Moving from vertical to horizontal(increase sine) is increasing leveraged load during handling on hinge/rig vs. horizontal tipping down/or up(increase cos) is relief of same leveraged(sine) load as very separate functions or phases. Another separate stage from other aspect is separation of pre and post tearoff considerations. i always look at cos benchmark as to cause, 100% when aligned to cause as normal position/support.
.
When y'all say some down , some over on hinge side ways into rig; i view that as letting load reach for/teasing it/load with where it wants to go(down) drawing it into my game to extrude/bargain some side motion out of the deal in trade. But then also using the downward motion to draw the rope tighter (if rigged cuz can affect some w/o rig), after sweat/swig as tight as possible.
.
Climber 2xEffort + 1x Bodyweight unique preTension position
PreTighten rope hard to restrict movement against load as best can, placing hitchpoint leveraged distance out from hinge but before CoG. Climber is in key position to help preTighten as can access load leg to give equal opposite force of arm or leg effort w/o friction buffer. Then on control leg the initial effort + bodyWeight alone or in concert with ground control preTighten efforts. The climber can apply this raw equal opposite of effort at hitchpoint or even leveraged farther out on rigid load. Can also climb up and induce into rope stretch also sometimes. Capitalizing on either or both strategies( leverage lift on load vs. rope stretch). Then take to sweat/swig after linearly tight as can for more leveraged return from less rubbery/more rigid lever(s).
.
Hitchpoint closer to CoG for more automatic preTightening and better balance and then more clearance after tearoff
With the length between hinge pivot and hitch point increased (but still short of CoG for predictable tipping down continuing after tearoff and not reversing to tips upwards) as a longer lever to induce rope even tighter as load tips down on hinge(but looser as hitchpoint tips towards support point) before tearoff. This gives less sudden impact of change at tearoff from hinge to rope support, as more of load already moved to rope already.
.
BUT, that tighter rope from teasing downward can then also induce stronger side wards pull to induce stronger hinge across(hinge strength always induced by force across thinnes of hinge)as also draws load around on this stronger pivot , w/tighter rope, placed at much greater leveraged support on load. More smooth graceful, predictable, less loaded, less impacting, slow is steady >>steady is fast (turtle beats hare) movement.
.
Sweat for remote Round Turn on overhead support for heavy loads
Another great sweat point is midway thru a Round Turn(RT) /single bottom arc on support grabbed with carabinier and leash. If need all that RT brake force this can really be great as also reduces support 2xLoad effect. If can take the heat/move slow, carabiner pull can be great magic to sweat/swig (while end of RT anchored)very tight, and aid in removal of RT also. So, can be installed and removed very remotely before climb. Can be awesome.
.
Sweatpoint of Prusic between hitchpoint and support
Another great sweat point can be Prusic midway on load leg , that also can sweat/tag to rig as coming down and delivery, sometimes that alone makes trickiest part easy to immediately simplify clean movement.
.
So I would rig/sweat tight employing climber, tip down some( knowing it can't, daring it to try) cutting to 10-2 line if can before slant to more across for back cut. Taperd hinge fatside up, drawing to about 45 degrees face slant. Have very tight rig that any drop on load turns around not as loss but frind to tighten rig more(either stays up or tightens rope win/win) , and far enough out for hitchpoint that tip down on hinge is real distance tightening. Load pull sideways force reveals to then force hinge stronger across to then carry less load ( as now more on rope) can be key. Then bargain with it knowing what it wants(down), how much clearance for that, to then extrude sideways etc. needed. Well placed rope points and using gravity as favorable power for rig, let rig be master not slave of gravity. Try to get hinge/rip pivot as just a strong butt tie that helps pivot hitchpoint to under support point, or rather just shy for safer light pull away from climber on tearoff. Then the butt tie(hinge/rip) is cut thru when very lightly loaded and load itself in correct position and mostly on rigging rope. Soft drift to upright as more balanced hitchpoint now pivot closer to CoG. Actually rigged a few tough ones with quick release, 2x just cut the butt tie to then find could use hinge/rip as same if command this modeling.
.
No face cheat sometimes
Another refinement possibly if far enough from parent to not ripple fiber or outright removing tree; is noFace of cutting down to load force and across to steer as can. 45degrees of 70.7% pull up against load(cos) as also 70.7% across pull(sine) is fair neighborhood. This would be more to a horizontal scenario, tipping down, using the leveraged length between saw and CoG as like guys on ground pulling at angle on arm to allow some down and yet gain some spin around at same time. Handling lighter and longer with above rigging techniques. Rip like is art can look unPro in rush but be so 'sloppy good' they will call it (dumb)luck the 1st 3x or so... Labor Under Controlled Knowledge; yeah, L.U.C.K.!
.
Sorry long again, but orchestration takes key component instruments played/balanced at high extremes to extrude sweetest music.
And I just luv this stuff.
.