Plane SurveyingTraverse, Electronic Distance

Measurement and Curves

Civil Engineering StudentsCivil Engineering Students

Year (1)Year (1)

Second semester – Phase IISecond semester – Phase II Dr. Kamal M. AhmedDr. Kamal M. Ahmed

Introduction Topics 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 sections E-mail listE-mail list TextbookTextbook SheetsSheets ExamsExams

Introduction

Example Of Current Research Based on Laser Distance

MeasuerementsLIDAR Terrain Mapping in Forests

USGS USGS DEMDEM

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 by LIDAR points colored by orthophotographorthophotograph

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

Package

Angles and Directionsاالتجهات و الزوايا

Angles and Directions1- Angles:1- 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

2- Directions 2- Directions االتجهاتاالتجهات ::• 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 “““مرجعمرجع• Types of meridians: Types of meridians:

• Magnetic: defined by a magnetic needle “Magnetic: defined by a magnetic needle “ ” ” ابرةابرة• Geodetic “ Geodetic “ جيوديسىجيوديسى” ” meridian: connects the mean meridian: connects the mean

positions of the north and south poles “ positions of the north and south poles “ ب ب اقطا ..””اقطا• Astronomic Astronomic الفلكىالفلكى : instantaneous : instantaneous لحظىلحظى , the line that , the line that

connects the north and south poles “ connects the north and south poles “ ب ب اقطا at that at that ””اقطاinstant. Obtained by astronomical observations.instant. Obtained by astronomical observations.

• Grid Grid شبكىشبكى : 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 Azimuthواالنحرافات الزوايا

• Azimuth Azimuth االنحرافاالنحراف: : – 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 “ االنحراف is measured at “ الخلفى the end of the line.

Azimuth and Bearingاالنحراف المختصر و االنحراف

• Bearing (reduced azimuth)Bearing (reduced azimuth): acute “: acute “حادةحادة “ “ 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 “ الرابع الرابع الربع ..““الربع

• Azimuth and bearing: which quadrant “ Azimuth and bearing: which quadrant “ ربع ربع اى ?? “ “ اى

N

N

AZ = B

AZ = 180 - BAZ = 180 + B

AZ = 360 - B

Departures and Latitudes

الصادية و السينية المركبات

Azimuth Equations

•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

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

A

B

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 100•In 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

α

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

LineLine AzimuthAzimuth Reduced Azimuth (bearing)Reduced Azimuth (bearing)

ABAB 120120° 40’° 40’

ACAC 310310° 30’° 30’

ADAD S 85 S 85 ° 10’ W ° 10’ W

A EA E N 85 N 85 ° 10’ W° 10’ W

Example (1)-Answer

LineLine AzimuthAzimuth Reduced Azimuth Reduced Azimuth (bearing)(bearing)

ABAB 120120° 40’° 40’ S 59S 59°° 20’ E 20’ E

ACAC 310310° 30’° 30’ N 49N 49°° 30’ W 30’ W

ADAD 256256°° 10’ 10’ S 85S 85° 10’ W ° 10’ W

A EA E 274° 50’274° 50’ N 85N 85° 10’ W° 10’ W

Compute the azimuth of the line :Compute the azimuth of the line :

- AB if Ea = 520m, Na = 250m, Eb = 630m, and - AB if Ea = 520m, Na = 250m, Eb = 630m, and Nb = Nb =

420m420m

- AC if Ec = 720m, Nc = 130m- AC if Ec = 720m, Nc = 130m

- AD if Ed = 400m, Nd = 100m- AD if Ed = 400m, Nd = 100m

- AE if Ee = 320m, Ne = 370m- AE if Ee = 320m, Ne = 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 α , from 0 to 360, measured clockwise from North.

Assume that the azimuth of the line AB is (αAB ), the bearing is B = tan-1 (ΔE/ ΔN)

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

- For the line (ab): calculate

ΔEab = Eb – Ea and ΔNab = Nb – Na - If both Δ E, Δ N are - ve, (3rd Quadrant)

αab = 180 + 30= 210- If bearing from calculator is – 30 & Δ E is – ve& ΔN is +ve

αab = 360 -30 = 330 (4th Quadrant)- If bearing from calculator is – 30& ΔE is + ve& ΔN is – ve,

αab = 180 -30 = 150 (2nd Quadrant)- If bearing from calculator is 30 , you have to notice if both

ΔE, ΔN are + ve or – ve,If both ΔE, ΔN are + ve, (1st Quadrant)

αab = 30 otherwise, if both ΔE, ΔN are –ve, (3rd Quad.)

αab = 180 + 30 = 210

Example (2)-AnswerLineLine ΔE ΔN Quad. Calculated bearingCalculated bearing

tan-1(tan-1(ΔE/ ΔN)

AzimuthAzimuth

ABAB 110110 170170 1st1st 3232°° 54’ 19” 54’ 19” 3232°° 54’ 19” 54’ 19”

ACAC 200200 -120-120 2nd2nd -59-59°° 02’ 11” 02’ 11” 120120°° 57’ 50” 57’ 50”

ADAD -120-120 -150-150 3rd3rd 3838°° 39’ 35” 39’ 35” 218218° 39’ 35”° 39’ 35”

AEAE -200-200 120120 4th4th -59-59°° 02’ 11” 02’ 11” 300300° 57’ 50”° 57’ 50”

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 BC.The azimuth of the lines AB and BC.

c)c) The internal angle ABCThe internal angle ABC

d)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 = = ΔEEABAB = 94.02, Lat = 94.02, LatABAB = = ΔNNABAB = 68.13m = 68.13m

DepDepBCBC = = ΔEEBCBC = -69.70, Lat = -69.70, LatBCBC = = ΔNNBCBC = -98.28m = -98.28m

b) Azb) AzABAB = = tan-1 (ΔE/ ΔN) = 54 °° 04’ 18”

AzAzBCBC = = tan-1 (ΔE/ ΔN) = 215 °° 20’ 39”

c) clockwise : Azimuth of BC =

Azimuth of AB - The angle B +180°

Angle ABC = AZABAB- AZBC BC + 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’ 18” 04’ 18”

LLADAD = = (94.02) (94.02)22 + (68.13) + (68.13)2 2 = 116.11m

Calculate departure = ΔEE = L sin (AZ) = 94.02m

latitude = ΔNN= 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 = 320Bearing 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