CELE Surveying (Geomatics) — Advanced and Geodetic SurveyingConcept Map

Concept

Triangulation

Sub Concepts

• Angle measurement
• Law of sines
• Baseline establishment
• Angle computation
• Side length determination

Relationship To Central

Primary method for establishing large-scale control networks

Concept

Trilateration

Sub Concepts

• EDM (Electronic Distance Measurement)
• Distance measurement
• Angle computation from distances
• Control network establishment

Relationship To Central

Modern alternative to triangulation using distance measurement

Concept

Stadia Measurement

Sub Concepts

• Stadia intercept (s)
• Interval factor (K)
• Additive constant (C)
• Horizontal sight distance
• Inclined sight correction
• Vertical component

Relationship To Central

Rapid distance measurement technique using telescope hairs

Concept

Geodetic Surveying

Sub Concepts

• Curvature-refraction correction
• Ellipsoid coordinates
• Latitude and longitude
• Spherical trigonometry
• Projection systems (UTM)
• Distance limitation for plane surveying

Relationship To Central

Accounts for Earth's curvature over large distances

Concept

Plane Surveying

Sub Concepts

• Earth treated as flat
• Euclidean geometry
• Limited to local areas
• Cost-effective approach

Relationship To Central

Simplified approach for small survey areas

Concept

Control Networks

Sub Concepts

• Horizontal control
• Vertical control
• Network density
• Adjustment procedures

Relationship To Central

Framework for establishing precise positions and elevations

Concept

Measurement Corrections

Sub Concepts

• Atmospheric refraction
• Earth curvature
• Instrument constants
• Target determination

Relationship To Central

Systematic improvements to measurement accuracy

Concept

Computational Methods

Sub Concepts

• Law of sines
• Law of cosines
• Trigonometric computation
• Coordinate transformation

Relationship To Central

Mathematical techniques for position determination

To

Law of sines

From

Triangulation

Strength

strong

Relationship

Triangulation uses law of sines to compute side lengths from measured angles and known baseline

To

EDM

From

Trilateration

Strength

strong

Relationship

EDM technology is essential for practical trilateration measurements in modern surveying

To

Horizontal sight distance

From

Stadia Measurement

Strength

strong

Relationship

D = Ks + C is the fundamental formula for horizontal stadia distance calculation

To

Vertical angle alpha

From

Inclined sight

Strength

strong

Relationship

Vertical angle determines horizontal and vertical distance components in inclined stadia sights

To

Curvature-refraction correction

From

Geodetic Surveying

Strength

strong

Relationship

Curvature correction hcr = 0.0675 D² accounts for Earth's curvature in geodetic measurements

To

Small areas

From

Plane Surveying

Strength

strong

Relationship

Plane surveying assumes flat Earth and is valid only for limited survey areas (typically under 5 km)

To

Spherical trigonometry

From

Geodetic Surveying

Strength

strong

Relationship

Large area surveys require spherical trigonometry to account for curved Earth surface

To

Triangulation and Trilateration

From

Control Networks

Strength

strong

Relationship

Control networks are established using either triangulation (angle-based) or trilateration (distance-based) methods

To

Rapid distance measurement

From

Stadia Measurement

Strength

moderate

Relationship

Stadia provides fast, convenient distance measurements over moderate ranges for preliminary surveys

To

Dh = Ks cos²alpha

From

Horizontal distance formula

Strength

strong

Relationship

Cosine-squared term reduces inclined stadia distance to horizontal component

To

V = 0.5 Ks sin 2alpha

From

Vertical component formula

Strength

strong

Relationship

Double-angle sine term extracts vertical elevation difference from inclined stadia sight

To

Stadia intercept s

From

Interval factor K

Strength

strong

Relationship

K (typically 100) multiplies stadia intercept to determine distance; K depends on telescope design

To

Latitude and Longitude

From

Geodetic positions

Strength

strong

Relationship

Positions are referenced to Earth's ellipsoid using geodetic coordinates

To

Planar coordinates

From

UTM projection

Strength

strong

Relationship

UTM converts geodetic coordinates to planar Easting-Northing grid for engineering calculations

To

Least squares

From

Network adjustment

Strength

moderate

Relationship

Network adjustment distributes measurement errors using least-squares methods to improve accuracy

To

Instrument design

From

Additive constant C

Strength

moderate

Relationship

Additive constant depends on telescope focal length; typically near zero for internal-focusing instruments

To

Theodolite or transit

From

Stadia measurement

Strength

moderate

Relationship

Stadia hairs in telescope reticle enable distance measurement without separate EDM

To

Foundation of network

From

Baseline establishment

Strength

strong

Relationship

Accurate baseline is foundation; all triangulation/trilateration extends from baseline measurement

To

Curvature becomes significant

From

Distance limitation for plane surveying

Strength

strong

Relationship

Beyond approximately 5 km, Earth's curvature causes measurable errors in plane surveying assumptions

To

Modern control networks

From

GNSS positioning

Strength

moderate

Relationship

GNSS provides high-accuracy coordinates for establishing or supplementing traditional triangulation/trilateration networks