CEE 317

GeoSurveying

• Required Readings:Chapter 1

Sections: 7-1 through 7-10

• Figures: 7-2

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

Lecture Outline• Contents:

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

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

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

• Class website: http://courses.Washington.edu/cive316.• Facebook/• The rest of the team.

Past President of the ASPRS - PSR

Example Of Current Research Based on Laser Distance Measuerements

LIDAR Terrain Mapping in Forests

USGS DEM

LIDAR DEM

LIDAR Canopy Model

(1 m resolution)WHOA!

Can

op

y H

eig

ht

(m)

Package

Raw LIDAR point cloud, Capitol Forest, WA

LIDAR points colored by orthophotograph

FUSION visualization software developed for point cloud display & measurement

Package

Syllabus, Exams, and Extra WorkThe packet• Syllabus: course structure and pace• Three Exams.• Extra Work: Purpose, weight

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

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

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

• Two Projects: group work and report.• Homework due dates, where to drop papers, honor system

• In hw1 you will use Wolfpack to solve the resection problem and find the coordinates of the point on the roof.

• Other Problems (see handouts)

Surveying• Definition: surveying is the science art and

technology of determining the relative positions of points above, on, or beneath the earth’s surface.

• Geo Surveying• History of surveying: earliest recorded

documents suggest that surveying began in Egypt thousands of years

ago the era of Sesostrs about 1400 BC for taxation purposes.

Aswan

Eratosthenes, 220 BC, measured the distance S knowing the speed of camel caravans and measuring the time. He then estimated the angle (α) from the length of the shadow of a vertical mast at the same time when the sun illuminated the bottom of a deep well in Aswan, same time in two summers. The extension of the vertical mast will pass by the center of the earth.

Determining the Dimensions of the Earth

• Why Surveying and what do surveyors do? {paper to ground and ground to paper}

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

Resolution satellite images,And GIS.

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

Surveying Measurements• Surveyors, regardless of how complicated the

technology, measure two quantities: angle and distances.

• They do two things: map or set-out • Angles are measured in horizontal or vertical planes

only to produce horizontal angles and vertical angles.

• Distances are measured in the horizontal, the vertical, or sloped directions.

• Our calculations are usually in a horizontal or a vertical plane for simplicity. Then, sloped values can be calculated if needed.

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

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

A

B

C

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

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

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

• Calculate the angle ABC and the length of BC• Setup the instrument, such as a theodolite, on B, aim at A• Rotate the instrument the angle ABC, measure a distance BC,

mark the point.• 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

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

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

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

and direction) and one in vertical to begin your project

Angles and Directions

Angles and Directions1- Angles:• Horizontal and Vertical Angles

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

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

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

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

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

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

Polygons

Figure (a) 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:• Direction of a line is the horizontal angle between the line

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

• Magnetic: defined by a magnetic needle.• Geodetic meridian: connects the mean positions of the

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

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

• Grid: lines parallel to a central meridian• Distinguish between angles, directions, and

readings.

Angles and Azimuth

• Azimuth: – Horizontal angle measured clockwise from a meridian

(north) to the line, at the beginning 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: acute horizontal angle, less than 90, measured 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 after the angle. For example: N30W is in the fourth quad.

• 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.

Bearing

Azimuth

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

and AC, then calculate azimuth of the lines AD and AE

Line Azimuth Reduced Azimuth (bearing)AB 120° 40’AC 310° 30’AD S 85 ° 10’ W A E N 85 ° 10’ W

Example (1)-Answer

Line Azimuth Reduced Azimuth (bearing)

AB 120° 40’ S 59° 20’ E

AC 310° 30’ N 49° 30’ W

AD 256° 10’ S 85° 10’ W

A E 274° 50’ N 85° 10’ W

How to know which quadrant from the signs of departure and latitudeFor example, what is the azimuth if the departure 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

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

AZab

AZab

+180-int angle

= AZbc

N

N

A

B

C

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

Nb = 420m

- AC if Ec = 720m, Nc = 130m- AD if Ed = 400m, Nd = 100m- 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)-AnswerLine ΔE ΔN Quad. Calculated bearing

tan-1(ΔE/ ΔN)Azimuth

AB 110 170 1st 32° 54’ 19” 32° 54’ 19”

AC 200 -120 2nd -59° 02’ 11” 120° 57’ 50”

AD -120 -150 3rd 38° 39’ 35” 218° 39’ 35”

AE -200 120 4th -59° 02’ 11” 300° 57’ 50”

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

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

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

b) The azimuth of the lines AB and BC.c) The internal angle ABCd) The line AD is in the same direction as the line AB,

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

a) DepAB = ΔEAB = 94.02, LatAB = ΔNAB = 68.13m

DepBC = ΔEBC = -69.70, LatBC = ΔNBC = -98.28m

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

AzBC = tan-1 (ΔE/ ΔN) = 215 ° 20’ 39”

c) clockwise : Azimuth of BC = Azimuth of AB - The angle B +180° Angle ABC = AZAB- AZBC + 180° =

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

Example (3) AnswerA

B

C

d) AZAD:

The line AD will have the same direction (AZIMUTH) as AB = 54° 04’ 18”

LAD = (94.02)2 + (68.13)2 = 116.11m

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

latitude = ΔN= 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

Homework 1

Problem 3?• compute Azimuth of AB• compute Azimuth of BC (-VE internal

angle)• compute dep and lat of BC• compute coordinates of CQuestions?

SOLVING THE RESECTION PROBLEM WITH WOLFPACK

Solving Triangle Problems with WolfPack