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Rock Climbing and Differential Equations: The Fall-Factor

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

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Rock Climbing and Differential Equations: The Fall-Factor

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  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.

  4. 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.

  5. protection point climber belayer

  6. protection point climber belayer

  7. protection point climber belayer

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

  9. DF DT

  10. The Fall-Factor: DT / 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.

  11. Fall-factor about 2/3

  12. Fall-factor 2 belay point

  13. position at start of fall 0 position at end of free-fall DF position at end of fall DT x

  14. During free-fall

  15. when so When After the rope becomes taut, the differential equation changes, since the rope is now exerting a force.

  16. The solution is

  17. Maximum force felt by the climber occurs when and

  18. The maximum force is given by

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