# Leveling, cont - University of Washington Leveling Levelinglecture lecture1: 1: Readings: Readings:4-1 4-1through through4-4, 4-4,4-5.2, 4-5.2,4-6 4-6through through4-12, 4-12,4-14 4-14 Lecture Lecture2:

2: Readings: Readings:5-1 5-1through through5-5, 5-5,5-8 5-8 Leveling {Differential Leveling} Lecture Outline

Definitions Datum Vials Levels: optical, laser, digital Rods Differential Leveling A leveling Loop What is the idea?? Compute the elevation of point B if the elevation of point A was 100.00 ft.

4.12 ft 100 ft 6.24 ft DATUM ELEVATION = 0.0 (MSL) Elevation B = 100 + 4.12 - 6.24= 97.88 ft What is the idea?? Compute the elevation of point B if the elevation of point A was 100.00 ft. 4.12 ft

6.24 ft Elevation B = 100+4.12-6.24= 97.88 Definitions Vertical Line: a line that follows the direction of gravity Level Surface: A curved surface perpendicular to the

direction of gravity at every point on it Level Line: a line that is perpendicular to the direction of gravity at every point on it, contained in a level surface and is a curved line. Horizontal Plane: a plane that is perpendicular to gravity at one point, a flat surface. Horizontal Line: a straight line perpendicular to the direction of gravity at one point

Vertical Datum: A level surface to which elevations are referred, for example: MSL. Elevation: the vertical distance from a vertical datum to a point or an object. Mean sea level (MSL): average height of the surface of the sea for all stages of the tide over a 19-year period. Benchmarks (BM): A relatively permanent artificial or natural object having a point of known elevation. Leveling: the process of finding elevations of points, or their elevation differences. North American Vertical Datum

Started in 1850s, first phase completed in 1929 Thousands of Points across the US and Canada were related to MSL and adjusted, the newly defined MSL defined a new datum called: National Geodetic Vertical Datum of 1929, or (NGVD 29) Due to the earths crust shifting and changes in MSL, new adjustment was done and more points were added (total of 1.3 million) which resulted in NAVD88 Shifts are larger in the west: 1.5m in the Rocky mountain

area MUST MENTION WHICH DATUM Level vials Tube level Other level vials Coincidence-Type level Bulls-eye level Levels

Major types: Tilting levels: the coincidence level must be adjusted before each reading, the telescope can be tilted by one screw. Very accurate. See figure 4-11 page 88 Automatic levels: use an automatic compensator to level the line of sight. The compensator is a group of prisms suspended by wires as a pendulum. Accuracy varies. Can include a parallel plate micrometer to measure to 1/100 mm. Automatic Compensator in an

automatic Level: Automatic Precise level Laser Levels Transmit laser beams, received on a detector. Create a horizontal or a vertical plane. May stop if not horizontal. More than one detector can be used simultaneously. Digital Levels

Employ digital image processing. A micro computer compares the image of the rod to a pre-stored image of the rod to compute the reading. Rod is bar coded. Rods Graded in feet or meters. Made of wood, metal or fiber

glass. Philadelphia: graded to 0.01 ft. Two pieces of 13 ft length. Pay attention when the rod is telescopic. Metric is graded to 1 cm, and decimeters. Dots for meters. A sliding micrometer can be used. Rod Remarks Before observing, understand the rod.

Where the zero is and how it is graded. Try a certain reading without a level. Pay attention if the telescope inverts the vision. Elevation computation: Compute the elevation of point B if the elevation of point A was 100.00 ft. 4.12 ft 6.24 ft Elevation B = 100+4.12-6.24= 97.88 Differential Leveling

Definition of Backsight (BS), and Foresight (FS) Elevation of line of sight (HI)= BM elevation + BS at BM Elevation of point X = HI - FS at X Consider X a new BM, and repeat for another point , etc.. Backsight (BS) at BM Foresight (FS) at X Elevation of point B = Elevation of point A + backsight at A - foresight at B A Leveling Loop WHY???????

Elevation of Final Point = BM elevation + (BS) - (FS) Errors in Differential Leveling Minimizing the errors: ElevationX = EBM + BSBM - FSX EX, with errors e1& e2 = EBM + (BSBM - e1)- (FSX e2) = EBM + (BSBM FSX) (e1 e2) When is the error not effective? The final computation of misclosure Adjustment of a Loop

Not the method in the text book. Errors are proportional to the distance, so are the corrections. Three wires leveling: The distance between the rod and the level for a reading (i) = di = 100 (U-L)

Elevation of Final Point = BM elevation + (BS) (FS), then: The difference in elevation between the first and last point = (BS) - (FS). What if you started and ended at the same point? Get the misclosure.

Compute the sums of: BS, FS, dFS, dBS, total (d). Correction per unit length= misclosure/ total (d) = C. Correction for each reading (i) = di * C = Ci. Add or subtract (Ci ) from each reading to compute the corrected reading. Compute the adjusted elevation of the desired points only. 900 Example

TP1 TP2 Considering the readings in the following table, compute the adjusted elevations of points TP1 and TP2. Elevation of point 900 is 900 ft. Point BS Dist 900 2.10 100

0.80 70 TP1 3.60 100 2.70 100 TP2

3.10 70 4.50 100 270 8.00 270 Sum 8.80

Corr Adj. BS FS Answer D Corr Adj FS Answer: Closing error = sum(BS) sum(FS) = 0.8. ft Correction per foot = C =closing error / total distance = 0.80 / 540 = 0.001841

Point BS Dist 900 2.10 100 TP1 3.60 TP2

3.10 Sum 8.80 D Corr =1.95 2.1-0.15 0.80 = 0.001841*100 0.148 70

0.104 100 3.45 =0.148 0.001841*100 2.70 100 0.148 70

=0.104 0.001841*70 3.00 4.50 100 0.148 8.00 270 0.4