Let's go a modeling, modeling   Robert Leverett   Dec 19, 2005 07:38 PST  Will, Jess, Don, Ed, John, et al:       On Saturday and Sunday, I ran more tests of the RD 1000 using information on design features that I received from consultant with LTI, Bill Carr, in Montana through Don Bragg. The information passed on by Bill is most appreciated and is helpful. Bill Carr has agreed to look at other test data that I may run on the RD 1000 and has suggested the possibility of a more powerful magnifier. This is pretty exciting stuff. I'd much rather see design improvements made to the RD 1000 rather than LTI start from square one.       Over the weekend, I ran a total of 70 indoor trials shooting flat targets of known widths and adjusting the distances to those targets according to the assumptions built into the design of the RD 1000. One reason that I used the flat targets is that I could control the reflectivity of the edges of the targets. I didn’t want to be introducing errors based on poor visibility of target edges. Another reason is that I didn't have graduated cylinders to act as tree trunks. But with the distance adjustment that I made, it didn't matter. My flat targets were fine.      The RD 1000 has been designed under the assumption that the object being measured has a cylindrical form and that distances given the RD 1000, are the level distances to the middle of the front of the trunks of the trees, not to their actual centers. So my distances to the flat targets had to be reduced by half the widths of the targets, the widths being treated as radii of imaginary cylinders. Both the width of the targets and distances to the targets were measured with a tape measure. I started with a variety of distances, but the last 45 of the 70 measurements were from the exact same location and distance to their targets, which varied in widths from 3 inches to 33 inches. The targets were set up at increments of one inch. Measurements of the smallest and largest targets were repeated, thus the 45 total measurements, i.e. there were 4 repeat measurements. I mixed up target size going from larger to smaller and back to larger so that I was always adjusting the scale . I didn’t want to develop an expectation of what the next readying would be by going in sequence of one-inch increments.      For the last 45 trials, the average difference between RD 1000 measurements and actual taped widths was 0.48 inches with a standard deviation of 0.19 and a range 0f 0.8 inches. All the targets were established at a base distance of 25.25 feet. The edges of most of the targets were highly visible. That was not always the case with the other 25 trials.     The first conclusion I felt safe in drawning from the 45 trials was unexpected. The magnitude of the measurement error is fairly constant over the range of target sizes, i.e. the differences between actual width and measured width is not strongly related to target width - such as smaller absolute errors for smaller sizes. There is a simple reason for this. At the distance of 25.25 feet (less half the width of the target) from the target, a change of 1 click in expanding or contracting the scale is worth 0.3 inches. The 0.3 is independent of the width of the target. The relatively stable absolute error that one can make obviously means that you make larger percentage errors with small targets, but the absolute magnitude remains fairly predictable.     The second conclusion I drew is at distances in the 25-foot range, the RD 1000 understates the actual diameter. Every reading over the 45 trials was exactly equal to (hooray) or under the actual diameter. This led me to wonder if the instrument tries to compensate for bark thickness. Understating the actual diameter occurred in 42 of the 45 trials. The other three trials were right on the money. The largest absolute error was 0.8 inches and that occurred 3 times within the 45 trials.      On a number of occasions I have mentioned that there is a limit to which you can expand or contract the RD 1000's scale. I did some tests on that. The following table tells the story. It is pretty self-explanatory. If you are at 45 feet from your target and its diameter is less than 4.2 inches, you cannot measure it by masking the object with the scale because you can't further shrink the scale. Of course you can do some estimating. If you are 35 feet away from the trunk of a very large tree, then 49.2 inches is the max the scale can be expanded. Obviously, one must shift positions to get measurements of very large and very small trees or of points on the same tree that reflect diameters outside the range allowed for the distance. There are limits to that, however, and at some point, one must estimate. RD 1000 Design Features Diameter Range Distance-ft Min Diam-in Max Diam-in          20         1.9 28          25         2.4 35.1          30         2.8 42.1          35         3.3 49.2          40         3.8 56.1          45         4.2 63.1          50         4.7 70.2          60         5.7 84.1          70         6.6 98.1          80         7.6 112          90         8.5 126         100         9.4 140         110        10.4 154         120        11.3 168         130        12.3 182         140        13.2 196         150        14.2 210          Over the full 70 trials, the average absolute value of the difference was 0.45 inches. The maximum distance from target was 36.58 feet. So these were all close targets. From previous tests, the best results have been obtained with the RD 1000 in the distance range of from 60 to 90 feet. The average error in that range is probably on the order of 0.2 to 0.3 inches where the target is highly visible. At distances of over 90 feet, the error becomes larger. Just how much larger, remains to be determined.      I am feeling fairly confident these days that I can find ways to compensate for measurement errors within a range of diameters and distances that will allow me to do a lot of quick modeling. I’m sure the RD 1000 was designed with a diameter range of trees in mind that don’t include really large trees or very irregular shapes. That is to be expected. Nonetheless, it is proving to be a highly useful instrument for me and despite its limitations, I wouldn’t want to be without it.      On Sunday, I re-measured several of Monica’s trees to check year-end growth with perfect visibility. I chose Monica’s tuliptree, fully visible from her living room window. I shot the tree from 3 locations, two from the outside of her house and at a lower vantage point and one from her living room. I shot multiple times from the 3 locations. The crown is gently curved and the highest point cannot be seen by the laser from the outside location. The difference is 0.8 feet. The outside locations yielded an average of 121.4 feet and the inside location averaged 122.2. illustrates how easy it is to miss the highest point. I also measured the DBH using the RD 1000 from a vantage point of 96 feet level distance from the trunk. I have an orange ribbon around the tree at DBH height and have measured the DBH with a tape. It is 24.8 inches. My first shot with the RD 1000 yielded a 22.5-inch DBH. The scale seemed to perfectly match the trunk. Knowing the result was low, I re-shot the trunk and justified another click to myself that yielded 23.6 inches. That is still 1.2 inches shy of the taped value.      A future field test of the RD 1000 will be to flag about a dozen of Monica’s trees at DBH height and then shoot them from various locations, comparing the results to the taped DBHs. At this point, I think that I can safely say that for trees in the 3-foot diameter range and under, the DBH measurements I have courtesy of the RD 1000 are not overstated. This means that volumes from my modest-sized white pine modelings are not overstated where trunk visibility was good.     In one final exercise, I modeled a straight sugar maple at the boundary of Monica’s property. It is 93.3 feet tall and 7.4 ft CBH. It’s young and still growing upward with a distinctly pointed top. The tree’s limbs are relatively small. The cubes in the trunk came out to 167. It looks like the total limb volume will add another 25% to 30% for this tree. The white pines in my modeling database of comparable DBH to the sugar maple have trunk volumes ranging from 159 to 200 cubes. Bob Robert T. Leverett Cofounder, Eastern Native Tree Society RE: Let's go a modeling, modeling   Will Blozan   Dec 19, 2005 11:05 PST  Bob, While testing the reticle method Jess and I found a billboard post 36.1 inches in diameter that worked great for testing the device over huge yardage ranges. Perhaps such a target would be better than a not-so-round tree trunk for ascertaining absolute values. Will 70 through 75   Robert Leverett   Dec 20, 2005 05:09 PST  Will, Jess, Don, John, Lee, Ed, et al:     Last night I added 5 more tests of the RD 1000 on target widths of 3.60", 6.36", and 25.08". The targets were all bright orange. So visibility of the edges was not a problem. The average measurement error was 0.4". I used the magnifier on two of the 5 trials. It improved visibility for my aging eyes, but the boost in the visual aspect did not translate into added accuracy in the results. The average difference between actual and measured was 0.38 inches. As with most previous trials, the RD 1000 measurements were under the actual target widths in all 5 trials. I am finally satisfied that at close distances for the smallest to largest targets that can be measured at close range, diameters are understated by 0.4 to 0.5 inches.      My next series of measurements will be at 50 feet. Then I'll move up to 75, 100, and finally 125. I am hopeful that I can establish a correction factor for all these distance ranges. Working with the consultant from Montana, I am optimistic that we can make the RD 1000 a truly efficient tool in trunk and limb volume modeling.      In yesterday's e-mail, I mentioned that I had remeasured Monica's tuliptree and got a season's end figure of 122.2 feet. I was so confident of this figure that I decided to use it to verify the Monica white pine, which I had at 132.0 feet. The problem is that from all my vantage points, seeing the absolute top is very difficult. I needed to get back farther. So I first established that the base of the pine is 0.5 feet lower than the base of the tuliptree. Then I went to the far side of Monica's house where I cannot see the lower portions of the two trees, but the crowns show up very well. I can see the tip of the white pine clearly. I established that from my vantage point that the tip of the white pine is 10.3 feet higher than the tuliptree. Based on 5 consecutive measurements, this is a conservative figure. So 10.3 + 0.5 = 10.8 feet that must be added to the tuliptree's height to get the pine. (122.2 + 10.8 = 133.0 ft). I'm finally satisfied that I've done justice to Monica's pine.      For our new members with intentions of mastering dendromorphometry, the patterns of measurements that I’ve recorded for Monica’s tuliptree and white pine illustrate the absolute necessity of being far enough back and high enough above the base to see clearly the candidate crown points. Even those of us who are measuring fanatics periodically have to re-learn that lesson - at least I do.     Courtesy of the additional foot of the pine, Monica's woods have a Rucker index of 109.7. Now to hunt for trees that will push the index higher. I believe it has about another foot to go before we can say we have the measure of the trees in the vicinity of Monica’s house. Bob Robert T. Leverett Cofounder, Eastern Native Tree Society   Home