Rigging a hammock with constrictor ropes (UCR's)...

[Frawg]

No - the experiments we performed had nothing to do with slipping under the load due to the load itself. An agent or force exterior to the system can induce the UCR constrictor section to loosen and when that happens it will not grab again - it will fail totally.

I'm gonna respectfully disagree here. I'm pretty sure I have a handle on the heavy / light load condition implications and the mechanics of what happens. I see a positive feedback mechanism, whereby any friction in the constrictor induces a radial constriction which in turn induces more friction. The dynamic coefficient of friction applies until enough of the constrictor is engaged to counter the applied load, at which point motion will slow and ultimately cease. The static coefficient of friction, which is always greater than the dynamic one, then applies and holds the constrictor in place. Certainly, there has to be enough length of constrictor to ensure that the total friction generated can overcome the maximum dynamic force applied. If friction does get distributed exponentially, per my guess below, then that necessary length will increase only as the logarithm of the applied force.

We even had the buried tail pulled through the constrictor section under the dynamic forces introduced. Can it happen? The probability is probably low, but definitely not zero. How low? Totally unknown and probably unknowable a priori.

Sounds to me like your constrictor was too short, relatively speaking. Again, I will respectfully disagree with your conclusion. I need to research the physics more -- and I may well be wrong here -- but I'm inclined to think that in stasis the force distributes as a decreasing exponential for the UCR, and as a hyperbolic cosine for the whoopie sling. The transition from slipping to stasis will be mathematically interesting because the coefficient of friction will be changing dynamically as well (nonlinear DEs?) . But it really depends on the length of the constrictor section as well as the friction coefficients and the dynamic forces applied -- perhaps not precisely knowable, but certainly boundable so that one could engineer any desired margin of assurance.

Would the rolling hitch help? unknown without a lot more experimentation.

Well, I have been experimenting, and it does appear to hold -- I've never had it slip -- but its contribution to the UCR is not the mechanism I initially anticipated.

My guess, based on a lot of experiment with friction knots in a suspension system, is no unless the rolling hitch is initially holding the full force exerted on the UCR, which I have found to not be possible. Once the constrictor section is induced to fail, the motion and dynamic forces will simply be more than a rolling hitch could be expected to hold. Just my guess though.

That was my initial thinking... that the friction hitch, of whatever stripe, would have to take up the friction deficit, as I called it in an earlier post. That wasn't the case, and its contribution turns out to be different. IME, the hitch acts as a drag, ensuring that any motion induces some initial radial compression in the constrictor. Once that compression begins, the positive feedback of friction induces more compression, ultimately forcing the constrictor to grab. In stasis, the force ends up distributed exponentially, IMHO, until released by an external agency. By inducing even a small amount of drag, the rolling hitch provides insurance against the unseen hand implicitly posited in your non-zero probability estimate. Anyway, that's what my experiments to date have led me to believe. I'll certainly defer to the physicists and MEs in the group on this.

For my part, I'd say let's keep thinking, researching, experimenting and documenting. An ounce of data is worth a pound of speculation, and I've contributed more than my share of the latter. I don't think I'm that far out in left field, but it'd be much appreciated if someone in the know would kindly point me toward a reference on the precise physics of braided rope deformation.