( Frisbee Simulation )

Goals

I worked on this project with Tyson Cook in the spring of 2005. Tyson and I are both physics majors, and we disc golf together often, so the physics behind disc flight is of utmost importance to us. We wanted to create a relatively realistic Frisbee disc flight simulation. Toward that end, we set out to:

1. Implement and analyze the following forces on the disc: gravitational, non-inertial, lift, drag.
2. Implement and analyze the torques produced by the lift and drag moments--since they act about the center of pressure (COP) and not the center of mass (CM), the lift and drag forces generate a moment about the CM which effects the flight.
3. Come to some physical insight into the dynamics of actual disc flight through our simulation.

Method

We first found resources by Hubbard and Hummel (see [1], below) detailing the mechanics of Frisbee flight, including forces and torques generated at the center of pressure of the disc by lift and drag. We re-derived their equations and came up with a set of slightly less accurate, simpler equations of motion for the disc. Next, using the Open Source Physics libraries, we set up a simulation in Java which would model the flight of a Frisbee using our equations.

Here is a screenshot of the simulation after initialization:



Our program took in a number of parameters (i.e. mass and diametral inertia of the disc) and initial conditions (e.g. initial position and velocity), and generated plots of: 1) a three-dimensional view of the disc flight; 2) the trajectory in the xz-plane; 3) the velocities in the x, y, and z directions versus time; and 3) the rate of change of angular velocities versus time. This allowed easy analysis of disc flight given any set of initial conditions or disc parameters.


Outcome

By the end of the project, we had completed a simulation of disc flight which effectively modeled the basic components of three-dimensional disc flight: motion in three axes (with gravity), quadratic drag, lift and drag forces/moments, and precession dampening effects of the air. We did not implement all of the equations derived by Hubbard and Hummel in our simulation, but instead implemented our own (simpler) set of equations to account for the physical effects.

Although H&H's is a more accurate representation reality, our simplified version enabled us to come to some fundamental insights about disc flight. These include the fact that the angular velocity about the symmetry axis is important for flight stability (without a strong spin, the disc will die); or that the lift of the disc has a strong impact on the distance of a throw (without lift enabled, the disc goes a much shorter distance--and maintains a horizontal component of velocity despite drag in the long-term limit). These computational insights matched well with personal experience with Frisbee flight. All in all, the project worked out well.


References / More Information

[1] Hubbard, M. and S. A. Hummel. "Simulation of Frisbee Flight". Presented at the 5th Conference on Mathematics and Computers in Sport, G. Cohen, Editor, University of Technology, Sydney, New South Wales, Australia, 14-16 June 2000.