Lab Theodolite Systematic Errors

Lab Theodolite Systematic Errors

This lab introduces an in-depth view of the theodolite/total station, its construction and error sources. To test a theodolite, do the following relationships.

1. Rotation of the cross hairs – sight a point on the left limb of the horizontal cross hair. Rotate the instrument to the left, the point should stay exactly on the cross hair as it moves right in the field of view.

Adjustment:loosen capstan screws and rotate crosshairs till test works

Cancel Error:use only central portion of cross hairs for pointing.

2. Line of sight perpendicular with the horizontal axis – sight a well defined point, take horizontal reading. Reverse telescope and take second reading on the same point. These should be different by 180. The “collimation” error in the line of sight is half of the amount by which the second reading missed exactly 180 difference.

or DOUBLE CENTER TEST: Sight BS point Direct, flop to reverse and set point about 150 ft from instrument. Sight same BS point Reversed, flop to Direct and set a point beside the first one. Measure the distance between the two foresight points, calculate the angular content of half of this distance. This error should equal the same value of the first test.

Adjustment:loosen capstan screws and move crosshair ring left or right to eliminate error.

Cancel Error:measure all angles at the same vertical angle position, or measure all angles in the Direct and Reversed position of the telescope and take the average.

Math Correction:calculate the effect on each reading, make correction mathematically

3. Horizontal axis perpendicular with vertical axis – Sight high point with telescope direct, drop line of sight to ground level and make a mark. Sight same high point with telescope reversed, drop line of sight and make a second mark. The two marks should be on top of each other. If not, an error exists.

Adjustment: move the adjustable end of the horizontal axis up or down as needed.

Cancel Error:measure all angles at same vertical angle position, or measure all angles in the Direct and Reversed position of the telescope and take the average.

Math Correction:calculate the effect on each reading, make correction mathematically

4. Sensitivity of plate level vial – center level vial with vial pointed toward a particular direction. Turn telescope 90 deg to that direction and make a mark about 150 ft from instrument. Re-align level bubble in that direction and use level screws to move the bubble through several marks on the tube. Turn telescope back to the direction of the first mark, and make a second mark. Measure the vertical distance between marks and calculate the angular content of this at the instrument. Divide this by the number of marks moved for the sensitivity.

5. Vertical Axis is along gravity – align level vial along two screws, turn 180 and observe amount of move in the bubble. Bring half way back and turn 180 again. Repeat until the bubble does not move upon reversal. Now align vial in direction of third screw, center, turn 180, observe move, bring back half way, and iterate until it does not move. At this location, the telescope can be pointed any direction and the bubble will not move. The vertical axis is now truly vertical with gravity.

Observe the position of the bubble, count the number of divisions off center, multiply the number by the sensitivity to get the total error in the level vial.

Adjustment:use an adjustment tool to raise or lower one end of the level vial until the bubble ends up in the center when tested as above. (with instrument vertical, move bubble to center)

Cancel Error: find the “high point in the level vial” as in the above procedure.

Math Correction:if the amount of “tilt” and the “direction of tilt” in the vertical axis is known, mathematical formulas can be applied to correct each reading to its proper value. Most total stations today have the “automatic compensation” software built into the processor. A pendulum senses the tilt, corrections are calculated and automatically applied to each reading.

6. Optical Plumb looks long the Vertical Axis – Perform in a classroom or lab.

(1) for optical plumbs located on the tribrach -- carefully lay the theodolite on its side on a table. Look through the optical plumb to a piece of paper on a wall about 5-6 feet away. Make a mark where the optical plumb hits the paper. Rotate the tribrach 180, and make second mark. If the optical plumb is out of adjustment, the optical plumb line will scribe out a circle on the paper. Measure the diameter of this circle between the two points. Calculate its radius, and calculate the angular content of this radius at the instrument.

(2) for an optical plumb on the instrument’s alidade – do the same as above, but put the instrument on a tripod and look down at a paper placed on the floor/ground.

Adjustment:use an adjustment tool to raise or lower the three corners of the “bullseye” bubble, until there is no circle scribed out.

Cancel Error:measure an angle with one position of the tribrach. Turn the tribrach 180 on the tripod, measure the angle again. Take the average.

Math Correction: none

7. Vertical Collimation – Index Error – with telescope direct, measure the zenith angle to a well defined point. Measure the zenith angle with the telescope reversed to the same point. The two zenith readings should add to 360. The difference is twice the index error of the theodolite. Calculate the index error. Is the error + or -? (+ if measured zenith angles are larger than true)