Surveying and Geodesy PDF

Surveying and Geodesy Week Week 2 Week 3 Week 4 Week 5 kulang notes about Positioning Notes September 11th lecture Outline Definition of Surveying and Geodesy Hist...

Surveying and Geodesy Week Week 2 Week 3 Week 4 Week 5 kulang notes about Positioning Notes September 11th lecture Outline Definition of Surveying and Geodesy History of Surveying and Geodesy Core Principle of Surveying and Geodesy Types of Surveying and Branches of Geodesy Instruments Applications Latitude, longitude (x,y coordinates) Understand the spaces and know how to interact with them Geodesy 💡 the discipline that deals with the measurement and representation of the Earth's surface Etymology geo - earth diao - divide Surveying and Geodesy 1  What they specifically study Gravity field in a 3D time-varying space (latitude, longitude, elevation) the Earth’s gravity changes over time (Satellite can provide precise measurements) Measuring the size and shape of the Earth Surveying 💡 determining angular and linear measurements to establish the form, extent, and relative position of points, lines, and areas on or near the surface of the Earth or on other extraterrestrial bodies using applied mathematics and the use of specialized equipment and techniques etymology serveoir - to overlook supervidere - to over see Relationship of Geodesy and Surveying 1. Geodesy: Bigger Scale (Earth-Wide) a. foundation of Surveying 2. Surveying: Local or Regional History of Surveying and Geodesy Stages 1. Embryonic Stage 2. The Birth Surveying and Geodesy 2  3. Framework establishment 4. The Modern World Embryonic Stage This stage started with the concept of “what is the shape of Earth?” People involved 1. Homer (Ancient Greek): believed that the Earth was flat and surrounded by water. Viewpoint was more literary than scientific 2. Anaximanes (Ancient Greek): believed that the Earth was a rectangle. Thought air was the fundamental substance of life. Used observation and rational thinking for conclusions on the Earth's shape. 3. Pythagoras and Aristotle: Pythagoras: Believed the Earth was a perfect sphere. Aristotle: Supported the spherical Earth using observational evidence (e.g., Earth's shadow on the Moon during a lunar eclipse). 4. Eratosthenes (Egypt): First to measure the Earth’s circumference. Used the sun’s position relative to Earth and geometry to calculate the size of the spherical Earth. Surveying aspect: Tax maps and Land Ownership Early civilizations lacked precise measurement documents. Instead, they used clay tablets to record land ownership and maps. The Birth Surveying and Geodesy 3  Early Contributions (Egypt ~ 2560 BC): The base of the pyramids was a near-perfect square, showing the use of precise measurement techniques. Instruments: Ropes and knots were used for consistent measurements; the plumb bob was employed to ensure vertical accuracy. Key Idea: “What can be mapped can be ruled.” Accurate land measurements made it easier for rulers to conquer and control territories. People involved: 1. C. Huygens (Dutch mathematicians and physicist) Proposed that the Earth is an oblate spheroid (flattened at the poles). Demonstrated that gravity increases from the equator to the poles. 2. A.C. Clairut: Developed Clairaut's Theorem, determining the Earth's shape based on gravitational forces. 3. W. Snell: Introduced the triangulation method for measuring distances on Earth's surface over hundreds of kilometers. Framework Development (1400-1700) Redefining the definition figure of the Earth Key Concepts: 1. Approximation mathematical surface Early geodesists sought to describe the Earth's shape mathematically, approximating it as an ellipsoid or spheroid to account for its slightly bulging equator. This shift from a perfect sphere to a more accurate oblate spheroid model was driven by observations of gravity and the Earth's rotation. Surveying and Geodesy 4  2. Physical surface of the Earth The physical surface of the Earth was recognized as being irregular, consisting of mountains, valleys, and varying sea levels, but mathematical models (e.g., ellipsoid) were developed as a reference to simplify measurements. What was developed during this period: Optics invention of telescopes The study of magnetism Magnetic compasses Understanding the Earth’s magnetic field The development of more accurate timekeeping devices Standardization of units angle, length, time Instrument books The Modern World After WW1 and WW2, the instruments were developed to measure accurately and precisely the Earth’s movement. Key Earth Movements Measured Post-War 1. Polar motion 2. Variations in the speed of the Earth’s rotation 3. Plate movement 4. Vertical crustal movement Modern technologies to measure Earth Movements (will be discussed later) Core Principles Surveying and Geodesy 5  Geodesy 1. Studying the size and shape of the Earth Expectation: Flattened at poles, bulging at sides (due to rotation) Actual Earth: Very lumpy and varies through time due to topography, changing ocean heights, etc. Mathematical shape: Ellipsoid simplified model used for mapping and calculating x, y coordinates. Physical (Real) shape: Geoid ( A more accurate representation of the Earth’s surface, accounting for gravitational consistency. Used for precise height measurements. 2. Define Datum and Coordinate Systems Datum: A reference system that defines the size, shape, and position of the Earth for geodetic purposes. Coordinate Systems: Used to describe locations on Earth’s surface, whether in Cartesian (x, y, z) or geographic (latitude, longitude, elevation) terms Surveying 1. Measuring Distance horizontal vertical 2. Angle and directions horizontal vertical 3. Position x,y,z latitude, longitude, elevation Types of Surveying Surveying and Geodesy 6  Plane Surveying: Scope: Applied to small areas (typically less than 250 km²). Assumption: The mean surface of the Earth is considered flat or a plane. Use Cases: Ideal for local surveys such as construction projects, land divisions, and smaller mapping tasks where Earth's curvature is negligible. Geodetic Surveying: Scope: Conducted over large areas (often national or continental scale). Assumption: Takes into account the true shape of the Earth (i.e., Earth’s curvature). Use Cases: Used for large-scale projects like national boundary mapping, infrastructure planning, and long-distance triangulation where precise accuracy is crucial and Earth’s curvature must be considered. Branches of Geodesy 1. Geometric Geodesy Focus: The size and shape of the Earth. Describes the Earth using an ellipsoid for simpler calculations and representation. 2. Physical Geodesy Focus: The size and shape of the Earth. Use: Understanding gravity variations to refine measurements of height and mass distribution on Earth. 3. Satellite Geodesy Focus: Determining position and measuring the gravity field using satellite technology. Use: Satellites are used for precise positioning systems (e.g., GPS) and to study the Earth's shape and movement. 4. Dynamic Geodesy Surveying and Geodesy 7  Focus: Studying the Earth’s movements over time, including polar motion, tectonic shifts, and changes in rotation speed. 5. Geodetic Astronomy Focus: Astronomical methods for determining position and time, used before the era of satellites. Historical Use: Involved observing the sun and stars to calculate position, now largely obsolete with the advent of satellite technologies. Not used in present times (before satellites) 1. hindi na ginagamit in present time 2. panahong wala pang satellite 3. Astronomical methods for position and time 4. Observing sun and measure , then you can measure where are u Surveying and Geodetic Instruments Surveying instrument Measuring Instruments 1. Theodolite Purpose: Used for angular measurements. Coordinates: Capable of measuring x, y, z coordinates. Notes: An older version of surveying instruments, widely used for precise angle measurements. 2. Total Station Purpose: Combines electronic measurement with angle measurement. Technology: Utilizes laser technology for distance measurement, providing both angular and linear data. Notes: A modern instrument that enhances efficiency and accuracy in surveying tasks. 3. Survey Grade GPS Purpose: Provides precise measurements of latitude, longitude, and elevation. Surveying and Geodesy 8  Notes: Essential for accurate positioning in geodetic surveys and large- scale mapping projects. 4. Autolevel Purpose: Used for leveling tasks to measure differences in elevation between points. Notes: Typically involves a telescope mounted on a leveling base. Supporting equipments 1. Tripod 2. Targets 3. UAV 4. Laser Scanner Geodetic Instruments satelite laser ranging (SLR) Very long baseline interferometry (VLBI) Gravity Field Measurement Sea Level Measurement Eart’s rotation Polar motion Measure - linear and angular Surveying Measurements Surveying measurements involve the process of determining the extent, size, or dimension of a particular quantity. Components of Surveying Measurements Surveying measurements consist of several physical operations, including: Measurement vs. Observation Surveying and Geodesy 9  Measurement: Definition: An entire process that includes preparation, pointing, matching, and comparing. Nature: Systematic and structured approach to obtain reliable data. Observation: Definition: A single, unadjusted determination of a linear or angular numerical value. Characteristics: May contain errors. Often referred to as raw data, as it has not yet been refined or adjusted. Variability of Measurements Causes: Physical fluctuations due to environmental factors can affect measurements. Solution: To acquire a final numerical value, multiple observations are necessary. For example, if observations yield values like 1, 2, 3, 4, 5, 6, 6, 8, 9, 11, 13, statistical measures can be applied: Statistical Measures 1. Mean: the average 2. Median: The middle value when the observations are arranged from lowest to highest. Example: For the values 1, 2, 3, 4, 5, 6, 6, 8, 9, 11, 13, the median is 6. 3. Midrange: The average of the highest and lowest values. 4. Mode: The value that occurs most frequently in the dataset. Example: In this set, the mode is 6. Measures of Quality Precision: Surveying and Geodesy 10  The consistency and refinement of performance, indicating how closely multiple measurements agree with each other. Accuracy: The degree of conformity of a given measurement to the absolute value of the quantity being measured. Characteristics: Measures how close an observation is to the standard or true value. Precision is relevant when comparing measurements to a standard value. Surveying core principles 1. Distance 2. Angle and directions 3. Position Distance Horizontal Vertical Slope Surveying and Geodesy 11  Horizontal Plane A plane perpedicular to the local direction of the gravity Hindi makikita ng mata during surveying Line of sight imaginary line from observer to target along horizontal line Vertical plane plane perpendicular to horizonal lane measuring linear distance between points on vertical plane Vertical line Line that follows the local direction of gravity as indicated by using the plumb line We need to make sure that it is plumb. Level surface curved surface which each point is perpendicular to the direction of gravity Horizontal distance linear distance between two points on horizontal plane 1. Slope Horizontal Distance measurement 1. Pacing Definition: Counting the number of steps taken to cover a specific distance. Usage: Reconnaissance Survey: Conducted before detailed surveys to estimate distances. Small-Scale Mapping: Useful for quick measurements in preliminary mapping tasks. Locating Details: Helpful in identifying specific features on the ground. Pace: Surveying and Geodesy 12  Definition: The length of a single step when walking. Relative Precision: 1/200 - 1/100 (seldom less than 1/300). Example: 1/200 - For every 200 meters, there could be a 1-meter error. Pace Factor: Defined as the length of one step in meters per pace (m/pace). Factors Affecting Pace: Speed of pacing Roughness of the ground Weight of clothing and shoes Fatigue Slope of the terrain Age and sex 2. Mechanical Devices Pedometer: Counts steps taken to estimate distance traveled. Passometer: Similar to a pedometer, specifically designed for measuring distance based on the number of paces. Odometer: Measures the distance traveled by a vehicle. Measuring Wheel: A wheel that measures distance as it rolls along the ground. Optical Rangefinder: Utilizes laser technology to measure distances accurately. 3. Tachometry Definition: An indirect method of measuring horizontal distances. Stadia Method: Uses a telescope equipped with two horizontal crosshairs (stadia hairs) and a graduated rod (stadia rod). Components: Upper Stadia Hair: Top crosshair for measurement. Surveying and Geodesy 13  Lower Stadia Hair: Bottom crosshair for measurement. Sometimes includes a Middle Stadia Hair. Precision Depends On: Refinement with which the instrument was manufactured. Skill of the observer. Length of measurement (longer distances yield smaller intervals). Distance Calculation: Formula: D=Ks+C D: Distance K: Stadia interval factor (100) S: Stadia interval (distance between upper and lower stadia hairs) C: Distance from the center of the instrument to the principal focus. (usually 0, unless stated otherwise) 4. Taping Definition: A method of measuring distance by physically stretching a tape measure between two points. Application: Commonly used for shorter distances where precision is important. 5. EDM (Electronic Distance Measurement) Definition: Measurement of distance based on the invariant speed of light or electromagnetic waves in a vacuum. Components: Consists of a transmitter (light) and a reflector. Formula: D = vt/2 v - speed of light t- back and forth Instrument 1. Electro-Optical GEODIMETER Max Range: Surveying and Geodesy 14  Daytime: 5-10 km Nighttime: 25-30 km Reason: Less light interference at night allows for longer distance measurements. Measurement Method: The instrument is placed at one end of the line, and a reflector is positioned at the other end to measure distance. 2. Electromagnetic TELLUROMETER High levels of electromagnetic interference can affect measurements, making it less reliable in certain environments. 3. Total Station Features: Equipped with a telescope, laser, and measurement capabilities (requires a reflector). Capable of rotating 360 degrees vertically and horizontally. Automatically counts time, eliminating the need for manual distance computations. Can measure multiple times and calculate averages. Measurements Capabilities: Distance Angle Position Advantages of Modern Surveying Instruments Speed and Accuracy: Quick operation with high precision of 1/1000 up to 1/100,000 Light and Portable: Easy to carry and set up in various field conditions. Low Power Consumption: Efficient energy use for extended operation. Ease of Operation: User-friendly interfaces allow for efficient use. Access to Various Terrains: Suitable for measuring in challenging landscapes. Surveying and Geodesy 15  Versatile Measurements: Capable of measuring both short and long distances. Automatic Display and Computation: Instant readouts and calculations for user convenience. Disadvantages Cost: These advanced instruments can be expensive, which may limit accessibility for some users or organizations. Vertical Distance Measurement 1. Direct Leveling Definition: A method for measuring vertical distances directly. Precision: Considered the most precise technique for determining elevations. Procedure: The middle reading of the leveling instrument is recorded to ensure accuracy. 2. Trigonometric Leveling Definition: A method that uses angles and can rotate vertically. Principle: Utilizes the relationship between the line of sight and slope, applying trigonometric principles to calculate elevation differences. Formula: Involves using basic trigonometry (e.g., sine, cosine) to relate angles and distances. 3. Barometric Leveling Definition: A method that measures elevation using a barometer. Principle: Uses the relationship between atmospheric pressure and elevation. Calculation:Elevation=Pressure differences(B−T) where B is the barometric pressure at the current elevation and T is the standard reference pressure. Elevation difference can be determined using pressure differences (B- T) 4. Gravimetric Leveling Surveying and Geodesy 16  Definition: A method that measures differences in elevation based on variations in gravitational acceleration. Principle: Explores how gravity changes with elevation; higher elevations experience slightly lower gravitational pull. 5. GPS Survey Type: Uses Survey Grade GPS technology. Functionality: Captures coordinates in three dimensions: x,y,z. Provides elevation data along with horizontal positioning. Orthometric height ?? height - until surface Surveying Measurements Part 2 Angle and Directions Components of an angle Reference Line: Typically the North-South line, which serves as a baseline for measuring angles. Direction of the Turn: Indicates whether the angle is measured in a clockwise or counterclockwise direction. Magnitude of the Angle: The actual measurement of the angle, typically expressed in degrees, grads, or other units. Meridian: A fixed reference line for determining the direction of lines Types of Meridians 1. True Meridian: A North-South line that passes through the geographic poles of the Earth. 2. Magnetic Meridian: A line that connects magnetic north and south. Surveying and Geodesy 17  Parallel to the magnetic lines of force of the Earth, indicated by the direction of a magnetized needle. Measured using a compass. 3. Grid Meridian: A line parallel to the central true meridian, is used to create a flat representation of the true meridian. 4. Assumed Meridian: A user-defined North-South line was established for specific surveying purposes. gagawa ka ng sarili mong North-South How do you measure magnitude?? 1. Degrees: a. Sexagesimal system, 1 whole circle = 360º b. 1º = 60’ (minutes) c. 1’ = 60“ (seconds) 2. Grads: a. Circle = 400 g (grads) b. 1g = 100 c (centesimal minutes) i. Vertical angle c. 1c = 100 cc (centesimal seconds) 3. Radians: a. Circle = 2π 4. MIL a. Used in Military operations i. Mas precise kasi ii. At maarte sila Surveying and Geodesy 18  b. Circle = 6400 mils c. 1600 mils = 90º Terminologies Target Points 1. Zenith Definition: The direction away from the center of the Earth, pointing directly above the observer’s head. 2. Nadir Definition: The direction towards the center of the Earth, directly below the observer. Instruments and Measurements 1. Vertical Angle Definition: The angle formed by a line that is parallel to the horizontal plane and tilted in the vertical plane. Description: Represents the angle of tilt from the first observation point to the last. Surveying and Geodesy 19  Above Horizontal: 0°