engineering surveying (221 be) distance & angle & angle.pdf · engineering surveying (221...

ENGINEERING SURVEYING (221 BE)

Distance & Angle

Sr Tan Liat Choon Email: [email protected]

Mobile: 016-4975551

INTRODUCTION

Types of Measurements in Surveying: Surveying is the art of making suitable

measurements in horizontal or vertical planes. This is one of the important subjects of civil engineering. Without taking a survey of the plot where the construction is to be carried out, the work cannot begin

2

INTRODUCTION

From the above definition, we conclude on two types of measurements in surveying. They are as follows: Linear measurements Angular measurements

3

INTRODUCTION

Linear measurements are further classified as follows: Horizontal Distance Vertical Distance

4

INTRODUCTION

Horizontal Distance A horizontal distance is measured

in horizontal plane if a distance is measured along a slope, it is reduced to its horizontal equivalent

5

INTRODUCTION

Vertical Distance A vertical distance is measured

along the direction of gravity at that point. The vertical distance is measured to determine difference in elevations in various points

6

INTRODUCTION

Angular Measurements Two sides meeting at an angle are

measured. The angle between them is measured and represented in degrees or radians

7

DISTANCE MEASUREMENT

Linear measurement is the basis of all surveying and even through angles may be read precisely, the length of at least one line in tract must be measured to supplement the angles in locating points

8


Is generally regarded as the most fundamental of all surveying observations

Many angles may be read, the length of at least one line must be observed to supplement the angles in locating points

In plane survey, the distance between two points means the horizontal distance

9


Methods of measuring a horizontal distance: Tacheometry (Stadia), Taping, EDM and GPS Distance from stadia: (High wire – Low wire) *

100 = Distance EDM & GPS are most common in today’s survey Direct measurement Indirect measurement

10


As simple as ABC:

11

New building site – how big is it?

60.159 m

60.159 m

32

.57

9 m

32

.57

9 m


Measurement must be straight:

12


Measurement around obstacle:

13

starting point closing point Obstacle to sight line


Measurement around obstacle: Horizontal angles α and β are used to transform the resulting horizontal lengths to an equivalent horizontal length along the measurement line H 2-4 = h 2-3 cos α + h 3-4 cos β

14

1

β α

5 4

3

2



15



16



17


Generally, measurements are made horizontally, but on even, often man-made slopes the distance can be measured directly on the slope, but the vertical or zenith angle must be obtained V = Vertical Distance S = Slope Distance H = Horizontal Distance

18 A

S V

H

B

C


c2 = a2 + b2 C = 90° = A + B sin A = a/c cos A = b/c tan A = a/b

19

A

c a

b

B

C


A + B + C = 180° Sine Rule: a/sin A = b/sin b = c/sin C Cosine Rule: a2 =b2 + c2 – 2bc cos A cos A = (b2 = c2 - a2)/2bc Area = 1/2 bc sin A = √ s(s - a) (s - b) (s – c) where s = (a + b + c)/2

20

A

c

b

a B

C

INTRODUCTION ON ANGLE MEASUREMENT

Measuring distances alone in surveying does not establish the location of an object. We need to locate the object in 3 dimensions. To accomplish that we need: Horizontal length (distance) Difference in height (elevation) Angular direction

21


Angles measured in surveying are classified as either horizontal or vertical, depending on the plane in which they are observed

Horizontal angles are the basic observations needed for determining bearing and azimuths

Vertical angles are used in trigonometric levelling stadia and for reducing slope distances to horizontal

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Determining the locations of points and orientations of lines frequently depends on measurements of angles and directions

In surveying, directions are given by azimuths and bearings

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An angle is defined as the difference in direction between two convergent lines

A horizontal angle is formed by the directions to two objects in a horizontal plane

A vertical angle is formed by two intersecting lines in a vertical plane, one of these lines horizontal

A zenith angle is the complementary angle to the vertical angle and is formed by two intersecting lines in a vertical plane, one of these lines directed toward the zenith

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25

TYPE OF ANGLE MEASUREMENT

Interior angles are measured clockwise or counter-clockwise between two adjacent lines on the inside of a closed polygon figure

Exterior angles are measured clockwise or counter-clockwise between two adjacent lines on the outside of a closed polygon figure

Deflection angles, right or left, are measured from an extension of the preceding course and the ahead line. It must be noted when the deflection is right (R) or left (L)

26


Angles to the right are turned from the back line in a clockwise or right hand direction to the ahead line

Angles to the left are turned from the back line in a counter-clock wise or left hand direction to the ahead line

Angles are normally measured with a transit or a theodolite, but a compass may be used for reconnaissance work

27


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ANGLE MEASUREMENT

Angle is a difference in direction of 2 lines

To turn an angle we need a reference line, direction of turning and angular distance

Angular units: Degree, minutes, second Circle divided into 360 degrees Each degree divided by 60 minutes Each minute divided into 60 seconds

A check can be made because the sum of all angles in

any polygon must equal. (n-2) * 180, where n is the number of angles

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MEASURING HORIZONTAL ANGLE

Set a bearing on the horizontal plate, and lock the upper motion

Release the lower motion, sight the backsight, lock the lower motion, and perfect the sighting with the lower tangent screw

Release the upper motion, turn to the foresight, lock the upper motion, and perfect the sighting

Record the horizontal bearing

Release the lower motion, invert the scope and point to the backsight in the reverse position, lock the lower motion, and perfect the sighting

Release the upper motion, turn to the foresight, lock the upper motion, and perfect the sighting

Record the second bearing 30

MEASURING ZENITH ANGLE

Point the instrument to the target object in a direct position

Lock the vertical motion, perfect the sighting and record the zenith angle

Loosen both the horizontal and vertical motions, plunge the scope, rotate the alidade 180° and re-point to the target in the reverse position

Lock the vertical motion, perfect the pointing and record the zenith angle

31

MEASURING ZENITH ANGLE

Direct 83° 28’ 16”

Reserve 276° 31’ 38”

Sum 359° 59’ 54”

360° Minus Sum 00° 00’ 06”

Half Value (error) 00° 00’ 03”

Plus Original Angle 83° 28’ 16”

Final Angle 83° 28’ 19” 32

USEFUL CONCEPTS Degrees: full circle = 360°

0°

45°

90°

135°

180°

225°

270°

315°

33

USEFUL CONCEPTS

34

BEARING AND AZIMUTH

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COMPARISON OF AZIMUTH AND BEARING

Because bearings and azimuths are encountered in so many surveying operations, there is important to know the conversion of these two. Example 1 The azimuth of a boundary line is 128° 13’ 46”. Convert this into bearing. The azimuth places the line in the southeast quadrant. Thus the bearing angle is: 180° 13’ 46” - 128° 13’ 46” = 51° 46’ 14”, and the equivalent bearing is S 51° 46’ 14” E Example 2 The first course of a boundary survey is written as N 37° 13’ W. What is its equivalent azimuth? Since the bearing is in the northwest quadrant, the azimuth is: 360° - 37° 13’ = 322° 47’

36


37

Azimuths Bearings

Vary from 0° to 360° Vary from 0° to 90°

Require only a numerical value Require two letters and a numerical value

May be geodetic, astronomic, magnetic, grid, assumed, forward or back

May be geodetic, astronomic, magnetic, grid, assumed, forward or back

Are measured clockwise only Are measured clockwise and counterclockwise

Are measured either from north only, or from south only on a particular survey

Are measured from north and south


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Quadrant Formulas for computing bearing angles from

azimuths

I (NE) Bearing = Azimuth

II (SE) Bearing = 180° - Azimuth

III (SW) Bearing = Azimuth - 180°

IV (NW) Bearing = 360° - Azimuth


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Example directions for lines in the four quadrants (Azimuths from north)

Azimuths Bearings

54° N 54° E

112° S 68° E

231° S 51° W

345° N 15° W

AZIMUTH

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Line Azimuth

O – A 54°

O – B 133°

O – C 211°

O – D 334°

COMPUTING AZIMUTH

41

N

B

A

C N

COMPUTING AZIMUTH

41° 35’ = AB + 180° 00’ 221° 35’ = BA + 129° 11’ 350° 46’ = BC - 180° 00’ 170° 46’ = CB + 88° 35’ 259° 21’ = CD - 180° 00’ 79° 21’ = DC + 132° 30’ 211° 51’ = DE

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211° 51’ = DE - 180° 00’ 31° 51’ = ED + 135° 42’ 167° 33’ = EF + 180° 00’ 347° 33’ = FE + 118° 52’ 466° 25’ - 360° = 106° 25’ = FA + 180° 00’ 286° 25’ = AF + 115° 10’ 401° 35’ - 360° = 41° 35’ = AB

When a computed azimuth exceeds 360°, the correct azimuth is obtained by merely subtracting 360°

BEARING

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Line Bearing

O – A N 54° E

O – B S 47° E

O – C S 31° W

O – D N 26° W

COMPUTING BEARING

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Line Bearing

AB N 25° W

BC N 68° E

CD S 17° W

DA S 62° W

BEARING Bearing of a line is the direction of the line Azimuth of a line is the horizontal angle between 2 lines

Designation of Bearings Whole circle bearing Reduced Bearing (RB) or quadrantal bearing (QB) Fore Bearing (FB) or forward bearing (FB) Back bearing or Backward bearing (BB) Calculated bearing

Whole Circle bearing Bearings measured from north in a clockwise direction is termed as whole

circle bearing The value varies from 0 degrees to 360 degrees

Reduced bearing/Quadrantal bearing The bearings measured either from the north or from the south towards east

or west whichever is nearer is known as reduced bearing The values vary from 0 degrees to 90 degrees for a particular quadrant It is also known as quadrantal bearing (QB)

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BEARING

Fore Bearing (FB) The bearings measured in the progress of surveying i.e. in the forward

direction of survey lines is known as fore bearing or forward bearing Back Bearing (BB) The bearings measured in opposite to the progress of surveying i.e. in

backward direction of survey line is known as Backward Bearing

Observed Bearing The bearings taken in a field with an instrument is known as Observed

Bearing

Calculated Bearing The bearings calculated from the field observation is known as

calculated bearing

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RECTANGULAR COORDINATE

47

POLAR COORDINATE

48

+P (r, θ)

y

x

r

u

P (x,y)

y

x

Cartesian coordinates

Perpendicular axes Origin at (0,0) Coordinates increase right & up of origin Coordinates decrease down & left of origin

(0,0) x +

+

-

-

COORDINATE IN A PLANE

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Cartesian coordinates

Coordinates of point given by bracketed pairs of numbers: (right,up)

(0,0) x

(3,4) x

(-3,-2) x

(x,y) (Easting,Northing) -depending on coordinate system used


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Often easier to avoid negative values by increasing origin coordinates

+

+

(1000,1000) x

(1004,1006) x

(1001,1002) x

(998,999) x

NOTE: Some countries (incl. Sweden) use on maps: y=East x=North Others use opposite (e.g. (England, USA)

We’ll use (Easting,Northing)


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p0 x

p1 x

Find coordinates of p1 in relation to p0

Easting

No

rth

ing

FINDING COORDINATE

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p0 x

p1 x

Reference bearing (N)

Instrument

p0 (instrument) has known coordinates (0,0) for the moment reference bearing is known (N)

p1 has a unknown coordinates

FINDING COORDINATE

53

ө Nort

hin

g =

d c

os(ө

)

Easting = d sin(ө)

Use instrument to measure: d = (horizontal) distance p0-p1 ө = angle between North & bearing of p1 from p0

p0

p1 x


ө = bearing from reference d = distance from p0 to p1

d

with trigonometry...

Polar Coordinates

FINDING COORDINATE

54

ө

Nort

hin

g =

d c

os(ө

)

Easting = d sin(ө) p0

x

p1 x


d 10m

36.87°

Easting = d sin(ө)

= 10 sin(36.87)

= 10*0.6

= 6m

Northing = d cos(ө)

= 10 cos(36.87)

= 10*0.8

= 8m

ө also called the azimuth

FINDING COORDINATE

55

ө

No

rth

ing

= d

co

s(ө

)

Easting = d sin(ө) p0

x

p1 x


d 10m

36.87°

(6,8)

p1(Easting) = p0(Easting) + (d sin(ө)) p1(Northing) = p0(Northing) + (d cos(ө)) So if p0=(1000,1000) then p1(Easting,Northing) = (1006,1008)

FINDING COORDINATE

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SURVEYING COORDINATE

57

For surveying we use a slightly different form of notation, instead of x, y,

+P ( E, N)

N

E

D

u

We use E, N (Easting, Northing)


Note:

Easting is always quoted first and then Northing

Θ is always measured in a clockwise direction from North

Θ is known as the whole circle bearing

We must be able to convert from Rectangular to Polar and from Polar to Rectangular very quickly

58


59

Any line has two bearings: N

N

u PQ QP

Q

P

u

We consider that the line PQ is a different line to line QP


60

Given the coordinates of two points, calculate the distance and bearing

between of the line joining them

Q N

u PQ P(E,N)

Q(E, N)

Q(1127.37) – P(937.77) =189.69

Q(850.04) – P(1341.50) = 491.46

b=491.46

a=18

9.6

9

sin A = a/c c2 = a2 + b2

c2 = 189.602 + 491.462

c=526.77

c (PQ) = 526.77

sin A = 189.60/526.77

A = 21° 05’ 45”

Azimuth PQ = 270° + 21° 05’ 45” = 291° 05’ 45” Bearing PQ = N 68° 54’ 15” W

A

Point Easting (E) Northing (N)

P 1341.50 937.77

Q 850.04 1127.37

LOCAL ATTRACTION

The deflection of a magnetic needle from its true position due to the presence of magnetic influencing material such as iron rod, magnetic rock, underground pipeline, electric cables, iron pipes and electric pole in its vicinity is called local attraction

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METHOD OF CORRECTING THE BEARING

There are two methods of correcting the bearing affected by local attraction: Included angle method Error computation method

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Included angle method: The included angles of the traverse

are calculated first, then starting from the line which is unaffected by local attraction and using the included angles, the corrected bearings of the traverse are computed

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Error computation method: The direction and the amount of local attraction

at each survey station is determined

Start from the line which is unaffected by local attraction, the corrected bearing of the traverse are computed

More accurate than the included angle method

It is adopted by most of the surveyors

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Question 1. Give the comparison between Azimuth and Bearing 2. From the figure below, please give the bearings of lines AB and BC.

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N

B

A

C N

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T h a n k Yo u & Q u e s t i o n A n d A n s w e r

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