79338922 survey-report
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INDEX
1. INTRODUCTION
2. RECONISSANCE SURVEY
3. ANGLE MEASUREMENT
4. LEVELLING
5. TRIANGULATION
6. TACHEOMETRY
7. PLANE TABLE
8. CONTOUR PLOTTING
9. OBSERVATION TABLES
1.INTRODUCTION
Surveying is the art of determining the relative positions of points on, above or beneath the
surface of the earth by means of direct or indirect measurements of distance, direction and
elevation. It also includes the art of establishing points by predetermining angular and
linear measurements. The application of surveying requires skill as well as the knowledge
of mathematics, physics, and to some extent, astronomy. It is a technique of preparing the
map of an area. In all Engineering Projects the preparations of accurate plans and sections is
the first necessity.
In this survey camp, i.e. in Survey Camp 2009(Dec 10 – Dec 23), we got the project,
“TOPOGRAPHICAL MAP OF PEC”, in which we have to plot the prominent features of PEC
on the map with the help of various surveying techniques. Topography is meant by the
shape or configuration of the earth’s surface. The basic purpose of topographical map is to
indicate the three dimensional relationships for the terrain of any given area of land. Thus,
on a topographic map, the relative positions of the points are represented both horizontally
as well as vertically.
To get a comprehensive idea of the area, we explored the area looking in prominent points/
features that we have to show on the map and also we looked for any difficulty that we
might encounter in future while plotting the points on the sheet. This type of process of
exploring the area in detail and looking for points where we can set our instrument to get
the points on sheet is known as Reconnaissance.
After reconnaissance, we got the rough map of the area and the points where we will set our
instrument i.e. instrument stations.
We first selected one instrument station from where we wanted to commence our work,
but, the problem was that we were not aware of the elevation of that point w.r.t. mean sea
level (Reduced Level of that point), as with the help of that R.L., we have to find out and plot
the R.L of points that we have to show on the map.
So, for that purpose, we have gone to Regulatory End of Sukhna Lake, whose R.L. was
known to us, and which was approximately 3 Kms from our college. With the help of
Levelling Instrument, we got the R.L of the points that were in the way from Sukhna Lake to
College. So, finally we got the R.L of the point from where we have to commence our work.
In college, we used the instruments like Total Station, Plane Tabling with telescopic alidade
to get the R.L of various points and to plot those points on the sheet.
CAMP SITE
PEC MAP
2.RECONNAISSANCE SURVEY
A reconnaissance survey provides data that enables design engineers to study the
advantages and disadvantages of a variety of routes and then to determine which
routes are feasible. You begin by finding all existing maps that show the area to be
reconnoitered. In reconnaissance, studying existing maps is as important as the
actual fieldwork. Studying these maps and aerial photographs, if any exist, will
often eliminate an unfavorable route from further consideration, thus saving
your reconnaissance field party much time and effort. Contour maps give essential
information about the relief of an area. Aerial photographs provide a quick means
for preparing valuable sketches and overlays for your field party. Direct aerial
observation gives you an overview of an area that speeds up later ground
reconnaissance if the region has already been mapped. Begin the study of a map
by marking the limits of the area to be reconnoitered and the specified terminals to
be connected by the highway. Note whether or not there are any existing routes.
Note ridgelines, water courses, mountain gaps, and similar control features. Look
for terrain that will permit moderate grades without too much excavating.
Use simplicity in alignment and have a good balance of cuts and fills; or use a
profile arrangement that makes it possible to fill depressions with the cut taken
from nearby high places. Mark the routes that seem to fit the needs and that should
be reconnoitered in the field. From the map study, determine grades, estimate the
amount of clearing required, and locate routes that will keep excavation to a
minimum by taking advantage of terrainconditions. Mark stream crossings and
marshy areas as possible locations for fords, bridges, or culverts. Have the
reconnaissance field party follow the route or routes marked earlier during the
map study. Field reconnaissance provides you with an opportunity for checking
the actual conditions on the ground and for noting any discrepancies in the maps
or aerial photographs. Make notes of soil conditions, availability of construction
materials, such as sand or gravel, unusual grade or alignment problems, and
requirements for clearing and grubbing. Take photographs or make sketches
of reference points, control points, structure sites, terrain obstacles,
landslides, washouts, or any other unusual circumstances. Your
reconnaissance survey party will usually carry lightweight instruments that are not
precise. Determine by compass the direction and angles. Determine the approximate
elevations by an aneroid barometer or altimeter. Use an Abney hand level
(clinometer) to estimate elevations and to project level lines. Other useful items to
carry are pocket tapes, binoculars, pedometer and pace tallies, cameras,
watches, maps, and field notebooks. Keep design considerations in mind while
running a reconnaissance survey. Remember that future operations may require
further expansion of the route system presently being designed. Locate portions of
the new route, whenever possible, along roads or trails that already exist. Locate
them on stable, easily drained, high-bearing-strength soils. Avoid swamps,
marshes, low-bearing-strength soils, sharp curves, and routes requiring large
amounts of earthmoving. Keep the need for bridges and drainage structures to a
minimum. When the tactical situation permits, locate roads in forward combat
zones where they can be concealed and protected from enemy fire. The report you
turn in for the reconnaissance field party must be as complete as possible; it
provides the major data that makes the selection of the most feasible route or
routes possible.
3.ANGULAR MEASUREMENT
Surveying and navigation often rely on the measurement of two phenomena in
order to determine position, those of distance (already covered in lectures) and
direction or bearing. These lecture notes will introduce the concept of bearings and
cover the instrumentation that has been developed over the centuries to facilitate
the determination of relative and absolute 'bearing'. In order to start, we will look at
the definition of some terms specific to the determination of direction.
3.1 Definitions:
Directions: - Simply that, a direction (over there).
Bearings: - A direction relative to a datum
Whole-circle bearings: The direction of survey lines is generally expressed as an
angle measured from a reference meridian, generally north, commencing from 0
degrees (0°) and increasing clockwise to 360 degrees (359°59'60"). Bearings are
never expressed as "North, X degrees East".
Angles: - The arithmetic difference between two directions or bearings.
Reference meridians:
True north (through the geographic poles about which the Earth rotates)
Magnetic north (through which lines of magnetic flux pass)
Grid north - An arbitrary meridian (one adopted for a particular project) - a
mathematically determined value
Magnetic meridian: - The direction of the earth's magnetic lines of force. This varies
with date, time and locality.
Magnetic declination - The angle between the magnetic and true meridians.
Angle measurement is a fundamental part of surveying field observations, as the
combination of a direction and a distance gives a polar vector to a point and hence a
unique location of that point in space. The instruments that have been developed to
facilitate angle (or direction) measurement are the magnetic compass , the sextant
and the theodolite.
3.2 The Magnetic Compass
The Magnetic Compass is an instrument which indicates the whole circle bearing
from the magnetic meridian to a particular line of sight. It consists of a needle or
disc magnetised so that it will align itself with the direction of the Earth's magnetic
flux, and some type of index scale so that numeric values for the bearing can be
determined. See diagram below.
The magnetic bearing is related to true bearings as follows:
d = Magnetic declination (positive when
clockwise)
qt = True bearing
qm = Magnetic bearingqt = q m + d
3.3 Variations in Declination
The geophysical phenomena that generate the Earth's magnetic flux are still not
fully understood. It is known that magnetic north moves quite considerably over
time, and has even reversed polarity in prehistory. Some of the phenomena that
effect the direction of magnetic flux (and hence magnetic north) are known as
variations in declination and are as follows:
Variation Cause Amount of Dd
Secular variation Rotation of magnetic pole around
geographic pole.
In 1933 - 8°
Diurnal variation Effect of sun during the day up to 10' In 1970 -
9°59'E
Irregular variation Sunspot activity up to 5°
Irregular variation
(cont)
Electrical storm up to 5°
Conclusion: Magnetic north is generally too unreliable for use as a survey
datum!
3.4 Local Attraction
The needle of the compass can also be 'attracted' by metallic objects close to the
point of observation. These objects cause local aberrations in the direction of
magnetic flux, and give rise to an effect known as local attraction. These local
disturbances in the Earth's magnetic field are often due to large iron masses, electric
cables, fences, cars and so on. They tend to occur locally, and if detected can
sometimes be compensated for in survey procedures. Magnetic anomalies caused by
underground minerals are a problem for surveyors, but form the basis of many
mineral exploration techniques so the news is not all bad.
Where a closed traverse consisting of compass bearings and distances has been
performed around a parcel of land (see later) it is possible to compensate for the
effects of local attraction and to distribute 'angular misclosure'.
This will be covered in more detail later but in summary the procedure consists of:
i. measuring forward and back bearing of each line
ii. computing angles and angle misclosure
iii. (misclosure = [180°(n - 2)] - S angles) {¹(n-2) - S angles} )
iv. adjusting each angle by adding to each
v. recomputing bearings from adjusted angles. (The bearing of one line must be
known or assumed).
The presence or otherwise of local attraction can be determined from the difference
between a 'forward' bearing and a 'reverse' bearing observed from, and to, a station.
If I was to measure from Point A to Point B, and then from Point B back to Point A
the difference in the bearings should be 180°. Any variation in this in excess of what
would be expected from random error would be most likely due to local attraction.
Needless to say both forward and reverse bearings are always observed when using
a compass for traversing.
3.5 Compasses
There are two main types of magnetic compasses used in the field by surveyors
navigators and orienteers: the Sunnto type and the prismatic type, as well as
compass-theodolites. There are others like the gyro-compass which are used in
inertial navigation systems, however they will not be addressed here.
Both the Sunnto type and the Prismatic type are held in the hand for use, and are
therefor subject to poor centring and an unstable platform. The effects of this are
reduced over long sight lines, which, when combined with the vagaries of the
magnetic meridian, combine to make the compass a reconnaissance or inventory
tool only. Neither the instruments nor the basis upon which they work are
sufficiently stable for any sort of precision work.
3.6 Measuring Horizontal Angles With Total Station Instruments
• Horizontal angles are measured in horizontal planes.
• To eleminate instrumental errors and increase precision, angle measurements
should
be repeated an equal number of times in each of the direct and reversed modes, and
the
average taken.
In the notes
1. the identification of the angle being measured is recorded in column (1)
2. the value of the first reading of the angle is placed in column (2)
3. it is only recorded for checking purposes, the fourth (final) reading is tabulated in
column (3)
4. the mean of the four readings, which produce the final angle, is given in column
(4)
3.7 Measuring Horizontal Angles by The Direction Method
4. LEVELLING
4.1 General
The primary reference at water-level recording stations is a set of stable bench-
marks, installed in locations where their level should not change. Upon initial set-up
of a station, the levels of the relevant parts of the installation are established and
recorded by means of accurate levelling. At least every two years, the levels of the
staff gauges, sensor level, internal gauge, tower structure and benchmarks should be
measured relative to each other as a check that records are not in error due to bank
subsidence or other movement.
Accurate levelling is thus a particularly important part of site establishment,
installation and quality assurance. All staff shall be thoroughly familiar with its
theory and practice.
Levelling and surveying methods are also used for measurements of river channel
and lake configurations. Often, less accurate methods can be used for this work than
for water-level recording stations, although the techniques are common.
4.2 Definitions
Differential levelling is the term applied to any method of measuring directly with a
graduated staff the difference in elevation between two or more points.
Precise levelling is a particularly accurate method of differential levelling which
uses highly accurate levels and with a more rigorous observing procedure than
general engineering levelling. It aims to achieve high orders of accuracy such as 1
mm per 1 km traverse. A level surface is a surface which is everywhere
perpendicular to the direction of the force of gravity. An example is the surface of a
completely still lake. For ordinary levelling, level surfaces at different elevations can
be considered to be parallel.
A level datum is an arbitrary level surface to which elevations are referred. The
most common surveying datum is mean sea-level (MSL), but as hydrological work is
usually just concerned with levels in a local area, we often use:
An assumed datum, which is established by giving a benchmark an assumed value
(e.g. 100.000m) to which all levels in the local area will be reduced. It is not good
practice to assume a level which is close to the actual MSL value, as it creates
potential for confusion. A reduced level is the vertical distance between a survey
point and the adopted level datum. A bench mark (BM) is the term given to a
definite, permanent accessible point of known height above a datum to which the
height of other points can be referred. It is usually a stainless steel pin embedded in
a substantial concrete block cast into the ground. At hydrological stations rock bolts
driven into bedrock or concrete structures can be used, but structures should be
used warily as they themselves are subject to settlement. The locations of
benchmarks shall be marked with BM marker posts and/or paint, and recorded on
the Station History Form. A set-up refers the position of a level or other instrument
at the time in which a number of observations are made without mooring the
instrument. The first observation is made to the known point and is termed a
backsight; the last observation is to the final point or the next to be measured on the
run, and all other points are intermediates.
A run is the levelling between two or more points measured in one direction only.
The outward run is from known to unknown points and the return run is the check
levelling in the opposite direction.
A close is the difference between the starting level of the initial point for the
outward run and that determined at the end of the return run. If the levels have
been reduced correctly this value should be the same as the difference between the
sum of the rises and falls and also the difference between the sum of the backsights
and foresights.
Height of Collimation is the elevation of the optical axis of the telescope at the time
of the setup.
The line of collimation is the imaginary line at the elevation.
Orders of levelling refer to the quality of the levelling, usually being defined by the
expected maximum closing error.
Order Purpose Maximum close (m)
Precision order Deformation surveys 0.001 x km
First order Major levelling control 0.003 x km
Second order Minor levelling control 0.007 x km
Third order Levelling for construction 0.012 x km
Table Levelling closes
The accuracy requirements for water-level stations relate to the standards; for
further information refer to next section.
Change points are points of measurement which are used to carry the
measurements forward in a run. Each one will be read first as a foresight, the
instrument position is changed, and then it will be read as a backsight.
4.3 Equipment
The level, its tripod, the staff and the staff bubble are all precision items of
equipment upon which the accuracy of the work is highly dependent. They shall be
kept correctly calibrated, and be used and stored with care. Levels shall be carried
in vehicles in a padded box, case or shelf in addition to the normal case, and staves
shall be kept in a canvas or plastic sleeve to prevent damage to the face and entry of
dirt.
Levels
A level is basically a telescope attached to an accurate levelling device, set upon a
tripod so that it can rotate horizontally through 360°. Normally the levelling device
is a bubble, but modern ones incorporate a pendulum. There are three basic types of
level, shown in figure below.
(a) Dumpy levels
These are more basic levels often used in construction work. The telescope is rigidly
attached to a single bubble and the assembly is adjusted either by means of a
screwed ball-joint or by footscrews which are adjusted first in one direction, then at
90°.
(b) Tilting levels
This type of level is fitted with a circular bubble for preliminary approximate
levelling and a main bubble which is attached to the telescope. For each observation
(not setup) the main bubble is viewed through an eyepiece and the telescope tilted
by a fine screw to bring the two ends of the bubble into coincidence.
(c) Automatic levels
This more modern type of level is now in general use. It has a compensator which
consists of an arrangement of three prisms. The two outer ones are attached to the
barrel of the telescope. The middle prism is suspended by fine wiring and reacts to
gravity. The instrument is first leveled approximately with a circular bubble; the
compensator will then deviate the line of sight by the amount that the telescope is
out of level.
Staves
The levelling staff is a box section of aluminium or wood, which will extend to 3 or 5
m in height by telescoping, hinging or addition of sections. One face has a graduated
scale attached for reading with the cross-hairs of the level telescope. These faces can
vary in pattern and graduation; 5mm graduations should be the maximum for
accurate levelling of gauging stations.
Many staves used these days are of aluminium because of its durability. However
aluminium has a co-efficient of thermal expansion of 0.000023m/metre of
length/°C and this can cause some potential inaccuracies. For instance, "Survey
Chief" and "Brookeades" staves are standardised at 27°C, and in very cold weather
these staves could be as much as 3mm too short over their full length. For low
temperature work consult the temperature table for each staff which should be with
its "instruction manual" or printed on the staff itself.
Staff bubbles
These are generally a small circular bubble on an angle plate which is held against
one corner of the staff to ensure that the staff is held in a vertical position. If the staff
is not held vertical, the reading will be too large and may be significantly in error.
A staff bubble shall be used at all times. If one is not available, the "chainman" (staff
operator) shall rock the staff slowly back and forth about the vertical in a line
towards the instrument. The observer notes the smallest reading which will occur
when the staff is vertical.
4.4 Care of equipment
• ensure that tripod screws and hinges are kept tight.
• always transport the level in a padded box.
• when removing from the box lift it by the centre and not by the eyepiece or
objective end of the telescope.
• screw it firmly onto the tripod, whilst holding it in one hand (make certain that it is
not cross-threaded and that threads are compatible).
• when carrying the level tripod assembly in the field, support it over the shoulder
or, in bush, crooked over an arm with the telescope unclamped (i.e. free to rotate).
• automatic levels should not be carried in a vertical or near-vertical position, as the
compensator will swing about and be prone to damage.
• staves are too much of a precision item of equipment to be used in place of a
slasher, vaulting pole, etc.
• staves shall be transported in their protective cases to protect the face from
damage.
• wooden staves which become wet should be dismantled and dried out before
storing away.
• any moisture which is evident in an instrument must be allowed to disperse by
storing the level out of its case in a warm room. Should it persist after several days
the instrument may require specialist servicing.
4.5 Checking the level’s accuracy
Levels can move out of adjustment so that their line of sight (line of collimation) is
not truly horizontal. This will cause errors in readings which become greater as the
viewing distance increases. However if a backsight and a foresight are exactly equi-
distant from the instrument, the error in each sighting will cancel each other out.
This feature can be used to check the accuracy of a level by the following simple
method which is depicted in figure below
• install three pegs or marks firmly in the ground at distances of 30 m apart in a
straight line; the centre peg is only to mark the distance, but the outside two shall be
firm enough for reliable change points
• set up the level over the centre peg and read the staff on each of the outside pegs
in turn. Book these values and calculate the height difference. This will be a true
height difference, as the distances are equal and any errors will be self-
compensating
• set up the level about 4 m to the far side of one of the outside pegs. Read the staff
on the peg 4 m away and then on the one 64 m away. Book these values and
calculate the apparent height difference
• compare the two height differences; if the instrument is in adjustment (i.e. its
collimation is true) they will be within 5 mm.
A method for checking the level accuracy
If the instrument's collimation appears to be out, recheck by repeating the process.
Then, whilst setup at one of the outside locations, adjust the instrument (according
to the manufacturer's instructions) so that it reads the correct value on the far staff,
checking it against the near one. Two staves are useful for this.
This type of level check shall be carried out at least once per year, preferably just
prior to carrying out a round of station inspections. The details and results of the
checks shall be recorded in a numbered level book and be readily retrievable as a
quality record, and the date of this calibration check shall also be recorded in the
instrument inventory.
4.6 Levelling procedures
(a) Setting up
• Backsight and foresight distances should be approximately equal to avoid any
errors due to collimation, refraction or earth curvature.
• Distances must not be so great as to not be able to read the graduations accurately.
• The points to be observed must be below the level of the instrument, but not lower
than the height of the staff.
(b) Elimination of parallax
Parallax is the apparent movement of the image produced by movement of the
observer's eye at the eyepiece.
It is eliminated by focusing the telescope on infinity and then adjusting the eyepiece
until the cross-hairs appear in sharp focus. The setting will remain constant for a
particular observer's eye.
(c) Booking
• level books or loose-leaf levelling sheets shall be numbered and indexed in a
register.
• details of the site, work, date, observer, chainman, booker, weather, wind,
instrument and any other relevant items shall be entered.
• enter the first observation (which is on a known point) in the Backsight column,
and sufficient detail in the Remarks column to identify it. Enter the point's R.L. zero
from the site register or plate on the BM, etc.
• enter all other points on subsequent lines as intermediates except the point
chosen as the foresight. Identify them in the Remarks column as above. Enter the
foresight on a further line in the Foresight column.
• change the instrument to the next setup. Enter the following backsight on the same
line as the previous foresight but in the Backsight column.
• repeat the above procedure at each setup on the outward run then reverse it to
work back to the starting point on the return run. The furthest point out is treated
as for all other change points.
4.7 Reducing the levels
Two methods are in general use; the "rise and fall" method and the "height of
collimation" method.
The latter reduces levels relative to the instrument height. As it has inferior in-built
checks it should not be used and will not be covered here.
The "rise and fall" methods shall be used for reduction of all site levelling. Reduction
shall be carried out on site before packing up to ensure that the levelling has been
done correctly.
• calculate the rises and fall between successive points and book them in the
appropriate column (one can determine whether each shot is a rise or fall by the
following rule of thumb: a higher value on top denotes a rise; a higher value on the
bottom denotes a fall)
• add up the backsight and foresight columns for the entire traverse and note the
difference between them; this is the close
• add up the rises and falls for the entire traverse, and compare the difference
between them with the difference between the backsights and foresights; they
should be the same
• carry the reduced levels in the R.L. column down the page by adding or subtracting
the appropriate rise and fall values to the successive values of R.L.
The final value of the original starting point will differ from the original value by the
amount of the close.
If the levelling has been done correctly and all arithmetic reductions are correct, the
differences between total backsights and foresights, total rises and falls, and starting
and finishing R.L.'s should be the same. This difference is the close; and for site
inspection purposes it should be within ± 2mm or ± 6mm, depending upon which
water-level standard is being followed, ± 3mm or ± 10mm.
4.8 Level books
All levelling shall be booked in either level books or levelling sheets which shall be
retained as permanent records .Level books shall be numbered so that they can be
referenced on station history and inspection forms . They should be stored in fire-
proof storage as for original record. They should also include an index.
Levelling sheets shall be filed in time-sequential order in site files, and also need to
be infire-proof storage as for level books.
5.TRIANGULATION
This method— triangulation —requires that distances be measured only at the
beginning, at specified intervals, and at the end of the survey. Both the triangulation
method and the traverse method of control are based on the character of the terrain,
and not on the degree of precision to be attained; that is, each system is equally
precise under the conditions in which each is used. Discussion of
triangulation in this chapter normally is limited to triangles having sides less than
3,000 yards in length and to triangulation nets that do not extend more than 25,000
yards. The triangulation method is used principally in situations where the chaining
of distances is impossible or infeasible except with the use of electronic measuring
devices. Suppose you want to locate a point, say, point C, which is offshore; and the
measured baseline, AB, is located on the shore. In this situation the triangulation
method is used because the chaining of distances is impossible. The chaining of
long distances, especially in rough country, also is not always possible; therefore,
triangulation is used to establish horizontal control in large-area surveys. In some
large-area surveys conducted by triangulation, you must consider factors
involving the curvature of the earth; hence, in such cases, geodetic triangulation is
involved. Whether or not the curvature of the earth must be considered depends
upon the area covered and the precision requirements of the survey. The error
resulting in horizontal measurements when you ignore the curvature of the earth
amounts to about 1 foot in 34 1/2 miles. This means that in most ordinary
surveying, an area of 100 square miles may be plane-triangulated without
significant error. In this discussion we are concerned with plane triangulation
only. For a discussion of geodetic triangulation, you should refer to commercial
publications. This section contains information on the three types of triangulation
networks and the usual procedure for conducting a triangulation survey. Also
covered are primary and secondary triangulation stations, types of signals used in
marking triangulation stations, and checking for precision and locations of points.
5.1 Supervision and triangulation surveys
In triangulation surveys, the duties of the EA1 are those of party chief; that is, he
directs the triangulation survey. He keeps the triangulation notes and should be at
the spot where any important measurement is made so that he can verify the
readings personally. He is responsible for selecting triangulation stations and
erecting triangulation signals and towers. He determines the degree of precision to
be attained. He also performs the computations necessary to determine horizontal
locations of the points in the triangulation system by bearing and distance.
Triangulation is used extensively as a means of control for topographic and
similar surveys. A triangulation system consists of a series of triangles. At least one
side of each triangle is also aside of an adjacent triangle; two sides of a triangle
may form sides of adjacent triangles. By using the triangulation method of control,
you do not need to measure the length of every line. However, two lines are
measured in each system—one line at the beginning and one at the closing of the
triangulation system. These lines are called base lines and are used as a check
against the computed lengths of the other lines in the system. The
recommended length of a base line is usually one sixth to one fourth of that of the
sides of the principal triangles. The transcontinental system established by the U.S.
Coast and Geodetic Survey (now the National Geodetic Survey) is an example of an
extensive high-order triangulation network to establish control across the United
States.
Chain of single triangles.
5.2 Types of triangulation networks
In triangulation there are three types of triangulation networks (or nets). They
are the chain of single triangles, chain of polygons, and chain of quadri-
laterals. Chain of Single Triangles The simplest triangulation system is the chain
of single triangles shown in figure 15-15. Suppose AB is the base line and
measures 780.00 feet in length. Suppose, also, that angle A (that is, the observed
angle BAC) measures 98°54´ and that angle ABC measures 32°42´. (In actual
practice you will use more precise values than these; we are using rough values to
simplify the explanation.) Subtracting the sum of these two angles from 180°, we
get 48°24´ for angle ACB. Next, solve for sides BC and AC by using the law of sines
as follows:
Now that you know how to find the length of BC, you can proceed in the same
manner to determine the lengths of BD and CD. Knowing the length of CDcan
proceed in the same manner to determine the lengths of CE and DE, knowing the
length of DE, you can determine the lengths of DF and EF, and so on. You should
use this method only when locating inaccessible points, not when a side of the
triangle is to be used to extend control. In comparison with the other systems about
to be described, the chain of single triangles has two disadvantages. In the
first place, it can be used to cover only a relatively narrow area. In the second place,
it provides no means for cross-checking computed distances using computations
made by a different route. In figure 15-15, for example, the only way to compute the
length of BC is by solving the triangle ABC, the only way to compute the length of CD
is by solving the triangle BCD (using the length of BC previously computed);
and so on. In the systems about to be described, a distance maybe computed by
solving more than one series of triangles. Technically speaking, of course, a
triangle is a polygon; and therefore a chain of single triangles could be called a
chain of polygons. However, in reference to triangulation figures, the term chain of
polygons refers to a system in which a number of adjacent triangles are combined to
forma polygon, as shown in figure 15-16 . Within each polygon the common vertex of
the triangles that compose it is an observed triangulation station (which is not the
case in the chain of quadrilaterals described later). You can see how the length of
any line shown can be computed by two different routes. Assume that AB is the
base line, and you wish to determine the length of line EF. You can compute this
length by solving triangles ADB, ADC, CDE, and EDF, in that order, or by solving
triangles ADB, BDF, and FDE, in that order. You can also see that this system can be
used to cover a wide territory. It can cover an area extending up to approximately
25,000 yards in length or breadth.
Chain of polygons.
6. TACHEOMETRY
6.1 Introduction
This method of survey consists of using either a level, theodolite or specially
constructed tacheometer to make cross hair intercept readings on a levelling staff.
As the angle subtended by the crosshairs is known, the distance can be calculated.
6.2 Definition
Tacheometry is an optical solution to the measurement of distance. The word is
derived from the Greek Tacns, meaning 'swift', and metrot, meaning 'a measure'.
Present day methods of tacheometry can be classified in one of the following three
groups. The last two groups will not be covered in these notes.
1. Stadia System: The theodolite is directed at the level staff and the distance is
measured by reading the top and bottom stadia hairs on the telescope view.
For further information about this process is provided in Theodolite
Tacheometry
2. Electronic Tacheometry: Uses a total station which contains an EDM, able to
read distance by reflecting off a prism.
3. Subtense Bar system: An accurate theodolite, reading to 1" of arc, is directed
at a staff, two pointings being made and the small subtended angle measured.
4. Optical Wedge system: A special theodolite with a measuring device in front
of the telescope s directed at a staff. One pointing of the instrument is
required for each set of readings.
There are two types of instruments used for stadia surveying. In the first type the
distance between the two stadia hairs in the theodolite telescope is fixed. In the
second type of equipment the distance between the stadia hairs is variable, being
measured by means of a micrometer.The most common method used involves the
fixed hair tacheometer, or theodolite.The notes below shows the calculation of the
distance (D) from the centre of the fixed hair tacheometer to a target.
From the diagram, triangles AOB, aOb are similar
OX=
U=
AB
Ox V ab
Also if OF = f = focal length of object lens
then 1/U + 1/V = 1/f (lens equation) and multiply both
sides by (Uf).
u = (U/V) .f + f
u = (AB/ab) .f + f
AB is obtained by subtracting the reading given on the staff by the lower stadia hair
from the top one and is usually denoted by s (staff intecept), and ab the distance apart
of the stadia lines is denoted by i. This value i is fixed, known and constant for a particular
instrument.
U = (f/i) .s +f
D = (f/i) .s + (f + c)
The reduction of this formula would be simplified considerably if the term f/i is
made some convenient figure, and if the term (f + c) can be made to vanish.
D = Cs + k
In practice, the multiplicative constant generally equals 100 and the additive
constant equals zero.This is certainly the case with modern instruments by may not
always be so with older theodolites.
The values are usually given by the makers but this is not always the case. It is
sometimes necessary to measure them in an old or unfamiliar instrument. The
simplest way, both for external and internal focussing instruments, is to regrad the
basic formula as being a linear one of the form:
D = Cs + k
a. On a fairly level site chain out a line 100 to 120m long, setting pegs at 25 to
30 metre intervals.
b. Set at up at one end and determine two distances using tacheometer or
theodolite, one short and one long. hence C and K may be determined.
i.e. D1 (known) = Cs1 (known) + k
D2 (known) = Cs2 (known) + k
Distance Readings Intervals
Upper
Stadia
Centre Lower
Stadia
Upper Lower Total
30.000 1.433 1.283 1.133 0.150 0.150 0.300
55.000 1.710 1.435 1.160 0.275 0.275 0.220
90.000 2.352 1.902 1.452 0.450 0.450 0.900
D =Cs + k
30.00 = 0.300 * C + k
90.00 = 0.900 * C + k
therefore C = 100 & K = 0
Any combination of equations gives the same result, showing that the telescope is
anallatic over this range, to all intents and purposes.
In order to avoid errors due to differential refraction of light through the
atmosphere, the lower stadia reading should not be too low on hot days, generally
not less than 0.5m. With respect to earth curvature both stadia readings are equally
affected and there is no effect on the value of the intercept. Correction for curvature
on the distance and level should be applied if the sight lengths are long enough.
The theory discussed so far, in The Stadia System, Measurement of Tacheometric Constants and
Refraction and Curvature, all applies to the situation where the staff is held vertically and
the line of sight of the telescope is horizontal. It is very seldom, however, that this
situation occurs in practice. Generally a theodolite is sighted to a level staff held
vertically (by use of a staff bubble), which gives rise to the situation below.
Since the staff is not at right angles to the line of sight of the instrument, the
intercept cut on the staff by the stadia hairs will be too large. Let the actual distance
between upper and lower stadia be s and the required projection of it at right angles
to IQ be s1
\ D = Cs1 + K, but s1 = s cos q
In practice, the slope distance D is not often required. What we really want is S, the
horizontal distance and V the vertical distance between the trunnion axis of the
telescope and the point of the staff cut by the centre hair.
Now S = D cos q
= Cs cos2 q + k cos q
AlsoV =
D sin q
= Cs cos q sin q + k sin q
=
Cs sin 2q+ k sin q
2
So now the horizontal distance S = Cs cos2 q + K cos q, and the vertical component is
given by V = Cs cos q sin q + K sin q. In practice these can be reduced to:
S = 100 s cos2 q and
V = 100 s cos q sin q
The difference in height between the two points is given by:
DH =HI + V - CL,
and the Relative Level (R.L.) of the point is given by
RL = RLA + HI + 100 s cos q sin q - CL
The use of these formulae gives the three dimensional location of the point. It is
quite easy to determine the coordinates of the point if the bearing is measured as
well as the staff intercepts and vertical angle, which of course is the standard field
procedure.
7.PLANE TABLE
7.1History
The earliest mention of a plane table dates to 1551 in Abel Foullon's "Usage et
description de l'holomètre", published in Paris.[3] However, since Foullon's
description was of a complete, fully-developed instrument, it must have been
invented earlier.A brief description was also added to the 1591 edition of Digge's
Pantometria.]The first mention of the device in English was by Cyprian Lucar in
1590. Some have credited Johann Richter, also known as Johannes Praetorius, a
Nuremberg mathematician, in 1610 with the first plane table, but this appears to be
incorrect.
The plane table became a popular instrument for surveying. Its use was widely
taught. Interestingly, there were those who considered it a substandard instrument
compared to such devices as the theodolite, since it was relatively easy to use. By
allowing the use of graphical methods rather than than mathematical calculations, it
could be used by those with less education than other instruments.
7.2 Plane table construction
A plane table cutaway.
This shows a plane table with part of the surface of the table cut away to show the
mounting on the tripod. The mount allows the table to be levelled. On the table, the
alidade with telescopic sight is seen
A plane table consists of a smooth table surface mounted on a sturdy base. The
connection between the table top and the base permits one to level the table
precisely, using bubble levels, in a horizontal plane. The base, a tripod, is designed to
support the table over a specific point on land. By adjusting the length of the legs,
one can bring the table level regardless of the roughness of the terrain.
7.3 Use of a plane table
In use, a plane table is set over a point and brought to precise horizontal level. A
drawing sheet is attached to the surface and an alidade is used to sight objects of
interest. The alidade, in modern examples of the instrument a rule with a telescopic
sight, can then be used to construct a line on the drawing that is in the direction of the
object of interest.
By using the alidade as a surveying level, information on the topography of the site
can be directly recorded on the drawing as elevations. Distances to the objects can
be measured directly or by the use of stadia marks in the telescope of the alidade.
7.4 Alidade
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Not to be confused with Adelaide.
A simple alidade for use with a ceiling projector
Several examples of alidade
An alidade (archaic forms include alhidade, alhidad, alidad) is a device that allows
one to sight a distant object and use the line of sight to perform a task. This task can
be, for example, to draw a line on a plane table in the direction of the object or to
measure the angle to the object from some reference point. Angles measured can be
horizontal, vertical or in any chosen plane.
The alidade was originally a part of many types of scientific and astronomical
instrument. At one time, some alidades, particularly those used on graduated circles
as on astrolabes, were also called diopters.[1] With modern technology, the name is
applied to complete instruments such as the plane table alidade.
Modern alidade types
A U.S. Navy sailor using a telescopic alidade.
The alidade is the part of a theodolite that rotates around the vertical axis, and
that bears the horizontal axis around which the telescope (or visor, in early
telescope-less instruments) turns up or down.
In a sextant the alhidade is the turnable arm carrying a mirror and an index to
a graduated circle in a vertical plane. Today it is more commonly called an
index arm.
Alidade tables have also long been used in fire towers for sighting the bearing to
a forest fire. A topographic map of the local area, with a suitable scale, is oriented,
centered and permanently mounted on a leveled circular table surrounded
by an arc calibrated to true north of the map and graduated in degrees (and
fractions) of arc. Two vertical sight apertures are arranged opposite each
other and can be rotated along the graduated arc of the horizontal table. To
determine a bearing to a suspected fire, the user looks through the two sights
and adjusts them until they are aligned with the source of the smoke (or an
observed lightning strike to be monitored for smoke).
7.5 Telescopic sight
Types
Telescopic sights are classified in terms of the optical magnification and the
objective lens diameter, e.g. 10×50. This would denote 10 times magnification with a
50 mm objective lens. In general terms, larger objective lens diameters, due to their
ability to gather larger amounts of light, provide a larger exit pupil and hence
provide a brighter image at the eyepiece. On fixed magnification sights the
magnification power and objective diameter should be chosen on the basis of the
intended use.
There are also telescopic sights with variable magnification. The magnification can
be varied by manually operating a zoom mechanism. Variable sights offer more
flexibility regarding shooting at varying ranges, targets and light conditions and
offer a relative wide field of view at lower magnification settings. The syntax for
variable sights is the following: minimal magnification – maximum magnification ×
objective lens, for example, 3–9×40.
Confusingly, some older telescopic sights, mainly of German or other European
manufacture, have a different classification where the second part of the designation
refers to 'light gathering power.' In these cases, a 4×81 (4× magnification) sight
would be presumed to have a brighter sight picture than a 2.5×70 (2.5×
magnification), but the objective lens diameter would not bear any direct relation to
picture brightness, as brightness is affected also by the magnification factor.
Typically objective lenses on early sights are smaller than modern sights, in these
examples the 4×81 would have an objective approximately 32mm diameter and the
2.5×70 might be approximately 25mm.
Optical parameters
Telescopic sights are usually designed for the specific application for which they are
intended. Those different designs create certain optical parameters. Those
parameters are:
Magnification — The ratio of the focal length of the eyepiece divided into the focal
length of the objective gives the linear magnifying power of telescopes. A
magnification of factor 10, for example, produces an image as if one were 10 times
closer to the object. The amount of magnification depends upon the application the
telescopic sight is designed for. Lower magnifications lead to less susceptibility to
shaking. A larger magnification leads to a smaller field of view.
Objective lens diameter – The diameter of the objective lens determines how much
light can be gathered to form an image. It is usually expressed in millimeters.
Field of view — The field of view of a telescopic sight is determined by its optical
design. It is usually notated in a linear value, such as how many meters (feet) in
width will be seen at 100 m (or 100 yd), or in an angular value of how many degrees
can be viewed.
Exit pupil — Telescopic sights concentrate the light gathered by the objective into a
beam, the exit pupil, whose diameter is the objective diameter divided by the
magnifying power. For maximum effective light-gathering and brightest image, the
exit pupil should equal the diameter of the fully dilated iris of the human eye —
about 7 mm, reducing with age. If the cone of light streaming out of the eyepiece is
larger than the pupil it is going into, any light larger than the pupil is wasted in
terms of providing information to the eye.
However, a larger exit pupil makes it easier to put the eye where it can receive the
light: anywhere in the large exit pupil cone of light will do. This ease of placement
helps avoid vignetting, which is a darkened or obscured view that occurs when the
light path is partially blocked. And, it means that the image can be quickly found
which is important when aiming at game animals that move rapidly. A narrow exit
pupil telescopic sight may also be fatiguing because the instrument must be held
exactly in place in front of the eyes to provide a useful image. Finally, many people
in Europe use their telescopic sights at dusk, dawn and at night, when their pupils
are larger. Thus the daytime exit pupil of about 3 to 4 mm is not a universally
desirable standard. For comfort, ease of use, and flexibility in applications, larger
telescopic sights with larger exit pupils are satisfying choices even if their capability
is not fully used by day.
7.6 Reticles
Rangefinder reticle.
Telescopic sights come with a variety of different reticles, ranging from the traditional
crosshairs to complex reticles designed to allow the shooter to estimate accurately
the range to a target, to compensate for the bullet drop, and to compensate for the
windage required due to crosswinds. A user can estimate the range to objects of
known size, the size of objects at known distances, and even roughly compensate for
both bullet drop and wind drifts at known ranges with a reticle-equipped scope.
For example, with a typical Leupold brand duplex 16 MOA reticle (of a type as shown
in image B) on a fixed power scope, the distance from post to post (that is, between
the heavy lines of the reticle spanning the center of the scope picture) is
approximately 32 inches (81.3 cm) at 200 yards (183 m), or, equivalently,
approximately 16 inches (40.65 cm) from the center to any post at 200 yards. If a
target of a known diameter of 16 inches fills just half of the total post-to-post
distance (i.e. filling from scope center to post), then the distance to target is
approximately 200 yards (183 m). With a target of a diameter of 16 inches that fills
the entire sight picture from post to post, the range is approximately 100 yards.
Other ranges can be similarly estimated accurately in an analog fashion for known
target sizes through proportionality calculations. Holdover, for estimating vertical
point of aim offset required for bullet drop compensation on level terrain, and
horizontal windage offset (for estimating side to side point of aim offsets required
for wind effect corrections) can similarly be compensated for through using
approximations based on the wind speed (from observing flags or other objects) by
a trained user through using the reticle marks. The less-commonly used holdunder,
used for shooting on sloping terrain, can even be estimated by an appropriately-
skilled user with a reticle-equipped scope, once the slope of the terrain and the slant
range to target are both known.
There are two main types of reticles:
Wire reticles
Etched reticles
7.7 Spirit level
A spirit level or bubble level is an instrument designed to indicate whether a surface
is level or plumb. Different types of spirit levels are used by carpenters, stone
masons, bricklayers, other building trades workers, surveyors, millwrights and
other metalworkers, and serious videographers.
Original spirit levels had two banana-shaped curved glass vials at each viewing
point and were much more complicated to use. In the 1920s, Henry Ziemann, the
founder of Empire Level, invented the modern level with a single vial. These vials,
common on most ordinary levels today, feature a slightly curved glass tube which is
incompletely filled with a liquid, usually a yellow-colored 'spirit' (a synonym for
ethanol), leaving a bubble in the tube. A spirit such as Ethanol is used due to its very
low viscosity. This provides an ideal element for a bubble to travel the tube quickly
and settle accurately with minimal interference generated from surface tension
between the transfer fluid and the glass housing. Most commonly, spirit levels are
employed to indicate how horizontal (level) or how vertical (plumb) a surface is.
Some are also capable of indicating the level of a surface between horizontal and
vertical to the nearest degree. The crudest form of the spirit level is the bull's eye
level: a circular flat-bottomed device with the liquid under a slightly convex glass
face which indicates the center clearly. It serves to level a surface in two
perpendicular directions, while the tubular level only does so in the direction of the
tube. The most sophisticated spirit levels are guaranteed accurate to five-ten-
thousandth of an inch (.0005) per inch and are much easier to read because of their
blue colour. Where a spirit level must also be usable upside-down, the banana-
shaped tube is replaced by a barrel-shaped tube. The upper internal surface of the
tube is thus always of the appropriate shape.
A spirit level
7.8 Plumb-bob
A plumb-bob or a plummet is a weight, usually with a pointed tip on the bottom, that
is suspended from a string and used as a vertical reference line, or plumb-line.
A plumb-bob
The instrument has been used since the time of the ancient Egyptians by
bricklayers, masons, and carpenters to ensure that their constructions are "plumb",
or perfectly upright. It may also be used in surveying to sight a point on the ground
that is not readily visible. Small plumb bobs are included in the kits of various
instruments such as levels and theodolites. They are used to set the instrument
exactly over a fixed datum marker, prior to taking fresh readings.[citation needed]
Plumb-bobs and chalk lines are often sold as a single tool.
7.9 Use
Up until the modern age, on most tall structures, plumb-bobs were used to provide
vertical datum lines for the building measurements. A section of the scaffolding
would hold a plumb line that was centered over a datum mark on the floor. As the
building proceeded upwards the plumb line would also be taken higher, still
centered on the datum. Many cathedral spires, domes and towers still have brass
datum marks inlaid into their floors, that signify the center of the structure above.
Plumb-bob with scale as an inclinometer
Although a plumb-bob and line alone can only determine a vertical, if mounted on a
suitable scale the instrument may also be used as an inclinometer to measure angles
to the vertical.
The early skyscrapers used heavy plumb-bobs hung on wire in their lift wells. The
weight would hang in a container of oil to dampen any swinging movement,
functioning as a shock absorber.
7.10 Determining centre of gravity of an irregular shape
Students of figure drawing will also make use of a plumb line to find the vertical axis
through the center of gravity of their subject and lay it down on paper as a point of
reference. The device used may be purpose-made plumb lines, or simply makeshift
devices made from a piece of string and a weighted object, such as a metal washer.
This plumb line is important for lining up anatomical geometries and visualizing the
subject's center of balance.
8. PLOTTING CONTOURS
Contours are lines that join points of equal value, in topographic surveying contours
represent points of equal height. It is difficult to observe contours directly in the
field, generally they are derived from field observations. There are two methods for
acquiring survey data for the production of contours, one using predetermined
gridded data points and the other using non-uniformly spaced data points. There
are various benefits and shortcomings with both methods.
8.1 Gridded Data Points
The points where height observations are taken are predetermined and their
locations are marked on the ground using an appropriate survey technique. This
then defines a group of rectangular prisms (see diagram) that have known
horizontal side dimensions (and a known plan area for use in volume computations,
see later).
The sides of the prisms travel over the surface of the ground between points of a
certain reduced level, and are assumed to change linearly between the corners of
the prisms. Somewhere between two points at the corners of a prism will be a point
on the line that has a value corresponding to the required contour value, generally a
whole metre or regular fractions thereof. The location of this point is then
determined by interpolating along the side of the prism.
In each of the interpolations the grid unit is known so the computations are simple
and readily automated. This is the only benefit of using gridded data, there are
however serious shortcomings.
The establishment of the grid in the field is tedious and time consuming, but more
importantly the location of the grid points is independent of the topography. The
grid ignores changes in grade, ridge lines or creek banks, and is not an accurate
method of describing the terrain. It is not recommended for use as a topographic
survey method, especially as the advent of computer reduction and plotting
packages has eliminated the hand computations.
8.2 Non-Uniformly Spaced Data Points
The field method of using non-uniformly spaced data points allows the topography
to be accurately represented. Observations are usually made to actual topographic
features such as changes in grade, tops and toes of banks or batter slopes, distinct
boundaries and so on. This is easily performed in the field using tacheometric
survey techniques, there is no need to establish points on a predetermined pattern.
While this is the most accurate representation of the terrain, the computations
involved are greatly increased in volume. The same interpolations are performed as
with gridded data (the mathematics are exactly the same) but now for each pair of
points the horizontal distance between them must be calculated or measured off the
plan. Computer packages make this very easy, but if the computations are being
performed by hand then the amount of work is substantial.
These sets of data points are known as TINs (Triangulated Irregular Networks) and
Digital Terrain Models. Examples of these are found in the notes on Volumes.
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