Man, I don't mean to ruffle feathers, and I know this thread is a few weeks old, but the math and dynamic load calcs in this thread are not correct, but unfortunately very common. Not picking on anyone here, because this happens in just about every thread discussing dynamic loading. Sorry, I've been commenting in another post about the calcs for dynamic loading and energy absorption being misinterpreted and misunderstood and this is a what I'm talking about.
Okay, so let's forget about the block for bit and just look at the rope and load. So here's how it's works. Load above block has potential energy, when load dropped potential energy converts to kinetic energy, when it loads rope kinetic energy is converted to spring potential energy and heat. So in the above, 4,000 lbs drops 6 ft to start loading line. That's 24,000 ft-lb of potential energy that got converted into 24,000 ft-lb of kinetic energy that's fixing to being converted into 24,000 ft-lb of spring potential energy and a tiny bit of heat. So all we know so far is the amount of spring potential energy and heat that will be created in the rope - but that tells us nothing about how much actual force will be on the rope. To find the force, you must divide the 24,000 ft-lb number by the 20% EA Factor that Yale gives you. So let's say the 20% EA is 400 ft-lb/lb. So (24,000 ft-lb)/(400 ft-lb/lb)=60 lb. That 60 lb is HOW MUCH OF THAT MODEL OF ROPE YOU NEED TO USE in order for the PEAK FORCE TO EXACTLY EQUAL 20% of THE ABS. Now, let's say that rope is 10 lb per 100 ft, so 60 lb of rope is 600 ft. So if I dropped that 4,000 lb log 6 ft onto that 400 ft-lb/lb EA rope and I had exactly 600 ft of rope between the load and friction device - AND I DID NOT LET THE LOAD RUN - the peak force would exactly hit 20% of the ABS. From there, you can figure out what the force would be on the block and rigging point. Now, to take it one step further, if I used the same model rope, but in a larger diameter, then I would not need as many feet of the rope to equal that same 60 lb requirement since the larger diameter provides more rope weight per 100 ft.
So what happens if you use less than 600ft in the above example, then your peak forces will exceed the 20% ABS. Let's say I only used 100ft of the 10 lb/100 ft rope between the load and friction device. That's 1/6 of what I should have used, which means I should have used a rope with 1/(1/6), or 6x the EA factor, or alternately, a rope with 6x the weight per 100 lb. Since I did not use a higher EA rope, or a heavier rope, but the 400 ft-lb/lb, 10 lb/100 ft rope, then I generated a peak force that was the square root of 6, or 2.45X times the 20% force, or in other words I just put a peak force of 48% the ABS on that rope. Let's look at another, since we're blocking down. Let's say I only used 30 ft of rope between the load and friction device, then 600 divided by 30 is 20, and the square root of 20 is 4.47, and 4.47 times 20% is 89% of the ABS. In this case you just hit the MBS dropping that load. So, where did the "square root" come from? Hang tight, I answer that below.
EA factors are specific to each X% of ABS. Meaning there is an EA for 10%, another EA for 20%, another EA for 30%, etc. Yale only publishes the 20% EA because that's the percent loading we have accepted out here in the industry. If you wanted to use 10% load max, you would have to talk Yale and the other manufacturers into providing it to you. Or, if you understand the elongation curves (% break vs % elongation), then you can actually derive it on your own. Raw derivation however gets complicated so I won't get into it here.
So, to derive a different EA from a 20% EA that you already have, here's how you do it. Energy Absorption of the rope is really just the area under the curve of Force vs Elongation normalized to 1 lb of rope. In calculus terms it is an integration to find that area. So if my Force vs Elongation curve is linear, then the integration yields a 2nd order function, which means we have an x-squared in the equation. So EA is then a function of the SQUARE of the percent break. So if I know the 20% EA, then to find the 100% EA, I divide 100% by 20%, get 5, then square 5 to get 25, then multiply 25 times the 20% EA, and I now have the 100% EA. If you look at Yale Polydyne with a 576 ft-lb/lb 20% EA, and you want to estimate the "Red" Ultimate EA, which Yale appears to be refering to the 90% break (i.e., MBS) then you divide 90% by 20% to get 4.5, then square 4.5 to get 20.25, then multiply 20.25 times the 576 ft-lb/lb 20% EA and you get 11,664 ft-lb/lb 90% Red Ultimate EA. Yale actually publishes the Red Ultimate EA at 11,187 ft-lb/lb. The minor difference would be attributable to the fact that the Force vs Elongation curve is not perfectly linear, over the graph.
