The Semi-Amazing Spider-Man

Anybody still read newspaper comics these days? I do, but sadly for the newspaper business I read them online. Worse, usually in the context of people making fun of them. On the other hand, there are a few gems out there. Is Spider-Man one of those gems? Uh...

Well, Shakespeare it ain't. But is Spider-Man justified in his optimism about being able to catch Mary Jane? If Doc Ock just drops her instead of throwing her (as he seems to suggest), she'll start with zero velocity and immediately begin to accelerate at 9.8 meters per second squared vertically downward. As soon as Spider-Man jumps to catch her, he'll do the same thing. To his advantage he's got webbing he can shoot to catch her right away, he doesn't have to do the classic Superman catch. Regardless of how he stops her, he has to do so smoothly and gently. It's a cliche but true nonetheless that it's not the fall that kills you, it's the stop. With plenty of time to catch her it's not a problem and I think she'd be safe here.

But what's more interesting is the worst-case scenario where our superhero is standing at ground level and has to catch the falling victim. It's a frequent conceit, but how realistic is it. Turns out, not very.

The velocity of an object falling from a distance h is:

This has to be reduced to zero before the victim hits the ground. The acceleration necessary to do this over the short distance between the point of catch and the ground (call it x) is:

Both of these equations come straight from the standard laws of 1-d accelerated motion. Substituting the equation for v into the equation for a, we get:

It's a simple equation, but a telling one. A human being wearing a seat belt in a car crash can generally sustain around 15 g's worth of acceleration without serious injury. Beyond that we rapidly climb the thresholds of serious injury and death. But the equation tells us that the required g force to stop the victim before hitting the ground is just the ratio of the initial fall height to the stopping distance. If Spider-Man brings her to a stop in 1 meter, she had better have fallen from 15 meters or less if she wants to escape injury. It doesn't matter how super-powered he is, that's just physics. If she falls from hundreds of feet, she's dead unless the catching process begins well above the ground.

Interestingly, the comic book Spider-Man is one of the very few characters who have actually dealt with this realistically - at least once. The comic book Gwen Stacy character dies when Spider-Man catches her too abruptly, killing her. Nobody said physics was always fun.

[At least a few of y'all did a few Amazon.com purchases from this site's link yesterday. Thanks, and thank you if any of the rest of you do it in the future! It's greatly appreciated and will go a long way. -Matt]

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How do you explain a man diving from 35 feet into water having a depth of 1 foot and living? Was that 35 g's? I believe the record is about half a foot of water, so that should be about 70 g's.

You should look at some facts before saying something like 15 g's being the threshold for injury. Our bodies are much tougher than that. One simple example would be the data in Table 1 on page 3 of this document

http://www.iihs.org/ratings/protocols/pdf/measures_frontal.pdf

that sets the thresholds used to evaluate car crash data. Note that an acceleration of 60 g's (as your back presses into the seat) and a chest compression of 5 cm (2 inches!) is considered "good". This is in the range where you walk away from the accident but have a nasty "survivor's bruise" across the chest from the shoulder harness compressing your chest, although some persons with a lighter build might suffer serious injury or death at that level. IIRC, the thresholds are set from an LD-50 (half die) of something like 80 g's to the chest, but I can't find the place where NHTSA documents what it uses for its 1 star (46% injury) cutoff in terms of forces or accelerations.

Also notice their discussion of 70g accelerations of the head. A recent story (August 26, 2009) on NPR (about looking for a link between concussions and early on-set dementia in NFL players) stated that impacts can produce 100 g to the player, usually to the head.

By CCPhysicist (not verified) on 02 Sep 2009 #permalink

That good rating still produces a 20% risk of "severe" injury. The 15g value I found was apparently a typical injury threshold, above which injury becomes probable. Keep in mind we're talking about two relatively thin arms, not an airbag or a cushion. In any case the main qualitative point is not affected - falls from appreciable height require more than any two-armed superhero can handle at ground level.

If the superhero can protect the person's head and keep the g shock to minimum duration, then the 35 g's or more should be OK. You can't compare the intellegent application of force to a dumb seatbelt.

(This is starting to sound like a "Seinfeld" episode.)

sometime back I surfed past a program on the physics of Spiderman. They actually had physicists involved in the (I think) second spiderman movie and all of spiderman's activities were said to have been calculated as physically possible. Sorry, as you can see, I didn't pay that much attention.

By Jim Thomerson (not verified) on 02 Sep 2009 #permalink

Hey, thanks for the link! Re: superheroes catching falling mortals: Superman, at least, has something of an out with his power of flight. He could theoretically catch the fallee while more or less matching their downward acceleration, then gradually change velocity, depending on how much room he had to work with.

Josh

Great blog for the web....

Certainly some will be injured, as I stated, but realize that you just confirmed that 80% of the adult population will not get more than a bad bruise when involved in a collision that produces a 60 g acceleration to the chest, and that includes injuries like broken bones when something like a wheel gets driven into the footwell by the crash, not forces to the chest by the seatbelt as you were discussing.

When those forces are spread out more uniformly, like with the 3" belts used in race cars (a better model for what Spidey would do with his web), the risk shifts more toward the internal injuries (like a torn aorta) that appear as you exceed 60 g. Medical books make for fun reading until you start to wonder who did the experiments on whom.

By CCPhysicist (not verified) on 03 Sep 2009 #permalink