The Physics of Superheroes: Spectacular Second Edition (11 page)

Fig. 8.
Scene from the story “Tests” in
Spider-Man Unlimited # 2
(May 2004), in which the caption boxes reveal Spider-Man’s thought process as he faces a practical application of Newton’s second law of motion.

“Realizing the girl had fallen, I naturally made a course correction on my glider in an attempt to save her. I began an immediate descent. But before I had a chance to reach her, Spider-Man did something incredibly stupid: Despite the speed of her fall, he chose to catch her in that rubber webbing of his. In the next instant, her neck was snapped like a rotten twig.”

It may have taken the Goblin nearly thirty years, but apparently he at last understands that it wasn’t “the fall” that killed Gwen Stacy, but the sudden stopping. If a twisted, evil maniac like the Green Goblin can learn his physics, then there is hope for us all.

FLASH FACTS—
FRICTION, DRAG, AND SOUND

IT WAS A DARK and stormy night in Central City as police scientist Barry Allen locked up for the night. Pausing by the chemical storeroom, he marveled at the large collection of chemicals that the CCPD possessed. Despite his scientific training, Allen was standing near an open window during the gathering storm and bore the full brunt of a lightning strike that entered the room. The lightning bolt shattered the chemical containers, dousing him while the electrical current passed through his body.

But the simultaneous exposure to lethal voltages and hazardous chemicals somehow only dazed Allen, knocking him off his feet. Later that evening, he was surprised to discover that he could easily outrace a departing taxicab and catch and restore a spilled plate of food in a diner in the blink of an eye. Realizing that the lab accident had somehow endowed him with superspeed, he naturally adopted a simple yet elegant red-and-yellow costume and used his newfound powers to fight crime as the Flash.
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There is a broad range of physical phenomena associated with speed, and John Broome, Robert Kanigher, and Gardner Fox, the main writers of the early Silver Age Flash comics, addressed many of them. Thanks to his ability to run very fast, the Flash was frequently depicted running up the sides of buildings or across the ocean’s surface; he would catch bullets shot at him, and drag people behind him in his wake. Are any of these feats consistent with the laws of physics? It turns out that all of them are, granting, of course, the one-time “miracle exception” of the Flash’s superspeed in the first place.

In his very first Silver Age appearance, “The Mystery of the Human Thunderbolt” in
Showcase # 4,
the Flash ran up the side of an office building, because with his “great speed he is able to overcome gravity.” Earlier we explored the simple relationship between Superman’s initial vertical velocity and the final height he can leap. As the Man of Steel rises, he slows down due to gravity, until at a height h his final speed is zero. We calculated in Chapter 1 that for Superman to leap to a height of 660 feet, equivalent to a thirty- to forty-story building, his initial liftoff velocity needs to be at least 140 mph. But the Flash can run much, much faster than this, and he should therefore be able to reach the top of a forty-story building with velocity to spare. So, as he approaches the side of a building, as long as he has a speed greater than the minimum v
²
= (2gh), he should be able to leap up its side without violating any laws of physics (aside from the fact that he is running several hundred miles per hour, that is). In contrast, the fastest that a non-superpowered human can run is on the order of 15 mph (though faster sprints are possible)—which would enable the runner to scale the side of a small tool shed.

The question, however, is not whether the Flash is able to move fast enough to leap a vertical height h, but whether he can maintain traction to actually run up the vertical side of the building. Some interesting physics underlies the simple act of walking, related to Newton’s third law, which states that forces come in pairs. When you run or walk, a force must be applied horizontal to the ground by your feet, opposite to the direction you wish to move. The ground exerts an equal and opposite force back on your feet, parallel to the ground’s surface, that counters the back-directed force exerted by your shoes. The origin of this parallel force is friction. Imagine trying to walk across a floor covered with a uniform layer of motor oil, and you will realize how crucial friction is to a process as simple as walking. Without friction between his boots and the ground, the Flash would never be able to run anywhere. Captain Cold, one of the first and most persistent supervillains that the Flash would regularly combat, possessed a “freeze ray” gun that could ice up any surface. Time and again, Captain Cold (who, incidentally, isn’t really a captain) would simply create a layer of ice directly in front of the Scarlet Speedster, denying him traction and rendering his superspeed useless.

No doubt due to its ubiquity and fundamental role in everyday life, the phenomenon of friction is generally taken for granted, despite its complexity. Exactly why does an object resist being dragged across another surface? While friction’s basic properties were first scientifically addressed by Leonardo da Vinci in the early 1500s and Amontons in the mid-1600s, a true understanding of the root cause of this phenomenon would not arrive until the atomic nature of matter was properly resolved in the 1920s.

There are primarily two ways in which atoms can be arranged to form a macroscopic object: (1) in a uniform, periodic, crystalline structure, or (2) in a random, amorphous agglomeration. Of course, most solids lie somewhere between these two extremes, and typically there will be regions of crystalline order randomly connected, sometimes separated by amorphous sections. The net result will be that even the smoothest macroscopic surface will not be truly flat when viewed on an atomic scale. In fact, one doesn’t have to go to such extremes: Even on length scales of a thousandth of a millimeter—much, much bigger than an individual atom—an object’s surface will more likely resemble a jagged mountain range than the stillness of a quiet lake. Consequently, when two objects are dragged past each other, regardless of the apparent smoothness of their finishes, on the atomic scale it is not unlike taking the Rocky Mountain range, turning it upside down, shoving it atop the Himalayas, and then dragging the upside-down Rockies at a steady speed across the Himalayan mountaintops. One would naturally expect enormous geological upheavals and large-scale distortions in this extreme form of plate tectonics, and the results are no less catastrophic at the atomic level. With every footstep, bonds between atoms are broken, new bonds are formed, and atom-size avalanches and atom-quakes are produced. All of this requires a great deal of force in order to keep these atomic-scale mountain ranges sliding past and through each other. The resistance to such atomic rearrangements is called “friction,” and without it, the Flash would only be running in place.

The amount of friction opposing the motion of an object along a horizontal surface is proportional to the weight of the object pressing down on the surface. The greater the weight of an object, the deeper the atomic “mountain ranges” interpenetrate, and the greater the frictional force that must be overcome to move the object. It is harder to get a big, heavy block to start moving than a smaller, lighter one. Engineering solutions for lifting heavy objects have been known since the time of the ancient Egyptians, who developed various ingenious schemes for moving giant limestone blocks during the pyramids’ construction.

One obvious trick is to use a ramp. On a horizontal flat surface, all of a block’s weight presses down perpendicular to the surface. On a sloped surface, on the other hand, the weight is still straight down, directed toward the center of the Earth (think of a plumb line held on the ramp). Only some of the weight is perpendicular to the surface of the tilted ramp, and the rest is directed down the ramp. The smaller the force pressing the atomic mountain ranges against each other, the less they will interpenetrate, and the easier it will be to move them past each other. So the frictional force, which is proportional only to the component of the weight perpendicular to the surface, is less for a block on a tilted surface compared with one on a horizontal surface. No matter how rough the surface, if the ramp is tilted at too steep an angle, the friction force holding the block in place will be insufficient to counteract the downward pull of the weight down the ramp, and the block will slide down the ramp. However, as the Flash runs up the vertical side of a building, there is
no
component of his weight perpendicular to the surface upon which he is running, that is, the building’s face. In principle, therefore, there should be no friction between his boots and the building’s wall, and without friction he cannot run at all.

So can he in fact run up the side of a building? Technically, no. At least, not “run” as we understand the term. He can, as he leaps up the side of the building, move his feet back and forth against the building’s side, which would make it appear as if he were running. In essence he is traveling a distance equivalent to the height of the building in the time between steps. Typically, as the Flash runs, his foot pushes down on the ground at an angle with the road’s surface so that the force the road exerts back on him (thanks to Newton’s third law) is also at an angle with the surface. The net effect is that he accelerates in both the vertical and horizontal direction. The vertical velocity gives him a bounce up off the ground, and the horizontal component propels him in the direction he is running. The greater the vertical velocity, the higher the bounce, while the larger the horizontal velocity, the farther he advances before gravity overcomes the small vertical velocity and brings his feet back to the ground, ready for another step. Very fast runners, which would certainly include the Flash, can have both feet up off the ground between steps. The faster they run, the longer their time “airborne” between steps. If the Flash bounces about 2 cm vertically with every step, then he is in the air for about one eighth of a second before gravity pulls him down for another step. But one eighth of a second is a long time for the Crimson Comet. If his horizontal velocity is 5,250 feet/sec or 3,600 mph, then the horizontal distance he travels between steps is more than 660 feet. This is approximately one eighth of a mile, which we used as the benchmark for the tall building that Superman leapt in Chapter 1. As long as the Flash maintains at least this minimum speed, he needn’t worry about losing his footing along the way, simply because he will scale the height of the building between steps.

Before he can scale a skyscraper, the Flash has to radically alter his direction from the horizontal to the vertical. As will be discussed in a later chapter, any change in the direction of motion, whether it is Spider-Man swinging on his webbing or the Flash changing his path at the side of a building, is characterized by an acceleration that requires a corresponding force. Rotating his trajectory by ninety degrees up the building’s face entails a large force, provided by the friction between the Sultan of Speed’s boots and the ground. In addition to superspeed, the Flash’s “miracle exception” must therefore also extend to his being able to generate and tolerate accelerations that few superheroes not born on Krypton could withstand.

Newton’s laws of motion can also explain how the Flash is able to run along the surface of the ocean, or any body of water, for that matter. Just as Gwen Stacy had to be concerned as she was about to strike the water while moving at her large, final velocity, the great speed of the Flash’s strides enables him to run across its surface. As one moves through any fluid, be it air, water, or motor oil, the fluid has to move out of your way. The denser the medium, the harder this is to accomplish. It requires more effort to walk through a swimming pool, pushing the water out of your way, than to walk through an empty pool (that is, one filled only with air), and it is harder still if the swimming pool is filled with molasses. The resistance of a fluid to flow is termed “viscosity,” which typically increases the denser the medium and the faster one tries to move through the fluid.

The density of water is much greater than that of air—water molecules are in contact with one another, while there are large, open spaces between air molecules. It is even more difficult to move through water when traveling at high speeds. But for the Flash, when running on top of the water’s surface, this is a good thing. Just as someone is able to water-ski if he or she is towed at a large velocity, the Flash is able to run faster than the response time of the water molecules. As his foot strikes the water’s surface at speeds greater than 100 mph, the water acts more like a solid than a liquid beneath the Flash’s fleet feet (to test this, try rapidly slapping a pool of water), and therefore his oft-shown ability to run across bodies of water is indeed consistent with the laws of physics. In fact, at the speeds at which he typically runs, it is practically impossible for him to not run across the water’s surface. However, in order to acquire forward momentum, the Flash must push back against the water. That is, even if the water does behave like a solid under the rapid compression under his feet, would the Flash be able to obtain traction in order to run? One way he could accomplish this is by generating backward propagating vortices under his feet, thereby gaining a forward thrust under Newton’s third law. This mechanism was proposed as the means by which water-strider insects propel themselves along the water’s surface. Here again comics were ahead of the curve. The Flash’s ability to run across a body of water was likened to a rapidly skipping shell skimming over the water in
Flash # 117
, more than thirty years before scientists understood the water strider’s method of locomotion.
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