1. Leveling Chapter 4

2. Why do we perform leveling surveys? To determine the topography of sites for design projects Set grades and elevations for construction projects Compute volumes of earthwork

3. Old Datum: Mean Sea Level Mean Sea Level (MSL) Average height over a 19-year period 26 gauging stations along the Atlantic Ocean, Pacific Ocean and the Gulf of Mexico

4. New Datum: NGVD88 National Geodetic Vertical Datum of 1988 (NGVD88) Completed in 1991, refined 1929 survey Included 625,000 km of additional leveling Single tidal gauge bench mark located in Quebec, Canada Tidal gauge bench called Father Point/Rimouski

5. Operators at Father Point

6. Leveling Terms

7. Effects of Curvature and Refraction The earth’s curvature causes a rod reading taken at point B to be too high. The effect of refraction is to make objects appear higher than they really are thus making the rod readings too low.

8. Effects of Refraction

9. Curvature Equations C f = 0.667 M 2 = 0.0239 F 2 (in feet)(U.S. Customary Units) And C m = 0.0785 K 2 (in meters)(Metric Units) Where: M – distance in miles F- distance in thousands of feet K – distance in kilometers

10. Refraction Equations R f = 0.093 M 2 = 0.0033 F 2 (in feet)(U.S. Customary Units) And R m = 0.011 K 2 (in meters)(Metric Units) Where: M – distance in miles F- distance in thousands of feet K – distance in kilometers The refraction correction is about one-seventh the effect of curvature but in the opposite direction.

11. Combined Equations h f = 0.574 M 2 = 0.0206 F 2 (in feet)(U.S. Customary Units) and h m = 0.0675 K 2 (in meters)(Metric Units) where: M – distance in miles F - distance in thousands of feet K – distance in kilometers

12. Effects of Curvature and Refraction For 300’ shot: h f = 0.0206 (300/1000) 2 = 0.0019’ For 1000’ shot: h f = 0.0206 (1000/1000) 2 = 0.0206’ Under the most adverse conditions (very hot humid conditions) the error associated with refraction can be as high as 0.10’ for a 200-foot shot.

13. Eliminating Effects of Curvature and Refraction Proper field procedures (taking shorter shots and balancing shots) can practically eliminate errors due to curvature and refraction.

14. Trigonometric Leveling Used in areas of very steep or rugged terrain or when you have inaccessible points.

15. Trigonometric Leveling Procedure

16. Equations: If S and the vertical angle are determined: V = S sin  or V = S cos z If H and the vertical angle are determined: V = H tan  orV = H tan z The change in elevation between points A and B is:  elev = hi + V – r where: hi – height of the instrument above point A

17. Equations (continued): and: r – rod reading at B when the vertical angle is read If r is made equal to the hi, then the two values cancel and the computations are simplified. These equations are applicable when shots are taken at less than 1000 feet. For shots longer than 1000 feet, the effects of curvature and refraction must be taken into account.

18. Trigonometric Leveling Procedure: Long Lines

19. Equations:  elev = hi + V + (C – R) – r where: (C –R) is computed from the equation: 0.0206 F 2 See Example 4-1 on page 82 and Example 4-2 on page 83.