Calibration john-@bcn.net Nov 06, 2003 19:01 PST
 Hi All, In regards to calibrating clinometers, first consider two distinct sources of error. First, there is reading and leveling error, caused by inaccuracies in determining the reading of the crosshair and of not pointing exactly at the target. For this, probably do a series (20?) of readings taken of a fixed point from a fixed point, hand held and all, then determine the standard deviation of the readings by the usual statistical formulas. Or, just see what the range of error is in the set. Next, there is instrument or systematic error. For measuring this, I offer a method my brother (a surveyor) suggested. It is called a "peg test". You set up two surveyor poles or other objects separated by say 100'. Set up a station midway between these objects. Preferably, the clinometer will be stabilized, either hold it against a wall or fasten it to a tripod. (The Suunto clinometers have a tripod mount point on the side.) Read and mark the point on each post that corresponds to 0 degrees. A helper is useful here. These points should be at the same elevation regardless of error, since the distance is equal (principle of similar triangles). Then go right next to one of the posts, and align 0 degrees with the mark there. There will be basically no error there, because the distance is minimal. Then sight and mark the point at 0 degrees on the other post. The difference between the two marks on that post is the systematic error. (Plus or minus the random error from above.) The length of the systematic error will be proportional to the distance to your target. In this example, you have determined the size of error in 100'. This can also be converted to a degree error. Since the systematic error in degrees is always the same, you should adjust all your measurements by that amount. The reading and leveling error is random, and reduces the accuracy of the measurement. You do not adjust for the random error, just accept it and report it. As for calibrating the rangefinder, I agree in principle with the post suggesting readings at varying clickover points, but would add, if you have time, to do a number of readings at each distance, to determine the variability (standard deviation, etc.) of the results. Basically, you want to account for both systematic and random errors, as above. I hope that helps further the accuracy of our measurements. John Eichholz Charlemont, Massachusetts neophyte tree measurer and ent seedling
 Re: Calibration Colby Rucker Nov 06, 2003 20:51 PST
 Howard and all, When I started using laser-based measurements, I spent a fair amount of time thinking up methods that were new to me, trying to increase the accuracy of my findings. I stretched tapes across the front yard, determining where laser readings intersected actual distance, and where they didn't. I shot to various colors of construction paper, and got different distance readings. I shot to material of various surface contours, and got different readings. I also got different readings on different days. I finally decided that I had only paid \$199 for the rangefinder, and it was not realistic to expect absolute accuracy. If it was supposed to be accurate to a yard, and it was consistent to several inches, that wasn't bad. Calibrating for all sorts of possible deviations would be a nuisance and might add as many (or more) errors than it corrected. I knew the equipment was reasonably close, but conditions (including body movement) were so changeable that I might as well accept things as they were. That said, there were lots of other things I could do to increase accuracy. These included carefully backing to clickover, eliminating multiple triangles, making careful basal adjustments, minimizing distances, and recording all measurement elements to 1/2 inch. As a result, I pretty much went to the pole method, and also using the pole and clinometer as a level to adjust basal measurements to 1/2 inch accuracy. I practiced recording clinometer angles to 1/10 of a degree, which is a judgment call, since the scale's only marked in full degrees. I don't abuse my equipment, and check it occasionally. When I remeasure certain trees, I get very compatible measurements. This indicates consistency as far as individual trees are concerned. Dale used the pole method on the Longfellow Pine and got an extremely accurate finding, compatible with the drop-line measurement. On the Seneca Pine, Dale and I cross-leveled the central basal contour on both sides of the tree to establish a basal starting point for Will's dropline. Otherwise, even a steel tape doesn't mean anything. So, there are lots of things that can and should be done to increase accuracy. At present, I don't think trying to calibrate an inexpensive piece of equipment beyond its inherent tolerance is one of them. Colby
 Re: Calibration Howard Stoner Nov 10, 2003 07:46 PST
 Colby, Thanks for the insights. Thanks also to John, your input is informative and I appreciate that, however, I am with Colby on trying to get more out of instrument than it is designed for. At every click-over point from 20 yds to 100 yds. my range finder is long by 1.5 to 3.5 feet. For example: 20 yds = 58.5', 50 yds =147.2', 60 yds=176.9', 80'=237.5, etc. Is my range finder the only one that is consistently this far off and always on the long side? Though it is true that these numbers will change some with different objects and conditions, it seems to me they achieve a more accurate result than multiplying my reading by 3. Convince me otherwise and I will throw out my calibration table. Is there such a thing as calibrating an inexpensive piece of equipment "to" its inherent tolerance? It seems to me it is worth an hour of my time every few months to try! Howard
 RE: Calibration Robert Leverett Nov 10, 2003 08:28 PST
 Howard:    You should keep your calibration table, because it is needed for your particular instrument. I was lucky enough to get a laser (the 800 meter one) that is extremely accurate. However, I have to watch carefully when I use either the 500 or the 400.    The testing and research that each of us does adds measurably to our collective understanding of our individual instruments, brand reliability, etc. There comes a point of trying to calibrate the "uncalibrateable", but that decision needs to be made for each instrument. Constant attention to the accuracy of our instruments is part of the price we pay to be Ents.     My experience with production models is that they get increasingly unreliable as cost-cutting leads to quality reduction. Nikons built in China is a case in point. Shame on Nikon for compromising their good name. Bob
 RE: Calibration john-@bcn.net Nov 10, 2003 22:51 PST
 Bob, Howard, Lee, all, (Summary: Theoretical means are used to show plausible error rates of +/-3 feet for typical measurements, with 3 out of 4 falling within +/- 1.5 feet) I've been doing a little work on theoretical rates of error. Hold on now, its not that bad. I think I can prove mathematically that the error in tree height that results from each degree of clinometer error is approximately between 1.75% and 1.9% of the horizontal distance to the trunk. To show this, let DT be the true distance to the tip and let DB be the true distance to the point directly below the tip. Let @ be the true angle to the tip, and let e be the measurement error of the angle. Let H be the true height of the tip above horizontal, and let H' be the height calculated from the true distance to the tip times the sine of the measured angle. Then H - H' is the height error due to angle error. It is true that H = DT*sin(@). We have decided that H' = DT*sin(@+e). It is also true that DT = DB*1/cos(@). So we can then be sure that: H - H' = DB*(1/cos(@))*(Sin(@)-Sin(@+e)). Why bother with all this? Because the factor: (1/cos(@))*(Sin(@)-sin(@+e)) is nearly a constant! Its range is a smooth progression from 1.74% at 0 degrees to 1.9% at 80 degrees. Because of this, we can safely say that an upper bound of clinometer error is 2% of baseline per degree of error no matter what the angle. I think I'm always within +/-0.4 degrees with my Suunto. This translates to +/-0.8 feet per segment on a 100 foot baseline, or +/-1.6 feet overall. This clinometer error is pointing and leveling error, but the same logic applies to systematic error. Rangefinder error contribution to height error is proportional to the sine of the tip or base angle. It varies more by angle, from very little at 0 degrees to 1:0.5 at 30 degrees to 1:0.86 at 60 degrees. If the rangefinder is off by a constant 1.5 feet across its range (like Howard's -- also 1/2 the clickover interval on mine), then we can expect an error in height of from 0 feet to 0.75 feet to 1.29 feet per reading due to rangefinder error, and it doesn't matter how far away! Since the bottom angle is usually smaller than the top angle, we can average this off to about 1.5 feet of error for every 1.5 feet of rangefinder error on the typical tree having angles of 60 degrees up and 10 degrees down. This rangefinder error is systematic error, but the same ratios apply to pointing error. It seems clear to me that getting rangefinder error at 1.5' and clinometer error of 0.4 degrees at 100' baseline have comparable effects on height accuracy, and that without statistical methods, we shouldn't be getting closer than +/-3 feet at these rates. Since we are getting better, more consistent results than that, our equipment accuracy is probably somewhat better than I have put forth here! (Actually, random results would be +/-1.5 feet 3 times out of 4.) If you got this far, thanks for putting up with my ramblings! John Eichholz
 Re: Calibration Howard Stoner Nov 11, 2003 05:41 PST
 John, Thanks for the calculations. Of course being a so called "mathematician" I am excited about your calculations and formulas and will be "scrutinizing" your work carefully to make sure there are no errors in your error calculation. (Just kidding!) I don't know statistics well but it seems there should be a principle of central tendency, law of averages or something like it. Meaning: no matter what the error, so long as it is distributed evenly on both sides of the true distance, the average of an increasing number of measurements will eventually approach the true value. How does one know that you are getting that even distribution other than field testing? I think we all agree that Will's drop-line measurements are the most accurate we will get. On two occasions I have been within .8 ft on one and .2 ft of his measurement on the second. This is certainly a small sample to be drawing major conclusions but at least it is a start. Is it possible that my calibration chart gives me that even distribution? It seems to me that it might! Howard
 RE: Calibration NR, Cook Forest Env. Ed. Nov 11, 2003 11:12 PST
 Howard, I consistently find one of my laser's to be off in your noted range, another is much closer after I had Forestry Suppliers 're-calibrate' it . They sent me one that was way over specs, at least in my humble opinion. The unit was brand new and was supposed to be within +/- 1 yard of actual distance. Trials at every click over point in 100 yards yielded an error off true by +1.5 yards. I've only had 3 lasers over the years, and I've had to run trials on them periodically to note any major changes in their readings. All of these lasers have always overstated the length to some degree during trials. I still use a "calibration" factor determined from each laser that brings me closer to the actual distance to target. It has helped me to be more consistent in the long run, especially in terms of comparing to Will's tape dropped trees at Cook Forest. Maybe this calibration method won't work for everyone, but I've found that when using ENTS methods with a properly calibrated laser rangefinder I am consistently within +/- 1ft of Will Blozan's taped dropped Seneca and Longfellow Pines. I'm not sure if calibrating lasers will work with everyone else when we start to examine other possibilities of error in terms of humans and equipment. Maybe my calibration works out just right to offset other possible errors. Anyway you look at it though, I think that if we can get to within +/- 1ft of the trees height consistently, we must be doing something right. Dale
 RE: Calibration john-@bcn.net Nov 11, 2003 12:24 PST
 Hi Bob, Howard, I am glad for all the peer review you can give. Peer review is our best asset and so important as theories are being formed. There is a lot going on out in the field and we are pushing these instruments to their limits (in a good way). Forgive me (and please share your work) if this has been gone over before. I am looking to establish how much error in height results from a given inaccuracy in measurement. This seems to be doable on paper using these formulas. In practice, good technique might be inspired by an understanding of the mechanics of the situation. For instance I am inclined to believe that setting up at clickover for the upper (largest) angle sightline would minimize total error, because rangefinder error on the horizontal has so little effect and by staying put, we can reduce clinometer (pointing) error caused by moving around. I am impressed, though that this group questions and discusses both theory and social policy at their intersection, as with the GPS issue. I had been watching with interest for only a short while, and yet I feel welcomed in my participation. Thank you very much. JE
 RE: Calibration Robert Leverett Nov 11, 2003 12:36 PST
 John:    A point worth noting about theoretical maximums versus actual errors. Sometimes the errors encountered from the laser and clinometer are partially offsetting, i.e. clinometer error going in one direction and laser in the other. This can certainly occur when you get the clinometer needle sticking. In addition Paul Jost found that the accuracy limits of the lasers was about +/- 0.75 feet despite the units of changeover of a yard/meter used. So at the changeover of laser readings, we're probably within +/- 1.0 feet of actual distance.     To get truly accurate measurements, statistics is definitely involved. At the simple end, Lee and I believe that it takes about 10 readings to be confident of an accuracy to less than +/-1 foot.     I'll have a simple spreadsheet for everyone tonight showing the laser error problem in a tabular layout. Bob
 RE: Calibration john-@bcn.net Nov 11, 2003 15:41 PST
 Don, Well, as long as the error "e" is "real" angle minus measured angle, it is both accuracy and precision. If we are talking about the clustering and variability of results around an average, then that component is precision, and the difference between that average and the "true" (if we could ever know that) is accuracy. But I believe my error covers both. (And is impossible to really know.) I'm really only saying if you put a wrong number in for angle, off by 1 degree from the "real" angle, and the "real" baseline is known, that your height measurement from the result will be off by no more than 2% of the baseline. Anything else thrown into the mix and all bets are off. But it does give you a reason to be precise to a certain level and an awareness of how your instrument capabilities may be influencing the result. Again, the results I am seeing on this list and in the field are surprisingly repeatable, and confirmed to be accurate using physical measurements. I think my analysis applies more to confirming the quality of our tools and methods than to justifying a claim to accuracy of the results. That is what is so valuable about everybody's experimental approach.    By comparing different methods and seeking replicable precision with verifiable accuracy we have met the real test of science. John Eichholz
 Re: Calibration Don Bertolette Nov 11, 2003 17:13 PST
 John- Thanks for the clear explanation! I've always considered simple clear explanations a measure of the depth of the understanding. Regarding "the error "e" is "real" angle minus measured angle", if the angle is measured like a transit, with the angle measured at the exact point of 'pivot', this would be in my mind a measured angle (with great potential for accuracy). Again in my mind, the real angle that we commonly use in the field (using a clinometer or similar angle measuring device) is truncated, as we reposition our head/eye for tree base and tree top measures...the 'pivot' point is actually somewhere (maybe as much as a half of a foot) behind the eye...that was my idea of error "e"... -Don
 Re: Calibration dbhg-@comcast.net Nov 11, 2003 17:28 PST
 Don, John, Howard, et al.:    Don, On occasion, I use simple reflectors, mostly paper. So maybe it is time to move up to the next level.    As promised from an earlier post today, the attached spreadsheet provides an easy way to show the maximum error with the laser rangefinder as a function of laser distance error along the hypotenuse line and the angle to the point being measured. For a fixed/maximum laser distance error, the error in the height is a function of the angle. Of course, the spreadsheet calculations cannot tell us the best location to seek. That is driven by crown and base visibility. However, for tall white pines in Mohawk, if you are close enough that your angle to the point you are measuring is over 60 degrees, there's an excellent chance you're not seeing the top. I try to reduce the angle to 55 degrees or less. If I can find a vantage point on a hill, I can usually get the angle down to between 35 and 50 degrees. So I can expect up to a 1 foot error from the chart. A 0.2 degree error with the clinometer is not unusual. So I can quickly account for a +/- 2 foot error range. Repeat measurements with different instruments can bring that down to about a foot.    I've got other spreadsheets that show the maximum range for various combinations of laser and clinometer error. I'll spruce it up and send it in a day or two. Bob
 Juggling the Errors dbhg-@comcast.net Nov 15, 2003 07:20 PST