Insultingly Stupid Movie Physics

by Tom Rogers

  Figure 2 shows a top view of the aiming line and the hypothetical line the bullet takes. Note the triangle formed by connecting the dots at A. elbow, B. muzzle, and E. a point directly across from the muzzle on the aiming line. Connecting the dots at A. elbow, C. bullet’s point of impact, and D. target forms a similar triangle. Anyone who has taken geometry will recognize that the properties of similar triangles can be used to calculate how far the bullet misses the target, given the distance to the target, the misalignment, and the elbow-to-muzzle distance as shown in the diagram. This is calculated as follows:

  If the muzzle is misaligned by only 2 inches (5 cm), the bullet will miss the target by a foot at a distance of 10 feet (3 m) from the shooter’s elbow. When aimed at its center, that’s enough to just graze the edge of a human-sized target. At a distance of 50 feet (15.2 m), the bullet will miss by 5 feet (1.52 m).

  To understand how easy it is to be misaligned by two or more inches, try a simple experiment with a laser pointer. Hold it as though shooting from the hip, aim at a target 50 feet away, and turn it on briefly to simulate a shot. Do not move the red dot while it’s turned on and note how far it misses the target. Try this multiple times from the same position on the same target.

  Invariably, the first shot will completely miss. Subsequent shots will get closer until by the third or fourth, the dot may be fractions of an inch from the target. Repeated shots provide the feedback required to hit the target and may seem like a substitute for gun sights. Unfortunately, this type of feedback doesn’t work as well with a handgun. First, recoil tends to misalign it, so you have to align from scratch after each shot. Second, it’s often hard to see where bullets are landing. And finally, in real situations, the target is probably going to be moving or even shooting back. Shooting from the hip or without using gun sights is woefully inaccurate for most shooters, especially if the target is more than 10 feet away.

  In Pulp Fiction [PGP] (1994) the moviemakers got just the right mix of physics precision and artistic ambiguity. During the movie two chatty hit men make a house call to remedy a misunderstanding. It seems that a misguided group has failed to uphold an agreement with the hit men’s employer. After the hit men collect the overdue account, they “enlighten” the hapless souls to ensure—in the most reliable way—that there are no future misunderstandings.

  Suddenly, a nervous shooter bursts from hiding across the room and empties his revolver at the startled hit men. He misses with all six shots and subsequently gets himself “enlightened,” courtesy of the hit men, who do not miss when they fire back.

  The scene is a classic movie moment embodying the enigmatic quality of great artwork. One hit man interprets the missed shots as a message from God wrapped in a miracle, the other as mere random chance. Had the shooter fired from the hip, random chance would have been the best explanation. But, the shooter fired in a police-style stance using both hands, making the chances of completely missing much lower. What’s more, we’re given a fleeting glimpse of the bullet-hole pattern in the wall behind the hit men. It looks like the bullets should have passed through the hit men, yet we can’t be sure. We’re left with an enigma that stirs thought long after the movie has ended.

  By contrast, the two-handed submachine gun shooting, discussed earlier, is neither artful nor realistic. While extremely dangerous to innocent bystanders, it would be marginal for stopping multiple bad guys. The combination of hip shooting and jarring Mac 10 recoil would all but guarantee that the bad guys would only be hit by random chance.When the firing begins, they would scatter and dive for cover. Less than two seconds later, when the good guy held empty Macs, the surviving bad guys would pop up and serve him the ketchup.

  Innocent bystanders would probably be oblivious to the danger until it was too late. A Mac 10’s bullets can injure at distances up to a mile. With the exception of heavy stone, brick, and concrete construction, the bullets can penetrate walls and injure or kill people on the other side. In a big city there would be many more innocent people within the deadly range of a Mac 10 than villains.

  The two-handed Mac 10–wielding action hero is the worstcase scenario for quickly running out of ammo when continuously firing a submachine gun. The best case is probably a Thompson submachine (or Tommy) gun equipped with a fifty-round drum magazine.These show up in 1930s-style gangster movies and could be fired continuously for a whopping five seconds, with an accuracy not much better than firing double Mac 10s. It’s hard to believe that anyone who’s serious about surviving a gun fight would shoot this way.

  THE GEOMETRY OF AIMING SNIPER RIFLES

  Shooting from the hip with a rifle is about as accurate as shooting from the hip with a handgun, but raise it to the shoulder, use the gun sights, squeeze the trigger—and a rifle becomes deadly accurate at much longer ranges. Carefully rest the rifle (a wellmade bolt-action one with a telescopic sight) against a stable object, and it can become a sniper weapon capable of taking out targets at distances on the order of 1,000 yards (914 m).

  Mathematically model rifle aiming like handgun hipshooting, and the distance AB (see Figure 1) becomes the distance from the shoulder to the muzzle of the rifle or about 1 yard (.914 m). Misalignments with a rifle fired from a steady position and using the gun sights are likely to be less than 1/16 inch (1.6 mm) compared to the 2-inch (5 cm) misalignment likely with a handgun fired from the hip.

  At 100 yards (91 meters) a 1/16-inch (1.6 mm) misalignment will cause the bullet to miss the point of aim by 6.25 inches (0.16 m). The shooter is not going to win any contests, but the bullet can still hit a human-sized target in a vital area. At 1,000 yards the same misalignment will cause the bullet to miss the point of aim by 62.5 inches (1.6 mm) or, in other words, completely miss a human-sized target.

  While hitting a human-sized target at distances less than 100 yards is no big deal when firing a rifle from a steady rest position, shooting at ranges near 1,000 yards is a Zen-like mix of physical awareness, physical control, and physics designed to release incredible violence from utter stillness. Simply jerking the trigger in an amateurish way, rather than squeezing it—a skill that takes both coolness and practice—can cause misalignment on the order of 1/16 inch and a complete miss of a human-sized target. Highly skilled shooters will time the trigger pull with their muscle tremors and heart beats. Breathing while aiming is out of the question. All thoughts of the rifle butt painfully recoiling into one’s shoulder, or other useless emotions, must be cast into the void. The rifle and shooter must become as one, with the singleminded purpose of sending the bullet to its target.

  Sniper rifles are the Stradivarius of firearms: finely tuned, precision instruments which exactly reproduce the right vibration pattern when “played.” Pull the trigger and the bullet exploding down the rifle barrel will vibrate it in a way analogous to drawing a bow across a violin string.Touch the barrel, tighten or loosen the screws holding it to the rifle’s stock, and the effect is like touching, tightening, or loosening a violin string. The change in vibration can change the impact point of the bullet in unpredictable ways. To hit the target at great distances, rifles have to be carefully sighted in and then left undisturbed until fired.

  So, how does the typical Hollywood sniper practice his coldblooded trade? He sits in front of a window, snaps open his custom brief case filled with rifle parts (each with a fitted slot in the case’s foam lining), twists together the parts of his weapon with that oh-sohigh-tech click, adjusts the scope, aims, and fires. However, by disassembling and reassembling his instrument, he runs the risk of detuning it to a different vibration pattern, which will give the bullet a different point of impact relative to the point of aim. If he’s shooting at a target less than 100 yards away (91 meters), no problem. At 1,000 yards (914 m) he’d have to spend roughly the price of a used compact car to get the engineering and craftsmanship required to create a breakdown rifle with the needed accuracy. Even then it would be questionable whether he could get it—but hey, a typical long-range assassin–(if such peo
ple exist) would probably consider it just another business expense. Besides, he’d probably do most of his work at less than 500 yards (457 m).

  Even with a precision rifle and a Zen master pulling the trigger, the rifle barrel has to be elevated above the horizontal, much like the cannon on a battleship, in order to hit a target at 1,000 yards. Figure 3 shows bullet trajectories for a 7.62-millimeter NATO rifle, which is considered the world’s most common sniper cartridge. When sighted in at 600 yards, but fired at a target only 300 yards away, the bullet strikes 36 inches (0.91 m) higher than the point of aim. When fired at a target 1,000 yards away, the bullet strikes 230 inches (5.8 m) low. At these distances even a gentle 10-miles-per-hour (16 kph) wind makes the bullet drift horizontally by a whopping 108 inches (2.74 m).

  If the target itself is moving sideways, the sniper must lead or aim ahead of it so that the bullet arrives at the same time as the target—the longer the distance to the target, the longer the lead. If the target is moving straight away or straight toward the shooter, the task is much easier, but still not as easy as shooting a stationary target. The long-range sniper must account for all these variables, which is a daunting task.

  On the other hand, neither bullet trajectory, wind, nor motion of the target are big problems when shooting a high powered rifle like the 7.62-millimeter NATO at ranges under 100 yards. At worst, the shot will go high by about 2 inches (assuming it’s sighted in at 200 yards), or drift from the point of aim by an inch (2.5 cm) in a 10-mile-per-hour (16 kph) wind. If the target moves it will have only about a tenth of a second to get out of the bullet’s path. At 100 yards the bullet has over four times as much kinetic energy as at 1,000 yards. At the closer range it is capable of blasting unimaginably gruesome wounds in whomever it strikes. A hit in the head, neck, or chest cavity will likely be fatal, even if the bullet smashes into its victim several inches from the most lethal point of impact.

  According to Oliver Stone’s controversial 1991 move JFK [RP], the Kennedy assassination was a conspiracy and could not have been carried out by an ex-marine using a scoped, highpowered, bolt-action rifle fired from a steady position, at a distance of 88 yards. Who knows? Maybe it was a conspiracy. Certainly, the CIA, mafia, communists, Cubans, police, and Girl Scouts could all be responsible. Yes, as bolt-action rifles go, Oswald’s Italian-made 6.5-millimeter Mannlicher Carcano was no Stradivarius and Oswald was no sniping maestro. But while not as powerful as a 7.62 NATO rifle, the Carcano could easily have inflicted a wound gruesome enough to be fatal, nearly anywhere on a person’s head. A couple inches of inaccuracy one way or the other would have been insignificant.

  Oswald was no rank amateur; he was trained to shoot by the U.S. Marines. And he was shooting at a distance well under 100 yards. At that time there were thousands of hunters, shooters, and ex-military people in the U.S. who had more than enough shooting skill to carry out the heinous act. What made Oswald uniquely capable was not his shooting skill, but his pathologically coolheaded and remorseless ability to squeeze the trigger with the president’s head in his gun sight.

  GETTING GUNFIGHTS RIGHT

  Some moviemakers do get gunfight scenes right, as in, for example, Black Hawk Down [GP] (2001). The movie depicts 123 elite U.S. soldiers fighting a desperate battle in Mogadishu, Somalia on Oct. 3, 1993, on a mission to capture a renegade warlord’s key associates. In realistic manner the characters rarely fire anything from the hip, even when firing fully automatic weapons. Large machine guns are actually reloaded and tend to be fired in short bursts lasting no more than a few seconds at most.

  One scene lends an unusual touch of realism when the hot, empty cartridge cases ejected from a rapid-firing minigun in an overhead helicopter shower down on a hapless soldier, giving him minor burns.These weapons look like old-fashioned, hand-cranked multibarreled Gatling guns, but that’s as far as the comparison goes. Unlike Gatling guns, miniguns are rotated at high speed by an electric motor, which gives them an incredible firing rate. Their multiple barrels are needed to keep them from melting. Even at that, empty cartridge cases ejected from them are too hot to touch.

  Moviemakers are intelligent, talented, and well funded. They can hire a busload of top experts for the price of a single supporting actor, but it does little good unless the experts are granted some power. In Black Hawk Down the moviemakers didn’t just pay experts, they paid attention to them.

  THE GEOMETRY OF DRIVING

  In The Italian Job [PGP-13] (2003), moviemakers once again shot from the hip with respect to geometry, but in a different manner. The movie is about a happy-go-lucky group of professional criminals who steal millions of dollars worth of gold, only to be double-crossed by one of their own, who kills their leader and swipes their haul. The survivors spend the rest of the movie trying to remedy the affront.

  Much of the movie’s plot centered on the Mini Cooper car. Supposedly, it’s so small that it could be driven down the 6-footwide hall of the villain’s house to the room where his safe was located.When the safe was opened, the Mini would be loaded with gold and driven away. This was all well and good, except that such a maneuver required 90-degree turns in the hallway and the Mini has a 17.5-foot turning radius.

  While it would be jolly fun to write a mathematical proof demonstrating that the turn cannot be made, the same thing can be done with a simple scaled drawing. Figure 2 shows clearly that the turn cannot be made; there just isn’t enough room.

  The Italian Job actually contained a sophisticated wire-framestyle 3-D animation of the car driving through the hallway. The term wire-frame means that the visual images of the car and hallway looked like see-through objects constructed with wire-framelike line drawings. The animation appeared to be drawn to scale and would have taken many hours to create. It could have been rotated on a computer’s screen and looked at from any conceivable angle, making it easy to spot clearance problems.

  There’s almost no way animators could have made such a model and not known the car couldn’t make the turns. At first glance it seems they would have made use of their own animation and avoided the problem by adjusting the dimensions of the hallway or eliminating the turns. Only they know why it was portrayed incorrectly. However, it’s safe to say that, as is the case with many examples of bad movie physics, it was probably based on a conscious decision, rather than an accident.

  Considering that physics is the most mathematical of all the sciences, it’s no wonder moviemakers routinely distort it. They can’t resist the urge to distort even simple mathematics.

  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, 3 being 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, 3 being the best.

  [–] [–] Shooting ridiculous amounts of ammo without reloading or the barrel overheating. When really overdone, a movie starts looking like a comic book.

  [–] Continuous bursts of fully automatic submachine gun fire lasting more than a few seconds.

  [–] Shooting from the hip and hitting anything smaller than a man-sized target at a distance of under 10 feet (3 m).

  [–] Shooting from the hip and hitting anything at a distance of over 10 feet (3 m).

  [–] Sniper rifles in brief cases.

  [–] Ignoring limitations imposed by simple geometry, such as maneuvering vehicles in impossibly small areas.

  [+] Depicting the fact that guns get really hot from rapid fire.

  CHAPTER 3

  CONSERVATION OF MASS AND ENERGY:

  Is Anything Sacred?

  LAWS VERSUS MODELS

  A few hundred years ago, the science of physics was started by an enlightened few who viewed the world as divinely created by a law-giving entity. These laws—the Ten Commandments—were provided to huma
nity, along with free will. Inanimate objects weren’t so lucky; they just got laws. The enlightened few began to realize they could attain magic-like power by taking advantage of the inanimate world’s order and lack of free will. Categorizing the universe’s order into the principles and laws of physics essentially gave the enlightened few an operating manual for the universe.

  In reality, the laws of physics are more like Barbie dolls than immutable laws of creation. Barbie is a model that avoids unneeded complexity and only deals with a few aspects of reality, but deals with them effectively. She is useful for modeling hair and clothing styles, in order to inexpensively predict what will look good on real people—at least on magnificently proportioned ones. Barbie lacks many real-world features such as fully workable joints, a pancreas, and a large intestine. Using her for surgery practice would be a poor application. Internal organs, however, aren’t needed for understanding clothing styles.

  Likewise, the laws or models of physics aren’t useful for modeling everything, but are remarkably helpful in the areas where they can be applied. For example, they allow engineers to predict that an aircraft will actually fly long before it’s completely built. Most modern innovations, including movie cameras, sound systems, and air-conditioned theaters, owe their existence at least in part to our understanding of the models of physics. Devices such as these have granted Hollywood the power to create entire celluloid worlds.

  Not every model in physics has achieved the status of being called a law. This term is usually applied only to the most tested and reliable of models. Due to their reliability, physics’ laws are never repealed, but they are sometimes refined. Often the refinement involves a better definition of the law’s limitations. For example, Newton’s second law does not work well when an object’s speed approaches the speed of light. For that situation, Einstein’s theory of relativity is needed. Yet for slower speeds, both Newton and Einstein gave the same answers.