by Tom Rogers
It’s hard to imagine that an object falling from a height of 1 mile would create the equivalent of a gigantic nuclear bomb blast—but then it wouldn’t. The blast would be worse than an exploding bomb. A falling 15-mile-diameter disk would act like a gargantuan piston. Air underneath would be forced sideways out of the gap between the piston and the ground, forming a horizontal blast wave in the process. A nuclear bomb releases energy upward as well as horizontally, but it’s the horizontal energy that destroys cities and countryside. The falling saucer would waste little of its destructive energy in the vertical direction. The drop would mostly unleash energy in a horizontal blast wave.
The air velocity out the gap would be equal to the downward velocity of the saucer times the ratio of the saucer’s area to the area of the gap at the saucer’s perimeter (assuming that the air underneath acted as though it were incompressible). As the saucer fell, the gap would get smaller and smaller. When the saucer was 0.25 miles above the ground, the area of the saucer would be fifteen times as large as the area of the gap. If the saucer were falling at about half the terminal velocity of a sky diver, sixty miles per hour (97 kph), the horizontal wind coming out of the gap would be 900 miles per hour (1450 kph).These velocities are easily comparable to those of the Hiroshima nuclear blast13. True, air is compressible and so the wind will be lower, but the gravitational potential energy of the spaceship that is not converted into wind speed will be converted into elevated pressure and temperature beneath the spaceship, both of which cause damage.
Make the same calculation at a height of 100 feet, and the area of the saucer would be 198 times as large as the area of the gap. The wind velocity would be nearly 12,000 miles per hour (19,300 kph)—an impossibly high number. Obviously, instead of the extreme wind speeds, air would now be compressed to very high pressures, attaining high temperatures in the process. Combustibles under the saucer would likely ignite and blast a high-speed wall of fire out the sides of the gap. Unlike a nuclear blast radiating in all directions from a point source, the saucer blast wave would occur along its 47.1-mile perimeter and be focused in a horizontal direction. The effect would devastate a much wider area than an equivalent nuclear bomb blast.
Okay, the saucer would probably tilt as it fell, but if it’s only 1 mile off the ground, the tilt would be less than seven degrees. If it fell from a height of, say, 15 miles, the tilt could approach ninety degrees, but then the ship would also have fifteen times as much potential energy. Besides, if the ship tilted as it fell, the first side to touch the ground would block air flow, meaning that airflow out the elevated side would be higher than if the ship did not tilt. Tilting is going to do little or nothing to moderate the severity of the disaster.
To be capable of traveling back to its mother ship, the saucer would need fuel with at least 1,000 times as much energy as the blast it set off by falling 1 mile. Imagine the environmental damage this would cause when it leaked out and/or exploded during the ship’s crash. Killing these Goliaths all around the globe would be no cause for celebration. It would change weather patterns, ignite massive fires, and fill the sky with debris that would blot out the sunlight.
As for the mother ship, while the Davids on Earth were readying themselves to fight the Goliath saucers, the nerdy Goldblum and ace pilot, Captain Steven Hiller (Will Smith) flew a captured alien fighter craft to the mother ship, bluffed their way inside, planted a virus in the mother ship’s computer, and left a—you guessed it—nuclear boogeyman. The pair made their escape just before the entire mother ship detonated. Talk about a lucky rock to the temple. The ship is one-fourth the size of the moon with an outside surface area nearly four times the land area of Texas. Under normal circumstances, blasting such a colossus with a single nuclear warhead would be as effective as tossing a firecracker at a hornet’s nest—just enough damage to make them really mad. But here the boogeyman apparently sets off the alien ship’s fuel supply, destroying the entire mother ship in the process.
The explosiveness of the mother ship’s fuel does not bode well for resistance forces back on Earth. Assuming the saucers’ fuel is the same as the mother ship’s, when the saucers crashed, their fuel would most likely explode, making a bad situation worse. Humanity would be lucky to survive. But there’s no such unhappy ending in the movie. The heroes return victorious, minus the usual brave but minor characters sacrificed to provide just the right touch of sadness, and humanity is saved.
INCOMING ASTEROIDS
In Armageddon [RP] a Texas-sized asteroid—bigger than Ceres, the largest known asteroid in the solar system—is headed toward Earth at a speed of 22,000 miles per hour. The usual lovable assortment of misfits and neurotics in a complete spectrum of shapes and sizes is gathered, trained, strapped into space shuttles and sent to drill an 800-foot-deep hole, plant a nuclear bomb on a convenient fault line, and split the asteroid in half—the preparations having been accomplished in a mere eighteen days. Curiously, this gigantic asteroid has been able to sneak into the solar system on a collision course with Earth, travel for around two decades, and avoid detection until it’s almost too late.
First, imagine an 800-foot hole (hardly Texas-sized) compared to the size of the asteroid it’s drilled in. Then imagine the overall damage if a nuclear bomb went off in such a hole drilled in “nowhere” Texas. The result: not much. Okay, maybe there would be some radioactive fallout and a big blast hole, but the Lone Star State is still going to be largely intact. It doesn’t seem likely that the same setup in a Texas-sized asteroid is going to do much more damage.
Of course, the movie’s military morons—there hasn’t been an intelligent movie general since Patton [PGP] (1970)—fail to appreciate the importance of the last few feet of depth in the hole. In fact, they fail to appreciate the hole. When the project falls behind and the last possible moment for detonation is fast approaching, they try to explode the bomb even though it has not been properly planted.
An asteroid the diameter of Texas (diameter = 1,271,900 m) with the same density as Earth would have a mass of about 6 1021 kilograms. The largest nuclear bomb ever built was a Russian device rated at 100 megatons TNT and weighed a whopping 60,000 pounds (27,000 kg), nearly the 24,400 kilogram payload of a space shuttle. If the bomb were miniaturized and used on the asteroid, and all of its energy went into pushing the halves apart with no energy wasted on the splitting, each half would end up with a velocity of 0.02 miles per hour (0.03 kph).
The drillers land on the asteroid after it has traveled past the moon, giving them around ten hours before it hits Earth. Allowing eight hours for drilling leaves only two hours before the halves reach Earth after the bomb is set off. Multiplying this time by the separation velocity of the halves equals the separation distance when they reach Earth: a whopping 66 yards (60 m) apart (assuming no gravitational attraction force between them).
A computer simulation is needed to account for gravitational attraction between the halves. Such a simulation calculates that the asteroid halves require a separation velocity of 4,738 miles per hour (2,119 m/s) to miss Earth by the 400 miles stated in the movie. This means that each asteroid half would have to gain 6.7 × 1027 joules of kinetic energy, requiring at least 64-billion 100-megaton nuclear bombs to do so. Earth’s gravitational pull would cause the asteroid halves to slingshot around the Earth and collide back together on the other side. The kinetic energy gained to separate the asteroid halves would then be converted back into heat about 1,000 miles above the Earth’s surface. The release of energy would be astonishing and likely cause fires and damage on Earth directly beneath the blast.
Here’s the scary part: slapping together a plan for destroying even a small incoming asteroid in a few weeks time and splitting or vaporizing it with a nuclear bomb is ridiculous. A realistic movie portrayal of Earth’s current ability to deal with asteroid strikes would have been a public service and a much needed wake-up call. Such a movie could not come from Hollywood, however, because it would lack the required happy ending. Armagedd
on makes no such errors. Its plucky drilling crew overcomes all the obstacles and blows the asteroid in half, albeit at the cost of several crew members. Nevertheless, this loss adds just the right amount of pathos to the joyous ending as humanity is saved, yet again.
RIDICULOUS ROTATION
Not to be outdone by other nuclear bomb follies, The Core [XP] has the Earth’s core stop rotating—caused, naturally, by military morons playing with their new earthquake weapon, which was invented by a brilliant scientist with an ego as big as a house and no head for long-term consequences. In this movie it takes a mere three months to build a magical ship called the Virgil that can carry a rescue team down to the core for restarting it with, guess what, nuclear bombs.
At least this time they send five bombs. If we assume that the bombs are 100 megatons each and 100 percent of their energy goes into restarting the core, the crew is still short by at least 685 bombs. Keep in mind also that currently the biggest bomb in the U.S. arsenal is only nine megatons.
There are other small details such as creating the twisting action, or torque, required to get the core spinning. Exploding nuclear bombs tend to create force in all directions, which would only produce a net force acting directly through the core’s center of mass. Such a force cannot cause rotation. For rotation, the force must be applied at a ninety degree angle to the core’s radius in order to produce the needed torque.
As usual, nothing goes as planned and the mission reaches the brink of failure.The movie’s five-star moron decides to restart the core by using the earthquake machine in reverse. This seems like a much better plan than drilling down to the core, but, alas, an enlightened Virgil crew member warns that it will cause all of Earth’s volcanoes to erupt. Use of the earthquake device would also doom the Virgil and its remaining crew members. Fortunately, the military moron’s scheme is foiled and the crew triumphs again, at a cost.The older, less good-looking crew members die, once more providing just the right mix of pathos and triumph for the joyous ending.
All of this assumes that Earth’s core could stop rotating while the crust and mantel continued happily spinning—an assumption that goes beyond silliness. There would have to be a zero viscosity, friction-free layer between the mantel and core for this to happen. The rotational kinetic energy of the previously rotating core would also have to go somewhere. About the only choice would be to turn it into heat. Surely an extra 69,000 megatons of TNT worth of heat appearing inside the Earth would cause earthquakes, volcanoes, tsunamis, or something. Certainly, it would take more than a military gismo to cause it and more to fix it than a device that, on a global scale, amounts to a military firecracker.
FALLING HUMANS
It’s a deadly but simple principle: the gravitational potential energy stored in an object becomes kinetic energy during a fall. It’s the same type of energy that makes bullets lethal.
Kinetic energy is calculated as follows:
(kinetic energy) = 1⁄2 (mass)(velocity)2
A .45-caliber bullet, for instance, has a mass of 0.015 kilograms and a muzzle velocity of around 254 meters per second, giving it a kinetic energy of 483 joules (Remington Express 230 MC). For comparison, let’s assume an action hero with a mass of 49.3 kilograms (108 lbs) falls out of bed. The bed is an old-style, double-post model that Lincoln could have slept in—a little higher than normal—say one meter high. Her gravitational potential energy in bed can be calculated from the following:
(Potential Energy) = (mass)(g)(height)
The gravity constant g is 9.8 meters per second squared (using metric units) on Earth. Thus, her gravitational potential energy in bed is 483 joules. Since this energy is converted into kinetic energy during the fall, the hero hits the ground with the kinetic energy of a .45-caliber bullet!
The hero lives because the energy of the fall is dissipated over a much larger area than the area of a bullet. But if you ask around, it’s usually easy to find a friend or acquaintance who has suffered a broken bone from a fall of a similar height. Elderly people, in particular, are vulnerable to such falls.
Each additional meter of height is like adding the kinetic energy of another .45-caliber bullet. From a kinetic energy standpoint, a mere 6-meter (19.8 ft) fall—routine for an action hero—is similar to being simultaneously shot by six .45-caliber bullets.
Suppose our hero is a 109-kilogram (240 lb) body builder instead of the wiry person mentioned in the first example. Now a 6-meter fall is like getting shot simultaneously by thirteen .45-caliber bullets at point-blank range. Indeed, it’s true that the bigger they are the harder they fall.
Yes, bullets are incredibly lethal because they can penetrate into vital organs and a fall on a sidewalk would lack this penetration. But, it’s pretty hard to completely avoid injury from being simultaneously shot point blank six times with a .45-caliber let alone thirteen times, even when wearing a bulletproof vest. A 6-meter (19.8 ft) fall directly onto a sidewalk would almost certainly break bones even with a good landing. Increase the height beyond 6 meters, and it could easily be fatal.
FALLING BULLETS
While humans falling from great heights are almost certain to be killed, humans struck by bullets falling from great heights can survive.To help understand the reasons, we can compare the terminal velocity of a falling bullet with that of a falling human. A human skydiver will reach a terminal velocity of around 120 miles per hour (193 kph). At this point the upward air resistance force is equal in size to the downward gravitational force on the person, giving a net force of zero; hence, the person cannot accelerate to a faster speed. Traveling at terminal velocity, a 154-pound (70 kg) person has a kinetic energy of 209 .45-caliber bullets. He will literally explode when hitting an unyielding surface such as a sidewalk.
By comparison, when a .45-caliber bullet is fired directly upward, it will go up at a very high velocity but come down at a terminal velocity only slightly higher than the sky diver—about 170 miles per hour (242 kph). At this speed the bullet will have a kinetic energy of only 43 joules, about 9 percent of its original kinetic energy and less than the average energy required to produce a disabling wound, 81 joules (60 ft-lb), as reported by U.S. Army ordnance expert Major General Julian S. Hatcher (Hatcher’s Notebook, 1962). However, the term average implies that sometimes a lower value is sufficient to produce a disabling wound. Also chances are very high that the bullet will strike its victim in the head, and no blow to the head can be considered harmless.
Indeed, doctors at the King-Drew Medical Center in Los Angeles claim to have treated 118 people for falling-bullet injuries (including 38 fatalities) between the years 1985 and 1992, mostly attributed to the massive discharge of firearms during celebrations such as New Year’s Eve14. These statistics suggest that about a third of the people hit by falling bullets die, but many questions have been raised about the validity of the numbers. First, minor injuries are typically not reported. Second, the criterion for listing a random falling bullet as a cause of a gunshot wound is very liberal, and witnesses are often less than forthcoming with details.
There are also many factors that can increase the harmfulness of a random falling bullet. Common rifle bullets, for example, tend to be more aerodynamic and come down at higher velocities than large-diameter bullets such as those of a .45-caliber handgun. When they strike a victim, longer and thinner rifle bullets dissipate more energy per unit of area than shorter and fatter handgun bullets, and are more likely to penetrate the skin. But the single biggest increase in danger is the fact that drunken revelers firing bullets in the air are not noted for their careful aim. They often don’t fire their bullets straight up into the air. Fired at even a slight angle, projectiles will come down nose first instead of base first, decreasing air resistance and increasing bullet speed in the process. If the angle is significant, the bullet can come down at a substantially higher speed.
The Mexican [PGP] is about the only movie to make a plot device out of a fatality caused by a falling bullet from a horde of drunken gun shoot
ers. Okay, it’s certainly possible but not predictable. On the other hand, imagine the plot possibilities for falling bullets on planets or moons with no atmospheres.
An assassin pauses next to the rover parked on the moon’s surface and carefully places a box beside it. He presses a button and steps back as the box silently emits puffs of smoke from its top for about two seconds. Concealed inside is a Mac 10 submachine gun with a special aiming mechanism that keeps it pointed exactly upward, and a solenoid to depress its trigger.The assassin removes the box and disappears. About 5.4 minutes later the victim starts working on the rover as thirty .45-caliber bullets rain down on his head. Since there is no air resistance, they strike the victim’s space suit at the same velocity they left the barrel of the Mac 10 a few minutes earlier. They hit with a slight amount of scatter caused by the recoil-induced vibration of the submachine gun, but there is no wind to blow them off course.The lack of an atmosphere opens up all kinds of creative possibilities for plot devices.
CARS AS WEAPONS
The hero walks down the narrow alley and looks behind as 3,000 pounds (1,360 kg) of dark sedan roars toward him at thirty miles per hour (48 kph) from a distance of 100 feet. At the last instant, he jumps out of the way—or, at the last instant he is hit and rolls over the top of the sedan. In either case, he grimaces, dusts himself off, and goes on his way. He is after all the hero. One wonders why the bad guys keep trying assassination by automobile. It never works.
