PART IV LEVELING A. Importance of Leveling The determination of elevations with a surveying instrument, which is known as leveling, is a relatively simple but extraordinarily important process. B. Definitions 1. Vertical line; a line parallel to the direction of gravity. At a particular point it is the direction assumed by a plumb bob string if the plumb -bob is allowed to swing freely. 2. Level surface; a surface of constant elevation, 3. Elevation of a particular point is the vertical distance above or below a reference level surface (normally sea level ) to the point in question. 4. Level Line; a curved line in a level surface a11 points of which are of equal surface elevation. 5. Horizontal Line; a straight line tangent to a level line at one point. 46
C. Methods of Leveling 1) Spirit 1eveling; vertical distances are measured in relation to a horizontal line and these values are used to compute the differences in elevations between various points. 2) Trigonometric leveling; leveling in which horizontal distances and vertical angles are measured and use to compute elevation differences. 3) Barometric 1eveling involves the determination of elevations by measuring air pressures. 4) GPS leveling involves positioning from signals processed from simultaneous readings on multiple satellites. D. Levels 1. Wye Level This level has its telescope supported in wye-shaped supports and is held in place by curved clips. The telescope for the wye-level can actually be removed and turned end for end for adjustment purposes. It also has an erecting eyepiece. 2. Dumpy Level Originally the dumpy level had an inverting eyepiece and as a result it was shorter (thus the name dumpy) than a wye level with the same magnification power. The dumpy level has fewer movable parts than does the wye-level and as a result it has fewer parts to become worn or get out of adjustment. 3. Tilting Level A tilting level is one whose telescope can be tilted or rotated about its horizontal axis. The instrument can be quickly and approximately leveled by means of a bull s eye or circular type level and the telescope is moved through a small vertical angle by means of a tilting knob until the telescope is level. Utilizes the "split bubble principle, where the two halves of a bubble (one a mirrored image) are made to coincide, in order to level the instrument. E. Differential Leveling 47
Self-leveling Level This instrument is leveled in the usual manner, but the level itself automatically does the fine-leveling. 3. Builder's Level This level, sometimes called an architect's or construction level, is less expensive than the usual level. Its bubble tube is less sensitive and its telescope has less magnification power. In addition, it has a horizontal scale for measuring angles. 1. Theory o f Spirit Leveling Procedure: Procedure: a) Set-up and carefully level instrument. b) Sight on the level rod held by the roadman on some point of known elevation (this sight is called a backsight, or BS). c) Add the backsight reading to the elevation of the known point, this value is the height of the instrument, or HI, that IS, the elevation of the line of sight of the telescope. EXAMPLE: HI = Elevation + BS = 100.0 + 6.320 = 106.320 m 48
d) Once HI is known, the telescope may be used to determine the elevation of other points in the vicinity by placing the level rod on same point whose elevation is desired and by taking a reading on the rod. Since the elevation of the point where the line of sight of the telescope intersects the rod is known (the H I ), the rod reading called a foresight (FS) may be subtracted from the HI in order to obtain the elevation of the point in question. e) The level may be moved t o another area by using temporary points called turning points (TPs). The telescope is sighted on the rod held at a convenient turning point. Then the level can be moved beyond the TP and set up a t a convenient location. A backsight is taken on the rod held at the turning point and the HI for the new locations is established. This process can be repeated over and over for long distances. 2. Definitions a) Bench mark (BM) is a relatively permanent point o f Known elevation. It should be easily recognized and found and should been fairly low in relation to the surrounding ground. It may be a concrete monument in the ground, a curb, the top of a fire hydrant, or a similar object that is not likely to move. Especially careful record should be made of bench marks because of their frequent use. b) Turning Point (TP) is a temporary point whose elevation is determined during the process of leveling. It may be any convenient point on the ground, but it is usually wise to use a readily identifiable point such as a rock, a stake driven in t o the ground, a mark on the pavement, so that the level rod can be removed and put back in the same location as many times as required. c) Backsight (BS) is a sight taken to the level rod held on a point of known elevation (either a BM or a TP) t o determine the height of the instrument ( HI ). Backsights are also frequently referred to as plus sights because they are added to the elevations of points being sighted on to determine the height of the instrument. d ) Foresight (FS) is a sight taken to any point to determine its elevation. Foresights are often called minus sights because they are subtracted from HI's to obtain the elevations 49
points. Notice for any position of the instrument where the HI is known, any number of foresights may be taken to obtain elevations of other points (intermediate foresights) in the area. The only limitations on the number of sights are the length of the level rod and the power of the scope on the level. 3. List of Common Errors Made in Leveling a) Misreading rod. b) Moving turning points. c ) Field note mistakes. d) Mistakes with using an extended rod (poor joint i.e. a gap between the two parts o f the rod). e ) Level rod not level. This can be rectified by waving the rod forward and backward over a small arc distance in the direction of the instrument. f) Settling of level rod. g) Incorrect rod length. h) Mud, snow, or ice accumulation on base o f rod. i) BS and FS distance not equal. BS distance MUST EQUAL FS distance in order to cancel the effects of the earth's curvature. BS & FS distances should not exceed 60 meters. j) Bubble not centered on level. k) Settling o f instrument. 1 ) Instrument out of adjustment. m) Improper focusing o f telescope (Parallax). If a person looks a t the speedometer o f a car from different angles, he wil1 read different values. This phenomenon is known as PARALLAX. Focusing the image and the cross-hairs on the same plane until they do not move in relation to each other when the eye is moved back and forth will eliminate parallax. n) Wind and heat waves. 50
4. Differential Leveling (Schematic) Note: Numbers have been rounded off to the nearest hundredth for illustration purposes only. 51
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5. Form of Differential Level Notes Left hand page Right hand page Note that all information dealing with one B.M. or one T.P. appears on one line in the notes. A single line in the notes does not record the B.S. and F.S. for a single instrument set-up. The difference between BS and FS gives the difference in elevation. If B.S. > B.S. we have moved up. If B.S. < F.S. we have moved down. The check, B.S. - F.S. = Difference in elevation must always be applied to check for arithmetic errors in the notes. H. Two Peg Test The two peg test for levels is performed to ensure that the level is in proper adjustment. Procedure 1. Choose a site where a line of sight equal t o - 60 meters can be established, locate a hub at each end. 2. With the level set up in the middle, sight on the level rod placed on each hub and record the readings as A and B in the field book (see sketch below). 3. Subtract A from B = X 53
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4. Setup level adjacent to point A [approximately 5 ft., or the minimum focal distance away). Sight on the level rod placed on each hub and record the readings as A ' and Bf in the field book. 5. Subtract A' from B' = Y. 6. If X = Y within tolerable limits then the level is in adjustment. EXAMPLE - Field Notes Two-Peg Test 0.200-0.180. level slightly out of adjustment, but tolerable for rough work. Any errors arising due t o the level being out of adjustment can be completely eliminated if 0.5. and F.S. distances are always made equal. Also for the example shown, we can calculate the slope of the line of sight as =. This correction can t be applied to the readings where the B.S. and F.S. distances are not equal. (Note: Line of sight slopes slightly upward in this example). If level is grossly out of adjustment, have a qualified person adjust it. 55
PROBLEMS 1. Complete the following level notes: 2. To produce an error of 1.0 mm in the reading, a 3 meter rod must to out of plumb by. 3. A level is set up 100 m from B.M.l having an elevation of 38.166 m. A foresight is taken on T,P,1 also 100 m from the level. The level adjustment previously checked determined that the line of sight pitches downwards at a rate of 0.8 m/100 m. The level man forgets to center the bubble on the foresight reading. What is the correct elevation of T.P.1? 4. In a two-peg test, the rod reading on A(2 m away) is 4.100 and on B (100 m distant) is 4.200. A is actually 0.300 ft. lower than B. The line of sight: a) slopes up b) slopes down c) is level d ) is horizontal e) has a slope which cannot be determined from the data. 56