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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
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. According to the lore of climbing, this need not be so.
belayer climber protection point
belayer climber protection point
belayer climber protection point
L = un-stretched length of rope between climber and belayer.
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.
Fall-factor about 2/3
Fall-factor 2 belay point
0 x DFDF DTDT position at start of fall position at end of free-fall position at end of fall
whenso When After the rope becomes taut, the differential equation changes, since the rope is now exerting a force.
The solution is
Maximum force felt by the climber occurs when and
The maximum force is given by
Rock Climbing and Differential Equations: The Fall-Factor Dr. Dan Curtis Central Washington University.
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