LEVELING. Definitions

Transcription

1 Definitions An elevation of a point : The vertical distance between the point and the reference level surface ( datum ),the most commonly used datum is the mean sea level (MSL ). Leveling : The process by which the elevation of a point above or bellow the reference level surface or the elevation difference between points is determined Bench Mark (BM) : well marked points whose elevation has been accurately measured. Level line: a line perpendicular to the direction of gravity at all points.

2 Level surface: A level surface is the equipotential surface of the earth s gravity field. It is a curved surface and every element of which is normal to the plumb line. Types of leveling: Barometric leveling: performed by measuring the atmospheric pressure using barometer. Trigonometric leveling: by measuring the horizontal or slope distance between points and the vertical angle. Differential leveling: by using a level.

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4 A level in proper adjustment, and correctly set up, produces a horizontal line of sight. The line of sight follows a constant height above mean sea level and hence is a curved line. Over short distances the two lines can be taken to coincide. Over long distances a correction is required to reduce the staff readings given by the horizontal line of sight to the level line equivalent. Refraction of the line of sight is also to be taken into account.

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6 Ccr = the correction for the curvature and refraction, d = the distance of the staff from the point of tangency, and R = the mean earth s radius. For the value of R = 6370 km and d in kilometre, the value of Ccr in metre is given as Ccr = d2

7 Differential leveling Mainly used for determining the reduced level (RL) for a large number of points such as the center line of highway, or an area to produce a contour plan Definitions: Back sight ( BS ): The first reading taken at every instrument station. Intermediate sight ( IS ): Any reading taken at an instrument station between BS & FS Foresight ( FS ): The last reading taken at every instrument station. Change or Turning point ( TP ): A point at which both BS & FS are taken before moving the staff. Station: A station is the point where the leveling staff is held Height of instrument (H.I.) or height of collimation: For any set up of the level, the elevation of the line of sight is the height of instrument. Reduced level (R.L.): Reduced level of a point is its height or depth above or below the assumed datum. It is the elevation of the point.

8 Calculations The height of Instrument (collimation ) method Height of instrument (HI)= Elevation of A + staff reading at A Elevation of B ( RL ) = HI staff reading at B The Rise and Fall method Elevation Difference = first reading at A second reading at B Elevation of B ( RL ) = elevation of A + Rise or Fall

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11 The Height of Instrument ( HI ) method:

12 Checks: # of BS reading = # of FS reading = 2 BS - FS= RL last point RL first point( = =1.219) 3- ( # of readings = 9 ) = (# of points) + (# of TP) = Sum of all RL excluding the first reduced level = sum of the HI for each setup multiplied by the number of IS and FS readings taken from that setup - sum of IS - sum of FS = ( = ) ( IS=7.595) ( FS =2.231) =

13 The rise and Fall method:

14 Checks: # of BS = # of FS = 2 ( # of readings = 9 ) = ( # of points = 8 ) + ( # of TP = 1 ) 3- ( BS - FS) = ( ) = = ( R - F) = ( ) = = ( RL last - RL1st ) = ( ) = 1.219

15 Special cases in leveling: Reciprocal surveying Negative readings Water bodies

16 Reciprocal leveling: It is used to determine the correct difference of level between two points which are far and where it is not possible to set up the instrument between the two points for balancing the sights. The difference of level between A and B is given by:

17 The allowable closure error in differential leveling is normally given in the form: ε = ± x K mm where: K Is the total leveled distance in kilometers. x = from 10 to 30 for ordinary leveling x = from 2 to 5 for precise leveling

18 Errors in differential leveling: Systematic errors: Inclination of the line of sight

19 BC = line of sight refraction from horizontal BD = error due to earth s curvature CD = Actual error in the staff reading = L² Where CD is in meter & L is in km

20 Errors in adjustment of the level collimation: H = m n =(a- ε1) (b- ε2) =( a b ) tanα (L1 L2) If L1 = L2 ( BS distance = FS) H = ( a b )

21 Random errors Blunders Closure errors: Closure correction for hi = (- ni / ni ) ( ε ) Corrected hi = measured hi + closure correction for hi ε (closure error) = h ( calculated elevation ) h ( known elevation ) ni refers to the number of level setups hi refers to the elevation difference between consecutive stations.

22 Level error:

23 Examples:

24 The distance between points X, and Y was measured to be 67 m. If the Level was at the midpoint between these two points and the reading on the leveling staff at point X was 1.37m and the reading at point Y was 3.17m. If the level was moved to point X where it was 1.52m above that point and the reading on the leveling staff at point Y was 3.41m. If the same level was used to determine the elevation of points (A, B, C, D, and E) Complete the following table:

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