ENG 200 - Surveying Ron Williams Website: .
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Transcript of ENG 200 - Surveying Ron Williams Website: .
ENG 200 - Surveying Ron Williams Website:
http://web.mnstate.edu/RonWilliams
SurveyingThe 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
N
Geodetic SurveysAllow for convergenceTreat EW lines as great circlesUsed 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
Inches, 1/4, 1/8, etc. 1/10, 1/100, etc. 10’ 4-5/8” = 10.39’ Measure to
nearest .01’ Meters
1 foot = 0.305 m 1 m = 3.28’
Stations
Rods - 16.5 ft Chains - 66 feet
4 rods = chainMiles - 5280 feet
80 chains = 1 mile320 rods = 1 mile
Others
Units of Measure
Math Requirements Degrees, Minutes, Seconds Geometry of Circles Trig Functions Geometry, Trig of Triangles
° - ‘ - “ to Decimal Degrees
1 degree = 60 minutes 1 minute = 60
seconds32°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°
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
23°18’
360° - 23°18’ = 336°42’
Total angle = 360°
4 quadrants - NE, SE, SW, NW - each total 90°
Angles typically measured East from North or East from SouthClockwise (CW) and Counterclockwise (CCW) angles add to 360°
NE
SESW
NW
Geometry of a Circle
Transit sited along line AB, 105°15’ clockwise from North.
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’
A
105°15’
B
N
C135°42’
224°18’
Or: 360° - 135°42’ = 224°18’
Transit is turned 135°42’ counterclockwise to site on C.
105°15’ + 224°18’ = 329°33’
Trig Functions Sin, Cos, Tan are ratios
relating the sides of right triangles o - side opposite the angle
oh
a - side adjacent to the angle
Sin = o/hoh
a
o
aa
h
Cos = a/h Tan = o/a
a
h - hypotenuse of triangle
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 Cos = a/h, a = h*Cos NB/A = lAB * Cos(72°14’)
= 115.15’
357.37
Sin = o/h; o = h*Sin EB/A = lAB * Sin(72°14’)
= 357.37’
115.15’
72°14’ 375.46’
A
B
Triangle Geometry, Trig Laws Sum of interior angles =
180° Sine law:
A B
C
cos222 BCCBA
sinsinsin
CBA
if A = B, = Cosine law:
if = 90°, A2 = B2 + C2