The Laws of Physics in an Animation Universe

Physics in TANGLED

Tangled is an animated feature length movie released by Walt Disney Animation Studio in 2010. This movie also celebrates Disney’s 50^th feature classic film counting from Snow White and the Seven Dwarfs in 1937. Tangled continues the tradition of creating a magical world with “happily ever after” mood. The story of a lost princess names Rapunzel, who got kidnapped by Gothel and lived in a towel for 18 years before Flynn Rider came and helped her chased after her dream.  Just like other previous films by Disney, Tangled maintained Disney’s realism style of animation. This means the way the world operates in the movie is depicted very close to our world in term of physics and the appearance of the characters.  Most of the time in Tangled, the characters’ movements followed the physics rules in our world, but there are a few exceptions. In this paper, I will discuss about the center of gravity, the falls, and the way Rapunzel’s hair works.

There are many scenes in Tangled that demonstrate the rule of central of gravity. Central of gravity is the average position of an object/character’s weight distribution. The human’s central of gravity is roughly in the middle of our body. This showed in minute 8^th of Tangled, when Flynn Rider used a rope tied just above his hip to lower himself from the roof to steal the princess’s tiara. The rope must be tied precisely around his center of gravity for him to be perfectly balance and parallel with the ground like in the movie. Another rule that follows, for an object or a character to be balance, the center of pressure (a vertical line that passes through the central of gravity to the ground) has to be inside the base of support. Base of support of a standing human character is the area under and between the two feet. The makers of Tangled were also well aware of this principle. In minute 15^th, Flynn Rider stopped at a big tree while running away from the castle’s guards. He extended his left hand and rested it on the tree to shift some of his weight over to the tree. By doing so, Flynn expanded the base of support from the area between his two feet to a triangle between his two feet and the tree. With a bigger base of support, Flynn established a more stable pose, which helped him rest his legs because now his legs no longer carried all of his body’s weight. The center of pressure and the base of support principle helped making the way the character fall down more believable. When Flynn Rider and Maximus stumbled on each other to get to the tiara, Maximus bit on Flynn’s boots while he tried to run forward, making his base of support smaller. Flynn’s body is running forward, his center of pressure point fell outside of his base of support, so he fell down. The law of physics not only helped created a realistic world in Tangled; it also helped the movement of the characters look more convincing.

         On the other hand, the makers of Tangled bent the rules of physics to create a magical world with contrast outcomes for the protagonist and the antagonist. For example, the same unfortunate events like falling down a high position for both characters, the protagonist tends to survive while the antagonist most the time would die (as if gravity favors the good ones). In Tangled, Flynn Rider and Maximus flied up and fell down several times and ended up being perfectly fine. To break down one of the falls, Flynn and Maximus fell for 11 seconds down a high cliff while fighting over the tiara. At first they were holding onto a tree branch, so air resistance was blocked by the tree branch, hence they fell down with the same velocity. Then, the branch hit a rock and broke in half while Flynn and Maximus continued to free fall to two different directions.  Without the tree branch, Flynn with the weight of about 170 pounds, will fall much slower than Maximus with the weight of around 1300 pounds (an average horse weight) due to air resistance. However, when Maximus landed on the ground, he stood up right away, unhurt and started looking for Flynn, who was already well prepared and hid behind a rock not far away. In reality, Flynn would fall down at least a few second after Maximus due to his much lesser weight, so he would not have enough time to hide, not to mention that both characters should be seriously hurt from such a brutal fall. Another example is at minute 80^th, when the Gaul thugs wanted to rescue Flynn from the castle. They put Flynn standing on one side of the seesaw and had another big guy jumped on the other end. The big guy took around 2.5 seconds from his original position to the seesaw and that force sent Flynn off flying for about 5 seconds and landed on the back of Maximus, who were waiting outside the castle wall. This can actually be done if the pivot of the seesaw is closer to where Flynn stood. However, Flynn landed his butt on Maximus’s back unhurt was not how things suppose to happen in real life. Flynn’s is around 77 kg, while free fall on Earth, he would pertain a force of around 1,735 Newtons on Maximus’s back. Because Maximus is a horse with bigger mass, he would probably be fine after Flynn landed on him, but based on Newton’s law of reaction: “for every action, there will be a reaction”, Maximus’s back will exert the same amount of force back on Flynn when he landed, which will cause his body some serious pain, or even bounce up after he landed. With the same concept, at the end of the movie, when mother Gothel fell from the towel to her death, her body disappeared before she crash to the ground. Suppose if her body did not turn into ashes, she would still die from the fall due to the force of gravity pulling her body down, and there wasn’t enough time for her body to reach terminal velocity. Predictably, antagonists falling to their deaths in the end are very familiar in Disney’s classic movies.

            

It would be a regretful thing to not mention Rapunzel’s hair in this paper because after all, her hair is the root of the story line. Rapunzel’s hair is very special, she has magical hair and for eighteen years of her life, she never cut it. Her hair is around 70 feets long and weight around 16-18 pounds. With a petite body structure like Rapunzel, carrying that much weight on her head is a burden. Yet, in the movie, she is a very energetic young girl, who jumps and dances around a lot. Of course in real life she would not be able to do all that with 18 pounds of hair dragging behind.

 However, this is still a magical world, so the animators have to make Rapunzel’s hair appear with less burden to Rapunzel, yet still maintains its weight. To make this movie, the film makers used software to stimulate the hair and make it look as believable as possible. One of the obstacles they faced was the fiction between the hair and the ground. If they keep the fiction match with real life then when Rapunzel walk, her hair will drag behind so much that it will create a 30 degrees angle from her head, which make it looks like she is really struggling with her hair. It doesn’t look very appealing to the audience. They tried to lower the fiction on the grounds, so that it would appear as if the hair is sliding on ice. This won’t work because her hair will end up sliding faster than her when she walks. To fix this, they would cut Rapunzel hair into two separate parts with two different level of fiction. They will decrease the level of fiction to the part of hair that connected with her head, so that when her body and head move forward, the hair will move closely with the body while the end part will move slower. There is another question that challenges the rule of physics in Tangled: how strong is Rapunzel’s hair, physically? Or more accurately, how strong is Rapunzel? She used her hair to grab, pull, hold on to objects or characters, and most of the time, she does it very effortlessly with a few exceptions. For instance, when she wrapped her hair around Flynn Rider and pulled him toward the closet, she had to use all of her strength. Then a few minutes later, she tied Flynn onto a chair with her hair and used only her left hand to easily move the chair around. Another time, she used her hair to grab Flynn’s hand and swing him across a 50 feets wide cannon. This shows that the actual physical capability of Rapunzel is very inconsistence. However, as an audience, I don’t find this distracting at all because this contrast is what makes up Rapunzel, who is sweet and innocence, yet also strong and independence.

            Disney’s 50^th animated feature length movie Tangled follows the tradition of creating a magical yet realistic world. This movie is a huge success for Disney Animation studio due to the excellent and refreshing animation, beautiful graphics, breath taking concepts, brilliant sound tracks and engaging story line. It has all the elements that a great entertaining movie should have. The animators are well aware and respect the center of gravity principle, which makes the characters move in a smooth and believable way. They also know when to bend the law of physics and gravity to support the story line and the outcome of the movie. One of the most fascinating things about this movie is Rapunzel’s hair. The way Rapunzel’s hair work in Tangled is most different thing in term of physics compare to the way human’s hair work in our universe.  And that created a beautiful and unique world in Tangled.