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Gear ratings - a physics question 25-Nov-2007 At 11:29:46 PM dougo

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Don't worry Macciza, your daughters got it right.

As a final nail in the coffin, and mainly because i'm bored, i did a bit of math on this and the only thing that really matters is the fall factor and the stretch of the rope. The actual distance of falling doesn't matter in the slightest. I added an anlalysis for those interested below.

taking the worst case scenario - a factor 2 fall, we get the following analysis:

suppose a climber falls X meters from stationary, under acceleration of gravity = 9.8 ms^-2.
final velocity^2 = initial velocity^2 + 2 x acceleration x distance
= 0 + 19.6 X

to calculate the stopping distance we consider that due to the factor 2 fall, there is 0.5X meters of rope, and with 30% elongation, we get a stopping distance of 0.15X meters.
The climber must go from velocity = squareroot(19.6X) to zero over this distance. Calculating the required deceleration:

final velocity^2 = initial velocity^2 + 2 x acceleration x distance
0^2 = 19.6X + 2 *a* 0.15X therefore a = 19.6X/ (2*0.15X)
the X's cancel out and we get a required deceleration of 65.33 ms^-2
we have to include the downwards acceleration due to gravity, hence the rope must have a total deceleration of 65.33 + 9.8 = 75.13 ms^-2

assuming 100kg climber,
Force = mass x acceleration = 75.13 x 100 = 7.5 kN.

For a factor 2 fall, there will be little or no reduction in this force due to friction in the system., so this is essentially the maximum force that your piece of gear can be subjected to barring any shock loading from partial anchor failure which is another kettle of fish all together.

Note that there will be some peak forces because the rope doesn't behave quite like a linear decelerator - more like a spring - but i seriously can't be bothered doing that.

As a final note i suppose i should say something relevant to the OP - forces is the right unit for gear rating, and most gear is rated to around 1.5 to 2 times the maximum force calculated above.