Spider-Man (2002)
[NR] Starring:Tobey Maguire, Willem Dafoe, Kirsten Dunst, James Franco, Cliff Robertson, Rosemary Harris
Directed by:Sam Raimi
Screenplay by:David Koepp
Based on the Comic Book Created by:Stan Lee, Steve Ditko
 

When awkward-acting Peter Parker (Tobey Maguire) gets bitten by a genetically altered spider he gets a shot at the ultimate nerd fantasy, knowing he has alternatives. While walking away from a confrontation may be the best alternative, it's nice to know it's not the only one. Maguire discovers this new found knowledge when he's accosted by the local school bully. The bully end up flying horizontally down a hallway. It was such a feel-good moment that we hardly noticed the questionable physics.

Meanwhile his friend's father, Norman Osborn (Willem Dafoe), gets a little hurried on one of his science experiments and overlooks a few details. Subsequently, he turns himself into an extremely strong homicidal schizophrenic. This eventually leads to a climactic showdown with Maguire but not until Maguire has several adventures alternating between saving innocent strangers and rescuing his love interest.

The whole movie is based on the scale-up fallacy which assumes that a small creature like a spider will have the same  strength-to-weight ratio when scaled up to a larger size (see Scaling Problems). For example, the scale-up fallacy indicates that a strand of spider web scaled up by a factor of 100 would still be able to carry 50 times the spider's weight if it could carry 50 times the weight of a spider in its normal size. Unfortunately, it doesn't work that way. The scaled-up web will only be able to carry half the spider's weight even though the web material is still stronger than steel. The diameter of the web strand would have to be increased by a total factor of 10,000 not merely 100 in order to carry 50 times the oversized spider's weight.

A spider's seemingly awesome strength is related primarily to its small size, not superior genetics. For example, if a spider can jump 50 times the length of its body, then the same spider scaled up by a factor of 100 will only jump half a body length. Spiders can react faster than a human because they have far less distance to send nerve impulses and far less inertia to overcome. They also have a much smaller and more specialized brain. Scale a spider up by a factor of 100 and it would barely be able to function, that is, if it didn't collapse due to its own weight.

There's also the web volume problem. A web strand would probably need to be at least 0.5 cm in diameter to support Spider-Man's web-swinging antics. If such a strand were 100 meters long, it would have a volume of 0.00196 m3 compared to Spider-Man's estimated volume of 0.0726 m3. Spider-Man will lose 2.7% of his volume every time he shoots a 100-meter-long web. Web swinging a mere kilometer of horizontal distance would use up 38% of his body volume (assuming his web makes a 45° angle with the vertical at the beginning and end of each swing and each web is 100 meters long). He would be skeletal by the time he arrived and would have to eat huge volumes of food to compensate.

Of course, this analysis assumes that the volume of the web producing chemicals stored in spidy are the same as the volume of the web they produce. However, even an error of a factor of two in the web volume analysis would not change the basic conclusion. Spidy's volume is going to go up and down a lot if he does much web swinging.

Our calculations indicate that Spider-Man could attain fairly high speed while web swinging. However, it would not be easy to land on moving cars. When he swung downward he'd speed up. When he swung upward he'd lose much of his speed. To prevent this loss of speed he'd have to extend a new web before he reached the bottom of his swing. If the web was too short it would fail to attach, too long and he'd swing into the ground. During his trip he would constantly be changing his height and velocity. Controlling his travel would be a nightmare.

To make the rapid web-swinging journeys, Spider-Man would also have to extend webs at much higher speeds than his rate of travel. Considering the large mass of the webs, shooting high-velocity strands would create a recoil problem. Again, such a mode of travel would be a real problem.

Still, Spider-Man is based on a comic book, and so we should expect comic book physics. It's like an implied contract. We're supposed to suspend our disbelief at least partially, and so we hesitated to even review it. However, it does have some interesting scenes to discuss.

Possibly the least-believable scene occurs when Dafoe, in the form of the Green Goblin, severs the cable to a cable car filled with children. Dafoe stands high atop a structure with the cable in one hand and Spider-Man's girlfriend in the other. If we assume the cable car and children weigh 4000 pounds (1818 kg), and the cable is massless and makes a 5° angle with the horizon, we can calculate the sideways force created on the Goblin as follows:

F = W/(2·tan q)

Where F is the magnitude of the force in the horizontal direction, W is the weight of the cable car and children, and q is the angle between the horizon and the cable.

       
  F =
    W

2 Tan q
       
  Where:
    F= the horizontal force
    W = the weight of the cable car and children
     q = the angle between the horizon and the cable
       

The side force would be about 23,000 pounds (102,000 newtons). Even if we suspend our disbelief that the Goblin could hold on to the cable, there is no way his feet would have enough friction to keep him from being pulled sideways, yet the Goblin doesn't even have to strain.

Spider-Man makes us willing to suspend most of our disbelief by giving us interesting characters, dialog, and an actual plot. Its unrealistic physics are used as a story-telling device not just as an end in themselves. The movie has heart and struck a chord in many areas. Obviously, there will be a Spider-Man II, so let's hope the moviemakers continue to use some restraint and don't allow it to degenerate into just another mindless action piece.

 


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