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 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
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
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 Equations
Cf = 0.667 M2 = 0.0239 F2 (in feet)
(U.S. Customary Units)
And
Cm = 0.0785 K2 (in meters)
Where:
M – distance in miles
F- distance in thousands of feet
K – distance in kilometers
(Metric Units)
Refraction Equations
Rf = 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 Equations
hf = 0.574 M2 = 0.0206 F2 (in feet)
(U.S. Customary Units)
and
hm = 0.0675 K2 (in meters)
where:
M – distance in miles
F - distance in thousands of feet
K – distance in kilometers
(Metric Units)
Effects of Curvature and Refraction
For 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 Leveling
Used 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.