Leveling-Theory, Methods, and Equipment PDF

- Lecture 1 Chapter 4: Leveling-Theory, Methods, and Equipment Objectives 1. Understanding of leveling terms 2. Understand basis of and differences in vertical datum’s 3. Understand effects of curvature and refraction in leveling 4....

- Lecture 1 Chapter 4: Leveling-Theory, Methods, and Equipment Objectives 1. Understanding of leveling terms 2. Understand basis of and differences in vertical datum’s 3. Understand effects of curvature and refraction in leveling 4. Understand how to correct for of curvature and refraction in differential leveling Work Required 1. Read: 4.1 through and including 4.5.2. 2. Problems: 4.1, 4.2 – (use 850-feet, 1387-feet and 2100-feet for distances) and 4.6. 4.1 Introduction Leveling is the general term applied to any of the various processes by which elevations of points or differences in elevation are determined. It is a vital operation in producing necessary data for mapping, engineering design, and construction. Leveling results are used to (1) design highways, railroads, canals, sewers, water supply systems, and other facilities having grade lines that best conform to existing topography; (2) lay out construction projects according to planned elevations; (3) calculate volumes of earthwork and other materials; (4) investigate drainage characteristics of an area; (5) develop maps showing general ground configurations; and (6) study earth subsidence and crustal motion. 4.2 Definitions Vertical line: A line that follows the local direction of gravity as indicated by a plumb line. Level surface: A curved surface that at every point is perpendicular to the local plumb line (the direction in which gravity acts). Level surfaces are approximately spheroidal in shape. A body of still water is the closest example of a level surface. Within local areas, level surfaces at different heights are considered to be concentric; the potential of gravity is equal at every point on the surface. Level line: A line in a level surface, therefore a curved line. Horizontal plane: A plane perpendicular to the local direction of gravity. In plane surveying, it is a plane perpendicular to the local vertical line. Horizontal line: A line in a horizontal plane. In plane surveying, it is a line perpendicular to the local vertical. Vertical datum: Any level surface to which elevations are referenced. This is the surface that is arbitrarily assigned an elevation of zero. This level surface is also known as a reference datum since points using this datum have heights relative to this surface. Elevation: The distance measured along a vertical line from a vertical datum to a point or object. If the elevation of Point A is 802.46-feet, then Point A is 802.46-feet above the reference datum’s base elevation of zero-feet. The elevation of a point is also called its height above the datum. Geoid: A particular level surface that serves as a datum for elevations and astronomical observations. Mean sea level (MSL): The average height of the sea’s surface for all stages of the tide over an 18.6-year period which is the length of a lunar cycle. It was arrived at from readings, usually taken at hourly intervals, at 26 gaging stations along the Atlantic and Pacific oceans and the Gulf of Mexico. The elevation of the sea differs from station to station depending upon local influences of the tide; for example, at two points 0.5 miles apart on opposite sides of an island in the Florida Keys, it varies by 0.3 ft. Mean sea level was accepted as the vertical datum for North America for many years and is commonly referred to as the National Geodetic Vertical Datum of 1929 (NGVD29) vertical datum. However, the current vertical datum uses a single benchmark as a reference (Father Point in Quebec, Ontario) and is referred to as the North American Vertical Datum of 1988 (NAVD88). Tidal datums: The vertical datums used in coastal areas for establishing property boundaries of lands bordering waters subject to tides. Tidal datums also provide the basis for locating fishing and oil drilling rights in tidal waters, and the limits of swamp and overflowed lands. Various definitions of tidal datums have been used in different areas, but the one most commonly employed is the mean high water (MHW) line. Others applied include mean high water (MHHW), mean low water (MLW), and mean lower low water (MLLW). Interpretations of tidal datums, and the methods by which they are determined, have been and continue to be the methods by which they are determined, have been and continue to be the subject of numerous court cases. Benchmark (BM): A relatively permanent object, natural or artificial, having a marked point whose elevation above a reference datum is known or assumed. Common examples are metal disks set in concrete, reference marks chiseled on large rocks, nonmovable parts of fire hydrants, curbs, etc. Backsight (BS): A level rod reading observed through the scope of an instrument on a point of known elevation or assumed elevation. Often termed a “plus sight” or “+ sight”. Height of Instrument (HI): The vertical distance from datum to the instrument line of sight. Foresight (FS): A level rod reading observed through the scope of an instrument on a point of unknown elevation. Often termed a “minus sight” or “- sight”. Leveling: Is the process of finding elevations of points or their differences in elevation. Vertical control: A series of benchmarks or other points of known elevation established throughout an area, also termed “basic control” or “level control”. The basic vertical control for the United States was derived from first and second-order leveling. Less precise third-order leveling has been used to fill gaps between second- order benchmarks, as well as for many other projects. 4.3 North American Vertical Datums (NGVD29 and NAVD88) Precise leveling operations to establish a distributed system of reference benchmarks throughout the United States began in the 1850s. This work was initially concentrated along the eastern seaboard, but in 1887 the U.S. Coast and Geodetic Survey (USC&GS) began its first transcontinental leveling across the country’s midsection. That project was completed in the early 1900s. By 1929, thousands of benchmarks had been set. In that year, the USC&GS began a general least squares adjustment of all leveling thus far completed in the United States and Canada. The adjustment involved over 100,000 km of leveling and incorporated long-term data from the 26 tidal gaging stations; hence, it was related to mean sea level. In fact, that network of - benchmarks with their resulting adjusted elevations defined the mean sea level datum. It was called the National Geodetic Vertical Datum of 1929 (NGVD29). Throughout the years after 1929, the NGVD29 deteriorated somewhat due to various causes including changes in sea level and shifting of the Earth’s crust. Also, more than 625,000 km of additional leveling was completed. To account for these changes and incorporate the additional leveling, the National Geodetic Survey (NGS) performed a new general readjustment. Work on this adjustment, began in 1978. Although - not finished until 1991, (planned completion date of 1988), it has been named the North American Vertical Datum of 1988 (NAVD88). Besides the United States and Canada, Mexico was also included in this general readjustment. This adjustment shifted the position of the reference surface from the mean of the 26 tidal gage stations to a single tidal gage benchmark known as Father Point/Rimouski, which is in Quebec, Canada, along the St. Lawrence Seaway. Thus, elevations in NAVD88 are no longer referenced to mean sea level. Benchmark elevations that were defined by the NGVD29 datum have changed by relatively small, but nevertheless significant amounts in the eastern half of the continental United States. However, the changes are much greater in the western part of the country and reach 1.5 m, (roughly 4.92 feet), it is therefore imperative that surveyors positively identify the datum to which their elevations are referenced. A good program to use to convert from NGVD29 to NAVD88, or from NAVD88 to NGVD29 is: http://www.ngs.noaa.gov/TOOLS/Vertcon/vertcon.html  The image to the left is a section of a B fiberglass level rod. Top of lines are even hundredths 7.48 -.... - - < Top of major tick lines are exactly a tenth of a foot This is what you would observe looking through the scope of the automatic level to obtain a rod reading. Depending on where the horizontal 7.46 crosshair of the instrument bisects the 7.44 -----'------- Smaller black numbers level rod would determine the rod are tenths of a foot reading observed. - 7.42 - - ----- 7.40 - - -------.- _.. 4 The red number indicates the “foot” portion of the rod reading. 7.29 ____- _... Next you would read the black number to obtain the tenth of a foot portion of the rod reading. 7.27 - - ------ 7.25 - - ---- - Last you would count the black hack 7.23 marks to determine the hundredth 7.21 Bottom of lines are - 2 portion of the rod reading. odd hundredths -I -.... / Large red numbers are whole feet Multiple examples of where the horizontal crosshair bisects the level rod are indicated to provide you with a variety of rod readings to practice with. More of this will be covered in the lab portion of this course to help you better understand how to read the level rod. -- J -.... " ~ 1 Top of large tick line next to red number is whole foot D 4.4 (a) Curvature (c) for Differential Leveling From the definitions of a level surface and a horizontal line, it is evident that the horizontal plane departs from a level surface because of curvature of the Earth. The deviation from a horizontal line due to curvature only is expressed by the following equations: c = 0.667(M)² (when the horizontal distance (HD) from the instrument to the level rod used in the equation is expressed in miles - M); Example: Horizontal distance from instrument to level rod = 1625-feet Initial reading on level rod = 10.51 feet What is the corrected rod reading? The value used in the equation for M would equal 1625/5280 = 0.307765152 miles c = 0.667(M)² c = (0.667)(0.307765152)² c = 0.06’ (answer rounded to 2nd decimal place) The departure of the level surface from the horizontal line (line of sight) due to curvature at 1625-feet would be 0.06’. Since this departure always results in reading the level rod too high the initial rod reading should be corrected by subtracting 0.06’ resulting in a “corrected rod reading”. The corrected rod reading would be: (10.51’) – (0.06’) = 10.45’ (answer) Line of si ht Level li ne 10.51’ 10.51' c 10.45’ 10.45 C I P1us sighrt M inus si ht e..,__ _...., 1625' ______..,____ _ _ D 1625’ c = 0.0239(F)² (when the horizontal distance (HD) from the instrument to the level rod used in the equation is expressed in 1000’s of feet - F); Example: Horizontal distance (HD) from instrument to level rod = 1625-feet Initial reading on level rod = 10.51 feet What is the corrected rod reading? The value used in the equation for F would equal 1625/1000 = 1.625 thousands of feet c = 0.0239(F)² c = (0.0239)(1.625)² c = 0.06’ (answer rounded to 2nd decimal place) The departure of the level surface from the horizontal line (line of sight) due to curvature at a horizontal distance of 1625-feet would be 0.06’. Since this departure always results in reading the level rod too high the initial rod reading should be corrected by subtracting 0.06’ resulting in a “corrected rod reading”. The corrected rod reading would be: (10.51’) – (0.06’) = 10.45’ (answer) Line, of s i ht Level li ne 10.51’ 10.51' c 10.45’ 10.45 P]us sighrt M inus si __ ht: e e2...,.._ _...., 1625' _ ____,...,...__ _ _ D 1625’ Cm = 0.0785(K)² (when the horizontal distance from the instrument to the level rod used in the equation is expressed in kilometers – K). Where the departure of a level surface from a horizontal line if Cf in feet or Cm in meters, M is the HD expressed as miles, F is the HD expressed in thousands of feet, and K is the HD in kilometers. Regardless if the rod reading is on a backsight observation or a foresight observation, the correction is always subtracted from the initial rod reading before additional calculations are conducted. The corrected rod readings are used for further calculations involving the leveling process 4.4 (b) Curvature and Refraction (c+r) for Differential Leveling Light rays passing through the Earth’s atmosphere are bent or refracted toward the Earth’s surface. The effects of refraction correct curvature slightly by 0.093(M)² = 0.0033(F)² for HDs measured in feet; Rm = 0.011(K)² for HDs in meters. The equation for the combined effects of curvature and refraction is: c+r = 0.574(M)² where 0.574 is a constant M is the distance in miles (1 mile = 5280’) Example: Horizontal distance (HD) from instrument to level rod = 1625-feet Initial reading on level rod = 10.51 feet What is the corrected rod reading? The value used in the equation for M would equal 1625/5280 = 0.307765152 miles c+r = 0.574(M)² c+r = (0.574)(0.307765152)² c+r = 0.05’ (answer rounded to 2nd decimal place) The departure of the level surface from the horizontal line (line of sight) due to curvature for a HD of 1625-feet would be 0.05’. Since this departure always results in reading the level rod too high the initial rod reading should be corrected by subtracting 0.05’ resulting in a “corrected rod reading”. The corrected rod reading would be: (10.51’) – (0.05’) = 10.46’ (answer) Line of si ht Level li ne 10.51’ c+r 10.46’ P1us sighrt M inus si.ht e e2...,..._ _ _ 1625’ 1625' - - -~ - - - - D Or when HD from instrument to level rod is given in feet, you can use this equation: c+r = 0.0206(F)² where 0.0206 is a constant F is the distance in 1000’s of feet Example: HD from instrument to level rod = 1625-feet Initial reading on level rod = 10.51 feet What is the corrected rod reading? The value used in the equation for “F” would equal 1625/1000 = 1.625 c+r = 0.0206(F)² c+r = (0.0206)(1.625)² c+r = 0.05’ (answer rounded to 2nd decimal place) The departure of the level surface from the horizontal line (line of sight) due to curvature for a HD of 1625-feet would be 0.05’. Since this departure always results in reading the level rod too high the initial rod reading should be corrected by subtracting 0.05’ resulting in a “corrected rod reading”. The corrected rod reading would be: (10.51’) – (0.05’) = 10.46’ (answer) Line of si ht Level li ne 10.51’ c+r 10.46’ P~us sighrt M inus si ht e e2 1625’ 1610’ As can be seen from these equations, using differential leveling, horizontal distances from the instrument to the level rod need to be large (roughly 700-feet or larger) for the correction to affect the rod reading. Fortunately, most levels run using differential methods have relatively short HDs to back sights and foresights rod readings. - The best way to eliminate the need to compute corrections for curvature and refraction is to make the HD from the instrument to the backsight rod reading roughly equal to the HD from the instrument to the foresight rod reading. (D1 roughly equals D2). Unless specifically instructed otherwise, you will always correct for curvature and refraction (c+r). Some problems ask you to only compute the correction for curvature, but in reality, you will always compute the correction for curvature and refraction, apply the correction obtained to determine “corrected rod readings” and use the “corrected rod readings” to determine the elevation of the HI (height of the instrument) and the elevation of foresighted objects (FS, or IFS). 4.5 Methods for Determining Differences in Elevation Differences in elevation have traditionally been determined by taping, differential leveling, barometric leveling, and indirectly by trigonometric leveling. A newer method involves measuring vertical distances electronically. 4.5.1 Measuring Vertical Distances by Taping or Electronic Methods Application of a tape to a vertical line between two points is sometimes possible. This method is used to measure depths of mine shafts, to determine floor elevations in condominium surveys, and in the layout and construction of multistory buildings, pipelines, etc. When water or sewer lines are being laid, a graduated pole or rod may replace the tape. In certain situations, especially on construction projects, reflectorless electronic distance measurement (EDM) devices are replacing the tape for measuring vertical distances on construction sites. 4.5.2 Differential Leveling This is the most commonly employed method of running levels. The basic procedure is that the instrument is set up and leveled within sight of a benchmark, (preferably with a published elevation), if not an assumed elevation can be used, and the loop adjusted later when tied to some datum if necessary. A level rod is placed on the benchmark and a back sight (BS) rod reading is taken looking through the instrument, (back sights with the exception of underground surveying where the control is in the roof), are plus sights (+). The rod is moved forward roughly the same distance away from the instrument as the distance to the back sight and a foresight (FS) rod reading is taken on a semi-permanent hard surface to be used as a turning point (TP), (foresights with the exception of underground surveying where the control is in the roof), are minus sights (-). Example: (for this example, assume that the horizontal distances (HD) between the instrument and the level rod are equal in length for the backsight (BS) rod readings and the foresight (FS) rod readings. This will negate the need to correct for curvature and refraction and simplifies the calculations for the height of instrument (HI) and the elevation of the turning point (TP). 1. Instrument is set up and leveled. 2. Level rod is placed on a benchmark (BM Rock) which has a published elevation of 1049.91 feet. 3. The backsight (BS) rod reading is 8.42 feet, (a plus sight) which is to be added to the elevation of the benchmark to obtain the height of the instrument (HI-1).  4. The height of the instrument (HI) is the elevation of the line of sight of the instrument wherever the center horizontal crosshair of the instrument intersects anything. 5. The rodman moves forward and places the rod on the turning point (TP1). 6. A foresight (FS) rod reading is taken of 1.20 feet, (a minus sight) which is subtracted from the height of the instrument to obtain the elevation on the turning point. BM + BS = HI 1049.91’ + 8.42’ = 1058.33’ (elevation of HI-1) HI – FS = Elevation on TP 1058.33’ – 1.20’ = 1057.13’ (elevation of TP1) -- -- - - -- BS= 8.42' HI-1 = 1058.33' BM Rock Elev. = 1049.91' Datum elev 0.00 This procedure is repeated to reach the job site where an elevation is established on some type of semi- permanent marker on or near the jobsite which is called a “temporary benchmark” (TBM). It is wise to set several TBM’s at/near the jobsite in case one is destroyed or disturbed. The procedure is repeated running from the job site, back sighting one of the temporary benchmarks, and carrying the elevations back to the original benchmark for a check. This is called closing the level loop. Without closing the level loop and completing this check, you have no way of knowing if you have an error in running your levels from the benchmark to the job site. Example Differential Level Notes This represents the lay-out for level note keeping that we will use for this course. There are a variety of level note keeping techniques, but for the most part they all have a similar format as what I will demonstrate with this type of note keeping. 1 2 3 4 5 6 Corrected Station BS (+) HI FS (-) IFS (-) Elevation Elevation Above each column label, I am writing the column number for instructional purposed only. You won’t write these numbers when you are labeling your column headings. The first column (1), labeled Station is for recording the name of the object that is being sighted on and will be on the same line as the elevation for the object sighted. The second column (2), labeled BS (+) for backsight, is where you would record the backsight rod reading in feet, tenths and hundredths of a foot. All three parts of the rod reading should be recorded. If the backsight rod reading is below the 1-foot mark, then a 0 should be recorded for the foot part of the backsight rod reading. Example backsight rod readings: 6.92’, 4.81’, 0.25’ The third column (3), labeled HI is for the calculation of the height of the instrument at that particular set-up. The HI is calculated by adding the backsight (BS) rod reading to the elevation of the benchmark (BM). The fourth column (4), labeled FS (-) for foresight, is where you would record the foresight rod reading, in feet, tenths and hundredths of a foot. Again, all three parts of the rod reading should be recorded. If the foresight rod reading is below the 1-foot mark, then a 0 should be recorded for the foot part of the foresight rod reading. Example foresight rod readings: 8.37’, 2.46’, 0.97’ The fifth column (5), labeled IFS (-) for intermediate foresight, is where you would record the intermediate foresight rod readings. Intermediate foresights (IFS) are taken on objects before foresights are observed on the foresight. When running a regular level loop, no intermediate foresights (IFS) are usually observed. For this example, level run problem, no information will be recorded in this column. Use of this column will be discussed in the next lecture. The sixth column (6), labeled Elevation is for the calculation of the objects that are sighted as foresights. To calculate the elevation, you subtract the foresight rod reading from the HI you just computed. The last column is for computing corrected elevations when the level loop doesn’t close with the precision required. Computing corrected elevations are not covered in this introductory course in surveying. No information will be written in this column for this course. We begin our note keeping by writing the description of the benchmark (the name it is called by) in the first column on line 1. For this example, BM A. Next, we need to know the elevation of the benchmark. Since it is considered a benchmark, somewhere there will be published information providing us with the value to begin our computations and level loop with. We find that the published information shows that the elevation for benchmark (BM A) is 2303.45’. We write this number under the elevation column on the same line as the description. I Station I BS (+) I HI I FS (-) I IFS (-) I Elevation I Corrected Elevation l _IBM AI I2303.45’_I We are now ready to begin running the level loop. The instrument is attached to the tripod and leveled using the bulls-eye bubble level. A member of our team would then place the bottom of the level rod on top of the benchmark (BM A). We would view the level rod through the scope of the instrument. Since this rod reading is on an object with a known elevation, it is considered a backsight (BS) rod reading. For this example, BS = 5.68’ HI-1 is then computed by adding the BS rod reading to the elevation for the BM A. 1111 - HI-1 = 5.68’ + 2303.45’ HI-1 = 2309.13’. ,.,,,,,,.. -- - - ----------------............... I Station I l // I BS (+) HI I FS (-) I IFS (-) I ', I Elevation \. Corrected Elevation I BM A J5.68’I.... ····► I2309.13’J 2303.45’ Next the rodperson would move ahead and select a hard surface to use as a turning point (TP). Since it is the first turning point, the description would be TP1. If none could be found, the rodperson could set a railroad spike in the ground and use the top of the spike as a turning point. Once a suitable turning point is established, the level rod is placed on the turning point. The instrument operator rotates the scope and focuses the crosshair and objective lens to obtain a clear sight on the level rod. Since this rod reading is on an object of unknown elevation, we are obtaining a foresight (FS) rod reading. FS on TP1 = 7.58’ The sight on the turning point is recorded in the foresight (FS) column. The elevation for TP1 is computed by subtracting the FS rod reading from HI-1. 1· ' Station - TP1 elevation = 2309.13’ – 7.58’ TP1 elevation = 2301.55’ BS (+) HI FS (-) J IFS (-) Elevation Corrected Elevation - BM A 5.68’ 2309.13’... J 2303.45’ - '... I TP1 _[J - l"..cJ. 7.58’ ----- ------ -- ----- ----- - -► 2301.55’ - - J - - I II The process in now repeated until we close the level loop. The instrument would then be moved forward, setup and releveled and a BS rod reading observed on TP1. BS = 9.42’ HI-2 is then computed by adding the BS rod reading to the elevation for the TP1. I' - HI-2 = 9.42’ + 2301.55’ HI-2 = 2310.97’. Station BS (+).,,.,.. -- - - HI - - - - FS (-) - 1 J -- IFS............... (-) Elevation Corrected Elevation - / ' BM A TP1 / 5.68’ 6 -- 9.42’ -~ -----► 2309.13’ 2310.97’ 7.58’ 1 J ,----- '" 2303.45’ 2301.55’ I - - -~ - ' ' I - 11 I I I J I I -11 - The rodperson would move forward and set TP2. The instrument would be rotated to observe the level rod on TP2, and a FS rod reading observed and recorded. FS = 5.81’ The elevation for TP2 is computed by subtracting the FS rod reading from HI-2. - TP2 elevation = 2310.97’ – 5.81’ TP2 elevation = 2305.16’ I Station I BS (+) I HI I FS (-) I IFS (-) I Elevation I Corrected Elevation I BM A 5.68’ 2309.13’ 2303.45’ TP1 9.42’ 2310.97’.... 7.58’ 2301.55’ nTP2 "' ' 7 ----- ----- -- ----- ----- -- ► 2305.16’l 5.81’ The instrument would then be moved forward, setup and releveled and a BS rod reading observed on TP2. BS = 9.26’ HI-3 is then computed by adding the BS rod reading to the elevation for the TP2. 1111 - HI-3 = 9.26’ + 2305.16’ HI-3 = 2314.42’. I Station I BS (+) I ,-- -- I -HI FS (-) I IFS (-) I -................... ~ Elevation I Corrected Elevation I BM A 5.68’ ,,,,. 2309.13’ 2303.45’ / TP1 TP2./ 9.42’ r1--7 9.26’ ____ 2310.97’ r -----► 2314.42’1 7.58’ 5.81’ ' ,. 2301.55’ \ I 2305.16’ The rodperson would move forward and set TP3. The instrument would be rotated to observe the level rod on TP3, and a FS rod reading observed and recorded. FS = 4.59’ The elevation for TP3 is computed by subtracting the FS rod reading from HI-3. - TP3 elevation = 2310.97’ – 4.59’ TP3 elevation = 2305.16’ Station BS (+) HI FS (-) IFS (-) Elevation Corrected Elevation BM A 5.68’ 2309.13’ 2303.45’ TP1 9.42’ 2310.97’ 7.58’ 2301.55’ TP2 9.26’ 2314.42’....__, 5.81’ 2305.16’ TP3 17 4.59’ ---- -------------------- -► 2309.83’I The instrument would then be moved forward, setup and releveled and a BS rod reading observed on TP3. BS = 6.45’ HI-4 is then computed by adding the BS rod reading to the elevation for the TP3. 1111 - HI-4 = 6.45’ + 2309.83’ HI-4 = 2316.28’. Station BS (+) HI FS (-) IFS (-) Elevation Corrected Elevation BM A TP1 5.68’ 9.42’ 7.,,,..,,,,,,,-- -- 2309.13’ 2310.97’ - - 7.58’ -................ 2303.45’ ;""'....2301.55’ TP2./ 9.26’ 2314.42’ 5.81’ '' 2305.16’ l TP3 6.45’ ---- ~ ----► I2316.28’I 4.59’ 2309.83’ The rodperson would move forward and set TP4. The instrument would be rotated to observe the level rod on TP3, and a FS rod reading observed and recorded. FS = 8.50’ The elevation for TP4 is computed by subtracting the FS rod reading from HI-4. I Station - TP4 elevation = 2316.28’ – 8.50’ TP4 elevation = 2307.78’ I I BS (+) HI I FS (-) I IFS (-) I Elevation I Corrected Elevation I BM A 5.68’ 2309.13’ 2303.45’ TP1 9.42’ 2310.97’ 7.58’ 2301.55’ TP2 9.26’ 2314.42’ 5.81’ 2305.16’ TP3 6.45’ 2316.28’....... 4.59’ 2309.83’....._ TP4 17 8.50’ ----- --- ----- -- ----- ---- ► I2307.78’I The instrument would then be moved forward, setup and releveled and a BS rod reading observed on TP4. BS = 9.59’ HI-5 is then computed by adding the BS rod reading to the elevation for the TP4. 1111 - HI-5 = 9.59’ + 2307.78’ HI-5 = 2317.37’. Station BS (+) HI FS (-) IFS (-) Elevation Corrected Elevation BM A 5.68’ 2309.13’ 2303.45’ TP1 TP2 9.42’ 9.26’ 7 ~ 2310.97’.,,,,,,....-- 2314.42’ -- 7.58’ 5.81’ -.............. i, 2301.55’ ~2305.16’ ~ TP3 / 6.45’ 2316.28’ 4.59’ ' 2309.83’ \. TP4 9.59’ ---- ~ ----► I2317.37’l 8.50’ 2307.78’ ' The rodperson would move forward and closes the level loop by placing the level rod on BM A. The instrument would be rotated to observe the level rod on BM A, and a FS rod reading observed and recorded. FS = 13.95’ The closing elevation on BM A is computed by subtracting the FS rod reading from HI-5. - ·1 Station I I BS (+) I I - Closing BM A elevation = 2317.37’ – 13.95’ Closing BM A elevation = 2303.42’ HI I I FS (-) II IFS (-) I I Elevation I I Corrected Elevation J BM A 5.68’ 2309.13’ 2303.45’ ~ -~ - I - - ~ TP1 -~ 9.42’ 2310.97’ -~ 7.58’ I - 2301.55’ ' TP2 9.26’ 2314.42’ 5.81’ I 2305.16’ - TP3..__ 6.45’ 2316.28’ 4.59’ - I -2309.83’ ~ TP4 - 9.59’ 2317.37’.,.._....,,._ 8.50’ 1 2307.78’ - - BM A r==J 13.95’ ----1.------------------- -► 2303.42’I I, I I I - The notes are not complete until the Page Check is done to ensure calculations are correct and the Misclosure of the level loop has been determined to see if accuracy requirements have been met. Corrected Station BS (+) HI FS (-) IFS (-) Elevation Elevation BM A 5.68’ 2309.13’ 2303.45’ TP1 9.42’ 2310.97’ 7.58’ 2301.55’ TP2 9.26’ 2314.42’ 5.81’ 2305.16’ TP3 6.45’ 2316.28’ 4.59’ 2309.83’ TP4 9.59’ 2317.37’ 8.50’ 2307.78’ BM A 13.95’ - -► 2303.42’ +40.40’ -40.43’ Sum the backsight column, then sum the foresight column. Page Check BM + (sum of BSs) + (sum of FSs) = ending elevation (2303.45’) + (+40.40’) + (-40.43’) = 2303.42’ Misclosure = (closing BM elevation) – (published BM elevation) = (2303.42’) – (2303.45’) = -0.03’