Science Fact or Cinematic Fiction

The Law of Acceleration in Current Film

Every once in a while, as we sit captivated in front of yet another creation of modern cinematography, we like to turn to our friends and quietly remark something along the lines of, “that didn’t look right”; or go all the way and proclaim aloud “look what they did there, that can’t possibly work!!” In animation, that sense of acute perception is somewhat deadened in us, but in viewing CGI movies it comes fully to life and makes us all critics. So, are we right in thus judging the carefully charted special effects, presented to us like the ultimate spice of a motion picture, purposefully designed to suspend our sense of disbelief, and push the known-to-all laws of physical reality just far enough to enhance our viewing pleasure? Or have we just not grasped enough knowledge of our own world to accept it on screen when it is shown to us so openly? To find out, let us examine a few popular films and scrutinize further to find those flaws, real or fake. And since we cannot pick them for all their potential mistakes, let us focus on a singular physical law which is at stake in all of them. For this paper, I have chosen to examine Newton’s second law, that of Acceleration, and how it fluctuates depending on the mass of the object and it force. For instance, something might appear to walk, jump, fly, etc, too quickly or too slowly depending on its apparent mass; or the reverse of that; it is a principle which we are so familiar with, having used it on a daily basis our entire lives, that we pick up on it right away, but often cannot explain why. To clarify this, the movies that I have picked are The Lord of the Rings: The Two Towers, The Iron Giant, and The Chronicles of Narnia: Prince Caspian.

To start off with the Two Towers, it must be said primarily that the film is flawlessly done, and even though it contains more than enough potential examples of gravitational flaws, it makes sure to work them out so that it looks entirely real or masks them to the best of the animators’ ability. Yet a few sequences suggest an overlooking of the aforementioned acceleration principles; we start to notice it better when the Ents come on the scene, those long legged giants, not too far off descendants of trees, which chose to stay out of the war until the sequence in question, when they all gather to fight the armies of evil by stomping on them and throwing massive boulders. But before all that (which, incidentally, looks very proportionate to how it would look in real life), the Ents have to walk to Entwood, their special place of gathering, and they do that in small intervals throughout the entire film. The two hobbits, Merry and Pippin, hitch a ride on the main and most important of the Ents by the name of Treebeard, gripping to him as to a large tree. Now, there are several such scenes, mainly for the purposes of dialogue, but the one I want to focus on is when the three characters enter into Entwood, a small glen in the middle of the woods and greet the others of their kind.

Even in the beginning of the relatively short sequence, we see that something isn’t right: the hobbits, clinging to the giant’s arboreal visage, move across the screen rather slowly given the estimated height of the tree person. If the average height of a hobbit is 3.5 to 4 feet, it becomes easy to guess the giant’s height when the three of them come into full view a few seconds later: Merry is sitting on top of the giants head, and measuring down from there, the Ent is approximately 5.5 hobbits tall, about 22 feet in all. Seeing him from head to toe, also allows for easy steps per frame measure; and here we see that it takes him no less than 60 frames to take a single step! Given that the movie’s frame rate is about 24 fps, that makes his walk 2.5 seconds per step, resulting in 5 times slower than the average speed of 12 frames per step. So far, the visuals match the calculations, unless we include the probability that the hobbits would not be able to ride as comfortably and smoothly at a height of 20 feet; be they as they may creatures used to harsh environments, the Ent simply would not be able to place his feet thus smoothly on the forest floor. However, the bigger issue is the background, as it doesn’t seem to match the speed of the giant’s gait. If he is 5 times as tall as a small human, and moves 5 times as slow, would he not travel 5 times the distance? And that does not seem to be conveyed in the short segment. Seeing the world on horseback, or moreover, the back of an elephant, already seems fast to us; so the background must at least be blurred or appear to move by at a more than average speed.

A similar problem occurs in the Iron Giant, in the scene towards second half of the film, when Hogarth, Dean and the Giant are at the lake. Hogarth is in the water, beckoning his iron friend to come into the lake as well; at which point the Giant turns around, goes amongst the trees and jumps in, creating an enormous all-sweeping tidal wave. We don’t see as he walks into the forest, but we hear each mechanized step; it takes him nine steps total to achieve a run and propel himself into the air, at least twice his own height. He is airborne for at least 8 seconds before reaching water, making the fall 25 feet per second (200 ft / 8sec). What becomes problematic in this particular sequence is the sheer height and mass of the giant; given those perimeters, he could not possibly push himself off the ground almost instantaneously and achieve that kind of flight afterwards.

We cannot see all the Giant’s movements, put judging purely by sound, it seems that it takes him no time at all to accelerate. To calculate his jump magnification, let’s estimate that his push time is no more than 2 frames and his push height a little less than a third of his total height, about 30 feet. Therefore, 200 ft / 30 ft = 6.7, the number of times by which his jump height is magnified. We can see clearly that the numbers simply don’t add up. A creature that size cannot just sweep into the air without proper preparation and acceleration, unless he has other means of propelling himself into the air besides strength and counter force.

And on the subject of force and acceleration, the opposite occurs with much smaller objects. For instance, in Prince Caspian, we see the fighting mouse, Ripacheep, bring down four grown men in armor with only himself and his sword. Just as the unnatural acceleration of too heavy objects occurs in the previous examples, here we see projection of too heavy a force from a small source. As in the Iron Giant, we don’t see his movements but the sounds and the eye trace is there, giving us an estimated speed of about 90-100 miles an hour. When he comes out of the grass and we see that he is indeed 1.5 feet tall, the proportions of an abnormally sized rat, it becomes plausible for his movements to be swift – he is a rodent after all. Yet the striking force remains a mystery; we know that the reaction must be at least equal to the action in order for movement to occur; moreover, the net force must not be lesser and the object acted upon may not be heavier in mass than the one that acts upon it. In all probability, a creature of that stature, i.e. 1/5 the size of a human, would weigh the proportionate amount of about 30 pounds. What it ultimately comes down to is Newton’s simple formula for the Second Law, F=ma. Going by estimate, we can say that m=30lbs and a=90 mph, coming to 2700 N on all four defeated soldiers. Given that the laws of the movie obey the laws of nature in our own universe, this would make an impossible strike, since N would have to equal at least 13,000, or the force projected by a human adult.

After this brief look into the world of all three films, we begin to understand just how altered our perception of the natural world becomes based on what we observe from entertainment sources. While one world was a replica of our own, except an animated version, the other two were based in the real world with heavy reliance on CGI to fulfill the missing pieces. From this we can only conclude that whether animation is the only means of communication or the spice that helps the main film be functional, it very often strays far from the truth to fulfill its objectives. Still, if its sole purpose is to please the viewer and enhance the story, all three fills do a great job of fulfilling that ultimate goal.