by Tom Rogers
KNIFE THROWING
Why would anyone in a life-or-death struggle want to throw away a perfectly good knife? Unlike a gun, a knife never runs out of bullets. Kept in the hand it can be used to attack or defend again and again.When thrown it has to stick in the target to do any real harm, but that’s just the first requirement.There’s a reason killers often stab their victims multiple times, and it’s not just viciousness. Stab wounds, even well-placed ones, are usually not immediately fatal. So, of course, knife throwing is a routine staple of action movies and invariably drops its victims instantly.
The first problem with knife throwing can be summed up in a word: rotation. Typically, a knife thrower will grasp the blade near the tip and raise the knife slightly over his head so that the hilt is pointed slightly backward. As the knife thrower swings his arm downward and forward, the hilt will be pointed toward the target just before release. The knife will have generally rotated at least a fourth of a turn during the act of throwing, even before it leaves the knife thrower’s hand. To get this rotation, a knife thrower has to create a force on the knife that does not act through the knife’s center of mass. Some knife throwers prefer to grip the hilt rather than the blade during throwing. Either way, the knife will be rotating in what could be called a forward direction as it leaves the hand and flies toward the target.
To stick the knife, the tip has to rotate more or less forward (within ±30°) when the knife strikes its target, or the knife may as well be a stone. Knifethrowing performers generally train themselves to throw their knives so that the blades rotate at a repeatable rate. Throwers then position themselves at a known distance from the target. Using this system along with a lot of practice, good knife throwers can stick their blades consistently. Place knife throwers at a different distance, and they lose at least some of their advantage. They can still stick a knife but have to estimate the distance and alter the way they throw enough to make their knives rotate properly.
By holding the knife at the hilt and snapping the wrist correctly as the knife is thrown, it’s actually possible to make a knife rotate backward from its normal direction of rotation as it travels toward its target.This would usually be considered a mistake, but done with moderation it can reduce the knife’s overall rotation rate.
So-called spear-style or rotation-free knife throwers use heavy knives usually 1 foot (30 cm) or more in length to minimize the tendency to rotate. By adjusting their grip, wrist snap (as mentioned above), and release point, along with lots of practice, they can significantly reduce the rate of rotation. Even then, however, their knives usually rotate at least one-fourth of a turn before striking the target.The stronger the throwing arm and the higher the linear velocity of the knife, the farther it travels before overrotating and failing to stick. Spear-style knife throwing can produce consistent results at distances under 15 feet (4.6 m). By contrast, the Olympic javelin throw record was 321.1 feet (98.49 m) by Jan on May 25, 1996. A well-designed spear thrown by a less talented person would not travel as far but could easily be “stuck” at distances on the order of 100 feet without any worry of rotation.
Spears can be easily thrown and stuck in targets without rotating while knives cannot because the throwing force applied to a spear almost has to act through its center of mass. In addition, there’s something called rotational inertia. Inertia is defined as resistance to a change in motion. With linear or translational motion (motion along a smooth curve or line) inertia is equal to an object’s mass. Rotational inertia, or the resistance to changes in rotation, is more complex. Like its linear cousin, it is directly proportional to mass but is also related to how the mass is distributed. Different shapes have different rotational inertia values even when their masses are equal. A knife or spear has a shape similar to a rod, which yields a rotational inertia as follows:
(rotational inertia) = 1/3 (mass)(length)2
According to the above equation, a six-foot-long spear is going to have at least thirty-six times more rotational inertia than a onefoot-long knife just from length alone. In most cases the spear will also have more mass than the knife, making the spear’s rotational inertia even higher. If the force used to throw the spear is slightly misaligned with the center of mass, the spear’s rotational inertia will resist the tendency to rotate far better than the knife would in the same situation.
The second problem with knife throwing’s effectiveness is bone; bone is hard to penetrate and tends to show up in inconvenient places for the knife thrower—for example, as protective armor for vital organs. A thrown knife delivers a single stab wound (assuming it sticks in the victim). If the knife hits bone, it may not penetrate far enough to inflict substantial damage. If it does penetrate, it may not disable a victim fast enough to prevent him or her from fighting back or calling for help. Even if stabbed directly in the heart, a victim can remain conscious for about 10 seconds. A highly motivated, adrenaline-fueled, or drugged victim can continue to fight back during at least some of this time. Stabbings are not at all like they’re depicted in the movies: victims don’t just quietly accept their demise the instant they are stabbed.
Although throwing a knife significantly reduces its effectiveness, it does extend its range—by at least a few meters. If a wildeyed terrorist across the room announces murderous intentions and brandishes a loaded AK-47, then by all means hurl a dagger at him. Why not? It might disrupt his aim. Rush him and hopefully wrestle away his weapon. But, other than desperate situations or circus acts, it’s best to hold on to one’s blade.Yes, having multiple knives helps, but even then, a thrown knife is more feasible as a distraction than an actual killing technique.
The movie Cellular [PGP] (2004) cleverly illustrates how a blade can be used effectively as a weapon. In the movie Jessica Martin (Kim Basinger) is kidnapped and left in a room with a smashed phone. She manages to piece it together well enough to make a highly improbable call to a random stranger’s cell phone. He (Chris Evans) spends the rest of the movie trying to rescue her. Not one to helplessly wait for Prince Charming, Basinger— a high school science teacher (not a good person to mess with)— knows anatomy and slices one of her kidnaper’s major arteries when he attacks her. As he quickly weakens, she stays just out of range from his grasp long enough for him to bleed to death, a satisfying moment for the audience.
While having a knife incurs a significant advantage over an unarmed opponent, the problem with knife fights is that both opponents have them. At the close range of knife fights, cutting an opponent is easy, but stabbing one in the vitals is hard. On the other hand, the main difference between slicing blood vessels in the arms and legs versus stabbing a vital organ is mostly the amount of time it takes for one’s opponent to lose enough blood to pass out or give up. The key to winning a serious knife fight is to make your opponent bleed faster than you do.
FIREARM SPIN
In movies, skill with firearms is as remarkable and common as knife-throwing ability. Shooting from the hip, as discussed in Chapter 2, has long been a Hollywood specialty, but now there is an even cooler handgun technique appearing in movies: the horizontal grip. Hollywood has spun yet another cliché without considering the physics of rotation.
Normally a handgun is gripped with the fist in a vertical position. This enables one to use the gun sights—a handy feature if one wants to hit something. When a handgun is fired in the vertical position, the gun barrel is above the fist and the recoil creates a force that pushes backward above the wrist joint, creating a twisting action on the fist that rotates both it and the gun barrel upward. Conveniently, gravity helps rotate it back, more or less to its original position. This up-and-down rotation can cause aiming errors in the vertical dimension. But the vital area on a personsized target is about twice as high vertically as it is wide horizontally. If a shooter is going to have an aiming problem, it’s best to have it in the vertical dimension.
Torque and Rotation of Firearms
The barrel of any type handgun will typically be located above
the pivot point in the wrist and will generate a torque equal to the recoil force times the distance r, as shown in the diagram. This torque will rotate the gun barrel upward as shown.
Grip a handgun, turn the fist horizontally, and it’s oh so cool, but all of the advantages mentioned above disappear. The first to go is the ability to effectively use gun sights. The head is in the wrong position. It’s too high. Raise the fist above shoulder level and it’s possible to get the sights to a usable level, but it places the arm in an awkward position. The handgun’s sights must also be adjusted for shooting with a horizontal grip, or accuracy is going to suffer.
When the shooter fires using a horizontal grip, the recoil will rotate the handgun horizontally and—guess what—there is no horizontal gravity to help restore it to its original position. Resulting errors are going to scatter shots horizontally, where they are more likely to miss a person-sized target. Okay, so maybe Billy Bob out in the Texas Panhandle has mastered the technique after years of practice on rattlesnakes. But it still doesn’t change the fact that a horizontal handgun grip is ridiculous for most people. It’s a good way to accidentally shoot an innocent bystander.
The confusion about rotation and translation (moving in a linear fashion) doesn’t just apply to handgun grip but also to how victims—hopefully bad guys—react when shot. Although conservation of momentum (see Chapter 13) rules out the cliché of shooting victims being blown off their feet and sent flying backward through the nearest glass object, the conditions required for translation also cast doubt on this scenario. To throw a person violently backward and slightly upward, a shotgun or handgun blast (as depicted below) has to hit in line with the person’s center of mass (about 2 in. below the navel). This means it has to be fired by a long-armed chimpanzee who can hold the weapon below knee level and fire it in a slightly upward direction. Shooting a person above the belt would tend to rotate him backward. Shooting him in the shoulder would add a spin similar to an ice skater’s spin but much more mild. Neither of these effects would send a person flying backward.
ROTATING CARS
Although people can theoretically act in unpredictable ways, inanimate objects such as cars cannot. Yet, even here Hollywood has difficulty. Watch a few hours of reality TV filmed by policecar-dashboard cameras, and it’s clear that cars rarely go airborne when they crash. Watch a few hours of Hollywood chase scenes, and cars routinely go airborne while doing more twists than an Olympic platform diver. Even when colliding with the backside of a parked car, the front end of the moving car invariably flips upward, sending it airborne with a half twist that causes it to land on its roof several car lengths in front of the parked vehicle.
To get the entire car airborne, the net force on it has to be large and upward. To flip up the car’s front, an upward force has to act on the front to cause it to vertically rotate around the car’s center of mass. To twist or rotate the car like a huge slow-moving bullet so that the car ends up on its top, a force has to be applied to one side of the car. Driving a car at high speed up a ramp gives it the large upward force needed to get it airborne. Adding a kicker plate gives the front end an upward rotation. (Kicker plates are short ramps that act only on the front wheels and then fall away.) Using the kicker primarily on one side gives the car the twisting motion that causes it to end up landing on its top. Placing the camera in front of the parked car hides the ramps, kicker plates, and so forth.
Air cannons can also be used to provide missing forces. These are large-diameter, short-barreled devices that are specially mounted inside cars and aimed at the ground. They generally shoot a section of a telephone pole propelled by air pressure. These act like large super-fast hydraulic jacks that almost instantly elevate the vehicle. While it might sound odd to use sections of telephone poles, they are just about the right size and weight, not to mention readily available. Some of the cannons are designed to use black-powder charges when fire and smoke are needed during a crash. If a moving car is supposed to roll over sideways, the cannon is mounted to the right of the driver where a passenger would normally sit. If the moving car is to flip with the car’s trunk rotating upward and forward over the cars’ hood, the cannon is installed near the center of the car’s trunk. By moving the cannon around relative to the car’s center of mass, it’s possible to get just about any type of rotation desired. When combined with ramps and a high forward speed, the stunt director can choreograph whatever type of motion is needed.
Roaring down the highway, pursued by submachine-gun wielding albino twins (Matrix II), Trinity triggered one of the most famous car wrecks in cinematic history. To pull off this scene, some of the stunt cars actually towed ramps behind them as they sped down the road. When the stunt drivers in ramptowing cars slammed on their brakes, cars behind them continued up the ramps and went airborne over the ramp-towing cars. Various combinations of air cannons and ramps had cars rolling, twisting, and flipping, all at the same time, in every conceivable manner. It was a veritable physics ballet—impressive and entertaining but not realistic.
It’s impossible not to admire the technical skill and daring that goes into spectacular car-wreck scenes. The individuals designing them are applied physicists, who must possess a finely tuned understanding of forces. The stunt drivers performing them are risk takers who must put their very lives in danger. Yet movies based entirely on spectacular car wrecks are like restaurants based on food fights. While experiencing them might be fun, they leave one hungry for sustenance.
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 rating. 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.
[–] Above-the-belt kicks and punches that throw victims horizontally backward significant distances.
[–] Throwing one’s knife as anything other than a pastime, circus stunt, or last-ditch tactic. Having multiple knives helps, but even then, a thrown knife is more effective as a distraction than an actual killing technique.
[–] The horizontal handgun grip used at any distance other than point blank.
[–] Spectacular car wrecks that could not happen in reality without ramps and air cannons.
[+] Winning a knife fight in an understated manner by severing an artery other than the carotid.
CHAPTER 17
HOLLYWOOD DISASTERS:
Global Warming, Tsunamis, Tornadoes, and Other Big Winds
GLOBAL EXAGGERATION
It’s the ultimate science experiment: dump trillions of tons of CO2 into the atmosphere for decades and see what happens. It takes a while but then, according to The Day After Tomorrow [RP] (2004), snow blankets Bombay, super-sized hail hammers Hong Kong, and terrible twisters trash Los Angeles (F5s on a scale of F1 to F5). Dare to engage in extramarital sex or, worse yet, inane live news coverage as one of these tornadoes approaches, and your demise is certain. But that’s just the beginning. The north polar ice cap suddenly melts, shutting down Atlantic currents and in the process triggers a massive hurricane-like blizzard covering North America. Since the North Pole’s ice cap floats, melting it does little to raise ocean levels, but then apparently ice sheets in Antarctica and Greenland also suddenly melt causing an immediate change in ocean level. This immediate change sends a super-tsunami selectively sweeping into New York City. Frigid upper layers of the atmosphere plummet downward and freeze people midconversation, and then comes the snow—biblical amounts of it.
In reality, the whole state of California—it’s definitely not Kansas, Toto—has never recorded a tornado rated greater than an F223, but there’s no law of physics that says it can’t. An ice age in North America from the season’s first snowstorm is also far-fetched, but again there’s no law against it. Why, howev
er, would New York City be a magnet for super-tsunamis that apparently hit nowhere else? The scientific explanation is obvious: the Statue of Liberty. It washed up on the beach symbolizing the decline of insensitive and thoughtless humans replaced by apes in Planet of the Apes (1968). It protruded from a frozen New York Harbor in A.I. (2001), symbolizing the decline of insensitive and thoughtless humans replaced by skinny robots. So, what could be better for symbolizing the decline of insensitive and thoughtless fossil-fuel-burning fools? Have the old gal get slapped in the kisser by a global-warming-induced super tsunami; that should do it. But destroy her—never! It would destroy all hope of a happy ending. So the movie leaves her protruding from the frozen harbor, still standing, as a symbol of hope.
At 305 feet (93 m) tall (including the pedestal)24, the venerable lady also puts things in perspective. Judging from its level on the statue, the tsunami has to be around 240 feet (72.8 m) high. This height means that the statue’s feet will be under nearly 90 feet (27.4 m) of water. Unless the statue instantly fills with water, its feet will be subject to about 2.7 atmospheres of water pressure, enough to crush the statue’s 0.09375-inch-thick (0.237 cm) copper sheet metal walls. Keep in mind that each square foot of the thin sheet metal in the base of the statue would have to resist a total force of over 5,700 pounds (25,000 N). Add the massive impact of the wave, and the grand lady’s days of symbolizing are over. She’s going to be a twisted sunken wreck.