ENG 200 - Surveying Ron Williams Website: http://web.mnstate.edu/RonWilliams

Surveying The art of determining or establishing the relative positions of points on, above, or below the earth’s surface

Determining or Establishing Determining: both points already exist - determine their relative locations. Establishing: one point, and the location of another point relative to the first, are known. Find the position and mark it. Most property surveys are re-surveys determining you have no right to establish the corners

History of Surveying First References Dueteronomy 19:14 Code of Hannarubi Egyptions used surveying in 1400 b.c. to divide land up for taxation Romans introduced surveying instruments

Surveying in America Washington, Jefferson, and Lincoln were survyors The presence of surveyors meant someone wanted land - often traveled with soldiers Railroads opened up the country, but surveyors led the railroad East coast lands were divided by “Metes and Bounds”, the west by US Public Lands

Types of Surveys Plane Surveys Assume NS lines are parallel Assume EW lines are straight N Geodetic Surveys Allow for convergence Treat EW lines as great circles Used for large surveys

Types of Surveys Land - define boundaries of property Topographic - mapping surface features Route - set corridors for roads, etc. City - lots and blocks, sewer and water, etc. Construction - line and grade for building Hydrographic - contours and banks of lakes and rivers Mines - determine the relative position of shafts beneath the earth’s surface

Safety Issues Sun Insects Traffic Brush cutting Electrical lines Property owners

Units of Measure Feet Meters Stations Inches, 1/4, 1/8, etc. 10’ 4-5/8” = 10.39’ Measure to nearest .01’ Meters 1 foot = 0.305 m 1 m = 3.28’ Stations

Units of Measure Rods - 16.5 ft Chains - 66 feet Miles - 5280 feet 4 rods = chain Miles - 5280 feet 80 chains = 1 mile 320 rods = 1 mile Others

Math Requirements Degrees, Minutes, Seconds Geometry of Circles Trig Functions Geometry, Trig of Triangles

° - ‘ - “ to Decimal Degrees 1 degree = 60 minutes 1 minute = 60 seconds 32°15’24” 24” = 24/60’ = 0.4’ 15’24” = 15.4’ = 15.4/60° = 0.2567° 32°15’24” = 32.2567° Most calculators do trig calculations using decimal degrees - CONVERT!

Decimal Degrees to DMS  = 23.1248° 23.1248° = 23°7’29.3” 0.1248*60 = 7.488 minutes 0.488*60 = 29.3 seconds 23.1248° = 23°7’29.3” Watch roundoff! 23.1° = 23°6’00” We do most work to at least 1 minute! Cheap scientific calculator - $12.00

Geometry of a Circle Total angle = 360° 23°18’ Total angle = 360° 4 quadrants - NE, SE, SW, NW - each total 90° NE SE SW NW Angles typically measured East from North or East from South Clockwise (CW) and Counterclockwise (CCW) angles add to 360° 360° - 23°18’ = 336°42’

Geometry of a Circle N Transit sited along line AB, 105°15’ clockwise from North. C 135°42’ Transit is turned 135°42’ counterclockwise to site on C. A 105°15’ 224°18’ Determine the direction of line AC. 105°15’ - 135°42’ = -30°27’ Counterclockwise – angle gets smaller Negative result – add 360 -30°27’ + 360° = 329°33’ B Or: 360° - 135°42’ = 224°18’ 105°15’ + 224°18’ = 329°33’

Trig Functions Sin, Cos, Tan are ratios relating the sides of right triangles o - side opposite the angle  a - side adjacent to the angle a h h h - hypotenuse of triangle o h a o o Sin  = o/h Cos  = a/h Tan  = o/a a

Using Trig Functions Line AB bears 72°14’ East of North Length of AB, lAB = 375.46’ Determine how far North and how far East B is from A 72°14’ 375.46’ A B Cos = a/h, a = h*Cos NB/A = lAB * Cos(72°14’) = 115.15’ 357.37 115.15’ Sin = o/h; o = h*Sin EB/A = lAB * Sin(72°14’) = 357.37’

Triangle Geometry, Trig Laws Sum of interior angles = 180° Sine law: A B C    if A = B,  =  Cosine law: if  = 90°, A2 = B2 + C2