Aston

Introduction

Have you ever watched that video on Youtube where a couple guys throw a basketball off a dam with and without spin? If you haven't, here it is!

Too lazy to click off this page? Don't worry: here's the summary. When a basketball is thrown off a dam without spin, the basketball effectively drops directly below where it was released; yet, when a basketball is thrown off a dam with some back spin, the basketball curls significantly and drops much farther away from where it was released!

But why does the basketball curl away from its original position?

The basketball curls away due to a phenomenon known as the Magnus effect. Suppose a ball rotates clockwise and translates from right to left through a fluid (gas or liquid). As the ball translates horizontally from right to left, the fluid, from the perspective of the ball, translates from left to right. As the fluid separates due to the motion of the ball, the clockwise rotational motion causes the fluid on the top of the ball to increase its velocity and the fluid on the bottom of the ball to decrease its velocity. Bernoulli's principle states that an increase in a fluid's speed corresponds with a decrease in static pressure or a decrease in the fluid's potential energy. Thus, the increased velocity of the fluid above the ball creates a low-pressure region while the decreased velocity of the fluid below the ball creates a high-pressure region. This difference in pressure compels the ball in the direction of the low-pressure region; the ball thus moves upwards as it translates and rotates.

Interested by the motion of objects experiencing the Magnus effect, I decided to conduct an experiment using a Magnus glider, a spinning toy constructed from two styrofoam cups conjoined with tape at their bases. I wanted to see whether I could predict how high a Magnus glider would go provided an initial angular velocity and initial linear velocity using a rubber band. I expected both initial angular velocity and linear velocity to strongly correlate with the maximum height of the Magnus glider; I expected a higher angular veloctiy to cause a greater difference in pressure between the top and bottom of the glider and a higher linear velocity to cause an increase in the Magnus force.

Methods and Materials

Materials:

  • Magnus glider

  • Rubber band

  • 240fps slow-motion phone camera

  • Phone stand

  • Grid paper

Methods:

1) Using a sharpie, a metal ruler, and a large sheet of paper, I constructed a grid paper (with each line separated by 2cm)

2) I taped the grid paper to the Pritzker wall

3) I set up a phone stand approximately three meters away from the grid paper (far enough to capture the entirety of the grid paper using the 240fps camera without loss of quality)

4) I placed my phone camera into the phone stand and began recording the slow-motion video

5) I wound up and released a rubber band around the Magnus glider besides the grid paper

Demonstration.mp4

A demonstration of how data was recorded (without slow-motion)

Raw Data

Displayed to the left is my raw data, collected from frame-by-frame analysis of the Magnus glider's movement. I analyzed the glider's maximum height (the dependent variable), its initial angular velocity, and its initial linear velocity. I determined the initial angular velocity by counting the number of frames necessary to obtain an integer number of rotations. Using a conversion factor of 240 frames per second, I converted the angular velocity into SI units (radians per second). I determined the linear velocity by subtracting the initial horizontal position from the final horizontal position (the horizontal position at which the Magnus glider obtains an integer number of rotations) and dividing the difference by the time mnecessary to move from initial horizontal position to final horizontal position (converted from frames).

Graphs

Based on expected relationships predicted by the Magnus force equation, I graphed the Magnus glider's maximum height against its initial angular velocity, its initial linear velocity, and both initial and angular velocities together.

Displayed to the right is a graph exhibiting the relationship between the Magnus glider's maximum height and its initial angular velocity. Based on the graph, I could not conclude a relationship between maximum height and angular velocity.

Displayed to the left is a graph exhibiting the relationship between the Magnus glider's maximum height and its initial linear veloicty. Based on the graph, I could not conclude a relationship between maximum height and linear velocity. When attempting to plot different tredlines over the graph, all had R2 values below 0.40.

Displayed to the right is a graph exhibiting the relationship between the Magnus glider's maximum height and both its initial angular and linear velocity. Again, based on the graph, I could not conlucde a clear relationship between the independent and dependent variables.

Discussion

Although I could find no observable relationship between the maximum height of the Magnus glider and both its initial angular and linear velocity, theoretical analysis conducted by the University of Science and Technology in China, as shown on the left, demonstrate that a linear relationship between angular velocity and linear velocity to the Magnus force exists.

Factors causing such uncertainty in the data include my release technique, the varying airflow throughout Pritzker, and my data analysis of the videos recorded. The observed motion of the Magnus glider depends highly on all of these factors, and slight alterations to even one of these factors may cause significant changes in its motion (as expected of experiements involving aerodynamics).

If I had the opportunity to redo the experiment (with unlimited budget), I would continue to use this procedure with better equipment in an environment with no airflow. Instead of launching the glider manually, I would launch the glider with a clamping mechanism at the wound rubber band that allows for instantaneous release of the glider when unclamped. Using a camera with higher FPS and recording quality, I could effectively record an accurate instantaneous linear and angular velocity from a given video.