fundermental surveying -theory and practice.pdf

8/19/2019 FUNDERMENTAL SURVEYING -THEORY AND PRACTICE.pdf

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Fundamentals of Surveying Theory and Samples Exercises

Division of Spatial Information Science

Graduate School Life and Environment Sciences

University of Tsukua

!rof" Dr" #u$i %urayama

Surantha Dassanayake


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• Surveying has to do with the determination of the relative spatial location of points on or near

the surface of the earth.• It is the art of measuring horizontal and vertical distances between objects, of measuring

angles between lines, of determining the direction of lines, and of establishing points by predetermined angular and linear measurements.

• Along with the actual survey measurements are the mathematical calculations.• Distances, angles, directions, locations, elevations, areas, and volumes are thus determined

from the data of the survey.•

Survey data is portrayed graphically by the construction of maps, profiles, cross sections, anddiagrams.

Land surveying is basically an art and science of mapping and measuring land. he entire

scope of profession is wide! it actually boils down to calculate where the land boundaries are situated. his is very important as without this service, there would not have been railroads,

s"yscrapers could not have been erected and neither any individual could have put fences

around their yards for not intruding others land.

The importance of the Surveying

Definition of Surveying


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Geodetic Surveying:

he type of surveying that ta"es into account the true shape of theearth. hese surveys are of high precision and e#tend over large

areas.

$lane Surveying%

he type of surveying in which the mean surface of the earthis considered as a plane, or in which its spheroidal shape is

neglected, with regard to horizontal distances and directions.

Types of Surveying


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• &ontrol Survey% 'ade to establish the horizontal and vertical positions of arbitrary points.• (oundary Survey% 'ade to determine the length and direction of land lines and to establish

the position of these lines on the ground.• opographic Survey% 'ade to gather data to produce a topographic map showing the

configuration of the terrain and the location of natural and man)made objects.• *ydrographic Survey% he survey of bodies of water made for the purpose of navigation,

water supply, or sub)a+ueous construction.•

'ining Survey% 'ade to control, locate and map underground and surface wor"s related tomining operations.• &onstruction Survey% 'ade to lay out, locate and monitor public and private engineering

wor"s.• oute Survey% efers to those control, topographic, and construction surveys necessary for

the location and construction of highways, railroads, canals, transmission lines, and pipelines.

• $hotogrammetric Survey% 'ade to utilize the principles of aerial photogrammetry, in whichmeasurements made on photographs are used to determine the positions of photographedobjects.

• Astronomical survey% generally involve imaging or -mapping- of regions of the s"y usingtelescopes.

Different methods of Surveying


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!ythagorean Theorem In a right triangle, the s+uare of the hypotenuse is

e+ual to the sum of the s+uares of the other two sides.

& / 0 A/ 1 (/

where% & is the hypotenuse 2side opposite the right

angle3. A and ( are the remaining sides.

Units of &ngular %easurement

he most common angular units being employed

in the 4nited States is the Se#agesimal System.his system uses angular notation in increments

of 56 by dividing the circle into 756 degrees!

degrees into 56 minutes! and minutes into 56

seconds. Therefore; 1 circle = 360° = 21,600´ = 1,26,000!

1° = 60´ = 3600!

1´ = 60!

'asic Trigonometry functions for

Distance and &ngular %easurements


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%ost useale functions of Trigonometry

All trigonometric functions are simply ratios of one side of a right triangle to a second side of

the same triangle, or one side over another side. he distinction between functions is which

two sides are compared in the ratio.he figure below illustrates the side opposite from and the side adjacent to Angle A, and the

hypotenuse 2the side opposite the right angle3. he trigonometric functions of any angle are by

definition%

Sine A = Opposite Side / Hypotenuse

cosine A= Adjacent Side / Hypotenuse

Tangent A = Opposite Side / Adjacent Side

and inverting each ratio, we have

cosecant = Hypotenuse / Opposite Side = /sine A

secant = Hypotenuse / Adjacent Side = /cosine A

cotangent = Adjacent Side / Opposite Side = /tangent A


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&lgeraic Signs of the Trigonometric Functions in each (uadrant

4sing the definitions on the previous page, we can determine the values of the functions for each

angle shown below. List the Sine, &osine, and angent of each angle in both fractional and

decimal form.

"u#dr#t 1

an8 0 79: 0 6.;61 8 0 )79< 0 )6.5666

&os =>61 8 0 ):9< 0 )6.>666

an =>61 8 0 )79): 0 6.;


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Distance %easuring )*haining surveying+

?nglish mathematician ?dmund @unter 2==)=5/53 gave

to the world not only the words cosine and cotangent, andthe discovery of magnetic variation, but the measuring

device called the @unters chain shown below. ?dmund

also gave us the acre which is =6 s+uare chains.

he @unters chain is =9>6th of a mile or 55 feet long. It is

composed of =66 lin"s, with a lin" being 6.55 feet or ;.B/

inches long. ?ach lin" is a steel rod bent into a tight loop on

each end and connected to the ne#t lin" with a small steel

ring.

Starting in the early =B66s surveyors started using steel

tapes to measure distances. hese devices are still called

Cchains to this day.


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• It must be remembered in surveying, that under most circumstances, all distances are presumed to

be horizontal distances and not surface distances.

• his dictates that every field measurement ta"en be either measured horizontally or, if not, reduced

to a horizontal distance mathematically.

• In many instances, it is easiest to simply measure the horizontal distance by "eeping both ends of

the chain at the same elevation. his is not difficult if there is less than five feet or so of elevation

change between points. A hand level or Cpea gun is very helpful for maintaining the horizontal position of the chain when Clevel chaining. A pointed weight on the end of a string called a

Cplumb bob is used to carry the location of the point on the ground up to the elevated chain by

simply suspending the plumb bob from the chain such that the point of the plumb bob hangs directly

above the point on the ground.

• Ehen the difference in elevation along the measurement becomes too great for level chaining, other

methods are called for. Fne option, Cbrea" chaining, involves simply brea"ing the measurement

into two or more measurements that can be chained level.

!rocedure of *haining


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Distance %easuring )Electronic Distance %eters+

In the early =B


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&ngle %easuring

'easuring distances alone in surveying does not establish the location of an object. Ee

need to locate the object in 7 dimensions. o accomplish that we need%

=. *orizontal length 2distance3

/. Difference in height 2elevation3

7. Angular direction.

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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Types of %easured &ngles

• Interior angles are measured cloc"wise or counter)cloc"wise between two adjacent

lines on the inside of a closed polygon figure.

• ?#terior angles are measured cloc"wise or counter)cloc"wise between two adjacentlines on the outside of a closed polygon figure.

• Deflection angles, right or left, are measured from an e#tension of the preceding

course and the ahead line. It must be noted when the deflection is right 23 or left 2L3.


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A heodolite is a precision surveying instrument! consisting of an

alidade with a telescope and an accurately graduated circle! and

e+uipped with the necessary levels and optical)reading circles. he

glass horizontal and vertical circles, optical)reading system, and allmechanical parts are enclosed in an alidade section along with 7

leveling screws contained in a detachable base or tribrach.

A ransit is a surveying instrument having a horizontal circle

divided into degrees, minutes, and seconds. It has a vertical circle

or arc. ransits are used to measure horizontal and vertical angles.

he graduated circles 2plates3 are on the outside of the instrumentand angles have to be read by using a vernier %


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'earings and &,imuths

he elative directions of lines connecting survey points may be obtained in a variety of ways. he

figure below on the left shows lines intersecting at a point. he direction of any line with respect to

an adjacent line is given by the horizontal angle between the / lines and the direction of rotation.

he figure on the right shows the same system of lines but with all the angles measured from a line

of reference 2F)'3. he direction of any line with respect to the line of reference is given by the

angle between the lines and its direction of rotation.


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The line of reference )%eridian+

There are several types of meridians- &stronomical or True. %agnetic. Grid. and &ssumed .

&stronomical or True %eridians A plane passing through a point on the surface of the earth and containing

the earths a#is of rotation defines the astronomical or true meridian at that

point. Astronomical meridians are determined by observing the position of

the sun or a star. Hor a given point on the earth, its direction is always the

same and therefore directions referred to the astronomical or true meridian

remain unchanged. his ma"es it a good line of reference.

Astronomical or true meridians on the surface of the earth are lines of geographic longitude and they converge toward each other at the poles. he

amount of convergence between meridians depends on the distance from the

e+uator and the longitude between the meridians.

%agnetic %eridian

A magnetic meridian lies parallel with the magnetic lines of force of the

earth. he earth acts very much li"e a bar magnet with a north magnetic pole located considerably south of the north pole defined by the earths

rotational a#is. he magnetic pole is not fi#ed in position, but rather

changes its position continually. he direction of a magnetized needle

defines the magnetic meridian at that point at that time. (ecause the

magnetic meridian changes as magnetic north changes, magnetic

meridians do not ma"e good lines of reference.


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Grid %eridians

In plane surveys it is convenient to perform the wor" in a rectangular

J coordinate system in which one central meridian coincides with a

true meridian. All remaining meridians are parallel to this central true

meridian. his eliminates the need to calculate the convergence of

meridians when determining positions of points in the system. hemethods of plane surveying, assume that all measurements are projected

to a horizontal plane and that all meridians are parallel straight lines.

hese are "nown as grid meridians.

he Fregon &oordinate System is a grid system.

Fn certain types of localized surveying, it may not be necessary to establish a true, magnetic, or grid direction.

*owever it is usually desirable to have some basis for establishing relative directions within the current survey.

his may be done by establishing an assumed meridian.

An assumed meridian is an arbitrary direction assigned to some line in the survey from which all other lines are

referenced. his could be a line between two property monuments, the centerline of a tangent piece of roadway, or

even the line between two points set for that purpose.

he important point to remember about assumed meridians is that they have no relationship to any other meridian

and thus the survey cannot be readily 2if at all3 related to other surveys

&ssumed %eridians

Azimuths

he azimuth of a line on the ground is its horizontal angle measured from the meridian to the line. Azimuth gives

the direction of the line with respect to the meridian. It is usually measured in a cloc"wise direction with respect

to either the north meridian or the south meridian. In plane surveying, azimuths are generally measured from the

north.

Ehen using azimuths, one needs to designate whether the azimuth is from the north or the south.

Azimuths are called true 2astronomical3 azimuths, magnetic azimuths, grid azimuths, or assumed azimuths

depending on the type of meridian referenced. Azimuths may have values between 6 and 756 degrees.


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!ractices for &,imuth and 'earings

4sing angles to the right, calculate the bearings and azimuths of each lines.


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*o/ordinates

In Surveying, one of the primary functions is to describe or establish the positions of points on the surface of

the earth. Fne of the many ways to accomplish this is by using coordinates to provide an address for the point.

'odern surveying techni+ues rely heavily on 7 dimensional coordinates.

0ectangular *oordinate System )or *artesian !lane+

In the right of figure, is what is described as a rectangular coordinate system. A vertical directed line 2y)a#is3

crosses the horizontal directed line 2#)a#is3 at the origin point. his system uses an ordered pair of coordinates

to locate a point. he coordinates are always e#pressed as 2#,y3.

he # and y a#es divide the plane into four parts, numbered in a counter)cloc"wise direction as shown in the

left of figure 77. Signs of the coordinates of points in each +uadrant are also shown in this figure.

Kote% In surveying, the +uadrants are numbered cloc"wise starting with the upper right +uadrant and thenormal way of denoting coordinates 2in the 4nited States3 is the opposite 2y,#3 or more appropriately Korth,

?ast.


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!olar *oordinates

Another way of describing the position of point $ is

by its distance r from a fi#ed point F and the angle

8 that ma"es with a fi#ed indefinite line oa 2the

initial line3. he ordered pair of numbers 2r,83 arecalled the polar coordinates of $. r is the radius

vector of $ and 8 its vectorial angle.

Kote% 2r,83, 2r, 8 1 756o 3, 2)r, 8 1 =>6o 3 represent

the same point.

ransformation of $olar and ectangular

coordinates%

%easuring distance et1een coordinates

When determining the distance between any two

points in a rectangular coordinate system, the

pythagorean theorem may be used. In the figure

below, the distance between A and B can becomputed in the following way :


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%easuring the &rea y *oordinates

Area of a trapezoid% one)half the sum of the bases times the altitude.

Area of a triangle% one)half the product of the base and the altitude.

he area enclosed within a figure can be computed by coordinates.

his is done by forming trapezoids and determining their areas.

rapezoids are formed by the abscissas of the corners. Frdinates at

the corners provide the altitudes of the trapezoids. A s"etch of the

figure will aid in the computations.

=. Hind the latitude and departure between points.

/. Hind the area of the figure.

&rape'oid

&riang(e

Answers


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Traverse

A raverse is a succession of straight lines along or through the area to be surveyed. he directions and

lengths of these lines are determined by measurements ta"en in the field.

A traverse is currently the most common of several possible methods for establishing a series or networ" of

monuments with "nown positions on the ground. Such monuments are referred to as horizontal control pointsand collectively, they comprise the horizontal control for the project.

In the past, triangulation networ"s have served as horizontal control for larger areas, sometimes covering

several states. hey have been replaced recently in many places by @$S networ"s. 2@$S will be discussed in

more detail later.3 @$S and other methods capitalizing on new technology may eventually replace traversing

as a primary means of establishing horizontal control. 'eanwhile, most surveys covering relatively small

areas will continue to rely on traverses.

Ehatever method is employed to establish horizontal control, the result is to assign rectangular coordinates toeach control point within the survey. his allows each point to be related to every other point with respect to

distance and direction, as well as to permit areas to be calculated when needed.

Types of traverses

here are several types or designs of traverses that can be

utilized on any given survey. he terms open and closed are

used to describe certain characteristics of a traverse. If not

specified, they are assumed to refer to the mathematicalrather than geometrical properties of the traverse.

A @eometrically &losed raverse creates a closed

geometrical shape, such as the first two e#amples in Higure

A. he traverse ends on one of two points, either the on

same point from which it began or on the initial bac"sight.

he first two traverses in Higure A are geometrically closed. )igure A


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!rocedure for running a traverse

o begin any traverse, a kno1n point must be occupied. 2o occupy a point means to set up and level the transit

or theodolite, directly over a monument on the ground representing that point.3 Ke#t, a direction must be

established. his can be done by sighting with the instrument a second "nown point, or any definite object,

which is in a "nown direction from the occupied point. he object that the instrument is pointed to in order to

establish a direction is "nown as a bac"sight. $ossible e#amples would be another monument on the ground, aradio tower or water tan" on a distant hill, or anything with a "nown direction from the occupied point. A

celestial body such as $olaris or the sun could also be used to establish an initial direction.

Fnce the instrument is occupying a "nown point, for e#ample point number /, and the telescope has been

pointed toward the bac"sight, perhaps toward point number =, then an angle and a distance is measured to the

first un"nown point. An un"nown point being measured to is called a foresight. Eith this data, the position of

this point 2lets call it point number =663 can be determined.

he ne#t step is to move the instrument ahead to the former foresight and duplicate the entire process.


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2o1 satellite distance is measured

he @lobal $ositioning System 2@$S3 is a navigational or positioning system developed by the 4nited States

Department of Defense. It was designed as a fast positioning system for /: hour a day, three dimensional coverage

worldwide.

It is based on a constellation of /= active and 7 spare satellites orbiting =6,B66 miles above the earth. he @$S

2KASA3 satellites have an orbital period of =/ hours and are not in geosynchronous orbit 2they are not stationary

over a point on the earth3. hey maintain a very precise orbit and their position is "nown at any given moment in time.

his constellation could allow a @$S user access to up to a ma#imum of > satellites anywhere in the world.

@$S provides $oint $osition 2Latitude9Longitude3 and elative $osition 2ector3. @$S can differentiate between

every s+uare meter on the earths surface thus allowing a new international standard for defining locations and

directions.

The !rinciples of G!S

Hor centuries man has used the stars to determine his

position. he e#treme distance from the stars made them

loo" the same from different locations and even with the

most sophisticated instruments could not produce a

position closer then a mile or two. he @$S system is a

constellation of 'anmade Stars at an orbit high enough to

allow a field of view of several satellites, yet low enough

to detect a change in the geometry even if you moved a few feet.

A typical conventional survey establishes positions of

un"nown points by occupying a "nown point and

measuring to the un"nown points. @$S is somewhat the

opposite.

Ee occupy the un"nown point and measure to

"nown points. In conventional surveying this is

similar to the process of doing a resection, the

slight difference is that the targets are =6,B66

miles away and travelling at e#tremely high speeds.


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2o1 satellite distance is measured

?ach @$S satellite continually broadcasts a radio signal.

adio waves travel at the speed of light 2=>5,666 miles per

second3 and if we measure how long it too" for the signal to

reach us we could compute the distance by multiplying the

time in seconds by =>5,666 miles per second. In order to measure the travel time of the radio signal, the

satellite broadcasts a very complicated digital code. he

receiver on the ground generates the same code at the e#act

time and when the signal is received from the satellite, the

receiver compares the two and measures the phase shift to

determine the time difference%

Differential G!S

o achieve sub)centimeter accuracies in positions, we

need a survey grade receiver and a techni+ue called

Differential @$S. (y placing a receiver at a "nown

location, a total error factor which accounts for all the

possible errors in the system, can be computed which

can be applied to the position data of the other receivers

in the same locale. he satellites are so high)up that any

errors measured by one receiver could be considered to

be e#actly the same for all others in the immediate area.


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Differential Leveling

Differential leveling is the process used to determine a difference

in elevation between two points. A Level is an instrument with a

telescope that can be leveled with a spirit bubble. he optical line

of sight forms a horizontal plane, which is at the same elevation as

the telescope crosshair. (y reading a graduated rod held vertically

on a point of "nown elevation 2(ench 'ar"3 a difference in

elevation can be measured and a height of instrument 2*.I.3

calculated by adding the rod reading to the elevation of the bench

mar". Fnce the height of instrument is established, rod readings

can be ta"en on subse+uent points and their elevations calculated

by simply subtracting the readings from the height of instrument.

In the following e#ample, the elevation at (')A is "nown, and

we need to "now the elevation of (')M. he level is set up at a

point near (')A, and a rod reading ta"en. he height of

instrument 2*I3 is calculated and a rod reading to a turning point 2$=3 is ta"en. he reading of the foresight is subtracted

from the height of instrument to obtain the elevation at $=. he

rod stays at $=, the level moves ahead and the rod at $= now

becomes the bac"sight. his procedure is repeated until the final

foresight to (')M .


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Digital Terrain %odels

A digital errain 'odel 2D'3 is numerical

representation of the configuration of the terrain

consisting of a very dense networ" of points of "nown

,J,N coordinates. 'odern surveying and photogrammetric e+uipment enables rapid three

dimensional data ac+uisition. A computer processes

the data into a form from which it can interpolate a

three dimensional position anywhere within the

model.

hin" of a D' as an electronic lump of clay shaped

into a model representing the terrain. If an alignment

was draped on the model and a vertical cut made

along the line, a side view of the cut line would yield

the alignments original ground profile. If vertical

cuts were made at right angles to the alignment at

certain prescribed intervals, the side views of the cuts

would represent cross sections. If horizontal cuts were

made at certain elevation intervals, the cut lines when

viewed from above would represent contours. A D' forms the basis for modern highway location

and design. It is used e#tensively to e#tract profiles

and cross sections, analyze alternate design

alignments, compute earthwor", etc.

generates a -Digital errain 'odel- 2D'3 from which it

then automatically e#tracts a regular grid -Digital

?levation 'odel- 2D?'3.


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2!

*ross Sections

%ro&& &ection& #re line& 0 degree& 'er'endicul#r to the

#lign(ent )*+ine, +ine, centerline of &tre#(, etc.-, #long

hich the configur#tion of the ground i& deter(ined /y

o/t#ining elev#tion& of 'oint& #t non di&t#nce& fro( the

#lign(ent.

%ro&& &ection& #re u&ed to deter(ine the &h#'e of the ground

&urf#ce through the #lign(ent corridor. The &h#'e of the ground

&urf#ce hel'& the de&igner 'ic hi& horiont#l #nd vertic#l

'rofile. nce the #lign(ent i& 'iced, e#rthor u#ntitie& c#n

/e c#lcul#ted. The e#rthor u#ntitie& ill then /e u&ed to hel'

ev#lu#te the #lign(ent choice.

4n #ddition to e#rthor c#lcul#tion&, cro&& &ection& #re u&ed in

the de&ign of &tor( &eer&, culvert e5ten&ion& #nd the &ie #nd

loc#tion of ne culvert&.

?#ample of alluvial terraces in a geologic cross section

across the Keosho iver alley

a"en from F&onnor, =B


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2"

0eferences

) Hundamentals of Surveying% Sample ?#amination,@eorge '. &ole $? $LS 2Author3

) (asic Surveying,aymond ? $aul 2Author3, Ealter Ehyte 2Author3

) ?lectronic vs. &onventional Surveys,. Di#on2Author3) http%99s+uidstation.net9Surveying.html

) www.ordnancesurvey.co.u"9gps9

) Kinth Annual Seminar$resented by theFregon Department of ransportation@eometronics, Fregon

fundermental surveying -theory and practice.pdf

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