Department of Geomatics

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The Department of Geomatics451-102 Surveying
for Builders (B.P.D.)
Lecture 3 - Linear Measurement Dr Allison Kealy
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Distance Measurement

• Direct
• Tapes
• Pacing
• Indirect
• optical
• Electronic
• Satellite

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Pacing

• Practical measure of distance.
• Consists of measuring the number of steps in the
  required distance.
• Varies uphill, downhill, with age.
• Accuracy sufficient for low accuracy
  applications.
• Can be used to determine blunders in other
  methods of distance determination.

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Direct Distance Measurement

• flat
• stepping
• catenary
• height difference

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Distance Measurement by Taping
Applying the known length of a graduated tape
directly to a line a number of times.
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Tapes

• Steel, invar, cloth, fibreglass.
• 100m, 20m, 30m.

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Taping - Field Procedure

• ranging rods set up between points A and B
• from A to B, set zero of tape at A
• tape unwound towards B
• A third range rod is ranged in at C
• Tape straightened, held taut and read at rod C
• C marked with an arrow
• for next bay, tape moved from A and zero set at C
  and so on

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Taping Slope Measurements

• Measure angle of inclination and slope distance.

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Taping - Errors

• Gross
• personal
• Systematic
• standardisation - calibration over time
• tension - manufactured and calibrated at a set
  tension
• temperature - manufactured and calibrated at a
  set temperature
• sag - in catenary the tape will sag under its own
  weight
• Random
• Plumbing, marking, interpolation

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Standardisation

• tape has a nominal length under certain
  conditions
• over time a tape stretches
• standardisation needs to be carried out
  frequently
• use reference tape or baseline
• L recorded length of line
• l nominal length of field tape (eg 30m)
• l standardised length of field tape (say
  30.011m)
• sign of correction depends on the values of l and
  l

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Tension

• tape length varies with applied tension
• steel tapes manufactured and calibrated to 50N
• use of standardisation tension better
• spring balance
• TF tension applied to the tape (N)
• TS standard Tension (N)
• A cross sectional area of the tape (mm2)
• E modulus of elasticity for the tape material
• sign of the correction depends on TF and TS

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Temperature Variations

• steel tapes expand and contract with temperature
• calibrated at a standard temperature of 20o C
• temperature should be recorded for improved
  precision
• allow tape and thermometer to attain stable
  conditions
• a the coefficient of expansion of the tape
  material
• tF mean field temperature (oC)
• tS temperature of standardisation (20oC)

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Catenary - Sag

• on irregular surfaces, might need to suspend the
  tape above the ground between the points
• use tripods or wooden stakes
• for long lines, need to align tripods or stakes
• tape will sag under its own weight in the shape
  of a catenary curve

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Catenary - Sag

• q the angle of slope between the tape supports
• w the weight of the tape per m
• TF the tension applied to the tape

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Combined Formula
What errors are left?
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Steel Taping - Examples

• A steel tape of nominal length 30m was used to
  measure a line AB by suspending it between
  supports. The following measurements were
  recorded
• Line Length Measured Slope Angle Mean
  Temp. Tension
• AB 29.872 3o 40 5oC 120N
• The standardisation length of the tape against a
  reference tape was known to be 30.014m at 20oC
  and 50N.
• If the tape weighs 0.17Nm-1 and has a cross
  sectional area of 2mm2, calculate the horizontal
  length of AB

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Steel Taping - Examples
horizontal length AB 29.872-0.06110.01390.00
52-0.0050-0.0022 29.823m
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Methods of distance measurement
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Principle of Operation
velocity distance/time
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EDM Classification
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EDM Classification
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EDM Classification
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EDM Classification
s
(ABd)
where A in mm, B in ppm, d distance (in
km) ppm - part per million, portion of error in
1000m eg 7ppm would be /- .007m
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EDM Classification

• Degree of integration with theodolites
• minimal range should be 500m
• small, light, low power requirements
• measuring beam of the instrument should move
  simultaneously with the line of sight of the
  theodolite
• automated
• horizontal and slope distances
• tracking
• minimum number of units

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EDM Classification
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Peripherals

• Atmospheric pressure
• pocket barometers
• hand held barometers
• Atmospheric temperature
• mercury in glass thermometers
• platinum resistance thermometers
• electronic thermistor thermometer
• Atmospheric Humidity
• aspiration psychrometer
• humidity sensor

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Reflectors

• reflects the light back to the instrument, should
  have the following properties
• good reflectivity
• complete illumination of the receiver optics of
  the instrument
• no change direction of emerging rays through
  small movement of the reflecting device, thus
  rendering a continuous alignment unnecessary
• solid glass prism reflector (most suitable)
• can be plastic, cats eyes, cheaper, short
  ranges
• acrylic retroreflector
• reflective sheeting

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Special Features of Modern Short range EDM

• on-board application of first velocity correction
• computaion of horizontal distance and height
  difference
• tracking mode
• audio signal
• automatic data recording
• computer assisted surveying
• setting out aids
• pointing aids

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Importance of Calibration

• quality control
• the significance of the corrections with respect
  to the work required of the instrument
• whether the instrument is working within the
  manufacturers specified s
• whether the instrument requires a service
• whether any systemmatic errors exist
• improvement of accuracy
• applying corrections to measured values improves
  the accuracy
• legal metrology

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Calibration Concepts

• baseline calibration (rigorous, mathematical)
• field calibration (practical)

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Instrumental Errors

• Reflector
• Distance Meter

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Reflector Constant

• EDM beam travels in air between instrument,
  reflector and instrument
• velocity of light in glass slower than in air
• correction due to non-coincidence between the
  reflecting plane and the prism house plumbing
  point
• can be combined with the additive constant for
  the EDM instrument

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Errors of Electro-optical Distance Meters

• Additive Constant
• Scale
• non-linear distance dependent
• Short periodic - cyclic

corrections rather than errors form components
of an overall instrument correction IC
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Additive Constant

• zero correction, index correction
• applies to both the instrument and the reflector

Definition Due to a difference between the
mechanically defined centres of the instrument
and reflector and their electrical (optical)
centres. The error when present and not allowed
for, produces an effect akin to miscentering of
the instrument by the operator and is independent
of range.
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Scale
Definititon The modulation frequency does not
correspond exactly with the design value. This
error originates mainly in the crystal controlled
oscillator and produces errors on measurement
directly proportionally to distances.
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Electrical or optical crosstalk

• electrical coupling between the reference signal
  and the measurement signal
• optical crosstalk between transmitter and
  receiver optics in EODMs

page 176 Electronic Distance Measurement, Rueger
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EDM Calibration

• instrument/reflector specific

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Field Calibration

• An EDM instrument can be tested and calibrated
  for all errors one at at time, or simultaneously
  using a baseline
• an easy method is to determine each error by a
  series of tests which should be performed in the
  following order
• Test to determine the degree of cyclic error
• Determine the value of the additive constant
• Measure known distances to find the scale error