Thanks
The software only took a few hours to write, but deriving the formula took a while - even though I wrote it, I don't have a strong background in vector mathematics.
In the end I used perverted trigonometry which evidently got the job done.
We don't use it in our everyday work at all.
It's interesting - now we've got it, it has changed the way I look at doing jobs. There are a few configurations that I won't discuss until I have video evidence, that could be advantageous to everyday use.
The system was developed specifically for works that we couldn't apply "opposing pendulums" rigging.
On this job, we couldn't safely work on the tree unless our rescue and access line were free of all rigging. This was not possible for a whole bunch of reasons. This was a big driver to produce the three rope system.
If we used two lines, the load would be displaced, shock loading everything, very high likelihood of dead wood falling. The dead wood has a hell of a run up, so it doesn't need to be big, or a direct hit to do catastrophic damage.
The tree itself had two bee-hives, and the top 40ft was too sketchy to climb and rig in a dynamic system (it would just fall apart). That is why we took 80ft in one hit, statically.
Ironically, the under story doesn't allow video viewers to see what we are dodging - but it shows what we can see; Nothing!