Lab Theodolite Random Errors

Lab Theodolite Random Errors Choose an electronic theodolite, total station OK. 1. Determine the precision of the reading mechanism, Er (error in reading) a. Sight a point target (speck on wall, etc) b.Take a reading with the theodolite 20 times in succession. Record all readings. c. Calculate the standard deviation of the readings. This is Er

2. Determine the precision of the combined operation of pointing and reading, Erp (error of pointing and reading) a. Sight a point target, center cross hair on target. b. Repeat sighting with upper motion and reading for a total of 20 readings. c. Calculate the sample's standard deviation. This is combined effect of pointing and reading, Epr.

3. Determine the precision of the combined effect of "centering" the theodolite, pointing, and reading the instrument, Erpc. a Read the horizontal angle on a tribrach-mounted target centered over a ground point at a sight distance of Dist = about 100 ft. Record Dist. b. Rotate the tribrach 90 degrees clockwise on the tripod head, recenter over the same ground point, resight and reread the same target. c. Repeat b. for a total of 20 readings with a 90 degree tribrach rotation between each reading. d. Calculate the sample's standard deviation for Erpc.

4. Determine the precision of the combined effect of reading, pointing, prism pole centering: Erp-pc. a. Sight and read the horizontal angle on a prism pole using a typical prism height of about 5 feet, held on a well defined point about Dist= about 100 ft from the instrument. Record Dist. b. Have the prism holder pick up the rod and reset it on the same point. Repeat reading on new rod settings for a sample of 20 readings. c. Take standard deviation for Erp-pc.

Reduce Data: 1. Calculate the precision of Pointing, Ep by the law of accumulation: Ep^2+Er^2=Erp^2 This is the observer's personal uncertainty (precision) in pointing. 2. Calculate the angular precision of Theodolite Centering, Ec Er^2+Ep^2+Ec^2=Erpc^2 This is how much theodolite centering causes uncertainty in a angular reading of sight length Dist. 3. Calculate the radius of the theodolite "wobble" caused by theodolite centering: Etd = Dist * tan(Ec) This is the radius on the ground of the actual theodolite centers. (express in feet, such as .003 ft, etc) 4. Calculate the angular precision of Prism Centering, Epc Er^2+Ep^2+Epc^2=Erp-pc^2 This is how much an angle is affected by prism uncertainty. 5. Calculate the radius of the prism "wobble": Epcd = Dist * tan(Epc) This is the radius on the ground of the prism wobbling due to the rod operator's use of the bull's eye bubble. .

Further Analysis: 1. Inspect your instrument centering data. Calculate four means -- where the tribrach had the same orientation: #1= Readings 1, 5, 9, 13, 17, #2 = 2, 6, 10,14, 18, #3 =3,7,11,15, 19, #4=4,8,12,16,20 Do the four means seem to cluster together at different values? Are the differences statistically significant?? If they differ significantly, how do you explain this??

Conclusions: 1. Write your observations in paragraph form. Does the data behave the way it should?? Discuss any abnormalities with logical explanations. 2. Based on your data, calculate the likely precision of an angle turned with your theodolite over a station, backsighting a prism pole only 15 feet away while foresighting a far target 1000 ft away?? Discuss your results. Are they reasonable??

Standard Form of a Lab Report: I. Title, II. Objective, III. Summary of Method, IV. Data Taken (OK to attach copies of field notes, V. Calculations, reductions, analysis, VI. Conclusions.