Eichholz  Error Spreadsheet John Eichholz Nov 24, 2004 20:42 PST
 Ed, I see what you are getting at. I'm not sure how you got the 2.62 feet and the subsequent errors, though. Actually, the situation is dependent on you assumptions. If you are starting with a given distance measurement to the top that is different from starting with a given distance horizontally. I have set up a spreadsheet with the latter assumption. This addresses the situation which I feel is most practical: You are standing a set distance from the tree and you want to know how much height error you will have if you don't read your clinometer accurately. (You might regret getting me started, but that is a different thing.) Actually, the error is nearly constant in this scenario, regardless of the angle. I have tried to make the spreadsheet as clear as I could. If you (or anyone) comes up with different numbers it is because we are making different assumptions. Not wrong, just different. I would like to continue with this if there are scenarios that people want to explore. As Colby said in one of the posts in this series (Nov 6, 2003), " 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. " The instruments are only "so" accurate, so don't try to split hairs. But, I still think an awareness of the source and magnitude of errors as they propagate in our calculations is useful. Also see many earlier posts in November, 2003 on this subject. John Eichholz Error xls file    analy20041124b.xls  File as a html webpage (non-interactive) p.s. if you don't have Excel, here are the formulas: 2004 11 24 Analysis of height error due solely to angle measurement error using the sine*distance (ENTS) method. Scenario: You are at a fixed distance from a tree. (DB) You accurately measure the distance to the top. (DT) You measure the angle to the top, or any other point on the tree, but there is an error in your measurement (e). Since we are focusing on angle error, we assume the tree is vertical. The only difference would be a change in the baseline. The "error as a percent of baseline" is still the same. DB is the true horizontal distance to the point directly beneath the top. DT is the true distance to the top. a is the true angle to the top. e is the angle measurement error. H is the true height. H' is the height calculated using the erroneous angle measurement. Facts: DT = DB/cos(a); H = DT*sin(a); H' = DT*sin(a+e) Formula used: H-H' = DT*sin(a) - DT*sin(a+e) = (DB/cos(a))*(sin(a)-sin(a+e)) My conclusion: At a given baseline, the height error due to angle measurement error is nearly the same no matter what the angle. Also, at 50 yards horizontal, the height error due to a 0.4 degree clinometer error is about 1 foot. Enter the angle error in b6. Enter the baseline distance to the tree in b7. angle error (degrees)>> 0.4 e true baseline distance to point below top (yards)>> 50 DB Here are a series of angles and the height error that results a a+e DT H H' H-H' (H-H')/H true angle true angle + error (yards) true height (feet) calc height (feet) height error (feet) hgt error percent of baseline -10 -9.6 50.77 -26.45 -25.40 -1.0478 -0.70% -5 -4.6 50.19 -13.12 -12.08 -1.0475 -0.70% 0 0.4 50.00 0.00 1.05 -1.0472 -0.70% 5 5.4 50.19 13.12 14.17 -1.0469 -0.70% 10 10.4 50.77 26.45 27.50 -1.0465 -0.70% 15 15.4 51.76 40.19 41.24 -1.0462 -0.70% 20 20.4 53.21 54.60 55.64 -1.0459 -0.70% 25 25.4 55.17 69.95 70.99 -1.0455 -0.70% 30 30.4 57.74 86.60 87.65 -1.0451 -0.70% 35 35.4 61.04 105.03 106.08 -1.0446 -0.70% 40 40.4 65.27 125.86 126.91 -1.0441 -0.70% 45 45.4 70.71 150.00 151.04 -1.0435 -0.70% 50 50.4 77.79 178.76 179.81 -1.0428 -0.70% 55 55.4 87.17 214.22 215.26 -1.0420 -0.69% 60 60.4 100.00 259.81 260.85 -1.0409 -0.69% 65 65.4 118.31 321.68 322.72 -1.0394 -0.69% 70 70.4 146.19 412.12 413.16 -1.0371 -0.69% 75 75.4 193.19 559.81 560.84 -1.0335 -0.69% 80 80.4 287.94 850.69 851.72 -1.0265 -0.68% 85 85.4 573.69 1714.51 1715.51 -1.0054 -0.67% 90 90.4 816227613880954000.00 2448682841642860000.00 2448623168969300000.00 59672673563136.0000 39781782375424.00%