Angle Measuring Equipment

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Angle Measuring Equipment

• Plane tables (graphical methods)
• Sextants
• Compass
• Tapes (or other distance measurement)
• Repeating instruments
• Directional instruments
• Digital theodolites and total stations

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Determining Angles Taping
Need to measure 90 angle at point X
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Determining Angles Taping
B
?
C
A
Need to measure angle ? at point A
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Determining Angles Taping
Need to measure angle ? at point A
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Determining Angles Taping
Need to measure angle ? at point A
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Repeating Instruments

• Very commonly used
• Characterized by double vertical axis
• Three subassemblies

7
Directional Instruments

• Has single vertical axis
• Zero cannot be set
• More accurate but less functional

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Total Stations Zeiss Elta 50R

• Combined measurements
• Digital display

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Measuring Angles

• Instrument handling and setup
• Discussed in lab
• Procedure with repeating instrument

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Repetition and Centering

• Repetition provides advantages
• Centering process

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Centering
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Measuring Angles

• Procedure with directional instruments
• Most total stations are directional instruments

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Measuring Vertical Angles

• Procedure
• Improving measurements

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Angle Measuring Errors and Mistakes

• Personal errors
• Mistakes

• Instrumental errors
• Natural errors

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Readings

• Chapter 8 sections 8.1 8.14, 8.20 8.22

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Horizontal Distance Methods

• Approaches
• Pacing
• Optical rangefinders
• Odometers
• Tacheometry (stadia or subtense)
• Taping
• Electronic Distance Measurement (EDM)
• Global Positioning System (GPS)
• Issues
• Often measure surface or slope distance
• Potential error or need to reduce to horizontal

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Incorrect Length of Tape

• Concept
• Solution
• Correction

• Example

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Variations in Tape Temperature

• Concept
• For steel coefficient of thermal expansion (k)

• Correction

• Issues

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Incorrect Tension

• Concept
• For steel

• Correction

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Sag

• Concept

• Correction

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Tape Not Horizontal

• Concept
• Occurs when tape is not kept level
• Solution
• Corrected using Pythagorean Theorem

• Or by approximate correction

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How Far Off Can You Be?

• Problem
• No matter how hard you try, never have a
  horizontal tape
• Question
• When does departure from horizontal cause
  significant error in result?
• In field
• Try to keep tape horizontal within this limit
• Or compute a correction

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Incorrect Alignment/Tape Not Straight

• Concept

• Incorrect alignment

• Tape not straight

• Correction

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Taping Correction Problem

• Background
• Steel tape calibrated at 68F (supported
  throughout) at 5 kg tension is found 30.006m
  between 0 m and 30 m marks
• Tape has cross-sectional area of 0.003 in2 and
  weighs 0.7 kg
• Problem
• Crew is taping by laying tape along ground down a
  uniform grade from point A to point B
• Point A is 190.45m AMSL and point B is 175.68m
  AMSL
• Temperature is 88F and tension is 7 kg
• Final recorded distance is 148.47m
• What is corrected length of tape?

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Tacheometry

• Concept
• Methods
• Stadia

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Tacheometry Stadia
L1
?
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Stadia Principles

• Need simple method for establishing
• Method

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Stadia Readings
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Stadia Principles
C
d
c
f
A
b
b'
i
S
a
a'
F
B
D

• A,B rod intercepts
• a, b stadia hairs
• S rod intercept
• F principal focus of objective lens

• C stadia constant
• K f/i stadia interval factor
• d distance from focal point to rod
• D distance from instrument center to rod

• f focal length
• i stadia hair spacing
• c distance from instrument center to objective
  lens center

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Stadia Equations

• From similar triangles

• Horizontal sights

• Inclined sights

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Issues with Stadia Measurements

• Stadia common for map data collection
• Accuracy of stadia
• Current situation

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Tacheometry

• Concept
• Determine distances indirectly using triangle
  geometry
• Methods
• Stadia
• Establish constant angle and measure length of
  opposite side
• Length increases with distance from angle vertex

• Subtense

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Tacheometry Subtense
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Subtense Principles

• Need simple method for establishing
• Issues

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Subtense Equation

• Derive equation for computing distance by
  subtense

?
L

• What value would you choose for L?

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Issues with Subtense Measurement

• Principles still useful in many situations
• Accuracy of subtense
• Current situation

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Readings

• Chapter 6 sections 6.6, 6.7, 6.14 6.16
• Chapter 16 section 16.9.2