Plane SurveyingTraverse, Electronic Distance

Measurement and Curves

Civil Engineering StudentsCivil Engineering Students

Year (1)Year (1)

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

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

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 Instructor (Facebook)Introduction of the Instructor (Facebook)

–– Background, honors, research interests, teaching, etcBackground, 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.

•• BreaksBreaks

•• Lecture slides: Lecture slides: NO DISTRIBUTION WITHOUT PERMITNO DISTRIBUTION WITHOUT PERMIT

SyllabusSyllabus

InstrumentsInstruments

Surveying Measurements

Surveyors, regardless of how advanced the Surveyors, regardless of how advanced the technology they are using, measure only technology they are using, measure only two quantities:two quantities:

–– AnglesAngles

–– DistancesDistances

Coordinates are computed from measured Coordinates are computed from measured angles and distancesangles and distances

Review the following concepts

Definition of horizontal and vertical anglesDefinition of horizontal and vertical angles

Kinds of horizontal angles:Kinds of horizontal angles:

–– Internal and externalInternal and external

–– Angles to the right and to the leftAngles to the right and to the left

Azimuth of a lineAzimuth of a line

Bearing of a lineBearing of a line

Relationship between bearing and azimuthRelationship between bearing and azimuth

Azimuth of successive linesAzimuth of successive lines

Tables of horizontal and vertical anglesTables of horizontal and vertical angles

Surveying Measurements

Surveyors, for civil engineering Surveyors, for civil engineering applications, mainly do two thingsapplications, mainly do two things

–– MapMap رفع رفع

–– SetSet--out out توقیعتوقیع

They map by measuring angles and They map by measuring angles and distancesdistances

They setThey set--out by marking where a out by marking where a computed angle and distance leads.computed angle and distance leads.

Surveying MeasurementsDistances are measured in theDistances are measured in the

–– Vertical: that is called “leveling” Vertical: that is called “leveling” میزانیھمیزانیھ using levelsusing levels

–– Sloped Sloped مائلمائل or horizontal using EDMs or horizontal using EDMs اجھزه قیاس المسافھ اجھزه قیاس المسافھااللكرونیھااللكرونیھ

Angles are measured in the vertical or horizontal Angles are measured in the vertical or horizontal ONLY (why?), using a theodolite ONLY (why?), using a theodolite تیودولیتتیودولیت

Surveying MeasurementsDistances are measured in theDistances are measured in the

–– Vertical: that is called “leveling” Vertical: that is called “leveling” میزانیھمیزانیھ using levelsusing levels

–– Sloped Sloped مائلمائل or horizontal using EDMs or horizontal using EDMs اجھزه قیاس المسافھ اجھزه قیاس المسافھااللكترونیھااللكترونیھ

Angles are measured in the vertical or horizontal Angles are measured in the vertical or horizontal ONLY (why?), using a theodolite ONLY (why?), using a theodolite تیودولیتتیودولیت

Surveying MeasurementsA surveying instrument that includes:A surveying instrument that includes:

–– Electronic (digital) theodolite for angle measurementsElectronic (digital) theodolite for angle measurements

–– EDM: for distance measurementsEDM: for distance measurements

–– Processor (computer) to run a software and perform Processor (computer) to run a software and perform functionsfunctions

Is called a TOTAL STATIONIs called a TOTAL STATION

LEICA TOTAL STATION

Major Parts of a Total Station

Major axis of a total station Angles and Directions

الزوایا و االتجھات

Angle MeasurementTheodolites

•• 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 planeand a horizontal plane..

•• Zenith Angle (Zenith Angle (زاویھ السمتزاویھ السمت): angle from Zenith): angle from Zenith

Kinds of Horizontal Angles

Angles Angles to the Right: clockwise, from the to the Right: clockwise, from the rear to the forward station, Polygons are rear to the forward station, Polygons are labeled counterclockwise. labeled counterclockwise.

Interior (measured on the inside of a Interior (measured on the inside of a closed polygon), and Exterior Angles closed polygon), and Exterior Angles (outside of a closed polygon).(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

Types of TheodolitesOlder Theodolites

Electronic Theodolites

Installtion Pluming and Centering التسامت

Optical Plummet

Leveling a Theodolite ضبط افقیھ التودولیت

DEFINITIONS

Geometric Conditions between the Axis FL and FRالوضعین المتایمن و المتایسر

If the vertical circle is to your left as you If the vertical circle is to your left as you observe, this is called FL observe, this is called FL وضع متایسروضع متایسر

If the vertical circle is to your right as you If the vertical circle is to your right as you observe, this is called FR observe, this is called FR وضع متایمنوضع متایمن

Relationships between readings FL and FR

Aiming at the same target FL and then FR:Aiming at the same target FL and then FR:

–– The difference between the horizontal readings is 180The difference between the horizontal readings is 180

–– The sum of the vertical readings is 360The sum of the vertical readings is 360

For the horizontal average angles:For the horizontal average angles:

–– Compute the mean of Compute the mean of FL and FR: keep the degrees of FL and FR: keep the degrees of either FL or FR and take the average of minutes and either FL or FR and take the average of minutes and secondsseconds

–– Subtract the mean angle by subtracting the mean readingsSubtract the mean angle by subtracting the mean readings

For the vertical: for each point add or subtract halfFor the vertical: for each point add or subtract half--if possibleif possible-- of the difference to 360of the difference to 360

Relationships between readings FL and FR

28”

13 2

1 2

20 2

=360 0 0 +41 36 19 -249 55 02

41

Vertical angles

49 2

-2

254

32

-234

22-- Directions Directions االتجھاتاالتجھات ::

•• 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 “ جیودیسىجیودیسى” ” meridian: connects the mean meridian: connects the mean positions of the north and south poles “ positions of the north and south poles “ اقطا باقطا ب””..

•• Astronomic Astronomic الفلكىالفلكى : instantaneous : instantaneous لحظىلحظى , the line that , the line that connects the north and south poles “ connects the north and south poles “ اقطا باقطا ب”” at that at that instant. 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 Azimuthالزوایا واالنحرافات

•• 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

الخلفى “ is measured at the end of the line.

Azimuth and Bearingالمختصر االنحراف و االنحراف

•• Bearing (reduced azimuth)Bearing (reduced azimuth): acute “: acute “حادةحادة “ “ horizontal angle, less than horizontal angle, less than 9090°°, 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: NW after the angle. For example: N3030W is in the W is in the fourth quad “ fourth quad “ الربع الرابعالربع الرابع“.“.

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

N

E

AZ = B

AZ = 180 - BAZ = 180 + B

AZ = 360 - B

1ST QUAD.

2nd QUAD.3rd QUAD.

4th QUAD.

New Material

Departures and Latitudes

المركبات السینیة و الصادیة

cos(AZ)L*ΔNΔΥ

sin(AZ)L*ΔEΔΧ

Azimuth Equations

= )tan(AZ AB

Latitude

Departure

NN

EE

N

E

AB

AB

•The following are important equations to memorize and understand

)cos(*

)sin(*

AZLN

AZLE

••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 (+m) and the latitude was (+20 20 m) ?m) ?

EB = EA + EAB NB = NA + NAB

AzimuthBC = AzimuthAB + ?

N

N

N

A

B

C

AZAB

AZAB

180°

B

AZBC = AZAB + 180 + B

AZBC

A

B

C

N

N

AZAB

AZAB

AZBC = AZAB + 180 - B

180

B

AZBC

A

B

C

N

N

N

A

B

C

N

N

الزاویھ الداخلھ ± 180+ انحراف الخط قبلھ = انحراف خط

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

Sign is + if the polygon is to the right “clockwise”: angles measured clockwise, letters are in a counterclockwise sequence.

•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

)

r

+P (r ,

N

Eu

u

-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 S 85 85 °° 1010’ W ’ W

A EA E N 85 N 85 °° 10’ W10’ W

Example (1)-Answer

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

ABAB 120120°° 40’40’ S 59S 59°° 20’ E20’ E

ACAC 310310°° 30’30’ N 49N 49°° 30’ W30’ W

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

A EA E 274274°° 50’50’ N 85N 85°° 10’ W10’ 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 = 420mNb = 420m

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

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

-- AE if Ee = 320m, Ne = 370mAE if Ee = 320m, Ne = 370m

Example (2) Note: The angle computed using a calculator is thereduced azimuth (bearing), from 0 to 90, from north orsouth, clock or anti-clockwise directions. You Mustconvert it to the azimuth α , from 0 to 360, measuredclockwise 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

tantan--1(1(ΔE/ ΔN)

AzimuthAzimuth

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

ACAC 200200 --120120 2nd2nd --5959°° 02’ 11”02’ 11” 120120°° 57’ 50”57’ 50”

ADAD --120120 --150150 3rd3rd 3838°° 39’ 35”39’ 35” 218218°° 39’ 35”39’ 35”

AEAE --200200 120120 4th4th --5959°° 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

((120120..1010, , 112112..3232), (), (214214..1212, , 180180..4545), and (), and (144144..4242, , 8282..1717) respectively. Calculate:) 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 AB, but 2020m longer. Use the azimuth equations to m 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 = = 9494..0202, Lat, LatABAB = = ΔNNABAB = = 6868..1313mm

DepDepBCBC = = ΔEEBCBC = = --6969..7070, Lat, LatBCBC = = ΔNNBCBC = = --9898..2828mm

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 = (AZIMUTH) as AB = 5454°° 0404’ ’ 1818””

LAD = LAD = ((9494..0202))2 2 + (+ (6868..1313))2 2 = = 116116..1111mm

Calculate departure = Calculate departure = ΔΔE = L sin (AZ) = E = L sin (AZ) = 9494..0202mm

latitude = latitude = ΔΔN= L cos (AZ)= N= L cos (AZ)= 6868..1313mm

120

E

C

B

A

115

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

A

115

90

110

105

30D