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Chapter 7

Differential Leveling

Differential leveling is a technique used to determine differences in elevation between points that are remote from each other. Differential leveling requires the use of a surveyor's level together with graduated measuring rods. An elevation is a vertical distance above or below a referenced datum. In surveying, the referenced datum is typically the MSL.



7-1. Some of the basic components for leveling are a level, a tripod, rods, and accessories. A level has three major components—a telescope, a level tube, and a leveling head. There are three types of levels used in differential leveling—automatic, digital, and optical-micrometer.


7-2. An automatic level uses a gravity-referenced prism or a compensator to orient the line of sight automatically. The instrument can be quickly leveled when a circular bubble level is used. When the bubble is centered, the compensator takes over and maintains a horizontal line of sight. Automatic levels are quick to set up and easy to use and can obtain second-order, Class II precision. The use of an automatic level entails using a freely moving prism that is suspended by a fulcrum or wire as a compensator. The compensator is sensitive to shock and must be kept nearly upright at all times. If the fulcrum or wire breaks, the instrument becomes useless. Gently tapping the instrument, while viewing through the telescope, will cause the line of sight to veer slightly. This verifies that the compensator is working properly.


7-3. The level has been advanced, along with other survey equipment, into using electronic measurements. The digital level uses electronic image processing to determine heights and distances and to automatically record data for future transfer to a PC. The digital level is an automatic level that is capable of normal optical measurements. When used in the electronic mode, together with a rod face that is graduated with a bar code, the instrument captures and processes the image of the bar code. The processed image of the bar code is compared to the image of the entire rod and is programmed in the memory of the instrument. The difference in height and distance is then determined. The digital level contains predetermined programs for running any type of line or making adjustments to a sighting. The programs store, compute, and transfer the data in a manner similar to that of a total station.


7-4. Optical-micrometer levels are similar to automatic levels in design. The optical-micrometer level can be purchased as an individual piece of equipment or as an attachment for some automatic levels. Optical-micrometer attachments employ a plane parallel-plate lens, which when rotated will vertically deflect the line of sight of the incoming light ray. The optical-micrometer level subdivides the smallest graduation of the level rod to an accuracy of about ±0.02 of the level-rod graduation, which means a recorded direct reading of 0.001 meter. FGCC standards require an optical micrometer be used for all first-order leveling. Some, but not all, digital levels are capable of meeting the required accuracy. Field operations for optical-micrometer leveling are nearly the same as for three-wire leveling except that optical-micrometer leveling uses double-scale invar rods and shorter sight distances.


7-5. Leveling rods are manufactured of metal, wood, or fiberglass. They are graduated in feet or meters and can be read directly to the nearest tenth of a foot or centimeter (Figure 7-1). To obtain a more precise reading, the reading is either estimated (single or three-wire method) or read with an optical micrometer or a digital image. Precision leveling requires one-piece rods that are calibrated for accuracy and thermal expansion. For less precise work, an extendable or folding rod may be used. The sole of the rods are made of a metal base, machined for accuracy. Precise rods have a built-in circular bubble level to maintain the plumb of the rod. Placing the rod on a stable, consistent surface and maintaining plumb are keys to completing accurate, differential-leveling measurements.

Figure 7-1. Traditional Rectangular Cross-Section Leveling Rods Showing a Variety of Graduation Markings



7-6. The sole of the rod is placed on the BM or a temporary turning point. The turning point can be any hardened surface with a definable and reproducible high point. Manufactured points (for example, the marlinspike and the base plate or turtle) can be used. The marlinspike is a stainless-steel pin that is driven into soft surfaces at an angle and a depth sufficient to support the level rod. The portable base plate is made of cast iron with a machined-steel point to place the rod on. The base plate weighs 2.5 kilograms or more, can be used on any surface, is more stable than the marlinspike, and is a requirement for higher-order vertical surveys.

7-7. There are two types of tripods available for leveling—the fixed-leg and the extension-leg. Either tripod is acceptable for second- and third-order leveling. Generally, fixed-leg tripods are preferred, but conditions and logistics may dictate using extension-leg tripods.


7-8. A collimation test for leveling (C-check) is a field determination of a geodetic level's collimation error (C-factor). If the instrument is placed precisely between two rods, the error is the same for the rear and forward readings and the measurement is the true DE (Figure 7-2). When the sight distances are unequal and collimation is not true, small errors are accumulated. The numerical value obtained during the C-check gives the correction to the observed DE because of the inequality of sight distances for a single setup or the inequality of the accumulated sight distance for a section of differential leveling. Methods for observing, computing, and adjusting a level are discussed further in Appendix C. Surveyors should follow these procedures:

  • Perform a C-check at the beginning of every day that geodetic leveling is performed or when the level is jarred.
  • Perform a C-check at midday if the temperature exceeds 95 degrees Fahrenheit (F). Leveling should be avoided during hot temperatures.
  • Perform a C-check at about the same time each day. Atmospheric refraction varies during the day and introduces systematic changes to the C-factor.

      Figure 7-2. Peg Test




7-9. Differential-leveling observations are a repetitive operation, which due to the regimen, often lead to a misunderstanding of the error sources. Due to the number of small systematic errors that are not discernible from geometric checks, it is imperative to adhere to the prescribed procedures.


7-10. The leveling party performs a recon of the level line. Existing BMs should be recovered and description/recovery notes prepared. BMs along the level line are established according to FGCC standards. At all orders of accuracy, the leveling party will verify that the starting BM elevation is correct by performing two-way leveling to the closest adjacent BM and back. These BMs should be part of the same level-line network that originally established them. All members of the leveling party should exercise caution in the choice of the route for leveling. High-traffic areas should be avoided, and if this is not possible, the leveling party should maintain high visibility at all times. Road-guard vests and additional personnel may be necessary to ensure the leveling party's safety. The ground over which the leveling progresses should be free of characteristics that will introduce anomalous measurements. Ground that radiates high refraction or that is soft or uneven should be bypassed if possible. Any time that high scintillation is observed between the level and the rod, sight distances must be reduced.


7-11. The terms differential leveling, direct leveling, geodetic leveling, and spirit leveling all describe the same activity—the determination of DEs by direct observation. These terms are used interchangeably in this publication. Follow these steps when performing third-order differential leveling:

Step 1. Determine the C-factor each day (just before leveling begins) and immediately following any instance when the level is subjected to an unusual shock. Record the results of the C-check and keep them in the project records.

Step 2. Start and end the leveling on BMs of third-order accuracy or higher.

Step 3. Use three-wire-leveling methods.

Step 4. Do not make observations closer to the ground than 0.5 meter. Do not make observations on the rod higher than the project specifications require.

Step 5. Leapfrog the rods forward.

Step 6. Observe an even number of setups between the starting and ending BMs.

Step 7. Place the rods in the red-rod-first sequence—rod number 1 or A of a matched pair of rods is marked (the foot of the rod is painted or a flagging is attached to the rod) to distinguish it from the other rod. The marked rod is observed and the readings are recorded first for each setup.

Step 8. Double-run the sections from the first BM out to the next BM and return.

Step 9. Determine the maximum allowable disclosure. It will be the lesser of the following computed values:

  • Twelve millimeters times the square root of the shorter-distance run between the BMs in kilometers.
  • Twelve millimeters times the square root of the perimeter of the loop (front and back runs combined) in kilometers.

Step 10. Ensure that any action not specified above complies with the specifications set forth by the FGCC.

Step 11. Ensure compliance with steps 1 through 10 at all times unless the customer sets forth specific methodology, standards, or specifications for performing the differential leveling in the request for survey support.


7-12. The field party consists of four members—two rodmen, a level observer, and a recorder. The duties of each member are identified as follows:

  • Rodmen. The rodmen hold the level rod; pace the sight distances between the instrument and the level rod to ensure that the minimum inequalities of the setup and the accumulated sight distances are maintained; hold the rod during readings in a plumb and steady vertical position using the handles of the rod; place the rod in precisely the same position for the backsight as it was for the foresight; carry the rod using the handles (not over the shoulder); and ensure that the rod face, the sole of the rod, and the circular bubble do not contact the ground or receive a sudden shock (the level rod is a precise-survey instrument and must be treated as such).
  • Observer. The observer performs the observations, is responsible for the care and condition of the instrument and accessories, ensures that the maximum sight distance is not exceeded when moving the level from the last foresight level rod to the next instrument setup, inspects the level tripod to ensure that all parts are secure and adjusted properly, deliberately places the level to provide a stable platform, carefully levels the instrument and reads the appropriate data, and never leaves the geodetic level unattended.
  • Recorder. The recorder is responsible for all documentation during the survey; completes all note forms properly; ensures that all requirements are satisfied; ensures that calculations and checks are performed without errors and expeditiously and that all technical specifications have been satisfied; and prepares the description of BMs and any supplemental vertical-control points.


7-13. Procedures for recording differential-leveling data are the same for all orders of accuracy. Differential-leveling data (include the names of the rodmen) is recorded on DA Form 5820 or any other single-sheet recording form authorized by the party chief (Figure 7-3). After recording the raw observations to three decimal places, use the following rules to determine the mean center-wire reading to four decimal places:

  • If the top interval is LARGER than the bottom, ADD the correction factor to the recorded center-wire reading to obtain the mean center-wire value to four decimal places.
  • If the top interval is SMALLER than the bottom, SUBTRACT the correction factor from the recorded center-wire reading to obtain the mean center-wire value to four decimal places.

7-14. The maximum permissible interval imbalance for third-order specification is 3 millimeters. Table 7-1 shows the correction factors for center-wire leveling.


    Figure 7-3. Example of Survey Notes for Three-Wire Leveling



Table 7-1. Correction Factors for Center-Wire Leveling

Difference in Intervals

Center-Wire Correction Value











7-15. The determination of the C-factor may be performed as a part of leveling or separately. In all cases, the C-factor determination must be recorded separately from other recordings and must comply with all requirements for note keeping. It is desirable to determine the C-factor under the same conditions that the leveling will be performed, including the sight distance, the slope of the ground, and the elevation of the line of sight above the ground.

7-16. Ensure that the circular bubble is carefully centered and that the observed ends of the bubble in the level vial are in coincidence (when applicable) before reading the three wires. If the C-factor is determined during the first setup of the leveling, perform the following steps:

Step 1. Observe and record the foresight readings on the C-factor note sheet after the regular foresight observations are recorded for the level line.

Step 2. Position the rear rodman to about 10 meters behind the level.

Step 3. Observe and record the rear-rod readings on the C-factor note sheet.

Step 4. Move the level to about 10 meters behind the front rod.

Step 5. Observe and record the front-rod readings on the C-factor note sheet.

Step 6. Observe and record the rear-rod readings on the C-factor note sheet.

7-17. The total correction for curvature and refraction (C&R) must be determined for each far-rod reading using the distance from the instrument to the far rod as the argument. Distances equal the product of the sum of the intervals (for a single set of three-wire readings) times the stadia-interval factor (SIF). The two corrections for C&R are algebraically added to the sum of the mean wire readings for the distant rod. The maximum permissible C-factor varies with the SIF. Instruments with a SIF of 1:100 may not have a C-factor of greater than ±0.004. Instruments with a SIF of 1:200 may not have a C-factor of greater than ±0.007. Instruments with a SIF of 1:333 may not have a C-factor of greater than ±0.010. If the C-factor is determined to be greater than what is permitted for the instrument's SIF, the instrument must be adjusted and the C-factor redetermined before performing differential leveling. The notes for the C-factor determination become part of the administrative notes for the leveling operation.


7-18. If the C-factor exceeds the SIF limits, a correction to the center wire must be made. Determine this correction by multiplying the total rod interval of the last foresight (distant rod) by the computed C-factor. Compute the correction to three places to the right of the decimal point and include the algebraic sign of the C-factor. The correction to the center wire is algebraically added to the last foresight mean wire reading. The result will be the corrected center-wire reading. Compute the corrected center-wire reading to three places to the right of the decimal point.

7-19. Follow the manufacturer's manual to adjust the level until the corrected center-wire reading is observed on the distant rod. Perform a C-check to ensure that the new C-factor is within the acceptable limits.


7-20. The SIF is required to compute the length (horizontal distance) from the stadia intervals and to determine the maximum AE for a level line. The SIF must be determined if the reticle (which contains the etched stadia wires) is replaced or changed. The notes from the SIF determination become part of the records that are kept with the level and the project files.

7-21. The SIF determination is made by comparing the stadia intervals that were observed over a course of known distances. Lay out the course on a reasonably level track, roadway, or sidewalk. Place nails or other marks in a straight line of measured distances of 25, 35, 45, 55, 65, and 75 meters. Plumb the optical zero point of the level over the zero marker on the ground and level the instrument. The optical zero point of the level is found in the manufacturer's manual. Read the rod at each of the six points and record the intervals. Compute the half-wire intervals as a check against erroneous readings. Compute the sum of the six interval readings. The SIF is the sum of the measured distances (300 meters total), divided by the sum of the six interval readings.

7-22. To check for errors, compute the SIF for each of the six readings and divide the measured distance by the total interval readings observed for that distance. The average of the six computations will serve as a numerical check. A tendency for the six computed values to creep in one direction indicates an error in plumbing the optical zero point of the level over the zero point on the ground.



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