First Term Paper: The Laws of Physics in "Frozen"

      Frozen is the latest Disney 3D musical animation film released in the winter of 2013. The movie can be regarded as a breakthrough in Disney world. Frozen tells a story about Elsa and her younger sister Anna who are princesses of Arendelle. Elsa was born with a magical power to manipulate ice and snow. One day when these two girls playing, Elsa accidentally hurts Anna. From then on, Elsa began to isolate herself from people (including Anna). On the day of Elsa’s coronation, Anna argues with Elsa for her marriage with Hans and takes Elsa’s gloves away incautiously. Without gloves, Elsa exposes her abilities, freezes the whole country and flees to the mountain. In order to bring Elsa back and end the winter, Anna decides to go up the mountain to find her sister. She meets Kristoff, the reindeer Svan and the snowman Olef and takes the adventures with them on her way to the mountain. Finally, “the act of true love” between Elsa and Anna saves their lives and helps Elsa to control her power and then bring the summer back to Arendelle. Frozen presents the audience an audio-visual feast and gives a “non-typical Disney” experience. When we are highly praising the visual impacts of the movie, it’s not difficult to notice the “hyper-realism” that Disney pursues. Generally, although the movie is all about a surreal fantasy, it still follows a series of laws and rules, which contribute to the authenticity in a logical sense. To be more specific, Disney’s “realism” is actually based on the theory of perspective and physics of the real world with “visually acceptable” exaggerations and deformations (totally different from “eccentric mise-en-scène”). In this paper, I will describe some of the scenes in Frozen which may or may not obey the physical laws of the real world and analyze the effects or functions of them.

      The first thing I want to talk about is the gravity. Gravity is the most common physical concept that everyone experiences in everyday life. With the gravity, things tend to fall freely on the surface of the earth. Here we need to mention the acceleration that the Earth imparts to objects, also known as “the gravity of earth” with a constant value of 9.8 m/s² , which means if an object is thrown into air or a person jumps, once their velocity decreases to zero, they will fall with an acceleration of that value. To be more straightforward, things cannot stay still in the air without external forces in real world. However, it would be different in the animation.

For example, when Anna knows the gate of the castle will open, she is very happy and then jump to the air to simulate the poses of the pictures hanging on the wall. It’s not hard to find that there is a period of stop in the air which is impossible in reality. Besides of that, the height that Anna jumps up to is also exaggerated. The elasticity of sofa is not as large as the trampoline after all. 

Another example is that when Kristoff is making an escape over a cliff, he continues flying horizontally even after his sledge falls off. It actually cannot happen in reality because Kristoff has the same velocity as the sledge, thus he should have a same path of motion with the sledge. 

The most attractive visual effects might be Elsa’s abilities to manipulate ice and snow. It’s kind of interesting to see that the natural phenomena will change according to human’s emotions and wills. Here I would like to point out two scenes related to Elsa’s magic. The first scene is that when Elsa is in extreme sadness (e.g. her parents’ deaths, Anna’s freeze), the snowflakes stay still in the air like there is no gravity any more. The second scene is that when Elsa is thawing the kingdom, snowflakes and ices are all flying upwards. According to my knowledge, human beings cannot generate such a force purely with their bodies to fight with gravity.

      The second thing is about the exaggerated resistance in the movie. In this paper I will only analyze friction. We all know that there are several types of friction in real world. 

In the scene that Anna slides a long distance horizontally on the wooden floor in the ballroom, it actually makes a change for kinetic friction. The value of the friction force is decided by both the coefficient of kinetic friction and perpendicular force. In reality, she cannot slide that long even with a comparatively small coefficient because of her weight. 

Comparing to kinetic friction, there is another type called static friction. According to the definition of Wikipedia, “static friction is friction between two or more solid objects that are not moving relative to each other and the static friction must be overcome by an applied force before an object can move”. In the scene that when Anna is climbing the steep mountain (almost upright), she grabbed the rocks without supports and didn’t fall, it means that the static friction between rocks and her hands must be able to support her weight, which is not possible in reality.

      The above two aspects prove that animations can create a world that doesn’t obey the laws and rules of the real world. However, it doesn’t mean it is isolated from the reality especially for Disney’s animations. When we look at the past Disney’s animations, it’s easy to notice that they are all based on a simulation of the real world. The good thing is in this way can animators shorten the distance between the audience and the fake world they created. The use of inertia in Frozen is a good example to show that. In the scene that little Elsa and Anna are playing on the ice, Elsa slips with her body leaning backward. The reason is because of inertia, her body keeps the still status when her feet suddenly moving forward. 

Another scene that reflects the same principle is that when Kristoff is riding his reindeer in a very fast speed and then suddenly stops, he continues “flying” forward for a short amount of time. These scenes can always be seen in reality. It’s like those characters are just like one of us and have real lives.

      In a conclusion, I think that even though the animation is made in the virtual world, the fundamental physical laws are still based on the real world. And even though some of the phenomena are unreal, the scenes are still believable. I summarized four reasons to explain that. First of all, the optical illusion is properly used with acceptable exaggerations by animators. Secondly, I may say that some of the physical laws are serving for plots (like the main characters cannot die even they fall from a really high height). Thirdly, the coherence of the logic may let people ignore the unreal physics. In other words, their exaggerated acts are shown for specific reasons. Last but not least, the existence of unreal physics can reflect emotions of the characters and increase dramatic effects.