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Class Objectives
CE 211 – SURVEYING ENGINEERING
CLASS 11: ANGLE MEASUREMENTS
• Define and measure vertical and zenith angles
• Identify directions for horizontal angle measurements
• Compute angles, bearings, and azimuths
Ahmed Abdel-Rahim, Ph.D, P.E.
Associate Professor, Civil Engineering
INTRODUCTION
Method of establishing a coordinate system: First, the
coordinates of station A and the direction of line EA are
assumed. Latitudes and departures are added to the
ordinates and abcissas, respectively, of the stations, to obtain
their coordinates.
VERTICAL ANGLES
Designation of vertical angles or zenith angles.
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VERTICAL ANGLES
HORIZONTAL ANGLES AND DIRECTIONS
• A horizontal angle may be described in one of
several different ways depending on how it is
measured.
– An interior angle is measured on the inside of a closed
polygon: an exterior angle is measured outside of the
closed polygon.
– An angle turned (measured) in a clockwise direction, from
the “rear” to the “forward” point or station, is called an
angle to the right.
– Pointing the instrument toward the rear station may be
called the backsight and toward the forward station, the
foresight; this terminology is similar to that used for
leveling.
FIGURE 6-3. Relationship between zenith angle and vertical angle.
HORIZONTAL ANGLES AND DIRECTIONS
A horizontal angle may be classified as an interior
angle, an exterior angle, an angle to the left, or an
angle to the right.
HORIZONTAL ANGLES AND DIRECTIONS
FIGURE 6-5. A deflection angle must be designated as being either
an angle to the left (L) or an angle to the right (R).
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HORIZONTAL ANGLES AND DIRECTIONS
HORIZONTAL ANGLES AND DIRECTIONS
• Azimuth and Bearing of a Line
– Azimuths
– Bearings
– Directions
• Computing Angles, Azimuths, and Bearings
The azimuth of a line is usually referenced to the north end of the meridian.
That is, AzimN differs from AzimS by 180°.
HORIZONTAL ANGLES AND DIRECTIONS
The bearing of a line is measured from the north or from the south
(whichever is closer), in a clockwise or counterclockwise direction
(whichever applies).
HORIZONTAL ANGLES AND DIRECTIONS
Conversion between azimuth and
bearing is best done by examining a
simple sketch of the line and
meridian.
A line can be designated by either its
forward direction or its back direction;
back direction is useful for computing
the azimuth of an adjoining line.
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HORIZONTAL ANGLES AND DIRECTIONS EXAMPLE
HORIZONTAL ANGLES AND DIRECTIONS
FIGURE 6-11. Solution for Example 6-1.
HORIZONTAL ANGLES AND DIRECTIONS
HORIZONTAL ANGLES AND DIRECTIONS –
MORE EXAMPLES
FIGURE 6-12. Illustration for Example 6-2.
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HORIZONTAL ANGLES AND DIRECTIONS –
MORE EXAMPELS
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