Rock Climbing and Differential Equations: The Fall-Factor
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This article explores the concept of the Fall-Factor in rock climbing through differential equations, drawing from Dr. Dan Curtis's research at Central Washington University. It examines how climbers utilize ropes and protective devices to mitigate fall consequences, challenging the notion that longer falls always result in greater force on the climber. By defining the Fall-Factor as the ratio of the fall distance to the length of rope, the article reveals that the maximum force exerted during a fall depends on this ratio rather than just the distance fallen.
Rock Climbing and Differential Equations: The Fall-Factor
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Presentation Transcript
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.
Climbers use ropes and protection devices placed in the rock in order to minimize the consequences of a fall.
Intuition says: The force exerted on the climber by the rope to stop a long fall would be greater than for a short fall.
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.
protection point climber belayer
protection point climber belayer
protection point climber belayer
L = un-stretched length of rope between climber and belayer.
DF DT
The Fall-Factor is defined as the ratio 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.
Fall-factor 2 belay point
position at start of fall 0 position at end of free-fall DF position at end of fall DT x
when so
when so
when so When
when so When After the rope becomes taut, the differential equation changes, since the rope is now exerting a force.
