Here is a force diagram of the Zeeko depower arrangement. The tension in the powerline T is split equally between the two lines coming up from the chicken loop, so each of these lines has a tension of T/2. The steel ring in the middle sees a tension of T/2, so the two lines entering and leaving the steel ring will each have a tension of T/4. This means that the line between the top pulley and the top attachment point sees a tension of T - T/4 = 3T/4. And this is also equal to the sum of the tension in the two lines descending from the top pulley, i.e. T/2 (left line) + T/4 (right line) = 3T/4.
I too am very impressed by the ingenuity of this arrangement. I made a Zeeko depower loop using steel rings (no pulleys) and 10mm polypropylene line, no stopper, and used it to fly my kite on the beach this afternoon. Pulling on the right line depowers the kite, pulling on the left powers it up. The force required to depower the kite is more than the force required to power it up. So I wondered whether this arrangement would be stable during times of high tension, like jumps, or whether it would slip and power up unexpectedly.
It worked perfectly. It is completely stable. The reason for the differential tension is because in the one direction (depowering) , you are pulling against the tension in the kite, while when pulling on the left side to power up, the tension in the kite is helping you.
I would need a stopper if I had to spin the bar, but I hardly ever do that, so I will leave it without a stopper.
Thanks for that analysis...i worked from the bottom up and wrote down the forces on each of the line segments, but couldn't figure out the short anchor section on the top, that you labeled 3/4T. If you look at my picture of the rings, you can see that I omitted that 3/4T section, and tied the short T/4 line directly to the pulley.
I do believe that even under a load causing failure ( a breakage somewhere in the system), that the rope will not slip through the pulley or rings. I base this hypothesis on the fact that yesterday, I was hot launching my 13M, and the rope did not slip. I did some fully loaded up 10 foot jumps, and the rope did not slip. It also did not "giggle" or loosen up from jerking on the line, or from whipping it. That is good enough proof for me to trust the system. I would guess that when the system is loaded up enough to fail, that the rope would break at one of the bends, where it goes around a ring. The rope will be weaker at the bend. Can you predict, from the force diagram where the rope will break? The highest tension would be in the 3/4T section, but that section is well anchored to the top of the pulley, and therefore should be less likely to break, than a section which has less tension, but is weakened by the more severe bends in the rope. I don't think the rings would break first, but the one pulley at the top might be the point of failure, if it is not strong enough. I think that there is only one pulley in the whole system. I think that the top of the chicken loop frame only has an 'axle' in the housing, not a pulley.
Since I will be using one of these systems, I have been trying to figure out what is likely to happen to the kite, when one detail or another of this system breaks... so far, I have figured out that some of the time the kite will be cut loose, and some of the time the kite will go to extreme full power, or be completely suspended on its rear lines. I don't have a plan for each of these contingencies, but would like to have one for each case. I could always release the kite with the one and only release I have in my safety-less system. I throw the bar to its safety, by simply letting go and it travels 12 feet, just like a mini-fifth safety line, so I don't need a separate safety mini-fifth line...less clutter!
I am very interested in using a very wear resistant component, where the double powerline passes through the bar... if the powerline breaks from fraying, then, the kite would go to full suspension on its rear lines.
I am glad that so many forum participants are interested in this kind of analysis.
So, would you want to try to guess where the weakest point is in the rope, pulley, ring, and axle system?