Fundamentals of Surveying

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1. Introduction to Surveying Definition: The art and science of determining the relative positions of points on, above, or beneath the surface of the earth. Objectives: To prepare a plan or map. To determine boundaries. To lay out engineering works. To determine quantities (e.g., earthwork). Branches of Surveying: Plane Surveying: Earth's curvature is neglected. Suitable for small areas ($ Geodetic Surveying: Earth's curvature is considered. For large areas and high precision. Principles: Working from whole to part. Locating a point by at least two independent measurements. 2. Linear Measurements Methods: Direct: Chaining, Taping. Indirect: EDM (Electronic Distance Measurement), Tachyometry, GPS. Instruments: Chain: Gunter's (66 ft), Engineer's (100 ft), Metric (20m, 30m). Tape: Linen, Metallic, Steel, Invar. EDM: Total Station. Errors in Taping: Standardization: Tape length incorrect. $C_s = L' - L$ (correction per tape length). Temperature: $C_t = \alpha (T_m - T_s) L$. $\alpha$: coeff. of thermal expansion. Pull (Tension): $C_p = \frac{(P_m - P_s) L}{AE}$. $A$: cross-sectional area, $E$: Young's Modulus. Sag: $C_{sag} = \frac{w^2 L^3}{24 P_m^2}$ or $\frac{W^2 L}{24 P_m^2}$. $w$: weight per unit length, $W$: total weight. (Always subtractive) Slope: $C_h = L - \sqrt{L^2 - h^2} \approx \frac{h^2}{2L}$ (Always subtractive) 3. Angular Measurements Units: Degrees, Grads, Radians. Bearings: Whole Circle Bearing (WCB): Angle measured clockwise from North (0° to 360°). Reduced Bearing (RB)/Quadrant Bearing (QB): Angle measured from North or South towards East or West (0° to 90°). e.g., N30°E. Azimuth: Angle measured clockwise from a reference meridian (usually North). Can be WCB. Deflection Angle: Angle from the prolongation of the preceding line to the succeeding line. Interior/Exterior Angles: Angles inside/outside a traverse polygon. Magnetic Declination: Angle between magnetic meridian and true meridian. Local Attraction: Disturbance of magnetic needle by local magnetic fields. Fore Bearing (FB) & Back Bearing (BB): $BB = FB \pm 180^\circ$ (Use '+' if $FB 180^\circ$). 4. Leveling Definition: Determining the relative heights or elevations of points. Terminology: Datum: Reference surface (e.g., Mean Sea Level). Bench Mark (BM): Fixed point of known elevation. Reduced Level (RL): Elevation of a point above/below datum. Line of Sight/Collimation: Line passing through optical center of objective and intersection of crosshairs. Backsight (BS): First reading taken on a point of known elevation. Adds to RL. Foresight (FS): Last reading taken on a point whose RL is to be determined. Subtracts from RL. Intermediate Sight (IS): Reading taken on any intermediate point. Subtracts from RL. Turning Point (TP): Point on which both FS and BS are taken. Methods: Height of Instrument (HI) Method: $HI = RL_{BM} + BS$ $RL_{new} = HI - FS \text{ or } IS$ Checksums: $\sum BS - \sum FS = \text{Last RL} - \text{First RL}$ Rise and Fall Method: $Rise = \text{Prev. Staff Reading} - \text{Curr. Staff Reading}$ (if positive) $Fall = \text{Curr. Staff Reading} - \text{Prev. Staff Reading}$ (if positive) $RL_{new} = RL_{prev} + Rise \text{ or } - Fall$ Checksums: $\sum BS - \sum FS = \sum Rise - \sum Fall = \text{Last RL} - \text{First RL}$ Errors: Curvature Correction: $C_c = -0.0785 D^2$ (km), always subtractive. Refraction Correction: $C_r = +0.0112 D^2$ (km), always additive. Combined Correction: $C = -0.0673 D^2$ (km). 5. Theodolite and Traverse Surveying Theodolite: Precision instrument for measuring horizontal and vertical angles. Parts: Tribrach, Lower Plate (scale), Upper Plate (vernier), Standards, Telescope, Vertical Circle. Temporary Adjustments: Setting up, Centering, Leveling, Focusing. Traverse: Series of connected lines whose lengths and directions are measured. Types of Traverse: Closed Traverse: Starts and ends at the same point, or at points of known position. Open Traverse: Starts at a known point but does not close. Used for roads, pipelines. Traverse Computations: Consecutive Coordinates (Latitudes & Departures): Latitude ($L$) = $l \cos \theta$ Departure ($D$) = $l \sin \theta$ Closing Error: $\sum L = 0, \sum D = 0$ for a perfect closed traverse. Error in Latitude: $E_L = \sum L_{computed}$ Error in Departure: $E_D = \sum D_{computed}$ Linear Closing Error: $E = \sqrt{E_L^2 + E_D^2}$ Relative Precision: $E / \sum l$ Balancing a Traverse (Corrections): Bowditch's Rule (Transit Rule): For both angles and distances measured with similar precision. $C_L = -E_L \frac{l_i}{\sum l}$ $C_D = -E_D \frac{l_i}{\sum l}$ Transit Rule: For angles measured more precisely than distances. $C_L = -E_L \frac{L_i}{\sum |L_i|}$ $C_D = -E_D \frac{D_i}{\sum |D_i|}$ 6. Area and Volume Computations Area from Field Notes: Mid-ordinate Rule: $A = d \sum h$ Average-ordinate Rule: $A = \frac{\sum h}{n+1} \times L$ Trapezoidal Rule: $A = d \left[ \frac{h_0 + h_n}{2} + h_1 + h_2 + ... + h_{n-1} \right]$ Simpson's Rule: (For odd number of ordinates) $A = \frac{d}{3} \left[ (h_0 + h_n) + 4(h_1 + h_3 + ...) + 2(h_2 + h_4 + ...) \right]$ Area from Coordinates: $A = \frac{1}{2} | (X_1 Y_2 + X_2 Y_3 + ... + X_n Y_1) - (Y_1 X_2 + Y_2 X_3 + ... + Y_n X_1) |$ Volume Computations: Cross-section Method: Trapezoidal Formula: $V = \frac{L}{2} (A_1 + A_2)$ Prismoidal Formula: $V = \frac{L}{6} (A_1 + 4A_m + A_2)$ Contour Method (Volume by Slices): $V = \frac{h}{2} (A_1 + 2A_2 + ... + 2A_{n-1} + A_n)$ (Trapezoidal) $V = \frac{h}{3} (A_1 + 4A_2 + 2A_3 + ... + 4A_{n-1} + A_n)$ (Prismoidal - for odd number of areas) 7. Remote Sensing & GIS Basics Remote Sensing: Acquiring information about an object or phenomenon without making physical contact. Passive: Detects natural radiation (e.g., sunlight reflected). Active: Emits energy and detects reflected energy (e.g., Radar, Lidar). GIS (Geographic Information System): System for capturing, storing, checking, integrating, manipulating, analyzing and displaying data related to positions on Earth's surface. Components: Hardware, Software, Data, People, Methods. Data Models: Raster: Grid of cells (pixels), good for continuous data (e.g., elevation, temperature). Vector: Points, lines, and polygons, good for discrete features (e.g., roads, parcels).