The Physics of Superheroes: Spectacular Second Edition (50 page)

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 1415, 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.
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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.

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.

In the previous chapter, we introduced the metaphor of the electronic states in a solid being like the seats in the orchestra of a theater, with the empty seats in the balcony representing a band of excited states at higher energy. Metals were described as like an orchestra in which only half the “seats” are occupied with electrons, so that a current could always be induced, because there was no energy barrier separating the highest occupied state and the lowest empty state. For metals, the seats actually correspond to matter-waves that can extend over the entire solid (to explain why this is so would be too much of a digression). This is why metals make such good conductors of electricity and heat—it takes very little energy to move these “free electrons” in response to an external stimulus. In a “covalently bonded” solid like diamond, each seat in the orchestra represents a rigid, directional bond between the atoms.

If there are no direct bonds holding the metal atoms together, what keeps the metallic solid from falling apart? Electricity! Each metal atom initially is electrically neutral, with as many positively charged protons in its nucleus as there are negatively charged electrons in probability clouds surrounding it. Remove an electron from each atom to roam over the solid, and the resulting original atoms are now positively charged. Try to compress the metal, and you are pushing the atoms closer together, and the positively charged atoms (called ions) repel each other, resisting the external pressure. This makes it strong. The lack of directional rigid bonds between atoms in a metal is why they are easy to deform, to pull out into long, thin wires or to flatten into sheets. The forces holding the metal together are not as strong as in most covalently bonded solids—we can easily bend and break a metal paper clip without superpowers!—but they are much stronger than one would expect, given how malleable most metals are.

There is, obviously, a fair amount of chemistry and materials science that determines the strength of a particular metal. For example, consider Adamantium, the strongest metal in the Marvel universe, which is bonded onto the X-Man Wolverine’s skeleton and claws. This miracle metal is strong not because it is dense, but apparently because it is a defect free covalently bonded solid. It takes more energy to remove a covalently bonded atom from all of its neighbors than just localizing a free electron onto an ion in a normal metal. Adamantium must somehow combine the electrical properties of metals with the strong covalent bonds found in diamonds, while avoiding having any network-weakening defects, making the resulting material “unbreakable.”

Defects weaken covalently bonded solids, but can actually make certain metals stronger.
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One way to improve the strength of steel is termed “work-hardening,” in which the metal is intentionally plastically deformed. This generates defects on the atomic scale within the metal. As there are no directional bonds in a metal, it is normally easy to move planes of atoms past each other when bending or drawing the material into a wire. Defects can block this atomic motion, and too many defects essentially form atomic-scale traffic jams that inhibit further deformations of the metal. This increase in strength comes at the expense of ductility. Cold rolled steel has a tensile strength comparable to titanium alloys, but both are flimsy compared with covalently bonded carbon nanotubes.

While we’re on the subject, we should address a common misconception regarding the chemical composition of Captain America’s shield. Wolverine’s claws are composed of pure Adamantium, but Captain America’s shield is a one-of-a kind alloy of steel and Vibranium. The steel is needed to provide rigidity, so that the shield can ricochet off walls and supervillain minions. Vibranium is an extraterrestrial material brought to Earth when a meteorite crashed in the African nation of Wakanda, which is ruled by the superhero the Black Panther. Vibranium has the ability to absorb any and all sound and convert the energy in the sound wave into some other, not-well-specified form, making it the perfect shock absorber, a quality strongly desired in a shield. Sound waves are alternations in pressure or density, and in a solid, sound is transmitted through the vibrations of the atoms. Vibranium possibly converts the atomic vibrations from an absorbed sound wave into an optical transition (which would explain why sometimes a glow is observed when Vibranium is used), thereby conserving energy in the process.