Engineering Survey I (CE153): Theodolite & Total Station Lab

• Total Station

• Tripod

• Prism and Prism Pole

• Pegs or Markers

A total station is an integrated electronic surveying instrument that combines the functions of an electronic theodolite for measuring angles and an Electronic Distance Meter (EDM) for measuring distances. The instrument’s microprocessor can calculate horizontal and vertical distances from the measured slope distance and vertical angle.

The EDM operates on the principle of measuring the time taken for an electromagnetic wave (typically an infrared beam) to travel from the instrument to a reflector (prism) and back. The distance is calculated as:

A traverse is a series of connected survey lines where the lengths and directions are measured. In a closed traverse, the lines form a polygon, starting and ending at the same point. This provides a mathematical check on the accuracy of the work. For a closed polygon with ‘n’ sides, the theoretical sum of the interior angles is given by the formula:

The difference between the sum of the measured angles and this theoretical sum is the angular misclosure. This error is typically distributed evenly among the measured angles to ensure the traverse is geometrically closed before further computations, like calculating coordinates, are performed.

1. Three survey stations (A, B, C) were established on the ground to form a closed traverse.

2. The total station was set up on the tripod and centered precisely over station A using the optical or laser plummet.

3. The instrument was levelled accurately using the electronic bubble and levelling foot screws.

4. The prism was set up on its pole over station C, and the instrument was aimed at the prism for a backsight. The horizontal angle was set to 0°00’00”.

5. The telescope was then turned clockwise to sight the prism, which was moved to the foresight station B.

6. The horizontal angle, vertical angle, and horizontal distance for the line AB were measured and recorded from the instrument’s display.

7. To minimize instrumental errors, the telescope was transited (face changed to right), and the foresight station B was sighted again, followed by the backsight station C. The angles and distances were recorded.

8. The instrument was then moved to station B. A backsight was taken on station A, and a foresight was taken on station C. The interior angle at B and the length of line BC were measured using the same dual-face procedure.

9. This process was repeated at station C, with a backsight to B and a foresight to A, to measure the final interior angle and the length of line CA.

10. All data was systematically recorded. The sum of the measured interior angles was calculated and checked against the theoretical sum for a triangle, (n-2) x 180°.

11. The angular misclosure was determined and distributed equally among the measured angles.

• Mean Interior Angle at A = 60° 10′ 21″

• Mean Interior Angle at B = 59° 50′ 31″

• Mean Interior Angle at C = 60° 00′ 01″

• Sum of Measured Angles = 60°10’21” + 59°50’31” + 60°00’01” = 180° 00′ 53″

• Theoretical Sum for a Triangle = (3 – 2) x 180° = 180° 00′ 00″

• Angular Misclosure = 180° 00′ 53″ – 180° 00′ 00″ = +53″

• Correction per angle = -53″ / 3 ≈ -18″

• Corrected Angle A = 60° 10′ 21″ – 18″ = 60° 10′ 03″

• Corrected Angle B = 59° 50′ 31″ – 18″ = 59° 50′ 13″

• Corrected Angle C = 60° 00′ 01″ – 17″ = 59° 59′ 44″ (one angle adjusted by 17″ to make sum exact)

• Final Sum = 180° 00′ 00″

The corrected interior angles for the closed traverse were determined as:

• Angle A = 60° 10′ 03″

• Angle B = 59° 50′ 13″

• Angle C = 59° 59′ 44″

The measured horizontal distances were:

• AB = 35.45 m

• BC = 42.10 m

• CA = 38.75 m

The total station polygon survey was successfully executed. The simultaneous measurement of angles and distances proved to be highly efficient. By taking dual-face readings, instrumental errors were minimized. The calculated angular misclosure was found and distributed, resulting in a geometrically correct polygon. This adjusted data is now suitable for further computations, such as calculating station coordinates or the area of the traverse.

The total station greatly simplifies the process of a traverse survey compared to using a separate theodolite and tape. The ability to digitally read angles and distances reduces human error in reading and recording. The small angular misclosure (+53″) indicates a good standard of fieldwork. This error could be attributed to minor inaccuracies in centering the instrument and prism, or slight atmospheric variations affecting the distance measurement system. The process of adjusting the angles is a fundamental step in surveying to ensure the geometric integrity of the final survey data.

• The instrument and prism pole must be centered and levelled with great care at each station.

• The prism height and instrument height must be measured and recorded accurately if vertical elevations are required.

• Dual-face (face left and face right) observations were taken for all angle and distance measurements to cancel out instrumental collimation errors.

• Tripod legs were firmly pressed into the ground to ensure the stability of the instrument during measurement.

• The correct atmospheric correction settings (temperature and pressure) should be entered into the total station for the most accurate distance measurements.

• Transit Theodolite

• Tripod

• Ranging Rods (or other targets)

• Pegs

A theodolite is a precision instrument designed for the accurate measurement of horizontal and vertical angles. A transit theodolite is one whose telescope can be rotated 180° in the vertical plane about its horizontal axis, a process known as “transiting” or “plunging.” This capability is essential for eliminating several systematic instrumental errors.

Angle measurements are taken in two positions: Face Left and Face Right. When the vertical graduated circle is on the observer’s left, the instrument is in the Face Left position. When it is on the right, it is in the Face Right position. By measuring an angle in both faces and averaging the results, errors such as the line of collimation not being perpendicular to the horizontal axis, and the horizontal axis not being perpendicular to the vertical axis, are effectively cancelled out.

The Method of Repetition is used to measure a horizontal angle with a higher degree of precision than the least count of the instrument’s vernier. The angle is measured multiple times, and the readings are accumulated on the horizontal circle. The final accumulated angle is then divided by the number of repetitions. This procedure minimizes random observational errors (like imperfect bisection) and systematic errors arising from imperfect graduations on the horizontal circle.

1. The theodolite was set up over the survey station ‘O’ and was accurately centered and levelled.

2. Two target points, ‘P’ (left station) and ‘Q’ (right station), were established using ranging rods.

3. The measurement was started with the telescope in the ‘face left’ position.

4. The vernier ‘A’ was set to read exactly 0°00’00” using the upper clamp and tangent screw.

5. The lower clamp was loosened, and the telescope was aimed at the left-hand target P. The lower clamp was then fixed, and bisection was perfected using the lower tangent screw.

6. The upper clamp was loosened, and the telescope was swung clockwise to sight the right-hand target Q. The upper clamp was fixed, and the bisection was perfected using the upper tangent screw. The reading on vernier A was noted. This was the first measurement of the angle.

7. To repeat the measurement, the lower clamp was loosened, and the telescope was turned back to sight the left target P again, with the previous angle still set on the circle.

8. The upper clamp was then loosened, and the telescope was swung to sight target Q again. This process accumulated the angle on the horizontal circle.

9. This procedure was repeated for a total of three repetitions. The final reading on the horizontal circle was recorded.

10. The face of the instrument was changed to ‘face right’ by transiting the telescope.

11. The target Q was sighted first, and the telescope was then swung anti-clockwise to sight target P. The same repetition procedure (three times) was followed.

12. The final angle was calculated by averaging the results from the face left and face right observations.

The mean value of the horizontal angle POQ, measured by the method of repetition using a theodolite, was found to be 45° 30′ 35″.

The method of repetition proved to be an effective technique for obtaining a precise measurement of a horizontal angle. By mechanically accumulating the angle on the horizontal plate and dividing the total by the number of repetitions, potential errors from reading the vernier and from non-uniform circle graduations were minimized. The practice of observing on both faces of the instrument successfully eliminated systematic instrumental errors.

The key advantage of the repetition method is the enhancement of precision beyond the least count of the theodolite. If the least count is 20″, dividing a tripled angle by 3 can yield a result with higher theoretical precision. The consistency between the face left (45° 30′ 30″) and face right (45° 30′ 40″) results indicates that the instrument was in good adjustment and the observations were made carefully. The small difference of 10″ is a random observational error, which is accounted for by taking the average.

• Accurate centering and levelling of the theodolite are fundamental for accurate angle measurement.

• Parallax between the crosshairs and the image of the target was eliminated by careful focusing of the eyepiece and objective lens.

• The upper and lower clamps and their corresponding tangent screws were used correctly to avoid disturbing the instrument’s position or the accumulated angle.

• To avoid backlash in the tangent screws, the final turning motion was always made in a clockwise direction.

• Ranging rods were checked to ensure they were held perfectly vertical over the station marks.