Another physics spinoff question - back leaning

[Bart_]

So far we've solved for three cases of puling a tree over'
First was set distance from the tree, what height/angle to set the rope. (diminishing returns)
Second was set height in the tree, what distance/angle to place the winch. (diminishing returns)
Third was fixed length of rope, what right-triangle to make with the rope. (45 deg best)


I pose a fourth question for solution. We know proportions or normalized amounts of pull over torque for the first three cases but they all had 90 degree upright trees. What about a back leaner? There's two parts to the answer. First part is pull torque analysis same as the first three cases. Matter of fact nearly same solutions likely apply. Second part of the answer is real world numbers based on tree characteristics for the torque preload caused by the backlean of the tree. Could be done in portions. First approx cylindrical trunk only, no top, wood species density, CofG hallway up, torque by offset of CofG x spar weight. Then maybe tapered spar, more real, lower height CofG, more complicated density/weight calc. Finally, trees with tops, goodness knows where to get data for this.

Perhaps there's some tables already published in good books?

 

[moss]

So much of what we do in rigging is "intuitive physics". Intuition is a vastly misused word. Applied to tree work I think of intuition as "cumulative knowledge acquired through experience". Nevertheless... always good to have numeric values to apply to planning a task when possible.
-AJ

 

[Bart_]

I figure in this case rating on the rope or winch/hardware and that it can get away on you going backwards brings the actual numbers to the forefront more so than the almost passing interest in making a plain pull over go a bit better.

Somewhere online years ago I recall a log weight chart existing or being posted.

 

[Bart_]

Well here goes some rock n roll math.

CofG half way up the spar. 40 foot spar. CofG moves 1 foot over center. say 1000 lb spar. gives 1000 ft*lbs torque preload. atan(1ft/20ft) = 3 degrees tilt.

30 degree rope pull angle ignore extra 3 degrees effect on effectiveness of rope attachment height. derate effectiveness of rope pull by cos(30 deg) = 87%, or 1/87% = 1.15 more tension needed than perfect perpendicular pull.

attach pull rope at 20 ft CofG. 1000 ft*lbs torque needs 1000/20= 50 lbs perfect pull, plus 15% = 58 lbs rope at 30 degrees pull

So the takeaway is 58 lbs / 1000 lbs = 6% of log weight for preload due to 3 degree back lean with rope attached at spar CofG with reasonably typical 30 degree winch rope angle.

CofG movement is roughly linear with lean angle for reasonable back lean angles so you can scale it proportionally.
Rope tension scales with log weight directly.
The higher or lower you attach your 30 degree pull rope inversely helps/hurts the required tension.



Anyone want to wash, rinse, repeat out a chart that includes real log diameters, lengths and weights?

edit: tcia green log chart per foot 24" dia honey locust 200 lbs/ft would be 200 lbs/ft x 40 ft = 8000 lbs
Our 60 lbs winch just became 500 lbs winch, add a tinge of stretch/back motion could become 1000 lbs winch in a hurry!

https://img1.wsimg.com/blobby/go/99dd5b87-e90d-4f2f-8ad0-9f1cea1a5f13/downloads/1d39p2ltj_110964.pdf

 

[Daniel]

What's the point?

 

[Dan Thornton]

edit: tcia green log chart per foot 24" dia honey locust 200 lbs/ft would be 200 lbs/ft x 40 ft = 8000 lbs
Our 60 lbs winch just became 500 lbs winch, add a tinge of stretch/back motion could become 1000 lbs winch in a hurry!

It took me a while to follow your calculations. Looks good.

To use this information requires some skills I'm still trying hard to develop:
1. estimating where is the Center of Gravity
2. estimating how heavy is the tree / piece / top

I think it was one of Patrick's videos (Muggs) where he stressed pulling on the pull line until you see it move the tree or top before committing to a cut. That is a practical way to see if there is enough force to pull the piece against the lean.

Still, it would be good to have a ballpark estimate of whether my gear can handle the forces before I commit to the job. I'm nervous about falling a 120' tree backleaning over a shed and only a couple feet from the shed. I'll probably hire my tree expert to do this one with me.

 

[Matias]

I do as you described from the video, though I havn't seen that one, just done it with my own trees. What kind of MA system do you have to get the pull? How many degrees off center? What kind of tree? DBH? Condition of the tree? If you're not sure you can pull it, don't fuck around when there's high value targets. Ask me how I know...

 

[Dan Thornton]

What kind of MA system do you have to get the pull? How many degrees off center? What kind of tree? DBH? Condition of the tree?

About 36" DBH. I'll set rope (5/8" Yale XTC) high in tree, pulling almost directly ahead, through block, to side, using a GRCS. Nothing wrong with the tree - a pine. Homeowner called it a yellow pine, but I haven't confirmed that, or discerned which kind of yellow it would be here in western Maryland. I'll use a rope puller to tension a second rope near the butt (Samson Stable Braid 1/2") above the cut to decrease chances of any butt kick back into the shed. I'll clear a few scrub trees from the landing area. I think it's a good plan, but would like my tree expert to be there let me know if I'm missing something.

 

[Matias]

Sounds like you got it in the bag with that setup, and a healthy looking tree, but you can never be too safe.

 

[southsoundtree]

Looks like possible codom- split at felling level.

 

[Matias]

Looks like possible codom- split at felling level.

Oh snap. Good eye.

 

[Dan Thornton]

Looks like possible codom- split at felling level.

Codom came down a long way, but not all the way to the felling cut.
I did benefit from my tree expert in three ways. One was the codom. When I climbed and tied the pull rope, I included leads from both sides of the codom in the running bowline loop, at his suggestion. Second suggestion he made was to cut the back cut a few inches higher than the front notch. I would not have thought of that. Third was more a warning. One of the trees that would be scraped by the falling tree was a very tall dead pine. I hadn't noticed how profoundly dead it was. So, we made sure everyone was prepared in case that tree fell to pieces sending shrapnel everywhere. It didn't explode, but we stayed clear until it stopped quivering back and forth.
Tree came down beautifully.

 

[shaddart]

Codom came down a long way, but not all the way to the felling cut.
I did benefit from my tree expert in three ways. One was the codom. When I climbed and tied the pull rope, I included leads from both sides of the codom in the running bowline loop, at his suggestion. Second suggestion he made was to cut the back cut a few inches higher than the front notch. I would not have thought of that. Third was more a warning. One of the trees that would be scraped by the falling tree was a very tall dead pine. I hadn't noticed how profoundly dead it was. So, we made sure everyone was prepared in case that tree fell to pieces sending shrapnel everywhere. It didn't explode, but we stayed clear until it stopped quivering back and forth.
Tree came down beautifully.

one thing to consider- I have had a pull rope (1/2 inch stable braid) tied around two leads with a running bowline,
when I applied enough tension (probably too much, with vehicle ) under load when the rope slipped through the
bowline as the leads compressed towards each other, the friction actually cut into the rope! this has happened to me
twice, both times with too much tension admittedly, but could have been disaster. One was a very tall poplar with
a bad base and people where standing around watching, etc. The rope cut half way through itself!

Paul

 

[evo]

I’ve only glanced at this brain soup so far.
My initial thoughts with back leaners is the pull rope no matter the placement sees the most force lifting the tree to 90 degrees. Up to the 90 degree or vertical mark some force has to be transmitted down to earth. Thus wasted energy, yet also need for thicker stronger hinge wood to avoid shearing the fibers.

 

[data farm 26]

So much of what we do in rigging is "intuitive physics". Intuition is a vastly misused word. Applied to tree work I think of intuition as "cumulative knowledge acquired through experience". Nevertheless... always good to have numeric values to apply to planning a task when possible.
-AJ

When I was a kid I rolled a lot of rocks around in the creek by my house. That's the foundation for my knowledge of physics

 

[TheTreeSpyder]

To me backleaners are different;
we pull/push CoG up the hill to over the hinge pivot as highest CoG point,
then past, to reverse the pivot from rear of hinge to front suddenly
to then splash down on the front side.
.
Greater range of movement, more favoring a balanced load across w/o side lean if can help.
Usually on forward lean, even if can fell straight into the lean, in good wood i try to fell as if a side lean for practice/art and less ground concussion as not felling straight into the strongest pull of the tree.
Not so good wood, or backleaners , favor fall on lean axis, w/o side pull as can.
.
Good wood no backlean favor Tapered Hinge as only thing that steers from first breath/movement of tree to tear off. Wedge and rope are temporary adjustments(unless rope 'arm wrestling smaller to ground whole tour). Dutchman a later adjustment, but invokes speedSQUARED as to be more volatile, but backlean w/sidelean, i might try Dutch step on lean side of splash down face.
.
To me a style difference also involves speedSQUARED
is slower, softer, more artful hinge fold that must setup right , as plays out on own at some point; speedSQUARED effect minimized
vs.
A hard 'throw' of speedSQUARED invoked, whereby if lined up right this inertia itself can fight sidelean more, as wedge or rope relieves it's guidance and sidelean if previously managed by rope or wedge pressure can impact back. Where on a slow'mo fall can be more pulled off course, and want Tapered Hinge geometry help when sidelean comes back/not ballasted by rope or wedge direction anymore. But, the inertia of a faster fall can continue as freight train, less affected by the smaller by ratio side pull. Sometimes as we share i think 2 that seem to conflict w/each other may be speed style applied. For weaker wood, is less hinge steering and wood endurance dependent
.
rope leverage reach x angle x direction x wood rigidity
vs.
CoG x leverage reach x angle x direction.
Even direction is a component.
All distances, directions, angles, rigidity spans calc'd from most compressed part of hinge as ground zero benchmark middleman war between effort vs. work translates thru. Most compressed Pivot is only front line strip of hinge if pure 100% forward lean. Most compressed Pivot is front corner towards sidelean otherwise, when only some forward lean. Only perpendicular pulls are full reveal of rope force 100%cos against target's 0%cos.
.
i picture the CoG piece of puzzle as sometimes like a metal donut, whereby the CoG is not on the framework but in empty space within the framework perimeter. But still must use framework to engage CoG w/efforts. i picture donut or tree framework as weightless and of (variable)rigidity, and CoG the only weight force that engage. Many codoms i have roped both codoms together and pulled from another carabiner, rope for a balanced pull from the SLACK rope pulled tight by 2nd rope between the codoms.