Total Station and Angle Measurements

Total Station Instruments

• Capable of measuring
• Angles in both the horizontal and vertical planes,
• Slope distances
• Can trigonometrically convert slope distances to their horizontal and vertical components of distances
• Can compute XYZ coordinates of points using observations. (Z is elevation)
• All information can be digitally recorded
• Can be used to stake-out engineering projects using coordinates
• Can measure multiple angles and average the results
• Displays measurements on liquid crystal displays
• All total stations have
• standards
• telescopes
• objective lens and focus
• eyepiece lens and focus
• both lenses must be focused to avoid parallax
• define axis of sight
• EDM
• horizontal axis
• vertical axis
• levels (many instruments use digital levels today)
• keypad
• display
• battery
• angle measurement system
• horizontal circle
• vertical circle
• horizontal and vertical motion screws
• lock screw
• tangent screw
• automatic compensator to correct for mislevelment - not on all instruments
• collimator - used to roughly sight on target
• Communication port
• optical/laser plummet
• base - permit interchange of equipment with tribrach
• tribrach

Tribrach

• Used to level instrument. Leveling screws use left-thumb rule. That is, bubble moves in direction of left thumb, right thumb should move in opposite direction.
• Used to center instrument over point
• Axis of scope in tribrach is aligned with vertical axis of instrument using right-angle prism
• Since focal distance is so short, parallax must be avoided
• ONLY FINGER TIGHTEN INSTRUMENT AND TRIPOD SCREWS!

Proper Handling

• Always store equipment in case when returned to locker
• Wipe down instrument and leave case open if equipment is wet
• Always loosen tripod screws when returning them to equipment room. Variable humidity can cause legs to swell. This will sometimes "lock" screws in place causing permanent damage to tripod.
• When moving equipment, always remove instrument from tripod, lower legs, and carry instrument either in case or by handle
• Always keep case closed and locked when in field
• Never place instrument on tripod until legs are firmly set in ground.
• When tribrach has circular bubble, remove tribrach from instrument and roughly level and center tribrach over point before returning instrument to tribrach.
• Procedure for setup over a point (Read Section 8-5 of textbook)
1. Remove tribrach from instrument in case, and place on tripod if it has an optical plummet.
2. Place legs such that two are downhill and are not in the lines of sight. This will prevent you from having to lean over legs in most instances.
3. Extend legs so that the shortest person in your crew can comfortably use total station without standing on tiptoes.
4. Roughly center and level tripod over point. You can use a coin or stone to check centering. Drop it from the center of the tripod and observe where it hits.
5. Place instrument on tripod if required. Make sure tribrach is centered on tripod head to ensure maximum flexibility in centering.
6. Focus optical plummet eyepiece and objective lens to bring ground and centering wires into sharp focus. Make sure parallax is removed.
7. Using leveling screws, center optical plummet over point
8. Using adjustable legs, carefully level circular bubble.
• Steps 8 & 9 should bring the instrument roughly centered and leveled over the point. If not, repeat steps.
9. Use precise level to roughly level instrument.
10. Loosen tribrach and center instrument over point. Be careful not to rotate instrument when sliding on head of tripod.
11. Fine level instrument using precise level, and tribrach leveling screws.
12. Check instrument centering
13. Check level.
14. Repeat steps 10-13 until instrument is precisely centered and leveled over point. (If it takes more than the first attempt, you are doing something wrong!)

Relationships Between Distances and Angles

• From Euclidean geometry we know that

S = R q

• where S is the arc length on a circle of radius R subtended by and angle q in radian units.
• Thus
• 1' of arc = 0.03 ft at 100 ft
• 1" of arc = 1 ft at 40 mi, or 0.5 m at 100 km, or 1 mm at 200 m
• 1" of arc = 0.000004848 radians
• 1 radian = 206,264.8" of arc
• A traverse that requires a precision of 1:20,000 implies an angular accuracy of

• Important to pick a target that matches the accuracy of your instrument, and desired resulting angle.

Example

A chaining pin is used as a site on a station that is 100 ft from the instrument. The chaining pin is 0.01 ft wide. It is estimated that the operator can center the sight within ±0.005 ft, or 1/2 of the pin. What resultant angular error can occur with this target? Would this be an appropriate target when using an instrument that has a specified accuracy of ±3"?

Measuring Horizontal Angles

• The procedure for measuring angles is dependent on the total station used.
• Read manufacturer's manual.
• There are two basic procedures for angle measurement.
1. Repetition method.
1. This method can only be done by some instruments.
2. Direction method.
1. Can be performed using any total station.
3. An angle must be turned at least once direct, and reverse to ensure that instrumental errors are compensated. A set of each is known as a position. 
• (1DR) means an angle turned once direct and once reverse. - 1 position
• (2DR) means an angle turned twice in the direct and reversed. 2 positions.
• etc.

General Procedures for Measuring Angles by Repetition Method

Refer to Figure (a) above when reading

1. With instrument at I sight on J (backsight)
2. Zero display
3. Turn instrument to K (foresight).
4. Read and record display.
5. Press button to hold value of angle on display. (Note: Not all instruments have this button.)
6. Plunge scope, and sight J.
7. Release angular value on display by pressing button. (Again, not all instruments have this feature.)
8. Turn instrument and sight on K.
9. Repeat steps 5-8 until desired number of turnings is obtained. (There must be an even number of angles to correct for instrumental errors.)
10. Record final angular value.
11. Take average of final value, and compare with first recorded reading to check consistency of angle turning. Repeat angle measurement procedure, if necessary.

Sample Note form

General Procedure for Measuring an Angle Using the Directional Method (SMI)

To complete the observation of the angle and distance. 

1. Sight the backsight station K and zero the instrument. For most instruments, zeroing can be done from the SETUP softkey menu.
2. From the Setup softkey menu find the SHOTS submenu. Press SETUP, NXT, SHOTS.
3. Press the BS softkey. This will read the instrument's horizontal and zenith angles and set the values in the BSDIR: line of the screen.
4. Sight the instrument on your foresight station K, and press SHOT from the SHOTS submenu.
5. Plunge the scope and resight the foresight station K. Press the SHOT softkey to read the circle in the reverse position.
6. Resight the backsight station J and press the BS softkey.
7. To measure the angle 2DR, press the SET1 softkey to toggle the data collector to SET2, and repeat steps a-f.
8. Press the EVAL softkey in the SHOTS submenu. This will display the average of the two pointings and the error. If the error is less than 1.96´DIN of your instrument accept the shots by pressing the STPTS (store points) key. If the error is too large you can delete a pointing and repeat the shot.
9. Once you willing to accept your observations press the STPTS (store points) button. The data collector will prompt to determine if this is a traverse point (TRAVR) or a sideshot (SIDES). Press TRAVR softkey. The data collector will accept the shots, move the occupied point to station 2 (the next station in the traverse), and the backsight point to station 1 (the previous occupied point). 

General Procedure for Measuring an Angle Using the Directional Method

Refer to figure (b) above.

• The advantage of this method is that it allows you to sight on multiple stations with little additional effort. 

1. With instrument at P, sight on Q.
2. Zero display.
3. Turn instrument to R. and read and record display.
4. Turn instrument to S and read and record display.
5. Plunge telescope.
6. Turn instrument to sight on Q.
7. Zero display.
8. Turn instrument to R. and read and record display.
9. Turn instrument to S and read and record display.
10. Repeat step 5-9 until angle(s) are measured desired number of times.

Sample Notes

Closing the Horizon

• Closing the horizon is the procedure of sighting on targets around the entire circle. In the above procedure, this would mean just one additional sighting back on station Q. The reading will typically not be 0°00'00" due to pointing errors and instrumental reading errors.
• After computation of angles, this allows the operator to check closure (S = 360°). The closure (discrepancy from 360°) should be within tolerances.
•  

Measuring Deflection Angles

• Deflection angles are measured from the extension of the previous line. 
• Can be turned either clockwise or counter-clockwise. Clockwise designated with a R and Counter-clockwise with a L.
• Used in alignment surveys.
• Seldom, if ever, used today.

Measuring Azimuths

• This procedure involves putting the azimuth of the backsight line in the display. The foresight(s) will then be the azimuth(s) of the line(s).
• This procedure is often used with data collectors.

Vertical Angles

• Zenith/altitude angles are angles measured in the vertical plane.
• Zenith angles have zero pointing toward the instrument's zenith.
• All total stations measure zenith angles.
• Altitude angles have zero pointing toward the instrument's horizon
; "+" when above the horizon and "−" when below the horizon
• Altitude angles were predominant with transits older transits.
• Relationship between zenith angle (z) and altitude angle (a) is

Direct mode    a = 90° - z

Reversed mode    a = z - 270°

• Indexing error is an error caused by the zero point on the vertical circle not truly being at the zenith.
• This error can be eliminated by reading zenith angles in both direct and reversed mode.
• For multiple turnings the average direct zenith angle is computed as

• where n is the number of positions (D&R) to be averaged.
• The second part of the equation is the amount of indexing error

Example

A zenith angle is observed 2DR. The direct readings were 88°17'50" and 88°17'46". The reversed readings were 271°42'12" and 271°42'17". What is mean zenith angle?

Common Field Procedures with Total Stations

• Prolonging a straight line - Use procedure known as double centering.
1. Backsight on A with telescope direct. Plunge and set point C'.
2. Backsight on A  with telescope reversed. Plunge and set C'.
3. Mark C at the midpoint between C' and C".
4. This procedure can be used to adjust the position of the vertical cross hairs in the telescope. (see Section 8-15)
5. Compensates for line of sight not being perpendicular to horizontal axis.
• Balancing-In - procedure to put instrument on line between to points. (See Section 8-16)

Instrumental Errors and Their Adjustments

• The precise observation of angles is dependent on the perpendicularity of the primary axes of the total station.
1. The plate level vial axis must be perpendicular to the vertical axis.
2. The vertical axis must be perpendicular to the horizontal axis.
3. The axis of the line of sight must be perpendicular to the horizontal axis.
• Errors
• Instrumental -
• Plate level vial out of adjustment
• Detection: Level instrument in two directions as per typical setup. Rotate instrument 180° from either of these directions, and bubble should remain centered. Any miscentering indicates that the plate level vial axis is not perpendicular to the vertical axis.
• Correction: Level instrument with bubble miscentered by 1/2 of the detected error (bubble run), or follow manufacturer's procedure for removal of error.
• Horizontal axis not perpendicular to vertical axis
• This error causes errors in both horizontal and vertical angles since telescope travels in inclined plane instead of vertical plane.
• Error can be removed by observing angles in both direct and reversed mode, and averaging.
• Dual-axis compensators can remove this error is the instrument is properly calibrated.
• Axis of sight not perpendicular to horizontal axis
• This error cause the telescope to scribe out a cone when it is plunged.
• Corrected by using double-centering technique when extending a line, and by doubling angles (measuring in both direct and reversed modes.)
• See Prolonging a Line of Sight
• Vertical indexing error - previously discussed.
• Eccentricity of the plates-Occurs when vertical axis of instrument does not coincide with center of plates. Compensated for by taking several readings about the plates and averaging. This happens automatically in surveying grade instruments.
• Circle graduation errors - Caused by irregularities in marking of plates. Take many reading about the plates and average. This is generally handled by modern total stations.
• Errors caused by peripheral equipment - Be sure that tripods, tribrachs, and targets are mechanically sound and in adjustment. Use targets that are appropriate for sight distances. 
• Natural errors -
• Wind. Vibrates tripod and target in windy condition. When this happens you can (1) protect instrument from wind by using shield, or (2) Wait until wind speed reduces.
• Temperature. Can cause uneven expansion of tripod and instrument parts resulting in instrument misleveling. When this happens you can shield instrument using umbrella.
• Refraction. Causes bending of sight line. Avoid having sight line close to objects (within 0.5 m) that can create microclimates such as the ground, cars, large trees. When this cannot be done, postpone observations until better conditions exist.
• Tripod settling. Avoid situation where legs are placed on different surfaces, and extreme soft-ground conditions. When this cannot be avoided such as in marshes and swamps, pound long wooden stakes flush with surface and set tripod on stakes. Most total station instruments have sensors to suspend observations when misleveling becomes to great.
• Personal errors-
  • Instrument miscentering. Can cause observed angle to be too large or small. Carefully center and level instrument. Size of error is reduced when angles have long sight lengths.
  • Target miscentering. Can cause observed angle to be too large or small. Use long sight distances to reduce effect on observed angles.
  • Improper use of clamps and tangent screws. Practice in formation of good observing habits and familiarity with equipment will reduce these errors.
  • Poor focusing. One of the most common errors. Be sure parallax is removed before taking observation. Avoid different operators during observation procedure.
  • Overly careful sights. This is a common beginner error. Take careful sights on targets, but do not redo procedure. Beginners tend to observe, then reobserve, then reobserve ... before taking sight. This process results in unsettling instrument and reducing pointing accuracy. Trust your eyes.

Last updated November 09, 2004
Penn State Surveying Program © 2001 - 2005