Physics of flying discs

A flying disc can fly through the air because of the combination of the lift and drag forces it generates when it hits the oncoming air flow. The trajectory of a disk is affected by its shape, mass, spin, attitude, deformation etc. Although wind effects are not intrinsic to disc flight, the apparent effect of wind on a thrown disc's trajectory and behavior is quite strong from the perspective of a ground-based observer.

A Wham-O Professional Frisbee

Suitability of a disc

A disc is suitable for flight if its air resistances in different directions are of an appropriate relationship, allowing its flight path to be more efficient in the direction in which it is thrown; and it can therefore be thrown farther than a ball. It must be made of an adequately dense material such that its velocity change due to air resistance is low and the force exerted by gravity is low enough for air flight. Additionally, the shape of the disc must be suited to the throwing action: a flat disc would be inappropriate due to the lack of grip that the thrower could get from the disc, resulting in accidental release.

Air resistance

The two major types of flying disc are the conventional design used in both Ultimate and Disc Golf and the aerobie ring. Although these designs are very different, they both use air resistance in the same way to fly.

Effect on flight distance

When a spherical ball flies through the air, it has the same cross-sectional profile causing air resistance in all directions, while a flying disc does not. Its shape causes it to have much more vertical air resistance (assuming horizontal flight) than horizontal air resistance. This is partly due to the large circular cross-sectional area vertically, but is enhanced by the rim around the edge of the disc which encloses air inside the disc in the same way as a parachute.

Because of this effect the disc is able to fly a longer horizontal distance in a flatter parabola.

In the image above the arrows represent the force of air resistance acting upon the disc in horizontal and vertical components.

The flight of a disc lasts longer than that of a ball due to high resistance to vertical velocity. The disc lands only when its velocity has decreased, therefore almost floating to the ground. The ball, on the other hand, hits the ground when it is still travelling at a high speed horizontally causing it usually to bounce or roll.

Effect on shape of path

The angle at which the disc is thrown alters the ratios of air resistances in different directions, affecting the direction of flight.

At low speed this can have the opposite effect, and a disc that is pitched upwards will usually fall backwards on its path as it falls through the plane of low resistance. The diagram below shows the path of a pitched disc that is thrown downwards.

The plane that matches the angle of the disc, as shown in the diagram, is the easiest direction for the disc to move in due to low air resistance, so if the disc is pitched or tilted it will follow a curved path as shown below.

The tilt of the disc can also cause the disc to ascend vertically if the disc is tilted upwards, without the need for the disc to be thrown in the upwards direction. This is because of the lift effect caused by the rim of the disc. This is the same principle that is used in the wing of an aeroplane. A disc that is thrown downwards at a tilted angle, and then ascends, performs a movement known as the air-bounce (or air-hop). The diagram below shows the airflow acting upon the disc.

The Aerobie

An 'Aerobie Sprint' flying ring

The Aerobie Superdisk is an alternative design of flying disc that, although somewhat differently shaped, still has very similar properties to the conventional disc. It has less air resistance. Because there is less resistance to motion, the Aerobie discs can fly farther than the conventional disc. The Aerobie flying ring has minimal drag and has held several world records for the longest flight by a human-thrown projectile. However, due to the lack of a rim, the Aerobie is less suited to angled, curved flights and air-bouncing.^{[citation needed]}

Spin of the disc

The spin of the disc helps to keep the disc stable in flight and prevent unplanned tilting. This is because a large angular momentum stabilizes the disc in the same way that it keeps a gyroscope steady, with the angular force forcing the mass of the disc away from the centre of mass, perpendicular to the axis of rotation. Any unequal force acting on a particular area of the disc is quickly redirected to be equal over the circumference of the disc.

As the disc spins faster, it becomes more stable due to the rapidity of the equalisation of forces.

The center of mass

On neither the aerobie nor the conventional design is the center of mass located on the disc itself. It is instead located in the space in the disc's center in the case of the aerobie, or just below the center of the physical disc in the case of a Frisbee.

Mass of the disc

The force required to accelerate the disc is directly proportional to the mass of the disc. This decreases the acceleration of the disc, assuming that the force of projection is constant. Therefore, discs come in a variety of weights, although those used for Ultimate are mainly 175 g in mass, heavier than the majority of discs and considerably heavier than an aerobie.