Elements Of Astronomy For Surveyors
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There are many variations of reticle pattern; this article concerns itself mainly with the most rudimentary reticle: the crosshair. Crosshairs are typically represented as a pair of perpendicularly intersecting lines in the shape of a cross, "+", though many variations of additional features exist including dots, posts, concentric circles/horseshoes, chevrons, graduated markings, or a combination of above. Most commonly associated with telescopic sights for aiming firearms, crosshairs are also common in optical instruments used for astronomy and surveying, and are also popular in graphical user interfaces as a precision pointer. The reticle is said to have been invented by Robert Hooke, and dates to the 17th century. Another candidate as inventor is the amateur astronomer William Gascoigne, who predated Hooke.
The first suggestion for etched glass reticles was made by Philippe de La Hire in 1700. His method was based on engraving the lines on a glass plate with a diamond point. Many modern crosshairs are actually etched onto a thin plate of glass, which allows a far greater latitude in shapes. Etched glass reticles can have floating elements, which do not cross the reticle; circles and dots are common, and some types of glass reticles have complex sections designed for use in range estimation and bullet drop and drift compensation (see external ballistics). A potential disadvantage of glass reticles is that the surface of the glass reflects some light (about 4% per surface on uncoated glass) lessening transmission through the scope, although this light loss is near zero if the glass is multicoated (coating being the norm for all modern high quality optical products).
Land surveyors measure horizontal positions in geographic or plane coordinate systems relative to previously surveyed positions called control points. In the U.S., the National Geodetic Survey (NGS) maintains a National Spatial Reference System (NSRS) that consists of approximately 300,000 horizontal and 600,000 vertical control stations (Doyle,1994). Coordinates associated with horizontal control points are referenced to NAD 83; elevations are relative to NAVD 88. In a Chapter 2 activity, you may have retrieved one of the datasheets that NGS maintains for every NSRS control point, along with more than a million other points submitted by professional surveyors.
You might wonder how a control network gets started. If positions are measured relative to other positions, what is the first position measured relative to? The answer is: the stars. Before reliable timepieces were available, astronomers were able to determine longitude only by careful observation of recurring celestial events, such as eclipses of the moons of Jupiter. Nowadays, geodesists produce extremely precise positional data by analyzing radio waves emitted by distant stars. Once a control network is established, however, surveyors produce positions using instruments that measure angles and distances between locations on the Earth's surface.
For these reasons, land surveyors rely on transits (or their more modern equivalents, called theodolites) to measure angles. A transit consists of a telescope for seeing distant target objects, two measurement wheels that work like protractors for reading horizontal and vertical angles, and bubble levels to ensure that the angles are true. A theodolite is essentially the same instrument, except that some mechanical parts are replaced with electronics.
To achieve this level of accuracy, surveyors must overcome errors caused by faulty instrument calibration; wind, temperature, and soft ground; and human errors, including misplacing the instrument and misreading the measurement wheels. In practice, surveyors produce accurate data by taking repeated measurements and averaging the results.
To measure distances, land surveyors once used 100-foot long metal tapes that are graduated in hundredths of a foot. (This is the technique I learned as a student in a surveying class at the University of Wisconsin in the early 1980s. The picture shown below is slightly earlier.) Distances along slopes are measured in short horizontal segments. Skilled surveyors can achieve accuracies of up to one part in 10,000 (1 centimeter error for every 100 meters distance). Sources of error include flaws in the tape itself, such as kinks; variations in tape length due to extremes in temperature; and human errors such as inconsistent pull, allowing the tape to stray from the horizontal plane, and incorrect readings.
Since the 1980s, electronic distance measurement (EDM) devices have allowed surveyors to measure distances more accurately and more efficiently than they can with tapes. To measure the horizontal distance between two points, one surveyor uses an EDM instrument to shoot an energy wave toward a reflector held by the second surveyor. The EDM records the elapsed time between the wave's emission and its return from the reflector. It then calculates distance as a function of the elapsed time. Typical short-range EDMs can be used to measure distances as great as 5 kilometers at accuracies up to one part in 20,000, twice as accurate as taping.
Surveyors have developed distinct methods, based on separate control networks, for measuring horizontal and vertical positions. In this context, a horizontal position is the location of a point relative to two axes: the equator and the prime meridian on the globe, or x and y axes in a plane coordinate system. Control points tie coordinate systems to actual locations on the ground; they are the physical manifestations of horizontal datums. In the following pages, we review two techniques that surveyors use to create and extend control networks (triangulation and trilateration) and two other techniques used to measure positions relative to control points (open and closed traverses).
Errors produced in an open traverse, one that does not end where it started, cannot be assessed or corrected. The only way to assess the accuracy of an open traverse is to measure distances and angles repeatedly, forward and backward, and to average the results of calculations. Because repeated measurements are costly, other surveying techniques that enable surveyors to calculate and account for measurement error are preferred over open traverses for most applications.
The surveyors next measure the interior angles CAB, ABC, and BCA at point A, B, and C. Knowing the interior angles and the baseline length, the trigonometric "law of sines" can then be used to calculate the lengths of any other side. Knowing these dimensions, surveyors can fix the position of point C.
Trilateration is an alternative to triangulation that relies upon distance measurements only. Electronic distance measurement technologies make trilateration a cost-effective positioning technique for control surveys. Not only is it used by land surveyors, trilateration is also used to determine location coordinates with Global Positioning System satellites and receivers.
Former student, Henry Whitbeck, (personal communication, Fall 2000) points out that surveyors also use total stations to measure vertical angles and distances between fixed points (prisms mounted upon tripods at fixed heights), and then calculate elevations by trigonometric leveling.
CORS and OPUS: The U.S. National Geodetic Survey (NGS) maintains an Online Positioning User Service (OPUS) that enables surveyors to differentially-correct static GPS measurements acquired with a single dual frequency carrier phase differential receiver after they return from the field. Users upload measurements in a standard Receiver INdependent EXchange format (RINEX) to NGS computers, which perform differential corrections by referring to three selected base stations selected from a network of continuously operating reference stations. NGS oversees two CORS networks; one consisting of its 600 base stations of its own, another a cooperative of public and private agencies that agree to share their base station data and to maintain base stations to NGS specifications.
Land surveyors use specialized instruments to measure angles and distances, from which they calculate horizontal and vertical positions. The Global Positioning System (and, to a potentially greater extent, the emerging Global Navigation Satellite System) enables both surveyors and ordinary citizens to determine positions by measuring distances to three or more Earth-orbiting satellites. As you've read in this chapter (and may know from personal experience), GPS technology now rivals electro-optical positioning devices (i.e., "total stations" that combine optical angle measurement and electronic distance measurement instruments) in both cost and performance. This raises the question, "If survey-grade GPS receivers can produce point data with sub-centimeter accuracy, why are electro-optical positioning devices still so widely used?" In November 2005, I posed this question to two experts--Jan Van Sickle and Bill Toothill--whose work I had used as references while preparing this chapter. I also enjoyed a fruitful discussion with an experienced student named Sean Haile (Fall 2005). Here's what they had to say:
In relative terms, over a local area, using good procedures, it is certainly possible to say that an EDM can produce results superior to GPS in orthometric heights (levels) with some consistency. It is my opinion that this idea is the reason that it is rare for a surveyor to do detailed construction staking with GPS, i.e. curb and gutter, sewer, water, etc. On the other hand, it is common for surveyors to stake out property corners with GPS on a development site, and other features where the vertical aspect is not critical. It is not that GPS cannot provide very accurate heights, it is just that it takes more time and effort to do so with that technology when compared with EDM in this particular area (vertical component). 2b1af7f3a8