Math question

[Kevin]

I'm trying to determine line pull on a back leaning tree being felled against the lay.
I have the weight of the tree, the distance it leans back from center and the angle and height of the rope where it is attached to the tree.
What I want to determine is, how much force the rope must endure pulling the tree vertical?
The tree is cut with a hinge.
Anyone have an equation for this?

[Flurida_BlackCreek]

Without calculating the resistance of the hinge. etc etc etc...

F=force (Ftlbs)
W=weight of tree
theta=acute angle of the tree
Y=height rope is tied to the tree
H=height of the tree


F=W*sin(theta)*(Y/H)


as is not proved!

[dan-l-b]

How about overall length of tree, swish area and circumference area in case of trouble (wedge prematurely breaks loose) ;)  
From other threads I respect your thouroughness and regard for safety--just thought I would poke a little fun :D :D Dan

[Kevin]

Thanks FBC, I'll have to try and get someone to check that out, I've been out of school a long time and I think this is one of those exercises that I said I would never have a use for.  :-/

Dan,

wedge prematurely breaks loose

That wouldn't happen, I don't use wooden wedges.  :D

[Larry]

Did quite a few similar calculations in my prior life for river crossings with telephone cable or river crossing wire.  Some as long as half mile.  Can't remember  the formula I used but do know it is a lot easier to plug in the lead or length of your rope rather than the angle.  You would also need to know the strength of your stem so you won't break it.

In reality I would go with your judgement and if in doubt use a steel cable that you think is the right size.

[Kevin]

Larry;
The general rule is you use the best bull rope you can buy for big trees and try and see if you can lift them before you commit.
I don't often get into any real big stuff and when I do it usually gets pieced down.
Cable is pretty much out of the question these days with the new synthetic bull ropes that are available.
Here's an example ... Samson
For monsters you might use a large steel cable with large winching forces to back it up but from what I understand you need rigging in the tree just to pull up the rigging.
We are talking 1 1/2"steel cable.
Most guys will tell you to use gut instinct but it wouldn't hurt to do a rough estimate just to confirm your thoughts.
Pulling from center of balance might not be a big deal but large back leaners could test your equipment.

[Wes]

 Kevin mabie you could post the numbers and someone could figure it out. That formula is greek to me, but I would like to see the results also.

[Kevin]

The tree is 90' tall
It weighs 10,000lbs.
It leans back 10' from center at the top
The rope is secured at 60'
The rope is 150' long and set at a 50^o angle
The tree is cut and wedged and just needs to be pulled over on the hinge.
What is the force required to pull the tree to center of balance?

[Flurida_BlackCreek]

Kevin,

I've been out of school a looong time myself. Home schooling my children so I've had to,  :P :P :P, to refresh myself on trig calculus and physics, plus my oldest is in college and has always liked to ask abstract questions. ;)

The function can be put into a spreadsheet as is. As I'm sure you know, it's not very complete i.e. wood density, tree taper, crown diameter/height/taper and weight, rope angle, hinge volume etc. etc. I don't fell trees so there may be other variables I'm not considering. ?

I'll work it out a little more tonight and post back.

[dan-l-b]

Hey Kevin, would the experts of GOL need to pull it?  Maybe your one of those guys.  ;)  Why the need to pull...it doesn't seem like your style  ;)  Leaving a tree notched for days while you figure forces doesn't seem consistant either.  Please don't take this as an attack, have read alot of your inputs and threads and have alot of respect for you.   Just curious.   DAN

[IndyIan]

Hi Kevin,

Can you estimate where the centre of gravity would be on the tree?  I think knowing the centre of gravity is important because then you can use force diagrams.  

Guessing that the centre of gravity is at 45' up the tree I calculated 1220 ft\lbs of force is needed on your 150' line.

Here's a pic of how I got this.  I'm not 100% sure this is the right way to do it but the numbers make sense.  I wouldn't park your truck behind the tree if your using 1220 lb rated line though!



Hope this helps,
Ian

[beenthere]

Ian
That looks pretty good. Do the line forces drop to zero when the tree is standing straight up? Didn't try to work out your numbers with the previous formulas.  I suspect the forces on the line go up pretty fast if in fact the tree is 11' off center at the top, rather than 10'.

[IndyIan]

OOPS!  I hope kevin hasn't tried to cut that tree yet! :-[   ;)

Beenthere prompted me to check my thinking again...

I tried running the numbers with the rope at 20 feet and the force doesn't get high enough...  

I'll get back to you guys when I've got it...

Ian
  

[Flurida_BlackCreek]

Well I screwed up too, inverterted H/Y should have been,

F=W*sin(theta)*(H/Y)

[Stephen_Wiley]

Kevin,

I know that TCIA and ISA in recent years have been promoting bull rope usage. And due to a lack of experience in application down play wire rope. Further make claims that 1 1/2' wire rope is needed.  This simply put is not true.

I operated a tree business for 20+ years and use used 150' of 3/8" wire rope. Greatly benefited me, especialy  for situations like your above proposed diagram.  Climbing with this cable is not that difficult. I would not trust many of the bull ropes which were much heavier to pack into the tree. I have had the misfotune of seeing bull ropes fail. But not once in 20 + years ever had my wire rope fail.

The cost of the wire rope would have been excessive, except that I found a tow truck supplier that had them made up with hook ends for 1/3 the cost of bulk wire.

[rebocardo]

I have only been doing this a short time, so take the advice with $0.01 because I do not have enough experience to even think about doing the tree you are.

I use a winch (or my truck) most of the time to pull trees over once the hinge is cut. I do it mostly so I am not near the tree once it starts to head over.

A 2" hinge in oak 36" wide will easily stall a 2,000 pound winch on a straight standing tree. Think of it as trying to break (18) 2x4s lined up straight across.

To pull this tree over, you have to break the hinge/wood fibers (since the grain follows the tree)  and pull that tree over to you, at this point there is no real holding fiber and the winch is doing all the work.

imo, If your truck is not heavy enough and the wire strong enough the tree will fall the way you do not want to.

I would only try this with a winch and line rated 1.0-1.5 the weight of the tree. Things to consider, a winch this big will heat up fast and drain the batteries fast. You will only get once shot at pulling this over unless it is a hydraulic winch because most electric winches can only pull about 1-2 min. max at their top load rating.

If this tree starts going the other way, you should have a second line on something heavy and immoveable to give you (or the winch) time to recover. Ideally, I would pull a foot at a time on the winch, then have the second vehicle tension its line.

Things to consider:

Fiber rope loses something like 30% of its strength at the knot or loop in a winch situation.

I have tested (nylon) rope to see when and where it breaks. From what I have done, it stretches a lot, then breaks at the knot or loop closest to the load.

Rope (and somewhat cable) loses its strength rating the longer it is and the greater the angle. A flat pull puts less stress on the rope than a 45 degree pull. Think of it like a log, compression and tension.

Most winches and their mounts are calculated at a straight pull. The greater the angle (especially the mount) the weaker they are.

A winch on its first layer of wire is probably capable of snapping the wire it came with from the OEM.

If you do not anchor the truck to another tree, it better weigh at least as much as the tree because once you have the winch going, it will lift up the pulling end.

Using my little 2k/6k winch I have buried my tires in the ground (I have four wheel hydraulic brake locks)  and compressed my suspension a good three-four inches before the tree gave way.

I think a 26K truck with a pintle hook would be the ideal dead weight vehicle to anchor the second line because empty it weighes probably 12k.

I would make sure where I put that winch line (I use 3/8 chain - you should probably use a 1/2 inch logging chain) the tree would not crack in 1/2 at the stress and have the top pop over.  

My experience has been rope and cable gets buried in a tree and cuts through it. A chain usually stays right on the top and does not go deeper than one inch into the wood and removes easily.

[Don P]

I've been trying to make a calc for this since Jeff asked me to take a look at it yesterday. The math was beyond me so I started E-mailing our resident physics professor Mitch  8).
He sent me another formula to use and I tried till almost midnight last night, I was worried. I E'd Mitch again last night and asked him to work the problem, he did that and sent me more info for working on the calc, it was here when I just walked in.

Here's the quick answer, if the center of gravity is halfway up the tree the force required is 1090 lbs, worst case is the CG is 3/4 way up and it becomes 1640 lbs. This is assuming the tree is cut through and freely pivoting....which it isn't, so account for that.

I'll work on it more tonight and put up what i've got after...food  ;D

Thanks Mitch  8) 8) 8). (we need a hat's off smiley)

[Wes]

 Dont forget wind.

 If it were me,I like the 1/2" cable idea, when I worked for the tree service we only used ropes, weve done a fiew similar to that with 1" bull rope, hooked to a tree truck or backhoe and the most important thing, goooood insurance.
  Since Ive been working for the state park service Ive been doing things a little differently, now I would use the cable.
  
 Kevin whats around the tree, that you have to pull it over backwards??

 Wes

[Flurida_BlackCreek]

Wind? Oh great, another abstract variable!

CG hmm. OK! I'd just overkill to be on the safe side but I do enjoy the math.

[Kevin]

Stephen;
The large cable was used and might still be out west on the large trees.
The information I passed on is a direct quote from Gerald Beranek who wrote the Fundamentals Of General Tree Work.
Gerald worked the big sticks on the West Coast for many years.
No disrespect meant here but I don't know of a single arborist who uses wire rope for pulling trees today with the high quality ropes that are available.

The tree in question is being pulled over by another qualified person in the U.S and is situated near power lines .
The estimate that he and another arborist came up with (separately) is in the 1200# range.
Don is attempting to make a calculator that takes some of the guess work out of it, the final responsibility is in the hands of the guy doing the tree work.
Because of all the variables involved it can only be used as a  guide.

Dan:

Leaving a tree notched for days while you figure forces doesn't seem consistant either.

Who said that?  
 :D

[Don P]

Mitch fixed my attempts and quickly put up a working version, take a looky here.

http://shagbarkfarms.com/LmbCalc/linepullclc_DonPF.html

Also go to his website and click on the Log/Lmb Calculators at the top of the page here:

http://shagbarkfarms.com

He has a nice site I'm sure many of you will enjoy looking around in.

[Kevin]

That looks really good Don.
I'll let you know what the critics think.  ;D

[Bro. Noble]

Hells bells and cockle shells,

Fall the DanG thing sideways :D

Tie it like you have shown in the pictures,  anchoring to something imovable-------you don't need a winch.

Make your notch 90 degrees from the lean and hold a corner when you backcut.

Even so,  wouldn't hurt to follow Wes's advice and have goooooood insurance ;D

[Kevin]

Yo Bro;
Thanks for the advice.
Even though a force of 1200 pounds is a decent pull a 5:1ma can reduce it to a little over 200 pounds so it looks like you might be right again, you might not need a winch.

[Don P]

Well now, Mitch found my problem from last night, in javascript angles need to be converted from degrees to radians.  8) 8)

https://forestryforum.com/members/donp/linepullclc.htm

He figured the inputs to use as this,

Center of gravity 45'
weight 10000 pounds
tree angle 83.6 degrees
height of rope 60'
angle of tree to rope 50 degrees

I've just been having fun substituting 90.0001 degrees for the tree angle. Shoot I can hold that puppy up no problem  :D

Don't forget the hinge wood Kevin  ;).