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by: Seth Mosciski


Seth Mosciski
GPA 3.61


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Class Notes
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This 6 page Class Notes was uploaded by Seth Mosciski on Saturday September 19, 2015. The Class Notes belongs to SUR 3393 at University of Florida taught by Staff in Fall. Since its upload, it has received 12 views. For similar materials see /class/207062/sur-3393-university-of-florida in Surveying & Related Areas at University of Florida.

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Date Created: 09/19/15
Ellipsoids Datums Coordinate Systems and Projections Ellipsoids Ellipsoidal earth models are required for accurate range and bearing calculations over long distances LoranC and GPS navigation receivers use ellipsoidal earth models to compute position and waypoint information Ellipsoidal models de ne an ellipsoid with an equatorial radius and a polar radius The best of these models can represent the shape of the earth over the smoothed averaged seasurface to within about onehundred meters Reference ellipsoids are de ned by semimajor equatorial radius and semi minor polar radius axes Datums Geodetic datums de ne the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth Hundreds of different datums have been used to frame position descriptions since the rst estimates of the earth39s size were made by Aristotle Datums have evolved from those describing a spherical earth to ellipsoidal models derived from years of satellite measurements Modern geodetic datums range from atearth models used for plane surveying to complex models used for international applications which completely describe the size shape orientation gravity eld and angular velocity of the earth While cartography surveying navigation and astronomy all make use of geodetic datums the science of geodesy is the central discipline for the topic Referencing geodetic coordinates to the wrong datum can result in position errors of hundreds of meters Different nations and agencies use different datums as the basis for coordinate systems used to identify positions in geographic information systems precise positioning systems and navigation systems The diversity of datums in use today and the technological advancements that have made possible global positioning measurements with submeter accuracies requires careful datum selection and careful conversion between coordinates in different datums Hundreds of geodetic datums are in use around the world The Global Positioning system is based on the World Geodetic System 1984 WGS84 Parameters for simple XYZ conversion between many datums and WGS84 are published by the Defense mapping Agency O 0 Coordinate Systems Coordinate systems to specify locations on the surface of the earth have been used for centuries In western geodesy the equator the tropics of Cancer and Capricorn and then lines of latitude and longitude were used to locate positions on the earth Various units of length and angular distance have been used over history The meter is related to both linear and angular distance having been de ned in the late 18th century as one tenmillionth of the distance from the pole to the equator Latitude Longitude Height 0 The most commonly used coordinate system today is the latitude longitude and height system The Prime Meridian and the Equator are the reference planes used to define latitude and longitude The geodetic latitude there are many other defined latitudes of a point is the angle from the equatorial plane to the vertical direction of a line normal to the reference ellipsoid The geodetic longitude of a point is the angle between a reference plane and a plane passing through the point both planes being perpendicular to the equatorial plane The geodetic height at a point is the distance from the reference ellipsoid to the point in a direction normal to the ellipsoid Universal Transverse Mercator UTM 0 Universal Transverse Mercator UTM coordinates define two dimensional horizontal positions UTM zone numbers designate 6 degree longitudinal strips extending from 80 degrees South latitude to 84 degrees North latitude UTM zone characters designate 8 degree zones extending north and south from the equator There are special UTM zones between 0 degrees and 36 degrees longitude above 72 degrees latitude and a special zone 32 between 56 degrees and 64 degrees north latitude Each zone has a central meridian Zone 14 for example has a central meridian of 99 degrees west longitude The zone extends from 96 to 102 degrees west longitude Eastings are measured from the central meridian with a 500km false easting to insure positive coordinates Northings are measured from the equator with a 10000km false northing for positions south of the equator State Plane Coordinates O O O 0000 In the United States the State Plane System was developed in the 1930s and was based on the North American Datum 1927 NAD27 NAD 27 coordinates are based on the foot While the NAD 27 State Plane System has been superseded by the NAD83 System maps in NAD 27 coordinates in feet are still in use Most USGS 75 Minute Quadrangles use several coordinate system grids including latitude and longitude UTM kilometer tic marks and applicable State Plane coordinates The State Plane System 1983 is based on the North American Datum 1983 NAD83 NAD 83 coordinates are based on the meter State plane systems were developed in order to provide local reference systems that were tied to a national datum Some smaller states use a single state plane zone Larger states are divided into several zones State plane zone boundaries often follow county boundaries Lambert Conformal Conic projections are used for rectangular zones with a larger eastwest than north south extent Transverse Mercator projections are used to define zones with a larger northsouth extent Public Land Rectangular Surveys 0 O O O O O O 0 Public Land Rectangular Surveys have been used since the 1790s to identify public lands in the United States The system is based on principal meridians and baselines Townships approximately six miles square are numbered with reference to baseline and principal meridian Ranges are the distances and directions from baseline and meridian expressed in numbers of townships Sections approximately one mile square are numbered from 1 to 36 within a township Quarter sections are divided into 40acre quarterquarter sections Quarterquarter sections are sometimes divided into lOacre areas Fractional units of section quarters designated as numbered lots often result from irregular claim boundaries rivers lakes etc Abbreviations are used for Township T or Tps Ranges R or Rs Sectionssec or secs and directions N E S W NE etc Projections httpergusgsgovisbpubsMapProjectionsprojectionshtml Map projections are attempts to portray the surface of the earth or a portion of the earth on a at surface Some distortions of conformality distance direction scale and area always result from this process Some projections minimize distortions in some of these properties at the expense of maximizing errors in others Some projection are attempts to only moderately distort all of these properties 0 Scale Conformality When the scale of a map at any point on the map is the same in any direction the projection is conformal Meridians lines of longitude and parallels lines of latitude intersect at right angles Shape is preserved locally on conformal maps Distance A map is equidistant when it portrays distances from the center of the projection to any other place on the map Direction A map preserves direction when azimuths angles from a point on a line to another point are portrayed correctly in all directions Scale is the relationship between a distance portrayed on a map and the same distance on the Earth When a map portrays areas over the entire map so that all mapped areas have the same proportional relationship to the areas on the Earth that they represent the map is an equalarea map Different map projections result in different spatial relationships between regions 0 Map projections fall into 3 general classes 1 Cylindrical projections result from projecting a spherical surface onto a cylinder When the cylinder is tangent to the sphere contact is along a great circle the circle formed on the surface of the Earth by a plane passing through the center ofthe Earth In the secant case the cylinder touches the sphere along two lines both small circles a circle formed on the surface of the Earth by a plane not passing through the center of the Earth O O When the cylinder upon which the sphere is projected is at right angles to the poles the cylinder and resulting projection are transverse When the cylinder is at some other nonorthogonal angle with respect to the poles the cylinder and resulting projection is oblique 2 Conic projections result from projecting a spherical surface onto a cone When the cone is tangent to the sphere contact is along a small circle In the secant case the cone touches the sphere along two lines one a great circle the other a small circle Azimuthal projections result from projecting a spherical surface onto a plane When the plane is tangent to the sphere contact is at a single point on the surface of the Earth In the secant case the plane touches the sphere along a small circle if the plane does not pass through the center of the earth when it will touch along a great circle Cylindrical Projections Cylindrical Equal Area 0 Cylindrical EqualArea projections have straight meridians and parallels the meridians are equally spaced the parallels unequally spaced There are normal transverse and oblique cylindrical equalarea projections Scale is true along the central line the equator for normal the central meridian for transverse and a selected line for oblique and along two lines equidistant from the central line Shape and scale distortions increase near points 90 degrees from the central line Mercator O O The Mercator projection has straight meridians and parallels that intersect at right angles Scale is true at the equator or at two standard parallels equidistant from the equator The projection is often used for marine navigation because all straight lines on the map are lines of constant azimuth areas are distorted Directions are true only along the equator The projection avoids the scale exaggerations of the Mercator map The Universal Transverse Mercator UTM projection is used to de ne horizontal positions worldwide by dividing the surface of the Earth into 6 degree zones each mapped by the Transverse Mercator projection with a central meridian in the center of the zone UTM zone numbers designate 6 degree longitudinal strips extending from 80 degrees South latitude to 84 degrees North latitude UTM zone characters designate 8 degree zones extending north and south from the equator Conic Projections Albers Equal Area Conic o A conic projection that distorts scale and distance except along standard parallels Areas are proportional and directions are true in limited areas Used in the United States and other large countries with a larger eastwest than northsouth extent Equidistant Conic o Direction area and shape are distorted away from standard parallels Used for portrayals of areas near to but on one side of the equator Lambert Conformal Conic 0 Area and shape are distorted away from standard parallels Directions are true in limited areas Used for maps of North America Polyconic o The polyconic projection was used for most ofthe earlier USGS topographic quadrangles The projection is based on an in nite number of cones tangent to an in nite number of parallels The central meridian is straight Other meridians are complex curves The parallels are non concentric circles Scale is true along each parallel and along the central meridian Azimuthal Projections Azimuthal Equidistant o Azimuthal equidistant projections are sometimes used to show airroute distances Distances measured from the center are true Distortion of other properties increases away from the center point Lambert Azimuthal Equal Area 0 The Lambert azimuthal equalarea projection is sometimes used to map large ocean areas The central meridian is a straight line others are curved A straight line drawn through the center point is on a great circle


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