For starters, I'm glad we're having this discussion...I'm learning a great deal about things I had previously taken for granted. I operate by the rule 'when in doubt, cut smaller,' so I have a greater margin of error in sticky situations. Maybe when I'm the Michael Jordan of tree cutting and too lethargic to climb higher and cut smaller, maybe then I'll start wailing on trees like a category 1 storm.
We're basically talking about a simple pulley system here, for clarity. Either the rope is run overhead through a pulley or through a natural crotch or over a limb.
So, in our examples the force multiplier of either the block or natural crotch is 1, correct? As others have stated before the difference in the lowering operations is the friction. So, it seems we've at least established that there is no extra force from mechanical advantage acting on the union when a block is present as compared to the rope running over a limb or through a crotch. And we all agree that the force of friction transforms a percentage of kinetic energy into heat.
Jeff and Sean both seem to agree that this transformation equals a net reduction of force on the overhead redirect. For me to best understand it, I look at it as an inverse relationship when when compared to lifting. In the case of lowering, the force on the redirect is reduced due to greater friction. In the case of lifting, the force on the redirect would be increased due to greater friction and the need for higher input to overcome this force.
Are we in agreement at this point?
When is motion not present?
And don't get me wrong, in rigging scenarios, the skill of the roper cannot be understated or taken for granted. A smooth run can reduce the dynamic loading considerably. This is why I like self-lowering