Shape of the EarthShape can be defined by several methods
While only 28% of Earth's surface is land. However, most studies and measurements are connected to the land masses.
Terrain described by a geodetic network of points
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HORIZONTAL CONTROL SURVEY ACCURACY STANDARDS |
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GPS ORDER |
TRADITIONAL SURVEYS |
RELATIVE ACCURACY REQUIRED |
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Order AA |
1 part in 100,000,000 |
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Order C |
First Order Second Order Third Order |
1 part in 100,000
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VERTICAL CONTROL SURVEY ACCURACY STANDARDS |
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ORDER AND CLASS |
RELATIVE ACCURACY REQUIRED |
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First Order Second Order Third Order |
2.0 mm × sqrt(K) |
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* K is distance between bench marks, in kilometers. |
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The current standards were created by the Federal Geographic Data Committee (FGDC) in 1998. To learn more about these standards go to the FGDC web site at http://www.fgdc.gov/standards/status/textstatus.html
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Accuracy Standards: |
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Accuracy Classifications |
95% Confidence |
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1-mm 1-cm 1-dm 1-m 10-m |
0.001 meters 0.010 meters 0.100 meters 1.000 meters 10.000 meters |
When control points in a survey are classified, they have been verified as being consistent with all other points in the network, no merely those within that particular survey. It is not observational closures within a survey which are used to classify control points, but the ability of that survey to duplicate already established control values. This comparison takes into account models of crustal motion, refraction, and any other systematic effect known to influence survey measurements.
Download the entire text of the new control standards in Adobe Acrobat file format (pdf)
THE NATIONAL SPATIAL REFERENCE SYSTEM
To meet the various local needs of surveyors, engineers, and scientists, the federal government has established a
National Spatial
Reference System (NSRS) consisting of more than 270,000 horizontal control monuments and approximately 600,000 bench marks
throughout the United States. The National Geodetic Survey (NGS) began control surveying operations as the Survey of the Coast
in 1807, changed to Coast Survey in 1836, to Coast and Geodetic Survey in 1878, and to a division of the National Ocean Survey
(NOS) in 1970. It continues to assist with and to coordinate geodetic control surveying activities with other agencies and with all
states to establish new control stations and upgrade and maintain existing ones. It also disseminates a variety of publications and
software related to geodetic control surveying. The NSRS is split into horizontal and vertical divisions. All control within each part
is classified in a ranking scheme based on purpose and order of accuracy.
HIERARCHY OF THE NATIONAL HORIZONTAL CONTROL NETWORK
HIERARCHY OF THE NATIONAL VERTICAL CONTROL NETWORK
The scheme of bench marks within the National Vertical Control Network may be classified as follows:
CONTROL POINT DESCRIPTIONS
To obtain maximum benefit from control surveys, horizontal stations and bench marks are placed in locations favorable to their
subsequent use. The points should be permanently monumented and adequately described to ensure recovery by future potential
users. Reference monuments placed by the NGS are marked by bronze disks about 3½ in. in diameter set in concrete or bedrock.
Figure 19-7 shows two of these disks.
Procedures for establishing permanent monuments vary with the type of soil or rock, climatic conditions, and intended use for the
monument. In cases were soil can be excavated, monuments are commonly set in concrete that goes a foot or more below the local
maximum frost depth. The bottom of the excavation is generally wider than the top to maximize monument stability during periods
of freeze and thaw. Another option commonly use is to drive a stainless steel rod using powered tools to refusal. Driving depths of
10 or more feet are common when using this technique. In bedrock, holes are often drilled into the rock and the monument is simply
epoxied into the hole. Other variations for monumenting can be used, as long as the resulting objects are stable in their positions
over their lifespan. The following image shows to of the more typical monuments
used.
The NGS makes complete descriptions of all its control stations available to surveyors. As an example, a partial listing from an actual NGS station description is given in Figure 19-8. These station descriptions give each station's general placement in relation to nearby towns, instructions on how to reach the station following named or numbered roads in the area, and the monument's precise location by means of distances and directions to several nearby objects. The station's specific description, such as, "a triangulation disk set in drill-hole in rock outcrop," is given, along with a record of recovery history. Data supplied with horizontal control-point descriptions include the datum(s) used and the station's geodetic latitude and longitude. Also given are the state plane coordinates, state plane convergence angle and scale factor, UTM coordinates, approximate elevation, and geoidal height (in meters).
Some station descriptions give geodetic and grid azimuths to a nearby station or stations. Geodetic and grid azimuths differ by an amount equal to the convergence angle, and therefore the appropriate azimuth must be selected for the particular surveying methods used.
As shown in Figure 19-9, published bench mark data include station locations and adjusted elevations in both meters and feet. Again the relevant datum is identified.
Besides control within the national network set by the NGS, additional marks have been placed in various parts of the United Slates by other federal agencies such as the USGS, Corps of Engineers, and Tennessee Valley Authority. State, county, and municipal organizations may have also added control. This work is frequently coordinated through the NGS, and descriptions of these stations are distributed by that agency.
As noted earlier, complete descriptions for all points in the National Spatial Reference System can be obtained from the NGS. This includes horizontal, vertical and GPS control points. The descriptions can be obtained in hard copy form, or in computer format on diskettes or compact disks. Only five compact disks are needed to store all NSRS data for the entire United States.
FIELD PROCEDURES FOR TRADITIONAL HORIZONTAL CONTROL SURVEYS
As noted earlier, in spite of the increasing prominence of GPS, horizontal-control surveys over limited areas are still
being
accomplished by the traditional methods of triangulation, trilateration, precise traverse, or a combination of these techniques. These
methods are described briefly in the sections that follow.
Traditional methods in horizontal control surveys require measurements of horizontal distances and horizontal angles. Basic theory, equipment, and procedures for making these measurements have been covered in earlier chapters. The following sections concentrate on procedures specific to control surveys, and on matters related to obtaining the higher orders of accuracy generally required for these types of surveys.
Triangulation
Prior to the emergence of electronic distance-measuring equipment, triangulation was the preferred and principal method for
horizontal-control surveys, especially if extensive areas were to be covered. Angles could be more easily measured compared with
distances, particularly where long lines over rugged and forested terrain were involved, by erecting towers to elevate the operators
and their instruments. Triangulation possesses a large number of inherent checks and closure conditions which help detect blunders
and errors in field data, and increase the possibility of meeting a high standard of accuracy.
As implied by its name, triangulation utilizes geometric figures composed of triangles. Horizontal angles and a limited number of sides called base lines are measured. By using the angles and base-line lengths, triangles are solved trigonometrically and positions of stations (vertices) calculated
Different geometric figures are employed for control extension by triangulation, but chains of quadrilaterals called arcs (Figure 19-10) have been most common. They are the simplest geometric figures that permit rigorous closure checks and adjustments of field observational errors, and they enable point positions to be calculated by two independent routes for computational checks. More complicated figures like that illustrated in the following figure have frequently been used to establish horizontal control by triangulation in metropolitan areas.
In executing triangulation surveys, intersection stations can be located as part of the project. In this process, angles are measured from as many occupied points as possible to tall prominent objects in the area such as church spires, smoke stacks, or water towers. The intersection stations are not occupied, but their positions are calculated, and thus they become available as local reference points. An example is station B in the following figure.
To compensate for the errors that occur in the measurements, triangulation networks must be adjusted. The most rigorous method utilizes least squares. In that procedure all angle, distance, and azimuth observations are simultaneously included in the adjustment, and are given appropriate relative weights based on their precisions. The least-squares method not only yields the most probable adjusted station coordinates, but it also gives their precisions.
Unlike triangulation, in which stations are normally widely separated and placed on the highest ridges and peaks in an area, traverse routes generally follow the cleared rights-of-way of highways and railroads, with stations located relatively close together. Besides easing field work, this provides a secondary benefit in accessibility of the stations. Traverses lack the automatic checks inherent in triangulation, and extreme observational caution must therefore be exercised to avoid blunders. Also, since traverses generally run along single lines, they are generally not as good as triangulation for establishing control over large areas.
Control traverses can be strengthened to provide additional checks in the data by establishing "offset stations" such as A', C' and E' of the following figure. An offset station is set near every-other primary traverse station. In performing the field measurements, instrument setups are made only at the primary traverse stations. All possible angles are measured with horizon closures at each station, and thus four angles are determined at single primary stations, and two angles are observed at primary stations with nearby offset stations. This observation scheme is shown in the following figure. Additionally, all distances are measured, i.e., at station 1 distances 1A and 1A' are observed, at station A, lengths A1,AA' and AB are measured, etc. When the field observations have been completed, the network can be adjusted using all measurements in a least squares adjustment, thereby providing geometric checks for all angle and distance observations in the traverse.
Additional geometric strength in the figure could be obtained by also measuring angles at the offset stations.
In traversing to gain overall project efficiency and improve angle accuracy, it is always preferable to have long sight distances. Also to avoid mistakes it is advisable to avoid using nearly "flat" angles (angles near 180°) whenever possible. To accomplish this, pre-survey reconnaissance is recommended. An oft-made mistake is to construct the traverse while collecting the observations. This technique works in low-order surveys, but frequently results in poorly designed control traverses.
For long traverses, checks on the measured horizontal angles can be obtained by making periodic astronomical azimuth observations. These should agree with the values computed from the direction of the starting line and the measured horizontal angles. However, if a traverse extends an appreciable east-west direction, as illustrated in Figure 19-13, meridian convergence will cause the two azimuths to disagree. In Figure 19-13, for example, azimuth FG obtained from direction AB and the measured horizontal angles should equal astronomic azimuth FG + q, where q is the meridian convergence. A very good approximation for meridian convergence between two points on a traverse is
(19-11)Procedures for precise traverse computation vary depending on whether a geodetic or a plane reference system is used. In either case, it is necessary first to adjust angles and distances for observational errors. Closure conditions are enforced for (1) azimuths or angles, (2) departures, (3) and latitudes. The most rigorous process, the least-squares method, should be used because it simultaneously satisfies all three conditions and gives residuals having the highest probability.
Trilateration
Trilateration, a method for horizontal control surveys based exclusively on observed horizontal distances, has gained acceptance
because of electronic distance measuring capability. Both triangulation and traversing require time-consuming horizontal angle
measurement. Hence trilateration surveys often can be executed faster and produce equally acceptable accuracies.
The geometric figures used in trilateration, although not as standardized, are similar to those employed in triangulation. Stations should be intervisible, and therefore placed on the highest peaks, perhaps with towers to elevate instruments and observers.
Because of intervisibility requirements and the desirability of having essentially square networks, trilateration is ideally suited to densify control in metropolitan areas and on large engineering projects. In special situations where topography or other conditions require elongated narrow figures, the network can be strengthened by reading some horizontal angles. Also, for long trilateration arcs, astronomic azimuth observations can help prevent the network from deforming in direction.
As in triangulation, surveys by trilateration can be extended from one or more monuments of known position. If only a single station is fixed, at least one azimuth must be known or observed.
Trilateration computations consist of reducing measured slope distances to horizontal lengths, then to the ellipsoid, and finally to grid lengths if the calculations are being done in state plane coordinate systems. Observational errors in trilateration networks must be adjusted, preferably by the least-squares method.
Combined Networks
With the ability to easily measure both distances and angles in the field, networks similar to that shown in Figure 19-11 are
becoming increasingly popular. In a combined network, many or all angles and distances are measured. These surveys provide the
greatest geometric strength, and the highest coordinate accuracies for traditional survey techniques.
FIELD PROCEDURES FOR VERTICAL CONTROL SURVEYS
Vertical-control surveys are generally run by either direct differential leveling or trigonometric leveling. The method selected will
depend primarily on the accuracy required, although the type of terrain over which the leveling will be done is also a factor. Direct
differential leveling can produce the highest order of accuracy. The Global Positioning System (GPS) can
be used for lower-order vertical control surveys, but to get accurate elevations using this method, geoidal undulations in the area
must be known, and applied.
Although trigonometric leveling produces a somewhat lower order of accuracy than direct differential leveling, the method is still suitable for many projects such as establishing vertical control for topographic mapping or for lower order construction stake-out. It is particularly convenient in hilly or mountainous terrain where large differences in elevation are encountered.
Differential leveling can produce varying levels of accuracy, depending on the precautions taken. In this section only precise differential leveling, which produces the highest quality results, is considered.
As noted in Table 19-3, the FGCS has established accuracy standards and specifications for various orders of differential leveling. To achieve the higher orders, special care must he exercised to minimize errors, but the same basic principles apply.
Special level rods are needed for precise work. They have scales graduated on Invar strips, which are only slightly affected by temperature variations. Precise level rods are equipped with rod levels to facilitate plumbing, and special braces aid in holding the rod steady. They usually have two separate graduated scales. One type of rod is divided in centimeters on an Invar strip on the rod's front side, with a scale in feet painted on the back for checking readings and minimizing blunders.
A second type of rod, shown in Figure 19-14, has two sets of centimeter graduations on the Invar strip, with the right one precisely offset from the left by a constant, thereby giving checks on readings.
Cloudy weather is preferable for precise leveling, but an umbrella can be used on sunny days to shade the instrument and prevent uneven heating which causes the bubble to run. (One design encases the vial in a Styrofoam shield.) Automatic levels are not as susceptible to errors caused by differential heating. Precise work should not be attempted on windy days. For best results, short and approximately equal backsight and foresight distances are recommended. Table 19-4 lists the maximum sight distances and allowable differences for first, second and third order leveling. Rod-persons can pace or count rail lengths or highway slab joints to set sight distances, which are then checked for accuracy by three-wire stadia methods. Precise leveling demands good-quality turning points. Lines of sight should not pass closer than about 0.5 m from the ground to minimize refraction. Readings at any setup must be completed in rapid succession; otherwise changes in atmospheric conditions might significantly alter refraction characteristics between them.
| TABLE 19-4 RECOMMENDED FIELD CONDITIONS FOR PRECISE LEVELING | |||||
| ORDER
CLASS |
First
I |
First
II |
Second
I |
Second
II |
Third |
| Maximum sight length (m) | 50 | 60 | 60 | 70 | 90 |
| Difference between foresight and backsight lengths never to exceed per setup (m) per section (m) |
2 4 |
5 10 |
5 10 |
10 10 |
10 10 |
It is generally advisable to design large-level networks so that several smaller circuits are interconnected to supply checks that isolate blunders or large errors. In the following figure, for example, it is required to determine the elevations of points X, Y, and Z by commencing from BM A and closing on BM B. As a minimum, this could be done by running level lines 1 through 4, but if an unacceptable misclosure was obtained at BM B, it would be impossible to discover in which lines the blunder occurred. If additional lines 5, 6, and 7 are run, calculating differences in elevation by other routes through the network might isolate the blunder. Furthermore, by including supplemental measurements, precision of the resulting elevations at X, Y, and Z is increased.
For long lines one procedure used to help isolate mistakes and minimize field time is to run small loops with approximately five setups between temporary bench marks. In this procedure as each loop is completed, it is checked for acceptable closure before proceeding forward to the next loop. This procedure increases the number of observations, and helps minimize the amount of time that is required to uncover an inevitable mistake. Each smaller loop is connected to subsequent loops until the entire network is observed. Figure 19-16 depicts this procedure.
In precise differential leveling, frequent calibration of the leveling instrument is necessary to determine its collimation error. A
collimation error exists if, after leveling the instrument, its line of sight is inclined or depressed from horizontal. This causes errors
in determining elevations when backsight and foresight distances are not equal. But they can be eliminated if the magnitude of the
collimation error is known.
A method originated at the U.S. Coast and Geodetic Survey can be used to determine the collimation error. It requires a base line approximately 300 ft (90 m) long. Stakes are set at each end of the line and at two intermediate stations located approximately 20 ft (6 m) and 40 ft (12 m) from the two ends. Figure 19-17 shows an example set of field notes for determining the collimation error and includes a sketch illustrating the base-line layout. With the instrument at station 1, center cross-hair readings r1 and R1 are observed on stations A and B, respectively. If there were no collimation error, the true elevation difference DH from these observations would be r1 - R1. If a collimation error is present, however, each observation must be corrected by adding an amount proportional to the horizontal distance from the level to the rod. The horizontal distance is measured by the stadia interval. Introducing collimation corrections, the true elevation difference DH is
In Eq. (a), i1 and I1 are the stadia intervals (differences between top and bottom cross-hair values) for the rod readings on stations A and B, respectively, and C is the collimation factor (in feet/foot, or mm/m, of stadia interval). A similar equation for the true elevation difference can be written for rod readings R2 and r2 taken on stations A and B, respectively from station 2, or:
Note that in Eqs. (a) and (b), uppercase R and I apply to the longer sights, and lowercase r and i are for the shorter sights. Equating the right sides of Eqs. (a) and (b) yields
(19-12)As previously noted, the units of the collimation factor calculated by Eq. (19-12) are either in feet per ft, or mm per m, of stadia interval. Computation of the factor is illustrated in Figure 19-17 for the data of the field notes (given in ft).
Because the collimation correction increases linearly with distance, it is unnecessary to apply it to each backsight and foresight. Rather the corrected elevation difference DH' for any loop or section leveled is computed from
where SBS is the sum of the center cross-hair readings of backsights in the loop or section, SFS is the center cross-hair total of foresights, and SIBS and SIFS are the sums of the stadia intervals for the backsights and foresights, respectively.
EXAMPLE 19-3
SOLUTION
DH' = (125.590 88.330) + (0.0041)(51.52 48.40)
= 37.260 0.013 = 37.247 m
Regardless of precautions taken in field observations, errors accumulate in leveling and must be adjusted to provide perfect mathematical closure.
For simple level loops, simple prorating adjustment techniques can be followed; for interconnected level networks such as that of Figure 19-15, the method of least squares is preferable.
Properties of a Triaxial
EllipsoidOne of the closest "mathematical" surfaces to a geoid, it the triaxial ellipsoid. The triaxial ellipsoid has a
Last updated:
September 19, 2006
Penn State Surveying Program,
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