The bottom line is this. On the State Plane coordinate grid, north is always parallel with the central meridian, but at the points on the Earth, north is along the meridian that passes through them. They are certainly not parallel with one another and certainly not parallel with the central meridian.
It is four times less precise than typical State Plane Coordinate systems with a scale factor that reaches 0. A Universal Transverse Mercator zone embraces a much larger portion of the earth than does a state plane coordinate zone. When you get a larger bite, a larger portion of the earth, the scale factor is less attractive. Yet, the ease of using UTM and its worldwide coverage makes it very attractive for work that would otherwise have to cross many different SPCS zones.
It is often said that UTM is a military system created by the U. At that time, the goal was to design a consistent coordinate system that could promote cooperation between the military organizations of several nations. Before the introduction of UTM, allies found that their differing systems hindered the synchronization of military operations.
Conferences were held on the subject from to , with representatives from Belgium, Portugal, France, and Britain, and the outlines of the present UTM system were developed. By , the U. Army introduced a system that was very similar to that currently used. Here is a convenient way to find the zone number for a particular longitude. Any answer greater than an integer is rounded to the next highest integer and you have the zone.
Round up to On the south, the latitude is a small circle that conveniently traverses the ocean well south of Africa, Australia, and South America. You will notice letters of the alphabet along the right edge of the illustration. There are a few letters missing. For example, C21 would be the square that you see just immediately above 21 in the Southern Hemisphere.
This is a useful method of referring to a particular quadrangle in a particular UTM zone. The designations are also used by the military. Unlike any of the systems previously discussed, every coordinate in a UTM zone occurs twice, once in the Northern Hemisphere and once in the Southern Hemisphere. This is a consequence of the fact that there are two origins in each UTM zone. This arrangement ensures that all of the coordinates for that zone in the Northern Hemisphere will be positive.
The origin for the coordinates in the Southern Hemisphere for the same zone is km west of the central meridian, as well. But in the Southern Hemisphere, the origin is not on the equator, it is 10, km south of it, close to the South Pole. This orientation of the origin guarantees that all of the coordinates in the Southern Hemisphere are in the first quadrant and are positive. In the southern hemisphere, each origin is given the coordinates:.
In the northern hemisphere, the values are:. The central meridian of the zones is exactly in the middle. The UTM secant projection gives approximately kilometers between the lines of exact scale where the cylinder intersects the ellipsoid. The scale factor grows from 0.
In State Plane coordinates, the scale factor is usually no more than 1 part in 10, In UTM coordinates, it can be as large as 1 part in The reference ellipsoids for UTM coordinates vary.
In such a context, there is, of course, a third element, that of height. Surveyors have traditionally referred to this component of a position as its elevation. One classical method of determining elevations is spirit leveling.
A level, correctly oriented at a point on the surface of the earth, defines a line parallel to the geoid at that point. Therefore, the elevations determined by level circuits are orthometric; that is, they are defined by their vertical distance above the geoid as it would be measured along a plumb line. In a normal course of things, a coordinate —YX, or northing easting, or latitude and longitude— is not fully a definition of a position.
We've discussed also Earth-Centered, Earth-Fixed XYZ coordinates, but it is typical for a horizontal coordinate to be given a height, or elevation. This third element, was most often originally determined by spirit leveling or, in some cases, by a technique known as trigonometric leveling. Despite the surveying method that was used in the past, it was based on optical instruments oriented to gravity, therefore oriented to the geoid.
Therefore, the heights were based upon gravity. There is a long legacy of benchmarks, recorded heights, and archives that are based upon this sort of methodology of determining heights.
And so, this is what we It follows that these values are generally what we think of as elevations —we think of orthometric heights based upon gravity. As mentioned before, modern geodetic datums rely on the surfaces of geocentric ellipsoids to approximate the surface of the Earth. But the actual surface of the Earth does not coincide with these nice smooth surfaces, even though that is where the points represented by the coordinate pairs lay. Abstract points may be on the ellipsoid, but the physical features those coordinates intend to represent are on the Earth.
Though the intention is for the Earth and the ellipsoid to have the same center, the surfaces of the two figures are certainly not in the same place. There is a distance between them. The distance represented by a coordinate pair on the reference ellipsoid to the point on the surface of the Earth can be measured along a line perpendicular to the ellipsoid - which differs from the direction of gravity. This distance is known by more than one name.
It is called the ellipsoidal height , and it is also called the geodetic height and is usually symbolized by h. The concept is straightforward. A reference ellipsoid may be above or below the surface of the Earth at a particular place. It is quite impossible to actually set up an instrument on the ellipsoid.
That makes it tough to measure ellipsoidal height using surveying instruments. In other words, ellipsoidal height is not what most people think of as an elevation. Said another way, an ellipsoidal height is not measured in the direction of gravity. It is not measured in the conventional sense of down or up. In the illustration, there is an instrument level on the topographic surface of the Earth. The direction of gravity does not coincide with the perpendicular to the ellipsoid.
In other words, it has the capability of determining three-dimensional coordinates of a point in a short time. It can provide latitude and longitude, and if the system has the parameters of the reference ellipsoid in its software, it can calculate the ellipsoidal height. You may wonder why in the world spend any time at all on this bizarre idea of an ellipsoid height. Since you can't measure it directly, you can't set up on the ellipsoid, what's the point?
Well, here's the point. They have no concept of where the surface of the Earth is. It will base that latitude and longitude on the ellipsoidal parameters in its microcomputer. It follows that the height that is determined up to the station that you're interested in will also be based upon the ellipsoid. However, ellipsoidal heights are not all the same, because reference ellipsoids, or sometimes just their origins can differ. It's worthwhile to note that ellipsoidal heights vary as the ellipsoid changes.
As the reference frame datum changes, the ellipsoid height changes. And that's what this image here is intended to represent. There is an approximately 2. Therefore, the heights —the small h, the ellipsoid height— derived from each of these would be different.
Quantifying this potential energy is one way to talk about height, because the amount of potential energy an object derives from the force of gravity is related to its height. There are an infinite number of points where the potential of gravity is always the same. They are known as equipotential surfaces. Mean Sea Level itself is not an equipotential surface at all, of course. Forces other than gravity affect it, forces such as temperature, salinity, currents, wind, and so forth.
The geoid, on the other hand, is defined by gravity alone. The geoid is the particular equipotential surface arranged to fit Mean Sea Level as well as possible, in a least squares sense. The geoid and the ellipsoid are not the same. Remember that the legacy heights determined by optical instruments in the past were always relative to the geoid, because, of course, the instruments were oriented to gravity.
So, while there is a relationship between Mean Sea Level and the geoid, they are not the same. They could be the same if the oceans of the world could be utterly still, completely free of currents, tides, friction, variations in temperature, and all other physical forces, except gravity. However, these unavoidable forces actually cause Mean Sea Level to deviate up to 1, even 2, meters from the geoid.
The geoid is completely is not smooth and continuous. It is lumpy, because gravity is not consistent across the surface of the earth. At every point, gravity has a magnitude and a direction, but these vectors do not all have the same direction or magnitude.
Some parts of the earth are denser than others. Where the earth is denser, there is more gravity, and the fact that the earth is not a sphere also affects gravity. The geoid undulates with the uneven distribution of the mass of the earth and has all the irregularity that the attendant variation in gravity implies.
They vary from about —8 meters to about —53 meters. A geoidal height is the distance measured along a line perpendicular to the ellipsoid of reference to the geoid.
Also, as you can see in the illustration, these geoid heights are negative. They are usually symbolized, N. If the geoid is above the ellipsoid, N is positive; if the geoid is below the ellipsoid, N is negative. It is negative here because the geoid is underneath the ellipsoid throughout the conterminous United States. In Alaska, it is the other way around; the ellipsoid is underneath the geoid and N is positive.
Please recall that an ellipsoid height is symbolized, h. The ellipsoid height is also measured along a line perpendicular to the ellipsoid of reference, but to a point on the surface of the Earth. However, an orthometric height, symbolized, H , is measured along a plumb line from the geoid to a point on the surface of the Earth.
By using the formula,. The ellipsoid height of a particular point is actually smaller than the orthometric height throughout the conterminous United States. Curved, because it is perpendicular with each and every equipotential surface through which it passes. The equipotential surfaces are not parallel with each other.
They converge toward the pole because the Earth is oblate therefore, the plumb line must curve to maintain perpendicularity with them all.
This deviation of a plumb line from the perpendicular to the ellipsoid reaches about 1 minute of arc in only the most extreme cases. Therefore, any height difference that is caused by the curvature is negligible.
It would take a height of over 6 miles for the curvature to amount to even 1 mm of difference in height. Major improvements have been made over the past quarter century or so in mapping the geoid on both national and global scales. And because there are large complex variations in the geoid related to both the density and relief of the earth, geoid models and interpolation software have been developed to support the conversion of GPS elevations to orthometric elevations.
This program allowed a user to find N , the geoidal height, in meters for any NAD83 latitude and longitude in the United States. It was computed at the beginning of , using more than 5 times the number of gravity values used to create GEOID Both provided a grid of geoid height values in a 3 minutes of latitude by 3 minutes of longitude grid with an accuracy of about 10 cm.
Next, the GEOID96 model resulted in a gravimetric geoid height grid in a 2 minutes of latitude by 2 minutes of longitude grid. The grid is 1 degree of latitude by 1 degree of longitude, and it is the first to combine gravity values with GPS ellipsoid heights on previously leveled benchmarks. NGS has an ongoing project known gravity mapping project known as GRAV-D, "The gravity-based vertical datum resulting from this project will be accurate at the 2 cm level where possible for much of the country.
The project is currently underway and actively collecting gravity data across the United States and its holdings. To participate in the discussion, please go to the Lesson 6 Discussion Forum in Canvas. That forum can be accessed at any time by going to the GEOG course in Canvas and then looking inside the Lesson 6 module.
Despite the fact that the assumption of a flat earth is fundamentally wrong, calculation of areas, angles and lengths using latitude and longitude can be complicated, so plane coordinates persist. Heights, orthometric, ellipsoidal and dynamic, may appear, at first, to be simple. The number of zones in a state is determined by the area the state covers and ranges from one for a small state such as Rhode Island to as many as five.
The projection used for each state is also variable; states that are elongate from east to west, such as New York, use a transverse Mercator projection , while states that are elongate from north to south, such as California, use a Lambert conformal projection note: Lambert is the name of the cartographer who designed the projection, the projection itself is a conformal conic projection.
The reasoning behind this is fairly simple; by changing the projection to maximize the number of zones used for gridding, the distortion within each zone in the state is minimized. Those states that support both feet and meters have legislated which feet-to-meters conversion they use. The difference between the two is only two parts in one million, but that can become noticeable when datasets are stored in double precision. The U. The international foot is 0. Used for most federal, state, and local large-scale mapping projects in the United States.
Arc GIS for Desktop. Description Projection method Why use State Plane? What is State Plane? Transverse Mercator. Lambert conformal conic. Were the old coordinates wrong? The old coordinates were not wrong, just different. Positions obtained using the North American Datums of NAD 27 and NAD 83 are based on different earth shapes--or ellipsoids--and used the best technology available at the time.
Mathematically, NAD 83 is a stronger datum because all previously existing horizontal stations and Changes to UTM values are generally larger, around meters, The UTM Universal Transverse Mercator coordinate system divides the world into sixty north-south zones, each 6 degrees of longitude wide.
UTM zones are numbered consecutively beginning with Zone 1, which includes the westernmost point of Alaska, and progress eastward to Zone 19, which includes Maine. When was the ,scale topographic map series for the conterminous 48 States, Hawaii, Alaska and Territories completed? Systematic topographic mapping was authorized by Congress in Although ,scale topographic maps were produced by the USGS as early as , a formal program to provide primary topographic map coverage at that scale for the entire Historically, USGS topographic maps were made using data from primary sources including direct field observations.
Those maps were compiled, drawn, and edited by hand. By today's standards, those traditional methods are very expensive and time-consuming, and the USGS no longer has funding to make maps that way. A new USGS topographic map series Filter Total Items: 4.
Davis, Larry R. View Citation. Davis, L.
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