1. Ping Pong Ball Flight Mathematical Modeling
Garren Plemmons and Kevin Kotecki
Enka High School and Wakefield High School
2008

2. Outline Introduction Problem Goals Background Information Equations
Collected Data
Conclusion
Bibliography
Acknowledgements

3. Problem?
How is the flight of a ping pong ball effected through the parameters of drag, lift, initial angle of the ball and velocity of the ball?

4. Goals
Prove the input of drag, lift, angle, and speed to create a different output when changed in different situations.
Model the flight of the ball through V-Python and collect informative and testable data.
Learn the effects of aerodynamics in spherical objects.

5. Background Information
Equipment:
Ball (40 mm)
Hardtop table (9’x5’)
6” net
Paddles

6. Background Information
Rules:
Two to four player.
A players must allow a ball played towards them only one bounce on their side of the table
Then must return it so that it bounces on the opposite side of the playing surface.
A point is scored when the opponent fails to return the ball.

7. Mathematical Values and Meanings
F = lift force
V = velocity of the ball
A = cross-sectional area of ball
C = lift coefficient
a= acceleration
= theta

8. Equations Newton’s Second Law of Motion F=force M=mass A=acceleration

9. Mathematical Equations
g=gravity 9.8 meters per second
c= drag coefficient
V=velocity of the y component
K=lift coefficient

10. Mathematical Equations
a = acceleration
dt = change in time

11. Mathematical Equations
a = acceleration
dt = change in time

12. Mathematical Equations
g=gravity 9.8 meters per second
c= drag coefficient
V=velocity of the y component
K=lift coefficient

13. Bernoulli’s Principle
Due to the conservation of energy the wing is not able to separate and settle the circulation predicament.
This creates a higher pressure are beneath the wing than above it. The pressure difference causes the wing to push upwards and lift is created.

14. Mechanical and Airfoil lift similarities
The overall behavior of Mechanical lift is similar to that around an aerofoil with a circulation which is generated by the mechanical rotation, rather than by aerofoil action.

15. Forces Affecting the Flight of a Ping Pong Ball
Magnus Force/Effect:
Perpendicular axis
High Pressure pushes the ball
Spin causes high pressure due to the pushed air

16. Force Diagram

17. Magnus Forces Rotation axis-the axis in which the ball spins Pressure
Topspin
Backspin
Pressure
The low and high pressure areas are on opposite sides of the ball.
The Magnus force is described as the low pressure area during the flight of the spinning ball.

18. Magnus Forces Velocity in Direction
The direction in which the ball is traveling
Perpendicular to the Magnus force and the rotational axis of the ball
Effects how radical the ball flies according to lift, drag, and spin.

19. Life Like Table
Bouncing table
Bouncing net
Limited bouncing

20. Variable Pitch Changed the initial angle only
Started at 0 and went to 75 by 15 increments
All other settings were at ‘default’

21. Variable Pitch

22. Variable Drag Changed drag coefficient only
Started at 0.0 drag co. and went to 2.0 drag co.
Increments of 0.5
All other settings at ‘default’

23. Variable Drag

24. Variable Lift Changed lift coefficient only
Started at 0.0 lift co. and went to 2.0 lift co.
Increments of 0.5
All other settings at ‘default’

25. Variable Lift

26. Variable Speed Changed the initial speed
All other settings set at ‘default’

27. Variable Speed

28. Variable Pitch with Drag
Changed initial pitch only
Started at 0 and went to 75 by 15 increments
Added drag coefficient of 0.5

29. Variable Pitch with Drag

30. Variable Pitch with Lift
Changed initial pitch only
Started at 0 and went to 75 by 15 increments
Added a lift coefficient at 0.5

31. Variable Pitch with Lift

32. Variable Speed with Lift
Changed initial speed
Started at 0.5 lift co.

33. Variable Speed with Lift

34. Variable Speed with Drag
Changed initial speed
Set 0.5 drag co.

35. Variable Speed with Drag

36. Variable Speed with Lift and Drag
Altered the initial speed only
Added a lift co. of 0.5
Added a drag co. of 0.5

37. Variable Speed with Lift and Drag

38. Variable Pitch with Lift and Drag
Changed the pitch from 0 to 75
Increments of 15
Added lift co. and drag co. of 0.5

39. Variable Pitch with Lift and Drag

40. Summary
The drag and lift coefficients on a flying ping pong ball was tested through trial and recording, finding the effects of angle, pitch, drag, and lift on a spherical object.

41. Conclusion
When experimenting with angle, speed, lift and drag we found that the parameters effect the flight of the ball to a considerable amount.
Drag decreases the efficiency of flight
Lift can increase the efficiency of flight but not always
Angle and speed create a variable flight path due to conditions

42. Bibliography http://library.thinkquest.org/2819/bernoull.htm

43. Acknowledgements Dr.Russell Herman and Mr. David Glasier SVSM Staff
UNC Wilmington
Mr. and Mrs. Cavender