Fundamental Surveying: Unit 4 Leveling PDF

**FUNDAMENTAL SURVEYING** **UNIT 4: LEVELING** ***Vertical Distance*** is the distance that is perpendicular to the ground or earth surface. *It is measured along the vertical axis to determine the difference in elevations between two points* ***Leveling*** is the process of directly or indirect...

**FUNDAMENTAL SURVEYING** **UNIT 4: LEVELING** ***Vertical Distance*** is the distance that is perpendicular to the ground or earth surface. *It is measured along the vertical axis to determine the difference in elevations between two points* ***Leveling*** is the process of directly or indirectly measuring vertical distances to determine the elevation points or their difference in elevations ***Level*** is basically a telescope attached to an accurate leveling device, set upon a tripod so that it can rotate horizontally in a full-circle basis. *Leveling device a bubble, however, in the insurgence of modern types of level, pendulums are used.* ***Dumpy Level, Automatic Level,*** and ***Tilting level*** are the three basic types of level ***Leveling Rod*** is a graduated rod in which vertical distance is measured **Level Surface** It is a curved surface in which any point on it is *perpendicular to the direction of the gravity or the plumb line.* It is [best represented by the surface of a large body of still water]. **Level Line** It is a curved line in a level surface in which all of its points are *normal to the direction of gravity and equidistant from the center of the Earth.* **Horizontal Surface** It is a plane that is tangent to a level surface at a particular point. It should be noted that the [horizontal surface is perpendicular to the plumb line at the same point]. **Horizontal Line** It is a straight line on a horizontal plane that is tangent to a level line at one point. In simplistic approach, this line is [perpendicular to the direction of the gravity at the point of tangency] (of this line to the level line). It should be noted that the lengths of a level line and a horizontal line are the same in short distances. **Vertical Line** It is a line parallel to the direction of the gravity. It can be [represented as the direction taken by a string supporting a suspended plumb bib passing through a point]. It should be noted that a plumb line passing at any point on its surface is always directed towards the center of the Earth (which is assumed to be true sphere). **Mean Sea Level** It is an imaginary surface of the sea which is midway between the high and low tides. It is taken as the [reference surface to which most ground elevations are referred]. This surface is considered to be at zero-elevation and is perpendicular to the direction of a particular area is referred from. **Datum** It is a level surface that is coincident or parallel with the mean sea level or any selected datum. **Elevation** It is the vertical distance, above or below the mean sea level or any selected datum. **Difference in Elevation (between two points)** It is the vertical distance between two level surfaces in which the points lie. **TYPES OF LEVELING** 1. **Direct Leveling** It is the most common employed method of leveling. In here, [the elevations of points some distance apart are determined directly *by conducting a series of setups of the leveling instrument along a selected route*]. This type of leveling is also called *spirit leveling*. 2. **Trigonometric Leveling** It is a leveling method in which the elevations of a point or the difference in elevation between points are measured indirectly -- *using trigonometric computations.* 3. **Barometric Leveling** It involves the determination of differences in elevation between points by measuring the variation in atmospheric pressure at each point by means of barometer. This leveling method applies the principle that *differences in elevations are proportional to the differences in atmospheric pressures.* 4. **Stadia Leveling** It is a modified trigonometric leveling wherein a stadia instrument is used. The instrument allows measurement of horizontal or inclined distances by the *application of tacheometry or optical geometrical*. **DETERMINATION OF ELEVATIONS OF POINTS BY DIFFERENTIAL LEVELING** **Differential Leveling** is one of the most common methods of leveling. It is a process of determining the elevations between two or more points which are some distance apart. - **Bench Mark -** It is a fixed point of reference whose elevations is either known or assumed. In most practices, a leveling operation [usually starts on this point since the elevation is known or given]. - **Backsight -** It is a reading taken on a rod held on a point of known or assumed elevation. It is a [measure of vertical distance from the established line of sight] to the point sighted and is always the first rod reading taken after the instrument has been set up and leveled. In simplistic approach, it is a reading on the rod by the leveling instrument which is *opposite to the direction of the survey.* - **Foresight -** It is a reading taken on a point whose elevation is to be determined. It is the opposite of backsight -- a [reading on the rod by the leveling instrument which is in the *direction of the survey*]. - **Backsight Distance -** It is the horizontal distance from the center of the instrument to the rod on which a backsight is taken. - **Foresight Distance -** It is the horizontal distance from the center of the instrument to the rod on which is taken. Is [usually made nearly equal to its corresponding backsight distance.] - **Turning Point -** It is an intervening point between two benchmarks upon which the foresight and backsight rod readings on this point are taken to [enable a leveling operation to continue from a new instrument position]. It is sometimes called as *change point.* - **Height of Instrument -** It is sometimes referred as the *height if collimation.* It is the elevation of the line of sight of an instrument above or below a selected reference datum. **TWO-PEG TEST** - [All instruments are subjected to errors ] One of the main errors in leveling instrument is [when the line of sight is not parallel to the line of collimation]. **Line of Collimation --** is the line joining the intersection of the cross-hairs to the optical center of the objective and its continuation. **Two-peg Test --** Applies the concept of ratio and proportion in determining the error propagation in the rod readings. It should be noted that the error is directly proportional to the distance of the leveling instrument to the rod being sighted. - This test can also [determine the correction needed to make the line of sight horizonta]l. **UNIT 5: TACHEOMETRIC SURVEYS** **Tacheometry --** Is the procedure of obtaining horizontal distances and differences in elevation between points using the optical geometry of the instrument employed. - This method uses the subtended intervals and angles observed with an instrument. - Two of the most common tacheometric methods are the ***[stadia method]*** and the ***[subtense bar method.]*** **Stadia Method --** The word *stadia* comes from the Greek word for a **unit of length** originally applied in measuring distances for athletic contests. - It is equivalent to 600 Greek units or 184 m and 93 cm (606 ft and 9 in). - Is [commonly associated with the cross hairs and rod used in making measurements]. - Equipment used for stadia [are two horizontal hairs] called *cross hairs* and a [graduated rod] called a *stadia rod.* F = focal length of the lens F1 = images distance or length from the center of the objective lens to the plane of the cross wires when the telescope is focused on some definite points F2 = object distance or length from the center of the objective lens to a definite point when the telescope is focused on that point i = distance or spacing between stadia hairs c = distance from the center of the instrument to the center of the objective lens C = distance from the center of the instrument to principal focus D = distance from the focal point in front of the telescope to the face of the rod D = distance from the center of the instrument to the face of the rod s = stadia or rod intercept, the difference between the upper stadia hair reading and the lower stadia reading **Stadia Method for Horizontal and Inclined Sights** - For **horizontal sights**, the [line of sight of the telescope employed is assumed to be level or horizontal]. - For **inclined sights**, the [line of sight of the telescope used is assumed to be tilting at a certain angle from the horizontal]. **Subtense Bar Method** - Is a procedure in measuring horizontal distances which involves the use of theodolite to read the horizontal angle subtended by two targets precisely spaced at a fixed distance apart on a subtense bar. - The unknown distance is computed through trigonometric relations. - This procedure uses a bar, which is precisely *two meters long.* - The principle of subtense bar method explained by [applying simple trigonometric calculations] **Effect of Earth's curvature and Refraction** - Errors can be observed especially when dealing with horizontal distances - The effect of earth's curvature is the amount by which the horizontal line departs from the earth surface which is a level surface. - Errors can be observed due to refraction.