The Physics of Superheroes: Spectacular Second Edition (53 page)

Fig. 42.
Panel from
World’s Finest # 86,
where the Man of Steel demonstrates a much-improved strength level compared with his first appearance in
Action # 1,
where he lifted an automobile over his head, provoking the startled onlookers to flee in panic. In contrast, no one in the amphitheater is overly perturbed that a flying man is carrying two high-rise office buildings over their heads.

If we compare Giant-Man to a redwood tree (and not just because his personality was sometimes a little stiff), we note that the taller the tree, the wider the trunk. In order to provide support for the large mass above it, a tree needs a very broad base. Around the time of the signing of the American Declaration of Independence, two mathematicians, Euler and LaGrange, proved that a column shorter than a certain height is stable, and will be compressed by the weight of material pressing down on its base, but above a certain height (whose value depends on the strength of the material comprising the column), the tower becomes unstable against bending. The slightest perturbation away from a perfectly vertical orientation leads to a large twisting force, that is, a “torque,” as in the case of the seesaw in Chapter 8, that will cause the column to bend under its own weight. Giant-Man could, in principle, grow as tall as a redwood tree, but he would have to be just as mobile (assuming he stayed below the height limit set by the cube-square law—see Chapter 25). Any attempt to run after or fight a supervillain would inevitably lead to the upper portion of his body leaning forward over his legs. The weight of his upper trunk would then cause his body to rotate, and before you could say “Stan Lee,” old High-pockets would be flat on the ground.

Just such a fate inevitably befell Stilt Man, an early foe of Daredevil’s. Stilt Man possessed a mechanized suit that contained two hydraulic legs that, when fully extended, enabled him to stand several stories tall. As sure as summer follows spring, Daredevil would use the cable in his billy club to tangle up Stilt Man’s legs, and the resulting loss of stability would bring the issue’s adventure to a rapid close.

Another mystery related to the center of mass is how Spider-Man’s foe, Doctor Octopus, is able to walk. Research scientist Otto Octavius employed four robotic arms that were attached to a harness around his waist, with which he manipulated radioactive isotopes. The inevitable explosive radioactive accident caused this harness and the arms to be fused to Octavius, and Doctor Octopus was born. But these arms are very heavy, and we frequently see him standing on his two legs while all four arms move behind him! They should therefore create a large torque that would put Doc Ock flat on his back, or on his face if they’re in front of him. Spidey should be able to disable (if not disarm) Doctor Octopus by simply tossing an apple at him whenever he spots the arms not anchoring him to the ground. The quick and unsatisfying resolution of these stories when the physics is taken too seriously should make abundantly clear why there is not a great demand for physics professors to write superhero comic books. Careful viewers will note that in the film
Spider-Man 2,
the filmmakers took care to ensure that Doc Ock always had his heavy robotic arms balanced around his body, or some of them tethered to the ground, in order to give Octavius at least some stability. After all, they couldn’t feature it in a film if it wasn’t true!

Another unrealistic feat of strength occurs in the conclusion of a 2001 adventure of the Justice League (by this time they had dropped the “of America” part of their team name, though the comic featuring their adventures still went by the acronym JLA). In
JLA # 58,
Superman, Wonder Woman, and Green Lantern are shown pulling the moon into Earth’s atmosphere in order to defeat a group of renegade Martians. Perhaps I had better back up and explain why they considered this a good idea.

Martians were introduced into the DC universe in 1955’s
Detective Comics # 225,
when a physics professor trying to develop an interstellar communication device accidentally created a transporter beam instead. He thereby forcefully brought J’onn J’onzz (the Martian Manhunter) to Earth. J’onn eventually adopted a costumed identity as a superhero crime-fighter, and was a founding member of the Justice League of America back in 1960. J’onn J’onzz possessed a dazzling array of superpowers that matched Superman’s—including flight, superstrength, invulnerability, Martian-breath (equivalent to Superman’s super-breath), super-hearing, Martian vision, and several that Superman could only dream of, such as mental telepathy, invisibility, and shape-shifting. Just as Superman needed Kryptonite to keep him from always solving every problem in a nanosecond, the Martian Manhunter, being more powerful, required an even more common Achilles’ heel in order to justify why he would ever bother teaming up and forming a league with other superheroes. It was therefore revealed that J’onn suffered, as did all Martians, from a vulnerability to fire. Consequently, rather than having to search for an exotic meteorite from the doomed planet Krypton, all you would need is a penny book of matches to incapacitate the Martian Manhunter.

It was revealed in the pages of JLA that J’onn J’onzz is mistaken when he considers himself the last survivor of the Martian race, when the Earth is attacked by a small army of evil Martians, each one possessing J’onn’s superpowers. The Justice League lures the evil Martians to the moon, where the lack of an atmosphere convinces the Martians that they have no reason to fear a fire weakening them. However, while J’onn J’onzz uses his mental telepathy to distract these villains, Superman, Wonder Woman, and Green Lantern employ an enormous cable to drag the moon into the Earth’s troposphere. An array of magic-based superheroes use their mystical powers to prevent both the moon and the Earth from suffering geological catastrophes from their intense gravitational attraction. Our satellite now possesses a combustible atmosphere, and the evil Martians quickly surrender and submit to banishment to another dimension (the Phantom Zone, in fact) rather than being incinerated. Even if you grant all of the above as one major-l eague miracle exception, there is still a serious physics problem with this story line.

Newton’s second law,
F
=
ma
, tells us that if a net force is applied to a mass, no matter how large, there will be a corresponding acceleration. By the late 1990s DC Comics had established that Superman was capable of lifting eight billion pounds. Let’s assume that, given the enormous stakes, both Wonder Woman and Green Lantern exerted themselves to provide an equivalent force as they pulled on the moon. So the total force that these three heroes can supply is twenty-four billion pounds. Since the magic-based heroes are nullifying the effects of gravity, we’ll assume that as the moon comes closer to the Earth there is no assist from Earth’s gravitational field (this will keep the calculation at a simple level). The moon has a mass of nearly seventy billion trillion kilograms. Newton’s law therefore indicates that the moon will indeed accelerate owing to this force, but the rate of change of motion will be very, very small. The acceleration of the moon will be 5 trillionths feet/sec
²
(the acceleration due to gravity on the surface of the Earth is 32 feet/sec
²
), and so it will take a very long time to displace the moon a significant distance. At this acceleration, the time needed for the moon to travel roughly 240,000 miles from its normal orbit to within our upper atmosphere is more than 735 years! We can only conclude that J’onn J’onzz performed some outstanding stalling in order to keep the evil Martians from realizing what was going on for more than seven centuries!

Another of the original members of the mutant team the X-Men introduced in 1963 was Warren Worthington III, whose mutant gift comprised two large, feathered wings growing out of his back. None of the other members of this superhero team possessed the power of flight, and aside from Iceman’s ice ramps, the Angel was the only character who could avoid walking or taking the bus when called upon to face off against the Brotherhood of Evil Mutants.
⁸⁵
Other winged superheroes or villains, such as DC Comics’ Hawkman or the Spider-Man villain the Vulture, used “antigravity” devices such as Hawkman’s Nth metal, to overcome gravity. They employed their wings connected to their backs in the case of Hawkman or Hawkgirl or sprouting from his arms for the Vulture, as steering devices to help them maneuver while airborne. In contrast, the X-Men’s Angel used his wings as a means of levitation. It certainly seems reasonable that having wings growing out of your back would enable you to fly, but could it really?

Birds and planes manage to slip the surly bonds of gravity through Newton’s third law—that for every action there is an equal and opposite reaction. A common misconception is that the pressure change induced by a fast-moving object (termed the Bernoulli effect), underlies how airplanes fly. We encountered this pressure differential when we considered the Flash dragging Toughy Boraz behind him in his superspeed wake in Chapter 4. A fast moving object such as the Scarlet Speedster must push the air out of his way as he runs, and consequently leaves a region of air with a lower density behind him. As the air races back to fill this partial vacuum, through the same principle as in our discussion of entropy in Chapter 13, it will push anything in its way, such as the litter swirling behind fast moving traffic or trains. However, if the difference in wind speed above and below the wing is a result of the wing’s contour, then planes should not be able to fly upside down, because the pressure difference generated by the Bernoulli effect would tend to push the plane toward the ground.

In any case, we can always rely on Newton’s third law, which tells us that forces always come in pairs. To provide an upward force on the airplane wing equal to or greater than the weight of the plane, an equivalent downward force from the wing must be applied to the air moving past it. The down draft of air in the region underneath the wing results in an upward lift that carries the plane into the wild blue yonder. When Superman leaps, he pushes down on the ground so that an equal and opposite force pushes back on him, starting him up and away. Similarly, birds flap their wings, pushing a quantity of air downward. The downward force of the wing on the air is matched by an upward force by the air on the wing. The greater the wingspan, the larger the volume of air displaced, and the greater the corresponding upward force. This is why it is impossible for Prince Namor the Sub-Mariner to fly using his tiny ankle wings. These petite wings are too small to provide sufficient lift to counter Namor’s weight.

If Warren Worthington III weighs 150 pounds (equivalent to a mass of 68 kilograms), then his wings must provide a downward force on the air of at least 150 pounds, such that the air’s reaction on his wings balances his weight and keeps him above the ground. Of course, if he wants to accelerate, then his wings have to provide a force greater than 150 pounds in order for there to be an excess force (upward lift minus downward weight due to gravity) to provide a net acceleration. If his wings provide an upward force of 200 pounds while gravity exerts a downward force of 150 pounds, then Warren experiences a net vertical force of 50 pounds. Force equals mass times acceleration, so this upward force of 50 pounds creates vertical acceleration of 11 feet/sec
²
. With this acceleration, the Angel will go from 0 to 60 mph in a little more than eight seconds, neglecting the considerable air resistance that he would have to overcome. Once he stops flapping his wings, the only force acting on him is gravity pulling him back to Earth. Of course he can glide once airborne, but he must continue to apply a downward force on the air to truly fly and not coast.

Two hundred pounds is a considerable force for his wings to apply, but it is not unreasonable that a person could bench press 133 percent of his body weight. Birds such as the California condor or the wandering albatross weigh roughly thirty or twenty pounds, respectively, and yet are able to generate sufficient force to fly. But Warren Worthington III is not built like a bird. Birds do not have wings growing out of their backs—their arms have evolved into wings. They have two additional modifications that assist their arm-wings: (1) They have a keeled sternum bone—that is, birds have a hinge built into the flat bone in the center of their chests that is comparable to your rib cage. This hinge acts as an anchor point for their other adaptation, namely (2) birds have two extremely large chest muscles, the supercorocoiderus and the pec toralis, used for beating their wings. Birds have so much breast meat because they need these muscles, their pectorals, to be large, as they provide the majority of the force to the wings in flight. Recall from chapters 8 and 25 that the strength of bone or muscle increases with its cross-sectional area. Consequently, the Angel must have enormous pectorals if he is to be able to use his wings to get off the ground. With a wingspan of 16 feet and a weight of 150 pounds, Warren has a weight-to-wingspan ratio of nine pounds per foot, in contrast to a ratio of three pounds per foot for a California condor. Warren’s arms do not participate in supplying a force to his wings, and he must provide an upward lift using only his chest and back muscles, making him a muscle-bound—and fairly ineffective superhero.

There are other adaptations for flight that Warren could possess that would require additional miracle exceptions. To reduce their body weight, birds have lightweight bones, with a very porous structure that yet remains remarkably strong. Birds also have very efficient respiratory systems, so that every single oxygen molecule residing in their lungs is replaced within two deep breaths. In contrast, with every breath we take, we exchange only 10 percent of the air molecules residing within our lungs. Birds need to be able to rapidly refresh their air supply, as their breast muscles are working so hard to maintain them aloft. Warren’s breathing could be similarly efficient. But for all this, unless he is to be drawn with enormous pectoral muscles—more fitting for some of the female superhero characters from the 1990s—the wings on his back are more ornamental than functional.