Flight of the Frisbee, Flying rings, and Mathematical Models

A laboratory practical examination and exploration

The distance that an object thrown parallel to the ground at a height h above the ground is given by the equation:
$d=\sqrt{\frac{2h}{g}}\times v_{\mathrm{horizontal}}$
Where d is the distance the object will travel, h is the height, g is the acceleration of gravity, and v_horizontal is the speed with which the object is thrown. In this situation the launch angle relative to the ground is 0°. The object only travels horizontally for the duration of the fall time. A graph of velocity versus distance will be linear of the form y = mx where the slope m will be the square root constant in the equation above. For a horizontal throw one meter above the ground the slope will be 0.45 seconds. This equation holds for objects that fall when thrown horizontally such as balls. Throw the object with twice the velocity, the object will go twice as far.

Objects that fly such as flying disks and flying rings should travel farther and outperform a non-flying object. This laboratory seeks to explore whether flying disks and rings outperform non-flying objects and to determine the nature of the mathematical relationship between velocity and distance.

Data Gathering

Gather velocity versus distance data. Use distance the disk flies divided by the time of flight to calculate the velocity. Note that this velocity is technically a mean velocity as the speed of the disk decreases during the flight. Launch velocities, however, are difficult to measure. Use the data gathered to determine the mathematical relationship between velocity and distance. Equipment will include flying disks, flying rings, timing devices, and distance measuring capability. Stopwatches, GPS units useful. Radar guns worth trying for launch velocity.

Questions to consider and to which to respond

1. Performance versus non-flying objects
   1. Does a graph of velocity versus distance demonstrate that flying objects outperform non-flying objects?
   2. How do they demonstrate this?
   3. By what factor do flying objects outperform non-flying objects? Suggestion: explore the percentage difference between the experimental slope and the non-flying object slope of 0.45
2. Nature of mathematical relationship
   1. What is the nature of the mathematical relationship between velocity and distance for the flying object?
   2. Linear, non-linear, or random?
   3. If non-linear, what mathematical model appears to best fit the data?