Fundamentals of Surveying
Theory and Samples Exercises
Division of Spatial Information Science
Graduate School Life and Environment Sciences
University of Tsukuba
Prof. Dr. Yuji Murayama
Surantha Dassanayake
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Fundamentals of surveying theories and Excercises, Slides of Survey Sampling Techniques
Fundamentals of surveying in explain their theory and samples of excercises written by Dr. Yuji Murayama from university of Tsukuba.
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Fundamentals of Surveying
Theory and Samples Exercises
Division of Spatial Information Science
Graduate School Life and Environment Sciences
University of Tsukuba
Prof. Dr. Yuji Murayama Surantha Dassanayake
- (^) 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, and diagrams. Land surveying is basically an art and science of mapping and measuring land. The entire scope of profession is wide; it actually boils down to calculate where the land boundaries are situated. This is very important as without this service, there would not have been railroads, skyscrapers 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
- (^) Control Survey: Made to establish the horizontal and vertical positions of arbitrary points.
- (^) Boundary Survey: Made to determine the length and direction of land lines and to establish the position of these lines on the ground.
- (^) Topographic Survey: Made to gather data to produce a topographic map showing the configuration of the terrain and the location of natural and man-made objects.
- (^) Hydrographic Survey: The survey of bodies of water made for the purpose of navigation, water supply, or sub-aqueous construction.
- (^) Mining Survey: Made to control, locate and map underground and surface works related to mining operations.
- (^) Construction Survey: Made to lay out, locate and monitor public and private engineering works.
- (^) Route Survey: Refers to those control, topographic, and construction surveys necessary for the location and construction of highways, railroads, canals, transmission lines, and pipelines.
- (^) Photogrammetric Survey: Made to utilize the principles of aerial photogrammetry, in which measurements made on photographs are used to determine the positions of photographed objects.
- (^) Astronomical survey: generally involve imaging or "mapping" of regions of the sky using telescopes. Different methods of Surveying
Pythagorean Theorem
In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. C 2 = A^2 + B^2 where: C is the hypotenuse (side opposite the right angle). A and B are the remaining sides.
Units of Angular Measurement
The most common angular units being employed
in the United States is the Sexagesimal System.
This system uses angular notation in increments
of 60 by dividing the circle into 360 degrees;
degrees into 60 minutes; and minutes into 60
seconds. Therefore;
1 circle = 360° = 21,600´ = 1,296,000˝ 1° = 60´ = 3600˝ 1´ = 60˝ Basic Trigonometry functions for Distance and Angular Measurements
Algebraic Signs of the Trigonometric Functions in each Quadrant
Using the definitions on the previous page, we can determine the values of the functions for each angle shown below. List the Sine, Cosine, and Tangent of each angle in both fractional and
- Quadrat decimal form.
- Tanθ = 3/4 = 0.
- Quadrat
- Sin 180-θ = 3/5 = 0.
- Cos 180-θ = -4/5 = -0.
- Tan 180-θ = 3/-4 = -0.
- Quadrat
- Sin 180+ θ = -3/5 = -0.
- Cos 180+ θ = -4/5 = -0.
- Tan 180+ θ = -3/-4 = 0.
- Quadrat
- Sin 360-θ = -3/5 = -0.
- Cos 360-θ = 4/5 = 0.
- Tan 360-θ = -3/4 = -0.
Distance Measuring (Chaining surveying)
English mathematician Edmund Gunter (1581-1626) gave to the world not only the words cosine and cotangent, and the discovery of magnetic variation, but the measuring device called the Gunter’s chain shown below. Edmund also gave us the acre which is 10 square chains. The Gunter’s chain is 1/80th of a mile or 66 feet long. It is composed of 100 links, with a link being 0.66 feet or 7. inches long. Each link is a steel rod bent into a tight loop on each end and connected to the next link with a small steel ring. Starting in the early 1900’s surveyors started using steel tapes to measure distances. These devices are still called “chains” to this day.
Distance Measuring (Electronic Distance Meters)
In the early 1950’s the first Electronic Distance Measuring (EDM) equipment were developed. These primarily consisted of electro-optical (light waves) and electromagnetic (microwave) instruments. They were bulky, heavy and expensive. The typical EDM today uses the electro-optical principle. They are small, reasonably light weight, highly accurate, but still expensive.
Principle of Chaining
- (^) To measure any distance, you simply compare it to a known or calibrated distance; for example by using a scale or tape to measure the length of an object. In EDM’s the same comparison principle is used. The calibrated distance, in this case, is the wavelength of the modulation on a carrier wave.
- (^) Modern EDM’s use the precision of a Quartz Crystal Oscillator and the measurement of phase-shift to determine the distance.
- (^) The EDM is set up at one end of the distance to be measured and a reflector at the other end.
- (^) The EDM generates an infrared continuous-wave carrier beam, which is modulated by an electronic shutter (Quartz crystal oscillator).
- (^) This beam is then transmitted through the aiming optics to the reflector.
- (^) The reflector returns the beam to the receiving optics, where the incoming light is converted to an electrical signal, allowing a phase comparison between transmitted and received signals.
- (^) The amount by which the transmitted and received wavelengths are out of phase, can be measured electronically and registered on a meter to within a millimeter or two.
Angle Measuring
Measuring distances alone in surveying does not establish the location of an object. We
need to locate the object in 3 dimensions. To accomplish that we need:
1. Horizontal length (distance)
2. Difference in height (elevation)
3. 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.
A Theodolite is a precision surveying instrument; consisting of an alidade with a telescope and an accurately graduated circle; and equipped with the necessary levels and optical-reading circles. The glass horizontal and vertical circles, optical-reading system, and all mechanical parts are enclosed in an alidade section along with 3 leveling screws contained in a detachable base or tribrach. A Transit is a surveying instrument having a horizontal circle divided into degrees, minutes, and seconds. It has a vertical circle or arc. Transits are used to measure horizontal and vertical angles. The graduated circles (plates) are on the outside of the instrument
and angles have to be read by using a vernier.
Bearings and Azimuths
The Relative directions of lines connecting survey points may be obtained in a variety of ways. The figure below on the left shows lines intersecting at a point. The direction of any line with respect to an adjacent line is given by the horizontal angle between the 2 lines and the direction of rotation. The figure on the right shows the same system of lines but with all the angles measured from a line of reference (O-M). The direction of any line with respect to the line of reference is given by the angle between the lines and its direction of rotation.
Grid Meridians
In plane surveys it is convenient to perform the work in a rectangular XY coordinate system in which one central meridian coincides with a true meridian. All remaining meridians are parallel to this central true meridian. This eliminates the need to calculate the convergence of meridians when determining positions of points in the system. The methods of plane surveying, assume that all measurements are projected to a horizontal plane and that all meridians are parallel straight lines. These are known as grid meridians. The Oregon Coordinate System is a grid system. On certain types of localized surveying, it may not be necessary to establish a true, magnetic, or grid direction. However it is usually desirable to have some basis for establishing relative directions within the current survey. This 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. This 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. The important point to remember about assumed meridians is that they have no relationship to any other meridian and thus the survey cannot be readily (if at all) related to other surveys Assumed Meridians
Azimuths
The 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 clockwise direction with respect to either the north meridian or the south meridian. In plane surveying, azimuths are generally measured from the north. When using azimuths, one needs to designate whether the azimuth is from the north or the south. Azimuths are called true (astronomical) azimuths, magnetic azimuths, grid azimuths, or assumed azimuths depending on the type of meridian referenced. Azimuths may have values between 0 and 360 degrees.
Practices for Azimuth and Bearings
Using angles to the right, calculate the bearings and azimuths of each lines.
Polar Coordinates
Another way of describing the position of point P is by its distance r from a fixed point O and the angle θ that makes with a fixed indefinite line oa (the initial line). The ordered pair of numbers (r,θ) are called the polar coordinates of P. r is the radius vector of P and θ its vectorial angle. Note: (r,θ), (r, θ + 360o), (-r, θ + 180o) represent the same point. Transformation of Polar and Rectangular coordinates: Measuring distance between 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 be computed in the following way :
Measuring the Area by Coordinates
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. The area enclosed within a figure can be computed by coordinates. This is done by forming trapezoids and determining their areas. Trapezoids are formed by the abscissas of the corners. Ordinates at the corners provide the altitudes of the trapezoids. A sketch of the figure will aid in the computations.
- Find the latitude and departure between points.
- Find the area of the figure. Trapezoid Triangle Answers