Surveying module 1

• Surveying has traditionally been defined as the science, art, and technology of determining the relative positions of points above, on, or beneath the Earth’s surface, or of establishing such points.
• The earliest applications of surveying were in measuring and marking boundaries of property ownership.
• Throughout the years, the importance of surveying has steadily increased with the growing demand for maps and other spatially related types of information and the expanding need for establishing accurate line and grade to guide construction operations.
• The science of surveying began in Egypt, as recorded by Herodotus.
• Sesostris, King of Egypt, divided the land of Egypt into plots for the purpose of taxation.
• Annual floods of the Nile River swept away portions of these plots, and surveyors were appointed to replace the boundaries.
• Early surveyors were called rope stretchers, since their measurements were made with ropes with markers at unit distances.
• Greek thinkers developed the science of geometry, and Heron applied science to surveying in 120B.C.
• Heron authored The Dioptra which related the methods of surveying a field, drawing a plan, and making related calculations.
• The Dioptra also described one of the first pieces of surveying equipment recorded, the diopter.
• Significant development in the art of surveying came from the practical-minded Romans.
• The engineering ability of the Romans was demonstrated by their extensive construction work throughout the empire.
• Surveying necessary for this construction resulted in the organization of surveyors guild.
• Ingenious instruments were developed and used by the Romans, including the groma, labella, and chorobates.
• Hc = k²/2R
• Change in elevation (based on the figure), ElevA + hi + hc + V - hr - r = ElevB.
• - hr = hc – hc/7
• The Groma was used for sighting, the labella was an A-frame with a plumb bob for leveling, and the chorobates was a horizontal straightedge for leveling.
• R² + T²= (R+h)²
• Barometer, an instrument that measures air pressure and can be used to find relative elevations of points on the Earth’s surface, is used in the past for work in rough country where extensive areas had to be covered but a high order of accuracy was not required.
• Hcr= hc
• Trigonometric Leveling by Inclined Stadia Sights, ElevA + r₃ - ( - VD₃) + VD4 - r4 = ElevC.
• The effect of refraction makes objects appear higher than they really are, thus making the rod readings too low.
• Hr= 1/7 hc
• If s and the vertical angle are determined, V = S(sin x) or V = S(cosz).
• Formula Derivation Assumption: K is small (k≈ straight)
• K² = 2Rhc+hc²
• If H and vertical angle are determined, V = H(tan ) or V = H/(tan z).
• ElevA + r₁ - ( - VD₁) + VD2 - r2 = ElevB.
• R² + k² = R²+2Rhc+ hc²
• For any slope classification, the horizontal distance (d) is determined by subtracting the slope correction Ch from the measured slope distance (s), where Ch is calculated using the slope classification.
• Corrected distanced measured or laid out with a tape that is too long or too short can be determined from the following equations: C = TL – NL, CL = C(ML/NL), CL = ML + CL, CL = ML + C (ML/NL).
• Steel tapes lengthen with rising temperature and shorten with falling ones, the coefficient of linear expansion for steel tapes is 0.0000065 per degree Fahrenheit and 0.0000116 per degree Celsius.
• The absolute value for the correction per tape length is determined from the difference between the true or actual length of tape and the nominal length of tape.
• A steel tape is stretched when it is pulled, and if the pull is greater than that for which it was standardized, the tape will be too long, an average value of the modulus of elasticity for steel is approximately 2×10⁵MPa, 2×10⁶kg/cm² or 29x10⁶psi.
• The 3rd rule states that when measuring or laying out lengths with a tape that is too short, the corrections are applied opposite to those stated in the first two rules.
• A steel tape not supported along its entire length sags in the form of a catenary, the sag correction formula is Cs= - w²L³cos²theta/24p², where w is the weight per meter length and theta is the angle of slope from the horizontal.
• Early civilizations assumed the Earth to be a flat surface, but by noticing the Earth’s circular shadow on the moon during lunar eclipses and watching ships gradually disappear as they sailed toward the horizon, it was slowly deducted that the planet actually curved in all directions.
• A Greek named Eratosthenes was among the first to compute the Earth’s dimensions.
• In determining distance AB, the steps include making an arc with a convenient radius R centering at A, drawing a line from B towards D, intersecting the arc at points a and b, measuring ab and marking point Cs its center, connecting points A and C and measuring its distance, determining AB.