● Instrument Man: Operates and maintains
Surveying surveying instruments.
● Recorder: Keeps record of observations and
● Surveying: The art of determining the measurements.
positions of points on or near the Earth's ● Computer: Computes survey data.
surface by measuring distance, direction, ● Head Tape Man: Ensures accurate linear
and elevation. measurements.
● Plane Surveying: Assumes the Earth is flat, ● Rodman: Holds leveling rod for readings.
suitable for small areas, less accurate, and ● Aidman: Provides first aid to team
economical. members.
● Geodetic Surveying: Considers Earth's
curvature, suitable for large areas, highly Types of Errors
accurate, requires special instruments.
● Systematic Error: Consistent and
Types of Surveys predictable errors due to instrument
limitations.
● Control Survey: Establishes a network of ● Accidental Error: Random errors due to
reference points. human limitations or environmental factors.
● Topographic Survey: Determines ground
shape, natural, and artificial features. Sources of Errors
● Land, Boundary, and Cadastral Survey:
Defines property boundaries. ● Instrumental Error: Resulting from
● Hydrographic Survey: Maps shorelines and imperfections in instruments.
underwater surfaces. ● Natural Error: Caused by environmental
● Route Survey: Plans and constructs linear factors.
projects like roads and pipelines. ● Personal Error: Caused by human
● Construction Survey: Guides construction limitations.
by marking locations and elevations.
● As-built Survey: Records final locations
Precision vs. Accuracy
after construction.
● Mine Survey: Guides mining operations and
● Precision: Consistency of measurements.
mineral exploration.
● Accuracy: Closeness of measurements to
● Photogrammetric Survey: Uses aerial
the true value.
photography for mapping.
● Industrial Survey: Ensures accurate layout
in industrial works.
Types of Measurements Measurement of Horizontal
Distances
● Direct Measurement: Direct comparison of
a quantity with a standard unit. ● Horizontal Distance: A straight-line
● Indirect Measurement: Measurement distance between two points along a
without direct application of instruments. horizontal plane.
● Linear, Area, and Volume Measurement:
Measuring lengths, areas, and volumes.
● Angular Measurement: Measuring angles
using degrees, radians, or grads.
Methods of Measuring Horizontal
Field Survey Party Roles Distances
● Chief of Party: Oversees and directs the 1. Pacing:
survey team.
○ Pace: Length of a step from ● Clothing or shoe weight.
heel-to-heel or toe-to-toe. ● Fatigue of the pacer.
○ Stride: Two paces (double step). ● Age and sex of the individual.
○ Pace Factor: Average distance
covered per pace.
Formula:
Errors in Taping
1. Instrumental Errors:
○ Errors due to faulty or worn-out
tape.
2. Taping (Chaining):
2. Natural Errors:
○Taping: Measuring distance using a
○Changes due to temperature, wind,
graduated tape.
or uneven terrain.
○ Chaining: Measuring distance
3. Personal Errors:
using a chain.
○ Chainmen: Persons responsible for
○ Incorrect handling, misreading, or
chaining.
careless recording.
○ Plumbing: Keeping the tape
vertical during measurement.
○ Lining In: Aligning the tape along
the desired direction.
3. Tachymetry (Tacheometry): Tape Corrections
○Tachymetry: Rapid method of 1. Temperature Correction:
measuring horizontal distance and
elevation using a telescope and ○ Tape length expands or contracts
stadia rod. with temperature changes.
○ Stadia Rod: A graduated rod used 2. Pull Correction:
for reading distance.
○ Stadia Hair: Crosshairs in the ○Applying tension to stretch the tape
telescope used to measure affects measurement.
distances. 3. Sag Correction:
○ Relative Precision: Measurement
accuracy ratio (1:300 to 1:1000). ○When a tape sags due to gravity, it
4. Mechanical Devices: shortens the measured distance.
4. Sea Level Correction:
○Tools such as odometers, distance
wheels, or electronic devices for ○Correcting for elevation above sea
measuring distances. level for precise measurements.
5. Photogrammetry: 5. Slope Correction:
○ The use of aerial photographs to ○ Converting slope distance to
measure horizontal distances. horizontal distance on inclined
ground.
Factors Affecting Pace Factor
Formulas
● Speed of pacing.
● Terrain roughness.
● Elevation: Distance from a vertical datum to
a point or object.
● Geoid: A level surface serving as a
reference for elevations.
● Mean Sea Level (MSL): Average sea height
over a 19-year period.
● Tidal Datum: Used in coastal areas for
property boundaries.
Surveying Benchmarks
● Benchmark (BM): Permanent object with a
known elevation.
● Vertical Control: A series of benchmarks
establishing elevation points.
where:
Methods of Leveling
○ kk = Coefficient of linear expansion.
○ LL = Measured length. 1. Direct (Spirit) Leveling: Measures vertical
○ TfT_f = Final temperature. distances directly.
○ TiT_i = Initial temperature. 2. Indirect (Trigonometric) Leveling: Uses
2. Sag Correction: vertical angles and distances.
3. Reciprocal Leveling: Determines elevation
difference between distant points.
4. Profile Leveling: Measures elevation
changes along a designated line.
5. Stadia Leveling: Uses stadia hairs in an
instrument for distance and elevation.
6. Barometric Leveling: Measures elevation
○ ww = Weight of tape. differences using atmospheric pressure.
○ LL = Length of tape. 7. Borrow Pit Leveling: Determines relative
○ PP = Tension applied. elevations in excavation areas.
Leveling Instruments
Leveling ● Automatic Level: Optical instrument used
for horizontal alignment.
● Leveling: Process of measuring vertical ● Leveling Rod: Graduated rod for measuring
distances to determine elevation differences. vertical distances.
● Vertical Line: Follows the local direction of ● Tripod: Provides stability for leveling
gravity, indicated by a plumb line. instruments.
● Level Surface: A curved surface
perpendicular to the local plumb line.
● Level Line: A curved line within a level
Errors in Leveling
surface.
● Horizontal Plane: A plane perpendicular to 1. Instrumental Errors: Incorrect calibration,
the local vertical line. tilted crosshairs, loose tripod.
2. Personal Errors: Misreading, parallax,
improper rod handling.
Elevation & Datums 3. Natural Errors: Earth's curvature, refraction,
temperature effects, wind.
● Vertical Datum: A reference surface with an
assigned elevation of zero.
Key Leveling Terms ● Benchmark (BM): Permanent point with
known elevation.
● Turning Point (TP): Temporary point used
● Backsight (BS): Rod reading on a known
for instrument repositioning.
elevation point.
● Backsight (BS): Reading taken on a known
● Foresight (FS): Rod reading to determine
elevation point.
an unknown elevation.
● Foresight (FS): Reading taken on a point
● Height of Instrument (HI): Elevation of the
with unknown elevation.
instrument's line of sight.
● Height of Instrument (HI): The height of the
○ Formula: HI = Elevation + BS
instrument's line of sight from a benchmark.
○ Elevation = HI - FS
○ Formula: HI = Elevation +
● Turning Point (TP): Temporary benchmark
Backsight
between points.
○ Elevation = HI - Foresight
Advanced Leveling Methods
● Three-Wire Leveling: Uses upper, middle,
Error of Closure (E.C.)
and lower stadia readings for accuracy.
● Error of Closure: Difference between initial
● Error of Closure: The difference between
and final benchmark elevation.
the initial and final benchmark elevations
● Two-Peg Test: Checks for collimation error
after a complete leveling circuit.
in leveling instruments.
● Correction: Divide the error equally across
all measured points.
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Stadia Surveying
Curvature and Refraction in ● Stadia Surveying: Method to measure both
distance and elevation using stadia hairs in a
Leveling leveling instrument.
● Stadia Interval Factor (K): Fixed multiplier
● Curvature Error: The Earth's curvature for converting stadia readings into horizontal
causes the line of sight to deviate downward, distances.
overestimating elevation differences. ● Instrument Constant (C): A fixed value for
● Refraction Error: Atmospheric bending of converting instrument readings into
light causes the line of sight to curve slightly real-world measurements.
downward, underestimating elevation ● Formula:
differences. ○ Distance = K × Stadia Interval + C
● Combined Correction (hcr): Formula used
to correct both curvature and refraction
effects.
Two-Peg Test
● Two-Peg Test: A method to check for
Differential Leveling collimation error (line-of-sight error) in
leveling instruments.
● Differential Leveling: Process of ● Purpose: Ensures the instrument reads
determining the elevation difference between horizontal lines accurately.
two points by setting up an instrument at ● Correction: Adjust instrument until the
different locations. forward and backward readings match.
Common Mistakes in Leveling Meridian
1. Misreading the rod. A reference line used for measuring directions in
2. Incorrect recording of readings. surveying.
3. Mathematical errors in elevation
computation.
4. Rod not fully extended, causing wrong
Types of Meridian
readings.
5. Moving the turning point, resulting in 1. True Meridian: Imaginary north-south line
inaccurate elevation. passing through a point based on Earth's
axis.
2. Magnetic Meridian: North-south line that
aligns with Earth's magnetic field.
3. Assumed Meridian: Arbitrary reference line
Summary of Errors and chosen for convenience in small-scale
Corrections surveys.
4. Grid Meridian: Straight north-south line
used in map projections and coordinate
Error Type Effect on How to Avoid systems.
Leveling
Methods of Establishing Meridians
Curvature Overestimates Apply correction
elevation formula.
● Magnetic Meridian: Established using a
magnetic compass.
● True North (Sun Method): Determined
using the Sun or Polaris (North Star).
Refraction Underestimates Avoid extreme
● Wrist Watch Method: Uses time and Sun
elevation heat.
direction to estimate true north.
Instrument Incorrect Perform
Error elevation collimation Units of Angular Measurement
readings check.
1. Sexagesimal System:
○ 1 full circle = 360°
Personal Misreading Focus and ○ 1° = 60 minutes (‘)
Error values recheck ○ 1’ = 60 seconds (“)
readings. 2. Centesimal System (Grads):
○ 1 full circle = 400 grads
○ 1 grad = 100 centesimal minutes
Natural Elevation shift Work in ideal 3. Radian Measure:
Error due to weather conditions.
○ 1 full circle = 2π2\pi radians ≈
6.2832 radians
○ 1 radian = 57.2958°
4. Mil (Military):
○ 1 full circle = 6400 mils (NATO ● Forward Azimuth to Back Azimuth:
standard) ○ If Forward Azimuth > 180°, subtract
○ 1 mil ≈ 0.05625° 180°.
○ If Forward Azimuth < 180°, add
180°.
● Bearing to Azimuth:
○ Convert N/S bearing to 0°-360°
Types of Angles azimuth.
1. Interior Angles: Angles inside a closed
polygon.
2. Exterior Angles: Angles outside a closed
polygon.
3. Deflection Angles: Angle between a line
and the prolongation of the previous line.
Bearings
● Bearing: Direction of a survey line from a
fixed reference point (North or South).
● Forward Bearing: Bearing observed in the
survey's progressing direction.
● Back Bearing: Bearing observed in the
opposite direction.
Azimuths
● Azimuth: Clockwise angle from a reference
direction (True North) to a line.
● Forward Azimuth: Azimuth measured in the
direction of the survey.
● Back Azimuth: Azimuth in the opposite
direction (Add/Subtract 180°).
Magnetic Declination
● Magnetic Declination: Angle difference
between True North and Magnetic North.
● East Declination (+): Magnetic North is east
of True North.
● West Declination (-): Magnetic North is
west of True North.
Conversion Rules
