Surveying and Mapping

Course Notes: Surveying and Mapping

Governments have historically conducted surveys over large areas to fix national and state monuments; charting coastlines and navigable waterways; precise location of reference points throughout the country's establishment of gravity reference stations; establishment of tidal water monitoring stations; extension of oceanographic charting; and topographic mapping.

The U.S. has achieved coverage of 50% of surface area with a map scale of 1:24,000 or 1in. in 2000 ft

Three divisions/classes of surveys:

Primary purpose of establishing boundaries of land.

Provide information for construction of public or private works.

High precision surveys conducted by governments.

Earth as a Spheroid

The earth is approximated as an oblated spheroid of revolution.

Reference	Polar Axis Minor (m)	Equatorial Axis Major (m)
Clarke (1866)	12,713,168	12,756,602
Hayford (1909)	12,713,824	12,756,776
Fischer (1960)	12,713,546	12,756,310

Lengths computed by Clarke are generally accepted by government land surveyors.

Hayford's dimensions first universally adopted around world.

Fischer's values are accepted by NASA.

The difference between polar and equatorial axis lengths is approximately 0.34% making it nearly impossible to differentiate from a perfect sphere.

If we assume the earth can be treated as a sphere. This surface of this perfect sphere is termed a "level surface."

A level surface at sea level is termed "mean sea level."

Assume a plane is passed through the center of the sphere,

Figure Missing!

If a plane is passed through the poles, the line defined by the intersection of the level surface is termed a "meridian."

Figure Missing!

A suitable framework, both horizontal and vertical, must be provided for all types of surveys.

Horizontal Datum - consists of 1) origin, 2) direction of a line from this origin, and 3) polar and equatorial axes of a shape that best fits the earth.

=>The horizontal datum now being used in the U.S. is the North American Datum of 1927 (NAD27).

Vertical Datum - a surface to which all vertical measurements are referenced.

=>The vertical datum currently used in the U.S. is called the National Geodedic Vertical Datum (NGVD).

Geodetic Surveying - this type of surveying takes into consideration the true shape of the earth.

Agencies

U.S. National Geodetic Survey

U.S. Geological Survey

Plane Surveying

Surface of the earth is considered to be a plane.

Majority of surveys are this type.

The length of an arc 11.5 mi (18.5 km) lying on the earth's surface is only 0.02 ft (0.007 m) greater than the subtented chord.

U.S. system of subdividing public lands employs the method of plane surveying. Curvature of the earth is taken into account via "primary lines of divisions".

Elevations are referenced to mean sea level -- a datum plane.

At a horizontal distance of 10 mi from a point of tangency on the earth's surface, the vertical distance of the plane above the earth's surface is 67 ft., or at 10 km this distance is 7.85 m.

=>Even for small surveys to determine elevation, the curvature of the earth must be considered.

Surveying Operations

Control surveys - establishment of horizontal and vertical positions of an arbitrary point.

Land, property, and boundary surveys - performed to determine the length and direction of land lines to establish the position lines.

Topographic surveys- made to secure data from which a topographic map can be generated to indicate the configuration of the terrain.

Hydrographic surveys - water body surveys for purposes of navigation, water supplies, and subaqueous construction.

Mine surveys - location of underground and surface works related to mining operations.

Construction surveys - performed to locate, layout, and monitor engineering works.

Route surveys - surveys necessary for the construction of lines of transportation and communication.

Photogrammetric surveys - aerial and terrestrial photographs are measured to determine the position of objects.

Units of Measurement

Sexagesimal - degrees, minutes and seconds for specification of angles

2p = 360°

1° = 60' (minutes) U.S.

1' = 60" (seconds)

2p = 400⁽⁸⁾ => 400⁽⁸⁾ = 360°

1^(g) = 100^{( c)}=> 1^(g) = 0.9° Europe

1^{( c)} = 100^{( cc)} => 1^{( cc)}= 0° 00' 32.4"

g grad

c centesimal minutes

cc centesimial seconds

Distance

Originally, the meter was defined as 1/10,000,000 of the earth's meridional quadrant, standardized in Paris in 1799.

U.S. Congress passed an act in 1866 to legalize metric weights and measures.

=>A ratio of 1200/3937 was assigned to convert from feet to meters, or

3 ft = 0.914401829 m

In 1960 the Systeme International d'Unite's (SI) System was established. A new standard was set, 1 m = 1,650,763.73 wavelengths of light produced by burning krypton at a specific energy level.

Subdivided units:

dm 0.1 m

cm 0.01 m

mm 0.001 m

m m 10^-6 m

h m 10^-9m

By executive order in the U.S. (1959) the yard (3 ft) was redefined as 0.9144 m, changing the foot to meter ratio to shorten the foot by 1 part in 500,000.

1 in (U.S.) 2.54 cm

1 ft (U.S.) 30.48 cm

=>The difference between the U.S. survey foot (1200/3937) and the International foot is very small and amounts to 0.2 m/100,000 m or 0.66 ft/60 mi.

Other U.S. Units

Guntr's chain 66 foot

=>This chain is divided into 100 links, each 7.92 in. in length.

1 mile = 80 chains = 320 rods = 5280 foot

=>Rods are sometimes called "perches" or "poles".

1 acre = 10 square chains = 160 square rods = 43,560 square foot

1 square mile = 640 acres

1 hectare = 10,000 m² = 2.471 acres

Drawings of Surveys

Maps
Profiles
Cross-Sections
Graphical Calculations

One element that all maps have in common is a scale … a 1:1000 scale means that 1 cm on the map represents 1000 cm on the object.

Map Projections

If an area is small, orthographic projection can be used to create maps with minimal distortion.

For larger territories this method is not adequate… control points are plotted by coordinators (longitude and latitude). Conformal mapping techniques are used in these cases to preserve angles.

State Plane coordinates have been developed for each state where points can be mapped using a simple orthogonal coordinate system with minimum distortion.

On a global basis, the Universal Transverse Mercator projection system is defined using the parameters of an international ellipsoid.

Maps

Type of maps often studied.

Historical line-drawn maps
Orthophoto maps from stereo photography

Further subdivision of these categories include…

Planimetric maps - graphical representation of streams and other physical features.
Topographic maps - include a representation of relief or contour of ground.

Maps are generally used for 1) public record of land division, or 2) a study of private and public works.

With the advent of the information age, digital maps now permit data to be assigned to a geographic location via Geographic Information Systems (GIS).