More Tangent Stuff

General discussions of measurement techniques and the results of testing of techniques and equipment.

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#1)  More Tangent Stuff

Postby dbhguru » Wed Feb 03, 2016 11:43 am

NTS,

  The role of the American Forests National Cadre is set to expand, although this is not yet a done deal. However, we are moving toward establishing stronger ties to the state big tree program coordinators. There will not be enough Cadre members to do all the certifying of candidates to the National Register, so state certification will continue to play a big role. This means that certifiers will often be urban and country foresters answering directly to the state coordinator. A few may own lasers, but the majority will continue measuring tree height using tape and clinometer. So, how will the Cadre assist the state coordinators minimize the kinds of tangent-based errors that we so commonly see?

  We have plenty of diagrams showing the source of tangent-based errors and formulas for calculating their magnitudes. We also have two methods for minimizing tangent-based errors: (1) crown-point cross-triangulation, and (2) positioning so that the line of sight to the trunk is at 90 degrees to the vertical plane containing the top and end of the baseline. But neither of these techniques is easy to apply in uneven terrain for trees with large crowns. The methods are easier to talk about from the relative comfort in front of  one's computer. This is the voice of experience speaking. Will Blozan and I measured many, many trees using cross-triangulation in the days before the infrared laser rangefinder. It is kind of fun to measure height by cross-triangulating, but you need an assistant and room to maneuver.

 What else can we do to help state people who will continue using tape and clinometer? One way is to develop rules for minimizing the impact of instrument error. An oft repeated rule for clinometer measurements is to get far enough back that the angle from eye to top does not exceed 45 degrees. How good is this advice? I set out to investigate and came up with some surprising results. Here is a summary.

1. If there is angle error, but no distance error, then height error due to the angle error is minimized at exactly 45 degrees - no more, no less. But remember, there can't be any error in the distance measurement for this to be correct.

2. If there is distance error, but no angle error, then height error due to distance error steadily decreases with greater distance, and consequently, diminishing angle.

3. If there is both a distance error and an angle error and they are both over or under (in the same direction), then their combined impact on height error is minimized somewhere between 30 and 45 degrees. As imprecise as this rule is, it is better than simply applying the 45-degree prescription.

4. If there is both a distance error and an angle error and they are in opposite directions, it's Katie bar the door. The combined impact on height error is all over the board. All bets are off.

 To help people analyze specific measuring scenarios, the attached Excel spreadsheet is attached. The green cells are for data entry. After entering a tree height and angle and distance errors, you can see the sweet spot, i.e. angle and corresponding distance for a tree of the specified height where the height error is minimized.

 As a spinoff of this kind of analysis, we might investigate offsetting errors. For example, if we specify a height, distance to the tree, and distance error, what angle error would offset the distance error. Conversely, we could specify height, distance, and angle error to get the offsetting distance error. This kind of analysis admittedly has limited value. But where a measurer has unknowingly made offsetting errors and argues that his/her technique is flawless, we need to be able to explain the intricacies of the interactions.

 As a final point, I realize that this discussion and the spreadsheet go far beyond what will hold the attention of casual tree measurers. They not need concern themselves with this discussion or look at the spreadsheet, but for state-level tree certifiers, there is no justification for tolerating the continuation of incompetence. Measurers who consistently mis-measure nominated trees by significant amounts and refuses to upgrade their skills is incompetent. These people need to be weeded out even if that leaves certain, otherwise, deserving trees from being certified. The credibility of state big tree programs is at stake, and sense the state programs will continue to feed the national one for at least several years to come, this is a problem that has to be solved.

Bob
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#2)  Re: More Tangent Stuff

Postby Don » Wed Feb 03, 2016 11:07 pm

Cadre-
These should be helpful to have down pat, when called upon to explain why the Tangent Method when employed by state coordinators in verifying contenders is inadequate. It's likely to happen, and we need to be able to easily dispel the myth, and be ready to advocate the Sine Method, and the joys of our workshops and webinars, and for those interested, the opportunity to join the Cadre.
The only thing off the top of my head to add to Bob's post is hopefully not often needed.  I suspect there may be some still measuring the distance aspect of tree height with rag/fiber tape.  In anything but flat table land, care to pull level distances should be taken by them. For steep terrain, correcting slope distance is essential. Would be a good opportunity to demonstrate how quick, easy, and accurate the laser rangefinder/hypsometer is.  
-Don
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#3)  Re: More Tangent Stuff

Postby Matt Markworth » Thu Feb 04, 2016 9:54 pm

Bob, Don, All,

Along with having a better understanding of tangent-based error sources, there is probably also a need to promote a better understanding of how to handle uneven terrain as Don mentions. Some clinometer/tape users may have never considered or utilized the cosine table on the back of some clinometers.

I have sketched out a scenario and provided a solution as an example. Of course, there are lots of reasons why sine-based would be so much simpler and more accurate in this example.

               
                       
slope correction.jpg
                                       
               


Steps
- Estimate where the top of tree is
- Estimate the spot on the ground vertically below the top of the tree
- Place a tripod at this spot with the tripod head at eye level
- Stretch a tape along the ground starting from the point on the ground under the top of the tree to the point where angle measurements will be taken. In this case it is 39'.
- Take an angle measurement to the top. In this case it is 58.5°.
- Take an angle measurement to the tripod head. In this case it is 19.5°.
- Take a zero degrees reading starting at the tripod head and find the point on the tree that is at zero degrees. Measure from this point to midslope. In this case it is 3'.
- Do the calculations:
      - Find the baseline: Cosine of 19.5° x 39' = 36.8'
      - Find the height of the big triangle: Tangent of 58.5° x 36.8' = 60'
      - Find the height of the small triangle: Tangent of 19.5° x 36.8' = 13'
      - Final tree height calculation: 60' - 13' + 3' = 50'

Matt
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#4)  Re: More Tangent Stuff

Postby Lucas » Thu Feb 04, 2016 10:17 pm

We travel the Milky way together, trees and men. - John Muir
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#5)  Re: More Tangent Stuff

Postby Don » Thu Feb 04, 2016 11:17 pm

Lucas-
Thanks for the graphic/URL, even though at first, they seemed 'tangential' to the topic at hand...; ~ }
Don Bertolette - President/Moderator, WNTS BBS
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#6)  Re: More Tangent Stuff

Postby Matt Markworth » Fri Feb 05, 2016 6:50 pm

All,

Just one additional note on the above scenario. If a tape was stretched along the ground to the base of the tree and used as a distance for the baseline the tree would be measured as 80', instead of the correct height of 50': tangent of 58.5° x 49' = 80'.

I think that if a novice clinometer/tape measurer can get comfortable imagining big right triangles when taking measurements, that might be a good starting point to understanding the sources of tangent-based errors.

Matt
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#7)  Re: More Tangent Stuff

Postby Don » Fri Feb 05, 2016 7:11 pm

Matt-
How about a 30-60-90 and 45-45-90 drafting triangles, with spirit levels bonded to the vertical and horizontal legs?
-Don
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#8)  Re: More Tangent Stuff

Postby Matt Markworth » Fri Feb 05, 2016 7:55 pm

Don,

Good idea! Maybe also a right triangle with expandable Opposite and Adjacent sides, with something like twine serving as the adjustable Hypotenuse. Some dead branches mounted on boards could serve as trees to measure with the triangle. A centimeter stick could be used for distance and a manual clinometer for angle, as measured using the window on the side of the clinometer.

Matt
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#9)  Re: More Tangent Stuff

Postby dbhguru » Sat Feb 06, 2016 5:19 pm

Matt,

  Yes, visualizing the "big" right triangles inherent in these problems is fundamental to understanding their solutions. A companion challenge is to get tangent measurers to understand that the correct baseline for a top is the level line from the eye in the direction of the top to the point of intersection with the vertical line from the top. In the sense the baseline usually ends in empty space, as opposed to touching the trunk. The latter has always been a convenience that fortunately works well enough for younger hardwoods and young to mature conifers. But old trees of both types have always caused problems, although unknown to many measurers.

  Your drawing of a tree on sloping ground where the measurer's eye is below the base and there also is a horizontal separation between top and base offers an additional problem type for us to illustrate. Good contribution.

Bob
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#10)  Re: More Tangent Stuff

Postby Matt Markworth » Fri Jul 22, 2016 10:11 pm

Bob,

Thanks. I'll have another tangent example coming soon that will be in the form of a video. Along the same lines as the brainstorming that Don and I were doing in previous posts, I'll be utilizing a tree model sitting on top of and in front of a white board, along with a tape measure, a protractor and other equipment as needed. The opportunities for tree measurement illustration with this setup will be nearly endless.

Matt

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