1. An Analysis of the Physics Behind Bungee Jumping
Mathematical Modeling
Will Leland, Sanket Prabhu
Tarboro High School, William G. Enloe High School
2008

2. Outline Background/History Model Data Conclusion Constants Equations
Force
Acceleration
Velocity
Conclusion

3. Problem
How do the spring constant, damping constant, and jumper mass affect the path of a bungee jumper?

4. Origin of Bungee Jumping
Created thousands of years ago, by the inhabitants of Pentecost Island
A group of 20 young men would take the leap of death
Used to please the gods in order to have plentiful crops
The land dive would symbolize the jumper’s transition from a child to a man

5. New Beginning of Bungee Jumping
The first modern day bungee jumps were executed on April 1, 1979 by the Oxford University Dangerous Sports Club
The sport’s popularity quickly spread across the world
The world record for the highest jump is 216 meters of off the Bloukrans River Bridge

6. Equipment
An elastic rope that is usually enclosed in a tough outer cover
A simple ankle attachment
A body harness
Jumping platform

7. Types of Jumps
Swallow Dive – classic jump, arms out wide and soar down like a bird
Water Touchdown – some sites are confident about the length that the cord will stretch, so at the bottom the jumper goes into the water
Sandbagging – extremely dangerous, you jump with a heavy weight, once you get to the bottom, you let go of the weight, the added elastic energy will make you fly much higher than from where you jumped from

8. What is Force, Velocity, and Acceleration?
Force- a push or pull
Velocity is the derivative of position
Acceleration is the derivative of velocity

9. Constants
K = spring constant - determines elasticity of cord, meaning how far it stretches
m = mass - determines mass of jumper
b = damping constant - a constant that is put in to represent the loss of energy

10. Physics Behind the Jump
L is the distance from the bridge to the position of the jumper
l is the length of the cord at rest
While L < l, the only force working on the jumper is projectile motion
When L > l, the cord starts to exert an upward force on the jumper
The spring constant factors in as it determines the magnitude of the upward force.

11. Equations
For L<l:
For L > l:

12. Bungee Cord Diagram

13. The Code:

14. The Model

15. Assumptions Bungee cord is in perfect condition
Ideal environment so that jumpers only move in one direction

16. Mass= 80 kg
Damping Constant= 25 Kg/s

18. Spring Constant= 500 N/m
Damping Constant= 25 kg/s

20. Spring Constant= 500 N/m
Mass=80 kg

21. Spring Constant= 500 N/m
Damping Constant= 25 kg/s
Mass= 80 kg

22. Spring Constant= 500 N/m
Damping Constant= 25 kg/s
Mass= 80 kg

23. Spring Constant= 500 N/m
Damping Constant= 25 kg/s
Mass= 80 kg

24. Spring Constant= 500 N/m
Damping Constant= 25 kg/s
Mass= 80 kg

25. Spring Constant= 500 N/m
Damping Constant= 25 kg/s
Mass= 80 kg

26. Changes Based on Findings
Add wind factor, so we would be able to manipulate a z factor as well.
Work on the rope so that when it came up it would produce slack and fold over
Model a water touchdown

27. Summary
Bungee jumping was created thousands of years ago and still continues today as a popular and exhilarating sport
Spring constant, damping constant, and mass vary the jumper’s fall by different magnitudes.

28. Conclusion
It was found that a high damping constant and mass results in the jumper coming to equilibrium faster
A larger spring constant limits the jumper’s oscillation amplitude.
The period looks to have linear relationships with the spring constant and mass

29. What We Learned The basics of VPython, Excel, and PowerPoint
The physics behind bungee jumping and how to manipulate the parameters
The long, rich history of bungee jumping

30. References http://library.thinkquest.org/C0123122/historybungee.htm

31. Acknowledgments
Special thanks to: Dr. Russ Herman and Mr. David Glasier for their generous aid in class and on this project
Also thanks to: the 2008 SVSM staff for providing an excellent social and learning environment
Thanks to our parents for the opportunity