Difference between tangent and sine-based calculations Error Spreadsheet Robert Leverett Nov 26, 2004 10:27 PST
 ENTS:       Our discussions on the difference between sin and tangent-based calculations and Will Blozan's recent suggestion to compare what the tangent-based height calculation would have been in our measurements by treating the point shot with the laser to have been vertically over the base led me to run comparative calculations on a sample of 1,330 trees measured with laser and clinometer. From an original larger selection, I eliminated those measurements in which the measurer would have been closer to the trunk than a chain's distance (66 ft) or at an angle of to the crown of 65 degrees or more. I considered these two situations to be improbable measurements from the standpoint of an experienced user of the tangent (% slope) method. The results are as follows: Differences between sin-based and tangent-based calculations for tree height. Covers above eye calculations. Differences are in feet. Diff       0-0.99  1-1.99  2-4.99  5-9.99  10-14.99  15-24.99  25-65.99  TOT Count     123      131      333      368       167        138           70       1330 Pct Tot    9.2%   9.8%   25.0%  27.7%    12.6%    10.4%      5.3% Cum Pct  9.2% 19.1%   44.1%   71.8%   84.4%    94.7%    100.0% Max diff:      65.32 Ave diff:        8.30      The average of the absolute value of the differences is 8.3 feet. The max difference is a whopping 65.3 feet. These statistics plus the ABOVE table of percentages tell most of the story. It is certainly possible to reduce the error of the tangent-based calculations by cross-triangulating the crown, but even that method has its limitation, visibility of the same crown point from sufficiently separated spots being the primary. Will Blozan and I did the crown cross-triangulating for several years and described the method fully in: "Stalking the Forest Monarchs - A Guide to Measuring Champion Trees".       The next series of charts will look more closely at subsets of these measurements. Please stay tuned. The above is enough for now.       I'll send the Excel spreadsheet holding the 1330 measurements to Ed in a couple of days. Bob
 RE: Difference between... MY REPLY Will Blozan Nov 27, 2004 14:52 PST
 Bob, The numbers came out kind of distorted in my email. However, the errors are very significant, especially given that in our ENTS measurements the true top has already been identified- a task that can take hours with cross-triangulation. Impressive and compelling! I think we should present a synopsis of our findings to the website and deliver it to certain parties for their "review". We have a strong case, one that should be spread to the public. I am ready for ENTS to make more of an impact in the tree related "playing fields". I also think a scientific push can be made as well as in ecological mensuration (nest heights, canopy layers, etc.) and in more utilitarian fields such as forestry. Also, how accurate are waterfall heights in the East? I have heard some seemingly outrageous heights claimed for waterfalls, and have often wondered about the accuracy. I suspect I do not want to know... Will
 RE: Difference between tangent and sine-based WILL IS ALMOST READY! Will Blozan Nov 27, 2004 19:36 PST
 Bob, John, ENTS, I have 10 trees of 10 species set up in EXCEL for calculations. I have chosen 5 gymnosperms (e. hemlock, C. hemlock, red spruce, loblolly pine, and white pine) and 5 angiosperms (tuliptree, white ash, red oak, sycamore, and black birch). To make my comparisons similar or identical to yours I need to know if you have corrected for slope in the conventional height calculations. I have set it up both ways, slope corrected and not, but I have some pretty serious angles on some of the trees. I could select less steep angles, but the steep tree measures are good to know as well, and are not undoable with cross triangulation. What would be good to know also is to "cross-triangulate" with the laser from two 90 degree opposing angles (same top) to map the top relative to the base, and then calculate the range of error over 360 degrees around the tree. We would need to pick a "pointy topped" tree for this with a prominent lean. I have also looked at the average lean, both + and - from the observer, and even with 10 samples the average is usually less than 2 feet. I find this very interesting, and the greatest lean is actually in the e. hemlocks (~5 feet). Some of my red oaks have a 30' "lean"! Also, I tend to shoot the base at the midslope on the side of the tree, not the closest portion. This way, in my calculations, I do not need to correct for the radius of the trunk. More to come!