Reply to post by Scott, on May 07, 2000 at 22:52:56:

To clarify the "measured deflection" a little more:

This may be back in the thread somewhere already, but I'll repeat. The measured deflection between B & D (i.e. d) is NOT the actual deflection off vertical at A NOR the actual deflection off vertical at B. It is the difference between the actual deflections off vertical at A & B.

Remember BOTH A & B are rotating off vertical. So if you measure back from the plumb line (a surrogate for A) to B you are NOT measuring back to vertical, you are measuring to a point that has also moved off vertical by something less than the movement at A (except at the level of F which is inaccessible). The deflection between the plumb line and B will ONLY equal the actual deflection of B off vertical if B is halfway between F & A.

It's the angle that matters, and that is constant and your math works to give us that (even if we don't know what to do with it). The point is that representing the measured deflection between B and D to be actual deflection off vertical stated with precision when in fact it is not undermines the credibility of the part of the exercise that works very well.

Reply to post by Scott, on May 07, 2000 at 22:22:55:

OK, we agree, still.

Except. . . [g]

For accuracy, you can't use the initial distance AB in subsequent measurements. Displacement d must be measured perpendicular to the plumb line, so as d increases, l will decrease. If you set the bob to just touch point B, then let it swing and measure B to the bob, you will not have length l, but distance AB. The figure is not a right triangle (ADB), but an isoceles triangle, with a whole different set of formulae. Much more complex.

Maybe I need to find some non-stretching string for my bob. Once again, how much accuracy do you really need? 1/4 inch of stretch over 60 inches is about 0.4 %.

Re: direction of lean: If you set up Point A with sufficient clearance, you only need one set up to measure lean in any directioni, and it is not sensitive to being directly in line with the lean. As long as the bob doesn't hit the trunk, you get useable readings, and don't have to adjust for direction. When the lean is only a few degrees, of the direction of lean changes (rotating about the stump), the bob system will work with on setup. Granted that the laser systems can measure with pin-point accuracy, you still have to establish the reference point that is stable, and measure the distance and direction of deflection. What is it worth to get the same information?

You know I'm a bit of a technofile and gadgeteer, but sometimes simple is better. You can have two or three trees done before your surveyor gets his GPS base established (with or without the unscrambled signals).

Reply to post by Scott, on May 07, 2000 at 23:23:42:

Whoa! Back to the beginning. This whole discussion has hinged around one thing, and both you (Scott) and I have expounded on this issue many times. Let's define some terms.

When you say deflection, I now realize you are talking about what I call displacement ("the difference between the initial position of something and any later position"). Deflection is "turning aside or off course; departure of an indicator or pointer from the zero reading of an instrument."

So if I go back and read your posts with "displacement" where appropriate, then we are in full and complete agreement. The tree is displaced more at A, being the higher point, than at B. And the higher you set B, the greater the displacement regardless of the location of A. That is true. But the deflection, which I defined in the first graphic as d, the distance from point B to the vertical plumb line, doesn't change with the position of A, as long as the distance between the points remains the same.

Now my question is why would you need to know the amount of displacement, except perhaps to determine the deflection? We are ultimately interested in answering 1) has the tree shifted, and 2) how much? The later is best defined as the change in angle, since measuring displacement is relative to the point at which it is measured. Saying the tree shifted 2 feet is tells me nothing. Was it a 10 foot tall dogwood (major shift) or a 100 foot hickory? If you say the tree moved 10 degrees, I can visualize and compare that to other trees.

So can we agree on displacement/deflection?

For the record, there is no way anyone can suggest a "tolerable" amount of lean. The variables are too. . . well, variable. And numerous. Soil texture, strength (shear and compressive), soil moisture, root size, location and condition, species, wind direction and force, canopy density, weight, balance and size, location of fulcrum point. . . You begin to see my point!

I've offered several formulae, even some software templates, to quantify various factors regarding trees. Measuring deflection (shift in the angle of the tree from a former position) is simply a tool. It helps the decision maker, in this case the arborist, decide the facts and plot a course of action. You measure the diameter of a tree- why? So you can use that information in the decision making process. Same for deflection. By itself it is worthless. It must be applied with knowledge and judgement to become useful.

Reply to post by Russ Carlson, on May 08, 2000 at 07:27:44:

Yes, I seem to have been misusing "deflection" or at least no defining it at the outset. What I've been talking about is movement. You're right the angle of deflection is the only constant way to describe the movement.

That said I think most people will visualize an amount of movement if you associate it with a point. And that's what we're doing with the nails, looking for movement at points. I agree... say it moved 10 degrees and we can make
some comparisons and visulaize lean. Say it moved 0.6 degrees and maybe I can visulaize movement of a point better.

So both the angle of deflection and the amount of movement are tools.

The surveyors, by the way, don't use either of our terms. They refer to "offsets."

I agree about the "tolerable" lean being useless in the abstract, and not much beter with the variables incorporated! I think you left out the most important variable. "How did it get there." If it grew that way it has incorporated all the others, at least to a point in time. If there is observable movement then something is changing... less anchorage, more load, whatever. If the system is failing who cares what the angle is we know it's failing.

Reply to post by Russ Carlson, on May 07, 2000 at 23:12:28:

I see. l is AD not AB (unless d is 0). What would the error in calculated angle be if you used AB and say d was 2"? I get back to thinking simply the observed movement, a positive d from last measurement tells me something is going on.

Reply to post by Scott, on May 08, 2000 at 23:06:47:

For samll movement, you can probably use the AB length, instead of measuring l, o AD, independently. It will follow a sin curve, so the error in the calculated angle will be small at first, and increase as d increases.

Reply to post by Scott, on May 08, 2000 at 23:33:31:

Yee Gads guys, I'm loving my total station more and more all the time!!!! The problem I see with all the figuring using plumb lines and reference points is that everything except the distance between A and B is changing. The rotational issues become very complex and there is no objective standard against which they can ALL be judged. You are measuring B-D to establish the angular dimension of BAD but are limited to equipment that is imprecise at best, a tape measure and moving plumb bob string.

Russ, you noted way up on this string that you doubted the repeatability of measuring your example angle of less then 2 degrees with a transit. The entire purpose of transit technology is precision and repeatability. By establishing two related points in the landscape (I will call them TP1 for "turning point" and BS for "backsight") and Russ's two reference points on the tree at any location and any distance apart, the deflection angles can be derived against the standard of a horizontal and vertical azimuth.

Establist TP1 at some distance from the tree, preferably at right angles to the lean but not necessarily so. Establish BS within line of site but at a long distance from TP1. Assign an elevation to BS, lets say 100 feet (totally arbitrary). Set up total station or transit on TP1 and with a surveyors level rod establish the difference in elevation between BS and the Height of instrument set up at TP1. Measure from the actual point TP1 in a vertical line to the center of the instrument scope and you can establish the relative elevation of TP1 for future reference.

Assign the horizontal azimuth between TP1 and BS to be 0.0' 0". Rotate the instrument to face the tree and take a horizontal and vertical azimuth for each of Russ's screw heads (for this I would prefer phillips screws myself). It doesn't matter if the screws are in vertical alignment but if they are not, record the horizontal angle between them as well. (this will be established automatically when you note the polar projection from TP1 to each screw head.

Always finish this type of measurement by returning your sight to BS and read the resulting angle. This allows you to catch field errors before you walk away, the horizontal angle should read 0.0' 0" as it was when you started. From now on, you can check the change by setting up on TP1, measure the height of instrument, backsight BS and set your starting azimuth and rotate back to Russ's screw heads. The smallest angular changes in the horizontal and vertical position of the screw heads will be detectable, so much so it may drive you nuts. From there you guys have sure proven that you have the command of trig. to calculate the movement!!

The beauty of this is you are working your tree movement against two absolutes, a baseline TP1 to BS, and the zenith azimuth of 0 degrees projected from the center of the earth to the depths of space. It eliminates many ambiguities. Careful, precise work is of course needed to make it work and the higher order your instrument the better. We run a 1-second total station and have run level loops over a two mile traverse and returned to our starting point with an error of closure of 1/68,000. For that matter, with the plumb bob and string method, should I measure to the right or left side of the string? (Great big grin!!)

Enjoy, I like your diagram Russ, may I use it for teaching purposes? I will of course reference the source.

Wayne

Reply to post by Wayne, on May 09, 2000 at 00:25:01:

Last first, Wayne. Go ahead and use the diagram (with citation, please).

Now, back to the measurements. We have the technology, so we must use it! How else can we justify spending that much money on it?

The basic issue here is whether you need that kind of accuracy, and are willing to pay the cost. For you, Wayne, having the equipment on hand and the capability to use it yourself, the cost might just be rolled into overhead. For Scott, who would have to hire a surveyor to send a truck, two employees and a shipment of equipment out, charge a half day rate, and then repeat the exercise every time you want another reading, would it be worth knowing the movement to within 1/68,000? As Scott pointed out, maybe all we need to know is whether the tree moved at all, not even by how much.

Yes, I grant that the laser equipment and GPS (How's your accuracy these days, Wayne?) is capable of measuring to the width of a fruit fly's hair, but is it necessary and cost effective? The problem is that with the technology available, everyone expects it to be used, whether it is needed or not.

FWIW, I've started using my biltmore a lot more, and the D-tape a bit less.

Reply to post by Russ Carlson, on May 11, 2000 at 10:23:37:

Well, I think we need to sort out issues here Russ.

At http://tree-tech.com/board/?topic=topic4&msg=502 you said

"3) 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..."

I think Wayne is simply responding that you can. It's a factual technical observation.

The key issue as you point out is "what level of accuracy do we need?" What technology we use follows. If precision is not a big deal we use the tools that are either cost effective or that we're most comfortable with. If accuracy is a bigger deal than cost, we spend what we have to spend to get it.

And there's the legal competence issue. We may think we're good, may even be good, but there may be credibility or liability issues if we are not legally competent. I found it very interesting in the case that brought all this up that the client's consulting P.E. wouldn't touch it and handed it off to a licensed surveyor. I would hope his trig is better than mine, and he wouldn't touch it.

We certainly need to stand up to the suggestion that technology must be used simply because it's there and failure to do so is sub-standard. It's results that get measured against a standard... that's what we need to understand and not overstate or understate confidence in results irrespective of technology.

As an aside, Wayne was talikng about transits and total stations, not GPS. GPS tells us where we are in relation to the rest of the world. Transits tell us where one point is in relation to another, we might not have a clue where we are. Even with descrambled sattelite signals sub-meter GPS is good accuracy. We're talking about sub-inch accuracy here and I don't think GPS fits into the discussion.

Now, was that a fruit-fly's nose hair or leg hair? They're different you know.

Reply to post by Russ Carlson, on May 11, 2000 at 10:23:37:

Russ,

To hire out a surveyor to do the readings is indeed expensive and hard to justify. However, surveying equipment can be rented for a small fee (40-60.00 per day to 400.00 per month) so the cost drops if you were to go that way. The techniques required are the absolute basics in surveying and could be gotten from any surveying text or from "Simplified Site Engineering for Architects and Builders".

Granted, the accuracy may be beyond the need, or is it. I would be more comfortable watching an attorney squirm over coordinate geometry then be the one squirming over what might be construed as an overly simplistic model or a level of "fudging" that I couldn't quantify. What bothers me about the plumb bob method is the issues of wind and the limitations of measuring with a tape with limited segmentation and without horizontal integrety, and then basing the remainder of the calculations on that. All of the measurements could be totally solid, but there is that opening for an opposing attorney to raise substantial doubts by creating a sequence of potentially flawed observations. The law has recognized long ago in property disputes that the principals of coordinate geometry as applied to surveying are standard and acceptable in determining locatin and movement of presumed solid objects, its just safe ground to base our observations on.

Thanks for permission to use the diagrams, this is a great brain exercise and I wish I had a leaning tree, hey wait, I do!! *G*

Wayne