Posted: Mon Feb 12, 2018 12:32 pm
by dbhguru

(This is an edited version of an earlier post.)

Part of my monthly routine is to perform tests on the calibration of my equipment and to put our tree measuring processes through their paces. I frequently tout the accuracy of the reticle-based monocular. So while it was raining outside, I set up a simple test in my basement. The target was a yardstick with each foot marked off. Measuring the middle foot was the objective. Distances to the ends of the 1-foot section were 21.120 and 21.172 feet as measured with a Bosch GLM80. The reticle reading was 48. This yielded a calculated target width of 1.0160 feet. The 0.016 feet equals 0.192 inches (approximately a fifth of an inch). I'll gladly take these results.

A second test measured an 18-inch ruler positioned slightly over 23 feet away. The error in the second case was 0.0131 feet or 0.1570 inches. Really, folks, we can expect to get any better than this? But the reasons we can achieve this remarkable level of accuracy include: (1) exact distances, and (2) the high performance of the reticle. This said, these tests are all conducted under highly controlled conditions. For example, visibility is never a problem.

For more distant and less distinct targets, we can expect some loss in accuracy, but so far the level is holding to between 0.25 and 0.5 inches. I would never have expected to achieve such results with any of our instruments when we started measuring trees using laser rangefinders and clinometers back in 1996. As John Wayne might have said staring at any one of us,"You've come along way, Pilgrim."

Along with better instruments, we have better methods. We now take into consideration factors that we hoped would be averaged out. The formula that does the work in the above tests is


It is what I named the TrapezoidDiagonal-2 formula. The width to be measured is treated as the diagonal of an isoceles trapezoid. Distances to the ends of the diagonal are L1 and L2. M1 is the reticle reading, which sees the apparent width line as though it were 90-degrees to the line of sight. The formula looks intimidating and probably causes many to shy away. So we usually supply an Excel calculator worksheet that calls for the inputs to be entered into green cells and returns the result in a beige cell(s). The user does not have to evaluate the underlying formula or formulas with a calculator. It's automatic.

My friend Don Bertolette and I collaborate on the design of these Excel calculators. Don's preference is to hide the formulas and their development processes from users as much as possible, and I'm forced to admit that he is right if our intention is gain wide acceptance for these Excel-automated methods. However, we'd like your input on what you'd like to see in the worksheets. For instance, we could present the calculator part up front without any formulas shown - just a diagram and input and answer cells. The calculator could then be followed by the developmental material for those who want to see how a method works. The question to answer is whether or not you think the latter is even necessary for the popular version. I still think it is up to some point in the initial stages. Here are my reasons why.

In 1996 when Will Blozan and I began using laser rangefinders and clinometers to measure tree height, I put my mathematician hat on and devised formulas to make use of the fact that we could shoot distances directly to a target (top or base of tree). The Sine Method was born in name. Unknown to me, Bob Van Pelt and Michael Taylor were also using the method, but probably without giving much thought to promoting it publicly. I'm sure that the method simply made sense to them, so they used it. It wasn't rocket science. Apparently, though, I had the biggest mouth of the trio and began promoting it in NNTS, giving names to it and its rival the Tangent Method. The rest is history.

But in those days, the Sine Method had not caught on beyond a tiny group. The standard for measuring tree height was still tape and clinometer and since it was taught in the forestry schools and used by the forestry profession, acceptance of the new method was predictably going to be a slow process. If people were going to understand where a method worked and where it failed, or at least was problematic, diagrams were needed and mathematical arguments rendered. The forum used was NTS, or ENTS in those days. More methods were developed and an analytical framework for evaluating the sensitivity of each new method to changes in input variables.

While from a computational standpoint, the Sine Method was no more involved than the Tangent Method, it became clear to me that getting people to put aside their institutional and professional experience and think along new lines was no small task. If I proposed a new method, shouldn't I lay the mathematical arguments on the table for all to examine and accept or reject? If I made errors in the logic, others would have the opportunity to find and point them out. Actually, this strategy worked when I came to know Michael Taylor. We thought through each others mathematical arguments and diagrams to the common benefit.

So now, we've moved into the bold new world of LIDAR, photo measuring, reticles, and super accurate distance and angle measurers. With these instruments, we can utilize their functionality to measure dimensions that previously we would not have attempted. For example, the missing line routine of LTI's TruPulse 360 allows us to measure the linear distance between two points in space. Practically, that converts to measuring limb length. Our friend Larry Tucei in Mississippi is making great use of the feature. And so it goes.

Over the past year, I've found myself increasingly using the term sport-based tree measuring to distinguish what we do from what is done in forestry and other professions that measure trees. We really need to make the distinction clearly and to explain to others that what works in one arena is not necessarily suited to another. This has not always been obvious. In fact, it still isn't.

In watching the Olympics, times measured in thousands of a second are relevant. Nobody challenges the need for such accuracy. However, in sport-based tree-measuring we still see methods used that produce results that can be in error by tens of feet. Is this acceptable in in NTS or the National Cadre? Of course not. It is up to us to set the standards for sport-based tree measuring and resist efforts to accept sloppy results that make the sport something not to be taken seriously.