[ QUOTE ]
...I know that a final equation for this is beyond the power of my brain...
[/ QUOTE ]
Not at all! You clearly have quite a knack for the math.
I would respectfully suggest there is no "equation" for this. You just have to plug in some reasonable assumptions for the way the stopping force is applied and then figure the answer based on the energy of the falling object. For the two simple cases I cited (uniform force or linearly increasing force from zero to max) you don't need any fancy math like calculus. A simple diagram and some high school geometry will get you the answer.
Now of course in the real world, no one is ever going to stop a load precisely according to one of my two calculated cases. It seems very likely to me, though, that a competent groundie will easily fall between my two cases, so those numbers should be of some value as a rule of thumb.
...I know that a final equation for this is beyond the power of my brain...
[/ QUOTE ]
Not at all! You clearly have quite a knack for the math.
I would respectfully suggest there is no "equation" for this. You just have to plug in some reasonable assumptions for the way the stopping force is applied and then figure the answer based on the energy of the falling object. For the two simple cases I cited (uniform force or linearly increasing force from zero to max) you don't need any fancy math like calculus. A simple diagram and some high school geometry will get you the answer.
Now of course in the real world, no one is ever going to stop a load precisely according to one of my two calculated cases. It seems very likely to me, though, that a competent groundie will easily fall between my two cases, so those numbers should be of some value as a rule of thumb.