Kevin Walsh
Ms. Brewer MAT 266
MWF/12:55-1:45
Spring 2010
The Frisbee
For decades, Frisbees have been a widely used source of amusement for people of all
ages. They have spawned numerous new sports (Ultimate Frisbee, disc golf and others) and each
year more of them are sold than baseballs, basketballs and footballs combined. The history of
the modern Frisbee dates to 1871 in Bridgeport Connecticut, William Russell Frisbie established
a bakery called the Frisbie Pie Company of New Haven. The bakery stayed in operation until
1958, the tossing of the company's pie tins, led to frisbie becoming a well known term describing
flying disc play in the Northeast. Several years after World War II, Walter Frederick Morrison
and his partner Warren Franscioni, investigated perfecting the pie tin into a commercial product.
First, they welded a steel ring inside the rim to improve the plate's stability, but without success.
Then, they switched to plastic and the Frisbee as we know it today was born. The initial design,
which incorporated six curved spoilers or vanes on the top, was vastly improved in 1951 and
thus became the Pluto Platter, the first mass-produced flying disc. This design, which
incorporates a slope on the outer third of the disc, has remained part of the basic design to this
day. The founders of Wham-O, a California toy company, became interested in this flying disc
in 1955 and about a year later began production after acquiring the rights from Morrison. The
name was changed to Frisbee after the company heard about the pie tin game on the east coast
called Frisbie-ing. In 1959, the first professional model Frisbee was produced.
The two main physical concepts behind the Frisbee are aerodynamic lift (or the Bernoulli
Principle) and gyroscopic inertia. A spinning Frisbee can be viewed as a wing in free flight with
the Bernoulli Principle being the cause of the lift and the angular momentum of the disc
providing its stability. Forward flight splits rushing air at the disk's leading edge, half goes over
the curved upper side of the Frisbee; half goes under the flat side. Because that edge is tipped up
at an 'angle of attack', the disk deflects the lower airstream downward. As the Frisbee pushes
down on the air, the air pushes upward on the Frisbee - a force known as aerodynamic lift. The
upper airstream is also deflected downward. Like all viscous fluids, flowing air tends to follow
curving surfaces, even when those surfaces bend away from the airstream. The inward bend of
the upper airstream is accompanied by a substantial drop in air pressure just above the Frisbee,
sucking it upward. In this way, forward motion is translated into vertical thrust.
Limits to the airstream's ability to follow a surface explain why a Frisbee flies so poorly
upside down. When the upper airstream tries to follow the sharp curve of an inverted Frisbee's
hand grip, its inertia breaks it away from the surface. A swirling air pocket forms behind the
Frisbee and destroys the suction, raising the air resistance. Once this air resistance has sapped the
inverted disk's forward momentum, it drops like a rock.
It is a true fact that Frisbees do not fly if they are not rotating, but rotation by itself does
not produce vertical thrust. This can be easily confirmed by noting that you can spin a Frisbee in
place, about a fixed axis, and it will not 'lift up'. You also can see that the Frisbee is still spinning
at nearly 'full speed' when it finally hits the ground, so you have another piece of evidence that
shows that the spinning doesn't lift the Frisbee. Rotation is crucial. Without it, even an upright
Frisbee would flutter and tumble likes a falling leaf, because the aerodynamic forces aren't
perfectly centered. Indeed, the lift is often slightly stronger on the forward half of the Frisbee,
and so that half usually rises, causing the Frisbee to flip over. 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. 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. And the tiny ridges on the Frisbee's top surface introduce
microscopic turbulence into the layer of air just above the label. Oddly enough, this turbulence
helps to keep the upper airstream attached to the Frisbee, thereby allowing it to travel farther.
With qualitative understanding of how Frisbees fly, we can progress in establishing a
quantitative understanding of how to predict their course of flight. So how far can an frsibee fly?
With the initial of attack angle and velocity of the object in motion known, the theoretical path of
flight can be determined. The height of the object over time can be calculated by the initial
velocity multiplied by the sin of the angle at which it was thrown and multiplied by the time,
subtracting one-half acceleration due to gravity multiplied by time squared, and the addtion
initial height.
1
𝑦(𝑡) = 𝑉𝑜 (𝑠𝑖𝑛(𝛂))𝑡 − 2 𝑔𝑡 2 + 𝑦0
(𝛂 = angle, g = 9.8 m/s² = 32 ft/s²)
The horizontal distance travel over time can be calculated by simply multiplying time with the
initial velocity and the cos of the angle of attack.
𝑥(𝑡) = 𝑉𝑜 (cos(𝛼))𝑡
The displacement of the object in flight or Frisbee can be determined by the addition of the
veridical and horizontal vectors, resulting in a vector sum with an x and y value. Given the
projection angle and equal initial and final elevations, the range of the Frisbee can then be
calculated. Range equals velocity squared divided by acceleration due to gravity multiplied by
the sin of 2 times the angle of attack.
𝑅=
𝑉0 2
𝑠𝑖𝑛(2𝜃)
𝑔
The velocity at which the average Frisbee is thrown is 14 m/s. and best angle of trajectory for
maximum range is 45º. The theoretical range is estimated to be about 20 meters or 65 feet.
However, these calculations are theoretical due to it negating motion in the z-plane, drag and lift.
In the case of a Frisbee the disc can fly much farther due to the counteracting force of lift to force
of gravity, even further if wind contributes to wind speed and therefore lift. In addition if the
Frisbee is throw with horizontal angle; it will experience a force in the z-plane. With the
appropriate vertical and horizontal angles lift can cause the flying disc to return to the origin like
a boomerang, those resulting in no net distance of flight. Distances of throw Frisbees have been
recorded at 150 meters and greater.
Just as people suspend explanation for a flying saucer from outer space, the Frisbee is one of
most over looked toy of its kind. The Frisbee it more dynamic in flight with its ability to defies
the laws of gravity. However by simply examining of the history and physics behind the origin
of the flying disc one is able to establish a new found appreciation for the Frisbee.
References:
Horowitz, Judy and Billy Bloom. Frisbee, More Than Just A Game of Catch. Leisure Press,
1983.
Johnson, Dr. Stancil, ed. Frisbee. A Practitioner's Manual and Definitive Treatise. New York:
Workman Publishing Company, 1975.
Malafronte, Victor. The Complete Book of Frisbee: The History of the Sport & the First Official
Price Guide. American Trends Publishing Co., 1998.
Tips, Charles. Frisbee by the Masters. Celestial Arts, 1977.
Tipler, Paul A.. 1995. Physics For Scientists and Engineers. Worth Publishers. 3rd ed.
Bloomfield, Louis A. “The Flight of the Frisbee” Scientific American, April 1999.
Hummel, Sarah A. “Frisbee Flight Simulation and Throw Biomechanics”. Rolla:
University of Missouri, 2003.
Motoyama, Eugene “The Physics of Flying Discs” , December 13, 2002.
Potter, Merle C., Wiggert, David C. “The Mechanics of Fluids”. Pacific Grove:
Brooks/Cole, 2002.