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