Accurate methods of position location and site mapping are issues of great concern with regard to site interpretation and relocation. This is particularly true for archaeologists working on underwater sites (even more so than terrestrial archaeologists) given the fact that there are no readily visible landmarks on which they can rely. Differential Global Positioning Systems (DGPS) offer archaeologists a means to accurately locate and map sites in an economical manner; however, some ongoing projects may be reluctant to utilize this method due to the fact that it can be difficult to access and correlate data previously obtained utilizing the traditional method of position location, that is sextants and beach markers, with new data obtained utilizing DGPS. The solution to this problem comes from a source that may surprise many archaeologists, that is, the commercial salvage community for whom these problems are similar, Salvors, Inc., The company contracted to salvage the wrecks to the 1715 fleet as part of the Florida East Coast Shipwreck Project, was greatly concerned with the question of accessing and correlating old data with the new, a problem that would be faced by any ongoing, long-term archaeological project. accordingly, Salvors, Inc., utilized triangulation based mathematical computations to locate the beach marker positions for each previous year of the project. utilizing this information, Ken Nehiley, a subcontractor for Salvors, Inc., was able to write a computer program that converts the sextant angles into latitude and longitude coordinates, and Bill Moore, the former laboratory conservator for Salvors, Inc., was then able to coordinate several computer programs in order to convert and map the locations of both the old sextant data and the new DGPS data. The resulting methodology is outlined in this paper, and once familiar with the process, the archaeologist can utilize this procedure to produce accurate site maps and artifact locations quickly and efficiently. Additionally, it will enable the project to utilize DGPS as a means of position location; a means that is less time consuming, easier, and as accurate as traditional methods.

    For a number of years Salvors, Inc., and the State of Florida's division of Historical Resources have been discussing changing the position location system for the Florida East Coast Shipwreck Project from the localized beach marker and sextant angle system to differential Global Positioning System (DGPS). With the decline in cost of differential signal receivers and GPS units (less than $1000 for both) and the availability of a free differentially corrected satellite signal from the Coast Guards Continuously Operating Reference Station (CORS) at Cape Canaveral, the decision was made that it was financially feasible to make such a change. The accuracy level of the equipment was another factor to be considered in this process. Research by Salvors, Inc., demonstrated an accuracy level of Garmin GPS receivers and GBR 21 differential signal receivers of potentially one meter if the readout is in degrees and decimal degrees (The accuracy in degrees, minutes, and seconds readout mode is three meters or 9.8 feet and in degrees, minutes, and decimal minutes is approximately two meters or six feet). The Garmin units readout to a level of five decimal places in the degrees and decimal degrees mode, which is approximately three feet. The other part of this is the accuracy of the differential signal broadcast from the Cape Canaveral station. according to Lieutenant Commander Gary Schenk, the officer in charge of the DGPS Management Division of the Coast Guard, the signal from Cape Canaveral is broadcast at an accuracy level of 2.5 meters (8.2 feet) 95% of the time within 100 nautical miles of the station and 3.5 meters (11.5 feet) 95% of the time for the next 100 nautical miles. Additionally, he stated the coast Guard had plans to update the CORS at cape Canaveral to an accuracy level of one meter within 100 nautical miles of the station and two meters for the next 100 nautical miles (Schenk, personal communication 1997). Two hundred nautical miles is the limit of the range of the signal from Cape Canaveral. Salvor, Inc., manually tested the accuracy of the equipment by taking both DGPS and sextant readings on site locations and comparing the results. The results demonstrated a consistent accuracy level of between three and seven meters (9.8 and 22.9 feet). The readings were taken in degrees, minutes, and decimal minutes (potential accuracy level of approximately 6 feet), and it was necessary to convert the data from NAD 83 to NAD 27 in order to match the base map plots of these locations done for the State of Florida's Division of Historical Resources (Gaither 1996). Given the error factor inherent in converting data and the numerous potential error factors of the beach marker and sextant system, it was agreed by both Salvors, Inc., and the State of Florida's Division of Historical Resources that DGPS readings taken utilizing the relatively inexpensive Garmin equipment are acceptably accurate. This being the case, there remained only one obstacle to changing to DGPS as a means of position location.

    While the DGPS readings were acceptably accurate, Salvors, Inc., and the State archaeologists were concerned about being able to access old data taken utilizing the sextant and beach marker system and plot it with the new data in DGPS readings so that overall artifact dispersal patterns could be demonstrated. The mathematics to make the conversion from beach marker and sextant readings to X and Y coordinates were already known to Salvors, Inc., as Bill Moore had utilized a CAD-like program called Key 3-D to crate a conversion program for one set of data at a time. The X and Y coordinates were then overlaid on a map of UTM lines created by Mr. Moore to create a plotted map of the location. The problem was that it could not be done for numerous readings at one time, and the UTM lines were simply a grid laid out to match the base maps created by the State's Division of Historical Resources. They were not tied in to any globally recognized grid system and the plotting feature was based on X and Y coordinates from a zero point, not actually UTM coordinates. The task of creating a computerized method of plotting batch data from any year of all years on any of the 11 sites in the Florida East Coast Shipwreck Project proved to be a daunting one, and its methodology is the focus of this paper.

    The problem facing both Salvors, Inc., and the State archaeologists was three-fold. First the beach markers, which had been surveyed in by State archaeologists over some 13 years of operations, had to be mathematically located in terms of some global system, that is latitude and longitude or UTMs or state plane coordinates. Second, a computer program had to be designed that could access the correct set of beach markers for each site and year, choose the correct markers for each sextant reading in a batch of readings that may span several years and different markers for each site, and mathematically calculate the global coordinates of each reading. Third, a computerized method of mapping these calculations had to be developed. Finances were a major concern as the State was limited with the funding it had available as was Salvors, Inc. Thus, Salvors, Inc., decided to pursue the goal of creating this methodology utilizing the staff available and by drawing from the variety of experience and knowledge available from the subcontractors who contract with Salvors each year to work these sites. With the cooperation and help of State archaeologist Jim Dunbar, Salvors, Inc., staff archaeologist Catherine Gaither, conservator Bill Moore, and subcontractor Ken Nehiley were able to put together a means of converting the old sextant and beach marker data to global coordinates. The process was done in three stages, which are described in the following pages.

    The mathematical conversion of the beach marker locations to a global system was a task that required utilizing 13 years worth of field notes provided by Jim Dunbar, and re-plotting the beach marker location in order to demonstrate their position to know benchmarks. The methodology used by Mr. Dunbar to shoot in the beach markers was one of transit and theodolite shots taken from known benchmarks shot in by the Department of Natural Resources. After locating a benchmark, Mr. Dunbar would take a distance reading to the next benchmark to the north or south depending on the direction he was moving (shots were usually to the north). Using this line as a zero line, he would then take an angle and distance reading out to an arbitrary position on the beach. This location would become the beach station from which he would shoot in the location s of the beach markers. After moving to the beach station, Mr. Dunbar would take a backshot on the benchmark from which he had started. He would then set up a zero line, usually relatively parallel with the beach, and shoot angles and distances to each of a varying number of beach markers for each site (Dunbar 1997). It should be noted that this is a simplified version of the process, and as most archaeologists are aware, a variety of field conditions may necessitate variations in the methodology. Variations did occur, however, for the purposes of describing this process, the simplified version will be used as the norm. The mathematics involved in the conversion of these locations to global coordinates is basic trigonometry; however, the process can become confusing as it is important to note the triangles that are formed and specifically which angles and distances are being calculated during any one step. Figure 1 presents one simple beach marker location, and the math used to calculate its location is presented in the steps following the figure. This demonstrates the basic calculations that are necessary. Other variations are possible, and thus, the total range of trigonometric calculations utilized in this stage is presented following this example.
 Figure 1: Beach Marker Location & Necessary Calculations

While this admittedly doesn't look very simple, it does represent the simplest set of calculations that had to be completed in this stage of the process. The following equations are given in order of completion:

1. (Distance a)2= (distance between both benchmarks)2 + (the distance between the starting pint benchmark and the beach station)2 - 2 X (distance between both benchmarks) X (the distance between the starting point benchmark and the beach station) X (cosine of the know Angle A). Distance a = the square root of (Distance a)2

The basic formula for this process is when give two known distances of a triangle, a and b, and a known angle in between, Angle A, the following is true when trying to find the unknown distance c: a2 + b2 - 2ab cos A = c2

2. To find Red A, let the following be true: a = a b = the distance between the two benchmarks c = the distance between the starting point benchmark and the beach station s = (a + b + c)/2 Given this: the Sin of 1/2 Red A = Ö(s - a)(s -c)/ac Once the square root of (s - a)(s - c)/ac is calculated take the Asin of the answer and multiply by 2 to get Red A.

3. To find Red B, simply take angle B - Angle C.

4. To find distance b, simply utilize the formula given in Step # 1. There are two known distances, the distance between the beach station and the marker, and the distance between the beach station and the starting point benchmark. Take the squares of both of these distances and add them together then subtract 2 times these two distances multiplied together multiplied by the cosine of Red B. The take the square root of that answer, which equals Distance b. Distance b is the distance between the beach marker and the starting point benchmark.

5. To find Red C, simply take Red B - Red A.

6. To find distance c, utilize the formula given in Step # 1. There are two known distances, the distance between the beach station and the beach marker, and the distance between the beach station and the second benchmark, which is Distance a. Square the two distances and add them together, then subtract 2 times the two distances multiplied together multiplied by the cosine of Red C. Take the square root of the answer, which is Distance c.

7. To find Red D, let the following be true: a = the Distance b b = the distance between the two benchmarks c = Distance c s = (a + b+ c)/2 given this the Sin of 1/2 of Red d =Ö(s - b)(s - c)/bc Once the square root of (s - b)(s - c)/bc is calculated, take the Asin of that number and multiply the answer by 2 to get Red D.

8. To find Red e, simply use the same formula in Step # 2, substituting the appropriate distances from Step # 7. Take the square root of (s -a)(s - c)/ac, then take the Asin of that answer and multiply it by 2 to Red E.

9. To find Red F, simply take 180 - (Red D + Red E).

10. To find Red G, let the following be true: a = the difference in longitude between the two benchmarks c = the know distance between the two benchmarks, represented in the figure by the black line between the two. Given this, the Sine of Red G = a/c. Take the Asin of the answer to get Red G.

11. To find Red H, simply take Red G - Red F.

12. To find X, take Distance b X cosine of Red F.

13. To Find Y, take Distance b X sin of Red F.

14. The final steps are to add Y to the longitude of the starting point benchmark and add X to the latitude of the starting point benchmark. Remember that longitudes increase as they go from east to west, but this may be different if UTMs or state plane coordinates are being used. Also note that this step may change to subtracting the numbers or a mixture of subtracting one and adding the other if the position of the marker is different than that represented in Figure 1.

Right Triangle Formulas | Oblique Triangle Formulas

    This was undoubtedly the most difficult portion of this project as it involved integrating a number of functions in one computer program. Mr. Ken Nehiley, a subcontractor with Salvors, inc., working on the 1715 sites, inquired about the project, and after discussing it with a friend of his, Mr. Al Tello who owns a survey company, they decided it could be done. Salvors, Inc., and the state of Florida's division of Historical Resources provided them with the information they needed to complete this stage. The problem in and of itself is complex for several reasons. As mentioned before, the location of the markers on each site changed from year to year. Additionally, none of the beach markers were ever in a straight line as might be expected due to the terrain. finally, the beach markers used for any one sextant shot might or might not be three adjacent markers. Thus, Mr. Nehiley and Mr. Tello had a very complex problem to solve. They had to create a program that would pick the correct beach markers from the correct year and then use those locations in conjunction with the sextant angles to perform a series of 21 formulas that include complex trigonometric functions on several data at once.

    Mr. Nehiley found that many computer programs were unable to perform the complex functions necessary to complete this process. After working with numerous programs, he decided to try Microsoft Excel, and found that it was able to perform all of the functions necessary, including the choice of the beach marker. The program is basically set up so that material from any site can be imported and pasted into the appropriate sections, but it is probably easier to have a page with these calculations in place for every site. In this manner, the beach marker locations fro every year on that site remain a constant on that page, and only the material to be plotted needs to be imported. With the beach marker locations in place, the data is imported and the calculations are completed. The beach marker selection is basically an "If, Then" function. If the data in a certain field reads A and the year is 1987, then the beach marker location is the data in the field that contains the location information for marker A, 1987. While this is the basics, it should be noted that the language to accomplish this is very complex, considering there may be several hundred possibilities. The calculations for converting the sextant angles are equally complex. Figure 3 presents a model, and the calculations that follow the figure demonstrate how this process is accomplished.
Figure 3: Model for Sextant Calculations
    With regard to the model present in Figure 3, the artifact location represented by the symbol 0 is actually the location of the data recorder who is using a sextant to shoot the angle between marker 3 marker 2, represented by M1, and the angle between marker 2 and marker 1, represented by M2. Thus, the givens in this process are M1, M2 and the beach marker locations. Everything else is calculated in the order presented below with the end goal being the coordinates of 0 (0n, 0e):
 

1. D = Atan[(3e - 2e)/(3n -2n)] Note: 3e - 2e = Ee, 3n -2n = En

2. C = Atan[(1n - 2n)/(1e - 2e)] Note: 1n =2n = Cn, 1e - 2e =Ce

3. A = 2Pi - (Pi/2) - C - D or 3600 - the 900 between C and D, and then - C - D

4. S = Pi - 1/2(A + M1 + M2)

5. Cn = ABS(1n - 2n)

6. Ce = ABS(1e - 2e)

7. En = ABS(2n - 3n)

8. Ee = ABS(2e - 3E)

9. t = Ce/Cos C

10. u = En/Cos D

11. f = Atan [(u sin M2)/t Sin M1)]

12. D = Atan [(1/Tan(f + pi/4) Tan S)]

13. X = S + D

14. E = Atan (En/Ee)

15. F = Pi - X- E, Note Pi = 1800

16. B = Pi - M1 -X

17. H = [u(Sin B)/Sin M1]

18. Fn = h(Sin F)

19. Fe = h(Cos F)

20. 0n = 3n + Fn

21. 0e = 3e + Fe

Note that the symbols in the calculations above that are not represented in the model are the functions designed to compensate for the fact that the beach markers are not in a straight line. These calculations yield the coordinates for the artifact location in whichever coordinates are chosen, that is latitude and longitude, UTMS or state plane coordinates. It should be noted that if latitude and longitude are used, the coordinates entered for calculation must be in a whole number, and thus, they would have to be in degrees and decimal degrees. Excel does not recognize degrees, minutes and seconds for calculation purposes, nor does Auto Cad for plotting purposes. For this reason, if DGPS readings are taken in degrees, minutes, and decimal minutes, or degrees, minutes, and seconds, those numbers will have to be converted into a whole number. This can also be done by batch in Excel. If, for example, the readings are taken in degrees, minutes, and seconds, and they are entered in one column of a spreadsheet program, with the numbers separated by spaces, rather than having separate columns for each, Excel has a feature that allows a single column to be separated into several different columns at certain tag indicators. One tag is the presence of a space. From there, the minutes column is divided by 60, and the seconds column is divided by 3600. The answers produced by these calculations are then added together and that answer is added to the degrees column, which remains unchanged. This yields a whole number in degrees and decimal degrees. If Microsoft Access is used as the spreadsheet program into which the raw data are entered, that data can be imported directly into Excel. Once all of these calculations are complete, the next stage is that of plotting the coordinates.

STAGE THREE: PLOTTING THE DATA

    The final stage is to plot the data, and once again, there are numerous variables to be considered. Mr. Bill Moore, conservator for Salvors, Inc., devised the methodology for plotting the data in Auto Cad Lite by manipulating the data through various other programs depending on what I desired as an end result. One of the considerations in this process is what coordinates are desired in the end, and according to which North American Datum (NAD), that is, NAD 27, NAD 83, WGS 84 or some other. These refer to benchmarks that have been surveyed through the years in the United States. Thus, NAD 27 refers to benchmarks surveyed in 1927, NAD 83 are those surveyed in 1983 and so on. The State of Florida's Division of Historical Resources has through the years produced base maps for these sites, with the beach markers in place, that are drawn according to NAD 27 surveys. With the change to DGPS, the most accurate way of receiving the data on the Garmin equipment is to set the receiver to receive according to the same datum surveys that the signal is broadcast in, that is, if the differential signal is broadcast in NAD 83, the receiver should be set to receive in NAD 83. If it is not, there is a slight error factor in the readings. Most differential signals are broadcast in NAD 83 or WGS 84. The signal from Cape Canaveral is broadcast in NAD 83 (Schenk, personal communication 1997). data can be easily manipulated between these various datums by utilizing a program available at no cost on the Internet. Corpscon version 4.0 is available at the National Oceanic and Atmospheric Administrationís (NOAA) website. It converts latitude and longitude, UTMs, and state plane coordinates for any state in the U.S. into any other of these coordinates, and it converts NAD 27 data into NAD 83 data and vice versa. Thus, if the coordinates are in UTMs, NAD 27, and need to be converted into latitude and longitude, NAD 83, Corpscon will do the conversions. These can be done in batches as well. The first step in this process is to create an ASCII file by creating a mail merge catalog in Microsoft Word utilizing queried data from a Microsoft Access or Excel spreadsheet. The file created should be saved in the Corpscon file or the program will not recognize the file. Following the instructions in Corpscon, the data can be converted as a batch, and it will be saved as an ASCII file, which can be imported into either Access or Excel. Thus, the data can be converted to any desired coordinate system. It should be noted, however, that there is an inherent error factor in converting any data. While this may be slight, the most accurate way to plot these data is to avoid conversions. Therefore, new data collected by means of DGPS will be most accurate if taken in whole numbers, i.e. degrees and decimal degrees, UTMs, or state plane coordinates, in NAD 83 or WGC 84, and plotted into Auto Cad directly without any conversions. Conversions on the old sextant and beach marker data cannot be avoided due to the nature of the original data; however, the answers should be provided in the desired plotting format to avoid having to make more conversions. To do this, the beach marker locations have to be in the desired coordinate system and North American Datum in the Excel calculations of Stage 2. Provided there is no need for conversions after the calculations in Stage 2 are completed, an ASCII file is created with the Microsoft Word mail merge feature and the resulting file is imported into Auto Cad Lite for plotting.

    Auto Cad Lite is a somewhat complex program, although not as complex as the full Auto Cad program. the advantages of Auto Cad Lite are that it allows for what is considered basic mapping by the surveyors who utilize the full auto Cad program as well as multiple layers of plotting. Thus, a digital map of the shoreline of the area of a site can be imported and plotted as one layer, and the data can be plotted on top of this layer. auto Cad Lite also allows for data layers to be "turned on or off" so that all of the data can be plotted, and then if, for example a map of only the copper artifacts is desired, the other data layers can be "turned off" and the result will only show those specific artifact locations for which the layers are left "on". Furthermore, maps of larger and smaller scales can be produced so that a map of a very large scale demonstrating artifact dispersal patterns and a map of a smaller scale, perhaps demonstrating alcove-up of a specific area of debris, can be produced from the same plotted data. This is done by zooming in or out on an area and saving that as a file for plotting or plotting it directly from the screen. Figure 4 demonstrates a map showing artifact locations plotted with Auto Cad Lite. Note that the digital map of the coastline of these sites, so graciously provided by State archaeologist Jim Dunbar, is not visible in this figure. This fact illustrates one of the disadvantages of Auto Cad Lite. There are several nuances of this program, and probably other CAD programs in general, that Salvors, Inc., has yet to master. One of these is changing the coordinate system from the state plane coordinates of the map provided by the State to the latitude and longitude coordinates preferred by Salvors, Inc. Another is the fact that it is possible to label artifacts, but this has to be done at a certain stage in the creation of a file, and this was unknown to Salvors, Inc., when it was setting up these initial files. One more is the fact that text boxes can be created and text typed in, but the specific magic required to save those boxes and make the text print out is yet to be discovered. All of these problems are more than likely easily remedied; it is just a matter of learning the program. This does, however, demonstrate that it might be advantageous to have someone well versed in Cad programs help with the initial set up, if at all possible. In the case of Salvors, Inc., this was not possible, and while Mr. Moore did an excellent job in learning a program with which he had absolutely no familiarity, he has since left the company to start his own buiness, and thus, new staff members are having to suffer through the process of learning a new program designed, more or less, specifically for professional surveyors, architects, and the like.

Figure 4: Map of a Specific Artifact Area

SUMMARY OF EQUIPMENT NEEDS

    The equipment needed to utilize this process is mainly computer equipment. Of course, if DGPS readings are still being taken, a GPS receiver, a differential receiver, and a differential antenna as well as access to a differential signal are required. The Garmin equipment described in the introduction can be purchased for under $1000, and the signal from the Coast Guardís CORS is free. All that is necessary to receive the signal is to obtain the signal frequency from the Coast Guard. They also provide this information free of charge. A computer with a least a 1 GB hard drive and at least 16 mg ( preferably 32 mg) of RAM is needed to run all of the programs in this process. unless the computer is dedicated solely to this process, the more memory and hard drive space available, the better. Fortunately, computers providing all of this and more have declined in price in recent months, and thus, a project should be able to purchase a suitable computer for anywhere from $1500 to $2500. Additionally, many computers come with Microsoft Office already installed. In order to get the Microsoft programs necessary for this process, Word, Access, and Excel, the professional edition of Microsoft Office is required, unless each of the programs are purchased separately. Once again, with impending release of Word, the "glitch-free" version of Microsoft Office 97, the professional edition, is available on some Internet sites for under $100. If conversions are necessary, Corpscon version 4.0 can be downloaded off the Internet at no charge. Thus, all of the equipment required for this process, given that the project is ongoing, can be purchased for under a total cost of $4000, and less if some of the necessary equipment is already available, as is probably the case with computers.

DISCUSSION

    The complexities involved in changing to DGPS as a means of position location, although daunting, are outweighed by the advantages of utilizing DGPS for position location and site maps. The 1997 season was the first season in which DGPS was used for this purpose on the wrecks of the 1715 fleet, and all of the subcontractors have remarked that it is far easier than the old sextant and beach marker system. Additionally, it is the belief of Salvors, Inc., that it is, in effect, a more accurate means of position location because it has less room for human error. The process of converting the old data to a global system means that all of the data will be available for computerized mapping and manipulation. This will give Salvors, Inc., and the State of Florida's Division of Historical Resources greater ability to manipulate the data for research purposes. Under the old system compiling yearly maps to view overall dispersal patterns meant hand plotting and overlays whereas with this new system, it is available with the click of a mouse. The development of this conversion program would have been far more difficult were it not for the availability of the knowledge and experience of people from a variety of fields. It is a program that should prove beneficial to any ongoing project that faces similar dilemmas.

ACKNOWLEDGMENTS

    The authors would like to thank Taffi Fisher and her parents, Mel and Deo Fisher, for their support and encouragement throughout the development of this process. Additionally, we wish to thank Jim Dunbar, archaeologist for the State of Florida's Division of Historical Resources, for his help in obtaining information and digital resources. Finally, this program could not have been developed without the knowledgeable assistance of Al Tello, professional surveyor with Schwebke, Shiskin, and Associates, Inc.

REFERENCES CITED

DUNBAR, JIM 1997 Archaeologist, State of Florida, Division of Historical Resources. Field notes and personal communication.

GAITHER, CATHERINE M. 1996 The Florida East Coast Shipwreck Project; Salvors, Incorporated 1996 Season Report. Florida, State Division of Historical Resources.

GLOVER, THOMAS J. 1995 Pocket ref. Littleton, Sequaia Publishing Inc.

SCHENK, GARY 1997 Lieutenant Commander, U.S. Coast Guard. Officer in charge of the DGPS Management division. Personal communication.

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