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CH. 3 LEVELING 4/15/03
Read Kavanagh Ch. 3: 3.1 Know these definitions (not verbatum) 3.2-3.3 Understand the divergence between a horizontal line and a level line, and the proportionality of error due to curvature and refractionwith distance of the shot. 3.4 Skim read, except read 3.4.2 Level Tube. Understand the relationship between the optical quality and precision of the level, and the radius of curvature of the level tube. 3.5 Skip. 3.6Know what a compensator does, and conceptually how it works. 3.7-3.8 Skim read. Become generally familiar with what a digital level is, and what a bar code is, and how they work. 3.9-3.10 Skim read. 3.11 Know what these terms mean. 3.12 Understand differential leveling procedure 3.13 Skim read for Field Exercise. Know how to hold a rod, and “rocking” (waving) the rod. Know how to read the rocking rod. Understand field notes for leveling 3.14 Skim read. 3.15 Skim read. Understand Table A.11 3.16 Differentiate between plan, profile, and cross-section views. Understand Fig. 3.22. Understand profile and cross-section field note formats. 3.17-3.20 Skip. 3.21 Understand the concepts of allowable error and adjusting a level loop. 3.22-3.24 Read for Field Exercise.
3.1 Definitions Leveling = a procedure used to determine elevations of points or differences in elevation between points Elevation = vertical distance above or below a reference datum. Datums Mean sea level = a universally employed reference datum. National Geodetic Vertical Datum (NGVD) of 1929. North American Vertical Datum (NAVD 88). MOST AREAS USE MEAN SEA LEVEL AS THEIR DATUM, either NGVD 29 or NAVD 88
VERTICAL DATUMS • MEAN SEA LEVEL DATUM OF 1929 • NATIONAL GEODETIC VERTICAL DATUM OF 1929 • (As of July 2, 1973) • NORTH AMERICAN VERTICAL DATUM OF 1988 • (As of June 24, 1993)
COMPARISON OF VERTICAL DATUM ELEMENTS • NGVD 29NAVD 88 • DATUM DEFINITION 26 TIDE GAUGES FATHER’S POINT/RIMOUSKI • IN THE U.S. & CANADA QUEBEC, CANADA • BENCH MARKS 100,000 450,000 • LEVELING (Km) 102,724 1,001,500 • GEOID FITTING Distorted to Fit MSL Gauges Best Continental Model
Benchmark (BM) = a reference mark whose elevation is known relative to a given datum. Backsight = a point which is to be used to determine the elevation and/or angular orientation of the surveying instrument Foresight = a point to which an instrument sighting is made for measuring or establishing its elevation and/or its horizontal position Turning Point = a temporary point whose elevation is determined during the process of leveling; used to establish the Height of Instrument Height of Instrument = in leveling, the height of the line of sight of the leveling instrument above the adopted datum; in horizontal angle measurement, the height of the center of the telescope (horizontal axis) above the ground or station mark.
Notes on How To Perform Differential Leveling • Level the instrument by centering the bullseye level • Focus two things: 1) cross-hairs; 2) object; to avoid parallaxerror • Rodperson starts at backsight (pt. of known elev.), rocks rod or uses level rod bubble • Field notes (see example). Note that sums of BS and FS should equal. • Rodperson: choose turning points for reproducibility • Avoid collimation error by making backsights and foresights the same length
3.3 Common Methods of Leveling There are 2 common methods of leveling: • Direct Differential Leveling (Spirit Leveling)= usual method of determining elevation differences. Uses a spirit level and a rod, or a digital level and rod. The instrument does not tilt; you set it up so the line of sight is in the horizontal plane. • Trigonometric leveling = horizontal and vertical distances are measured to compute elevation differences. Good for inaccessible points e.g. mountain tops, offshore construction, etc. (Nowadays when large distances are involved, GPS is commonly used instead of trigonometric leveling.)
3.4 Instruments Commonly Used for Leveling Dumpy Level = in common use up to the last few decades. Some contractors still use them. Called “dumpy” because optical system allowed them to be shorter than previous levels (for the same magnifying power). Main components: telescope,leveling tube,leveling head.
Automatic or Self-Leveling Levels = modern types most commonly used nowadays. Automatic levels have bullseye level to get instrument approximately level. The instrument then sets itself level. It has a swinging prism or mirror compensator which maintains a horizontal line of sight by allowing only the horizontal rays coming into the instrument to pass through the optical center of the instrument. Good instruments to use because they can maintain level even if the instrument is jiggled around a little. Cautions when using automatic levels:1) the compensator is hung by fine wires that easily break with rough handling; 2) the compensator can occasionally get hung up. Tap the end of the telescope or turn one of the leveling screws slightly. The cross hairs should appear to deflect momentarily before returning to its original rod reading.
Tilting Level (Can be used for precision work, or use automatic levels)
Laser Level = commonly used by contractors for grading, setting forms, etc. Two types: 1) fixed single laser; 2) rotating laser. The rotating laser provides a level plane from which particular distances can be measured. Good < 1000 ft.
Transits and theodolites may be used in lieu of a level, but give poor results. Total stations give comparatively better results, but are not generally as accurate for levelling as automatic levels, and should generally not be used for vertical control of construction projects, or where 3rd order or better accuracy is needed.
3.5 The Telescope High-powered telescope (20x to 45x power) with a spirit bubble tube attached.
Main parts of the telescope: 1) Positive objective lens = forms an image of the object sighted. The image would be formed ahead of the cross hairs. 2) Negative focusing lens = diverges the light rays to bring them into focus on the cross hairs. 3) Reticle = glass with the cross hairs on it. 4) Eyepiece = actually a microscope to enlarge the image from the reticle. Focusing the eyepiece, e.g. focusing the cross-hairs, changes the distance between it and the cross hairs (twist the eyepiece to focus). 5) Hanging prisms = swings on wires to keep line of sight level
3.6 Level Bubble The accuracy of any survey instrument is generally most affected by the alignment (or misalignment) of the level bubble. Sensitivity% f ( radius of curvature) = angle of tilt / one division of scale on glass But the larger the radius of curvature, the more difficult it is to level!
Example: If it takes 20" of arc to move the bubble by 2 mm then the radius of curvature is: For first order leveling, the instruments have 2" bubbles (2" of arc to move the bubble 2 mm) with "680 ft radius. Two types of level bubbles: 1) tube; and 2) bullseye. Sensitivity principle = same for both.
3.7 Sighting Through the Telescope Inaccurate sightings occur if the cross-hairs and the scope are not properly focused. This is due to the problem of parallax. Parallax = the apparent displacement of the position of the point being sighted occurring when moving the eye up or down while looking through the telescope Proper procedure to avoid parallax: 1) Focus the cross-hairs on the eyepiece. Hold a paper about six inches in front of the lens so that it appears fuzzy, and twist the eyepiece until the cross-hairs come into focus 2) Sight the intended rod or object. (Use the pointing system on top of the barrel to help locate the rod or object). Focus on the rod or object. 3) Check for parallax by moving the eye up and down or sideways while watching the rod. If the cross hairs appear to move with respect to the image sighted, then either the cross-hairs or object are not properly focused.
3.8 Correction for Inclined Line of Sight (“Collimation Error”) If instrument is not quite level but distance D is same for both BS and FS, then the errors cancel.
3.9 Common Leveling Mistakes (Blunders) 1) Misreading rod 2) Moving turning point 3) Field not mistakes 4) Rod not fully extended 5) Forgot to level the instrument
3.10 Common Leveling Errors 1) Level rod not vertical 2) Settling of level rod on turning point 3) Mud, snow or ice buildup on bottom of rod 4) Rod damaged 5) Incorrect rod length (same as incorrect tape length) 6) BS & FS distances not equal (collimation error) 7) Bubble not centered / compensator not swinging free 8) Settling of level legs (tripod) 9) Instrument out of adjustment 10) Improper focusing of instrument (parallax error) 11) Heat waves 12) Wind or vibration causing instrument movement 13) Bumping into tripod
3.11 Corrections: Curvature and Refraction Curvature error, c = the divergence between a level line and a horizontal line over a specified distance c = 0.667K2 c in ft, K is dist. In miles Rays of light are refracted downward under normal P,T conditions. Thus, line of sight is bent downward, and curvature effect on error is reduced. Under normal atmospheric conditions, refraction error is . 1/7th curvature error. (c+r) = 0.574K2 = 0.0206M2 M in thousands of feet
3.12 Level Loop Adjustments Application: when you close a level loop and find your closing elevation for the benchmark to be different than your initial value. Use judgment. If you suspect that some points are weaker than others (either foresights or backsights) apportion more error to those weak points rather than other, stronger points. Examples of weaker shots: 1) long distance shots; 2) heat waves; 3) poorly defined turning point; 4) instrument settling 5) reading high up on extended rod (on hill)
3.12 Tides Tidal datums are used to: 1) establish property lines at tidal lands 2) estimate coastal flood elevations Types of tides (References 37; examples Ref. 38, 41) Tidal terms and definitions (Ref. 42) Local relationships between tides and common datums varies (Ref. 43)