Plane SurveyingTraverse, Electronic Distance

Measurement and Curves

Civil Engineering StudentsCivil Engineering StudentsYear (1)Year (1)Second semester Second semester Phase IIPhase II Dr. Dr. KamalKamal M. AhmedM. Ahmed

IntroductionTopics in Phase II: Angles and Directions, Traverse, Topics in Phase II: Angles and Directions, Traverse,

EDM, Total Stations, Curves, and Introduction to EDM, Total Stations, Curves, and Introduction to Recent and supporting technologiesRecent and supporting technologies

Introduction of the InstructorIntroduction of the Instructor Background, honors, research interests, teaching, etc.Background, honors, research interests, teaching, etc. Method of teaching: Method of teaching: ))what to expect and not to expect, what is allowed.what to expect and not to expect, what is allowed.))Language used.Language used.))Lecture slides: NO DISTRIBUTION WITHOUT Lecture slides: NO DISTRIBUTION WITHOUT

PERMITPERMIT))BreaksBreaks

Lab sectionsLab sectionsEE--mail listmail listTextbookTextbookSheetsSheetsExamsExams

Introduction

Example Of Current Research Based on Laser Distance

MeasuerementsLIDAR Terrain Mapping in Forests

USGS DEMUSGS DEM

LIDAR DEMLIDAR DEM

LIDAR Canopy ModelLIDAR Canopy Model

(1 m resolution)(1 m resolution)WHOA!WHOA!

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Package

Raw LIDAR point cloud, Raw LIDAR point cloud, Capitol Forest, WACapitol Forest, WA

LIDAR points colored LIDAR points colored by by orthophotographorthophotograph

FUSIONFUSION visualization visualization software developed software developed for point cloud for point cloud display & display & measurementmeasurement

Package

Angles and Directions

Angles and Directions11-- Angles:Angles: Horizontal and Vertical AnglesHorizontal and Vertical Angles

Horizontal Angle: The angle between the projections Horizontal Angle: The angle between the projections of the line of sight on a horizontal plane.of the line of sight on a horizontal plane.

Vertical Angle: The angle between the line of sight Vertical Angle: The angle between the line of sight and a horizontal plane.and a horizontal plane.

Kinds of Horizontal AnglesKinds of Horizontal Angles Angles to the Right: clockwise, from the rear to the Angles to the Right: clockwise, from the rear to the

forward station, Polygons are labeled counterclockwise. forward station, Polygons are labeled counterclockwise. Interior (measured on the inside of a closed polygon), Interior (measured on the inside of a closed polygon),

and Exterior Angles (outside of a closed polygon).and Exterior Angles (outside of a closed polygon).

Angles to the Left: counterclockwise, from the rear to the Angles to the Left: counterclockwise, from the rear to the forward station. Polygons are labeled clockwise. forward station. Polygons are labeled clockwise. Right (clockwise) and Left (counterclockwise) PolygonsRight (clockwise) and Left (counterclockwise) Polygons

22-- Directions Directions :: Direction of a line is the horizontal angle between the line Direction of a line is the horizontal angle between the line

and an arbitrary chosen reference line called a meridian. and an arbitrary chosen reference line called a meridian. We will use north or south as a meridian We will use north or south as a meridian Types of meridians: Types of meridians:

Magnetic: defined by a magnetic needle Magnetic: defined by a magnetic needle Geodetic Geodetic meridian: connects the mean meridian: connects the mean

positions of the north and south poles positions of the north and south poles .. Astronomic Astronomic : instantaneous : instantaneous , the line that , the line that

connects the north and south poles connects the north and south poles at that at that instant. Obtained by astronomical observations.instant. Obtained by astronomical observations.

Grid Grid : lines parallel to a central meridian: lines parallel to a central meridian

Distinguish between angles, directions, and Distinguish between angles, directions, and readings.readings.

Angles and Azimuth

Azimuth Azimuth : : Horizontal angle measured Horizontal angle measured

clockwise from a clockwise from a meridian (north) to the line, meridian (north) to the line, at the beginning of the lineat the beginning of the line

-The line AB starts at A, the line BA starts at B.

-Back-azimuth is measured at the end of the line.

Azimuth and Bearing

Bearing (reduced azimuth)Bearing (reduced azimuth): acute : acute horizontal angle, less than 90horizontal angle, less than 90, measured from the , measured from the north or the south direction to the line. Quadrant is north or the south direction to the line. Quadrant is shown by the letter N or S before and the letter E or shown by the letter N or S before and the letter E or W after the angle. For example: N30W is in the W after the angle. For example: N30W is in the fourth quad fourth quad ..

Azimuth and bearing: which quadrant Azimuth and bearing: which quadrant ? ?

NN

AZ = B

AZ = 180 - BAZ = 180 + B

AZ = 360 - B

Departures and Latitudes

cos(AZL*Nsin(AZ)L*E

====

Azimuth Equations

= )tan(AZ ABLatitude

DepartureNNEE

NE

AB

AB ==

The following are important equations to memorize and understand

Azimuth of a line (BC)=Azimuth of the previous line AB+180+angle B

Assuming internal angles in a counterclockwise polygon

)cos(*)sin(*

AZLNAZLE

==

How to know which quadrant from the signs of departure and How to know which quadrant from the signs of departure and latitude?latitude?

For example, what is the azimuth if the departure was (For example, what is the azimuth if the departure was (-- 20 20 m) and the latitude was (+20 m) ?m) and the latitude was (+20 m) ?

AB

C

N

N

N

A

B

C

N

N

Azimuth of a line such as BC = Azimuth of AB The angle B +180

In many parts of the world, a slightly different form of notation is used.instead of (x,y) we use E,N (Easting, Northing) .In Egypt, the Easting comes first, for example: (100, 200) means that easting is 100In the US, Northing might be mentioned first.It is a good practice to check internationally produced coordinate files before using them.

N

P (E ,N)

E

L

Easting and Northing

Polar Coordinates

+P (r , )

N

E

r

-The polar coordinate system describes a point by (angle, distance) instead of (X, Y)

-We do not directly measure (X, Y in the field

-In the field, we measure some form of polar coordinates: angle and distance to each point, then convert them to (X, Y)

Examples

Example (1)Calculate the reduced azimuth of the lines AB and AC, Calculate the reduced azimuth of the lines AB and AC,

then calculate the reduced azimuth (bearing) of the then calculate the reduced azimuth (bearing) of the lines AD and AElines AD and AE

S 85 S 85 1010 W W ADAD310310 3030ACAC

N 85 N 85 1010 WWA EA E

120120 4040ABABReduced Azimuth (bearing)Reduced Azimuth (bearing)AzimuthAzimuthLineLine

Example (1)-Answer

S 85S 85 1010 W W 256256 1010ADAD

4949 3030310310 3030ACAC

N 85N 85 1010 WW274274 5050A EA E

5959 2020120120 4040ABAB

Reduced Azimuth Reduced Azimuth (bearing)(bearing)

AzimuthAzimuthLineLine

Compute the azimuth of the line :Compute the azimuth of the line :-- AB if Ea = 520m, Na = 250m, AB if Ea = 520m, Na = 250m, EbEb = 630m, and = 630m, and

NbNb = 420m= 420m-- AC if AC if EcEc = 720m, = 720m, NcNc = 130m= 130m-- AD if Ed = 400m, AD if Ed = 400m, NdNd = 100m= 100m-- AE if AE if EeEe = 320m, = 320m, NeNe = 370m= 370m

Example (2)

Note: The angle computed using a calculator is the reduced azimuth (bearing), from 0 to 90, from north or south, clock or anti-clockwise directions. You Must convert it to the azimuth , from 0 to 360, measured clockwise from North.

Assume that the azimuth of the line AB is (AB ), the bearing is B = tan-1 (E/ N)

If we neglect the sign of B as given by the calculator, then, 1st Quadrant : AB = B , 2nd Quadrant: AB = 180 B,3rd Quadrant: AB = 180 + B,4th Quadrant: AB = 360 - B

- For the line (ab): calculate Eab = Eb Ea and Nab = Nb Na

- If both E, N are - ve, (3rd Quadrant)ab = 180 + 30= 210

- If bearing from calculator is 30 & E is ve& N is +veab = 360 -30 = 330 (4th Quadrant)

- If bearing from calculator is 30& E is + ve& N is ve,ab = 180 -30 = 150 (2nd Quadrant)

- If bearing from calculator is 30 , you have to notice if both E, N are + ve or ve,If both E, N are + ve, (1st Quadrant)

ab = 30 otherwise, if both E, N are ve, (3rd Quad.)

ab = 180 + 30 = 210

Example (2)-Answer

4th4th

3rd3rd

2nd2nd

1st1st

Quad.

--5959 02 1102 11

3838 39 3539 35

--5959 02 1102 11

3232 54 1954 19

Calculated bearingCalculated bearingtantan--1(1(E/ N)

300300 5757 5050120120--200200AEAE

218218 3939 3535--150150--120120ADAD

120120 57 5057 50--120120200200ACAC

3232 54 1954 19170170110110ABAB

AzimuthAzimuthNELineLine

Example (3)The coordinates of points A, B, and C in meters are The coordinates of points A, B, and C in meters are

(120.10, 112.32), (214.12, 180.45), and (144.42, (120.10, 112.32), (214.12, 180.45), and (144.42, 82.17) respectively. Calculate:82.17) respectively. Calculate:

a)a) The departure and the latitude of the lines AB and The departure and the latitude of the lines AB and BCBC

b)b) The azimuth of the lines AB and AC.The azimuth of the lines AB and AC.c)c) The internal angle CABThe internal angle CABd)d) The line AD is in the same direction as the line The line AD is in the same direction as the line

AB, but 20m longer. Use the azimuth equations to AB, but 20m longer. Use the azimuth equations to compute the departure and latitude of the line AD.compute the departure and latitude of the line AD.

a)a) DepDepABAB = = EEABAB = 94.02, = 94.02, LatLatABAB = = NNABAB = 68.13m= 68.13mDepDepBCBC = = EEBCBC = = --69.70, 69.70, LatLatBCBC = = NNBCBC = = --98.28m98.28m

b) b) AzAzABAB = = tan-1 (E/ N) = 54 04 18AzAzBCBC = = tan-1 (E/ N) = 215 20 39

c) Anti-clockwise: Azimuth of BC = Azimuth of AB - The angle B +180 Angle CBA = AZABAB- AZBCBC+180 =

= 54 04 18 - 215 20 39 +180 = 18 43 22

Example (3) AnswerA

B

C

d) AZd) AZADAD::The line AD will have the same direction The line AD will have the same direction (AZIMUTH) as AB = 54(AZIMUTH) as AB = 54 04 1804 18LLADAD = = ((94.02)94.02)22 + (68.13)+ (68.13)2 2 = 116.11m

Calculate departure = EE = L sin (AZ) = 94.02mlatitude = NN= L cos (AZ)= 68.13m

120

E

C

B

A115

90

110

105

30D

Example (4)

In the right polygon ABCDEA, if the azimuth of the side CD = 30 and the internal angles are as shown in the figure, compute the azimuth of all the sides and check your answer.

Example (4) - Answer

Bearing of DE = Bearing of CD + Angle D + 180= 30 + 110 + 180 = 320

Bearing of EA = Bearing of DE + Angle E + 180= 320 + 105 + 180 = 245 (subtracted from 360)

Bearing of AB = Bearing of EA + Angle A + 180= 245 + 115 + 180 = 180 (subtracted from 360)

Bearing of BC = Bearing of AB + Angle B + 180=180 + 120 + 180 = 120 (subtracted from 360)

CHECK : Bearing of CD = Bearing of BC + Angle C + 180= 120 + 90 + 180 = 30 (subtracted from 360), O. K.120

E

C

B

A115

90

110

105

30D