Science Fact or Cinematic Fiction? Wednesday, November 25, 2009 |
The visual palette of Tron was revolutionary. Never before had computers been utilized so extensively to create special effects in a feature film, a foreshadowing of visual effects development in the entertainment industry in the years to follow. The day would come when computers would seemingly take over the world and be welcomed with open arms, but not in 1982. Despite its tremendous technological achievements in special effects and computer animation, the Motion Picture Academy refused to nominate Tron for the special effects Academy Awards category, feeling that the team behind Tron's visual effects and computer animation had cheated through the use of machines. It was not until 1997, fifteen years after its initial release, that Ken Perlin of the Mathematical Applications Group, Inc. (MAGI, an early innovator in the area of computer graphics, responsible for the computer animation in Tron, particularly the light cycles and battle tanks) won an Academy Award for Technical Achievement for his invention of Perlin Noise first used in Tron. Perlin Noise would go on to influence computer graphics for years to come, much as Tron would continue to influence the film medium and entertainment industry.
While Tron's computer graphics were truly innovative for their time, they were not without their limitations. MAGI was the first production house utilize ray tracing to generate images, as well as constructive solid geometry techniques, yet the machines of the day were hard pressed to keep up with the FLOPS (floating point operations per second) required for realistic simulations. As such, the computer simulated physics seen throughout Tron, and in particular the climatic light cycle race, are quite lacking by today's highly technical standards. A number of properties inherent to our physical world are violated in the process including, but not limited to, the laws of momentum and inertia, gravitational pull and acceleration due to gravity, and optics of light.
As the light cycle race begins, we see three users confronted by three computer controlled opponents, facing off in a death-match style race. The vehicles themselves were modeled in the vein of futuristic motorcycles propelled by streams of light rather than traditional combustion engines. The vehicles were designed by conceptual artist and industrial designer Syd Mead, most popular for his series of vehicle designs for the films Bladerunner, Aliens, and of course Tron. Throughout the race the light cycles take a number of miraculous, and seemingly impossible, ninety degree turns without and loss of traction or momentum. According to Newton's first law of motion, an object will remain in motion at a constant velocity until acted upon by any net external forces.
Imagine a car in motion on the highway being driven by a single person. When approached with a sharp curve the car can indeed turn to follow the road. However, a force is exerted upon the driver. This occurs due to the the law of inertia. The driver has a tendency to remain in constant motion. The car turns only due to the friction between its rubber tires and the road, a net external force acting upon the car. The driver likewise will remain in constant motion following a linear path until an external force alters the path of motion and redirects it, typically the car's seat belt or interior body acting upon the driver. If it were even physically possible for a driver to instantaneously turn the car at a right angle as accomplished by the light cycles in this chase scene, the results would be disastrous.
The term centripetal force, or g-force, can be misleading when it does not refer to a force at all, but rather an acceleration. G-force is a common measurement crucial to fighter pilots while soaring the skies in combat situations. Contemporary fighter jets can typically sustain a force of no more than 12 G. In comparison, a Sprint missile, a two-stage, solid-fuel anti-ballistic missile, armed with a W66 enhanced radiation thermonuclear warhead, reaches an acceleration of 100 G and a cruising velocity of Mach 10 (7500 mph), in 5 seconds. G-force thresholds vary, with an untrained individual losing consciousness somewhere in the 4-6 G range. A trained, fit individual wearing a G-suit (or perhaps more accurately named an anti-G suit), such as a fighter pilot can sustain up to 9 G without loss of consciousness, but not without some difficulty. Lacking a g-suit, 9 G has the potential to be lethal.
The effects that the driver experiences are split between inertia and centripetal force. Thanks in large part to the gridded racing surface, the velocities of the light cycles can be determined. The drivers of the blue team, and leading characters in the story, are three men approximately 6 ft tall. The length of each light cycle is a bit longer than the length of the men, around 10 ft. Each grid on the racing surface is about as long as each vehicle, forming squares 10x10 ft. Using the standard frames-per-second of film, 24, and the amount of squares passed in 24 frames of film, approximately 13, the light cycles are traveling at roughly 130 ft/s, or 88.636 mph. When the cycle makes an abrupt right angle turn at this speed, its forward velocity vector changes from 130 ft/s to 0 instantaneously, while the horizontal velocity vector explodes from 0 to 130 ft/s (conserving energy and momentum within the turn). Due to inertia, the body of the driver will continue with its forward velocity until acted upon by another force, in this case the interior of the vehicle's cockpit.
A modern statement of Newton's second law is a vector differential equation, where force is equal to the change in momentum over the change in time. This form is typically reduced to a more algebraic friendly equation that is more commonly known, F = ma. However, the form F = mv/Δt allows one to calculate the force of an object in relation to its mass and velocity. According to online research, the average weight (mass) of a 6 ft tall male (the driver) is around 180 lbs, or 81.647 Kg. Plugging this into the equation, along with the previously calculated velocity of 39.624 m/s (130 ft/s) for the cycle (the passenger is within the same inertial frame of reference therefore has the same velocity of the cycle itself) and the change in time (1 frame to turn at 24 fps = 1 s, which would be 1/24 s or 0.0417 s) yields a force of 77582.272 N. (*Note: the speed limitations of film, 24 fps, greatly influences the change in time, as Δt should be much much smaller than a single frame and this would greatly increase the force of impact) This is the force of the body striking the interior of the light cycle's cockpit at the point in time it makes an instant ninety degree turn. It is essentially the force of a human body striking an unmovable object at 90 mph and is more than capable of killing a human being.
These extremely sharp turns also bring into play centripetal force, or g-force. G-force is actually an acceleration, not a force, and is therefore calculated as such. Using the equation F = mv²/r, where F is force, m is mass, v is velocity, and r is radius of curvature. Another force equation can be used, F = ma, to plug in ma for F in the first equation, eliminate mass altogether, and what is left is the equation A = v²/r, or g-force. The velocity of the light cycles has already been calculated as 39.624 m/s. The radius of curvature of a right angle is 0, or almost, due to the fact that a ninety degree angle lacks any sort of curvature at all. The radius of curvature is in fact the limit of r as it approaches 0, or in layman's terms, a very very very small number. Plugging in these values yields a g-force of infinity. We have established that even with modern technology and space-age anti-G suits, the human body can take very little more than 9 G. A value of infinity G acting upon the driver of a light cycle amidst a right angle turn could only result in instantaneous death.
Now that it has been established that the driver of a light cycle is already dead, either due to the law of inertia slamming the body against the interior of the cockpit or the extreme amount of centripetal force exerted upon the driver (the result is sadly the same), other parts of the scene require further analysis. For one, the gravitational field in which this light cycle race is taking place is a bit off. A good way to get a feel for the physical world of these events is to determine the force of gravity due to acceleration within the gravitational field. For this we need a falling object within the scene. It just so happens that as one of the light cycles crashes into a wall of the racing arena, its tire falls to the floor in perfect view of the camera.
The equation d = 1/2gt² will yield the distance of a falling object in an environment with gravity g and fall time of t. Rearranging the variables yields g = 2d/t². A standard motorcycle tire stands approximately 20 inches tall; 1.667 feet or 0.508 meters. In the scene the tire falls roughly eight times its total height (diameter) in 41 frames, or 1.708 seconds. Plugging these values into the equation results in a field of gravity with an acceleration of 2.786 m/s², less than the acceleration of gravity on earth and much closer to the acceleration due to gravity on the moon (1.62 m/s²). This is readily evident in the shot as the tire as an unnatural feel to its falling animation, as if it were falling upon the moon's surface.
The original concept behind the light cycle design was to create a futuristic vehicle propelled by light. This idea of a light propelled vehicle has an alluring appeal to it, both aesthetically and technically. However, it contains one major flaw. According to Newton's Laws of Motion in classical mechanics, for every action there is an equal and opposite reaction. This law of reciprocal actions is what propels individuals from one place to another on a daily basis, whether it be a foot pushing against the pavement and the pavement causing the body to move forward or jet propulsion propelling an aircraft through the skies by passing a jet of fluid in the opposite direction to the direction of motion. In either case, a mass of significant force must be pushed or propelled in the opposite direction of the direction in which you wish to move.
The problem arises when this propulsion is no longer based on a body part (such as the leg and foot) or jet stream, but designed around light. Light is electromagnetic radiation of any wavelength, visible or not. Light exists in miniscule packets called photons, and exhibits properties of both waves and particles (wave-particle duality). In order for a stream of light to possess the ability for jet propulsion, it must have mass. General relativity declares that any particle with mass m is equal to an energy E, as given by the famous equation E = mc². A photon also has momentum, and with both energy and momentum, it seems as though it should have some mass to it. However, it is widely accepted that a photon has a mass of zero, or no mass at all, the subject of which goes far beyond the scope of this paper. Leaving the study to far greater minds than my own, I accept a photon as mass-less. With the mass of a photon being equal to zero, it becomes impossible for a stream of photons and electromagnetic radiation (light) to propel anything according to Newton's third law of motion. Thus, a light cycle is impossible.
For all of its shortcomings (by today's standards), Tron was nether the less a technological feat in the 1980's. It revolutionized and transformed the film and entertainment industry and greatly contributed to the course computer animation and visual effects has taken over the years. Under appreciated and deemed a complete failure in 1982, years after its development and release Tron has finally become the cult classic it was meant to be. The animation and computer graphics are crude in comparison to the blockbuster films of today, but it contains little more flaws of physics than current films. Most importantly, Tron is a work of science fiction. Within that genre anything is possible, including cycle vehicles propelled by streams of photons. This possibility of anything and breaking of conventional physics is what makes the science fiction genre so entertaining. It is a necessary evil captivate and thrill the audience.
This analysis and critique holds Tron's computer graphics and visual effects up into the light of our physical world. However, the world of Tron cannot truly be compared to our own. In fact, it is not a physical world at all, but a virtual world, governed only by the laws and syntax for the hardware and software that creates it. The story takes place within the confines of a computer, and who is to say what the gravity of this virtual world is, or whether or not it fluctuates or remains stable. The true genius behind Tron is its ability to completely absorb us within a digital world. Comparing the physics of our world to the digital world of Tron is impossible. They exist as two distinctly separate worlds, varying frames of reference, parallel universes that are similar yet simultaneously vastly different.
Computer graphics have come a long ways since 1982:
