11.11.05

1. 11.11.05

2. Outline • Introduction • Physics of Disc Flight • Airfoil • Gravity • Drag • Lift • Aerodynamic Moments • Gyroscope • Angular Momentum • Wobble • Flight • Horizontal Straight Flight Introduction

3. Introduction • The original Frisbees were pie tins when hungry pie eating college students realized that the tins could be thrown and caught. • In 1948, Walter Frederick Morrison and a partner, Warren Franscioni, invented the modern Frisbee made of plastic that could fly more accurately and further than pie tins • Wham-O Toy company bought the rights to the flying disc from Morrison and began to produce them in 1957 • There are now more than 50 companies that make Frisbees. • The average Frisbee is 8-10 inches in diameter and range in color and design

4. Abstract This presentation explores the physics behind the Frisbee. It illustrates the basic Newtonian laws of physics, both linear and rotational, as well as certain concepts of fluid dynamics that are key to the flight of a Frisbee. It also covers the two current explanations behind the phenomenon of lift.

5. Airfoil • An airfoil is something designed with surfaces that produce lift when air flows over and under it. • The surface should produce the greatest amount of lift with the least amount of drag. • e.g.. Airplane Wings, and of course Frisbees!

6. Gravity • Gravity is a constant force that acts on the center of a mass to pull the mass to the ground • g= 9.8 m/s2 (acceleration due to gravity) • L= Lift • D= Drag • COP = Center of Pressure • COM = Center of Mass • = Angle of Attack Roll (R), Pitch (M), Spin Down (N)

7. Drag D= ½ru2ACd • In General Drag is determinant on 3 Factors • Reynolds's Number, Re • Spin Parameters, S • Angle of Attack, a

8. Drag (cont) • Reynolds Number  Re= rvd/ m • The ratio of inertial forces to viscous forces • Spin Parameters  S = r w/ v • Ratio of the angular velocity to the linear velocity • Angle Of Attack  a • Angle at which the Frisbee is thrown, compared to • the horizon

9. Drag (cont) Drag Coefficient Cd vs. Angle of Attack a

10. Lift • Lift is required to keep the Frisbee in the air. • There are a couple of Explanations of why Lift occurs • Longer Path Explanation • Newtonian Explanation

11. Lift -Longer Path Explanation • This explanation depends on the fact that the top surface is more curved than the bottom • p + ½ rV2 + rgh = constant • Bernoulli's equation states that as the speed of a fluid increases • its pressure decreases. • Since the pressure on the top surface decreases due • to its longer length, the pressure on the bottom • Remains higher, produce a net upward force.

12. Lift –Problems with LPE • This explanation relies on the fact that the two particles that “separate” at the top and bottom of the front and rejoin at the back. This does not happen, the particles have no “knowledge” of each other and there is no logical reason why they should end up at the same point at the rear of the disc. • It is true in many ways but does not include symmetric object, like the wings of an airplane. By this explanation planes would not be able to fly upside down.

13. Lift – Newtonian Explanation • Newton theorized that the air molecules hitting the bottom surface acted as individual shotgun pellets. As each air molecule hit the bottom surface they were deflected. • By Newton’s Third Law (For every action there is an equal and opposite reaction), the air molecules would hit the disc and produce an upward force, “Lift”

14. Lift– Problems with NE • The top surface of the wing is left completely out of the picture. The top surface of a wing contributes greatly to turning the fluid flow. When only the bottom surface of the wing is considered, the resulting lift calculations are very inaccurate. • The fluid (air) that moves over the surface doesn’t actually hit the surface, it is deflected before it reaches the surface, therefore air molecules cannot act as “shotgun pellets”.

15. Lift L= ½ rv2ACL Lift coefficient CL versus angle of attack, a

16. Aerodynamic Moments Roll Moment R = (CRr + Crp) ½ rv2Ad Pitch Moment M = (CM + CMa + CMq) ½ rv2Ad Spin down moment N = (CNr) ½ rv2Ad

17. Gyroscope • The spin of a Frisbee is unaffected by the pitch and roll, and does not affect the lift or drag. Spin however is a critical aspect in the stability of the disc. It provides angular stability and gyroscopic precession • Angular Momentum (H) • A product of the spin angular velocity (w) and the inertia (I) • H = Iw • Wobble • Wobble is caused by improper throwing or collision with an object. The tendency of gyroscopic precession levels the disc off and reduces wobble.

18. Flight Horizontal Straight Flight There are no real world conditions that can produce a perfectly straight, horizontal flight, but approximations can be made. mg= ½ rv2ACL This must be true, lift must be at least equal to mg in order to stay above the ground. From this equation we get the velocity needed for such lift. v = 2mg rA(CL0+ CLaa)

19. Flight Horizontal Straight Flight (cont) This graph shows that as velocity decreases the angle of attack must increase in order for the Frisbee to still have lift

20. Bibliography and Resources • http://www.ultimatehandbook.com/Webpages/Beginner/physics.html • http://mae.engr.ucdavis.edu/~biosport/frisbee/frisbee.html • http://inventors.about.com/library/weekly/aa980218.htm • http://www.google.com • http://mae.engr.ucdavis.edu/~biosport/frisbee/frisbee.html • http://www.howstuffworks.com/ • Hummel , Frisbee Flight and Throw Biomechanics • (1997)