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Dave CusterCenter for Sports Innovation
Massachusetts Institute of Technology
a simple estimate of load rate during
climber fall arrest
Yowie, ISEA 2006 2
an overview of this talk final thoughts
the starting point
the simple model
some compli-cations
Yowie, ISEA 2006 3
•determine degree of “impact”
•make impact accessible
•guide safety system design
both ice and ice screws exhibitreduced strength with increased load rate. a 100 X increase in ratehalves the strength.
motivation
objectives
Yowie, ISEA 2006 4
methods
determine the load rate based on a (very) simple rope model
compare the simple model to complicated models (Wexlerand Pavier)
compare the simple model to data (Mägdefrau)
Yowie, ISEA 2006 5
expected kinematics behavior
Yowie, ISEA 2006 6(based on Wexler work)
the simple model
Yowie, ISEA 2006 7
the simple estimate of load rate
Yowie, ISEA 2006 8
inclusion of potential energy of stretch
Yowie, ISEA 2006 9
complications
•rope damping
•carabiner friction
•belayer behavior
•energy absorbing systems
Yowie, ISEA 2006 10
how does one compare a spring to adamped spring system?
I haveno simpleanswer;rather, 4complicatedones.
Pavierspringspring/dashpotmodel
Wexlerspringmodel
Yowie, ISEA 2006 11
damping I
here, theadditionof damping increasesload rate
same force
same stretch
Yowie, ISEA 2006 12
damping II
“critical” dampingproduces a loadrate midway between the top spring and the two springs in series.
Yowie, ISEA 2006 13
carabiner friction1) increases the force on the top anchor but does not change the proportionality of the yowie factor
2) decreases the effectiverope length and thus also
increases the fall factor; expect a 20%increase in load rate &
reduced proportionality
Yowie, ISEA 2006 14
belayer behavior
the belayer can reduce the energy absorbedby the rope by allowing rope to slip through the belay device and by being lifted up. thereduced energy results in reduced force,increased time, and thus reduced load rate.
Yowie, ISEA 2006 15
energy absorbing systems
EAS reduce load rate
Yowie, ISEA 2006 16
model compared to data
model and data correlate only loosely
Yowie, ISEA 2006 17
conclusionsas a rule of thumb:
•climbers can apply the rule by protecting the belay and usinglow “modulus” ropes.
•in the future, the rule might be used to guide the design of better ice screws and perhaps the use of plastic anchor components.
•use EAS and a dynamic belay.
Yowie, ISEA 2006 18
acknowledgements• title slide photo by Luca Marinelli• many thanks to the folks at MIT’s
aero/astro department and center for sports innovation
• kudos to Susan Ruff for patient editorial comment
Mägdefrau, H., (1989) Die Belastung des menschlichen Körpers beim Sturz ins Seilund deren Folgen, dissertation, Ludwig-Maximilians University, translated by David LiaBraaten, 1994.
Pavier, M. (1998) Experimental and theoretical simulations of climbing falls, Sports Engineering, 1, 79–91.
Wexler, A. (1950) The theory of belaying, American Alpine Journal, 7, 379-405.
abridged bibliography
Yowie, ISEA 2006 19
Yowie, ISEA 2006 20
stray EASgraphs
Yowie, ISEA 2006 21
Yowie, ISEA 2006 22
alternate expression