Basic 2D Land Surveying

1
Basic 2-D Land Surveying

• ALAN A. LEW
• OUTLINE
• Surveying
• COGO
• The Compass
• Compass Triangulation
• Compass Traverse
• The Theodolite

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Surveying

• Co-ordinate Geometry COGO
• Distance and Direction (bearing)
• most precise method of entering map data
• direct entry from surveyors notes
• Direction - measured with
• Plane Table, Compass, Theodolite, Stars
• Distance - measured with
• Pacing, Tape, Infrared electronic instruments
• Both can be determined from
• Compass Theodolite measured Triangle Angles

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Prismatic Compass

• Prism allows Siting Object Reading Angle
• Parts Prism, Brake, Wire, Peep-site, Vane
• Compass Card
• Imprinted Degrees
• 0 North 180 South
• 90 270 East OR West
• 0 to 90 degrees
• 0 North and South 90 East and West
• Brunton Compass
• Uses Mirror instead of Prism

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Compass Error

• Instrument Error
• mis-alignment of Vane, Peep-site, Wire
• inaccurate tic marks on compass card
• External Error
• local influences or local iron
• Magnetic North
• changes daily up to .3 deg
• Magnetic Declination - Singapore 19 degrees
  (est.)
• User Error
• compass not flat or moving
• Use Tripod, Stick or Arm brace

5
Compass Accuracy Level

• 1/4 of a degree (15 minutes)
• Maximum accuracy rare
• under 1 degree
• assuming no Local Influences
• .5 degrees
• based on averaging or repeated readings
• Theodolite
• accuracy of 1 minute (1/60 degree)
• Advantage of a Compass
• error limited to individual readings
• not compounded from previous reading

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Mapping with a Compass

• Two Methods Triangulation and Traverse
• Compass Triangulation
• aka Compass Sketch or Intersection and
  Resection
• fixing positions of landmarks by Intersection
• then fixing objects near landmarks by Resection
• allows detailed field mapping of a large area
• requires
• Prismatic or Brunton Compass
• Sketching Board with light graph paper
• Protractor
• Sharp pencil and an eraser

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Compass Triangulation Method

• Measure a base line on the ground
• from each end can see all landmarks to map
• length should be at least 10 cm long on the final
  map
• Take Landmark Bearings from each Baseline End
• use the Protractor to draw Bearing Rays on graph
  paper
• Intersections location
• Right Angles Intersections most accurate
• New baseline additional bearings if necessary
• 3 Bearings second best accuracy
• allow First and Second Class point precision
• Objects further away less accurate

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Triangulation Resection

• other objects and details are identified and
  mapped
• based on their Bearings to the Landmarks
• Similar to Plane-Table Surveying
• flat table is used to sketch bearing rays on
• Similar to Theodolite Triangulation
• each points is part of a triangle in a Triangular
  Grid
• Uses of Compass Sketch
• Reconnaissance mapping prior to triangulation
• Sand dune distribution
• Tree and Shrub positions

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The Compass Traverse

• Surveying Routes and Lines
• bed of a stream, route of a trail
• boundary of an area (polygon)
• Leg
• a straight line segment w/ distance direction
• Mapping is done after measurements
• different from Compass Sketch
• Chain Survey
• uses Compass and a measuring Chain

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Chain Survey of a Area

• Mark corners of the Area to be surveyed
• Take Bearing from first corner (A) to second (B)
• Measure A-B distance using Chain or Tape
• Optionally, take Offset Readings en route of
• Objects Crossed Nearby Objects
• and their Distance Bearing (may be estimated)
• At Point B - take a Back Bearing to Point A
• if 2 or 3 deg off, use average the two readings
• if gt 3 deg off, then redo initial reading
• Continue each subsequent leg in this way

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Note Taking during Traverse

• need to be very clear
• actual plotting is done away from location
• any surveyor should be able to understand
• make Sketches of Offset Objects
• Bearings should be Degree and Decimal
• DO NOT INCLUDE Degree Symbol
• too easily mistaken for a 0
• Include
• NAME and PURPOSE of the traverse
• Name of SURVEYOR

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Notes on OVERHEAD

• Centre Column Traverse LEG
• no real width
• Starts with a Station Point - identified by a
  CIRCLE
• ends with a Line
• only shows distances from last Station Point
• objects encountered/offset are sketched in
• although not to any particular scale
• Left Column Bearings
• kept separate to avoid confusion with distances

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Plotting Error

• Plotting the Traverse
• Distance Bearing information in AutoCAD
• entered as _at_mltddms - e.g., _at_33lt90d10'3
• Error of Closure
• All surveying has some degree or error
• Two Types of Traverses
• 1 - Closed Polygons
• main error polygon ends do not meet
• 2 - Open Lines
• main error end of line not at expected point

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Traverse Error

• Bearing measurement
• instrument error
• external error
• local iron, magnetic North
• mentioned previously
• Distance measurement
• Longer Traverse greater error
• but more Error Averaging
• Shorter Traverse
• error due to a single distance or bearing

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Creating Closure

• spread the error among the Station points
• recommended method
• Stations share of error based on distance to it
  from last point
• First Station does Not Change
• Can adjust other stations share of error if
  suspect
• Adjusting a Line Traverse
• ONLY if End Point is clearly known
• needed to determine Error of Closure at the end
  point
• same method of adjustment as Area Traverse

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Overhead Notes

• to determine this, draw a line representing
  entire length of the traverse
• then mark off the distance from the POB of each
  station
• draw a perpendicular line at the end station that
  is equal to the closure error distance (same
  scale)
• draw another line starting at the same POB, but
  ending at the top of the perpendicular line
• draw perpendicular lines from each Station point
  to the second line
• these show the proportion of the error that each
  point will bear in adjusting the traverse
• NOTE Can change the true locations of the
  stations along the first line to adjust for one
  station that was more difficult to survey and
  more likely to be the source of the error
  forcing it to have a greater share of the overall
  error than the method above would normally apply.

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Non-Compass Traverses

• Traversing with only a Ruler
• starting at a clearly defined landmark
• lay ruler on paper and mark direction to a
  landmark
• pace distance to the landmark
• using ruler - realign the paper to the last
  landmark (back bearing)
• draw a new line to the next landmark and Pace it
• Traversing with only a Rope
• takes two people
• hold rope taught and straight between two
  landmarks/stations
• mark direction on paper as with Rule
• can be Very Precise

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Triangulation with a Theodolite

• Most common survey method
• Theodolite a Telescope mounted on a Tripod
• moves Horizontally Vertically
• gives readings at the minute (or less) level
• baseline is precisely measured and recorded
• Theodolite placed (using plumb-line) over end of
  the base line
• measure angle to the other end of the baseline
• measure angle to other stations
• move to next station
• Distances between stations are calculated on the
  Angles
• additional baselines are drawn to ensure overall
  accuracy
• Mapping is done back in office from field notes

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Triangular Survey Grid

• Used to create Control Point network in many
  countries
• Triangle sides in the UK average 56 km
• longest is 160 km
• Triangles in India range 18 to 48 km
• Theodolite can also measure
• elevation changes
• Using Vertical angles (and, optionally, a
  Measuring stick)
• Latitude and Longitude of a point
• Using angle to the Sun and polar stars
• Brunton Compass can measure elevation changes
• using built-in Angle Measuring scales

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Summary

• Surveying
• Distance and Direction
• COGO
• Compass
• Prismatic
• Brunton
• Compass Triangulation
• Compass Traverse
• Error Closure
• Theodolite Triangulation
• Triangular Survey Grid