1. Rock Climbing and Differential Equations: The Fall-Factor Dr. Dan Curtis Central Washington University

2. Based on my article: “Taking a Whipper : The Fall-Factor Concept in Rock-Climbing” The College Mathematics Journal, v.36, no.2, March, 2005, pp. 135-140.

3. Climbers use ropes and protection devices placed in the rock in order to minimize the consequences of a fall.

7. Intuition says: The force exerted on the climber by the rope to stop a long fall would be greater than for a short fall.

8. Intuition says: The force exerted on the climber by the rope to stop a long fall would be greater than for a short fall. According to the lore of climbing, this need not be so.

9. belayer climber protection point

10. belayer climber protection point

11. belayer climber protection point

12. L = un-stretched length of rope between climber and belayer.

13. DFDF DTDT

14. The Fall-Factor is defined as the ratio D T / L

15. The Fall-Factor is defined as the ratio D T / L Climbing folklore says: The maximum force exerted by the rope on the climber is not a function of the distance fallen, but rather, depends on the fall-factor.

16. Fall-factor about 2/3

17. Fall-factor 2 belay point

18. 0 x DFDF DTDT position at start of fall position at end of free-fall position at end of fall

19. During free-fall

23. whenso

24. whenso

25. whenso When

26. whenso When After the rope becomes taut, the differential equation changes, since the rope is now exerting a force.

28. The solution is

29. Maximum force felt by the climber occurs when and

30. Maximum force felt by the climber occurs when and

31. The maximum force is given by