BRAE 237 Final

Errors: Blunders

• Due to mistakes, faulty measurements, or wrong methods

• Does not follow statistical rules

• Must be avoided with care and control routines

• Detected by redundancy (multiple observations)

• AKA “Gross Errors” or “Outliers”

• Example: recording 50° 32’ 50.9’ instead of 50° 32’ 5.9”

Errors: Random

• Unpredictable, non-systematic deviations

• Caused by instruments, environment or human factors

• Smaller errors occur more often than larger ones

• Positive and negative errors occur equally

• Average tends toward zero with many observations

• Studied with: probability and statistics

Errors: Systematic

• Follows physical or mathematical rules

• Affects results in a consistent way

• Causes: instrument calibration, environment, human routines

• Strategies:

  • Calibrate instruments

  • Improve measurement routines

  • Apply corrections

• Example: Tape with constant 5 inches error

Datum

Level surface taken as a surface of reference

• Elevation = vertical distance from the datum

• Benchmark = a permanent object, having a marked point whose elevations relative to a specific datum is known

Stationing

• Defines position along curvilinear feature

• Used on any type of “Route” project

• Similar to distance

  • Always measured along the feature

  • Along the arc of the curves

• Shown by adding a “+” between the 100ft and 10ft marks

  • Example: 1234.56 = 12+34.56

Contour

Lines of equal elevation

• Contour interval = vertical difference between adjacent contours

• Index contours = contour with heavy line work and labels

• Never cross, always close on themselves, parallel each other

Scale

Distance on the ground / Distance on Map

• Always use engineering scale

• Example:

  • Horizontal scale: 1” = 40’

  • Vertical scale: 1” = 10’

Profile Survey

A surveying method used to measure and document ground elevations along a specific, linear alignment

• Select critical points along profile line

  • select intermediate points between critical points

• Also when starting a critical point

  • note general direction of intersection linear features (paths)

Precision

The quality of the repeatability of measurement

Accuracy

Absolute relationship between the measured value and the true value

Averaging Doubled horizontal angles

• Measure HA of BS

• Meaure inverted angle of BS

• Measure HA of FS

• Measure inverted angle of FS

• Subtract FS from BS

• Subtract inverted FS from inverted BS

• Take averages

Calculating horizontal distance from total station measurements

• EDM (Electronic Distance Measurement) of the Total Station measures the SD (Slope Distance)

• HD = sin (ZA) x SD

  • HD → Horizontal Distance

  • ZA → Zenith Angle

  • SD → Slope Distance

Calculating elevation from total station measurements

Elevation_prism = Elevation_setup + hi + VD - HR

• hi → Height of Instrument

• VD → Vertical Distance

• HR → Height of Rod

Directions: Azimuths to Bearings

• 0-90° = does not change

• 90-180° = 180 - X

• 180-270° = X - 180

• 270-360° = 360 - X

Directions: Bearings to Azimuths

• 0-90° = does not change

• 90-180° = 180 - X

• 180-270° = 180 + X

• 270-360° = 360 - X

Directions: Horizontal angles to Azimuths

Back Azimuth = Forward Azimuth + 180°

• Example: Back Azimuth_BA = Forward Azimuth_AB + 180°

  • BA = 210° 30’ 00” + 180° 00’ 00” = 390° 30’ 00”

  • Normalize → 390° 30’ 00” - 360° 00’ 00” = 30° 30’ 00”

  • BA = 30° 30’ 00”

Forward Azimuth = Back Azimuth + Angle to the Right

• Example: Forward Azimuth_BC = Back Azimuth_BA + Angle_B

  • BC = 30° 30’ 00” + 95° 45’ 00” = 126° 15’ 00”

  • BC = 126° 15’ 00”

Traversing: Reduce Field Notes

RECORD HORIZONTAL ANGLE TO NEAREST 10 SECONDS (10”)

Traversing: Adjust interior angles of closed Traverse

• Adjust the average angles so that the sum equals (n-2) x 180° by incrementally adjusting each angle in increments of 5 seconds

• To determine which angles should be adjusted if you cannot equally adjust each angle, apply larger corrections to those angles that had the largest split between the direct angle and the inverted angle

Inversing

• Determining direction and distance from known positions

• Use the coordinate values to determine Latitude and Departure

• Use Latitude and Departure to determine Azimuth and Distance

  • Distance = √(latitude)² + (departure)²

  • Azimuth = tan^-1(departure / latitude)

Leveling: Set up field notes correctly

| STA | BS | HI | FS | ELEV | LOSD |

• STA = Station

• BS = Backsight

• HI = Height of instrument

• FS = Foresight

• ELEV = Elevation

• LOSD = Length of sighted distance

Leveling: Determining Elevations

ELEV₁ + BS = HI

HI - FS = ELEV₂

• Example:

  • ELEV₁ at BM A91 = 256.89’

  • BS at BM A91 = 6.53

  • 256.89’ + 6.53 = 263.42’

  • 263.42 = HI

Leveling: Determining Error of Closure

Error of closure = | Measured_EndELEV - Known_EndELEV |

Leveling: Determining Allowable error

Allowable Error = 0.06√E

• E = Distance of Loop in Miles