Home > Clement's Game, Marvel > Superheroes Round 4: Spiderman

Superheroes Round 4: Spiderman

Spiderman.  There have been four movies in the last decade.  Wow.  I’m mostly going to cover the 2012 reboot, since I just saw that one on a plane, but I’ll give a mention to the others in passing.  As ever, here there be spoilers.

The movie is, in fact, about this guy.  He gets bitten by this spider...

The movie is, in fact, about this guy. He gets bitten by this spider…

Doesn’t Know His Own Strength

This was beautifully done, and I think, not well addressed in other cases where a character suddenly gets a ridiculous strength boost.

The morning after getting bitten by a spider, poor Peter Parker discovers that he lives in a world of cardboard.  He gets up, and tries to squeeze some toothpaste onto his toothbrush.  He overshoots, splatting a whole bunch onto the mirror.  Puzzled, he scrapes a bit off with his toothbrush, then turns the knob of the faucet… breaking it off.  Panicking, he jabs it back on over the water spewing out of the pipe, wraps it in a towel.  When he first tries to open one door, he breaks off the handle.  He manages to open the second door… very, very carefully.

And, consistent with learning to control his strength, he still has occasional oops-too-much moments later in the film.  But, just how strong is Spiderman?


Okay, folks, it’s physics time!

There are several scenes in the film where Spiderman propels himself upward by first throwing a bit of webbing, stretching it, then springing upwards.  Let’s see just how ridiculous this gets.

Per one scene near then end on the OsCorp tower, let’s say the webbing stretches up about 20 m, and that each strand had a diameter of about 0.001 m.  Spiderman stretches the two strands by about his height.  Let’s call that 2 m, just to make the math easy.  That’s then enough energy to vault Spiderman for about the height of the webbing.  Assuming Spiderman weights about 75 kg, that means it takes 15 kJ of energy to send him up that high.  That means he has to store that much energy in the spring (of the webbing), which put the spring constant k at about 7500 N/m.  That’s how much force you have to exert to stretch the webbing per meter.  So, at maximum extension, that implies Spiderman is exerting a force of about 15000 N.  To put this into perspective, that’s enough force to lift a small car.  … and probably also enough force to cause some serious damage to the building, not to mention Spiderman himself.

Doing a little more math with that spring constant and the dimension of the webbing, I can estimate the pressure applied — which comes out to about 5×10^9 Pa, or 5 GPa.  This is approximately the ultimate tensile strength of even carbon fiber… at least according to Wikipedia.  That is, the point at which it starts to narrow in width… which occurs not too long before breaking.  (It’s also beyond the yield point of most materials, which is where they will no longer return to their original shape after stretching.  And the Hooke’s Law discussion above no longer works.)  Thus, the webbing would have to be something like carbon nanotubes…

… then again, these material concerns also apply to Spiderman’s flesh and bone.

Suffice it to say, this trick is a bit of a stretch.

Mass Conservation

Shapeshifters goof this one up all the time.  And it bothers me.

In this case, it’s Dr. Curt Connors first regrowing his arm… then growing into a superhuman lizardman.  I mean, come on.  Where is the mass for all of the extra muscle and bone coming from?  Was he guzzling a bunch of protein shakes and some bone meal beforehand, or what?  And he’s not the only one with this problem — The Hulk, Mystique, The Thing… where does all that mass come from?  Or go, when they shrink back down?  At least for Connors we get to see the material all peel away when he de-powers.

There’s one book I’ve read before, where werewolves existed.  However, transformation was not only messy, but any bits that “fell off” got eaten in order to converse mass.  So, they weighed the same before and after.  And they were also hungry a lot of the time.  I’d say what book it was, except I can’t remember the title or the author, and it wasn’t all that great.

Unconscious = Dead

Whenever somebody dies heroically on film due to being shot or the like, people start mourning as soon as the person passes out.  The person’s probably just in shock (at least to start with) due to blood loss and so forth.  They’re not dead yet.  Call an ambulance, do CPR, try to slow the bleeding… stuff like that.  Don’t just start crying like there’s nothing you can do.  And it happens twice in this film!

Seriously, Spiderman, take a first aid course.

  1. michaelbusch
    2012/12/19 at 7:47 pm

    Another problem with the webbing:

    20 m of webbing with a 1 cm^2 cross section and a density of 1 g/cm^3 masses 2 kilograms. That slingshot maneuver costs Parker >5% of his body mass.

    The more webbing he uses, the more mass he goes through. A few-kilometer trip across the city would need more mass than than Parker’s body.

    Welcome to The Physics Of Superheroes.

  2. 2012/12/20 at 2:30 am

    Hm. I was assuming a rather smaller cross section (.1 cm)^2 due to some of the scenes earlier, which would save a couple of orders of magnitude on the mass — so he’d only be lugging a couple of kilos of mass in his webslingers. In the new movie, he actually made a device for this, rather than the difficulties of growing spinnerets in his wrists.

    That still seems like rather more volume than he can fit on in the costume shown, at 20 cm^3 per shot in the small-cross-section case, unless there’s a lot of compression going on. We know there has to be some, otherwise the webbing wouldn’t be able to fly upward 20 m…

    On the plus side, the larger cross section makes some of the material problems with the strength of the webbing less of an issue. Then again, the forces are still a problem.

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