New measurement method Robert Leverett Jan 11, 2007 06:51 PST
 ENTS,      As I mentioned in a prior e-mail, at the April 2007 ENTS rendezvous at Cook Forest, I will be giving an update presentation on our ENTS measurement methods to include new measurement techniques. As an example of what will be included, what follows is a new formula for measuring tree height above eye level using nothing but a clinometer and tape measure. The advantage of the method is that it avoids the pitfall of the top being measured not being directly over the base. However, there is an assumption that absolutely must be met. The measurer is on a patch of level ground that allows forward and/or backward movement. The method works as follows.     From a vantage point, either the angle to the crown point or the slope percent is determined (left scale angle, right scale slope percent on the Suunto clinometer with those scales). The measurer then moves directly forward or backward a known distance to a second point where the crown point is still visible. The crown point, measurer's original position, and measurer's new position all fall in the same line. The measurer's eye level remains unchanged. The measurer takes the angle or slope percentage of the crown point from the new position. The measurer takes the distance between the two points of measurement. This is a level distance.     So we end up with three measurements: two angles or two slope percentages from the eye to the crown point and the linear distance between the two points of measurement. If the assumptions are fulfilled, the following formula calculates the height of the crown point above eye level. Let:     D = level distance between the two measurement points          A = angle of eye to crown point from nearer location        B = angle of eye to crown point from more distant location     H = height of crown point above eye level Then:     H   = [(D)tan(A)tan(B)] / [tan(A) - tan(B)]     The algebraic derivation of the above formula along with others will be handed out at the Cook Forest rendezvous.      Note that the reading of the right scale of the Suunto clinometer with a percent scale is just the tangent of the angle expressed as a percent. The measurer need only move the decimal place two positions to the left to get the tangent. Consequently, no trigonometry tables need to be accessed. The calculations can be done by the simplest calculators.     The dangers of carelessly applying this technique are the same as the simple baseline to trunk and slope angle to crown. If the measurer is indeed on level ground then adding height to eye level gives the full height of the crown point above the tree's base. However, if that is not the case, then the procedure for shooting the crown can be applied to shooting the base. I suspect that many would-be measurers will find the procedure to already be too calculation intensive, but it avoids the pitfall of assuming the crown point is directly over the base - the most common source of tree height calculation errors.     Note that no assumption has to be made as to how distant the trunk is. There is no baseline from measurer to trunk. So this method can be applied where getting to the base of the trunk is difficult such as when there is an intervening stream. Of course, the base of the trunk has to be visible.      A caution is immediately in order for the users of the percent slope scale of a clinometer. It cannot be read to a sufficient number of decimal places to replace actually calculating the tangent of the angle. However, the process, as described above, still provides a better height approximation than ignoring the horizontal offset of the crown-point from the tree's base. As is frequently pointed out, measurers armed with only clinometer and tape measurer usually apply the vertical telephone pole in the level parking lot model that is the basis for the height-measuring instructions accompanying clinometers and hypsometers.      The fundamental lesson to be learned in the application of all these measurement techniques is that the measurer MUST understand the assumptions made behind the model and verify that those assumptions are fulfilled. Ignorance is not bliss. Our ENTS workshops will increasingly focus on different models, the assumptions behind the models, and the magnitude of the errors introduced when assumptions are not fulfilled.     This new method in no way replaces the much preferred sine top-sine bottom method, but should be useful as an interim method for folks who possess a clinometer and tape measure and who are saving their pennies for a laser rangefinder. Bob Robert T. Leverett Cofounder, Eastern Native Tree Society
 Re: New measurement method Jess Riddle Jan 11, 2007 19:57 PST
 Bob, Seeing a new strategy for measuring trees proposed is exciting. When I saw how you had the triangles set up, I had to try and derive the formula myself. What I came up with produces the same results as the formula you provided, but is much messier to use. In checking the formulas, it appears to me that the distances involved with applying this technique are realistic for practical application. Shifting 15 or 20' will provide a reasonably large angle difference to work with for a 100' tall tree. The one part of your explanation that I didn't follow regarded calculating the tangents instead of reading them directly off the clinometer. How does using a calculator to find the tangents increase the resolution of the clinometer? If you calculate the tangents from the angle in degrees read off the clinometer, aren't you just 'rounding' to some irrational number that you obtained after rounding the degrees? This technique's ability to preclude projecting heights to an illusionary top (produced by the high point not being over the base), and doing so without complicated calculations, give it great potentially. Certainly, the requirement for level ground will restrict the use, but many state big tree programs could still improve a significant proportion of their data if they used this method instead of the standard tangent method where applicable. Jess
 Back to Jess Robert Leverett Jan 15, 2007 05:46 PST
 Jess,    You are absolutely correct. Good thinking. I thought about the rounding error situation after I submitted the e-mail. Having all those extra digits from a tangent table based on an approximate clinometer reading is of no real value to accuracy. Two heads are definitely better than one, especially if one of the heads is yours.    I had intuitively settled on 20 feet as the baseline between the two angles, but had not done any calculations to investigate sensitivity. I have a process in the mill for dealing with the situation where the baseline between the two measurement points is not level. The math is messy and I doubt that anyone would want to adopt it, but I'll submit it nonetheless. Bob
 Dendromorphometry extended Robert Leverett Jan 19, 2007 05:23 PST
 ENTS,    Not all ENTS-developed formulas are destined for high use in the field, but nonetheless form part of our "fleshing out" of the new discipline of dendromorphometry.    I recently gave a formula for calculating the height of a crown-point above eye level that requires only a clinometer and tape measure. The assumptions that must be fulfilled for the formula to be used are: two clinomter angle measurements are made of the same crown-point from locations that are on the same level. The crown-point, eye position of the first measurement point, and eye position of the second measurement point all lie in the same vertical plane. If:    a1 = clinometer angle to crown-point from nearer measurement point    a2 = clinometer angle to crown-point from more distant measurement point    D = level distance between two measurement points (eye position to eye position)    H = height of crown-point above eye level then:    H = [(D)tan(a1)tan(a2)]/[tan(a1) - tan(a2)]    Since, the right scale of a clinometer with a degrees and percent slope scale is just the tangent of the angle x 100, one can use the above formula without trigonometry tables. That makes it attractive to people who want to avoid trigonometry. Jess Riddle independently tested the formula and stated that a baseline of 15 or 20 feet should be sufficient to get sufficient angle differentiation to allow the formula to do its work.    The toughest condition to be met is the requirement that both eye positions be at the same level. In mountainous terrain, this condition often cannot be met will keeping the two eye positions and the crown-point all in the same vertical plane. One might be able to move laterally at the same level, but that would violate a key requirement that the three points lie in the same vertical plane.    Suppose that the second observation point is not at the same level as the first. Can we still solve the problem? Suppose the second, more distant eye position is at a higher elevation. In this case more triangles that must be constructed to model the situation and the calculations become more involved, as can be seen below. If:    a1 = clinometer angle to crown-point from nearer measurement point    a2 = clinometer angle from eye-level at second measurement point down to eye level at first measurement point (note that a2 here is not the same as a2 in the first formula)    a3 = clinometer angle to crown-point from more distant measurement point (at the hiher elevation)    d5 = straight-line distance from the eye at first measuremet point to second the eye at the second measurement point. The line d5 is sloped.           Remember that the crown-point, first eye position, and second eye position all lie in the same vertical plane. If the assumptions are met, then the height of the crown-point above the first eye position is:    h = [tan(a1){d5cos(a2)tan(a3) + d5sin(a2)}] / [tan(a1) - tan(a3)]    This toad strangler of a formula is not likely to take the measuring world by storm, but it can be used by those who want as many tools in their toolkit as they can get.    Both formulas with accompanying diagrams will be thoroughly explained at the April ENTS event at Cook Forest. Bob Robert T. Leverett Cofounder, Eastern Native Tree Society
 Refinements on tangent-based calculations Robert Leverett Jan 29, 2007 05:26 PST
 ENTS,    What follows below is a more complete treatment than was previously given for measuring the height of a crown-point above eye level using a clinometer and a baseline between two measurement points that are aligned with the crown-point. The procedure and formulas that are presented below are not meant as substitutes for sine-based measuring, but the tangent-based procedure can fill the accuracy gap that ordinarily accompanies the typical use of a clinometer.     First a quick review. If the measurer is able to see top of the tree and the top is directly over the base, then a baseline from eye to trunk and the slope % to the crown top is all one needs to compute height above eye level. A similar procedure can be used for height below eye level. The slope percent converted to the equivalent decimal value times the level baseline distance from eye to trunk gives the height of the tree above eye level. This is the standard clinometer-baseline procedure for instruments that have a percent slope scale. The two scales for a clinometer that make the most sense are degrees and percent slope. Of the two, degrees is the most important.     But what if the crown-point is not directly over the base? What can be done to get an accurate height measurement if one does not know where a plumb line from the crown-point to the ground would fall? Some timber specialists develop a good eye and can make educated guesses, but that is risky, especially for broad-crowned hardwoods. There is the crown-point cross-triangulation method as described in our guidelines, but that process is difficult to implement without two long tapes, an assistant, and continuous visibility of the crown-point being measured as one moves from one location to another. However, there is another procedure that one can apply that uses just the clinometer and tape.    The measurer positions himself/herself at a spot where the target is visible and shoots the angle to the target (or percent slope). The measurer then moves back to a second vantage point and takes a second reading with the clinometer. The height of the crown spot above the eye position at the first vantage points is calculated by using any of the three formulas below. DEFINTIONS: d5 = straight line distance between positions of the eye at first and second vantage points. This is the baseline. Note that it does not go from measurer to the trunk, which is the traditional baseline. a1 = angle to crown spot an closer vantage point a2 = angle to crown spot at farther vantage point a3 = angle between eye positions at the two vantage points (You may nned a pole to keep track of the locations.) FORMULAS FOR THE THREE SITUATIONS: (1). Baseline between two vantage points is level h = [(d5){tan(a1)tan(a2)}] / [tan(a1) - tan(a2)] (2). Baseline is not level, more distant point at higher elevation h = [(d5)tan(a1){sin(a2)+cos(a2)tan(a3)}] / [tan(a1)-tan(a3)] (3). Baseline is not level, more distant point at lower elevation h = [(d5)tan(a1){sin(a2)-cos(a2)tan(a3)}] / [tan(a3)-tan(a1)]     I used a combination of brackets, braces, and parentheses to make the formulas clearer.     It's apparent that cases (2) and (3) lead to awkward calculations. I doubt many people will want to use these formulas. However, case (1) is more straightforward, and again, please note that the distance from the measurer's position to the tree does not have to be determined. This may come as a surprise. Also note that the crown-point, eye position #1, and eye position #2 all must lie in the same vertical plane. Also, please bear in mind that the tangent of angles a1, a2, and a3 can be determined directly from the right scale of a Suunto clinometer with a degrees and percent slope scale. You simply divide the percent slope read from the right scale by 100 to get the tangent of the angle. Slope, defined as the rise divided by the run IS the tangent of the angle. The challenge in applying this technique is find a place to get a level baseline. This new procedure is especially useful when the measurer cannot get to the trunk of the tree (across water, surrounded by briars, poison ivy, etc.). DISCUSSION ABOUT THE PROCEDURE:     I highly doubt that the above procedure is going to take the measuring world by storm. Those who have a laser rangefinder, clinometer, and scientific calculator can apply the much superior sine top-sine bottom method. Those who don’t need high accuracy, but do need great efficiency in the forest, will likely not employ a technique that is calculation-intensive. Those who nourish delusions about tree form aren’t reachable. However, there is a third group of intrepid souls who want to measure the best way, but are operating on a razor thin budget. They are saving their pennies for the needed equipment, but in the interim, they want to be out in the forest measuring trees. The above procedure could be of help. Bob Robert T. Leverett Cofounder, Eastern Native Tree Society