The Measurement of Distance

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The Measurement of Distance

• Techniques, errors and computations

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Distance

• Traditionally, long distance measurement was
  difficult
• So it was generally avoided
• Distance on land was hard, distance at sea even
  more so
• Developments in the industrial revolution made
  the process easier
• Rapid advances since WWII

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Measuring devices

• Guessing
• Pacing
• Knotted bits of rope
• The Surveyors Chain
• Steel measuring bands
• Radar, laser, GPS

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The Pharaoh's tax collectors
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Triangulation

• For centuries, the determination of distance was
  done by triangulation
• One baseline was measured accurately
• The rest was done by forming connected triangles
• Laser distance meters and GPS have killed this!

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Triangulation of Victoria

• Performed with one distance, measured at Werribee

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The Survey of India
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Gunters Chain

• Invented in 1620
• Comprised 100 links
• Subject to wear
• But used for centuries

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The Surveyors Band

• Made from steel, marked every whole unit only.

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(No Transcript)
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Radar

• Developed during WWII
• Deployed soon after for geodetic distance
  measurement

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The Stylon tape
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Laser EDM

• Uses either visible or near-visible laser
• Light amplification by simulated emission of
  radiation
• Determines the distance by effectively timing
  the laser pulse as it travels to the object and
  back
• We need to know the speed of light

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Principles
EDM

• Errors include the length travelled through the
  reflector, the speed of light, and others

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Lunar Laser Ranger

• Monitors the distance to the moon by measuring to
  banks of prisms left by the Apollo Missions
• Yes, the US did land on the moon!

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Systematic Errors

• All the physical devices based on steel are
  subject to systematic errors
• Those based on laser or radio are also subject to
  systematic errors
• Somewhat more involved, leave most until 2nd year
• ALL of them need to be corrected for slope

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Slope

• Whilst we consider the Earth to be a plane, it is
  not flat.
• Our reference plane is flat, so we need to
  correct ALL distances to the horizontal
• It applies to tapes, bands and EDM

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Slope
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Slope Correction
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Slope Correction

• Failure to apply slope correction is a MISTAKE,
  not an error
• There may be many slopes along a long line
• Each needs to be applied separately

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Other Systematic Errors

• Standardisation
• It is 50.000m when it says it is 50.000m
• Temperature
• Steel expands and contracts
• Tension
• Steel also stretches under tension
• Sag
• Happens to us all, steel hangs in a catenary

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Standardisation

• Required by legislation for cadastral surveys
• Steel based bands and tapes tend to stretch over
  time
• The field tape is compared to a standard tape

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Standardisation
for example l
226.20m assumed tape length 30.000 m
actual tape length 30.005 m
L 226.20 x L 226.238 m
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Temperature

• Steel expands by about 1mm per degree Celsius per
  hundred meters
• c1.15 x 10-5 m/C
• If it is hot, the reading on the steel tape will
  be shorter than the actual length
• This needs to be corrected

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Temperature
L l (l . c . ?t) for example, if
standard temp 20C (usual)
field temp 37C (hot!) and we measure a
distance l 79.984 c1.15 x 10-5
m/C then L 79.984 (79.984 x 1.15 x
10-5 x 17) L 80.000 m
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Sag or Catenary

• The correction is as follows
• We need the mass/unit length
• We need to measure the tension
• Best to avoid sag!

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Sag
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The Global Positioning System (GPS)

• The fundamental of GPS is the measurement of
  distances from the satellites to the receivers
• It is a very involved process, but it works!

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Applications

• Measurement of land boundaries
• The occupation needs to be measured using tapes
  or chains
• Topographic mapping
• Generally using a total station
• Engineering construction
• The lay-out of structures
• The monitoring of structures