CEE 316

Surveying EngineeringSurveying Engineering

•Required Readings:Chapter 1

Sections: 7-1 through 7-10

•Figures: 7-2

•Recommended solved examples: 7-1 and 7-2Recommended solved examples: 7-1 and 7-2

•The packetThe packet

Lecture Outline• Contents:Contents:

• Introduction: instructor, syllabus, exams, extra work, Introduction: instructor, syllabus, exams, extra work, labs, homework.labs, homework.

• Definition of surveying.Definition of surveying.• Geodetic and plane surveying.Geodetic and plane surveying.• Horizontal and vertical angles.Horizontal and vertical angles.• Azimuth and bearing.Azimuth and bearing.• Total stations.Total stations.

Introduction• Instructor:Instructor:• Kamal Ahmed. Room 121c.Kamal Ahmed. Room 121c.• Office hours: see syllabus.Office hours: see syllabus.• Email: kamal@u.Washington.eduEmail: kamal@u.Washington.edu

• Class website: httpClass website: http://courses.Washington.edu/cive316. ://courses.Washington.edu/cive316.

• The rest of the team.The rest of the team.

Past President of the ASPRS - PSR

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!

Can

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ht

Can

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(m)

(m)

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

Syllabus, Exams, and Extra Work• SyllabusSyllabus: course structure and pace: course structure and pace• Two Exams.Two Exams.• Extra Work: Extra Work: Purpose, weight Purpose, weight

• Ideas: AoutCAD, C++, New SubjectIdeas: AoutCAD, C++, New Subject• See the page on “ extra work” for more details. See the page on “ extra work” for more details.

• Labs: Labs: • First two labs: First two labs: keep good notes for the rest of the quarterkeep good notes for the rest of the quarter

• Resection: no report, you will need data from the lab to solve Homework.Resection: no report, you will need data from the lab to solve Homework.• Leveling: Group work and report.Leveling: Group work and report.

• Two Projects: group work and report.Two Projects: group work and report.

• Homework (1) Homework (1) and homework and homework (2) (2) due as in syllabus:due as in syllabus: • use Wolfpack to solve the resection problem and find the use Wolfpack to solve the resection problem and find the

coordinates of the point on the roof. coordinates of the point on the roof. • Other Problems (see handouts)Other Problems (see handouts)

Surveying• Definition: Definition: surveying is the science art and technology of determining the surveying is the science art and technology of determining the

relative positions of points above, on, or beneath the earth’s surfacerelative positions of points above, on, or beneath the earth’s surface..• History of surveying: History of surveying: began in Egypt thousands of years ago for taxation purposes. began in Egypt thousands of years ago for taxation purposes.

Sesostrs about 1400 BCSesostrs about 1400 BC• Why Surveying and what do surveyors do? {paper to ground and ground to paper}Why Surveying and what do surveyors do? {paper to ground and ground to paper}

• Present and future: Present and future: technological advances and application: GPS, LIDAR, technological advances and application: GPS, LIDAR, softcopy Phtogrammetry, remote sensing and high.softcopy Phtogrammetry, remote sensing and high.

Resolution satellite images,Resolution satellite images,And GIS.And GIS.

• Geodetic & plane: Geodetic & plane: • 0.02 ft in 5 miles difference.0.02 ft in 5 miles difference.• Accuracy considerations.Accuracy considerations.

Surveying Measurements• Surveyors, regardless of how complicated the technology, Surveyors, regardless of how complicated the technology,

measure two quantities: angle and distances.measure two quantities: angle and distances.• They do two things: map or set-out They do two things: map or set-out • Angles are measured in horizontal or vertical planes only Angles are measured in horizontal or vertical planes only

to produce horizontal angles and vertical angles.to produce horizontal angles and vertical angles.• Distances are measured in the horizontal, the vertical, or Distances are measured in the horizontal, the vertical, or

sloped directions.sloped directions.• Our calculations are usually in a horizontal or a vertical Our calculations are usually in a horizontal or a vertical

plane for simplicity. Then, sloped values can be calculated plane for simplicity. Then, sloped values can be calculated if needed.if needed.

• For example: maps are horizontal projections of For example: maps are horizontal projections of data, distances are horizontal on a map and so are data, distances are horizontal on a map and so are the angles.the angles.

• Assume that you are given the horizontal Assume that you are given the horizontal coordinates X (E), and Y (N) of two points A and B: coordinates X (E), and Y (N) of two points A and B: (20,20) and (30, 40). If you measure the horizontal (20,20) and (30, 40). If you measure the horizontal angle CBA and the horizontal distance AC, found angle CBA and the horizontal distance AC, found them to be: 110them to be: 110 and 15m, then the coordinates of C and 15m, then the coordinates of C can easily be computed, here is one way :can easily be computed, here is one way :• Calculate the azimuth of AB, then BCCalculate the azimuth of AB, then BC• Calculate (Calculate (X, X, Y) for BCY) for BC• Calculate (X, Y) for C Calculate (X, Y) for C

A

B

C

• But, if you were given a slope distance or a slope But, if you were given a slope distance or a slope angle, you won’t be able to compute the location angle, you won’t be able to compute the location (Coordinates) of C.(Coordinates) of C.

• What we did was to map point C, we found out its What we did was to map point C, we found out its coordinates, now you plot it on a piece of paper, a coordinates, now you plot it on a piece of paper, a “map” is a large number of points such as C, a “map” is a large number of points such as C, a building is four points, and so on.building is four points, and so on.

• Now, if point Now, if point CC was a column of a structure and we was a column of a structure and we wanted to set it out, then we know the coordinates wanted to set it out, then we know the coordinates of C from the map: of C from the map:

• Calculate the angle ABC and the length of BCCalculate the angle ABC and the length of BC

• Setup the instrument, such as a theodolite, on B, aim at ASetup the instrument, such as a theodolite, on B, aim at A

• Rotate the instrument the angle ABC, measure a distance BC, Rotate the instrument the angle ABC, measure a distance BC, mark the point.mark the point.

• You set out a point, then you can set out a project.You set out a point, then you can set out a project.• In both cases, you need two known points such as A and B In both cases, you need two known points such as A and B

to map or set out point Cto map or set out point C• We call precisely known points such as A and B “control We call precisely known points such as A and B “control

points”points”• In horizontal, we do a traverse to construct new control In horizontal, we do a traverse to construct new control

points based on given points.points based on given points.• You need at least two points given in horizontal ( or one You need at least two points given in horizontal ( or one

and direction) and one in vertical to begin your projectand direction) and one in vertical to begin your project

Angles and Directions

Angles and Directions1- Angles:1- Angles:• Horizontal and Vertical AnglesHorizontal and Vertical Angles

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

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

• Kinds of Horizontal AnglesKinds of Horizontal Angles– Interior (measured on the inside of a closed polygon), and Interior (measured on the inside of a closed polygon), and

Exterior Angles (outside of a closed polygon).Exterior Angles (outside of a closed polygon).– Angles to the Right: clockwise, from the rear to the forward Angles to the Right: clockwise, from the rear to the forward

station, Polygons are labeled counterclockwise. Figure 7-2.station, Polygons are labeled counterclockwise. Figure 7-2.– Angles to the Left: counterclockwise, from the rear to the forward Angles to the Left: counterclockwise, from the rear to the forward

station. Polygons are labeled clockwise. Figure 7-2station. Polygons are labeled clockwise. Figure 7-2– Right (clockwise) and Left (counterclockwise) Polygons Right (clockwise) and Left (counterclockwise) Polygons

Figure (a)Figure (a) Figure (b)Figure (b)

angles to the right angles to the left

right angles Left angles

right left

Clockwise angles Counterclockwise angles

Counterclockwise clockwise

Labeled in a Counterclockwise fashion

Labeled in a clockwise fashion

In this class, I will refer to the polygons as follows

Pol

ygon

Pol

ygon

2- Directions:2- 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 meridianWe 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 meridian: connects the mean positions of the Geodetic meridian: connects the mean positions of the

north and south poles.north and south poles.• Astronomic: instantaneous, the line that connects the Astronomic: instantaneous, the line that connects the

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

• Grid: lines parallel to a central meridianGrid: 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 meridian clockwise from a meridian (north) to the line, at the (north) to the line, at the beginning of the linebeginning of the line

-Back-azimuth is measured at the end of the line, such as BA instead of AB.

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

Azimuth and Bearing

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

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

N

E

AZ = B

AZ = 180 - BAZ = 180 + B

AZ = 360 - B

1ST QUAD.

2nd QUAD.3rd QUAD.

4th QUAD.

Example (1)Calculate the reduced azimuth Calculate the reduced azimuth (bearing) (bearing) of the lines AB of the lines AB

and AC, then calculate and AC, then calculate azimuthazimuth of the lines AD and of the lines AD and AEAE

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

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

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

Azimuth Equations

)AZcos(*d

)AZsin(*d

Latitude

Departure

YY

XX = )tan(AZ

AB

ABAB

Important to remember and understand:

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

Assuming internal angles in a counterclockwise polygon

A

B

C

N

N

N

A

B

C

N

N

Azimuth of a line BC = Azimuth of AB ± The angle B +180°

Homework 1

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

Azimuth of DE = Bearing of CD + Angle D + 180 = 30 + 110 + 180 = 320Azimuth of EA = Bearing of DE + Angle E + 180 = 320 + 105 + 180 = 245 (subtracted from 360)Azimuth of AB = Bearing of EA + Angle A + 180 = 245 + 115 + 180 = 180 (subtracted from 360)Azimuth 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

SOLVING THE RESECTION PROBLEM WITH WOLFPACK

Solving Triangle Problems with WolfPack