Why a Frisbee Flies so Well

The secret of lift and drag of a frisbee

We explain how the rotation of a frisbee makes the frisbee into an efficient airfoil generating substantial lift at small drag. The rotation makes the boundary layer turbulent which delays separation and thereby increases lift and reduces drag.

A Frisbee Acts Like a Wing
Inventor and Patent
Shortcut to Action of a Wing
Action of a Frisbee

A Frisbee Acts Like a Wing

That the rotation of a frisbee improves flight stability and eliminates wobbling is easy to understand. To

understand that the rotation also increases the distance a frisbee can travel, is less obvious. To understand the remarkable flight characteristics of a frisbee, it is necessary to understand how the wing of an airplane or bird is capable of generating large lift L with small drag D, with a lift/drag ratio L/D between 10 and 20. This is explained in the Knol Why It Is Possible to Fly and Why It Is Possible to Sail and with this basis, we now take on the problem of explaining the flight of a frisbee, starting with the observation that a frisbee acts like a wing or sail with a curved shape generating lift and drag just like a wing or sail.

Inventor and Patent

The original for the popular plastic disk was a pie tin from the Frisbie Baking Company of Bridgeport, Connecticut, which supplied many New England colleges with baked goods. Though they should have been studying, the students there found that the empty pie tins were good fun to toss around, and in time every dorm room had a "Frisbie´´ devoted to that purpose.

In the late 1940s, an alumnus and inventor who worked as a Los Angeles building inspector, Walter Morrison, built a plastic prototype of the familiar metal tin, thinking that the lighter object would fly farther. He patented what he called the Pluto Platter, then showed his gizmo to Rich Knerr and Arthur Melin, who had a little company they called Wham-O. Knerr and Melin—who would go on to market such faddish toys as the SuperBall and the Hula-Hoop—were enthusiastic, and they licensed Morrison’s patent.

The frisbee patent.

Shortcut to Action of a Wing

In the following pictures we decribe how the flow of air around a wing generates large lift and small drag by a perturbation of zero lift/drag potential flow arising from a mechanism of instability at separation changing the pressure distribution around the trailing edge. The perturbed flow does not separate at the crest because the boundary layer is turbulent which in a fluid of small viscosity acts like a slip boundary condition. On the other hand, viscous flow with a laminar boundary layer separates at the crest and gives poor lift and large drag.

Sideview of velocity and pressure, and topview of streamwise vorticity of Naca0012 wing at aoa = 14. Observe the turbulent streamwise vorticity emanating from separation instability. Computed solution of the Navier-Stokes equations with slip boundary condition [1]. It is possible that the rims (and holes of some frisbees) of a frisbee trigger transition to turbulence in the boundary layer and thus improves
the flight.

Principle of action of a wing: Potential flow (upper left) with zero lift/drag modified by low-pressure counter-rotating rolls of streamwise vorticity from instability mechanism at separation (upper right), switching the pressure on rear wing (bottom left ) to give both lift and drag (H high, L low pressure). Viscous flow separating at the crest with low lift and large drag (bottom right).

Action of a Frisbee

The rotation of a frisbee makes the boundary layer turbulent even with moderate forward speed of the frisbee, which makes the frisbee into an efficient wing with L/D allowing a long distance of travel

under moderate initial speed.

A rotating frisbee with L/D = 20 will fly 20 meters upon loosing 1 meter of altitude and thus can be expected to fly 20 meter farther than a frisbee without both lift and drag.

What determines if the boundary layer is turbulent (which is good) or laminar (which is bad) is the

Reynolds number = Re = UL/v where U is a relevant speed, L is a relevant length scale and v is

(kinematic) viscosity which for air is about 0.00001. The switch from laminar to turbulent boundary

layer occurs at Re ~ 100.000. This means that for a non-rotating frisbee at normal throwing speeds, the boundary layer is laminar with separation on the crest and poor lift/drag ratio. On the other hand, for a

rapidly rotating frisbee, the boundary can become turbulent which can drastically improve the lift/drag

quotient and improve flight characteristics. Experimental evidence of this effect is given in [1].

The dimples of a golf ball have a similar effect of drag reduction by causing a turbulent boundary layer as

shown in the Knol Why a Topspin Tennis Ball Curves Down. It is likely that the riblets (or holes) along the rim of a frisbee similarly can trigger transition to turbulence and thus improve flight characteristics.

The effect of different separation of laminar and turbulent boundary layers is also exposed in the Knol Why a Topspin Tennis Ball Curves Down. It thus appears that the mathematical theory of flight presented in e.g. Why It Is Possible to Fly can help to explain also why a frisbee flies so well.

The WFDF WFDF World Record of indoor distance frisbee throw is 143 meters, to be compared with outdoor discus throw: 74m, hammer throw: 81m, and javelin throw: 98m.