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Introduction to Surveying

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Introduction to Surveying

Surveying is an art, and also called the science of determining the relative position of objects on, above or below the surface of the earth by direct or indirect measurements of distance, direction and elevation; and representing this information on paper maps or on computer-based maps.

History of Surveying
Surveying science has a very long history, dating back to the 'rope stretchers' of Babylonia and the Egyptian dynasties.

  1. Around 4000 BCE, the Babylonians were already making records of land ownership of clay tablets which contained the measurements of the land and the signature of the 'surveyor'.
  2. Around 2780 BCE, for setting out the constructions, the pyramids were constructed using standard units of measurement and simple devices. Wall frescos in pyramids depict the 'rope stretchers' re-measuring the Pharo's (King of ancient Egypt) lands after the annual Nile floods (for taxation purposes naturally).
  3. Astronomy was practiced in Mesopotamia, China, the Pacific, and South America.
  4. From around 600 BCE to 400 BCE there were major advances made in philosophic/ scientific/mathematic thought.
    Many of the well-known Greek philosopher/mathematicians make contributions during this period: Pythagoras, Anaximander, Democritus (600BCE±); Socrates, Plato, Aristoteles, (500-400 BCE); Euclid, Archimedes, Apollonius, Eratosthenes (300 BCE±). Eratosthenes determined the radius of the Earth by measuring shadows at Alexandria and Seyne and was only about 320 km off the radius we use today.Also around this period other major civil engineering works were constructed, a six-mile canal was constructed at Mt Athos during Xerxes time, the Romans constructed aqua appia and via appia, as well as bridges and tunnels.Around 150 BCE, a school of surveying was established by the Romans.
  5. Around 120 BCE Ptolemaios (Ptolomy) produced maps, and established the doctrine that if the earth was spherical then a proper representation could be obtained by a geometrical projection of that surface. He was also an astronomer and instrument maker and developed a cartographic philosophy that lasted centuries.
  6. Developments now moved from the Greeks and Romans to the Arab world, where many of the terms used in astronomy and navigation today originated (nadir, azimuth, and algebra for example).
  7. Developments continued in China and in India, regular contact between these three regions ensured dissemination of knowledge. Surveying developments in Europe stagnated until Arab conquests revived investigations in this area. European research was generally confined to monasteries and religious orders. Also during this epoch, there appeared the ‘zero’, sine tables, algebra, tangent functions.
  8. 1400-1700±, developments occurred in telescope design and construction, measurement of time, measurement of magnetic declination, standardization of units of measurement, determination of longitude, surveying instruments, and reference books are written on surveying methods. Da Vinci, Kepler, Napier, Dürer, Pascal, Newton, Galileo, Coppernicus.
  9. Mercator invented the map projection known by his name and still commonly used.
  10. From 1700±, the new age of geodesy begins. Soon we have differential calculus, logarithms, Descartes' analytic geometry, sextants, octants, the Harrison's ships chronometer, the spirit level, micrometer theodolites, and many other products of the industrial revolution.
  11. The 1800s saw the development of photography, then aerial photography and architectural photography. In the 1864 Aimé Laussedat made a map of Paris from photographs taken from rooftops, building the foundation for photogrammetric mapping as practiced today. Instruments were designed to aid in the measurement of photographs for map production.
  12. The 1900s saw the rapid development of the mapping sciences as a result of the two major wars. Aerial photography and reconnaissance, mapping, radio, radar, lasers, jet engines, space exploration, the establishment of geodetic survey networks across the countries.
  13. The digital revolution is now in progress; satellite position fixing, measurement by light and radio waves, imaging from satellite and other spacebourne platforms, map production from digital images, dynamic real-time mapping, high-speed computing and telecommunications, 3D Visualisation, faster computers, network communications. The list of innovations grows, further changing the face of geomantic science.

Principal of Surveying
The techniques of land surveying are founded on five basic principles.

  • Working From the Whole to the Part
    The first is that of “working from the whole to the part” which means establishing an initial framework of control points (seemed to be free from error after being established and adjusted) that is then “broken down” into smaller networks with points closer together. Subsequent work is based on this framework by using less elaborate methods, and adjusted to it. Errors in small frameworks are localized and are not magnified and the accumulation of errors is controlled to achieve consistency and accuracy.
  • Consistency
    The second principle is that of consistency in work. Consistency refers to…
    • Relative standard of accuracy of the linear and angular measurements should be consistent.
    • The precision of angular and linear measurements (or instruments) should be consistent.
    • Methods and instruments for the same type of surveys should be of similar standard.
    • the precision of parts of a survey within a properly controlled framework should be consistent
    • final accuracy of a survey is dependent upon the accuracy of the overall controlling framework together with the precision to which the various parts have been measured
    • the subsequent survey can never exceed the accuracy of the controlling framework
  • Economy
    The third principle is that of an economy, namely that since higher accuracy in general costs more money the surveyor should seek no higher accuracy than is necessary and sufficient for the task at hand.
    • Standard of accuracy achieved < the specified ð useless
    • Accuracy attained > the specified ð wastage of time, money and effort because high accuracy requires very costly precise instruments, more field work, and more extensive computations.
    • So, prior to any survey project, weigh of the accuracy is essential which it hopes to attain against the time and money available
  • Independent Check
    The fourth principle is that of applying an independent check on the data wherever possible. For example, measure the all three angles of a triangle even though the third angle measurement is redundant. This has the effect of providing built-in quality control.
    Survey should be conducted so that errors do not pass undetected – should be a suitable provision of checks or survey work should be self-checking.
  • Location of a Point From Measurements of at Least Two Points
    The last fifth one is Location of a point from measurements of at least two points. For examples…
    Traversing Triangulation Trilateration Offset

Primary Division of Surveying
Made on the basis whether the curvature of the earth is considered or not.

  • Plane Surveying
    It refers to the surveys of the small extent where it is assumed that the mean surface of the earth is a horizontal plane for the area concerned. The curvature of the earth is neglected. Gravity direction is considered parallel throughout the survey region. The shortest distance between points is the straight line.
    For plane surveying
    • A+B+C = 1800 ; A,B,C are plane angles
    • Sine Rule : a/SinA = b/SinB = c/ SinC
    • Plumb lines parallel
    • Cosine rule : CosA = (b2+c2-a2)/2bc
    • For small area
    • Surveys for the location and construction of highways, railways, canals
  • Geodetic Surveying
    It refers to surveys of larger areas where the above assumption of the earth as a horizontal plane is invalid and allowance must be made for the curvature of the earth. Gravity lines are not parallel and concentric toward Centre of earth. Shortest distances are curved lines.
    The object of the geodetic survey is to determine the precise position the surface of the earth, of a system of widely distant points which form control stations to which surveys of less precision may be referred.
    For geodetic surveying
    • A+B+C = 1800+ Spherical excess; A,B,C – Spherical angles
    • Sine Rule: Sina/SinA = Sinb/SinB = Sinc/SinCPlumb lines not parallel; level lines- curved
    • Cosine rule: CosA = (cosa - cosb.cosc)/sinb.sinc
    • For large area
      Field measurements for geodetic surveys are usually performed to a higher order of accuracy than those of plane surveys. Geodetic surveying, the curved surface of the earth is considered by performing the computations on an ellipsoid. It is now becoming common to do geodetic computations in a three-dimensional, earth-centered Cartesian coordinate systems. Geodetic methods: to determine relative positions of widely spaced monuments and to compute lengths and directions of the long lines between them.

Shape and Size of Earth

  • Geoid
    The Geoid is the equipotential surface which approximates the mean sea level. Approximately spherical, there is a slight bulge at the equator and flattening at the poles due to the rotation of the Earth, In addition, variations in rock density that impact the gravitational field, there are many local irregularities. Hence, geoid is a complex surface.
    • The surface of the earth with its topography is far too irregular to be a convenient basis for computing position.
    • Observations reduced buy the surveyors to the gravitational surface, which approximates mean sea level that is geoid but geoid is too complex surface.
    • To simplify computing of position, the geoid is approximated by the nearest mathematically definable figure, the ellipsoid (spheroid).
    • The ellipsoid is effectively a ‘best fit’ to the geoid.
    • However, there are many ellipsoids available, each of them uniquely named and defined either based on their semi-minor axis, semi-major axis or, more usually, a ratio of these axes called ‘inverse flattening’.

Methods of Surveying
From two known points of reference, the location of a point to be surveyed/can be surveyed by the following method.

  1. By measuring the two distances from that point to the known reference points.
    Trilateration -The method of control surveying where points are established by measuring all three sides of a triangle.
  2. By measuring perpendicular distance from a point to be surveyed to that line of joining two known reference known points and distance of foot of the perpendicular from one of two points. The length of perpendicular is called offset.
  3. By measuring the distance of a point from one of two known points and angle made by this distance with the line joining these known points. Used for detailing and equally applicable for control points extension as well – In traversing directions and distances of serially connected lines are measured.
  4. By measuring two angles made by lines joining point and known reference points with the line joining the two known points. The basis for control points fixing by triangulation and intersection method. Extensively used for detailing by intersection Triangulation - Method of control points establishing where three angles of a triangle are measured.
  5. There exits one more method but different from above methods as it uses at least three known reference points instated of two as above. Measurement of angles at the point to be surveyed between the known points. Used for control point fixing rather than detailing & called resection.

References

  • Arora, K.R., 2010. Surveying Volume-1: Levelling Principles (260-307)
  • Punmia, B.C., Jain, A.K., Jain, A.K. (2005) “Surveying Volume-I”, Laxmi Publications Pvt. Ltd.
    New Delhi.

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