Introduction
Frisbees, for many years now, have been a source of recreation used commonly by people belonging to all age groups. Frisbees or flying disks are the base for many games such as fricket, disk golf, etc. The disks made of plastic can travel long distances. The history of the flying disk goes back to the 1800’s in a place called Bridgeport, in Connecticut where W.R.Frisbie ran a small bakery, called the Frisbee Pie Company. The bakery’s pies were liked at Yale University, which was near to Frisbee’s bakery, and the students started passing the pie tins around by throwing them. Over time, the tins began to be called ‘Frisbees’. It wasn’t popular until when Wham-O manufactured its trademark ‘Frisbee’ in 1958.
HOW DOES A FRISBEE FLY?
Frisbees are a common source of sport and entertainment, although the physics behind its flight s taken for granted. They work on the principles of aerodynamic lift and gyroscopic stability. When in flight, it can be pictured as an airplane wing. The curved top of the airplane wing causes the air to move faster than it does across the concave shaped bottom. Due to the difference in pressure between the two faces of the Frisbee, a lift is generated (there is a lower pressure in the top face as compared to the bottom of the Frisbee or the airplane wing). The net force on the Frisbee, hence, will be upwards, thereby producing the much-needed lift. The turning and spinning of the flying disk produces stability by keeping the disk level in flight. This is called gyroscopic stability, that is the Frisbee remains spinning at the same angle. But, the turning of the Frisbee in flight has nothing to do with the aerodynamic lift, which is generated. But, the Frisbee wouldn’t even fly if it wasn’t for the gyroscopic stability as it conserves the momentum, and the Frisbee’s angular momentum would resist any type of change in its bearings.
This was just a very short description of the process. To delve into a little bit of detail, the first force acting upon the Frisbee does the thrower of the disk provide the thrust? After the disk has been thrown, while in flight, the aerodynamic forces start governing the flight of the Frisbee.
AERODYNAMIC FORCES
The principle aerodynamic forces acting upon the disk are lift and drag. The calculations of these forces involve some basic physical relations. For the drag force, I found out the Reynolds number of the structural arrangement. Reynolds number of the system is given by,
R=ρvd/η (1)
Where, ρ (rho) is the air’s density, v is the relative velocity of air to that of the Frisbee, d is the diameter of the Frisbee, and η is the fluid’s viscosity. The density 1.2041 kg/m^3, the average velocity of a throw is around 15 m/s, its diameter is 24 cm, 1.983 x 10^(-5) is air’s viscosity. Substituting the above values for their corresponding values in the above equation gives the value of R to be 2.186 x 10^5(R is a dimensionless quantity). As the value of Reynolds’s number is high, we need to find out the drag force, which is given by,
〖 F〗_d= -(C_D ρAv^2)/2 (2)
The drag coefficient is dependent on the angle at which the Frisbee’s released. The angle is that formed between the plane of the disk and velocity vector.
〖 C〗_D=C_D0+C_Dα (α – α_0 )^2 (3)
Except α, all values are constants. The lift experienced by the disk is very similar to that of the wings of an airplane and Bernoulli’s principle is used to calculate the lift force. According to Bernoulli’s principle,
(v_1^2)/2+p_1/ρ+gh_1=(v_2^2)/2+p_2/2+gh_2 (4)
Where h represents the height at which the fluid is placed, p is for the pressure, d is for density, g for acceleration due to gravity and rho for the density of air. We cancel the ‘gh’ term from both sides because the difference between the two sides of the Frisbee (h) is negligible.
Another assumption made is that the velocity of air flowing on top of the Frisbee is proportional to the velocity of air flowing under the Frisbee (V1=C (V2)). Now, we are left with,
(C^2 v_2^2)/2+p_1/ρ=(v_2^2)/2+p_2/ρ (5)
Substituting p1-p2 as F/A, where F is the lift force, we get,
F_L=1/2 ρv^2 AC_L (6)
Hence, we found out the values of the drag and the lift forces.
GYROSCOPIC STABILITY
The Frisbee’s rotation is an important element in terms of the flight of the Frisbee. Had it not been for rotation, a Frisbee would have hit the ground straight away (just like a leaf) and would not be able to go long distances, which amuses people who play games related to the Frisbee. This is due to the fact that the lift and drag forces acting on the Frisbee do not act on its center. The lift generated on the back half is lesser than the lift on the front portion of the Frisbee that results in the torque.
The diagram above displays the center of mass and the center of pressure, which are not located in the center of the Frisbee.
This torque (of very small amplitude) causes the Frisbee to flip over when it is not spinning, also causing all chances of flight to diminish. If a Frisbee is thrown with a lot of spin, it gains a lot of angular momentum that has a vector. The torque vector points to the right part of the Frisbee. We can find this out using the equation:
(τ ) ⃗=r ⃗ × F ⃗ (7)
As,
τ ⃗=(dL ⃗)/dt (8)
The vector for angular momentum will start pointing towards the right part. This is the main reason why Frisbees thrown tend to move away from the desired direction and tend to deviate to the left or the right side of the desired line of travel. The stability of the Frisbee depends upon the initial angular momentum and they are directly proportional to each other.
HOW TO THROW A FRISBEE
Many of us have thrown Frisbee’s in the past but not many of us know the most advisable way to throw the Frisbee in. While throwing a Frisbee, the grip is very important. Your thumb should be on top of the Frisbee and all other fingers should be on the backside to give support and provide a good grip. If right handed, ones right leg should be in front (vice-versa in case of left handers) and the feet should be normal to the target to be aimed at.
Elbow should be projecting towards the outside. While pointing at the target, you should move your arm quickly and with appropriate force, you should release the Frisbee.
Bibliography
“How to Throw a Frisbee.” WikiHow. N.p., n.d. Web. 29 Sept. 2014.
Physics Department, Mount Allison University, Sackville, Nb Canada E4L 1E6, and (Vrmrrsn@mta.ca). The Physics of Frisbees (n.d.): n. pag. Web.
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.