Leveling

1
Chapter 7

• Leveling

2
Differential Leveling

• Necessary Definitions
• A Bench Mark (BM)
• Is a relatively permanent point of known
  elevation. A bench mark should easily be
  recognized and found, and should be set fairly
  low in relation to to the surrounding ground.
• A Turning Point (TP)
• Is a temporary point whose elevation is
  determined during the process of leveling. It is
  recommendable to use points that are easily
  identifiable so that the level rod can be removed
  and put back as many times as required.

3
Differential Leveling

• Necessary Definitions
• A Back Sight (BS)
• Is a sight taken to the level rod held on a point
  of known elevation, it can be either a BM or a TP
  to determine the height of an instrument (HI).
• A Foresight (FS)
• Is a sight taken to any point to determine its
  elevation. The only limitation to the number of
  sights are the length of the rod and the power of
  the telescope on the level.

4
Differential Leveling

• Is the process of determining the difference in
  elevation between 2 points. The initial BS can be
  taken to be a point of known elevation, a bench
  mark, or to a point of assumed elevation. If the
  starting point is a BM the elevations for the
  subsequent points are actual elevations.
• However if the elevation of the starting point is
  an assumed elevation, than the elevation of the
  subsequent points are considered relative
  elevations.

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Differential leveling
6
Earth Curvature and Atmospheric Refraction

• To this point we have been assuming that when the
  instrument is leveled, its line of sight will
  represent a level line.
• This is not truedue to atmospheric refraction.
• When rays of light pass through air strata of
  different densities, they are refracted, or bent
  downward. This amount of refraction is dependent
  on temperatures, pressures, and relative
  humidities.

7
Corrections

• Accounting for earth curvature
• D2 E2 ( EC)2
• this is equivalent to C 0.0001263 D2 miles
• When we change the value to feet
• C (0.0001263)(5280) 0.667 D2 ft
• Due to refractions
• An average value is assumed 0. 093 ft in 1 mile
  sight distance.
• Note that the errors are compounded

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Corrections
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Corrections

• The combination of the earth curvature, and
  atmospheric refraction
• C (0.667 0.093) 0.574 ft in 1 mile.
• C 0.574 M2
• For SI units C 0.0675 k2, C is in meters, and
  k is distance in Km.

10
Verniers

• Is a device for making readings on a divided
  scale closer than the smallest division on the
  scale. Was invented in 1620 by Pierre Vernier a
  Frenchman.
• On rod readings, most verniers scales are of 10
  divisions, or the measurements can be accurate to
  the 0.001 ft.
• 10 divisions on the verniers scale coincide with
  9 divisions on the rod, I.e. each division on
  the vernier is 0.009 ft.

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Verniers how does it work?

• To read the a level rod vernier, the bottom of
  the vernier is lined up with the horizontal cross
  hair and the reading is determined by counting
  the number of vernier divisions until a division
  on the vernier coincides with a division on the
  rod. This reading is than added to the last
  division on the rod below the bottom of the
  vernier.

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Verniers
13
Level Rod Targets

• For long sights or for situations in which
  readings to the nearest 0.001 ft are desired, a
  level rod target may be used. Targets are small
  elliptical pieces of metal painted in red and
  white, a vernier is part of the target.

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Rod Target
15
Common Mistakes

• Misreading the Rod
• Moving turning points
• Field note mistakes
• Mistakes with extended rods

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Leveling errors

• Level rod not vertical
• Settling of level rod
• Mud or snow accumulated on base of the rod
• Rod not fully extended
• BS and FS distances not equal
• Bubble not centered on level
• Improper focusing of telescope
• Heat waves
• Wind

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Suggestions for good leveling

• Anchor Tripod legs firmly
• Check to be sure that bubble tube is centered
  before and after rod readings
• Take as little time as possible between BS and FS
  readings
• Try to set up the level as distances from BS and
  FS are equal
• Provide rodmen with level rods that have level
  tubes so the rods can be plumbed or they can
  wave the rod slowly toward and away from the
  instrument
• On slopping ground, two of the tripod legs should
  be placed on the down hill side.

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Precision of Differential Leveling

• Rough Leveling
• or 0.4 ?M
• Average
• or 0.1 ?M
• Excellent
• or 0.05 ?M
• M is the number of miles leveled.