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  • INTRODUCTION OF SURVEYING
    • INTRODUCTION
    • REFERENCE ELLIPSOID
    • BASIC MEASUREMENTS
    • The geoid
    • PROTECTION AND REFERENCING
    • CONTROL NETWORKS
    • The ellipsoid
    • BASIC SETTING-OUT PROCEDURES USING COORDINATES
    • LOCATING POSITION
    • COORDINATE SYSTEMS
    • USE OF GRIDS
    • PLOTTING DETAIL
    • Geodetic coordinates
    • SETTING OUT BUILDINGS
    • Computer-aided design (CAD)
    • Cartesian coordinates
    • Error and uncertainty
    • Plane rectangular coordinates
    • SIGNIFICANT FIGURES
    • Height
    • ERRORS IN MEASUREMENT
    • WEIGHT MATRIX
    • LOCAL SYSTEMS
    • Probability
    • ERROR ANALYSIS
    • Deviation of the vertical
    • INDICES OF PRECISION
    • VARIANCE-COVARIANCE MATRIX OF THE PARAMETERS
    • COMPUTATION ON THE ELLIPSOID
    • COMBINATION OF ERRORS
    • Uncertainty of addition or subtraction
    • Eigenvalues, eigenvectors and error ellipses
    • BLUNDER DETECTION
    • RELIABILITY OF THE OBSERVATIONS
    • PRACTICAL CONSIDERATIONS
    • ESTIMATION IN THREE DIMENSIONS

  • LEVELLING
    • LEVELLING
    • OPTICAL METHODS
    • CURVATURE AND REFRACTION
    • MECHANICAL METHODS
    • EQUIPMENT
    • Weiss quadrilateral
    • INSTRUMENT ADJUSTMENT
    • PARAMETER VECTOR
    • Single wires in two shafts
    • Automatic level
    • DESIGN MATRIX AND OBSERVATIONS VECTOR
    • GYRO-THEODOLITE
    • PRINCIPLE OF LEVELLING
    • Plan network
    • SOURCES OF ERROR
    • Distance equation
    • LEVELLING APPLICATIONS
    • Direction & Angle equation
    • Direct and Indirect contouring
    • Controlling earthworks
    • RECIPROCAL LEVELLING
    • PRECISE LEVELLING
    • Parallel plate micrometer
    • ERROR ELLIPSES
    • Field procedure
    • Booking and computing
    • DIGITAL LEVELLING
    • Factors affecting the measuring procedure
    • TRIGONOMETRICAL LEVELLING

  • CONTOURING
    • TAPES
    • Introduction of Satellite positioning
    • FIELD WORK
    • GPS SEGMENTS
    • Measuring in catenary
    • GPS
    • DISTANCE ADJUSTMENT
    • SATELLITE ORBITS
    • Sag
    • BASIC PRINCIPLE OF POSITION FIXING
    • ERRORS IN TAPING
    • DIFFERENCING DATA
    • Tension,Sag and Slope
    • GPS OBSERVING METHODS
    • ELECTROMAGNETIC DISTANCE MEASUREMENT (EDM)
    • Kinematic positioning
    • ERROR SOURCES
    • Global datums
    • GPS SYSTEM FUTURE
    • DATUM TRANSFORMATIONS
    • GALILEO
    • ORTHOMORPHIC PROJECTION
    • APPLICATIONS
    • ORDNANCE SURVEY NATIONAL GRID
    • (t – T) correction
    • PRACTICAL APPLICATIONS
    • Contouring
    • HEIGHTING WITH GPS

  • Theodolite Surveying
    • PLANE RECTANGULAR COORDINATES
    • PRINCIPLE OF LEAST SQUARES
    • PRINCIPLE OF LEAST SQUARES
    • TRAVERSING
    • LINEARIZATION
    • LEAST SQUARES APPLIED TO SURVEYING
    • Reconnaissance
    • NETWORKS
    • LINEARIZATION
    • Sources of error
    • Traverse computation
    • TRIANGULATION
    • Resection and intersection
    • Resection
    • NETWORKS
    • INSTRUMENT ADJUSTMENT
    • FIELD PROCEDURE
    • Setting up using the optical plumb-bob
    • MEASURING ANGLES
    • Measurement by directions
    • SOURCES OF ERROR

  • Simple Curves
    • CIRCULAR CURVES
    • Plotted areas
    • RESPONSIBILITY ON SITE
    • PHOTOGRAMMETRY
    • SETTING OUT CURVES
    • PARTITION OF LAND
    • COMPOUND AND REVERSE CURVES
    • CROSS-SECTIONS
    • SHORT AND/OR SMALL-RADIUS CURVES
    • VOLUMES
    • TRANSITION CURVES
    • Effect of curvature on volumes
    • Centrifugal ratio
    • MASS-HAUL DIAGRAMS
    • CONTROLLING VERTICALITY
    • The equation of motion
    • Coefficient of friction
    • CONTROLLING GRADING EXCAVATION
    • Sources of error
    • SETTING-OUT DATA
    • ROUTE LOCATION
    • LINE AND LEVEL
    • Highway transition curve tables (metric)
    • THE OSCULATING CIRCLE
    • Transitions joining arcs of different radii (compound curves)
    • Coordinates on the transition spiral
    • VERTICAL CURVES
    • Vertical curve design
    • Sight distances
    • Permissible approximations in vertical curve computation

Branch : Civil Engineering
Subject : Surveying-I
Unit : INTRODUCTION OF SURVEYING

The geoid


Description:

Having rejected the physical surface of the Earth as a computational surface, one is instinctively drawn to a consideration of a mean sea level surface. This is not surprising, as 70% of the Earth’s surface is ocean. If these oceans were imagined to flow in interconnecting channels throughout the land masses, then, ignoring the effects of friction, tides, wind stress, etc., an equipotential surface, approximately at MSL would be formed. An equipotential surface is one on which the gravitational potential is the same at all points.

 

 

It is a level surface and like contours on a map which never cross, equipotential surfaces never intersect, they lie one within another as in Figure  Such a surface at MSL is called the ‘geoid’. It is a physical reality and its shape can be measured. Although the gravity potential is everywhere the same the value of gravity is not. The magnitude of the gravity vector at any point is the rate of change of the gravity potential at that point. The surface of the geoid is smoother than the physical surface of the Earth but it still contains many small irregularities which render it unsuitable for the mathematical location of planimetric position. These irregularities are due to mass anomalies throughout the Earth. In spite of this, the geoid remains important to the surveyor as it is the surface to which all terrestrial measurements are related.

 


As the direction of the gravity vector (termed the ‘vertical’) is everywhere normal to the geoid, it defines the direction of the surveyor’s plumb-bob line. Thus any instrument which is made horizontal by means of a spirit bubble will be referenced to the equipotential surface passing through the instrument. Elevations in Great Britain, as described in Chapter 2, are related to the equipotential surface passing through MSL, as defined at Newlyn, Cornwall. Such elevations or heights are called orthometric heights (H) and are the linear distances measured along the gravity vector from a point on the surface to the equipotential surface used as a reference datum. As such, the geoid is the equipotential surface that best fits MSL.

 

 


Equipotential surfaces

 

 

 

 

and the heights in question, referred to as heights above or below MSL. It can be seen from this that orthometric heights are datum dependent. Therefore, elevations related to the Newlyn datum cannot be related to elevations that are relative to other datums established for use in other countries. The global MSL varies from the geoid by as much as 3 m at the poles and the equator, largely because the density of sea water changes with its temperature, and hence it is not possible to have all countries on the same datum.

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