'd argue most of the interior space would be designed to circulate and pump air along thin metal fins in order to cool and extract excess heat out of the unit.

    3. Stability, stability is going to likely be a mix. First you have numerous muscular fiber bundles that are computer controlled. Think Segway and numerous other self balancing devices. And let's not forget the agile quadrocopters. Then combine that with a fusion reactor turbine, Two actually. Both spinning larger circular systems. In an effect - giant gyroscopes.

    4. Darn it, a little imagination. But as anyone knows. It's a matter of materials and designs. We build numerous bridges and buildings today that 150 years ago would have been thought impossible. The Burj Dubai, the Russky Bridge and the Three Gorges Dam. Structures that would have been considered impossible to build. Heck, the Burj Dubai seems nigh impossible even though it's built.

    But advances in design, and materials engineering has allowed those structures to be built.

  • dewstarpath says:

    - All super mecha jokes aside, I have a question: How do the monsters escape through an 'interdimensional' portal at the bottom of the ocean without draining the entire Pacific Ocean ? I don't think they can turn it (the portal) on and off at will. Just saying.

  • dewstarpath says:

    - And - how do they 'push past' the torrent of the water pouring in without getting sucked back down due to the whirlpool on the other side ?

  • William says:

    Who ever wrote this article seems to forget that science is continually destroying previously limiting laws of physics and establishing new limits. For a long time science considered it impossible to break free of the gravity of Earth or that anything could exceed the speed of light, but both of these assumptions have been proven wrong. he laws dictating size limits is also disregarded as technology improves. The Egyptians could never have built a building like Taipei Tower or Burj Khalifa yet it is possible with modern technology. In many instances science fiction gives way to science fact, simply because someone followed an idea and made it possible. Modern flight would not be possible if people had not dreamed of flying as birds do, nor would we have people in orbit around the planet if not for others wondering what was out there and if it was possible to get there. Time is the only limiting factor in truth, for in time what we believe is impossible may very likely become possible or even common place.

    • Leeroy says:

      No object of mass has ever exceeded the speed of light (in the strict sense). Einstein's theories of relativity are 100 years old and have been shown to be correct in every verifiable way possible to date.

  • John says:

    Hmm, if I were to build a giant robot, yes mass would be a factor, so to get around that problem... one would have to find away to deplete normal matter of the Higgs Boson. Its supposedly statistically there, so perhaps in a future syncrocyclotron one could build something like a gravity based penning trap to catch it before it reintegrates. That would give you the structural material to build said giant robot. Or like in star gate invent an inertial dampener. Anyway, the next big issue is power, I really don't like fission / fusion based power supplies cause unless you find a reaction that purely generates electrons at potential, you have a ton of waste heat to deal with. My fave would be the Arc Reactor concept. You take some new metaloid, make a toroid out of it, coat it with a fancy refracting insulating polymer, wrap some room temp super conducting wire around it, use ac induction to bring the reactor to life, and get Q gain on the secondary coil, note: can only build one of these in a cave or back ally Russian based work shop. Or my next favorite power source would be anti matter, but that stuff is really dicey... one itty bitty loss in confinement and good by billion dollar robot and am your 10 trillion dollar kilo of anti matter. For a good example of how really big machines behave, check out the speed of the space shuttle transporter and the foot print of the Big Musky walking drag line.

  • Multiplication Q? says:

    In the example you give, wouldn't the person's heart also increase by a factor of 8? After all, their heart is a volume, just the same as their circulatory system. Every organ should scale up by a factor of: V=w*l*h -> w*l*2h = 2V or w*l*h -> 2w*2l*2H = 8V, if you prefer. The real problem would be that there is now much more heat being produced, which dissipates through the surface area, which only increases by the square. Alternatively, the problem is not that the heart's volume increases at a slower rate than the rest of the body, but that the force required to pump a certain amount of blood a certain distance increases more than linearly. Thus, although the person now has a heart 8X as big, to pump blood 8X as far it has to work 16X. (I'm not sure of the actual equation for the force required to move liquid a certain distance.) Still, the problem isn't with the size of the heart, it's with dissipating the heat output or the force required. Am I misinterpreting?

    • jks says:

      Yes, that post is misstated. The heart will be 8 times as massive/heavy, just like the rest of the body. The problem is that the heart's muscle strength, or blood pushing power will only be 4 times as strong. Same goes for every muscle and bone in the body. 8 times as heavy, 8 times as massive, only 4 times as strong, only 4 times as durable. At some point the weight/mass will overtake the strength/durability. An elephant is unbelievably powerful, but it can be killed by it's own weight i.e. falling.

  • The "Square-Cube Law" is also why Voltron is a cartoon, and why the Zords and monsters on Power Rangers are models.

  • neko says:

    I think the movie's science is terrible, but this is yet another article where most of these aren't actually problems. The Kaiju aren't made using earth biology... although they seem to have organs, you can just insert whatever exotic materials, since they bleed floursent blue toxic waste, I'd say comparison to elephants and mice is almost as silly as they are to begin with... why would you think the mouse model would work when the monsters are composed of unknown chemicals?

    As for the machines, I see other people have covered the topic already above. The Jaegers seem to be mostly hollow and are composed of uknown materials tech. It's dumb to build a weapons system like that anyway.... that's really a much larger problem.

    I have to say, sometimes too much physics confuses you. Every physics student seems to begin restating the problem with the unspoken "Assuming the mass is evenly distributed and it's a geometric solid... "

    Of course that often works and simplifies the problems, but engineers must all now begin rolling their eyes and shaking their heads. Well, as long as it's all academic, be my guest.

    • Suresh says:

      Newton never expected someday skyscraper will be built,he would have said skyscrapper will collapse on it own gravity(he didnt know about steel).Enstein never thought his E=mc2 is feasible until he saw world going nuclear.They all underestimated technocrats.What if jaeger's feet & its lower legs are made of steel & irridium and rest of the body with titanium.Also some parts by graphene.Not talking about cost now.

      • Tolotos says:

        I think Graphene would be required for almost all the parts, as the whole robot would just be too heavy otherwise. And Graphene is much stronger than any other material anyway.

  • jason says:

    the dual driver mind thing was just way to far out i mean how stupid is this writer we can control robots using a suit now size would not matter ask any crane driver

  • George says:

    Actually, the Kaiju should suffer from the same problem, yet can FLY.
    I think the Kaiju, being from a parallel dimension, don't follow the same natural laws we do, and thus neither do the jaegers, made using science founded in Kaiju biology.

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  • You forgot to mention that the sea water was wet.

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  • Itse says:

    The Main reason that we can't build giant man controlled robots is that our government can 't pay
    The cost's if they do they would be broke of course there are Some problems to solve but it isn't impossible

  • Carcotas says:

    Within the opening 15 or so minutes Charlie Hunnam's voice-over establishes the reality of a future where monsters (the Kaiju) repeatedly invade earth, to stem this humans have created giant robots (Jaegers) to combat them in increasingly badass iterations. This opening does a great job in conveying the scope of a film which is big, not just regular big, but like, Jason Biggs in 1999 bigg. entering the cinema from a world where these events rarely occur is initially a lot to throw at the audience, but it's handled so effectively and without tongue in cheek that it quickly becomes a world I had a blast experiencing. Maybe it was the incredible effects shots of robot related destruction used as a throwaway shots, but what I think really sold the opening sequence and the film as a whole is the enthusiasm Del Toro clearly has for the story he's telling.

    The cast is essentially a rogues gallery of TV's better dramas playing variations on roles they've nailed in the past (see: Elba, Hunnam and Klattenhoff) and some inspired casting of It's Always Sunny's Charlie Day who, as should be expected provides some effective comedic relief. Added onto this the score comes courtesy of Ramin Djawadi who's masterful use of themes on Game of Thrones is carried over to this film for some great emotional cues and many a rad motif courtesy of Tom Morello on guitar.

    It's appropriate Del Toro has a Frankenstein adaptation lined up as a follow up project as Pacific Rim can at times can feel stitched together from all the sources of inspiration the film has. This comes from many areas such as Japanese manga, the personalities of the actors from previous films and the imagery of robots destroying buildings which transformers ran into the ground. But Del Toro succeeds time and time again at allowing these disparate elements to fit together believably by way of some very confident filmmaking. I could easily take issue with the oft hammy dialogue and macho relationships but where the film succeeds in other areas and revels in creativity trumps the dissatisfaction one could take from these scenes. I also found Hunnams character a tad lacking in charisma and internal conflict but whatever, it's not the end of the world. Oh wait, yes it is hahahaha…

    The films successes go beyond its imagery and continued invention within battle scenes as the script is very economical when it comes to pacing. The films battle scenes are so engaging and exciting due to clearly established stakes present which left me devoid of the "action fatigue" transformers loves to throw my way. And although the Kaiju battles seem to never be in short supply, the film essentially follows the rule of three when it comes to battle sequences and left me oh so satisfied.

    In conclusion, I give it points for being one of the funner summer blockbusters in recent memory, for being an original property and for its sheer tenacity to exist which all amount to what is just a darn good time at the movies.

    More about the movie you can also find it here

    http://movieinfodb.com/en/movie/68726/Pacific+Rim-2013

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  • Duke says:

    Explain Sauroposeidons then. Those dinosaurs were freaking huge.

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