The Physics of Superheroes: Spectacular Second Edition

by Kakalios, James

  Unstable molecules may do the job in the Marvel universe, but what keeps the Justice League of America’s uniforms intact in DC comics? A variety of explanations have been provided for the durability of superhero costumes in the DC universe, all with a slight patina of scientific justification. Back in the Silver Age, it was explained that Superman’s costume was composed of the same fabric that the baby Kal-El was swaddled with, when his birth parents sent him off in a rocket ship to Earth moments before Krypton’s destruction. The fabric’s extraterrestrial origin accounted for its indestructibility. In later years, it was posited that a thin aura of invulnerability extended from the Man of Steel’s body, which is why his suit could survive devastating forces or being in the heart of the sun, but his cape would not escape damage. This same protective aura also accounted for the Flash’s costume being able to resist shredding when the Scarlet Speedster ran at his top velocity.

  Batman’s costume would display the wear and tear that one might expect would result from fighting crime in Gotham City. Similarly, Spider-Man, being more of a loner in the Marvel universe (at least when he first appeared in the 1960s) was apparently not on the “unstable-molecule distribution list,” and he would regularly also have to deal with a torn and damaged costume (not having Batman’s advantage of a millionaire alter ego and a live-in butler, this was more of a burden on Peter Parker, living with his aged aunt in Queens, NY).

  The DC hero the Atom had a unique solution to the problem of needing a costume that accommodated his shrinking power. As will be explained in detail later, the Atom’s ability to change his size and weight from his normal six feet and 180 pounds down to essentially zero feet and zero pounds stemmed from his mastering miniaturization technology that employed a remnant of a white-dwarf star. This exotic material was fashioned into the Atom’s blue and red costume. The miniaturization mechanism that enables the Atom to fight crime at six inches or six nanometers is built into his costume—consequently, his superhero suit is covered under the same miracle exception that accounts for the Atom’s powers. In fact, the Atom never has to worry about changing out of his street clothes because his costume only appears when he is reduced in size. When he resumes his normal height, his costume stays miniature, and his street clothes grow with the rest of him. Consequently, the Atom is the only superhero who deliberately gives himself a wedgie whenever he returns to his secret identity!80

  Now that we have addressed the materials science underlying their uniforms, we come to the two main rules of superhero costumes. Rule One: No capes! Rule Two: Accessorize! We next turn to the physics issues concerning some of the more famous crime-fighting accoutrements.

  DOOM OF THE STAR DIAMOND

  Two years after the Caped Crusader made his debut in Detective # 27 in 1939, another millionaire playboy took up a costumed identity, also fighting criminals without the benefit of superpowers and armed only with his wits and a variety of technological weapons of his own design. Green Arrow was a fairly transparent attempt to replicate Batman’s earlier success. Millionaire Bruce Wayne would dress like a giant bat and, together with his teen sidekick Robin, drive from the Batcave in the Batmobile to Gotham City, where he would use the high-tech wonders in his utility belt to fight common criminals and costumed villains. Millionaire Oliver Queen, on the other hand, would dress in a modified Robin Hood costume and, together with his teen sidekick Speedy, drive from the Arrow Cave in the Arrow Car to Star City, where he would use a quiver full of “trick arrows” to fight common criminals and costumed villains. Green Arrow’s technological wonders included a boomerang arrow, an exploding arrow, a handcuff arrow, a boxing-glove arrow, an arrow that projected a net near a target, an acetylene-torch arrow, and, particularly useful for underwater adventures, an aqua-lung arrow. I understand why you might need to bring a small breathing tank along with you on an underwater case, but what possible benefit you would derive from mounting it on the head of an arrow, I cannot begin to imagine.

  Making his first appearance in the same issue of More Fun Comics that featured the debut of Aquaman, Green Arrow was created by writer Mort Weisinger (who also co-created the Aquatic Ace) and drawn by George Papp. Both Green Arrow and Aquaman would continue to be published through the transition period between the Golden Age of comics and the Silver Age, appearing as backup features in issues of Superboy comics. While Aquaman was one of the original set of heroes tapped for membership in the Justice League of America in 1960’s The Brave and The Bold # 28, Green Arrow would not be offered membership until a year later, when he managed to save Wonder Woman, Aquaman, Flash, Green Lantern, and the Martian Manhunter from the “Doom of the Star Diamond” in Justice League of America # 4. As shown in fig. 41, the JLA were trapped within a large diamond prison, and were freed only when Green Arrow struck the crystal cage with a diamond-tipped arrow, fired with sufficient force at the only stress point of the diamond prison. The conclusion of Green Arrow’s first adventure with the Justice League demonstrates some real materials science, related to crystalline defects, elastic-strain energy of bows, and the centuries-long history of trick arrows.

  Let’s first consider the diamond trap holding the Justice League. Diamonds are hard to break not because they are dense, but because the carbon atoms in the crystal are connected via very stiff covalent bonds. The strength of a material is primarily governed by the nature of the chemical bonds holding the atoms together in the solid phase. The strongest chemical bonds are termed “covalent bonds,” where the individual atoms quantum mechanically share their outermost electrons with their atomic neighbors. In order to break these bonds, one must remove the electrons from all of the bonds connecting an atom to all of its neighbors. How the carbon atoms are configured relative to their neighbors will determine the strength of the bonds. It turns out that the overlap of the electronic matter wavefunctions that occurs when the carbon atoms all lie in a plane results in stronger bonds between the carbon atoms than those in a diamond. That is, the carbon planes that peel off on a sheet of paper when writing with a pencil have stronger bonds than those in a diamond crystal. Flaws or imperfections in a diamond occur at regions in the solid where atomic bonds, through strains or the inclusion of impurities, are broken or weakened. It is at these locations where the covalent bonding network is easiest to break, either by a jeweler cutting a diamond or by Green Arrow with his diamond-tipped arrow.

  Fig. 41. Green Arrow, about to conduct an empirical test of stress fracture in covalently bonded solids, in Justice League of America # 4 (May, 1961).

  The construction of an archery bow also involves considerable materials science, as a premium is placed on substances that can be bent without breaking. A bow is essentially a spring, and the stored potential energy in the bow is converted into kinetic energy in the arrow. Recall from Chapter 12, and our discussion of the Principle of Conservation of Energy, that the definition of Work in physics is when an external force is applied across a given distance. Pulling back on the bowstring does not change the length of the string—the force supplied by the archer results in the flexing of the bow. The ideal bow will store the most potential energy per mass—that is, one wants a lightweight bow that is nevertheless strong and elastic. In materials physics, an object is termed “elastic” if, following compression or stretching, it returns to its original configuration. If the force results in a permanent alteration, then this is called a “plastic” deformation.

  As it relates to Green Arrow, the larger the force necessary to reach the elastic/plastic transition, the more force he can apply without fear of breaking his bow. The more potential energy that can be stored in the bow, the more kinetic energy can be transferred to the arrow. In turn, the faster the arrow leaves the bowstring, the greater the distance it will fly through the air. With a superior bow, one could stand farther from the target and still score a bull’s-eye effectively.

  It has been said that the British longbow archers of the Middle Ages were the finest in the world. In the battle of Agincourt in 1
415, despite having a nearly ten-to-one advantage in troop size, fifty thousand French soldiers were defeated by six thousand British soldiers, of whom roughly 4,800 were longbow archers. Nearly none of the French troops were archers, demonstrating the advantage that superior technology provides in warfare. While the British archers were no doubt accomplished, it was their longbows made of yew wood that secured their victory. Of all the woods available for constructing a bow, that of the yew tree has the greatest strength-to-weight ratio.81 A cross-section of a yew tree finds an outer ring of softer sapwood, which is highly elastic, and an inner core of harder heartwood. By forming a bow from the interface of these two regions, the inner layer of heartwood resists compression upon bending, while the outer layer of sapwood’s elasticity enables the bow to quickly spring back to its original configuration when released. Of course, any knots or imperfections in the wood would act the same as defect points in a crystal, where fracture would be likely to occur. Consequently, it was difficult to extract more than one functional longbow from a single yew tree. Their superior stress/strain properties ensured that this type of lumber commanded a high price by the British monarchy—with the effect that by 1600, there was massive deforestation of yew trees throughout all of Britain and Europe. Recently, yew trees and shrubs have returned to Europe and the United States, and this time they are desired for their lifesaving properties. The bark of Pacific yew trees was, up until recent advances in synthetic fabrication, the primary source of the anticancer drug Taxol (generic name paclitaxel), and once again, groves of these trees were highly valued.

  Modern science and materials research have led to vast improvements in archery technology. The design of the bow itself has been subject to innovation, most notably in the 1960s, when Holless Allen invented the compound bow. By adding pulleys at the ends of the bow, a mechanical advantage is provided that increases the applied force provided by the archer pulling back on the bowstring and thereby increases the stored potential energy. The composition of the bow has also evolved from the sixteenth century. The strength-to-weight ratio of yew wood has been eclipsed by carbon fiber-reinforced polymers, which combine the high bonding strength of graphitic carbon-carbon bonds with the low-bulk density of plastics. Graphite filaments are braided into fibers, and once aligned, are epoxied into a particular form. These composite materials are finding applications not just in archery, but in other sporting equipment, in high-performance race cars, in helicopter blades, and even in bridge supports.

  The only thing stronger and lighter than a composite of graphite fibers is a single filament of carbon, called a carbon nanotube. These materials consist of a single sheet of graphite rolled up into a hollow cylinder only three atoms in diameter and a single atom thick. Since the strongest covalent bonds are between carbon atoms in the planes of graphite, these carbon nanotubes, if synthesized free of defects, can have a strength-to-weight ratio two hundred times greater than steel, and twenty times stronger than spider silk. If these nanometer filaments can be synthesized in macroscopic lengths, a carbon nanotube cable only one millimeter in diameter could support a weight of nearly fourteen thousand pounds—a fiber no wider than the period at the end of this sentence could hold up two average-size sport-utility vehicles. An indication of how strong carbon nanotubes are can be found in Tony Stark’s investigations of an alternate universe’s Hulk. In an experiment designed to stress test the Hulk, Stark’s researchers are stunned to discover the source of Hulk’s invulnerability—there are carbon nanotubes in his skin!

  One can easily imagine replacing a standard metal or flint arrowhead with one comprised of a large, single-crystal diamond, as employed by Green Arrow in Justice League of America # 4. Adding a small high-intensity siren to an arrowhead, producing a sonic offensive capability, is also plausible. One could incorporate an altitude monitor into the arrowhead, to indicate when the projectile is at the highest point in its trajectory, which could in turn be used to determine when a net could be ejected from the device. Less reasonable are some of the more exotic arrows Green Arrow would use to fight criminals, such as a mummy arrow (which encircled its target in a tight-fi tting cloth wrapping) or handcuff arrows, the aerodynamics of which are dubious at best. But the concept of “trick arrows” is older than Green Arrow comics—by more than one thousand years! Flaming arrows and “Greek Fire” played a major role in maintaining the hegemony of the Byzantine Empire. While the exact chemical composition is still being debated, tipping the arrowheads in a mixture of petroleum and bitumen (sulfur) compounds led to an incendiary projectile that, when ignited, was difficult to extinguish and would even burn when submerged in water. Compared with such lethal “trick arrows,” a boxing-glove arrow seems rather tame.

  BULLETS AND BRACELETS

  In Chapter 22 we speculated that our discussion of quantum physics, coupled with a thorough knowledge of superhero comic books, would provide you, Fearless Reader, with enhanced romantic charms. Indeed, William Moulton Marston, the creator of a founding member of the Justice League of America, was, like Tony Stark and Erwin Schrödinger, a “ladies man” whose personal life would definitely not win approval by the Comics Code Authority.

  In 1921, Marston had a B.A., an L.L.B. (an undergraduate law degree), and a Ph.D. is psychology, at a time when only approximately 3.3 percent of the American population had a college degree or higher. In 1917, he published a paper positing a correlation between a person’s systolic blood pressure and attempts to deceive, which formed the basis of his later claim to being “the father of the lie detector.” Teaching positions at American University and Tufts were followed by a year, in 1929, as the director of public services at Universal Studios in Hollywood. While he had taught at a variety of institutions, he had never obtained tenure, and after 1929, his academic publishing seems to have stopped. At this point, he set upon developing a career as a public psychologist, first in Hollywood, followed by writing a series of books, some technical while most containing popular psychology, and eventually becoming a consulting psychologist for Family Circle magazine.

  It was in an interview in Family Circle in 1940, written by Olive Richard, entitled “Don’t Laugh at the Comics,” where Marston defended comic books as a mechanism for education, rather than dismissing them as cheap, mind-destroying juvenile entertainment. As described in Les Daniels’ Wonder Woman: The Complete History, this article attracted the attention of M. C. Gaines and Sheldon Mayer, who offered Marston a position on the editorial advisory board of DC and All-American comics. Marston would then go on, writing under the pen name Charles Moulton, to pitch a new comic-book character that would serve to illustrate his personal convictions concerning the moral and psychological superiority of woman. In the December 1941-January 1942 issue of All-Star Comics # 8, Wonder Woman, was introduced, and her Amazon strength, bullet-deflecting bracelets, and golden lasso of truth (a personal and portable lie detector) were pressed into service in the four-color fight for justice.

  Because Wonder Woman’s superpowers were magic-based (as opposed to being derived from much more scientific means, such as light from our yellow sun, or being bitten by a radioactive spider), there isn’t too much physics that relates to her exploits, with one notable exception. In her very first adventure, when she competed in Amazonian versions of track-and-field events for the right to accompany American airman Steve Trevor back to the States after his plane had crash-landed on the secret Paradise Island, the final challenge involved the potentially deadly “sport” of Bullets and Bracelets. Two women faced each other and fired pistols at their opponents. The goal of the contest was to deflect the bullets with their wrist bracelets, which were composed of the unique metal Amazonium, worn to remind the Amazons of their previous years in the captivity of men. In this “ultimate test of speed of eye and movement” (as described in 1942’s Wonder Woman # 1), Wonder Woman’s bracelets become “streaks of silver flashes of streaking light as they parry the death thrusts of the hurtling bullets.” Well, assuming that Wonder Woman does
indeed have the speed of Mercury and reflexes fast enough to deflect a bullet, what must the composition of her Amazonian bracelets be to withstand this barrage?

  First, we must ascertain the maximum force that the bracelets must withstand. This involves a calculation of the force that the bullet exerts on the metal band when deflected by Wonder Woman. We will use the same formula from Chapter 3 that we employed to determine how much force Spider-Man’s webbing must exert to stop the falling Gwen Stacy—that is, Force multiplied by time is equal to the change of momentum. In order to deflect a bullet with a mass of 20 grams traveling with a muzzle speed of 1,000 feet/sec, with a time of collision of one millisecond (a thousandth of a second), a force of 2,700 pounds is required. Given that the area of the bullet is so small, this corresponds to a pressure of seventy thousand pounds per square inch, which is more than 4,600 times greater than atmospheric pressure. What type of metal can resist this pressure without suffering plastic deformation? Nearly all of them! A typical high-strength steel alloy can easily withstand pressures from seventy five thousand psi up to one million psi. Wonder Woman’s bracelets appear to be roughly half a centimeter thick, which should be enough to deflect a speeding bullet. Amazonium seems to be nothing more exotic than cold-rolled steel.

  The next basic question is if metals are so strong, why can they so easily be drawn out into long wires or fashioned into decorative jewelry? How can the atoms be so loosely bound that the resulting solid is easily manipulated, yet not fall apart under the slightest disturbance? The answer lies in electrostatics.