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Concepts

Presentation Concepts v1

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Concepts

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Exterior angle

255° 18

Looped Station A is Fixed Connecting Stations A & B are Fixed

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Foresight line

Prolongation of backsight line

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?

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The bearing of a line isthe direction of the line

with respect to a givenmeridian. A bearing is

indicated by thequadrant in which the

line falls and the acuteangle that the line

makes with themeridian in that

quadrant.

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The azimuth (or bearing) from A to B ( ) is determined by reducing the observed azimuth to therelative quadrant. In Figure, if the azimuth from Point A to the Azimuth Mark is 320° , and observed angle "" from Station A between the reference azimuth point and Point B is 105° , then the azimuthof the line from Point A to Point B "" is computed from:

Azimuth ( ) from A B = 105° - (360° - 320° ) = 65° [or bearing N 65° E ]

The computation of the difference in northing (dN) and the difference in easting (dE) requires thecomputation of a right triangle.The distance from Station A to Station B ("s" in Figure, reduced tohorizontal, sea level, corrected for grid scale, etc.) is the hypotenuse of the triangle, and thebearing angle (azimuth) is the known angle.The following formulas are used to compute dN and

dE:  dN = s · cos () dE = s · sin ()8

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� Differences in elevation are measured with respect to a horizontal line of sight established by theleveling instrument.

� Once the instrument is leveled (using either a spirit bubble or automated compensator), its line of sight lies in a horizontal plane.

� Leveling comprises a determination of the

difference in height between a known elevationand the instrument and the difference in height from the instrument to an unknown point by measuring the vertical distance with a precise or semi-precise level and leveling rods.

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� Applies the fundamentals of trigonometry to

determine the differences in elevation

between two points by observing horizontal distance and

vertical angles above or below a horizontal plane

� Trigonometric leveling is generally used forlower-order accuracy vertical positioning.

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� Trigonometric elevations over longer lines may needto be corrected for curvature and refraction.

� Corrections are insignificant (< 0.02 ft) and

unnecessary for topographic survey distances of 1,000 feet or less.� Wolf and Brinker formula is used to determine the

combined curvature and refraction correction fortrigonometric elevations observed over longer lines.

h = 0.0206 (F)2

whereh = combined correction for curvature and refraction infeet and 

F = length of observed line in thousands of feet 

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� Uses the differences in atmospheric pressureas observed with a barometer or altimeter to

determine the differences in elevationbetween points.� Least accurate of determining elevations.� Should only be used when other methods are

not feasible or would involve great expense.� Generally, this method is used for elevations

when the map scale is to be 1:250,000 orsmaller.

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� Carrying a level circuit across an area over

which it is impossible to run regular

differential levels with balanced sights.� Most level operations require a line of sight to

be less than 300 or 400 feet long.

� May be necessary to shoot 500-1,000 feet, or

even further, in order to span across a river,canyon, or other obstacle.

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3-wire leveling are short cross lines thatcannot be mistaken for the long centralline used for ordinary leveling.

The rod is read at each of the three lines and

the average is used for the final result.Before each reading, the level bubble is

centered.The half-stadia intervals are compared to

check for blunders.

Upper Wire:  8.698 2.155 :Upper Interval

Middle Wire: 6.543 Lower Wire: 4.392 2.151 :Lower Interval

Sum 19.633  Difference = 0.004 only

Average 6.544  18

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44

2

1

32

0

1

1

etc.

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International Terrestrial ReferenceFrame (ITRF). North American Datum of 1983 (NAD 83).

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Retro-reflectorprisms

Extendable

rods 20 feetand above

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Ref erence ase  Remote (Rover)

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3D Laser Scanner Laser scanned and Rendered Image

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Rules WCB RB Quadrant

1 0 - 90 = WCB - 0 NE

2 90 - 180 = 180 - WCB SE3 180 - 270 = WCB - 180 SW

4 270 - 360 = 360 - WCB NWN

W E

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Rules RB WCB Quadrant

1 0 - 90 = RB - 0 NE

2 90 - 180 = 180 - RB SE3 180 - 270 = RB + 180 SW

4 270 - 360 = 360 - RB NWN

W E

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� Direction of survey line

Bearing (direction relative to any meridian) or

Angle with relation to another line

� Bearings

True meridian (with imaginary line betweengeographical north and south poles)

Magnetic meridian (direction shown by a freelysuspended magnetic needle)

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Thank you