Basic%20Surveying

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Basic Surveying

• CE 263

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Introduction to Surveying

• Definition
• Surveying is the science and art of determining
  the relative positions of points above, on, or
  beneath the earths surface and locating the
  points in the field.

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The work of the surveyor consists of 5 phases

1. Decision Making selecting method, equipment and
   final point locations.
2. Fieldwork Data Collection making measurements
   and recording data in the field.
3. Computing Data Processing preparing
   calculations based upon the recorded data to
   determine locations in a useable form.
4. Mapping or Data Representation plotting data to
   produce a map, plat, or chart in the proper form.
5. Stakeout locating and establishing monuments
   or stakes in the proper locations in the field.

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2 Categories of Surveying

• Plane Surveying surveying with the reference
  base for fieldwork and computations are assumed
  to be a flat horizontal surface.
• Generally within a 12 mile radius the pull of
  gravity is very nearly parallel to that at any
  other point within the radius and thus horizontal
  lines can be considered straight.
• Geodetic Surveying surveying technique to
  determine relative positions of widely spaced
  points, lengths, and directions which require the
  consideration of the size and shape of the earth.
  (Takes the earths curvature into account.)

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7 Types of Surveys

1. Photogrammetry mapping utilizing data obtained
   by camera or other sensors carried in airplanes
   or satellites.
2. Boundary Surveying establishing property
   corners, boundaries, and areas of land parcels.
3. Control Surveying establish a network of
   horizontal and vertical monuments that serve as a
   reference framework for other survey projects.
4. Engineering Surveying providing points and
   elevations for the building Civil Engineering
   projects.

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7 Types of Surveys

• Topographic Surveying collecting data and
  preparing maps showing the locations of natural
  man-made features and elevations of points o the
  ground for multiple uses.
• Route Surveys topographic and other surveys for
  long narrow projects associated with Civil
  Engineering projects.
• Highways, railroads, pipelines, and transmission
  lines.
• Hydrographic Surveying mapping of shorelines
  and the bottom of bodies of water.
• Also known as bathymetric surveying.

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Brief History of Surveying

• Surveying had its beginning in Egypt about 1400
  BC
• Land along the Nile River was divided for
  taxation. Divisions were washed away by annual
  floods.
• ROPE-STRETCHERS Egyptian surveyors were created
  to relocate the land divisions (measurements were
  made with ropes having knots at unit distances).
• Extensive use of surveying in building of
  Egyptian monuments
• Greeks expanded Egyptian work and developed
  Geometry.
• Developed one of the earliest surveying
  instruments Diopter (a form of level).

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Brief History of Surveying

• Romans developed surveying into a science to
  create the Roman roads, aqueducts, and land
  division systems.
• Surveyors held great power, had schools and a
  professional organization
• Developed several instruments
• Groma cross instrument used to determine lines
  and right angles
• Libella A frame with a plumb bob used for
  leveling
• Chorobates 20 straight edge with oil in notch
  for leveling
• Middle Ages land division of Romans continued
  in Europe.
• Quadrans square brass frame capable of turning
  angles up to 90 and has a graduated scale
  developed by an Italian named Von Piso.

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Brief History of Surveying

• 18th 19th Century in the New World the need
  for mapping and marking land claims caused
  extensive surveying, especially by the English.
• 1785 United Stated began extensive surveys of
  public lands into one mile square sections
• 30 states surveyed under the U.S. Public Land
  System (also called the Rectangular
  System)
• 1807 United States Geological Survey founded to
  establish an accurate control network and mapping
• Famous American Surveyors George Washington,
  Thomas Jefferson, George Rogers Clark, Abe
  Lincoln and many more.

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Brief History of Surveying

• 20th Century and Beyond As technology advanced,
  population increased, and land value caused
  development of licensure for surveyors in all
  states.
• Educational requirements for licensure began in
  the early 1990s
• Capable of electronic distance measurement,
  positioning using global positioning systems,
  construction machine control, and lidar
  (scanning) mapping
• Involvement in rebuilding of the infrastructure
  and geographic information systems (GIS)
• Shortage of licensed professionals is projected
  well into the 21st century

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Measurement of Distance

• Linear measurement is the basis of all surveying
  and even though angles may be read precisely, the
  length of at least one line in a tract must be
  measured to supplement the angles in locating
  points.
• 
  Methods of measuring a
  horizontal distance
• Rough Measuring Pacing, Odometer readings,
  Tacheometry (stadia), Taping, EDM, and GPS
• Only the last three meet survey accuracy
  requirements
• Distance from stadia (High wire-Low wire) 100
  Distance (ft)
• More accurate measuring taping, EDM (1966), GPS
• EDM and GPS are most common in todays surveys
• In pacing, one establishes the of paces/100 by
  counting the of paces over a pre-measured 300
  line

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Measurement of Distance

• Taping applying the known length of a graduated
  tape directly to a line a number of times.
• 
  2 Problems exist in Taping
• Measuring the distance between two existing
  points
• Laying out a known distance with only the
  starting point in place

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Measurement of Distance

• 6 Steps of Taping
• Lining in shortest distance between two points
  is a straight line.
• Applying tension rear chain is anchor and head
  chain applies required tension.
• Plumbing horizontal distance requires tape to
  be horizontal.
• Marking tape lengths each application of the
  tape requires marking using chaining pins to
  obtain total length.
• Reading the tape the graduated tape must be
  read correctly.
• Recording the distance the total length must be
  reported and recorded correctly.

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Types of Chains and Tapes

• Before the ability to make steel rods and bands,
  sticks were cut into lengths of 16.5 (Rod) and
  they were laid end to end to measure.
• Gunters Chain
• 66 long with 100 link w/each link being 7.92
  inches or 66 feet long
• Developed by Edmund Gunter in 1600s in England
  and made with individual wires with a loop at
  each end connected
• Chain had between 600-800 wearing surfaces which
  with hard use would wear and cause chain to
  elongate
• Measurements were recorded in chains and links
• 7ch 94.5lk 7.945 ch 7.945 X 66/ch 524.37
• 1 chain 4 rods 80 chains 1 mile

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Types of Chains and Tapes

• Engineers Chain
• Same construction as Gunters Chain, but each
  link is 1.0 long and was used for engineering
  projects
• Surveyors and Engineers Tapes
• Made of ¼ to 3/8 wide steel tapes in 100
  200 300 lengths
• Multiple types of marking and graduation
• Available in chains, feet, and metric
• Graduated
• Throughout feet and tenths marked the entire
  length
• Extra foot feet marked the length of the tape
  with additional foot at the 0 end graduated in
  tenths and hundreds of the foot

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Types of Chains and Tapes

• Invar Tapes
• Made of special nickel steel to reduce length
  variations due to temperature changes
• The tapes are extremely brittle and expensive
• Used most of the time for standard comparison of
  tapes
• Cloth, Fiberglass, and PVC Tapes
• Lower accuracy and stored on reels. Used for
  measurement of 0.1 accuracy requirements
• Accessories
• Chaining Pins set of 11, used to mark the tape
  lengths
• Hand Level used to determine required plumbing
  height
• Plumb Bob used to transfer the mark from the
  tape to ground
• Tension Handle used to maintain correct tension
  on tape

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Taping (Field Process)

• The line to be taped should be marked at both
  ends
• Keeps measurement on line
• Rear chain person should keep the head chain
  person on line
• 1 of line error/100 0.01 error in length
• Applying Tension
• Rear chainman is anchor and should hold 100 mark
  over point
• Tension is applied by head chain person
  normally 12 to 30 pounds of pull
• Tapes are standardized at 12 lbs., but greater is
  utilized to compensate for sag

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Taping (Field Process)

• Plumbing
• One end of tape is raised to maintain a
  horizontal measuring plane. ONLY one end is
  elevated
• This allows measurements to be made on uneven
  ground
• If a high spot exists in center, break tape by
  measuring to the top and then move forward to
  complete the distance

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Slope Measurements

• Generally, measurements are made horizontally,
  but on even, often man-made slopes the distance
  can be measured directly on the slope, but the
  vertical or zenith angle must be obtained.
• Horizontal Distance sin Zenith Angle X Slope
  Distance
• Horizontal Distance cos Vertical Angle X Slope
  Distance

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Stationing

• Starting point is 000 and each 100 is one
  station ?700 from starting point is Station 700
• If distance is 857.23 from starting point, it is
  expressed as Station 857.23

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Taping Error

• Instrumental Error a tape may have different
  length due to defect in manufacture or repair or
  as the result of kinks
• Natural Error length of tape varies from normal
  due to temperature, wind and weight of tape (sag)
• Personal Error tape person may be careless in
  setting pins, reading the tape, or manipulating
  the equipment
• Instrumental and natural error can be corrected
  mathematically, but personal error can only be
  corrected by remeasure.
• When a tape is obtained, it should either be
  standardized or checked against a standard.
• Tapes standardized at National Bureau of
  Standards in Maryland
• Standardized at 68 degrees F and 12 lbs. tension
  fully supported.
• 
  

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Tape Error Correction

• Measuring between two existing points
• If a tape is long, the distance will be short,
  thus any correction must be added
• If tape is short, the distance will be long, thus
  any correction must be subtracted
• If you are setting or establishing a point, the
  above rule is reversed.
• Generally can correct for tape length,
  temperature, tension, and sag, but tension and
  sag are negated by increasing tension to
  approximately 25 30 lbs.

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Error in Taping

• Tape Length Correction per foot Error in
  100/100
• If tape was assumed to be 100.00 but when
  standardized was found to be 100.02 after
  distance measured at 565.75
• then Correction (100.02-100.00)/100.00
  0.0002 error/ft
• 565.75 X .0002/ 0.11 correction and based
  upon rule, must be added, thus true distance
  565.86
• If tape had been 99.98 then correction would be
  subtracted and true distance would be 565.64

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Error in Taping

• Temperature Tapes in U.S. are standardized at
  68?F the temperature difference above or below
  that will change the length of the tape
• Tapes have a relatively constant coefficient of
  expansion of 0.0000065 per unit length per ?F
• CT 0.0000065(Temp (?F)-68) Length
• Example Assume a distance was measured when
  temperature was 30F using a 100 tape was
  872.54 (68 30) X 0.00000645 X 872.54
  0.21 error tape is short, thus
  distance is long, error must be subtracted and
  thus 872.54 0.21 872.33
• (note temperature difference is absolute
  difference)

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Surveying Metric Conversion

• 1 Survey Foot 1200 / 3937 meters
• 1 Meter 3937 / 1200 Survey Feet

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Transit

• Transit is the most universal of surveying
  instruments primary use is for measurement or
  layout of horizontal and vertical angles also
  used to determine vertical and horizontal
  distance by stadia, prolonging straight lines,
  and low-order leveling.
• 
  3 Components of the Transit
• Alidade Upper part
• Horizontal limb Middle part
• Leveling-head assembly Lower part

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Transit

• Alidade (upper part)
• Circular cover plate w/2 level vials and is
  connected to a solid conical shaft called the
  inner spindle.
• Contains the vernier for the horizontal circle
• Also contains frames that support the telescope
  called STANDARDS
• Contains the vertical circle and its verniers,
  the compass box, the telescope and its level vial

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Transit

• Horizontal Limb (middle part)
• This is rigidly connected to a hollow conical
  shaft called the outer spindle (which holds the
  inner spindle)
• Also has the upper clamp, which allows the
  alidade to be clamped tight
• Also contains the horizontal circle

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Transit

• Leveling-Head Assembly (lower part)
• 4 leveling screws
• Bottom plate that screws into tripod
• Shifting device that allows transit to move ¼ to
  3/8
• ½ ball that allows transit to tilt when being
  leveled
• The SPIDER 4-arm piece which holds the outer
  spindle
• Lower clamp allows rotation of outer spindle

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• Telescope Similar to that of dumpy level, but
  shorter
• Parts objective, internal focusing lens,
  focusing wheel, X-hairs, eyepiece

• Scales horizontal plate or circle is usually
  graduated into 30 or 20 spaces with graduations
  from 0? to 360? in both directions
• Circles are graduated automatically by machine
  and then scanned to ensure accuracy
• They are correct to with in 2 of arc

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Verniers

• Least count Lowest of reading possible
  determines accuracy
• Least Count (Value of smallest division on
  scale)/( of divisions on vernier)

Scale Graduation Vernier Divisions Least Count
30 30 1
20 40 30
15 45 20
10 60 10
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Verniers

• 3 Types of Verniers
• Direct or single vernier reads only in one
  direction must be set with graduations ahead of
  zero
• Double vernier can be read clockwise or
  counterclockwiseonly ½ is used at a time
• Folded vernier avoids a ling vernier plate
• ½ of the graduations are placed on each side of
  the index mark
• Use is not justified because it is likely to
  cause errors

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Verniers

• The vernier is always read in the same direction
  from zero as the numbering of the circle, i.e.
  the direction of the increasing angles
• Typical mistakes in reading verniers result from
• Not using magnifying glass
• Reading in the wrong direction from zero, or on
  the wrong side of a double vernier
• Failing to determine the least count correctly
• Omitting 10, 15, 20, 30 when the index is
  beyond those marks

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Properties of the Transit

• Designed to have proper balance between
• Magnification and resolution of the telescope
• Least count of the vernier and sensitivity of the
  plate and telescope bubbles
• Average length of sight of 300 assumed in design
• Specifications of typical 1 gun
• Magnification 18 to 28X
• Field of view - 1? to 1?30
• Minimum focus 5 to 7
• X-hairs usually are with stadia lines above and
  below
• The transit is a repeating instrument because
  angles are measured by repetition and the total
  is added on the plate
• Advantages of this
• Better accuracy obtained through averaging
• Disclosure of errors by comparing values of the
  single and multiple readings

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Handling the Transit

• Hints on handling and setting-up the transit
• Pick up transit by leveling head and standards
• When carrying the transit, have telescope locked
  in position perpendicular to the leveling head
  with objective lens down
• When setting-up, keep tripod head level and bring
  plumb bob to within ¼ of point to be set over,
  then loosen leveling screws enough to enable you
  to move transit on plate, then move transit until
  it is over the point

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Operation of Transit
A
B
C

• 9 Steps
• Set up over point B and level it. Loosen both
  motions
• Set up the plates to read 0? and tighten the
  upper clamp. (Upper and lower plates are locked
  together)
• Bring Vernier to exactly 0? using upper tangent
  screw and magnifying glass.
• Sight on point A and set vertical X-hair in
  center of point, by rotating transit
• Tighten the lower clamp and entire transit is
  locked in
• Set X-hair exactly on BS point A using the lower
  tangent screws. At this point the vernier is on
  0?00 and the X-hairs are on BS

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Operation of Transit
A
B
C

• Loosen the upper clamp, turn instrument to right
  until you are near pt. C. Tighten the upper
  clamp
• Set vertical X-hair exactly on pt. C using the
  upper tangent screw.
• Read ? on vernier
• If repeating ?, loosen lower motion and again BS
  on A (using only lower motion), and then loosen
  upper motion to allow ? to accumulate.
• If an instrument is in adjustment, leveled,
  exactly centered, and operated by an experienced
  observer under suitable conditions, there are
  only 2 sources for error.
• Pointing the telescope
• Reading the plates

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Transit Field Notes
1d? Mean ?
0?-90? (4d?)?4
90?-180? (4d? 360) ? 4
180?-270? (4d? 720) ? 4
270?-360? (4d? 1080) ? 4

• Use longest side for backsite

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TOTAL STATIONS
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TOTAL STATION SET UP

• WHEN TOTAL STATION IS MOVED OR TRANSPORTED, IT
  MUST BE IN THE CASE!!!!!!!!
• ESTABLISH TRIPOD OVER THE POINT.
• OPEN THE CASE AND REMOVE TOTAL STATION, PLACING
  IT ON THE HEAD OF THE TRIPOD AND ATTACH SECURELY
  WITH CENTER SCREW.
• CLOSE THE CASE.
• GRASP TWO TRIPOD LEGS AND LOOK THROUGH THE
  OPTICAL PLUMB, ADJUST THE LEGS SO THAT BULLSEYE
  IS OVER THE POINT (KEEP THE TRIPOD HEAD AS LEVEL
  AS POSSIBLE).
• UTILIZING THE TRIPOD LEG ADJUSTMENTS, LEVEL THE
  TOTAL STATION USING THE FISH-EYE BUBBLE.
• LOOSEN THE CENTER SCREW TO ADJUST THE TOTAL
  STATION EXACTLY OVER THE POINT IF NEEDED.
• COMPLETE LEVELING THE TOTAL STATION USING THE
  LEVEL VIAL.
• CHECK TO MAKE SURE YOU ARE STILL ON THE POINT.

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TURNING ANGLES WITH TOTAL STATION

• SIGHT ON THE BACKSIGHT UTILIZING THE HORIZONTAL
  ADJUSTMENT SCREW.
• ZERO SET THE INSTRUMENT (THIS PROVIDES AN
  INNITIAL READING OF
• 0 SECONDS.
• LOOSEN TANGENT SCREW AND ROTATE INSTRUMENT TO
  FORESIGHT.
• TIGHTEN TANGENT SCREW AND BRING CROSS HAIR EXACT
  ON TARGET WITH ADJUSTMENT SCREW.
• READ AND RECORD ANGLE AS DISPLAYED.
• TO CLOSE THE HORIZON
• SIGHT ON FORESIGHT POINT FROM ABOVE AND ZERO SET
  INSTRUMENT.
• ROTATE TO FORMER BACKSIGHT AND ADJUST INSTRUMENT
  TO EXACT.
• READ AND RECORD ANGLE AS DISPLAYED.
• ANGLE FROM DIRECT AND INDIRECT SHOULD EQUAL 360
  DEGREES.

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TOTAL STATION DISTANCE MEASUREMENT

• POINT THE INSTRUMENT AT A PRISM (WHICH IS
  VERTICAL OVER THE POINT.
• PUSH THE MEASURE BUTTON AND RECORD THE DISTANCE.
• YOU CAN MEASURE THE HORIZONTAL DISTANCE OR THE
  SLOPE DISTANCE, IT IS IMPORTANT THAT YOU NOTE
  WHICH IS BEING COLLECTED.
• IF YOU ARE MEASURING THE SLOPE DISTANCE, THE
  ZENITH ANGLE MUST BE RECORDED TO ALLOW THE
  HORIZONTAL DISTANCE TO BE COMPUTED.
• IF YOU ARE COLLECTING TOPOGRAPHIC DATA WITH
  ELEVATIONS, IT IS IMPORTANT THAT THE HEIGHT OF
  THE INSTRUMENT AND THE HEIGHT OF THE PRISM BE
  COLLECTED AND RECORDED.
• THIS CAN ALSO BE SOLVED BY SETTING THE PRISM
  HEIGHT THE SAME AS THE INSTRUMENT HEIGHT.

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TOTAL STATION RULES

1. NEVER POINT THE INSTRUMENT AT THE SUN, THIS CAN
   DAMAGE THE COMPONENTS OF THE INSTRUMENT AS WELL
   AS CAUSE IMMEDIATE BLINDNESS.
2. NEVER MOVE OR TRANSPORT THE TOTAL STATION UNLESS
   IT IS IN THE CASE PROVIDED.
3. DO NOT ATTEMPT TO ROTATE THE INSTRUMENT UNLESS
   THE TANGENT SCREW IS LOOSE.
4. AVOID GETTING THE INSTRUMENT WET, IF IT DOES GET
   WET, WIPE IT DOWN AND ALLOW TO DRY IN A SAFE AREA
   BEFORE STORAGE.
5. BATTERIES OF THE TOTAL STATION ARE NICAD AND THUS
   MUST BE CHARGED REGULARLY. AT LEAST ONCE PER
   MONTH, THE BATTERY SHOULD BE CYCLED.
6. CARE SHOULD BE TAKEN AT ALL TIMES, THESE UNITS
   ARE EXPENSIVE (8,000 - 45,000)

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Angles and Determination of Direction

• Angle difference in direction of 2 lines
• Another way of explaining is the amount of
  rotation about a central point
• 3 kinds of Horizontal angles Exterior (? to
  right) Interior Deflection
• To turn an angle you need
• A reference line
• Direction of turning
• Angular distance
• Angular Units
• Degrees, minutes, seconds (sexagesimal system)
• Circle divided into 360 degrees
• Each degree divided by 60 minutes
• Each minute divided into 60 seconds
• Radians
• 1 radian 1/2? of a circle 0.1592360
  57?1744. 8
• Grads (Centesimal System) now called Gon
• 1/400 of a circle or 0?5400 (100 gon 90?)

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Angles and Determination of Direction

• Angles turned in field must be accurate 3X
  least count is max. error
• Check 1 Close horizon when turning
• If traverse closes sum of the interior angles
  should equal the sum of
• (N-2)X180, N Number of sides
• 3 angles (3-2) 180 180?
• 4 angles (4-2) 180 360?
• 8 angles (8-2) 180 1080?
• 25 angles (25-2) 180 4140?
• If an exterior angle exists, subtract it from 360
  to obtain the interior ?
• Angular closure should be checked before leaving
  the field

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Angles and Determination of Direction

• If angular adjustment does not divide out
  equally
• Do not go to decimal unless instrument reads to
  decimal
• Observe field notes for angles with poor closure
  or where problems turning angles existed. Apply
  excess to these angles evenly.
• If unable to view field notes or no apparent
  source, generally apply excess to angles with
  shortest sides
• Bearings/Azimuths
• Bearing of a line is the acute horizontal angle
  between a reference meridian (North and South)
  and a line
• Azimuth of a line is the horizontal angle
  measured from the North meridian clockwise to the
  line

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Example
M
N
L
P
Q
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Angles and Determination of Direction
4 Point Comparison 4 Point Comparison 4 Point Comparison
Bearing Azimuth
1. Numeric Value 0-90? 0-360?
2. Method of Expressing 2 letters number Number only
3. Direction Clockwise counterclockwise Clockwise
4. Position of 0 point North and South North
It is always very important to have your field
sketch properly oriented
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Angles and Determination of Direction

• Rectangular Coordinates
• Totally based on computation of right triangle
• North South Movement Latitude D X cos A
• East West Movement Departure D X sin A
• Latitude running North are , South are
• Departure running East are , West are

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Angles and Determination of Direction

• Basic Procedure
• Determine Latitude and Departure
• Sum Lat. and Departure to calc. closure
• Obtain balanced Lat. and Dept. (Compass Rule)
• Determine coordinates
• Once rectangular coordinates are known on point,
  their exact location is known with respect to all
  other points in the network

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Example
B
47-28-00 483.52
F
99-39-30 421.97
279.33 320-42-00
392.28 188-27-30
A
E
26-16-30 452.66
C
236-27-00 886.04
D
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Angles and Determination of Direction

• Balancing Methods
• Compass Rule (Bowditch) Used when accuracy of ?
  and length measurement is equal
• (Error Lat./Perimeter length) X Distance
  Latitude Correction
• (Error Dept./Perimeter length) X Distance
  Departure Correction
• Transit Rule Used if angles are more accurate
  than distances (more accurate direction)
• Correction Latitude (Side) (Lat. Side/Sum all
  Lat.) X Lat. error
• Correction Departure (Side) (Dept. Side/Sum all
  Dept.) X Dept. error
• Crandall Method Used when larger random error
  exists in linear measurements that angular.
  Directional adjustments from balancing are held
  fixed and distances are balanced by a weighted
  least squares procedure
• Least Squares Based on the theory of
  probability. Angular and linear adjustments are
  made simultaneously. Hand methods are long and
  complex ?not often done. Computer adjustment
  through existing software make it feasible, which
  is why it is often used today

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Area, Inverse, Intersection

• Once rectangular coordinates are established on
  all points, the relationship to all other points
  is known. You can
• Determine area of all or any portion
• Determine length and direction between any 2
  points
• Locate new points by intersection

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Area, Inverse, Intersection

• Area Method is area by cross multiplication
• Using example from traverse lecture
• 
  
  NA X EB NB X EC NC X ED ND X EE NE
  X EF NF X EA Sum N
• EA X NB EB X NC EC X ND ED X NE EE X NF
  EF X NA Sum E
• Difference in Sums/2
  Square feet
• Square feet/43560 Acres

A 10000.0000 5000.0000
B 10326.7981 5356.3614
C 9938.7277 5298.7122
D 9448.9156 4560.3990
E 9854.7405 4760.8417
F 10070.8565 4583.9559
A 10000.0000 5000.0000
Sum N 294,119,678.8 Sum E 293,663,353.6 456,3
25.2 / 2 228,162.6 ft2 5.24 Ac?
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Area, Inverse, Intersection

• Example Determine Area of A, D, E, F, A

A 10000.0000 5000.0000
D 9448.9156 4560.3990
E 9854.7405 4760.8417
F 10070.8565 4583.9559
A 10000.0000 5000.0000
N 186,116,759.8 E 185,971,439.3 145,320.5 /
2 72,660.25 ft2 1.67 Ac ?
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Area, Inverse, Intersection

• Inverse With known coordinates of any two
  points on a system, you find the distance and
  direction between the two
• C 9938.7277 5298.7122
• D 9448.9156 4560.3990
• 489.8121 738.3132
• To find the Inverse between 2 Points
• Find difference in N E of coordinates
• Plot
• Use point you are going from 1st
• Plot longest side 1st
• Determine length using Pythagorean (a2 b2 c2)
  
• Determine reference direction
• Determine local ? using tan A a/b
• Determine line direction

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Area, Inverse, Intersection

• Example Determine direction and distance D-A

D 9448.9156 4560.3990 A 10000.0000
5000.0000 551.0844 439.6010
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Area, Inverse, Intersection

• Intersection Determination of unknown point
  location with directions from two points known
• Determine difference in coordinates
• Plot points and line projections
• Set up dual formulas (as Latitude and Departure)
• Solve for length
• Compute coordinate as sideshot

C 9938.7277 5298.7122 D 9448.9156 4560.3990
489.8121 738.3132
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Area, Inverse, Intersection

• Example What are the coordinates of the point
  of intersection of line C-F and D-A.
• Azimuth D-A 38?3446.
• Coordinates of D N 9448.9156, E 4560.3990

C 9938.7277 5298.7122 F 10070.8565
4583.9559 132.1288 714.7563
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Horizontal and Vertical Curves

• Horizontal curves are the basis for most Right of
  Ways
• Go through formulas
• Angle at PC and PT are always 90?
• Given any 2 elements T, L, C, R, D the remainder
  can be completed
• Example Horizontal curve, PC STA 20100
• D 36?1500
• R 1200.00
• T
• L
• C
• Seg
• PI STA
• PT STA

67
Horizontal and Vertical Curves

• Vertical Curves Two major methods used to
  calculate vertical curves Tangent offset and
  Equation of Parabola
• Information needed
• Grade or slope on each side of curve
• Elevation and station of PVI
• Curve length (Horizontal distance PVC PVT)

68
Horizontal and Vertical Curves

• Tangent Offset Method
• Procedure
• Compute the elevation of the PVC and PVT
• Compute the elevation of Chord midpoint
• Compute offset to curve at midpoint
• Determine total number of stations covered
• Determine tangent elevations at stations
• Compute curve offset at stations
• Combine data and determine vertical curve
  elevations

69
Horizontal and Vertical Curves

• Equation of Parabola Method
• Equation r g2 - g1 / L
• g1 initial grade
• r change in grade/sta.
• g2 final grade
• L length of curve in stations
• Procedure
• Compute PVC and PVT elevations
• Calculate total change in grade/station
• Insert data to chart and compute final curve
  elevations
• To find the elevation at the high point or low
  point,
• find the station at which it fall and include
  that
• station in the elevation computations
• The equation gives the distance from the PVC in
  stations

70
Leveling

• Leveling is the determination of the elevation of
  a point or difference between points referenced
  to some datum
• Terms
• Datum any level surface to which elevations are
  referenced
• Mean Sea Level (MSL) the average height of the
  surface of the sea for all stages of the tide
  over a 19 year period at 26 tide stations along
  Pacific, Atlantic and Gulf
• National Geodetic Vertical Datum nationwide
  reference surface for elevations throughout the
  U.S. made available by National Geodetic Survey
  (NGS), based on 1929 adjustment.
• Benchmark relatively permanent object bearing a
  marked point whose elevation above or below an
  adopted datum.

71
Leveling

• Most often Mean Sea Level is used
• MSL varies along the coasts
• Pacific is almost 2 higher than Atlantic and
  Gulf
• U.S. System National Geodetic Vertical Datum of
  1929
• Has been used as reference for extensive network
  of BMs
• BMs are periodically adjusted as to elevation
• Best to check with USGS or NGS for current
  elevation of a BM and also best to check between
  two known BMs to verify elevation difference.

72
Leveling

• The level surface parallels the curvature of the
  earth ?a level line is a curved line, normal (?)
  at all points to plumbline
• Line of sight is only normal at point of
  instrument
• A line with a sight distance of 1 mile using the
  earths radius as 3959 mile, curvature change is
  0.667 feet.
• Refraction of line of sight of level is downward
  by a small amount
• The combined curvature refraction amounts for
  short distances (normal sight dist. for levels)
  are
• 100 0.0002
• 200 0.0008
• 300 0.0019
• 500 0.0052

Value is small ? for most instances can be
neglected
73
Leveling

• Most common leveling instrument today is the
  Automatic or Self-leveling level has an
  internal compensator that automatically provides
  a horizontal line of sight and maintains this
  through gravity (prism hanging on pendulum)
• Differential Leveling (Spirit Leveling) Most
  common type today
• Determine the difference in elevation using a
  horizontal line of sight and readings on
  graduated rod
• Circuit must be closed on BM of origin or on BM
  of equal accuracy
• Process
• Reading on point of known elevation (BS)
• BS reading BM elevation HI
• Reading on point of unknown elevation (FS)
• HI FS elevation of new point

74
Leveling

• Systematic Error in Leveling
• Inclination of line of sight due to curvature of
  earth and refraction generally very minimal due
  to short sights
• Inclination due to maladjustment of instrument
• Both can be alleviated by equalizing length of BS
  and FS legs
• Changes in scale of rod due to temperature
• Usually ignored except in very precise work
• Would use same process as tape correction
• Rod not held plumb
• Minimized by carefully plumbing the rod or more
  commonly known as Rocking the Rod and taking
  the lowest reading

75
Leveling

• Peg Test
• Set 2 marks at 300 apart, also mark center point
  in a relatively flat area
• Set level at midpoint and take readings at each
  end
• Determine difference in readings (difference in
  elevation)
• Move level to one end and setup so that level is
  just in front of rod on point
• Read rod by looking backward through scope
  (X-hair not visible), hold pencil on rod to
  determine reading
• Read rod at other end in normal manner
• Difference in readings should equal 3
• If values are not equal, there is error
• Most instruments have adjustment screws
• Adjust and repeat test as a check

76
Seven Basic Rules of Differential Leveling

1. Balance length of BS and FS (300 max)
2. Make sure gun is level and pendulum free
3. Turn through all BMs
4. Give complete description of BMs and TBMs
5. Have rod rocked
6. Make sure turning points are solid
7. Close all circuits on BM of same degree of
   accuracy

77
Other Random Errors

1. Incorrect rod reading most common viewing foot
   number above and recording it
2. Parallax having the X-hair not properly focused
3. Heat Waves limit shot lengths

78
Field Notes

• STA BS HI FS ELEV
• Sum BS Sum FS Difference of Elevation

79
Closure Error

• Difference in measured elevation and know
  elevation
• Correction factor closure / turns
• Error 0.09
• Turns 12 Correction 0.0075 / turn
• If TBMs set, break circuit into sections
• Figure correction factor the same
• Figure correction by taking CF X turns in
  section

80
Precise Leveling

• Precise Leveling Accuracy obtained by quality
  of instruments and care taken in the field
• High quality automatic levels are utilized
• Level rods are equipped with rod level, rod shoe
  (to allow better setting on BMs) scale (on rod)
  is made of invar steel (not affected by temp
  generally called Invar Rod)
• Reading either taken by optical micrometer or a
  process called 3-wire leveling is used (all 3
  wire are read and averaged)
• Optical micrometer line of sight deflected by
  turning micrometer screw to read subdivision on
  rod.
• Rod division is read as normal then fractional
  reading taken from micrometer screw, thus on
  normal rod readings to 0.0001 are possible

81
Topographic Surveying

• Topographic surveying is the process of
  determining the positions, on the earths
  surface, of the natural, and artificial features
  of a given locality and of determining the
  configuration of the terrain.
• Planimetry location of features
• Topography configuration of the ground
• Both produce a topographic map which shows the
  true distance between objects their elevations
  above a given datum
• Topos can be done by field methods, or by
  photogrammetric methods. (Photo also requires
  some field work)
• Topo map is 1st step in a construction project

82
Topographic Surveying

• Scale and accuracy Both depend on what used for
• Method of Representing
• Most common is Contour Line Imaginary line on
  surface of the earth passing through points that
  have equal elevation
• Contour Interval Vertical distance between
  lines
• Topo map with contour lines shows elevation of
  points on ground shapes of topographic features
  (hills, etc.)
• USGS Topo 10 or 20 contour intercal
• Subdivision 2 or 4
• Index Contour every 5th contour drawn heavier
  on maps
• Slopes X-sections can be obtained from contours

83
Topographic Surveying

• Interpolating can find elevation of any point
  or find contour line with known elevation of
  point
• Contour lines that close represent either a hill
  or depression and can be represented as
• Marks are called hatchures (used most in
  depressions)

84
Characteristics of Contours

1. Each contour must close upon itself with within a
   map or outside its borders a contour line
   cannot end on a map except at the edge
2. Contours do not cross or meet except in caves,
   cliffs vertical walls where they can meet
3. Contour lines crossing streams form Vs pointing
   upstream
4. Contour lines crossing a ridge form Us pointing
   down the ridge
5. Contour lines tend to parallel streams

85
Characteristics of Contours

1. Contour lines are uniformly spaced on uniform
   slopes
2. Horizontal spacing between contour lines
   indicated steepness of slope on ground
3. Contours are generally perpendicular to direction
   of maximum slope
4. Contours can never branch into 2 contours of the
   same elevation

86
Field Methods of Topos

• Factors That Influence Method
• Scale of map
• Contour interval
• Type of terrain
• Nature of project
• Equipment available
• Required accuracy
• Existing control
• Extent of area to be mapped

87
Field Methods of Topos

• Methods
• Cross section railroad of highway
• Trace contour drainage or impoundments
• Grid small areas
• Controlling point large area, plane table
• Theodolite EDM - radial

88
Field Methods of Topos

• Cross Section Method (Plus Offset)
• Equipment used Transit, tape, and level
• Establish horizontal control traverse between
  control points stakes set at cross section
  intervals
• Run profile of traverse line
• Take cross section
• Locate planimetric features from traverse line

89
Field Methods of Topos

• Trace Contour
• Contour is by traverse
• Establish elevation of each station
• Contour elevation established and is then
  followed by rodperson
• Contour elevation is marked, then tied to
  traverse line by plus-offset
• Most accurate and expensive work
• Elevation of reservoir water line
• 2 transit use

90
Field Methods of Topos

• Grid Method
• Establish baselines
• Estimate grid of uniform size smaller grid
  more accurate
• Number grid
• Shoot elevation at each point
• Tie existing objects to grid points

91
Field Methods of Topos

• Controlling Point Method (old and sketched in
  field)
• Determine position elevation of pre-selected
  control points
• Depends greatly on experience judgment of
  people doing work
• Required traverse of area (CPs)
• Locations are made elevations obtained along
  control points then intermittent topo sketched
  in

92
Field Methods of Topos

• Theodolite EDM (Radial)
• Replaces tacheometry (stadia)
• Establish control points (horizontal and
  elevation)
• Shoot locations and turn vertical angles
• Used for large areas

93
Field Methods of Topos

• Common mistakes in topo surveys
• Improper selection of contour interval
• Unsatisfactory equipment or field method for the
  particular survey and terrain conditions
• Insufficient horizontal and vertical control of
  suitable precision
• Omission of some topographic details

94
Mine Surveying

• Points are on roof of mine
• Reasons needed
• Location in respect to boundaries
• Location in respect to other shafts
• Accurate maps (above and below ground)
• Quantities
• Equipment and Terms
• Spad Beams that you hold plumb bob from
• Bracket Mounting instrument from timber
  supports
• Trivet Tripod thats about 1 tall
• Gyroscope Locate north
• Laser vertical collimator located point at top
  of vertical shaft platform
• Plumb shaft Using piano wire then wiggle in at
  bottom

95
Global Positioning Systems (GPS)

• Developed in early 1980 s (Dept. of Defense)
• Made up of 26 satellites (24 functioning 2
  spares)
• Each satellite is 20,000 km high (off Earths
  surface)
• Each satellite is in a fixed position
• Minimum of 3 satellites needed, but 4-5 preferred
• Need satellites at least 15 above horizon
• Locate positions on Earth by distance-distance
  intersection
• Need 2-3 receivers (80-100K per system)
• Most accurate with double occupancy (no other
  checks)
• Differential GPS one receiver on known point,
  other receiver on unknowns

96
Global Positioning Systems (GPS)

• Biggest advantage
• Distance and direction in-between 2 points
  without being seen
• Downfalls/Limitations of GPS
• Multipath bouncing off of walls of buildings
• Blocked signals clouds, trees, etc.
• Sunspot defraction from atmosphere
• DOP (Delusion of Position) bad satellite
  position
• Set up error not set up exactly over point
  (human error most common)

97
Global Positioning Systems (GPS)

• Methods
• Static observation time is at least an hour
• Ideally set points in triangular fashion
• Accuracy 1/10 million
• RTK (Real Time Kinematic) stand for 30-60
  seconds minimum
• Base receivers transmission, does corrections,
  sends corrections to receivers
• Limitations limitation of transmitter signal

98
Geographic Information Systems (GIS)

• GIS are computer programs that allow users to
  store, retrieve, manipulate, analyze and display
  spatial data
• Spatial Data (Geographic data) any data that
  represents information about the Earth
• GIS components
• Recent definitions of GIS suggest that is
  consists of
• Hardware (computer and operating system)
• Software
• Data
• Human Operators and Institutional Infrastructure

Geographic/Spatial Non-Geographic/Aspatial/Attrib
ute
99
GIS Data Structures

• Vector Made up of points, lines, and polygons

100
GIS Data Structures

• Raster (Grids) Made up of pixels of computer
  screen

101
GIS Data Structures

• DEM (Digital Elevation Model) Digital terrain
  representation technique, where elevation values
  are stored in raster cells

102
Future of Surveying

• Major advances in future
• Remote Sensing (Government and Military)
• Arial Photographs
• Design Professions
• Every 10 years, must justify to Legislature that
  need for our license exists
• Surveyor have ULTIMATE liability
• Standards ? Laws
• Continuing Education Enough points every 2
  years