«AZIMUTHS IN CONTROL SURVEYS ABSTRACT With the advent of GPS for control surveying, a problem has arisen. Many existing control stations established ...»
AZIMUTHS IN CONTROL SURVEYS
With the advent of GPS for control surveying, a problem has arisen. Many existing
control stations established by conventional methods (i.e. first order triangulation
stations) are in locations not suitable for direct occupation by GPS equipment. Eccentric
observations are often possible, with the eccentric station located up to 100 m away. In
order to connect the eccentric station to the main station, an azimuth is necessary.
Occasionally, a companion GPS station is set, and the angle is measured. More often, it is necessary to observe an astronomic azimuth. Various methods are explored for determining azimuth, with a discussion of the theory of each method, equipment and procedures, and accuracy attainable. The different methods examined include astronomic, gyrotheodolite, azimuth pairs by GPS, and use of azimuth marks. Existing Standards and Specifications address the issue of azimuths only in the context of controlling traverses and triangulation networks, with accuracies of 0.5” to 2” the goal. This paper addresses the issue of lower accuracy azimuths, in the range of 5” to 20”. Also discussed is the difference between astronomic, geodetic, and grid north. A discussion is made for potential inclusion in the "Input Formats and Specifications of The National Geodetic Survey Data Base" of the different types of azimuths besides the presently accepted polaris azimuth, when the distances are short and the required accuracy is lower.
INTRODUCTIONOver the years, various methodologies have been used to obtain azimuth control when extending horizontal control whether by traverse or triangulation. In the eastern part of the US, old photographs show that in the early part of this century, much of the area had few trees, having been timbered and cleared for farming. Many of the triangulation stations, located on high hilltops, had good visibility to an adjacent station or at least to an azimuth mark. Over the years, most of the rural areas have reforested, and the urban areas have become built up. It is a rare occurrence now that a recovered 1st order station has any kind of available (i.e. visible from the ground) azimuth reference. This was probably one of the main reasons why local surveyors often did not make ties to this control. Instead, many surveys used assumed datums with assumed azimuths. Some surveyors simply backsighted the nearby reference marks, thereby introducing large errors into their surveys.
When GPS arrived in the mid 1980’s, there was precious little satellite coverage in a day.
When establishing a survey network to be used by conventional equipment, the clients often specified that an intervisible azimuth mark was to be established. Because of the high cost of GPS equipment and the short GPS window, usually stations were established individually, and astronomic observations were then made at some or all of the stations to establish azimuth marks. Now, with 24 hour coverage and shortened observation times, stations are frequently established in pairs. Still, it is not always possible to set an intervisible station a sufficient distance away in a location that is suitable for GPS.
John Hamilton 1 email@example.com Geodetic Engineer 412-341-5620 Before the establishment of HARN (High Accuracy Reference Network) stations, it was necessary (and still sometimes is) to use existing triangulation stations for control, which are often located in wooded or otherwise obstructed locations. The NGS (and its predecessor, the USC&GS) utilized Bilby towers, ranging in height up to 110+ feet, to achieve intervisibility between main scheme stations. At many of these stations, although a direct occupation is not possible, it is possible to locate an eccentric GPS station less than 50 meters away. This necessitates observing an astronomic azimuth between the eccentric and the existing station. Another common situation is when a survey station, for example a property corner, is not occupiable by GPS, but it is possible to establish a GPS station nearby. The Federal Geodetic Control Committee (FGCC, now FGCS) specifications for conventional control surveys, last updated in September 1984, do not specifically address these situations. However, the document does specify that Astronomic Azimuths are required every X number of segments in a traverse, and X number of triangles in a triangulation network, depending on the order of the survey. The azimuths are implied to be polaris azimuths (or other star) by the “Observations per Night” and “Number of Nights” criteria, as well as the standard deviation (0.45” for first order up to 1.7” for third order) required. While this accuracy is certainly important for controlling extensive traverse/triangulation nets, it is much higher than necessary for a short eccentric reduction. The difficulty of working at night, and the unfamiliarity of
using Polaris had the following effects:
• assumed datums, because the surveyor did not have survey orientation to start and end the survey, and therefore did not use the geodetic control
• use of nearby (inaccurate) reference marks for azimuth control
• assuming an azimuth for a traverse starting leg, then rotating the entire traverse to fit the ending coordinates, sometimes including angular blunders in the network
• use of intersection stations (which are third order, and may be subject to movement)
• having to go much further for control for GPS, or using lower order stations All of these resulted in survey networks which were less (sometimes much less) accurate than would have otherwise been possible.
The purpose of this paper is to review the concepts for determining azimuths, particularly astronomic methods, and to give an idea of the accuracies and complexities of each method. The azimuth accuracy required at a distance of 30 m to achieve an accuracy of
0.003 m is 20”, which, as will be shown, is easily obtained using any visible object in space, whether polaris, other stars, sun, moon, or planets, when proper observational and computation procedures are followed. What follows is often a simplification, appropriate to the accuracies discussed. Corrections applied to first order azimuths, such as polar motion, and diurnal aberration, are not considered.
John Hamilton 2 firstname.lastname@example.org Geodetic Engineer 412-341-5620 WHAT IS AN AZIMUTH?
An azimuth is defined as a horizontal angle reckoned clockwise from the meridian. There are several types of "north". Astronomic north is with respect to the astronomic meridian, which varies from point to point in an irregular manner under the influence of gravity. Geodetic north is with respect to the ellipsoidal meridian, which differs from the astronomic meridian by a varying amount. Grid north is with respect to a central meridian of a mapping projection. Finally, magnetic north is the direction of the magnetic field of the earth. This also varies from point to point (and over time) in an irregular manner. The astronomic north is often used (incorrectly) in geodetic computations, although the geodetic north is what is required. The difference between the two (Laplace correction) is due to the deflection of the vertical in the prime vertical, caused by variations in gravity. Actually, the Laplace correction is a function of the east-west slope of the geoid. Astronomic north does have some uses, for example, to align inertial navigation systems. The magnetic declination at a point can be interpolated using a model from the USGS. However, the accuracy of determining geodetic north using a compass is about 1°, at best, and will not be addressed further. This paper will deal with the first three types of north mentioned, namely astronomic, geodetic, and grid, and the relationships between the three. For explanation purposes, P1 is the standpoint (i.e. occupied by the theodolite) and P2 is the forepoint (i.e. occupied by a target).
The astronomic azimuth is defined as the angle measured in the horizontal plane between the astronomic meridian of P1 and the vertical plane spanned by the vertical at P1 and by point P2. This value is physically measurable, and is what we measure when we observe the sun, polaris, or other objects in space using an instrument which measures with respect to the local plumb line (i.e. theodolite). The astronomic azimuth can also be determined by using a gyro-theodolite, such as the Wild GAK-1.
The geodetic azimuth is defined as the angle measured in the horizontal plane between the ellipsoidal meridian of P1 and the vertical plane spanned by the normal to P1 and by point P2.
This appears to be the same as the definition given above for astronomic azimuth. There are two differences, namely the meridian (ellipsoidal versus astronomic) and the vertical (affected by gravity) versus normal (normal to ellipsoid, mathematical quantity) reference.
The geodetic azimuth is what is determined using GPS, but is not directly measurable using any other common survey equipment. However, if one were to sight another survey station, and compute the geodetic inverse, then the resulting azimuth is a geodetic azimuth.
Similarly, this is the type of azimuth required in the “direct” geodetic problem, where it is desired to compute the coordinates of P2, given the coordinates of P1, the geodetic azimuth, and the ellipsoidal distance between the two. Although the difference between the astronomic and geodetic azimuths is usually small, it is important to understand the difference, and know how to transform one to the other when needed.
The grid azimuth is defined as the angle measured in the horizontal plane between the grid meridian (which is parallel to the central meridian of a plane rectangular coordinate system, for example state plane or UTM) of P1 and the vertical plane spanned by the normal to P1 and P2. This is very similar to the definition of the geodetic azimuth. It is possible to convert
AZIMUTHS BY GPSThe Global Positioning System (GPS) can be (and often is) used to establish the azimuth between two points. Code GPS (differentially corrected) gives sub-meter accuracy with proper equipment. Differential Code GPS results in two positions, rather than a vector between the two points. Suppose it is desired to establish a pair of points separated by 500 m, and assume the accuracy of the processed point positions as 0.5 m. The azimuth would then have an uncertainty of almost 4 minutes of arc. However, if carrier phase observations are made, the resulting vector (∆X, ∆Y, ∆Z) would have an accuracy of about 3 seconds of arc. This is true even if the stations are not connected to a control network. However, if, for example, a NAD 1927 azimuth is needed, then it is important to use at least two control stations, since there can be local distortions of up to 10” or more between WGS84 and NAD27. Care must also be taken when using a non geocentric (i.e. local) datum, as the difference in longitude between WGS84 and the local system directly affects the azimuth, and can be computationally corrected.
GYROTHEODOLITESeveral manufacturers make a gyro attachment for a theodolite. The details of its operation can be found in the manufacturers manuals. The gyroscope oscillates about the astronomic meridian through a point, and the location of this meridian can be determined to an accuracy of 20” or better. These instruments are often used in tunneling and mine surveying. The high cost ($25,000 in the mid-80’s) made their common use hard to justify. However, it is now possible to purchase used units for about $4500 (including theodolite).
These instruments are ideal for the short eccentric lines mentioned above, as the accuracy is sufficient, and they work independent of weather.
AZIMUTH MARKS & INTERSECTION STATIONSFirst order triangulation stations were usually set in the US with an azimuth mark, which was simply another mark visible from the ground at least ¼ mile distance. Whenever a prominent landmark object (church steeple, radio tower, etc) was visible from several main scheme stations, observations were also made to them. The azimuth marks and intersection stations are considered third order, and provide azimuth orientation to about 5” to 10”. One of the main problems with using intersection stations is determining if the correct point is being used, and, if so, whether it is in the same position as during the original observations. For example, church steeples are replaced, antennas are added to and modified, etc. In no case should nearby reference marks be used for azimuth control, as that was not the intent when they were established. An examination of triangulation descriptions will find situations where the station was revisited 30 years after the original observations, and discrepancies of a minute or more are found to reference marks.
Due to the simplicity and robustness of the hour angle method, that is the only method to be discussed here. Based on the availability of precise ephemerides, accurate timepieces, accurate observer positions, there is no compelling reason to require Polaris for azimuth observations of 5” accuracy or less. In fact, any object in space, with a good ephemerides, can be used. For accurate observations (better than 5”), it is still recommended that Polaris be used.
TIME Time is the key to an accurate determination of astronomical azimuth. There are many types of time, and several important ones will be discussed here. International Atomic Time (TAI) is a continuous scale resulting from analyses of atomic time standards in many cooperating countries. The fundamental unit is the SI second, which is defined as the duration of 9,192,631,770 cycles of radiation corresponding to the transition between two hyperfine levels of the ground state of Cesium 133. Coordinated Universal Time (UTC) is the time scale available from broadcast time signals, and differs from TAI by an integer number of seconds (+32 seconds since Jan 1, 1999). It is kept close (within ±0.9 seconds) of the actual rotation of the earth (see UT1, below). Local time is really UTC offset by a integer number of hours (here in the US eastern time zone, -4 during daylight savings time, -5 otherwise).