leveling chapter 4. why do we perform leveling surveys? to determine the topography of sites for...
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Leveling
Chapter 4
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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
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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
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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
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Operators at Father Point
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Leveling Terms
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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.
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Effects of Refraction
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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
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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.
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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
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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.
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Eliminating Effects of Curvature and Refraction
Proper field procedures (taking shorter shots and balancing shots) can practically eliminate errors due to curvature and refraction.
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Trigonometric LevelingUsed in areas of very steep or rugged terrain or when you have inaccessible points.
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Trigonometric Leveling Procedure
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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
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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.
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Trigonometric Leveling Procedure: Long Lines
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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.