Physics of X Episode 6: The Science of Hitting Cat Sith in the Air

This week, we go back to what seems like a very basic physics question—speed versus acceleration. Harry Dresden uses this concept very effectively when fighting supernatural creatures. Before I reveal what Harry does, let’s talk about speed versus acceleration. For a quick overview of this question, you can check out the YouTube video below like you can with any episode in this series:

One of the most basic questions in physics is how an object’s position changes in time. An amazing outcome of careful study is that essentially all you need to know is that speed measures the change in position in time and acceleration measures the change in speed in time. And those are the only two “changes in time” one generally needs to describe everything about the motion of an object. You might think you need to also know how the acceleration changes in time and how the change in acceleration changes in time, etc., but in fact you do not!

One caveat, direction matters deeply for motion, as I discussed in Episode 4, so you really want to consider velocity not speed. But for simplicity, in this post, I will focus on changes in magnitude (the size of changes) and not direction changes.

What is interesting about the history of our understanding of motion is that a really careful description of acceleration is attributed to Galileo in the late 1500s and early 1600s. This is incredibly late in human history. Prior to that time period, the focus was on speed—the change in position with time of objects. We were most concerned with how fast things were moving and what motion even is. I suspect that this is in part because human scale accelerations (change in speed with time) are not particularly large.

In comparison, I would suggest that the common experience with cars helps people understand speed versus acceleration in a more intuitive way. For example, we regularly talk about the “top speed” of a car and know that this is the distance traveled in a certain amount of time, such as 120 miles per hour. We discuss the top acceleration of a car separately and know that this refers to the change in speed, such as 0 to 60 miles per hour in 8 seconds. We also understand when speed is relevant (How long does it take to get to my destination?) versus acceleration (Can I get up to a high enough speed to merge onto the freeway in time).

Now let’s turn to the impact of speed and acceleration when fighting supernatural bad guys, whether magical or “super-powered” as in Marvel or DC. In general, we tend to use the adjective “fast” for characters with a high speed and “quick” for characters that change speed quickly or have a high acceleration. Keep in mind, even if you are able to go 500 mi/hr, if it takes you three days (small acceleration) to get to that speed, it is not all that helpful in your typical battle between heroes and villains! Likewise, if you have awesome acceleration, but your speed maxes out at 0.1 mi/hr, you are probably not that dangerous.

The really dangerous characters have high maximum speed and high acceleration. This makes them incredibly difficult to hit and often allows them to move before you can even react. From an aiming-to-hit point of view, acceleration is probably the tricky one as it can cause sudden changes in speed that make the position you are going to be in very different than expected. But, here is the trick: accelerations do not just happen — they require a cause.

The fact that accelerations have a cause was Newton’s big breakthrough. This is the heart of Newton’s Second Law—forces cause accelerations. Now, this matters in a battle. If your speed is constant, your position becomes highly predictable. Tracking an object moving at constant speed is one of the things humans have evolved to do! But imagine a person running in a straight line but randomly slowing down, speeding up, stopping, and starting—it can be hard to predict where they will be next. All of those changes in speed require a force to cause an acceleration which is the definition of a change in speed.

When you are running along the ground, the force that causes your acceleration is the interaction between your feet and the ground. Here is where you get to take advantage of Newton’s Third Law. For every interaction between two objects (in this case, your feet and the ground), there is an equal and opposite force on each object. So, when you push on the ground, it also pushes on you. There are some limits. For example, friction is necessary for you to be able to push forward and backward. But, ultimately, you get some level of control over the force exerted on you by controlling the force you apply to the ground and that determines your acceleration.

Once an object is in the air, things are very different. Unless you have a form of propulsion or the ability to push significantly on the air (such as a bird’s wings), once in the air, the only interaction you have with anything is the force of gravity between you and the Earth. This is a very interesting situation because even though the force of gravity causes acceleration, this is a special case of constant acceleration. Once again, your motion becomes highly predictable (and to be fair, direction does now matter despite my statement earlier about ignoring direction!).

Objects moving through the air only under the force of gravity are so special that we give them a name in physics. We call it projectile motion. Just think about the act of throwing a ball. Once it is in the air, it moves in such a way that we can track it and catch it! (Well, most of the time, and with some practice!) Or think about a receiver catching a football. When catching it on the ground, they have the chance to suddenly change direction, fake out a defender, and run for more yards. When catching it in the air, they really cannot change direction and are generally hit immediately by a defender (unless they were so wide open no one was nearby).

Now we can return to Harry Dresden as he faces Cat Sith in Cold Days. Cat Sith has supernatural speed and acceleration and is about to attack Harry. Because the book is from Harry’s point of view, Jim Butcher nicely gives us insight into Harry’s thoughts. Harry knows that he would have no real chance against Cat Sith’s speed and agility in most situations. But, he also knows that once Cat Sith leaps into the air, he has become an example of projectile motion. His trajectory is now determined, and though he can twist his body, he cannot change his path of motion. Harry uses this moment to strike him and send him flying!

There are many examples I can think of where Harry Dresden (and other characters) take advantage of moments when someone faster and quicker is not able to leverage enough force to utilize their potential for high accelerations. In the comments here or on the video, let me know your favorite examples of characters using the physics of acceleration to defeat the supernaturally fast!

Originally posted on Medium.