Transcript Introduction

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.
• Instructor:
Introduction
• Kamal Ahmed. Room 121c.
• Office hours: see syllabus.
• Email: [email protected]
• 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
LIDAR DEM
USGS DEM
LIDAR Canopy Model
WHOA!
(1 m resolution)
Canopy Height (m)
Raw LIDAR point cloud,
Capitol Forest, WA
LIDAR points colored by
orthophotograph
FUSION visualization
software developed
for point cloud display
& measurement
Syllabus, Exams, and Extra Work
The 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.
Determining the
Dimensions of the Earth
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.
• 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
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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
C
B
A
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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.
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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 Directions
1- 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
In this class, I will refer to the polygons as follows
Figure (b)
angles to the left
right angles
Left angles
right
Clockwise angles
Counterclockwise
Labeled in a
Counterclockwise
fashion
Polygon
angles to the right
left
Counterclockwise angles
clockwise
Labeled in a clockwise
fashion
Polygon
Figure (a)
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?
Azimuth
N
4th
Bearing
1ST QUAD.
QUAD.
AZ = 360 - B
AZ = B
E
2nd QUAD.
3rd QUAD.
AZ = 180 + B
AZ = 180 - B
Example (1)
Calculate the reduced azimuth (bearing) of the lines AB
and AC, then calculate azimuth of the lines AD and
AE
Line
AB
AC
AD
AE
Azimuth
120° 40’
310° 30’
Reduced Azimuth (bearing)
S 85 ° 10’ W
N 85 ° 10’ W
Example (1)-Answer
Line
Azimuth
AB
120° 40’
Reduced Azimuth
(bearing)
S 59° 20’ E
AC
310° 30’
N 49° 30’ W
AD
256° 10’
S 85° 10’ W
AE
274° 50’
N 85° 10’ W
How to know which quadrant from the signs of
departure and latitude
For example, what is the azimuth if the departure was
(- 20 ft) and the latitude was (+20 ft) ?
Azimuth Equations
Important to remember and understand:
tan(AZ
AB
)=



XB  XA
YB  YA

Departure
Latitude
  d * sin( AZ )
  d * cos( AZ )
Azimuth of a line (BC)=Azimuth of the previous line AB+180°+angle B
Assuming internal angles in a counterclockwise polygon
N
B
AZab
= AZbc
N
AZab
-int
angle
+180
C
A
Azimuth of a line BC = Azimuth of AB - The angle B +180°
N
C
N
B
N
N
N
B
A
A
Azimuth of a line BC = Azimuth of AB ± The angle B +180°
Homework 1
C
Example (2)
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
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)-Answer
Line ΔE
ΔN
AB 110
170
AC 200
-120 2nd
-59° 02’ 11”
120° 57’ 50”
AD -120 -150 3rd
38° 39’ 35”
218° 39’ 35”
AE
-59° 02’ 11”
300° 57’ 50”
-200 120
Quad. Calculated bearing Azimuth
tan-1(ΔE/ ΔN)
1st
32° 54’ 19”
32° 54’ 19”
4th
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 ABC
d) 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.
B
Example (3) Answer
A
C
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”
a)
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
Example (4)
E
A
105
115
110
B
120
D
30
90
C
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
A
E
105
115
110
B
120
D
30
90
Azimuth of DE = Bearing of CD + Angle D + 180C
= 30 + 110 + 180 = 320
Azimuth 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.
Homework 1
Problem 3?
•
compute Azimuth of AB
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compute Azimuth of BC (-VE internal
angle)
•
compute dep and lat of BC
•
compute coordinates of C
Questions?
SOLVING THE RESECTION PROBLEM WITH WOLFPACK
Solving Triangle Problems with
WolfPack