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potholer said:Energy is proportional to the square of the speed.
However, energy is also proportional to change in height.
My first stab at analysis would be:
If someone of mass M is travelling at a given speed X m/s, to maintain that speed, the descending system (descender and rope) has to absorb an energy of MgX over 1 second (since that's the energy gained in 1 second by travelling at X m/s.
If the person is descending at 2X m/s, the descending system has to absorb energy of 2MgX over 1 second.
For maintaining speed, energy absorption should be linearly related to speed
Correct - the total amount of energy to dissipate over a pitch is given by mgh (mass x little-g x height) little=g = 9.81 m/s ~10m/s
The total rate of energy dissipation is the total energy over the time taken to descend.
[as an aside the wattages dissipated across the cams get surprisngly high for big people at speed]
http://www.wcms.org.uk/pages/scary_srt_physics_feb2005.shtml
But the issue is that there is a critical speed beyond which the Stop will not bite, this has nothing to do with energy dissipation and everything to do with how friction varies at speed.
Also, the stop requires a retarding force on the rope-tail to make the rope wrap tightly around the cams, thus massively increasing the area over which this frictional force is applied.
In theory a stop can be stopped at ANY speed just by grabbing the rope and pulling it tightly agaonst the cams - the only trouble is this requires teflon hands - and again we come back to a maximum critical speed beyond which you cannot grab the rope without flaying your hand - and still being unable to grasp it.