I prepared this document over the last month. I tried to forward this final copy to the various people mentioned prior to posting here, but it appears that the email have not gone through to the adressee's inboxes. I think the ISP, Comcast, in its infinite wisdom, has decided through its email filters that this post with an attachment is some sort of a phishing scheme. This is in spite of the fact that I get dozens of junk emails every day that are obvious phishing schemes that make it through the company's email filters. I have tried to email this through the BBS and my cc copy comes back labeled a phishing scheme. I give up. If any of the people mentioned have additional comments or corrections, please post a reply here, and I will revise the document.
Beginnings of Laser Rangefinder Sine Based Tree Height Measurements
By Edward Frank, October 9, 2012
For years the standard method of measuring tree heights in the forestry industry was to first measure the distance to the base of the tree, then measure the inclination to the top of the tree with a clinometer. The height of the tree above eye level was equal to the tangent of the inclination times the distance to the base. This is the tangent method of tree height measurement. Indeed many clinometers were sold with a percentage slope scale, or even a scale that allowed a direct tree height reading using this method when the observer was a specified distance from the base of the tree – generally 66 feet. The method works adequately for measuring the height of marketable timber on these trees, but does not provide a good measurement of the total tree height for champion tree purposes or as data for scientific research and modeling.
Height above eye level = tan(a) x distance to tree trunk
People with an engineering or surveying background will realize that if the point sighted using the clinometer as the top of the tree is not directly over the base of the tree, a right angle triangle is not formed, and the tree height measurements will incorrect. The amount of error in the height will be equal to the amount of offset in the direction of the observer times the tangent of the inclination to the top. Common errors even when the measurements are made perfectly may be in the range of ten to twenty feet or more in the case of many broad crowned trees. In addition if the top of the tree is not correctly identified, the resulting height will also be wrong. For example sighting on a forward reaching branch can result in errors of up to 50 feet or more.
A simple solution to the methodological problems of the tangent method became available with the development of laser rangefinders. The first hand-held total station, which included a laser rangefinder and an electronic clinometer, was the Criterion released in 1992 by Laser Technology, Inc. http://www.lasertech.com/default.aspx
At this time there were a number of big tree hunters that already were measuring tall trees using the improved surveying techniques to replace the inadequate tangent method. There are several approaches to problem of accurately measure tree heights. One approach is to locate the point on the ground directly underneath the topmost point of the tree. Once this point is located, rather than just arbitrarily using the base of the tree trunk, the tangent based methods can be used to obtain true tree heights. If the point on the ground is directly under the top of the tree, then a right triangle is formed. The height of the tree above eye level in this right triangle is the tangent of the inclination to the top times the distance to the point at eye level directly under the top. The position on the ground directly under the top was found through cross-triangulation methods. Alternatively regular surveying techniques could be used to measure tree heights. If a direct line of sight to the top could be found from two different locations, and a direct line of sight could be obtained between the two or more) observation points, the angles between the survey stations, the angles from each to the top of the tree, and the distance between the survey station measured, then the position of the top of the tree in space relative to the survey station can be calculated. A third viable measurement technique is to climb the tree an directly measure the tree’s height using a long tape measure. All of these methods are time consuming and difficult to implement.
When using a laser rangefinder a much easier, quicker, and more straight forward methodology can be used to measure tree heights. It allows the surveyor to directly measure the distance from his position to the top of the tree. The using a clinometer the inclination to the top of the tree can be measured from the same position. The height of the tree above eye level is simply the sine of the inclination times the distance as measured by the laser rangefinder.
Height above eye level = sin (a) x distance to the top
With the use of a rangefinder, the height of the top and base above or below eye level can be measured independently. It no longer made any difference in the accuracy of the measurement if the top of the tree was not directly over the base or trunk of the tree. Nor did the amount of offset make any difference. This eliminates one major source of error present in the tangent method.
The other major source of error when using the tangent method is misidentifying the true top of the tree. Even with practice it is difficult to determine based upon visual clues alone which of several tops is actually the tallest. In addition to directly measuring the distance to the top, a laser rangefinder allows the surveyor scan the top of the tree to correctly identify which sprig is actually the tallest point of the tree visible from that position. In general, among several potential tops at similar angles, the sprig that is farthest away is tallest of the group.
The basic trigonometry of the situation shows the overall superiority of the sine based height measurements over the tangent based measurements. This should be readily apparent to anyone with a mathematically oriented background. Indeed the engineers at Laser Technologies built a Vertical Distance (Vd) routine into the Criterion instrument. Unfortunately they also included a tree height measurement routine based upon the tangent method as a paen to this long ingrained methodology typically used by forestry professionals.
At least three different people began using the sine based methodology to better pursue their tree measurement exploits. These people, Robert Van Pelt http://www.humboldt.edu/redwoods/faculty/vanpelt.php , Michael Taylor http://en.wikipedia.org/wiki/Michael_Taylor_%28forester%29 and http://www.landmarktrees.net/ , and Robert Leverett http://www.nativetreesociety.org/people/ents_executive.htm each began using the method independently in the late 1990’s. The first person to use the sine method, via the vertical distance routine in the Criterion, was Robert Van Pelt in northwestern Unites States.
Will Blozan http://www.appalachianarborists.com/default.html (email 2012-10-01) talks about a conversation he had with Robert Van Pelt around this time:
I met BVP in 1993 when he stopped by a display I was presenting on big trees (in GRSM) at an ESA meeting in Knoxville. He gave me some leads on some trees which he had measured via tape drag triangulation. His display had some early versions of his GOPC drawings and he suggested getting a laser for measuring. This facet of tree documentation was then brought home at Cook Forest with the Longfellow Pine. [Longfellow Pine measurement was taken in 1997]
Steve Sillett http://www.humboldt.edu/redwoods/sillett/ (email 2012-10-01) writes:
I remember in the early 1990s working with Michael Taylor and he was using the tangent method because neither of us had a laser. In the mid-90s we started working with Van Pelt who had Jerry Franklin's Criterion. I think that was the first time any of us started using the sine method, which was obviously superior to the tangent method. All along my preferred method has been direct tape drop, which is the most accurate, though not always practical!
There are more accounts of the Longfellow Pine measurement available to confirm this event:
Longfellow Pine Update, Cook Forest, PA, by Dale Luthringer, April 10, 2008, History of measurements of the Longfellow pine: 11.1 178.1 July 1997 avg height of Impulse laser, surveyor's transit, laser rangefinder/clinometer by VanPelt, Leverett, Blozan, Soban http://www.nativetreesociety.org/fieldtrips/penna_cook_forest/longfellow_pine_update_pa.htm
Michael Taylor another west coast tree hunter in an (email 2012-09-29) also confirms that Robert Van Pelt was the first person he saw using a laser rangefinder to measure tree heights. He can also fairly be considered an inventor of the use of the sine method. He writes (email 2012-09-29):
I was also using an optical range-finder [and Suunto clinometer] which I bought in 1993 (1994?) and was using the sine method with the optical rangefinder then as well. I still have that old thing. It was just accurate enough to be of some use.
I purchased my first reflector-less laser in 1994 (1995?), a Lytespeed-400 for $350. It was one of the first ever sold by Bushnell in California. I was on a waiting list for almost 6 months. I knew right away the benefits of finding the hypotenuse to the top with a reflector-less laser after I saw Bob using his Criterion 400. The price range had finally come into my reach. In 1994 the Criterion 400 was way out of my price range.
I used the sine method immediately with the Lytspeed 400. It was the obvious choice due to lean of tree being already figured out when you take the hypotenuse to the top.
In the eastern United States Robert Leverett was already by this time an obsessed tree measurer. Robert had been measuring tree heights using the standard tangent method as part of his documentation efforts to locate patches of old growth forests in the eastern United States. The story here is more detailed because of his extensive writing in the forums of the Eastern Native Tree Society and its successor the Native Tree Society. In 1992 he met with Jack Sobon, a professional surveyor among other skills, to measure the height of the Jake Swamp white pine and Joe Norton white pine at Mohawk Trail State Forest in MA. Jake Swamp is currently the tallest known tree, as of fall 2012, at just over 170 feet tall. In February 2006 http://www.nativetreesociety.org/native/jake_swamp.htm he wrote:
The Joe Norton and Jake Swamp Pines are both white pines. Back in November of 1992 when Jack Sobon and I first measured the two trees with a transit. Before that, I'd only measured Joe, using crude techniques. Yep, I think that was in 1990. Am I obsessed or what? When Jack and I measured the two, Joe was 155.6 feet tall and Jake was 155.3. Joe has suffered more crown damage over the years.
This experience brought home the problems with the tangent method of tree height measurement and he set out to find ways to get better height measurements. Jumping to 1994, Robert Leverett wrote http://www.nativetreesociety.org/entstrees/early_ents_history.htm in July 2006:
Will Blozan, who worked for the GSMNP at the time, got into tree heights in a big way as a consequence of a joint mission we spawned in 1994. I'm sure Will had measured literally thousands of trees for diameter before that - far more than I had. We really got going as a team on our tree height mission in 1995 first as a consequence engineering the crown cross-triangulation method and later through acquiring the LiteSpeed 400 Laser Rangefinder from Bushnell, courtesy of information we got from BVP (who else?). The LiteSpeed 400, the Suunto Clinometer, the scientific calculator, and the proper application of nothing more than high school-level trigonometry has since revolutionized the measuring of tree heights.
Robert Leverett (email 2012-09-30) write more about the introduction of the laser rangefinder into the process:
I, like Michael, independently saw the application of the sine method with the Litespeed 400, and introduced it to ENTS in 1996. Will and I both bought Bushnell Litespeed 400s as a consequence of that model being recommended to Will by BVP at their first meeting in Tennessee...
The history is admittedly a little convoluted, partly because it is the obvious technique to employ if you can measure hypotenuse and angle. I would imagine countless scientists and engineers would just do it without giving thoughts to names. However, in terms of introducing the method by name to ENTS, i.e. sine method, that's me…and me alone.
I came to understand Bob's methodology in a later conversation when we discussed how we were actually measuring tree height. In the course of the conversation Bob explained that he used the "sine" method as one of the returns of the Impulse laser despite the traditional tangent method, which is programmed into the Impulse as an official tree height method.
I expect that BVP and possible Steve Sillett were the first to actually use the technique with infrared laser measuring equipment. Steve will have to explain when he first entered the picture. But, as it now stands, I would say that the sine method appears to have been arrived at independently by BVP, Sillett?, Michael Taylor, and yours truly. If there are others, they have not revealed their identity to us in conversation or writing.
Now, here is an important point. The sine method is the logical choice for measuring tree height if you have the equipment to measure hypotenuse distance and angle regardless of what name you affix to what you are doing. It is a no-brainer. Basic trigonometry. The forestry profession's fixation on tree trunks and insistence in establishing a common baseline to measure both the top and bottom height components turned a simple problem in basic trigonometry into an ocean of errors, as we have all witnessed.
I hope this sheds light on the issue. I cannot speak for others, so if they have additional information or clarifications, I do hope they'll come forward and speak for themselves. I'll close with a final point. I suppose sine method is as much a political name as an engineering or scientific one coined by me to hammer home the inefficacy of the slope or tangent method in measuring tree height.
Will Blozan (email 2012-10-01) confirms and expands upon this account of the methodology coming to ENTS:
I bought my first laser a few months after Bob L. after numerous phone conversations- who explained to me on the phone what to do (I still have my notes). I toyed around with some Smokies trees but my first major survey with the laser was in CONG, December 1996. Bob L. introduced the SINE method to me.
A description of the method was first published in 1997. Robert Leverett (email 2012-09-30) writes:
In terms of explaining the sine method in a publication, so far as I am aware, that occurred in "Stalking The Forest Monarchs - A Guide to Measuring Champion Trees", published by Will, Jack Sobon, and myself and brought to the 1997 old growth conference in PA in June 1997. However, we had been using the technique since sometime in 1996 - thanks to the Litespeed 400, which again, was recommended to Will by BVP in their initial meeting. Here is a for instance in the chronology. In Dec 26, 1996 Will went to Congaree for the first time to measure those trees using the Litespeed 400.
Robert Leverett wrote in January 2004 http://www.nativetreesociety.org/threads/looking_back.htm more about the publication of this book:
Back in 1995, Will Blozan, Jack Sobon, and I set out to write book. We researched the available material on eastern big tree sites and individual species such as the white pine, tulip tree, American sycamore, baldcypress, etc. We wanted to set the record straight about the giants of yesteryear. We also wanted to describe methods by which an interested person could accurately measure tree dimensions. We were on a holy crusade to clean up the champion tree registers, principally the National Register of Big Trees. The book, published in 1997, was entitled "Stalking the Forest Monarchs - A Guide to Measuring Champion Trees."
Even though it is currently out of print an excerpt from the book can be found online here: Excerpt from Stalking the Forest Monarchs http://www.whitepines.org/Tree%20Measuring%20Guide.pdf
Since these beginnings the use of the sine method of measuring tree heights has spread among many big tree hunters in the western United States, among the measurers of Native Tree Society, and among scattered people around the globe associated with these groups. An interesting example of this methodology spreading can be documented from Australia. After the introduction of laser rangefinders in the mid 1990’s, there were a number of publications from the Australia that detail the use of lasers for tree height measurement. Two examples from Tasmania are: Tasmania’s tallest trees by J.E. Hickey, P. Kostoglou and G.J. Sargison, in Tasforests Vol. 12 December 2000 http://22.214.171.124/assets/0000/0184/tasfor_12_09.pdf and A survey of ultra tall eucalypts in southern Tasmania, A report to Forestry Tasmania By Parry Kostoglou, June, 2000 http://www.forestrytas.com.au/uploads/File/pdf/tall_trees_survey_report.pdf . In both of these investigations they used a laser ‘Impulse Series 2000’ rangefinder manufactured by Laser Technology Inc. It is clear from the descriptions that the tree height function utilizing the tangent method was being used by the investigators based upon their description of usage and the errors generated.
The change to the sine method was documented in a publication from 2002: Victoria’s tallest trees by Brett M. Mifsud in Australian Forestry Vol. 66, No. 3 pp. 197–205, Revised manuscript received 25 November 2002, http://svc043.wic023v.server-web.com/pdf/pdf-members/afj/AFJ%202003%20v66/AFJ%20Sept%202003%2066-3/Mifsud%20final.pdf Brett Mifsud writes:
Measuring tree heights
New techniques for measuring tall trees were used in this study. Initially, a Bushnell ‘500 Yardage Pro’ laser rangefinder was used in conjunction with a Suunto clinometer to estimate tree heights in all regions. The previously-used ‘simple tan’ method of measuring tall trees was discarded in favour of the ‘sine’ method (M. Taylor pers. comm. 2000; A. Goodwin, Forestry Tasmania, pers. comm. 2001). In order to measure the height of the tree from eye level to the top-most leaves or dead branch, a direct distance from the ground to the top was measured with the rangefinder, then the angle to the top was measured by the clinometer, and trigonometry was used to calculate the vertical height. The same technique was used to calculate the difference in height between ground level at the base of the tree and eye level. Ground level was determined as the average between the high and low points of ground at the base of the tree. The rangefinder was also used for a second check on potentially tall trees: it was fired from directly below the canopy at an angle of elevation of close to, or exactly, 90°. As many mature mountain ash have open irregular crowns, it was often possible to record the tallest leaves in this fashion from directly below, thereby confirming the height assessed from a distance. When trees of extreme height were found, that is those ≥88 m, an arborist climbed the tree and used a tape measure to get an accurate height figure; that is, to the nearest 10 cm. (Fig. 3). The arborist also was often able to locate taller or equally tall trees across the skyline of the forest canopy. The difference between the height estimated by laser and the arborist’s direct tape drop never differed by more than ±75 cm and was usually within 30 cm, so the laser-estimated heights for trees that were not subsequently climbed can be considered to be accurate ±75 cm.
Special thanks to Tom Greenwood for his tree climbing expertise, Michael Taylor for his generosity in providing both the rangefinder and the knowledge of how to use it properly, and James Ashton for invaluable assistance in the presentation of this report.
It is particularly interesting to see these comments documenting the point at which the sine method was adopted halfway around the world from its multiple birthplaces here in North America.
In a more recent publication, The Effect of the Black Saturday Bushfires - on Victoria's tallest trees by Brett Mifsud, The Forester, Volume 55, Number 1 - March 2012 Mifsud comments on the effect of laser rangefinders on tree surveys:
However, the assumption that Cumberland did indeed have the tallest trees was proven quite incorrect with the advent of laser rangefinders in the late 1990s. By using a rangefinder, a single surveyor could accurately measure hundreds of trees in a single day. Following the first major surveys of the old growth E. regnans forests in Melbourne‘s water catchments, it was found that many hundreds of trees in the Wallaby Creek and O‘Shannassy catchments far exceeded the heights of those in the Cumberland Tall Trees Scenic Reserve (Mifsud 2003). http://www.forestry.org.au/pdf/pdf-members/forester/The%20Forester%20March%202012.pdf
The Native Tree Society continues to promote the adoption of the sine method through our website, BBS, Facebook page, publications, events, conferences, personal communications, interviews, and measurement workshops. A more detailed explanation of the methodology and discussions can be found in Tree Measuring Guidelines of the Eastern Native Tree Society by Will Blozan (October 2004, revised 2008) http://www.nativetreesociety.org/measure/Tree_Measuring_Guidelines-revised1.pdf and in ” The Really, Really Basics of Laser Rangefinder/Clinometer Tree Height Measurements” by Edward Frank, January 12, 2010 http://www.nativetreesociety.org/measure/really_basic_3a.pdf Critical reviews of the sine method have been published by U. S. Forest researchers: Bragg, Don C., 2008. An improved tree height measurement technique tested on mature southern pines. South. J. Appl. For. 32(1): 38-43. http://www.treesearch.fs.fed.us/pubs/29564/ and Bragg, Don C., 2007. The sine method as a more accurate height predictor for hardwoods. P. 23–32 in Proc., 15th Central Hardwood Forest Conf., Buckley, D.S., and W.K. Clatterbuck (eds.). US For. Serv. Gen. Tech. Rep. SRS-101. http://www.srs.fs.usda.gov/pubs/gtr/gtr_srs101/gtr_srs101-03.pdf