by Tom Rogers
Assuming the craft has a mass of 1,000 kilograms, it will take the energy equivalent of about 1,400kg (3,100 lb) gallons of gasoline to reach the escape velocity of this Earth-like planet—25,000 miles per hour (40,300 kph), a paltry speed by cosmic standards. None of this, however, is going to strain the cosmic Toyota’s fuel supply.
The cosmic Toyota obviously isn’t running on gasoline. It has some exotic energy source—say, antimatter. Combining 2.2 pounds (1 kg) of antimatter with 2.2 pounds (1 kg) of ordinary matter would release the energy of about 1.5 billion gallons of gasoline. But there are a few problems. First, storage: antimatter instantly explodes if it contacts ordinary matter. Second, source: there isn’t any. Oh well, surely these can be solved in a distant time and galaxy. So, what’s the real problem? In a word: thrusters.
Thrusters require an energy source, but they also need a supply of mass to produce the thrust. They work using conservation of momentum. Blast some high-velocity mass out the back of the cosmic Toyota’s thrusters, and the craft will gain the same momentum in the forward direction as the expelled mass has in the opposite. The thrust force developed is as follows:
Thrust = (velocity of exhaust) (mass flow rate of exhaust)
Using a very optimistic expelled mass velocity of 50,000 m/s, the Konstantin Tsilokovsky rocket equation predicts that a 1,000 kg Cosmic Toyota will have to expel 800 kg or 80 percent of its mass to reach escape velocity. But the need for mass is actually much worse when blasting off a planet against gravity and air resistance forces. Air resistance does drop to zero outside the atmosphere but is substantial for the first few minutes of liftoff. All these factors together make the mass required for liftoff huge, explaining why NASA needed a behemoth rocket 95 feet 4 inches (29 m) long and 10 feet (3 m) in diameter just to launch the first American, John Glenn, into a relatively low Earth orbit at considerably less than escape velocity. To send three astronauts and their supplies to the moon, NASA required a 363-feet-(111-m-) long 33-feet-(10-m-) diameter Saturn V. Forget energy requirements, a vehicle designed to leave an Earth-sized planet is going to need an enormous mass supply to do so.
As long as it’s in an atmosphere, the cosmic Toyota could intake air in the front and exhaust it out the back at a higher velocity, similar to the way a ramjet engine works. Unfortunately, atmospheres tend to be remarkably shallow compared to the distance one must travel to reach escape velocity. So, the supply of mass provided by the atmosphere quickly runs out. Getting a Toyota-sized vehicle off an Earthlike planet using thrusters is impossible without a way to store large quantities of mass.
Once liberated from the Earth-like planet, the cosmic Toyota could cruise around in outer space on a more limited tank of mass, since it would no longer have to overcome a gravity force or air resistance, but it’s still going to be a mass hog if its driver is an acceleration freak. If cosmic Toyotas became the rage, the galaxy might become dotted with mass stations. Assuming the cosmic Toyotas came with a few years’ supply of antimatter, their thrusters could use just about any form of matter. It might be possible to run them on water or discarded banana peels.
Hollywood could go wild over the opportunities for specialeffects scenes. Wreck a cosmic Toyota and its 22-pound (10 kg) fuel tank would explode with the energy of 4.3 nuclear bombs rated at 100 megatons TNT each (the biggest nuclear bombs ever built). An entire disaster movie could be based on a single chase scene and a single wreck.
One could hope that in the faraway time and galaxy heretofore undiscovered, principles of physics or breakthroughs in engineering might solve the problem of the excessive mass needed for escaping from a planet, not to mention the problems of antimatter storage and supply. Sadly, barring such luck, the cosmic Toyota is just too small for shuttling personnel between a planet’s surface and an orbiting mother ship, not to mention interstellar travel.
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.
[–] [–] Recoil-free rail-guns.
[–] [–] Shuttle craft the size of Toyotas using thrusters with the ability to escape from an Earth-like planet’s gravity.
[–] [–] Shooting victims blown backward large distances, especially when they crash into glass.
CHAPTER 13
JFK AND MOMENTUM:
Hollywood’s Conspiracy to Assassinate History
BACK AND TO THE LEFT
As the open-top limousine cruises silently into view, the president appears to grasp his throat, and is then struck in the head by an assassin’s bullet. His head moves back and to the left, its motion captured in shocking detail by the Zapruder film—a bystander’s film of the actual events—embedded in Oliver Stone’s controversial 1991 movie JFK [RP]. During Stone’s depiction of the Clay Shaw (Tommy Lee Jones) trial for conspiring to assassinate the president, the scene of Kennedy’s head moving back and to the left is repeated again and again as District Attorney Jim Harrison (Kevin Costner) hammers away that it conclusively proves there was a second shooter firing from a position in front of the limousine and not just the lone shooter, Lee Harvey Oswald, firing from behind. His premise is that the victim’s head will always be blasted in the opposite direction from the shooter. The physics say otherwise.
ANALYSIS OF KENNEDY’S HEAD MOTION
If the bullet that hit Kennedy in the head had remained embedded in his skull causing no exit wound, Kennedy’s head motion would have been easy to analyze with a simple conservation of momentum equation. The analysis would have predicted a forward head motion away from the direction of the shooter. But when the bullet exited the head along with a significant amount of high-velocity tissue, the situation became far more complex. While a simple analysis can no longer be considered conclusive, it can establish if it’s possible for the head to move backward instead of forward when struck in the back. We will model the motion as though the head rotated about a pivot at the base of the neck and will use conservation of rotational momentum. A rotational momentum analysis is slightly different than the linear momentum analysis used in the previous chapter, but both obey a conservation of momentum law.
Officially, Kennedy was shot in the back of the head by a 10.37-gram full-metal jacketed bullet fired from a 6.5 × 52- millimeter Italian Carcano WWII surplus military rifle. The bullet’s velocity would have been about 552 meters per second at 100 yards distance. We calculate the bullet’s rotational momentum as though the bullet is rotating around the base of the neck the instant before it hits as follows:
Where:
L = rotational momentum
I = rotational inertia
ω = angular velocity
Assume all objects in the analysis can be modeled as point masses. The rotational inertia for a point mass is
Where:
m = mass
r = distance from pivot
Let LB1 = The momentum of the bullet before collision
LB1 = IB1 ωB1
But
Substitution of 13.2 and 13.3 into equation 13.1 yields:
L = (m • r2) • (v / r)
The military-style bullet that struck Kennedy’s head broke into several fragments that cracked the windshield and dented metal trim inside the limousine. Let’s assume that the fragments retained 33 percent of the bullet’s initial rotational momentum when it exited.
A human head weighs about 11 pounds (5 kg)15.
Assume that about 10 percent of the head’s mass (or 0.5 kg) of brain, blood, and bone tissue exited the head wound in the forward direction after the bullet exited the head. Also assume that the neck’s rotational inertia is minor or negligible compared to the head, and the dimensions of the head are as sh
own in Figure 20. Zapruder’s camera was running at about 18 frames per second, or roughly one frame every 0.057 seconds. The shutter would have been open for about 0.025 seconds during each frame16 [Zavada, Roland J. “Dissecting the Zapruder Bell & Howell 8mm Movie Camera,” http://www.jfk-info.com/zavada1.htm, 10/24/98]. While this sounds like a very short time, it’s enough to blur moving objects, making them harder to see. A moving particle, for example, would look like a blurry streak. To calculate an object’s average velocity, a researcher would have to estimate how far it displaced and how much time it took to move, then divide displacement by time. But, there would be no good way to know exactly when the motion started. If the motion started halfway through the time the shutter was open, the average velocity would be twice as high as if it had started at the beginning of the shutter opening, assuming the blurry streak was the same length. Even worse, in every frame, the shutter would close for about 0.032 second so the film could be advanced. No photographic record would be made during this time. These facts alone place limits on the amount of information available for analysis of the bullet’s high-speed collision with its target.
There is no evidence of the head shot in frame 312 of the Zapruder film. Frame 313 clearly shows tissue expelled in a forward direction from a head wound. It also shows that a particle was ejected from the wound at an upward angle a distance of over 1.5 meters. It’s probably a rotating bone or bullet fragment with at least one reflective side. Its image on film looks like a series of evenly spaced dots (probably corresponding to instances when the reflective side rotated so that it caught the light) connected by a blurry line extending all the way from Kennedy’s head. This implies the particle exited the wound after frame 313 had begun. If the particle had exited before the shutter opened, it would have been some distance from Kennedy’s head when the photographic record of frame 313 began. There would have been a gap between the President’s head and the starting point of the particle’s image.
Assuming that 0.5 kg of mass exited the wound and traveled 30 cm (11.8 in) during the 0.025 second the shutter was open in frame 313 gives an average velocity of 12 m/s (26.8 mph or 43.2 kph). The forward rotational momentum of the exiting mass would be as follows:
Let Lm = The rotational momentum of the mass exiting the wound.
From equation 13.4:
Let LB2 = The momentum of the bullet after collision
Let LH = The momentum of the head after collision
From conservation of momentum:
Therefore, the head would have had to move backward for conservation of momentum to be true.
But
In two frames of the Zapruder film, this would have been a motion of about 22 degrees in 0.11 seconds, which is enough to give the perception that the head was being snapped backward (see Figure 21).
Admittedly, the model is too simplistic to be considered conclusive, but it does indicate that a backward motion of the head could be caused by a shot from behind—a possibility that’s not even considered in Stone’s film.
Conservation of momentum equations—similar to those demonstrating that a shotgun blast won’t blow a shooting victim violently backward—can also show that blasting open a head can make it move in the opposite direction of the bullet’s motion (see “Analysis of Kennedy’s Head Motion”). In the Kennedy assassination, a significant amount of brain, blood, and bone tissue (there’s no way to say it delicately) exited the president’s head wound with a forward and to-the-right velocity. This jet of exiting tissue acted like a thruster pushing the president’s head back and to the left. In addition, when Kennedy was shot in the back prior to the head shot, he raised his hands toward the exit wound in his throat and elevated his right shoulder causing him to lean slightly to the left. This lean may have assisted the leftward motion of the head.
OK, it takes a lot of simplifications and estimations to make these momentum calculations, and so by themselves the numbers presented above are not conclusive. However, experiments with paint-filled skulls, shown in a November of 1988 NOVA program on PBS, agree that if the bullet passes through the skull and expels fluid at high velocity out the exit hole, the skull will consistently move in the opposite direction of the bullet. Experiments with objects such as melons (Penn and Teller among others have performed this demo17), turkey carcasses, and an assortment of other objects have been repeated many times and have shown similar results. Material ejected in the same direction as the bullet acts like a small rocket thruster or jet that pushes the object it was ejected from in the opposite direction. This head motion explanation has become known as the “jet effect.”
Normally speaking, exit wounds are significantly larger than entry wounds. Certainly in the Zapruder film, the wound toward the front of Kennedy’s head appears much larger than any wound in the back. There are no signs of expelled tissue out the back of the head. This means that if Kennedy were shot in the front of the head, the bullet should have been found in his skull. But if bullet fragments had mysteriously exited from the back of his head with little or no blood spray, they would have fallen in the street since Kennedy was sitting in the back of the limousine. The only bullet fragments found from the head shot were recovered in the front seat area of the car, suggesting that they entered the head from the back and exited from the front, as is consistent with a shot fired from behind.
Still, Kennedy’s head motion may have had little to do with conservation of momentum. It may have been nothing more than a random reflex reaction. The analysis of the backward motion of a shooting victim (see Chapter 12) as well as the above analysis shows that victim motion caused by bullets is subtle. Being shot in the head has a tendency to stimulate random nerve impulses. These may have caused Kennedy’s neck muscles to involuntarily snap his head back and to the left. The claim that the back and to the left motion of Kennedy’s head proved that a second shooter located in front of the limousine fired the head shot is an unsupported conjecture.
How Movies Distort Judgment about Shootings
In films, bullet impacts are generally simulated with “bloodpacks,” exploded when the victim is supposedly shot. The explosion often sprays a noticeable amount of simulated blood toward the shooter (the opposite direction of the bullet’s motion). Exit wound blood splatter is often not simulated. (Why waste a perfectly good blood pack on the victim’s back where it’s hard to see?) By contrast, in real life there is some blood spray out the entry wound, but the majority of blood and tissue are expelled at higher velocity out the exit wound. On this basis alone, the Zapruder film indicates that Kennedy was shot in the back of the head and the bullet exited the front. But a person whose only knowledge of gunshot effects comes from movies would likely not be convinced by the spray pattern.
Such a person would have seen simulated shooting victims blown violently off their feet and sent flying backward in movies many, many times—pure nonsense according to physics. A movie-indoctrinated person would expect body motion to always be in the direction of the bullet’s motion. To this person, any backward motion, such as the backward motion of Kennedy’s head, would be convincing evidence that he had been shot from the front. Again, the physics casts doubt.
Could there have been a conspiracy as suggested by the movie JFK? Who knows? The motion of the president’s head certainly does not support the theory of a second shooter in front of the limousine, which is a key element in the movie’s conspiracy theory. Like most things Hollywood, JFK seems to have been far more concerned with generating ticket-sale-increasing hype than with presenting insightful analysis.
COUNTING SHOTS (AGAIN)
After over forty years, available forensic evidence still indicates that a lone gunman fired three shots from the fifth floor of the Book Depository Building, two of which hit President Kennedy. The first hit—now known as the magic bullet—is where much of the conspiracy fun begins. This bullet struck Kennedy in the upper back, exited his throat, and struck Texas Governor John Connelly in the torso, wrist, and thigh.The bullet was la
ter found lying on a stretcher. At first glance, it looks like it’s in pristine condition, but closer examination reveals that it is significantly flattened on one side. The bullet was a full-metal-jacketed type, specifically designed for military use requiring maximum penetration with minimal deformation, as required by the Hague Convention of 1899. For humanitarian reasons, this convention banned easily deformed expanding bullets for military use.
The magic bullet lost a large part of its kinetic energy when it passed through Kennedy’s neck but had little deformation because it struck no major bones. While passing through Connelly’s torso, the bullet glanced off Connelly’s ribs, losing more of its velocity in the process. It had tumbled sideways by the time it eventually collided with a major bone in Connelly’s wrist; this explains why the bullet was flattened on one side.