Calculating Rope Strain for 90' Tree Cut

[JJMH]

I have to cut a tree down that is 90' tall and weighs 12000 lbs. It is leaning 10 deg from vertical away from the direction of pull. My rope is tied at 50' up on the tree and the angle from horiz for the pull rope is 15 deg. I would like to how much strain will be on the rope as I cut the tree. Thanks Jeff

 

[Danger]

Welcome to PF, Jeff.
I'm not into the math stuff, but it seems to me that the weight distribution within the tree is very important. Usually, I would expect the bottom half to be much heavier than the top half.

 

[turbo]

Jeff, is this a homework question? If so, it should be posted in the homework section, properly formatted.

As Danger alluded to, the distribution of weight is critical. If you are allowed to assume that the tree is a cylinder, your problem is solvable. If not, then the problem is more complex than you think. The weight of fully-hydrated foliage in the summer months is significant.

Welcome to PF!

 

[JJMH]

Jeff, is this a homework question? If so, it should be posted in the homework section, properly formatted.

As Danger alluded to, the distribution of weight is critical. If you are allowed to assume that the tree is a cylinder, your problem is solvable. If not, then the problem is more complex than you think. The weight of fully-hydrated foliage in the summer months is significant.

Welcome to PF!

This isn't a homework question - I'm actually going to cut this tree. The tree is probably slightly heavier at the base but for my safely I would like to assume it as a cylinder.

 

[LURCH]

Is the rope attached to a fixed point, or to your pickup? If attached to a truck, the amount of strain on the rope is determined by the truck, and not the tree. It would require two people, and I would suggest that this is the safest way to go, as you can use the throttle in the truck to put tension on the rope. This tension will only decrease as the tree is cut, rather than increasing. That way, if the rope is going to break, it will do so before the cutting begins.

I have to say, be carefull! If the rope breaks, it can come through the back window of the vehicle, potentially injuring the driver. Also, make sure the rope is more than 40' long after you tie it (you wouldn't believe how many people make that mistake!), and that the driver keeps tension on the rope as the tree begins to fall.

Also, is it important that the tree fall in the direction of pull? Or is it merely imoprtant that it not fall in the direction it is leaning?

 

[turbo]

Just a caution: It is not a good idea to tie a vehicle to a tree that out-weighs it so badly, unless you want the driver to have a really bad ride.

 

[Ranger Mike]

now yer talkin!
call a tree service..but..ifin you want to try it yer self...do not attach a rope to the tree..mucho trouble,,,ya got to make a 45 degree cut on the fall si8de of the trunk, 40 percent into the diameter of the trunk...when doing this..you MUST eyeball the cut to be perpendicular to the axis of fall..nother words...the tree going to fall square to the groove..most likely, the bottom segment of separation ...
ok.you cut the fall groove..next , make a cut above and in back of the initial groove..make is straight and intersect as close to the bottom most portion of the initial cut so you got a flat stump...the tree will fall once the fibers give way and for goodness sakes..once you here the tree start to crack...back way off and stand clear...the falling tree can back kick and kill ya..

let me know ifin you live thru this drill
ranger mike

 

[turbo]

now yer talkin!
call a tree service..but..ifin you want to try it yer self...do not attach a rope to the tree..mucho trouble,,,ya got to make a 45 degree cut on the fall si8de of the trunk, 40 percent into the diameter of the trunk...when doing this..you MUST eyeball the cut to be perpendicular to the axis of fall..nother words...the tree going to fall square to the groove..most likely, the bottom segment of separation ...
ok.you cut the fall groove..next , make a cut above and in back of the initial groove..make is straight and intersect as close to the bottom most portion of the initial cut so you got a flat stump...the tree will fall once the fibers give way and for goodness sakes..once you here the tree start to crack...back way off and stand clear...the falling tree can back kick and kill ya..

let me know ifin you live thru this drill
ranger mike

And once you make the back cut, do NOT nick the front cut! That sucker can twist off the stump, kick out and make your wife a widow.

 

[Danger]

Am I the only one who still cuts down trees with primacord?

 

[Ranger Mike]

det cord does it too, claymore is too sloppy, 1 pound C4 properly shaped is the lazy way
but i digress

 

[Danger]

 

[uart]

To answer the original question, the tension T (in pounds force) in the rope will be given by the following equation.

$$T = \frac{12000 d \sin(10) }{50 \cos(25)}$$,

Where "d" is the distance up the tree (in feet) to the center of mass.

Numerically this comes out to about T = 46 d. So for example if the distance to the center of mass were 45 feet up then the tension would be T = 46*45 = 2070 pounds.

Make sure you leave plaenty of safety margin though.

 

[LURCH]

The question about the direction of fall is quite important. If you're only interested in keeping the tree from falling in the direction is leaning, this could be done by attaching a brace. Rather than tying a rope around the tree, nail a long 2x8 to the spot, with the other and placed against the ground. No way the tree is going to fall in that direction, then. It will fall 90^o from it.

But if there is some way you can still get det chord involved, I think we're all in favor of that!