Measurement of Vertical Distances - · PDF fileGE 100 Elementary Surveying Lecture No. 3...

Measurement of Vertical

Distances

Lecture No. 3

Caraga State University

College of Engineering and Information Technology

GE 100: General Surveying I

GE 100

Elementary Surveying Lecture No. 3

Measurement of

Vertical Distances

Leveling

It is the process of directly or

indirectly measuring vertical

distances to determine the

elevation of points or their

difference in elevation.

GE 100


Measurement of

Vertical Distances

Definition of Terms

1. Level Surface – it is a curved surface which is at any point perpendicular to the direction of gravity or the plumb line.

2. Level Line – it is a curved line in a level surface all points of which are normal to the direction of gravity and equidistant from the center of the earth.

3. Horizontal Surface – it is a plane that is tangent to a level surface at a particular point. It also perpendicular to the plumb line at the same point.

GE 100


Measurement of

Vertical Distances

Definition of Terms

4. Horizontal Line – a straight line in a

horizontal plane which is tangent to a level

line at one point. It is perpendicular to the

direction of gravity at the point of tangency.

5. Vertical Line – is a line parallel to the

direction of gravity.

6. Mean Sea Level – is an imaginary surface of

the sea which is midway between high and

low tides.

GE 100


Measurement of

Vertical Distances

Definition of Terms

7. Datum – is any convenient level surface coincident or parallel with mean sea level to which elevations of a particular area are referred.

8. Elevation – is the vertical distance above or below mean sea level or any other selected datum.

9. Difference in Elevation – is the vertical distance between the two level surfaces in which the points lie.

GE 100


Measurement of

Vertical Distances

To Earth’s

Center

Ver

tical

LineVer

tical

Li

ne

Ver

tical

Line

A

B

C

MEAN SEA LEVEL

Level Line Thru C

Level Line Thru A

Level Line Thru B

Elevation

of B (+)

Elevation

of C (-)

Elevation

of A (+)

Diff. in Elev.

Between B & C

Diff. in Elev.

Between A & C

Diff. in Elev.

Between A & B

Earth’s Surface

Relationship Between Level

Surfaces

GE 100


Measurement of

Vertical Distances

Leveling Methods

1. Direct or Spirit Leveling – method of determining the elevation of points some distance apart by a series of set ups of a leveling instrument along a selected route. It is also referred to spirit leveling since the device used is a spirit level.

Forms of Direct Leveling

a. Differential Leveling

b. Double – Rodded Leveling

c. Three – Wire Leveling

GE 100


Measurement of

Vertical Distances

Leveling Methods

2. Reciprocal Leveling – is the process of accurately determining the difference in elevation between two inter visible points located at a considerable distance apart and between which points leveling could not be performed in the usual manner.

3. Profile Leveling – is used to determine difference in elevation between points at designated short measured intervals along an established line to provide data from which a vertical section of the ground surface can be plotted.

GE 100


Measurement of

Vertical Distances

Leveling Methods

4. Trigonometric Leveling – is employed in determining by trigonometric computations the difference in elevation between two points from measurements of its horizontal and slope distance and the vertical angle between the points.

5. Stadia Leveling – combines features of direct leveling with those of trigonometric leveling. It is in fact a form of trigonometric leveling.

GE 100


Measurement of

Vertical Distances

Leveling Methods

6. Barometric Leveling – it involves the determination of differences in elevation between points by measuring the variation in atmospheric pressure at each point by means of barometer.

7. Cross-Section Leveling – in highways or railroad construction it is often necessary to obtain a representation of the ground surface on either side of the centerline.

8. Borrow-Pit Leveling – is a method of determining the relative elevations of points in borrow-pit excavations for the purpose of calculating volumes of earthwork.

WYE LEVEL

DUMPY LEVEL

GE 100


Measurement of

Vertical Distances

Types of Levels

GEODETIC LEVEL

TILTING LEVEL

BUILDER’S LEVEL

AUTOMATIC LEVEL

TRANSIT AS A LEVEL

LASER LEVEL

HAND LEVEL

GE 100


Measurement of

Vertical Distances

DUMPY LEVEL WYE LEVEL

BUILDER’S LEVEL

AUTOMATIC LEVEL

GE 100


Measurement of

Vertical Distances

TILTING AND

GEODETIC LEVEL

LASER LEVEL

LASER SYSTEM

MOUNTED ON

BUILDER’S LEVEL

HAND LEVEL

GE 100


Measurement of

Vertical Distances

Leveling Rods

It is a graduated rod

which is used for

measuring the vertical

distance between the

line of sight through a

leveling instrument

and the point whose

elevation is either

required or known.

GE 100


Measurement of

Vertical Distances

2. Target Rod – it is the type of rod has a sliding target which is set and read by a rodman at the position selected by the instrumentman.

1. Self-Reading Rod – it is the most commonly used type of leveling rod. It can be read directly by the instrumentman through the telescope by noting the apparent intersection of the horizontal hair on the rod.

Two Classification of Leveling Rod

GE 100


Measurement of

Vertical Distances

Other Types of Rod

1. Rods Named

After Cities or

States

2. Rod Ribbons

3. Precise Rod

4. Geodetic Rod

5. Tape Rod

Philadelphia Rods

GE 100


Measurement of

Vertical Distances

Rod Level

• It is a device used for fast and correct plumbing of a leveling rod.

• It is L-shape in design and consists of a small circular spirit level fastened the rod or to small bracket held against the side of the rod.

GE 100


Measurement of

Vertical Distances

Targets

• It is a small device

attached to the rod

when extremely

long sights make

direct reading of

the rod difficult or

impossible.

GE 100


Measurement of

Vertical Distances

Other Forms of Targets

GE 100


Measurement of

Vertical Distances

Telescope

• It is a metal tube

containing a system

of lenses which are

used to fix the

direction of the line

of sight and is

magnifying the

apparent size of the

objects in its field of

view.

Objective Lens

GE 100


Measurement of

Vertical Distances

Parts of Telescope

Eyepiece

Cross Hairs

GE 100


Measurement of

Vertical Distances

Cross Hair Ring or Reticule

GE 100


Measurement of

Vertical Distances

Types of Telescope

1. Internal Focusing Telescope • It has an additional auxiliary lens which moves

back and forth between the objective and the

cross hairs as the focusing screw it turned.

2. External Focusing Telescope • It has an objective lens mounted on a sleeve

which moves back and forth in the telescope

barrel as an object is brought into focus.

GE 100


Measurement of

Vertical Distances

GE 100

Elementary SurveyingLecture 3

Measurement of

Vertical Distances

GE 100

Elementary SurveyingLecture 3

Measurement of

Vertical Distances

Internal Focusing Telescope

External Focusing Telescope

dust cap

Objective Lens

Auxiliary

Lens Reticule

Eyepiece

Eyepiece

Reticule Objective Lens Draw Tube

GE 100


Measurement of

Vertical Distances

Magnification of the Telescope

• It is the ratio of the apparent size of an

object viewed through a telescope to its

size as seen by the unaided eye from the

same distance.

• It may also be taken as the amount by

which an object is increased in apparent

size.

GE 100


Measurement of

Vertical Distances

Level Vial

• It is sealed graduated glass tube containing some

amount of liquid and a small air bubble.

• It is used to determine the direction of gravity.

GE 100


Measurement of

Vertical Distances

Coincidence Bubble

• Type of bubble used on

most modern precise instruments such as the tilting and automatic level.

• It employs an optical device which splits the bubble longitudinally, then turns one end around to make it appear adjacent to the other end.

Appearance of Bubbles Before Centering

And Direction Taken in Turning the

Leveling Screws

Appearance of bubbles

when Centered

GE 100


Measurement of

Vertical Distances

Tripods • It serves as a base to prevent movement of the instrument after it is

set up.

• It consists of three wooden or aluminum legs which are securely

fastened the tripod head by means of a hinged joint.

Fixed-Leg Tripod Extension Tripod

GE 100


Measurement of

Vertical Distances

Setting up the Level • The leveling instrument may be set up at any suitable or

desired location.

• Solid ground should be selected when setting up the instrument.

• Tripod legs are spread so that the foot plate will be approximately horizontal and they should be pushed firmly into the ground to make it stand stable.

• The preferable and convenient of set up is one which will enable the instrumentman to sight through the telescope without having to stretch or stoop.

• The legs of the tripod when setting up on hillsides or along a slope, one leg should extend uphill and two legs downhill.

GE 100


Measurement of

Vertical Distances

Leveling the Instrument

1. Instruments with Four Leveling Screws

Direction of Bubble Movement

Motion of

Left Thumb

Motion of

Right Thumb

Motion of

Left Thumb

Motion of

Right Thumb

Direction

of Bubble

Movement

GE 100


Measurement of

Vertical Distances

Leveling the Instrument

2. Instruments with Three Leveling Screws

Direction of Bubble Movement

Motion of

Left Thumb

Motion of

Right Thumb

Motion of

Left Thumb

Direction

Of Bubble

Movement

GE 100


Measurement of

Vertical Distances

Holding the Leveling Rod

• The leveling rod is held on a point by a rodman when a sight is to be taken on it.

• The rod be held plumb when the reading is made.

• The instrumentman checks the rod by observing through the telescope and noting if its is held parallel to the vertical cross hair.

• The rod is lightly supported between the fingers of both hands and is allowed to balance on its own weight.

• The fingers must not cover the face of the rod.

• The graduations of the rod are always clearly visible and not obstructed.

GE 100


Measurement of

Vertical Distances

Taking a Rod Reading

POSITION THE ROD

FOCUS ON THE ROD

READ THE ROD

GE 100


Measurement of

Vertical Distances

Determining Difference in

Elevation

Horizontal

Line of Sight

A

B

A B

Rod

Horizontal

Line of Sight

Difference in

Elevation between

A and B

GE 100


Measurement of

Vertical Distances

Length of Sight • It is always best to take sights at moderate

lengths to attain speed and accuracy in leveling work.

• A very short or extremely long sights should be avoided.

• The most suitable sight lengths will depend upon the required degree of precision, the surface of the terrain, the type of instrument used, and upon the distance at which the rod remains readable to the instrumentman.

• It should not exceed 90 m where elevations to the nearest 0.001 m are desired.

GE 100


Measurement of

Vertical Distances

Waving the Rod

• Is used to determine whether the rod is plumb

when a reading is taken on it.

• It is accomplished by slowly waving or tilting

the top of the rod through the arc, first toward

the instrument and then away from it.

GE 100


Measurement of

Vertical Distances

Carrying the Instruments

• The levels should always be kept in a box when it is not used.

• It should remain in its carrying case when transported to the work site or when ot has to be moved to another distant set up or over rough terrain.

• The level does not detached from the tripod when transferring to another nearby station provided that it is securely fastened to the tripod and is carried properly.

• In open spaces, the level may be carried on the shoulder in preferably a near-vertical position.

• The spindle is clamped slightly so that the telescope does not rotates when carried.

• In densely forested areas, the level should be cradled between the arms and held close to one’s chest left or right chest.

GE 100


Measurement of

Vertical Distances

Arm and Hand Signals

Move Right or Left

Give a Sight

All Right

This a Point

Move Back

Pick Up Instruments

Raise or ( Lower ) Target

Come In

Plumb the Rod

Establish a Turning Point

This is a Turning Point

Wave the Rod

Face the Rod

Reverse the Rod

Move Forward

Use the Long Rod

GE 100


Measurement of

Vertical Distances

Sources of Error in Leveling

1. Instrumental Errors

– these errors are attributed to imperfections

in the instruments either from faults in their

manufacture or from improper adjustment.

Examples: • Instruments out of Adjustmennt

• Rod not Standard Length

• Defective Tripod

GE 100


Measurement of

Vertical Distances


2. Personal Errors - occur largely due to the limitations of the senses of touch,

sight or hearing of individuals, skills, training, and teamwork

of the members of a leveling party.

Examples: • Bubble not Centered

• Parallax

• Faulty Rod Readings

• Rod not Held Plumb

• Incorrect Setting of Target

• Unequal Backsight and Foresight

GE 100


Measurement of

Vertical Distances


3. Natural Errors – errors due to natural sources and could not be

totally removed but their effects can be reduced by applying corrections and using good judgment.

Examples: • Curvature of the Earth

• Atmospheric Refraction

• Temperature Variations

• Wind

• Settlement of the Instrument

• Faulty Turning Points

GE 100


Measurement of

Vertical Distances

Common Mistakes in

Leveling

The following are some of the most

commonly made mistakes in leveling

work:

1. Misreading the Rod

2. Incorrect Recording

3. Erroneous Computations

4. Rod not Fully Extended

5. Moving Turning Points

GE 100


Measurement of

Vertical Distances

Adjustment of the

Dumpy Level The following are the three field adjustments often required

for a dumpy level:

1. Adjustment of the Cross Hair

– the reticule or the cross hair ring is adjusted to see to it the horizontal cross hair lies in a plane perpendicular to the vertical axis of the instrument

2. Adjustment of the Level Vial

– is to make the axis of the level vial perpendicular to the vertical axis of the instrument.

3. Adjustment of the Line of Sight

– the line of sight is adjusted to make it parallel to the axis of the level vial.

GE 100


Measurement of

Vertical Distances

Two Peg Test

TWO-PEG TEST

A

B

L1

L2

d

d’

a

TDE

b’b

c

GE 100


Measurement of

Vertical Distances

where:

a = rod reading on A with instrument set up near A.

b = rod reading on B with instrument set up near A.

c = rod reading on B with instrument set up near B.

d = rod reading on A with instrument set up near B.

The computed difference in elevation for the two set ups are:

DEa = ( a-b ) and DEb = ( d-c )

Note: If the two differences in elevation are equal, the line of sight is in adjustment.

GE 100


Measurement of

Vertical Distances

TDEa = a – (b-e) and TDEb = (d-e) - c

2

)()(

2

2

)()(

2

cdba

cedeba

cedeba

TDETDETDE ba

If DEa is not equal to Deb, the correct rod reading at A with

the instrument still set up near B is :

2

)()('

cdbacTDEcd

GE 100


Measurement of

Vertical Distances

ALTERNATE PROCEDURE FOR

TWO-PEG TEST

ALTERNATE PROCEDURE FOR TWO-

PEG TEST

L1

L2

A

BM

P

TDE

Da

Db

(Db-Da)

a

c

c’

en

d

d’

b

Ief

GE 100


Measurement of

Vertical Distances

where:

a = rod reading on A with instrument set up at M.

b = rod reading on B with instrument set up at M.

c = rod reading on A with instrument set up at P.

d = rod reading on B with instrument set up at P.

c’ = correct rod reading on A for a horizontal line of sight.

d’ = correct rod reading on B for a horizontal line of sight.

Da = horizontal distance between points A and P.

Db = horizontal distance between points B and P.

en = error in the reading on the near rod ( held at A )

ef = error in the reading on the far rod ( held at B )

I = inclination of the line of sight in the net distance.

GE 100


Measurement of

Vertical Distances

The true difference in elevation between the two pegs:

TDE = DEm = a – b

DEp = c – d

The inclination of the line of sight from the horizontal is:

I = DEm – DEp = ( a – b ) – ( c – d )

The error in the reading on the far rod at B can be determined by proportion as follows:

)( IDD

Deor

DD

D

I

e

ab

bf

ab

bf

GE 100


Measurement of

Vertical Distances

The correct rod reading d’ at the far rod ( held at B ) for a horizontal line of sight. Thus,

d’ = d – ef

Similarly, the error in the reading on the near rod at A is:

The correct rod reading c’ at the near (held at A) for a horizontal line of sight. Thus,

c’ = c – en

To check the computation, we have:

( a – b ) = ( c’ – d’ )

)( IDD

Deor

DD

D

I

e

ab

an

ab

an

GE 100


Measurement of

Vertical Distances

EXAMPLE PROBLEM

GE 100


Measurement of

Vertical Distances

Example # 1:

1. In the two-peg test of a dumpy level, the following observation were taken:

• Determine if the line of sight is in adjustment.

• If the line of sight is not in adjustment, determine the correct rod reading on A with the instrument still set near B.

• Determine the error in the line of sight for the net distance AB.

• Explain how the line of sight of the instrument should be adjusted.

Rod Reading Instrument Set up

Near A

Instrument Set

up Near B

on point A 1. 505 m. 0. 938 m.

on point B 2. 054 m. 1. 449 m.

GE 100


Measurement of

Vertical Distances

Illustration:

TWO-PEG TEST

A

B

L1

L2a

d c

b

GE 100


Measurement of

Vertical Distances

Example # 2: In the two-peg test of a dumpy level, the following observations are taken:

Point M is equidistant from both A and B, while P is 2.50 m. away from A along the extension of line AB and 79.27 m. from B.

a. determine the true difference in elevation between points A and B.

b. Check if the line of sight is in adjustment.

c. If the instrument needs to be adjusted, determine the “false” difference in elevation, inclination of the line of sight, and the error in the reading on the far rod.

d. With the level still set up at P, determine the rod reading on B to which the line of sight should be adjusted

e. Perform the customary check.

Rod Reading Instrument Set up

near M

Instrument Set up

near P

on point A 0. 296 1. 563

on point B 0. 910 2. 140

GE 100


Measurement of

Vertical Distances

Illustration: ALTERNATE PROCEDURE FOR TWO-

PEG TEST

L1

L2

A

BM

P

La=2.5 m.

Lb = 79.27

(Lb-La) = 76.77 m.

a=0.296 m.

c=1.563 m.

d=2.140 m.

b=0.910 m.

Measurement of Vertical Distances - · PDF fileGE 100 Elementary Surveying Lecture No. 3...

Documents

Transcript of Measurement of Vertical Distances - · PDF fileGE 100 Elementary Surveying Lecture No. 3...