How Physics Applies to Disc Golf

Kinematics: Describing the throwing motion and disc flight

Written by Team Disc Store Member Joseph Johnson

Kinematics is a section of physics in which we describe motion without reference to the forces that cause or change that motion. Where is our disc? Perhaps on the tee where displacement equals zero or 100 meters down the fairway. How fast is the disc moving? When Anthony Barela throws his disc 79 miles per hour, we can look at that as the final velocity after he accelerated it from rest or as the initial velocity as it begins to fly. Using clearly defined terms like displacement, velocity, and acceleration, we can clearly say where an object is and how it is moving, predict where it will be and how its motion changes, and infer where it was and how it got there. As it turns out, these ideas are all related quantities. If we know where something is and how it is moving, we should be able to figure out where it will end up. Calculus, algebra, and trigonometry give us useful windows into how these variables are related to each other. Most intro physics course summarizes these relationships into four kinematic equations (specifically used when acceleration is constant):

These equations are extremely useful. They show how velocity changes based on how much something is accelerating and how position and displacement are dependent on velocity, acceleration, and time. Another handy tool is to make graphs to visually show these same relationships. A position-time graph shows where an object is at any given time. It also shows how fast something is moving given how steeply sloped the graph is. Similarly, a velocity-time graph can show us how fast something is going, how far it has gone (area under curve), and how much it is accelerating (slope).

Ok, thanks for staying with me so far. What does all of this have to do with disc golf? Everything. These concepts are the most fundamental ways to understand how your disc and your body are moving when you throw. A few years ago, Nate Perkins, an amazing disc golfer and even better person, stopped by our local club to do a clinic and allowed me to take a few videos of him throwing a backhand drive. I used a program called Logger Pro made by Vernier to analyze the video and generate graphs of the motion of his disc and his center of mass. Looking first at the motion of the disc, check out the graph of the position of his disc throughout his x-step and throw.

This graph shows how the disc is moving horizontally throughout the throwing motion. We see initial gradual forward motion (first image below), followed by a slight backwards motion of the disc with his reach back (second image), finally we see very rapid motion as he throws.

The slope of this graph shows us how quickly the position is changing. The steeper the slope, the faster it is going and the larger the velocity. In the first image, we see a positive (upward) slope indicating that the disc is moving forward. In the second image, the slope is negative (downward), so the disc is actually moving backwards. The third image is a positive slope and much steeper than before, so the disc is moving much faster. We can calculate exactly how fast it is going by finding the slope (about 26 m/s or 58.2 mph at release) or we can look at the graph of velocity vs time.

This graph will tell us how fast the disc is going at every point in the throw. The final velocity is the release velocity after the disc has been accelerated and released. Notice the steep slope at the end of the throw as the disc rapidly speeds up. Calculating the slope of the graph will tell us the acceleration of the disc, 159 m/s² at its largest! If we knew the mass in grams of the disc, we could use Newton’s 2^nd law to figure out exactly how much force the disc is experiencing.