by Tom Rogers
The distance the person could run is calculated as follows:
If the person were standing on the edge of a dock and dove off a dock exactly 0.15 seconds before the fireball arrived, the distance he or she would fall toward the water would be calculated as follows (assuming that the person could not push off the dock in a way which gave an initial velocity in the downward direction):
Where:
dy = the vertical distance fallen
g = the acceleration due to gravity. (On Earth g = 9.8 m/s2)
Obviously, the person is going to get flamed before he or she hits the water. But, not all fireballs travel at the same velocity. If the fireball traveled at a much more sedate speed of say half the speed of sound, the person attempting escape would have a whopping 0.3 seconds to escape and could fall 17.2 in (44 cm) toward the water—a short enough distance to still get torched.
Within 50 m of the explosion, victims are pretty much doomed to be engulfed by the fireball (assuming it’s big enough) and slammed by the shock wave. Even in the best case scenario, with a “slow” moving fireball, victims will have at most a few tenths of a second to run and jump in the nearest body of water. If they are neither knocked unconscious nor killed outright by the shock wave, flying debris, or shrapnel; and they hit the water soon enough to avoid severe burns, they might even survive.
The probability of survival without horrible injuries increases rapidly with increasing distance from the blast. But the benefits of running and jumping in water remain limited. Fireballs with enough energy to travel great distances usually do so at high velocities. Such enormous high-temperature fireballs also emit large amounts of infrared radiation (IR) that can burn victims at a distance even when the fireball does not contact them. The IR radiation travels at the speed of light—a little hard to outrun. If a person is close enough to the blast to be in grave danger, chances are he or she will not have the time to run and jump in the water. On the other hand, if a person has the time to run and jump in the water, chances are he or she is too far away from the blast to be in any real danger.
So how do movies do it? The actor stands in front of the fuel dump, building, or whatever is to be blown up and is filmed using a telephoto lens.This makes the actor appear to be standing close to the object to be blown up when in reality he or she is at a safe distance. The camera is turned off, a stunt person is substituted for the actor, the camera is turned back on, and ka-boom. The explosion is started with a black powder blast demolishing a container of fuel, the fuel mixes with air, and a second black powder explosion is used to ignite the vapor into a fireball. The fireball’s image fills the entire screen making it look enormous. Black powder in combination with a fuel is ideal because its explosion produces lots of highly visible smoke and flame with relatively little damaging blast power (compared to more powerful explosives like dynamite, TNT, or C-4, which give off very little smoke and flame with powerful blasts). Energy used to produce smoke and flame is essentially wasted because it’s unavailable for producing the high-pressure blasts that pulverize materials. The more powerful explosives are less visible and less spectacular precisely because they are more efficient and effective for just about every purpose but movies.
Saving Private Ryan and the miniseries Band of Brothers did an excellent job of depicting explosions. Neither artillery shells nor hand grenades produce large fireballs in these movies. In real life, even grenades such as those containing white phosphorus or thermite designed for marking targets or starting fires do not produce the typical fireballs of burning gasoline seen in movies. An exploding white phosphorus grenade looks very similar to a white fireworks shell bursting on the ground and sending glowing streamers flying outward in every direction. Although white phosphorous burns at about 5000°F (2760°C), a white phosphorus grenade does not produce a large-sized yellow-orange fireball. Thermite grenades typically are not even designed to burst. They burn vigorously in a local area at temperatures of around 4000°F (2200°C) and produce a by-product of molten iron. These grenades work extremely well for destroying enemy equipment such as artillery pieces. By contrast, the commonly used general purpose fragmentation grenade produces even less fire and smoke. It’s designed to convert the grenade’s explosive energy into the kinetic energy of hundreds of pieces of high velocity shrapnel. For such a grenade, fire and smoke are a waste of energy.
EXPLOSIONS IN SHAFTS AND TUNNELS
There are many variations of the running from explosions theme, such as the fiery elevator shaft. The heroes are climbing out of the elevator shaft as a fireball races up from below. They pull themselves out just as the flames sweep past—not a problem, they’re heroes. Long tubes such as elevator shafts confine fiery blasts and increase their pressure thereby increasing their velocity.Yet, heroes—in moments of great stress—have that unique ability to tap into their simian ancestry of millions of years past and conjure up long dormant genetic abilities to climb out of elevator shafts hundreds of times faster than competitive runners can run.
There are also the escapes in which a hero on a motorcycle blast velocity skillfully outruns a gigantic blast-wave/fireball. If he’s 100 m from the blast and going 100 mph (161 kph), he’s got 0.33 seconds to escape. This is naturally enough time for him to glance backwards repeatedly at the impending doom and lay down the motor cycle just in time so he ends up in a convenient ditch as the blast passes overhead—all with no injuries.
Collateral Damage [PGP-13] combined the fiery explosion in a tunnel and the motorcycle escape into a single scene when a pair of villains on a motorcycle set off a natural gas explosion, racing down a tunnel while firing a handgun at the movie’s hero, Arnold Schwarzenegger. Arnie, naturally, not only dodges the bullets but also outruns the blast and ducks behind a door just before the explosion hits. The less fortunate villains are knocked off their motorcycle by the blast (they are, after all, villains and aren’t expected to outrun it). While bruised and battered, they, nevertheless, are able to engage in lengthy hand-to-hand combat with Arnie who eventually proves to be far more deadly than the explosion. This illustrates yet another law of Hollywood: really evil villains can never die from the first few fatal causes.
This chapter has been able to debunk numerous typical Hollywood movie scenes with a single basic kinematic equation: the equation for constant velocity, which is often taught in one class period at the beginning of high school physical science—not exactly rocket science. So why do moviemakers assume that their audiences won’t notice? As described in Chapter 1, they’re counting on the power of the movies: combine rousing music with dramatic images in adrenaline-pumping scenes, and even silliness can go straight into the brain unopposed by logic.
Summary of Movie Physics Rating Rubrics
The following is a summary of the key points discussed in this chapter that affect a movie’s physics quality. These are ranked according to the seriousness of the problem. Minuses [-] rank from 1 to 3 with 3 the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3 with 3 being the best.
[-] [-] Planets that explode in a few seconds.
[-] [-] Heroes outrunning or outclimbing nearby fiery explosions, especially those in elevator shafts or tunnels.
[-] [-] Traveling the galaxy or even around a large-sized solar system with spacecraft powered by conventional thrusters.
[-] [-] Fragmentation hand grenades or high explosives such as TNT, C4, or dynamite detonating with large fireballs.
[0] Terrestrial fireballs traveling great distances at hypersonic speeds (incorrect but forgivable).
[+] [+] Fragmentation hand grenades or high explosives such as TNT, C4, or dynamite detonating without large fireballs.
CHAPTER 8
HOLLYWOOD BOMBS:
How Filmmaker Physics Misses the Boat
THE PHYSICS OF BOMBING
Sailors sleep as the aircraft approaches, its bombardier squinting throu
gh his bombsight at the toy-like image 9,840 feet (3000 m) below. When the aircraft is directly over the target below, the bombardier releases his deadly payload. It falls straight down, penetrating deep into the USS Arizona and blasting it into history as the emblem for the United States’ worst military defeat. No, it’s not the day of infamy. It’s the movie Pearl Harbor [PGP-13] (2001) perpetuating the infamous physics misconception that bombs dropped from moving aircraft fall straight down.
If all the Japanese bomber crews had shown such ignorance of physics, none of their bombs would have hit their targets and the USS Arizona might today be a floating museum rather than a sunken tomb. At best—or worst, depending on whose flag one saluted—only Japanese torpedo planes would have damaged ships during the first-wave attack.
Had the attack been planned by physics fools, even the torpedoes would have gone awry. Pearl Harbor was notoriously shallow, so torpedoes dropped from aircraft had to be modified with wooden fins and dropped from a carefully determined height to keep them from going too deep and slamming into the muddy bottom. Errors in understanding the physics would have rendered the torpedoes useless.
Dive bombers might have remained effective even in a time of physics foolishness, but then they didn’t attack ships—at least, not in the first wave. Dive bombers used what could be called bombing physics for dummies or, more correctly, bombing physics for maniacs. Start from the same altitude as highlevel bombers, dive straight at the target, release the bomb at maniacally close range, then pull up sharply to avoid becoming as one with the target—hopefully without blacking out from multiple gs. Unlike a bomb dropped from a high level that depended only on gravity for downward velocity, a dive bomber’s load would already have a high downward velocity when released and would travel a much shorter distance to the target, making it easier to predict the bomb’s path. American dive bomber pilot Harold Buell described the process as “shooting” a bomb at the target7.
By contrast, the erudite practice of high-level bombing required accurate knowledge of a bomb’s physics if its path were to be predicted reliably enough for proper arrival at its destination. Although bomber crews were denied the joy of making the calculations, a bomb’s physics had to be precisely designed into the bombsight and the altitude and speed of the aircraft carefully controlled for the bombsight to work.
A bomb dropped from 9,840 feet (3000 m) takes about 25 seconds to reach the ground whether dropped from a moving airplane or a stationary blimp (see Pearl Harbor Bomb Drop Calculations). Combining the bomb’s constant horizontal velocity with the ever-increasing downward velocity caused by gravity would make the bomb fall in a downward sloping parabolic path. The situation is similar to drawing with the popular toy called Etch a Sketch®. Turn one knob and a horizontal line appears on the screen. Turn the other knob and a vertical line appears. Obviously, the two knobs are independent. But turn both knobs simultaneously and it’s possible to obtain a curved line.
Remarkably, a bomb’s motion in the horizontal dimension has no influence over its motion in the vertical dimension. They are like two entirely separate worlds. Speeding up the horizontal velocity will not make the object fall more slowly or more quickly. Likewise, making an object fall in the vertical dimension will not influence velocity in the horizontal dimension.
Ironically, films of real WWII bombing runs, shot through cameras mounted in bomb bays, are often misinterpreted as proof that bombs fall straight down. In the films, the bombs look like they’re falling straight down and exploding directly below. But the camera isn’t stationary. It’s moving forward with the airplane. To give the appearance of falling directly below the camera, the bomb has to be moving forward at roughly the same speed as the camera. The films also confirm that the air resistance slowing the bomb’s forward motion is negligible. If air resistance acting on the bomb were significant, the bomb would appear to fall behind the aircraft.
PEARL HARBOR BOMB DROP CALCULATIONS
To calculate the time for a Japanese bomb to fall and strike the USS Arizona, we can use the simple mathematical model, or kinematic equation, shown below. Since this equation will be used in both the vertical (or y-dimension) and the horizontal (or x-dimension), we will use x and y subscripts to denote the respective dimensions.
Where:
d = displacement
a = acceleration
vo = starting velocity
t = time
Assumptions:
1. The acceleration is constant.
2. There is no air resistance.
In a bomb drop, the starting downward y-dimension velocity is zero. This simplifies the model as follows:
To solve for the time the bomb falls before hitting its target, we rearrange the equation and substitute the acceleration due to gravity for ay and the altitude of the bomber for dy as shown:
Now that we know the time, we can switch to the x-dimension and solve for the horizontal distance the bomb travels before hitting its target. In this dimension the bomb starts out moving at 225 miles per hour (101 m/s). Because we ignore air resistance, there is no horizontal force, hence, no horizontal acceleration. (Gravity acts only in the y-dimension.) The equation simplifies to:
In the 24.7 seconds it takes the bomb to fall, the bomb travels 2,490 meters, or 1.55 miles. In other words, the bomb has to be dropped 1.55 miles before the aircraft reaches the target in order to hit it.
The logic of using high-level horizontal bombers against ships in the first wave rather than the more accurate dive bombers was simple: the physics were favorable. Having ships tied up at dock simplified the bombing physics, while the physics required to defend the ships was horrific. For starters, shipboard antiaircraft guns were only marginally effective at the distance bombs were dropped. WWII warship antiaircraft guns ranged from rapidfiring .50 caliber machine guns to slow-firing five-inch cannons. At the moment a bomb was released from a high-level bomber, the aircraft would be 1.55 miles (2,490 m) away, measured horizontally. Antiaircraft guns would have to start shooting long before the airplane reached this point to have any hope of downing the attacker. At such distances only cannons would have had the required range.
Actually hitting a small fast-moving target such as an aircraft at long range is a major physics problem beyond the capabilities of human intuition. An antiaircraft cannon’s projectile fired upward would have a noticeable arc caused by the downward force of gravity. The projectile would be less massive and travel much faster than a bomb, making the effects of air resistance significant. To down an aircraft, the projectile and aircraft would have to arrive at exactly the same location at the same time or, at least, come close enough for the projectile to explode near the aircraft.
To make the required calculations, a gunner needed to measure the range, height, and velocity of the aircraft, not to mention have detailed information about the cannon shell’s curved path. To make the projectile explode near the aircraft, he had to calculate exactly how long it would take for the projectile to arrive and set the fuse accordingly. He could never aim directly at the target. Instead, he would have to calculate an aiming point that accounted for all the variables.
Making physics calculations using pencil and paper in the heat of battle would, no doubt, have been jolly fun and stress relieving were it not for the time constraints. A Japanese horizontal bomber would have been closing at a speed of 3.75 miles (6.04 km) each minute. If the gunner spotted an incoming bomber at 5 miles (8.05 km) away, he and his crew would have had less than a minute to make the required measurements and calculations, set the fuse, and load and aim the cannon in order to fire before the aircraft dropped its bomb. The results of failing this physics test would be far worse than a failing grade.
Calculating devices, ironically called “directors,” were available during WWII. Directors were mechanical computers that used gears and levers to make physics calculations. Several individuals had to keep the crosshairs of velocity-, altitude-, and range-finding devices aligned with incoming aircraft. Th
ese devices fed data to the director, which processed it and provided gun crews much needed information about where to aim and how to set their cannon shell fuses. Unfortunately, the antiaircraft directors weren’t much better than Hollywood directors at making accurate physics calculations. A standard U.S. Navy five-inch cannon shell fired at an enemy aircraft had no better than a 0.1 percent chance of downing it during WWII8.
On the other hand, catching a large stationary battleship by surprise on a clear day was a horizontal bomber’s dream. Under normal battle conditions in open water, these ships would be zigzagging while laying down smoke screens to obscure their position and, of course, shooting back in a most uncooperative manner, not to mention having extremely annoying fighter aircraft cover.
In sufficient numbers, American fighter planes could have swept Japanese bombers from the sky, so the first wave of dive bombers focused on destroying the planes before they could take off. The higher accuracy of dive bombers was needed to hit the small targets of airplanes sitting on runways. Because they attack at fairly close range, dive bombers were more susceptible to antiaircraft fire than high-level horizontal bombers. However, with the element of surprise, a dive bomber could blow up parked aircraft with relative impunity. Compared to ships, air fields were not well guarded by antiaircraft guns. They depended primarily on getting their fighters in the air for protection.
