Abstract
Within the last decade in particular, geo-spatial measurement technologies have undergone significant advancement in terms of automation, processing, and levels of accuracy. These developments hold many advantages for archaeoastronomers engaged in the collection and analysis of field survey data. This chapter examines azimuth and location measuring techniques and assesses how some of the recent developments can assist those engaged in such fieldwork.
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Introduction
Field surveys of prehistoric/historic sites and monuments are generally undertaken by archaeoastronomers to enable specific research questions to be addressed within culturally relevant frameworks and agendas. Investigations may, for example, be commissioned by an excavation director where the spatial setting or design of a discovered structure could suggest a function that cannot be explained by the material finds or other archaeological evidence alone (e.g., Prendergast 2012; O’ Connell 2013). In all such cases, the spatial data element must first be recorded and processed to appropriate levels of quality.
Archaeoastronomers invariably come from diverse academic or professional backgrounds outside of (though not exclusively) archaeology. These include astronomy, surveying, engineering, mathematical sciences, science history, and computer science. The acquisition of spatial data, and its subsequent evaluation, can present many challenges. For some, the necessary field or analytical proficiencies may be established, but for most, a degree of specialized training or learning is required to redress a particular skill deficiency. This chapter will focus on field-surveying techniques and computational methods as commonly used during the initial stages of a site survey.
Pioneers of archaeoastronomy used nothing more than a theodolite, chain and compass in the field, and logarithmic tables or analogue calculators for data reduction (e.g., Somerville 1923; Thom 1967). Nonetheless, they achieved high-quality results and their legacies remain valid to this day – at least in terms of accuracy (as distinct from their interpretative outcomes in some cases). Moreover, certain aspects of computational theory and theodolite usage have not significantly changed either since those early surveys. Now, however, the digital revolution in measurement and positioning technologies, terrain modeling methods, mapping products, and landscape analysis software, all demand high levels of technical expertise in order to leverage their full potential. Many of the modern techniques can be complex, and any detailed description of their use is beyond the scope of this chapter. A comprehensive treatment of best surveying practice, and of horizon profile survey and data reduction techniques, has been published by Ruggles (1999, pp 164–171). Additionally, the orientation of visibility measurements has been described by Fraser (1988), and these need not be reconsidered in this chapter. Instead, and particularly for the benefit of those new to this field of study, more recent advances in surveying procedures, and updates to established methodologies where this is appropriate, are described here. Additional information drawn from case studies undertaken by the writer is also given elsewhere in this volume (see Chap. 107, “Irish Neolithic Tombs in Their Landscape”; Chap. 108, “Boyne Valley Tombs”).
Axis Before Azimuth
At the outset, attention is drawn to nomenclature and the terms “orientate/orientation” and “align/alignment”. Here, orientation is taken to mean the measured direction of a structure’s façade or axis with respect to the local meridian (azimuth), while the use of “aligned” is reserved for cases where human intentionality in a monument’s axial direction toward a target is argued. The noun “alignment”, however, can be archaeologically defined as meaning three or more related structures placed in a line. Where these conventions have not been rigorously followed in the literature and “orientation” loosely interchanged with “alignment”, etc., Darvill (2002, p 301) correctly argues “…this is careless usage. All objects and structures will have an orientation whether or not anything is aligned on them”.
The majority of archaeoastronomical surveys are undertaken to initially determine, inter alia, the orientation of a site, monument, or tomb. When combined with location (latitude) and profiles of the local horizon (azimuth and altitude), these data computationally yield astronomical declinations of the indicated positions of prominent celestial bodies of interest – either on the local horizon (rise/set), or of non-horizon events such as a transit phenomenon (see Chap. 30, “Basic Concepts of Positional Astronomy”; Kelley and Milone 2005, pp 9–47). Where combined with the date/period of construction (if known), declination is then commonly used to interpret any potential calendrical link or suspected ritual function in a cultural context.
A monument’s axis is rightly regarded as the most enduring evidence of ancient architectural principles. Often, it functioned as a ceremonial entrance and pathway, and symbolically incorporated formality and power, especially if aligned on a prominent astronomical event or target. It is emphasized here that if deliberate alignment in the past toward any type of target was ever intended (it may not have been), an astronomical explanation is only one of a wide range of possible alternatives. These include an association with ritual topographies, local settlements, burial sites, or resources (see Chap. 25, “Best Practice for Evaluating the Astronomical Significance of Archaeological Sites”).
Structural Axis Definition
The morphological irregularity encountered in entrance passages can often defy any precise attempt to determine their mean axial line. In such cases, the careful positioning of the observer equipped with a handheld compass, theodolite, or gyro station (see section “Gyro Station Techniques”) at one end of the axis line is all that may be required. Provided due care is taken to visually determine the best-fit line through the stones of the passage and entrance, the measured/derived azimuth (see below and section “Astronomical Azimuth Techniques and Instrumentation”) of this line should adequately reflect the axial orientation of that structural element. Subsequently, the calculation of indicated astronomical declination may provide evidence of design or other intent.
In Fig. 26.1, for example, the unroofed/uncovered Neolithic court tomb at Creevykeel, Co. Sligo is shown. Here, the observer was positioned at P and was equipped with a handheld compass and inclinometer (see Fig. 26.2). These instruments were used to measure the magnetic bearing (clockwise direction with respect to local magnetic north) of the tomb axis and the altitude (angular distance above or below the horizon) of points on the distant skyline indicated by the axis, with an accuracy of about half a degree.
The magnetic declination at Creevykeel (angular deviation between magnetic and true north) was calculated using an algorithm obtained from the Irish Meteorological Service and by using the online NOAA magnetic field calculator (http://www.ngdc.noaa.gov/geomag-web/#declination). Both methods determined the declination component of the local magnetic field. The other components (inclination and total force) are not relevant here. Figure 26.2 illustrates the tools used in this type of survey.
It is evident from this survey that the orientation of the tomb suggests neither an interest in the horizon position of the rising sun at the solstices (winter or summer) or at the equinoxes (vernal/autumnal). This leaves open the possibility of a range of alternative interpretations including a random hypothesis (see Chap. 27, “Analyzing Orientations”; Chap. 33, “Lunar Alignments - Identification and Analysis”; Chap. 35, “Stellar Alignments - Identification and Analysis”).
For greater accuracy, the orientation of a line/axis can be numerically determined provided that the planimetric or grid coordinates of the defining points of interest have been measured in the national map projection system (see section “Geodetic Techniques for Azimuth Determination and Location”). This method can also to be applied to deduce the orientation of a building façade, regardless of its size. In Fig. 26.3, for example, the reconstructed architectural elements of a recently discovered Iron Age post enclosure at Lismullin, Co. Meath are shown. The national grid coordinates of all recovered postholes (only the buried sockets survived) were accurately recorded by archaeologists during the excavation by using a geo-referenced total station. This allowed linear regression analysis of the avenue data by the writer to calculate the mean axial orientation and goodness-of-fit of the avenue sides to the best-fit line.
In that analysis, the equation of each best-fit line through the postholes forming the north and south sides of the avenue takes the form
where the direction of each line (m) is the tangent of the angle that the line makes with the positive direction of the x-axis. Because these data points represent plan coordinates (easting or x, northing or y), then 90° – tan-1 m yields the grid bearing (α°) of each avenue side. The respective azimuths (A°) of the lines (avenue sides) are then obtained from
where
and C = meridian convergence (the angular difference between true north and the north grid line) at the location of the site on the Transverse Mercator map projection. All units are in degrees and in the above, \( \Delta \lambda \) is the difference in longitude between the site and the central meridian of the projection, and \( \phi \) is the latitude of the site. Table 26.1 summarizes the method of analysis and includes the correlation coefficients (goodness-of-fit to a straight line) obtained from the site data.
The azimuth of the avenue, the altitude of the indicated horizon, and the latitude of the site were subsequently used to compute the astronomical declination indicated by the entrance avenue to the enclosure.
Astronomical Azimuth Techniques and Instrumentation
The azimuth of any structure, or a baseline, can be obtained from the following:
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Astronomical observations (with respect to the vertical)
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Gyro station observations (with respect to the vertical)
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Geodetic observations of position (with respect to the normal to the local ellipsoid – the mathematical surface that best-fits the geoid/mean sea-level surface)
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Magnetic bearing observations
As previously described, other (indirect) methods of azimuth determination are possible, such as where a plane grid bearing is calculated from measured plane grid coordinates and then corrected for meridian convergence. In addition, azimuth can be computed using geodetic coordinates (of two points) procured from Google Earth imagery.
Astronomical Preliminaries
Field astronomy can present significant challenges for new users in terms of the theory (see Chap. 30, “Basic Concepts of Positional Astronomy”), method of data acquisition (time and angle measurements), and processing. Here, the writer will describe a comparatively simple method which obviates the need to solve spherical equations. It is essential to use an astronomical ephemeris (a tabulation of the precise positions of celestial objects in an orderly sequence for a specified date range). One such ephemeris, and as used in the examples that follow, is MICA (Multiyear Interactive Computer Almanac).
MICA Ephemeris
This low-cost software system is supplied on CD with an excellent instruction manual (U.S. Naval Observatory 1998–2005). It provides high-precision astronomical data in user-specified tabular form for the sun, moon, planets, and 22 bright stars. Semidiameter values of the sun and moon are also determined, as well as their zenith distances (essential if either limb of the sun or moon are observed). The current edition has a computational date range from 1800 to 2050. For any user-specified celestial object sighted with a theodolite, the geodetic location of the observation station and the time of the observation in UT1 scale (see Fig. 26.7) are first entered. The software then returns the relevant azimuth and zenith distance (90° – altitude°) as shown in Fig. 26.4. Complex calculations for azimuth are thus avoided.
Apart from the accuracy of the method, the significant advantage of this approach is in its versatility. For example, if neither the sun nor moon is above the horizon at the time of the survey, or are obscured by cloud cover, then any prominent star or planet that may be visible in the sky can be observed as an alternative. The writer has successfully used both limbs of the moon and the very bright planets and stars for azimuth, especially when these become visible in the daytime or evening sky.
For azimuth determination, correct identification of the celestial object sighted in the field is crucial. Apart from the sun and moon whose identities are certain, this is not necessarily the case with stars and planets. Mistaken identity can easily occur and with disastrous results. Practitioners should therefore exercise maximum care when sighting stars and planets and, ideally, use at least two different celestial objects for error detection purposes. For sky object identification and session planning, the writer has used touch screen astronomy applications (Apps) that are compatible with, for example, the Apple iPad and iPhone. Either “Star Walk” (http://vitotechnology.com/star-walk.html), or “Go Sky Watch Planetarium” (www.gosoftworks.com/), which is freeware (Fig. 26.5), is excellent for this purpose.
Whichever tablet device is used as an aid for field astronomy, a 3 G or 4 G phone SIM card must be installed to obtain geo-referenced sky scenes in real time.
Instrumentation for Field Astronomy
Archaeological sites of interest are invariably remote or located off-road. Where access is difficult, the overall weight of equipment that can be carried to the site becomes a crucial issue. As a general rule, minimal is best. A complete survey will typically record site description, location, orientation, horizon profile, horizon range, and intervisibility with other sites. The equipment inventory will be comprised of a field book, map(s), related literature, theodolite/total station, tripod(s), ranging pole(s), sun filter, stopwatch, measuring tape, torch, camera, and an iPad/iPhone or equivalent (optional). A GNSS (Global Navigation Satellite System) device is also essential for position finding/determination and as a time signal source in UTC (Coordinated Universal Time). Some of these devices are illustrated in Fig. 26.6.
Astronomical Azimuth Techniques
Observing procedures for azimuth determination vary according to the application of the data. For geodetic purposes, azimuth for orientation may require rigorous observing procedures and choice of instrumentation (Bomford 1980; Ghilani 1996). For most archaeoastronomical applications, a final accuracy of several arc minutes is usually satisfactory, and this allows for a relaxation in rigor. Nonetheless, it is prudent to observe data to a higher level of accuracy than what is actually required.
In Fig. 26.7, the writer observed timed transits (hour angle method) of the left/trailing limb of the sun made with the stationary vertical stadia line of the theodolite in order to determine the azimuth of the reference object (RO). The stopwatch was initialized to UTC using the time display on a Garmin GPS60 GNSS receiver. The recorded split times of six horizontal transits of the sun’s limb were then added to the initialization time of the stopwatch in UT1 scale (the astronomical time scale used by MICA to determine azimuth and other astronomical parameters). The difference (correction) between UTC and UT1 is DUT1 (see note in Fig. 26.7).
The full set of observations included three successive observations for time and direction with the theodolite in the face left (FL) position, followed by three similar observations with the theodolite in the face right (FR) position. The set commenced with a FL reading of the direction of the RO and ended with a similar reading on FR. This technique is quick, minimizes movement and handling of the theodolite and filter, and provides adequate redundancy for error checking purposes.
To demonstrate the versatility and simplicity of field astronomy for azimuth using MICA, celestial objects other than the sun’s limb were additionally observed at the test baseline and at different dates. The center and left limb of the sun, various stars and planets, and the moon’s limbs were each used. The resulting azimuths, including those obtained by nonastronomical methods are shown in Table 26.2 (the nonastronomical methods are discussed in sections “Gyro Station Techniques” and “Geodetic Techniques for Azimuth Determination and Location”).
The accuracies shown here demonstrate the level of compatibility and consistency that can be achieved with astronomical, geodetic, and magnetic methods. Although the Roeloff prism is no longer manufactured, it can be procured on the web. The design enables the sun’s center to be directly sighted (this avoids the need for limb corrections), and for the filter to be opened and closed with ease while observing. A low-cost and safe alternative can be simply constructed from an A4 sheet of Baader AstroSolarTM Safety Film (http://www.baader-planetarium.com/sofifolie/sofi_start_e.htm). Instructions for making the filter are included with the pack. With a little practice, the sun’s center can be estimated to near arc minute accuracy with such a filter and by using the cross-hair graduations of the theodolite eyepiece. Both devices are illustrated in Fig. 26.6. Overall, best results are obtained by observing celestial objects with altitudes below about 40°.
Gyro Station Techniques
A gyro station is the combination of a theodolite and a suspended gyroscope. It is primarily designed for underground use, such as in the mining industry, although it has many other applications. All types use a suspended spinning gyro-motor/rotor which precesses in the horizontal plane due to the rotation of the earth and the effect of gravity. At any location below about latitude 75°, it will precisely define (1˝–20˝ depending on the model) the direction of the local meridian on the horizontal circle of the theodolite. This allows for the azimuth of any observed target or line to be easily determined (see Fig. 26.8b). A gyro station has many potential advantages, especially when used for rapid or high-accuracy orientation surveys such as inside a burial chamber, a tomb, or a building. Provided cost and availability are not an issue, its use is a viable alternative in situations where a view of the sky for astronomical or satellite measurement is not possible. Sources of further information on these instruments are given in Table 26.3.
Geodetic Techniques for Azimuth Determination and Location
GNSS receivers are now routinely used for a wide variety of positioning, mapping, and navigation tasks. They also disseminate time in UTC scale. Each of these properties makes them indispensible tools for archaeoastronomy. Applications include measuring the locations of sites/points of interest and baseline stations in three dimensions; deriving azimuths as an alternative to astronomical, gyro station, or magnetic methods; and navigating to predetermined locations in wilderness areas. Primarily, there are two types in common use, that is, high-cost survey grade receivers capable of delivering sub-centimeter levels of relative positional accuracy (Fig. 26.8a) and low-cost autonomous code-only receivers (Fig. 26.8c). The latter can deliver an instantaneous positional accuracy in plan to better than 10 m in an open sky environment. With position averaging over an extended period of time (c. 5 min), and with good satellite visibility (c. 10 satellites), the code-only type instrument can achieve an improved horizontal accuracy of up to 1–2 m. This capability makes both of these devices especially useful for azimuth determination.
With a GNSS receiver, geodetic coordinates (latitude and longitude) are determined on a mathematical model/datum, such as the WGS84 ellipsoid, of the global geoid. The direction of the shortest line between any two points on this surface (the geodesic) defines the geodetic bearing of such a line. Globally, the difference between a geodetic bearing and azimuth is extremely small (up to a few arc seconds). This permits a geodetic bearing that is calculated from a pair of coordinates to be equated for most applications (including archaeoastronomy) to azimuth as obtained by astronomical methods or with a gyro station. On a cautionary note, the accuracy of any geodetic bearing is a function of the accuracy of the relevant baseline coordinates. In turn, this is dependent upon the system/method of GNSS surveying used, that is, with a Network Real-Time Kinematic (NRTK) or any other differential system, or with a code-only handheld receiver. NRTK methods provide precise positional correction data in real time but require the user to have licensed access to a suitable broadcast infrastructure (Martin and McGovern 2012). Further information on this, and on the providers of these systems throughout Europe, is given in Table 26.4.
Azimuth and distance are now easily and precisely computed from measured/given GNSS coordinates (expressed in degree format) with the aid of online calculators. The majority of these use Vincenty’s formulae (inverse method) which is a high-precision tool (Vincenty 1975). The accuracy of the derived azimuth is a function of the longitudinal and lateral position errors in the baseline coordinates and the distance between the terminal stations. Longitudinal errors (in the direction of the baseline) have no effect on azimuth accuracy. Lateral errors (at right angles to the baseline) will have maximum effect on azimuth accuracy, and this is modeled in Fig. 26.9 using three levels of assumed error. It is shown, for example, that for a lateral error of 0˝.1 in the coordinates (one tenth of an arc second), the resulting error in azimuth will likely not exceed about 6 min of arc for a baseline length of about 1 km. At a range of 2 km, this reduces to about 3 min of arc. It should be appreciated that 1 arc sec at the equator is the equivalent of c. 30 m on the ground. Thus, for sub-centimeter levels of accuracy, an NRTK receiver will display geodetic coordinates to ±00′′.00001 which is consistent with millimeter precision (see Table 26.6).
For verification of the modeling shown in Fig. 26.8, data was recorded at five suitably spaced stations on test baselines using a Trimble 5800 series antenna with a TSC3 logger operating in NRTK mode and a Garmin GPS60 device. The results of these tests are shown in Table 26.5. Because of their very high relative accuracy, the NRTK values can be effectively regarded as error free for comparative purposes.
These tests broadly confirm the modeling shown in Fig. 26.9. The calculation of azimuth from geodetic coordinates computed with data for the longest baseline (data-line 5 in Table 26.5) is given in Table 26.6 as an example.
The online calculators tested here for the calculation of azimuth are given in Table 26.7.
The use of these techniques will facilitate azimuth calculation with ease and reliability from field coordinates recorded to an appropriate level of accuracy.
A Tomb with a View: Synthesis and Conclusion
In the north-east midlands of Ireland, the clustered Neolithic passage tomb complex at Loughcrew consists of 31 monuments distributed on three prominent hilltops (Prendergast 2011). Three kilometers to the south-east of Cairn T, which is the highest in the distribution, an additional ruined isolate of this type is located on lower ground in the townland of Thomastown. Sufficient stones of the passage have survived to allow the passage axis to be approximately defined. A preliminary survey undertaken by the writer indicated the tomb (as like others in the complex) to be aligned toward the elevationally higher focal summit tomb (Cairn T). An orientation and profiling survey was subsequently undertaken to investigate this phenomenon, and any potential astronomical event of significance at this site. For this, the astronomical azimuths and altitudes of multiple natural points on the horizon were observed with a theodolite. Using these as control, the horizon image was transformed in ArcMap 10 (a component of ESRI’s ArcGIS software) from arbitrary to a local topocentric horizon coordinate system (azimuth and altitude). A minimum of three observed control points are required for this type of transformation (five were used). Figure 26.10 shows the resulting gridded image.
Computation of the indicated astronomical declination of the summit tomb (see Fig. 26.10) suggested that a sunset phenomenon would also occur at the period of summer solstice. A revisit to the site observed and confirmed the expected phenomenon (Fig. 26.11).
In the Neolithic, the setting sun would have appeared tangential with the burial cairn when viewed from the tomb at Thomastown. This is due to the effect of obliquity (tilt of the earth’s axis) change in the intervening 5,000 years. Perhaps, this tomb exhibits evidence of a mingling of two culturally relevant phenomena, that is, an apparent significant astronomical alignment and an alignment that is directed at the elevationally higher and focal Cairn T at the center of the Loughcrew complex (see Chap. 24, “Nature and Analysis of Material Evidence Relevant to Archaeoastronomy”). Such a hypothesis typifies the kind of research question that confronts all archaeoastronomers, and which is addressed by this and other writers elsewhere in this volume.
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Prendergast, F. (2015). Techniques of Field Survey. In: Ruggles, C. (eds) Handbook of Archaeoastronomy and Ethnoastronomy. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6141-8_31
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