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Measuring Progressing Lean Revisited
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<Scott Cullen>
posted
http://tree-tech.com/board/?topic=topic4&msg=422

This earlier thread focused mostly on measuring from some point on the tree to some fixed reference point. A couple of concerns with that are 1) the need to set up instrumentation like a transit at the fixed point or 2) tampering or other movement of the "fixed" reference point.

Has anyone thought of or tried usinag a clinometer against the trunk? Say set a small wood bearing surface that will read 0 or 90 degrees (or the actual existing lean) if the clinometer is held against it at the start of monitoring. It would be quick and straightforward to go back and time and just hold the clinometer up to the surface again.

So what are the potential problems? Tampering with the test surface is one. Sensitivity or precision? Calibration of instrument(s)? Any insights from the gang?
 
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<Russ Carlson>
posted
Reply to post by Scott Cullen, on April 27, 2000 at 11:57:52:

I do use a clinometer to measure tree lean by either holding it against the trunk or by standing back and visually aligning the edge with the trunk. I don't count either as being all that accurate, but can get you within a degree or two with practice. This is not enough to judge small shifts over time, however. I have never used time comparisons to judge shifting of the tree, but I don't think it would be that reliable with this method.

Consider that a 60-foot tall tree that shifts 0.5 degrees has moved 6.28 inches at the tips. [(sin 0.5) x 720 inches]
 
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<Mark Hartley>
posted
Reply to post by Russ Carlson, on April 27, 2000 at 11:57:52:

Guys,

Get with the technology. Try a digital level. You can ven get them with lasar pointers attached.

mark
 
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<Scott>
posted
Reply to post by Mark hartley, on April 27, 2000 at 22:59:34:

It's just so hard to keep up with the new stuff. Can Russ upgrade his new tricorder with a digital level laser or is it out of date already?
 
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<mike ellison>
posted
Reply to post by Scott Cullen, on April 27, 2000 at 11:57:52:

The simple methods are often the most practical to use. Try two nails friven into the underside of the leaning stem positioned so that two plumb lines can be hung from them. The measurement between the lines will increase as the lean increases.
 
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<Scott>
posted
Reply to post by Mike Ellison, on April 27, 2000 at 11:57:52:

I like it. I had re-visieted the "lean" thread and left it titled that way. This tree is actually straight up and down at the moment and the task would be to see if it's shifting at all.

I suppose if I was confident it was absoultely tamper proof I could affix a frame or upper and lower arms to the trunk, hang a plumb bob from the upper, make a witness mark on the lower and check for movement.
 
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<mike ellison>
posted
Reply to post by Scott, on May 05, 2000 at 16:03:23:

This method has improved at a stroke thanks to your reply. Modifying what you have said, two nails and a single plumb line will measure the progressive lean, in even a near vertical tree.

1)Drive in two round-head nails, one a short distance above the other
2)Cut a shallow nick in the top edge of the head to the upper nail
3)Tie plumb line to top nail and hang through the nick and over the end of the nail
4)Drive the lower nail so that the face of the nail-head meets the plumb line

If the tree has a lean of more than say 30 degrees, revert to the plumb line x2 method.
 
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<Scott>
posted
Reply to post by Mike Ellison, on May 05, 2000 at 18:36:43:

Cool!

A little more refinement. I have a supply of stainless screws. Your notch is the key to repeatable precision and the stainless won't rust over time at the cut. With a pilot hole (stainless is soft and won't take much torque) they could be easily and precisely set, particularly the bottom one.

Longer screws would allow the installation to be made with a "stand off" distance if it's on the top side of potential lean... in that instance the plumb bob will swing towards the tree and you'll need room. (Even on the under side where the bob will swing away you'll need clearance for the radius of the bob. (I have seen a flat 'lies against the wall' bob in the woodworking catalogs.))

It might be nice to select either upper or lower side... avoid standing in the fish pond, less tamper tempting to the passer-by, whatever.

And I suppose stainless common nails would work almost as well.

The monitoring log should probably record the location and initial "standoff" distance of each screw/nail so it can be confirmed to rule out tamperimg at each session.

Now, if you'll double check my very rusty school geometry. The plumb bob movement relative to the lower reference point should indicate absolute movement of the upper point irrespective of the vertical distance between the upper and lower points. Correct?
 
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<Scott>
posted
Reply to post by Scott, on May 06, 2000 at 03:11:17:

The idea is appealing in its simplicity, but I'm afraid it's not really that simple.

If we assume the trunk is leaning from a fulcrum point more or less on center and at a point below grade approximating trunk radius at grade we can project both the center point and the trunk points as they rotate from the fulcrum. If the upper nail point rotates x distance the lower nail point will be rotating with it something less than x. The difference in rotation distance will increase as the distance between the nails increases. If the nails are close together the difference will be quite minor and it is only that distance that the plumb bob will register relative to the lower reference point, significantly under registering the actual movement of the upper point, if noticeably at all.

So while movement might be detected the amount of movement will not be read directly. That puts us back to accurately reading changes in angle.... of the plumb bob string or the trunk itself it doesn't really matter... and you need an instrument (or reliable movement distances to calculate it which this method does not provide).

I suppose an equation could be developed inputting the distance from the fulcrum point to both trunk points and the distance between trunk points to convert the registerd movement to actual movemnet and from that angles, but then it's not so simple anymore.

Oh well.
 
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<Russ Carlson>
posted
Reply to post by Scott, on May 06, 2000 at 07:29:59:

ItÂs not really that difficult to calculate.

Fig. 1 shows the tree in the initial state, when you first measure it.
Point A is the upper anchor point, where you hang the plumb bob.
Point B is the lower reference point.
Point F is the fulcrum point, or the point that the tree rotates around.
Line BC is horizontal from the reference point B
Length l is the length of the plumb bob line
Length d is the amount of displacement of the bob


In Fig. 2 the tree has begun to lean, causing the bob to swing away from B. d is now a positive number, the distance the bob moved. We need to know how far the tree leaned, or more precisely, the change in angle of lean.

Some simple geometry will solve this. Since Points A and B are anchored to the tree, and do not move in relation to Point F, any change in the angle at A will equal the shift in the lean of the tree. To determine the change in the angle, you need just 2 measurements: Length l and displacement d. Displacement d is the distance horizontally from Reference B to the bob line. Length l is the length of the bob line from A to the point where d is measured. (For small changes in the angle of lean, you can use the length for A to B.)

Now the math. We have a simple right triangle, ADB. We know the lengths of 2 sides, l and d. The tangent of angle DAB equals displacement divided by the length of the bob line, or
tan DAB = d / l

This means the angle of DAB is the arc tangent, or DAB = arc tan (d / l). Any calculator with trig functions can do this for you, right in the field. You will also know the direction of lean, since it is the same as the direction fromn B to the bob line.

Fig. 3 is a brief sample chart of the displacement and shift in the angle of lean. It doesnÂt matter what units you use (English or metric). The first column is l, the length of the bob line. LetÂs say we made the two points 6 feet apart, or 72 inches. We come back later and find that there is now 1 inch of displacement. This means the tree changed its position by 0.79 degrees. Hmmm, not very much. Scan down the chart, and you will see that if the displacement of the bob is 12 inches, we only have about 10 degrees of lean in the tree. (Note that the last line in the chart is a displacement of 72, which yields a 45 degree angle. I put this in to show that the numbers work out- that is a 1:1 slope, or 45 degrees)

Now comes the BIG question: How much lean is tolerable?

Back to you, Arborists.
 
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<Russ Carlson>
posted
Reply to post by Scott, on May 06, 2000 at 03:11:17:

Using the screws, you already have that notch that Mike referred to, in the screwdriver slot. Just leave it lined up vertically.
 
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<Scott>
posted
Reply to post by Russ Carlson, on May 06, 2000 at 09:34:29:

Very nicely done Russ!

I'll have to print this out and study it a little more. It indicates movement, but won't d understate the actual deflection of point A? Remember both B and A are rotating in the direction of lean.

Also do the calculations become easier if we install the system on the side of the tree, that is 90 degrees to the axis of lean and over the assumed fulcrum?

Also do the calculations change if we assume the fulcrum point is not on center? Say at a point somewhere out under the flare or compression roots (picture the typical uprooted tree... it rotated at a point where the compression roots fracured or bent or pulled out of the soil?

Scott
 
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<Scott>
posted
Reply to post by Russ Carlson, on May 06, 2000 at 09:34:29:

Russ asked: "Now comes the BIG question: How much lean is tolerable?"

This type of system or analysis might be focused on a couple of fundamentally different questions.

1. What is the lean, is it tolerable? You might not need to record movement to answer this.

2. Is there movement? Is it just deflection in the trunk as it increase in weight (seasonally or over time)? Or is this baby going?

A constant lean may not be troubling, especially if the tree grew that way. Any movement at all might be cause for action, particularly if associated with other indications like soil cracking or trunk cracking or buckling (as described by Mattheck for example).
 
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<mike ellison>
posted
Reply to post by Scott, on May 07, 2000 at 00:09:29:

Scott

Below is my response to your earlier quetion. I have just picked up the excellent reply from Russ, which is basically the same as the solution I came up with.

-------

Thanks for the feedback. I recognise the shortcomings and have given the problem a little thought. I'm not too strong on math so I have taken the simple route again.

Drive one nail into the stem at ground level and the second at a height of say 2.0 metres. Attach plumb line to second nail and measure the distance from the line to the first nail. This will give you the angle from vertical. If necessary you could add in the extra distance to the projected pivot point.
------

Mike
 
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<Scott>
posted
Reply to post by Scott, on May 07, 2000 at 00:09:29:

Actually, I checked it graphically rather than running the equations.

The deflection measured from point B to the plumb line will be less than the actual deflection of point A off the vertical (or other starting angle). The closer B is to the level of F the smaller the difference will be. So if the exercise is just to check for movement the closer B can be to F and the longer l can be the more sensitive the d at B will be to movement.

The calculated angle using d at B will equal the calculated angle using d & l at other points... it's constant and the plumb line is a valid indicator. And you're right, the calculated angles are small... smaller than could be reasonably read of a clinometer say, and a digital instrument would have to be quite sensitive and well calibrated.

So the "fix" Mike made, moving B toward grade is not necessary for accuracy of angle, but it makes the system more sensitive in registering movement.

So that gets us back to your question. How great an angle of deflection is acceptable. I think that would have to depend on a lot of variables... what's the source (simply bending in the trunk or physical cracking or fracturing of trunk or roots or root movement through soil)? What's the target? What's the loading (wind, etc.)? How quickly is it happening?

I tend to think the more common and important question would be "is there deflection?" Coupled with the other observations above and other indications like soil cracking, movement alone might be a reason for action. Are the calculations of angle even necessary?

The system can be installed fairly quickly and montored fairly easily but there are some practical problems.

I've posted a separate note on the filed problems.
 
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<Russ Carlson>
posted
Reply to post by Scott, on May 07, 2000 at 08:11:23:

**Scott wrote: The deflection measured from point B to the plumb line will be less than the actual deflection of point A off the vertical (or other starting angle). The closer B is to the level of F the smaller the difference will be. So if the exercise is just to check for movement the closer B can be to F and the longer l can be the more sensitive the d at B will be to movement.

The calculated angle using d at B will equal the calculated angle using d & l at other points... it's constant and the plumb line is a valid indicator. And you're right, the calculated angles are small... smaller than could be reasonably read of a clinometer say, and a digital instrument would have to be quite sensitive and well calibrated.**

Wrong! It doesn't matter where A or B or F are located in relation to each other, or how high or low they are to the ground. That's the beauty of this simple system. You are measuring the CHange in deflection as a shift from verticle. The plumb bob line is the vertical reference that all is measured against. If the tree is leaning when you start, if the trunk is bowed, etc, you will still be measuring the shift of the vertical line from A against the position of B. Doesn't matter which direction the tree goes in relation to A or B (assuming there is sufficient room for the plumb line to hang vertically).

IF. . . Point B is not attached to the tree, say it is a stake or reference point in the ground, then you have variables introduced that can affect accuracy. The ground itself may shift and be carried with the movement of the tree, or the fulcrum point (not accurately known in any event) may cause a variance in other angles. But if B and A are both attached to the tree, and the tree doesn't suffer severe fiber buckling or shrinking, then the deflection from vertical is all you need to calculate the change in lean over time.
 
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<Scott>
posted
Reply to post by Scott, on May 07, 2000 at 00:09:29:

OK I tried one in the field today. Here are some issues.

1. It may be difficult to install the lower point at grade. It's got to go above the flare or else point A has to standoff enough to be plumb above it.

2. Standoffs can be a problem... the longer they are the more they can be out of square or plumb with the trunk and the other point. They are also more vulnerable to tampering or accidental movement.

3. To get maximum sensitivity point A should be as high as possible. But you don't have to get too high at all before you need a lader or something else to stand on to hang the plumb bob. Oops some simplicity goes away. And then you have to secire the line up there and climb down to check registration against point B... oops it's too low or too high gotta go back up. Mike initial system with close spacing between A & B has it's advantages.

4. Setting accuracy. The first one (assume A) is pretty easy. Pick a point and set it. You want to be on axis with anticipated lean or deflection or 90 degrees to it. Take a guess at standoff distance, based on diameter of plumb bob, any flare at B and any rough bark or other obstruction in between. Then you need to pick a location for B. It needs to be i) plumb below A and ii) a chosen distance below A if you intend to use that distance in calculation. Mark and set (drill a pilot first if using screws). Even if careful you'll probably find the set fixture is not precisely plumb below A (off square, hole wasn't precisely right). You may have to use pliers to bend it to be plumb under A.

5. WIND. This particular tree is in a site that is ALWAYS windy. That's part of why it's a problem. It was very difficult to i) get the plumb bob to hang still and ii) be sure that the plumb bob was not still but being blown off plumb. Block the wind with your body and then you're not eye level with point B. Remember it's this first set up that's critical and you may be trying to bend fixture B into plumb.

6. Hardware selection. Screws worked very well. Should be 3.5" or longer #12 or 14 to take torque. Drill pilot holes. Cordless drill/driver makes it easy, but you'll need a hand driver if you're going to align plumb to a slot or notch. Both slot and notch worked well. You may find that large screws (like deck screws) come with phillips or square drive heads rather than slots. The slot is easily made with a trianglular file.

All in all, installation and reading problems, accuracy, etc., if I had a good transit available I might prefer to set a single point on the trunk 90 degrees to axis of deflection, set a fixed ground point also 90 degrees to axis of deflection, plumb the instrument over it, reference the instrument to one or two other known points to establish a repeatable angle to the tree point and then check for movement from that.
 
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<Russ Carlson>
posted
Reply to post by Scott, on May 07, 2000 at 00:09:29:

No matter if the fulcrum is not under center. Here the fulcrum is out beyond the line of the trunk, pivoting about a large root, for example. The angle DAB is measured against the vertical constant, as is the lean of the tree. In this image, note that DAB is the right complement to DAC (90 - DAB), so DAC is the shift from horizontal. That may help to visualize it.

Even if there is variance in the angle AFB, for example if the root bends between the trunk and the fulcrum point F, the measurement still stands up.
 
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<Russ Carlson>
posted
Reply to post by Russ Carlson, on May 07, 2000 at 08:11:23:

The angle DAC as shown is NOT the complement of DAB. The angle ABD is the complement, and equals the angle between the line of the trunk (black) and the horizontal line CD.
 
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<Scott>
posted
Reply to post by Russ Carlson, on May 07, 2000 at 21:11:20:

I think we agree Russ. If I'm wrong you're wrong!

The angle IS constant regardless of distance between A & B or distance from F. Read my post agian. I agree with you.

The deflection distance between B and the plumb line WILL vary with distance between A & B. It is NOT constant and it is NOT the same as the actual deflection off vertical at A except at the same level as F if you could get there. That's the way it is... but it does not matter in the calculation of deflection angle. Points A & B do NOT move the same distance off vertical. You are NOT measuring from the plumb line to previous vertical. You are measuring from the plumb line to the rotated point B. Those two distances will be equal ONLY if taken halfway between F & A.

You're right, point B off the tree would have to be remote enough to not be affected by tree movement and would only work in one direction.
 
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<Russ Carlson>
posted
Reply to post by Scott, on May 07, 2000 at 08:11:23:

Debunking mode:

1) Doesn't need to be at grade, unless you have a problem with aesthetics or tampering (intentional or not). It can be anywhere.

2) Standoffs are not really necessary, except that the plumb line has to be attached at A, and must be free to hang to or past B.

3) CORRECTION: to get maximum sensitivity, A must be *as far as possible from B*. But, consider the chart in the first image. You will see that a one-inch deflection is less than 1 degree of lean. You can probably measure to less than one inch with reasonable accuracy. This was over a 6 foot distance from A to B. If you have a 5- foot (60 inch) base, 2 inches of deflection is 1.909 degrees of lean; less than 2 degrees. I doubt you can get that accuracy repeatedly with a transit system (and you thought setting up a ladder was inconvenient?), certainly not with a clinometer, as you said.

4 i) No, it doesn't matter if B is not plumb below A. You will just have some deflection at your first reading, and then take the difference between that and the next reading. So you don't have to work so hard at setting B in a perfect spot. Remember, you are not measuring absolutes, but the changes in deflection.

4 ii) The distance does not matter, either. If you measure the deflection horizontally from B to D, mark the point of D on the plumb line. The distance from that mark to A is the length l in the diagram. Actually, using this measurement is more accurate than always using the set distance from A to B.

5) I can't argue with WIND. [g]

6) Hardware should fit the job, of course. You don't really need to have long screws or nails hanging out, as long as the bob can hang freely past B. Actually, a short nail at B, just sticking out enough that it won't become included, is sufficient for this method. You should make sure A has some system that allows accurate repeating of the hang point, like a notch or screwdriver slot.

I see a problem with using a transit- How do you know where 90 degrees to the angle of lean is? What if it changes (The starts to rotate)? These are errors that would be much more difficult to determine and correct. The more I think about this, the better it becomes. By using the plumb line system, you measure the deflection and hence the shift in lean, and you can measure the direction of lean and any changes over time.

Now back to the other question: How much is enough?
 
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<Russ Carlson>
posted
Reply to post by Scott, on May 07, 2000 at 21:25:32:

OK, I'll agree that we agree, except on one point. The distance from F to B, or how close B is to grade, is not really the issue. The disatance from B to A is the key to accuracy. If you have a 72-inch base (AB), the deflection you measure will be the same regardless of whether B is at ground level or 20 feet high. And it won't matter where F is located.

So, put the hardware where it's most convenient to measure.
 
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<Russ Carlson>
posted
Reply to post by Mike Ellison, on May 07, 2000 at 08:11:23:

Yep, your trig might be rusty, but the concept is correct.

But since we can't tell really where the pivot point (F) is, you would be introducing an error by projecting the pivot point. You would need at least two measurements, tied to outside references, for each of two points on the tree to determine exactly where it is.
 
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<Scott>
posted
Reply to post by Russ Carlson, on May 07, 2000 at 21:55:21:

"Debunking mode:" Well yes you are, but some of it was not necessary!

"1) Doesn't need to be at grade, unless you have a problem with aesthetics or tampering (intentional or not). It can be anywhere."

Yes I agree, I was just responding to Mike's "fix."

"2) Standoffs are not really necessary, except that the plumb line has to be attached at A, and must be free to hang to or past B."
So they are necessary sometimes, that's what I said.

"3) "I doubt you can get that accuracy repeatedly with a transit system"
I'd have to try it out... or wait for Wayne to check in.

"4 i) No, it doesn't matter if B is not plumb below A. You will just have some deflection at your first reading, and then take the difference between that and the next reading. So you don't have to work so hard at setting B in a perfect spot. Remember, you are not measuring absolutes, but the changes in deflection."
Personal preference I guess. I'd rather set it right the first time and not have to record and figure in the initial error. But that works too.

"4 ii) The distance does not matter, either. If you measure the deflection horizontally from B to D, mark the point of D on the plumb line. The distance from that mark to A is the length l in the diagram. Actually, using this measurement is more accurate than always using the set distance from A to B."
You're right you can enter any distance into the equation... it just might be convenient to have a whole number. You can drop the bob below point B and line up the string rather than the point of the bob... but then you have to be concerned about the string dragging and the bob not swinging free to plumb. I would not rely on the mark on the string. Braided plumb bob line (designed for the purpose from a surveying supplier) stretches and shrinks back. Over 3 feet 6 inches on this tree I had a half inch stretch in the plumb line.

"5) I can't argue with WIND. [g]"

"6) Hardware should fit the job, of course. You don't really need to have long screws or nails hanging out, as long as the bob can hang freely past B. Actually, a short nail at B, just sticking out enough that it won't become included, is sufficient for this method."
See # 2.

"You should make sure A has some system that allows accurate repeating of the hang point, like a notch or screwdriver slot."
I think I said that, so we agree, no debunking needed.

"I see a problem with using a transit- How do you know where 90 degrees to the angle of lean is? What if it changes (Tree starts to rotate)? These are errors that would be much more difficult to determine and correct."
You probably have some indication of initial lean, or of weakness or of partcular loading. Why else would you be setting the system up? It you want to monitor two or more axes, the plumb bob system would probably be easier to replicate. But how do you know where to set just one of them? It's no different.

"The more I think about this, the better it becomes. By using the plumb line system, you measure the deflection and hence the shift in lean, and you can measure the direction of lean and any changes over time."
Maybe very useful that way, but probably most sensitive if either in line with axis of lean or 90 degrees to it.

"Now back to the other question: How much is enough?"

I'm not sure I would be comfortable with saying x, y or z lean is good or bad in the absence of lots of other facts. My principal interest would be for detecting movement. Sudden movement may be a cause for action.
 
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<Scott>
posted
Reply to post by Russ Carlson, on May 07, 2000 at 22:15:28:

Can't you get these people to accept punctuation in the headers?

Distinguish the measured deflection and the calculated angle.

The angle will be constant regardless of where it's taken. We agree.

The measured deflection will vary if AB varies (l and d both vary in the equation and calculate to same angle). The deflection at A will constantly increase as it moves farther from F. Measured deflection at B is a function of actual deflection at A. If B is a constant distance below A (say 72") it does not change the fact that B will vary with A as the both move away from F.

The relationships are constant that's why the angle is constant. But the measure deflections vary with distance if deflection is rotation on a point rather than shift along a plane.
 
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