Leveling

Chapter 4

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

Old Datum: Mean Sea LevelMean Sea Level (MSL)

Average height over a 19-year period

26 gauging stations along the Atlantic Ocean, Pacific Ocean and the Gulf of Mexico

New Datum: NGVD88National Geodetic Vertical Datum of 1988 (NGVD88)Completed in 1991, refined 1929 surveyIncluded 625,000 km of additional levelingSingle tidal gauge bench mark located in Quebec, CanadaTidal gauge bench called Father Point/Rimouski

Operators at Father Point

Leveling Terms

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.

Effects of Refraction

Curvature EquationsCf = 0.667 M2 = 0.0239 F2 (in feet) (U.S. Customary Units)

And

Cm = 0.0785 K2 (in meters) (Metric Units)

Where:

M – distance in miles

F- distance in thousands of feet

K – distance in kilometers

Refraction EquationsRf = 0.093 M2 = 0.0033 F2 (in feet) (U.S. Customary Units)

And

Rm = 0.011 K2 (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.

Combined Equationshf = 0.574 M2 = 0.0206 F2 (in feet) (U.S. Customary Units)

and

hm = 0.0675 K2 (in meters) (Metric Units)

where:

M – distance in miles

F - distance in thousands of feet

K – distance in kilometers

Effects of Curvature and RefractionFor 300’ shot:

hf = 0.0206 (300/1000)2 = 0.0019’

For 1000’ shot:

hf = 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.

Eliminating Effects of Curvature and Refraction

Proper field procedures (taking shorter shots and balancing shots) can practically eliminate errors due to curvature and refraction.

Trigonometric LevelingUsed in areas of very steep or rugged terrain or when you have inaccessible points.

Trigonometric Leveling Procedure

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 or V = 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

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.

Trigonometric Leveling Procedure: Long Lines

Equations:elev = hi + V + (C – R) – r

where:

(C –R) is computed from the equation: 0.0206 F2

See Example 4-1 on page 82 and Example 4-2 on page 83.