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

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Presentation on theme: "Rock Climbing and Differential Equations: The Fall-Factor Dr. Dan Curtis Central Washington University."— Presentation transcript:

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

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

4

5

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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. According to the lore of climbing, this need not be so.

8 belayer climber protection point

9 belayer climber protection point

10 belayer climber protection point

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

12 DFDF DTDT

13 The Fall-Factor: 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.

14 Fall-factor about 2/3

15 Fall-factor 2 belay point

16 0 x DFDF DTDT position at start of fall position at end of free-fall position at end of fall

17 During free-fall

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

19 The solution is

20 Maximum force felt by the climber occurs when and

21 The maximum force is given by


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