Post
by **dbhguru** » Wed Jan 23, 2013 12:49 pm

NTS,

The interaction of angle and distance variables with the measuring method (tangent versus sine) can lead to results that are not always intuitive. Some general principles can be given, but then there are "behaviors" that don't seem intuitive, at least to me. I've attached an Excel workbook with two spreadsheets to hopefully shed some light on this area of NTS analysis. The first spreadsheet follows tangent errors based on a 100-foot baseline to both top and base over a fixed range of top to base angle of 60 degrees, i.e. top angle - base angle stays constant at 60 degrees. We impose a fixed angle error of +1 degree, i.e. we're over a degree at the top and at the base. We then follow the impact as we swing from +30 degrees top to -30 degrees base to +85 degrees top and +25 degrees bottom. As we see the height error is close to canceling out where the top angle is +30 degrees and the base angle is -30 degrees. Then the tangent method starts to fall apart.

By contrast, the sine method yield good results at all but the most extreme combinations and even then, it isn't bad. What is NOT obvious is that with the sine method, the largest errors occur at the lowest angles, not the highest ones, which is the case with the tangent method. So the implication is that you want steeper angles for the sine method. This implies that one wants to get closer to the target. Ideally, you are positioned well above the base of the tree, so that the unsigned values of the angles to top and bottom are closer to one another.

For most of the trees that we measure and for the typical range of clinometer errors we can expect, calibration isn't a consideration. However, in actual field conditions, we often must mix the methods, e.g. sine top and tangent bottom. We may be able to see the base of a tree with our eye and thus get a clinometer reading, but not be able to shoot through the clutter with the laser. Since lean won't likely be much of an issue upon the trunk where we can get a laser shot, the preferred combination would be high angle to crown for the sine part of the calculation and low angle to the base for the tangent part of the calculation.

The interaction of angle, distance, and mixed methods along with errors creates a complex stew with unpredictable behaviors. In the second spreadsheet, we're looking at the impact on sine-based calculations of a fixed clinometer error and repositioning to a closer/or more distant vantage point on the same level base line. We're only looking here at shots to the crown. We position ourselves 100 feet horizontal distance from the target and compute the height error associated with a 1-degree clinometer error. Then we move to a more distant spot level with the first and shoot the target and compare the errors we get at both locations. We try another scenario. What we keep fixed in the new trial is the distance between the two measuring points. Notice that the difference between errors remains fixed for that particular difference between measuring locations. I've filled up the spreadsheet with trials that speak for themselves. More discussion of this type of analysis to come. I's put out there as food for thought at this point.

What should be apparent to all is that the very simple rules of the road accompanying most tree measuring guides don't offer a clue as to how all the variables interact.

Bob

Robert T. Leverett

Co-founder, Native Native Tree Society

Co-founder and President

Friends of Mohawk Trail State Forest

Co-founder, National Cadre