Your math works out differently than mine so lets keep this discussion going as I very well could be wrong here and would like to know if I am. Here are my notes and assumptions about 3:1 systems:
Loading any of these items within 20% of breaking strength is VERY unsafe. To be safe you should be loading at 50% or lower than breaking strength.
- “Knot efficiency” is between 40% and 80% and depends on rope type and knot
--Figure 8: 69%
--Bowline: 63% (almost impossible to untie after 1,000 lbs)
--Double Fishermans: 73%
- An adult can pull 120% of their body weight with belay or 60% when pulling on a rope with their hands
- If everything is in good shape the prussic is supposed to slip and possibly melt the rope before anything breaks. This is why you use 6mm prussic line with two prussic wraps. Any more prussic wraps and it won’t slip like it should for safety.
Attached is a diagram that I put together to show loads and breaking strengths of the various components of a 3:1 system based on 6 people pulling. My diagram might be a little confusing so please let me know if you have any questions about it or if you can correct any errors I may have made.