Abstract Spinning objects such as Frisbees possess unique flying characteristics. They are in essence spinning wings gliding in mid-air propelled by the forces of torque and aerodynamic lift. The relationship between Newton's Laws of Motion and the flight of the Frisbee will be discussed. This paper will attempt to highlight and show the different physical motions involved behind the spinning edge of the Frisbee and the similar forces it shares with other heavier winged objects. Lastly, how major improvements in the redesign of the Frisbee contributed to its increased stability and precision in its flight in the air. The Flight of the Frisbee Objects that fly are designed to push air down.

The momentum of the air going down is what causes Frisbees or winged objects to travel skyward. This type of force acting on a flying disk is typically known as the "aerodynamic lift" (Bloomfield, 1999, p. 132). Consider a flying kite, which in essence is also a winged object. When a kite's flat bottom surfaces are angled into the wind, air gets pushed down and the kite glides upward. Kites must rely on the wind to keep it suspended in mid-air, while flying birds and insects utilize their muscular flapping motions to maintain their flight in motion.

Airplanes rely on spinning propellers and turbine fans to provide adequate momentum for take off from the runway. With flying Frisbees, that momentum is generated primarily by the tossing power of the human arm and wrist motion. The Frisbee's course of flight is "directly related to the torque or twist force" applied by the individual throwing the flying disk (Fisher & Phillips, 2003, p. 12). To narrow down more on the details involved in the flight of the Frisbee, there are four fundamental forces that affect a flying Frisbee: lift, weight, thrust, and drag.

Aerodynamic lift acting on the Frisbee is considered a positive force, and happens when "the Frisbee pushes down on the air, the air pushes upward on the Frisbee" (Bloomfield, 1999, p. 132). This in turn causes the air pressure under the disk to be higher than the air pressure over the top of the disk, thereby creating the effect of an upward air vacuum. In order for a Frisbee to fly straight and stay in the air, its center of aerodynamic lift must remain near its center of gravity over a wide range of airspeeds and angles of attack. Thrust is the other positive force which propels the Frisbee forward, a momentum generated by the arm and elbow motion that launches the disk towards its direction of flight. In addition, the quick spring-release action of the wrist and fingers on the Frisbee is a key contributing factor to setting the Frisbee into a spinning motion.

This physically powered and precise twist is transferred to the Frisbee in order to launch the disk spinning at the highest possible angular velocity. Angular velocity is the term used to measure the Frisbee's rate of spin expressed in revolutions per minute (RPM). Prior to the Frisbee taking flight, "the net force required behind each twist is formulated based on how quickly the disk is able to reach its full speed or angular acceleration, versus how much the Frisbee resists being twisted or in this case the rotational inertia" (Fisher & Phillips, 2003, p. 12). As indicated by Newton's First Law of Motion, inertia is the tendency of the Frisbee at rest to remain at rest and while it is in motion to remain in motion. As such, the amount of twisting force that is needed to produce the highest possible spin on the Frisbee is described as the torque.

The torque on the flying Frisbee is the product of multiplying the angular acceleration by the rotational inertia. As stated by Professor Bloomfield (1999), "Rotation is crucial. Without it, even an upright Frisbee would flutter and tumble like a falling leaf, because the aerodynamic forces aren't perfectly centered" (p. 132). There are two major external forces acting against the flying Frisbee. To sustain flight in the air, the Frisbee must retain sufficient torque or twist to overcome firstly, the inertia of its body and secondly, the viscous friction of the air.

The relative importance of these forces is largely influenced by the size and the mass distribution on the Frisbee itself. For instance, the weight or gravitational force, which is a negative force pulling the disk downward, works directly against the forces of lift and thrust. The force of gravity, or Earth's downward pull on the Frisbee, pulls the disk back to Earth after it is released and spun in the air. According to Newton's Law of Universal Gravitation, the amount of gravitational force between objects depends on their mass, and the amount of matter an object contains.

The smaller an object's mass, the smaller its gravitational pull. "A spinning Frisbee, though, can maintain its orientation for a long time because it has angular momentum, which dramatically changes the way it responds to aerodynamic twists, or torques" (Bloomfield, 1999, p. 132). The second negative force acting on the Frisbee is the drag or air resistance.

As mentioned by Bloomfield (1999), air flows "like all viscous fluids" (p. 132). Drag in this case, is the resistance of the air to the Frisbee moving through it, as air itself is considered to contain mass similar to that of water. Air resistance occurs when the Frisbee is released from the hand and glides into the air. Friction from the air begins to push the disk back and slackens its speed. Once the drag or air resistance overtakes the Frisbee's momentum, the disk starts its descent to the ground.

For this reason according to Bloomfield (1999), "the careful design of the Frisbee places its lift almost perfectly at its center. The disk is thicker at its edges, maximizing its angular momentum when it spins" (p. 132). If friction dominates, "a Frisbee would be required to maintain torque continuously to overcome the viscous forces acting on it" (Fisher & Phillips, 2003, p. 13). As the torque on the Frisbee stops, the angular velocity declines to zero almost instantly causing it to fall to the ground like a brick.

However, "the relative importance of Frisbee inertia and friction is thus far only a calculated assumption, and the time line over which Frisbees and other flying disks adapt to aerodynamic forces spanning across a typical competitive Frisbee event remains for the most part unknown" (Nye, 2001, p. 52). It is likely that large Frisbee must overcome inertial forces when they accelerate or turn, whereas smaller Frisbees must overcome the viscous forces acting on the disk itself. Current designs of flying disks on the market assume that inertia plays a relatively minor role in the dynamics of even large Frisbees, thus setting most flying disks apart from other weighted flying objects such as rockets and jet planes. Successful attempts over the years at the redesign of the Frisbee have further improved the disk's stability in the air. Mechanical engineer Alan Adler has designed an aerial disk that flies farther than a Frisbee.

The problem with the traditional, convex Frisbee is its instability during flight. According to Adler (cited in Ashley, 1995), if a disk is spinning clockwise and its center of lift moves ahead of the center of the disk, the upwards force acts on the right side of the disk, causing it to tilt and curve to the left. After two decades, Adler finally solved the Frisbee's stability problem by designing a two-piece disk with a flexible plastic central plate surrounded by a concave rim with ridges both above and below the plane of the disk. A sharp ridge at the upper edge separates the airflow at the leading edge.

These ridges act as spoilers to create turbulent airflow, which confines the center of lift to the center of the disk. The result is an aerial disk that flies better and farther than the Frisbee. In conclusion, the Frisbee is an effective studying tool for introducing and examining the basic principles involved in the mechanics of flying winged objects. Newton's Laws of Motion is reiterated throughout its design processes, while its application can be closely observed in its real three-dimensional form.

References Ashley, S. (1995, August). Flying farther than a Frisbee. Sports Technology for Air, Land, and Tee, 89-90. Retrieved October 20, 2004, from InfoTrac database.

Bloomfield, L. A. (1999, April). The flight of the Frisbee.

Scientific American, 280, 132-133. Retrieved October 20, 2004, from EBSCOhost database. Fisher, D. , & Phillips, T. (2003, April). Launch a Frisbee into orbit.

The Technology Teacher, 10-15. Retrieved October 20, 2004, from InfoTrac database. Nye, B. (2001, July 1). The flight of the Frisbee. Time, 52.

Retrieved October 20, 2004, from InfoTrac database.