Fluid Dynamics and the Frisbee

[For the official course page, click here .]

With a name coined by the students at Yale who used to toss pie-plates, the frisbee has a rich heritage with university students. Ultimate frisbee, frisbee golf, or just tossing a frisbee at the beach are all well-known pastimes. A frisbee is simply a disk that is hand-launched with some spin. The behavior of a frisbee in flight may be understood by examining the fluid dynamics of the frisbee. A frisbee is a type of airfoil that cuts through a fluid - i.e. air. It is then not unlike the wing of an airplane. According to The Exploratorium, the rim of a frisbee is crucial for frisbee flight:

What effect does the rim of a frisbee have on its flight?

The primary purpose of the rim on a frisbee is to create an
airfoil with a deep curvature. When you throw a frisbee,
the edge of it comes in contact with the air. As the air
flows over the top of the frisbee, it speeds up and the
pressure drops. This creates lift.

A frisbee without a rim can still fly, but it won't fly as
well as one with a rim. A completely flat disk will fly but
the "angle of attack" becomes more of a factor as to how
well it flies. A disk without a rim will be less stable in
flight. You can try a simple experiment to see what role
the rim plays in the flight of the frisbee. Try to fly a frisbee
upside down, then compare your results to throwing a
frisbee in the conventional way.

http://www.exploratorium.edu/sports/ask_us_sports_october.html

Unlike an (typical) airfoil, a frisbee has gyroscopic rotation. This serves to provide stability for the travelling frisbee, which would otherwise wobble in the air and fall to the ground.

Is it possible to mathematically model fluid-frisbee interactions? Anyone familiar with fluid dynamics might imagine that doing so would involve a solution to the compressible Navier-Stokes equations, while incorporating gyroscopic and gravitational effects. There are, in fact, several researchers working on 3D mathematical models of the frisbee. There is a working model involving 10 aerodynamic coefficients estimated with experimental flight data. Given the initial data, it can predict the flight trajectory:

http://mae.engr.ucdavis.edu/~biosport/frisbee/frisbee.html

Another researcher is using wind tunnel tests on a flying disc model to understand the aerodynamics of a frisbee. The goal? To develop an Unmanned Air Vehicle (UAV) based on a spin-stabilized axi-symmetric flying disc:

http://www.frisbee.com/research/potts.html