Leveling lecture 1 Readings 4 -1 through 4

Leveling lecture 1: Readings: 4 -1 through 4 -4, 4 -5. 2, 4 -6 through 4 -12, 4 -14 Lecture 2: Readings: 5 -1 through 5 -5, 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 1850’s, 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 earth’s crust shifting and changes in MSL, new adjustment was done and more points were added (total of 1. 3 million) which resulted in NAVD 88 Shifts are larger in the west: 1. 5 m in the Rocky mountain area MUST MENTION WHICH DATUM

Level vials Tube level

Other level vials • • Coincidence-Type level Bull’s-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: • Elevation. X = EBM + BSBM - FSX • EX, with errors e 1& e 2 = EBM + (BSBM - e 1)- (FSX e 2) = EBM + (BSBM – FSX) – (e 1 – e 2) • 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, d. BS, 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 TP 1 TP 2 Considering the readings in the following table, compute the adjusted elevations of points TP 1 and TP 2. Elevation of point 900 is 900 ft. Sum 8. 80 270 Answer 8. 00 270

Answer: Closing error = sum(BS) – sum(FS) = 0. 8. ft Correction per foot = C =closing error / total distance = 0. 80 / 540 = 0. 001841 2. 1 -0. 15 = 0. 001841*100 0. 148 =1. 95 0. 148 3. 45 = 0. 001841*100 270 0. 148 = 0. 001841*70 3. 00 0. 104 Sum 8. 80 0. 104 0. 148 0. 40 8. 4 Answer 8. 00 270 0. 4

Remarks – Precision: allowable misclosure. Construction: C = 0. 02 n ft. • Federal Geodetic Control Subcommittee suggests: C = m k mm Where K is the length of the loop in Kilometers, C is in mm, and m is a constant according to order and class (first order-class I, first order-class II, etc. ): 4, 5, 6, 8, and 12 mm. • – Level position is not important, rod position is. – Rod is not supposed to move or sink while the level is moved. – Distance between the rod and the level is limited to 100 ft, for our use. – Record the three readings: upper lower and middle to compute the distance. – Observation table: how does it grow? – Field work.

Lab Procedure