Latest Contributions by SimonKettle

The Central European Net (CEN ) The European datum began its life as the Central European First-Order Triangulation Adjustment (Hough, 1947) this project began in April 1945 after the U.S Third Army with the HOUGHTEAM captured the trigonometrical section of the Reichsamt für Landesaufnahme in the town of Friedrichsroda, Thuringia (after the raid in Saalfeld - part 2). This group were taken to Bamberg, in the United States Occupation Zone, for interrogation. It was discovered that the captured Germans, led by Professor Erwin Gigas, had been completing an adjustment of the first-order triangulation of the Greater Reich with the intent to expand this adjustment across the German occupied territories... “…the material of observation for the triangulation of Central Europe available at the end of the war was almost entirely based on new observations. Thus it appeared advisable to readjust this new material, introducing all astronomical data and the base lines remeasured in the meantime. This task was assigned to the Central Survey Office -- now known as the Land Survey Office -- an organization founded in Bamberg by the U S. Army.” Hough 1948 The assigned Land Survey Office (operating under the Army Map Service and U.S Coast and Geodetic Survey) based in Bamberg commenced the adjustment of the first-order triangulation in June 1945 (Whitton, 1952). It was here, overlooked by the US Army and led by Erwin Gigas, that the German trigonometrical section started a review of all points previously calculated highlighting those of sufficient reliability to be used in the first-order triangulation… …by adopting the area of the whole of North Western Germany unchanged [,] use of the numerous astronomic observations was rendered impossible. Therefore, the so arising final German Reiehsdreieeksnetz, though constituting a sufficient basis for Germany herself, was no adequate nucleus for any Central European or even European Network…” Hough 1948 This review of German triangulation points created a list of data points that were originally used as area controls rather than individual arcs.  Selecting from the list of first-order points arcs were chosen and thus the framework for the triangulation adjustment was constructed. The captured Germans at Bamberg performed a least-squares adjustment of Western Europe utilising the HOUGHTEAM’s captured data (see list at the end of this blog). The work plan for the adjustment is laid out as 10 points in Hough, 1947. The adjustment was conducted using methods like the Bowie Junction method (Adams and Oscar, 1930)  which was previously incorporated into the successful adjustment of the North American Datum 1927 (EPSG: 6267). Work was designed to follow a network of arcs following as much as possible meridians and parallels from the existing triangulation. Bowie method is an arc method of adjusting a triangulation network, where length and azimuth of one side of a triangle at every junction between arcs (chains) are assumed correct and carried into a suitable figure of the junction. Directions or angles in arcs between these figures are then calculated, the corrections in the individual chains calculated, and the misclosures passed into the longitudes and latitudes of the initially fixed sides in the junctions by an adjustment of the entire network, using the method of least squares. Locational calculations were incorporated from over 140 years of German records choosing the most logical values for astronomic and angle observations, bases and Laplace azimuths. This incorporation ultimately resulted in the Deutsches Hauptdreiecksnetz (EPSG: 6314). The HOUGHTEAM was disbanded in September 1945 after completing a hugely successful operation for the war effort. During its 11-month mission the collection can be summarised as: Obtained complete geodetic data coverage of four provinces of Germany, discovered in the combat area, delivered direct to the artillery and put into an immediate operational use at the front. Selected captured enemy material shipped to Army Map Service: 202 boxes of geodetic data on 900,000 stations in Europe, giving nearly complete coverage of first, second, third, and fourth control in all German and Allied operational World War II areas of the continent 627 boxes of captured maps, covering approximately the same areas noted above (a) Large quantities of photograph prints and dispositives for portions of above areas 371 boxes of various surveying and photogrammetric instruments, including seven Zeiss stereoplanigraphs Geodetic and cartographic library reference books on all countries in Europe. Acquisition of a nucleus of German geodesists and mathematicians and their removal to the United States Area of Occupation for use on scientific projects by U.S. forces. Technical supervision of the adjustment of European first-order triangulation to a common geodetic datum, ED50. The compilation of the magnetic atlas of Europe, epoch 1944-45, published in 1950 by the Army Map Service. List taken from http://disturbedgeographer.com/?p=199 Whilst German triangulation and locational work was carrying on, the First International Geodetic Conference on the Adjustment of European Triangulation was held on August 7th 1946 in Paris (Hough, 1948). Here it was discussed and the decision made to examine the triangulation adjustment problem of Europe, as a whole, based on joining work currently being carried out on the Central European Adjustment with the ultimate aim of creating a common European Datum. Due to the suffering under occupation of most European nations by the Germans contempt lay at the decision to have them involved in the project. As an alternative the United States chose the engineering task to be carried out by the Army Map Service for the first phase of the European-wide adjustment. Each nation taking part reported their… “observed directions prepared from its latest first-order triangulation observations, its bases, Laplace azimuth, astronomic latitude and longitude observations, descriptions of stations, together with a technical report on the data with recommendations as to its use in the adjustment and relative weights to be accorded” (Hough, 1948) …in total some 1500 first-order stations were contained in the triangulation adjustment. The Central European First-Order Triangulation Adjustment was completed in June 1947. The triangulation arcs can be visualized in Hough, F. W. (1947), The readjustment of European triangulation, Eos Trans. AGU, 28(1), 62–66, doi:10.1029/TR028i001p00062. Expanding the net to create a European Datum Other blocks were intended for connection to the Central European Net, these included a North-European Net, South-West European Net (Whitten, 1952), South East European Net and East European Net (Weber, 2000). The incorporation of these new blocks into the CEN required large amounts of calculations and processing, a primary place to introduce the use of computers. Charles Whitten, the Chief Geodesist at NOAA, and advocate of using computers to process geodetic computations passed on his methods to incorporate the blocks into a single triangulation network created the European Datum. International cooperation The readjustment of the Western European Bloc was completed on June 30 th , 1950 along with the combination of additional “blocks” of retriangulation which resulted in the European Datum 1950 (Hough, 1951). This is one of the first examples of true international cooperation, a project that was born out of the combination of national jealousies and war but resulted in a continent-wide standard in cartography, positional science and the study of the shape of the Earth. Fittingly Floyd Hough wrote appropriate words on the creation of the European datum placing it as one of the major projects of cooperation in European and world history born out of the contrasting chaos of war. “The term ‘cooperation’ is one of the most satisfying and comprehensive words in the English language. If we were to have complete cooperation in all matters between individuals and nations, the acme of human aspiration would be reached; selfishness would be abandoned; universal peace would be a fact; the millennium would be at hand.” Hough, (1951) The triangulation was tied to the International Ellipsoid 1924 (Hough, 1948) built upon some 173 astronomic latitudes, 126 astronomic longitudes and 152 azimuths (Barsky, 1971), no one station can be designated as the datum origin rather a fundamental point is designated at the Helmert Tower in Potsdam, Germany (52°22’51.45”n Latitude 13°03’58.74”e longitude). The design of the first-order triangulation network was designed so that any further triangulation and positional calculations were made using this rigid base, as Hough (1948) described: “Interior triangulation of the area can be adjusted at will to this rigid framework much as the inner portion of a modern steel building is fitted to its network of beams and columns.…” Hough 1948 This was the story about how the European Datum of 1950 was created and has formed the basis of a standard positional framework for the European Continent. The European Datum 1950 Origin: Potsdam (Helmert Tower). 52°22’51.45”n Latitude 13°03’58.74”e longitude Ellipsoid: International 1924 Prime Meridian: Greenwich ... View more

Introduction In Part 1 of this series we saw the setting for the development of a proto European-wide datum by the Germans. This super-National Datum was originally driven from the need of political and military powers in central Europe to comprehensively understand the world around them. Part 2 of the story will concentrate on the Second World War and the Allied military operations that ultimately led to the creation of the European Datum of 1950. “During the war the German Army also connected triangulations of other European nations to [the German national datum]" Hough 1948 Before 1939 the responsibility with Military Survey at the British War Office was vested in the Geographical Section of the General Staff known as MI4. This Section operated under the Director of Operations and Intelligence, was headed by a Royal Engineer Colonel. Typically the Royal Engineer Colonel would be assisted by Royal Artillery and Infantry Officers. This speaks to the principal application of Military Survey, artillery bombardment and infantry navigation. During the inter-war period a Geodetic sub-section was setup to acquire foreign survey and triangulation data. With increasing evidence in the 1930's that Germany was intending and preparing to launch another war a programme to comprehensively map (and update) the whole of north-eastern France and Belgium (at 1:50,000) began. This effort was led by Colonel P. K. Boulnois under War Office control. To see some of these maps have a look at the plates included in the HMSO book. After the Munich Agreement in 1938 and war with Germany becoming inevitable survey officers were assigned to units for mobilisation. To see more detail concerning MI4 and its organisation see HMSO "Maps and Survey" Books from the War Office e.g. Chapter 01. War was declared on Germany on the 1 st September 1939 after the German invasion of Poland. By June 1940 the German’s had triumphed in the Battle of France which Adolf Hitler coined "the most famous victory in history”. During the Battle of France the defending British Expeditionary Force was trapped along the northern coast of France, forced to scramble an evacuation of over 338,000 troops to England in the Dunkirk evacuation. After Dunkirk, Germany dominated Western Europe. The British Military reported to Prime Minister Winston Churchill on 4th October that even with the help of other Commonwealth countries and the United States, it would not be possible to regain a foothold in continental Europe in the near future. Through this interlude where Allied forces fought Axis forces outside of Europe a plan for the invasion of Europe was developed. Born out of war The decision to undertake a cross-channel invasion within the next year was taken at the Trident Conference in Washington in May 1943. Operation Overlord (D-Day) The Allied operation that launched the successful invasion of German-occupied western Europe during World War II. The U.S Office of the Chief of Engineers was deployed in WW2 and one of its commitments was to produce, with cooperation of the other allied groups, through revisions and new position readings (see here), battle field situation maps such as the Normandy Landings on 6th June 1944. Millions of maps were produced throughout the war. The Normandy invasion alone required 3,000 different maps with a total of 70 million copies for keeping the military command fully aware of the operational situation on the ground, in the air and at sea. As the war progressed mapping became more small scale covering larger areas for strategic purposes and it quickly became apparent the lack of geodetic control the allies held over Europe. Probably through national jealously as well as security purposes very little geodetic data was publically available. Army Group, 12 th Engineer Section. August 2, 1944, HQ Twelfth Army Group situation map. Library of Congress Geography and Map Division Washington. http://www.loc.gov/item/2004629096/ HOUGHTEAM (October 1944 to September 1945) This lack of geodetic data was particularly noticeable when pushing through France and into Germany making artillery bombardment inaccurate particularly so where shelling took place over the horizon and without seeing the target through gun sights. In this situation of shells going awry the Office of the Chief of Engineers formed a secret intelligence unit in 1944 (Hough, 1947), from the Army Mapping Service (AMS), that was allowed to operate throughout the European Theatre without restrictions. This unit was known as the HOUGHTEAM, named after U.S. Army Major Floyd W. Hough (Chief of the Geodesy Division of AMS) the unit consisted of a team of 3 commissioned officers, 10 enlisted men and 4 engineer consultants. Their task was to move in behind infantry advancements with the aim of gathering as much cartographic and geodetic information as possible from the enemy, calculating the geodetic transformations into the military mapping system and passing the information onto the army and artillerymen in particular (Hough, 1947). The HOUGHTEAM moved into Europe in September 1944 and set up in Paris to research and identify targets. The team spent time between in Paris as well as on the front typically arriving on the day it was cleared of enemy personnel. By the spring of 1945 the unit was in Germany and working with the 3 rd and 7 th armies, providing materials to survey and artillerymen greatly assisting in battle performance. During this time the team captured vital geodetic material for the occupation of Baden-Baden, Württemberg and Bavaria. “…the war in Europe offered a unique opportunity to exploit known targets and thus to procure from enemy sources captured material of this type both for immediate use of artillery units and for preparation of operational maps.” Hough 1948 Saalfeld, Thuringia The most famous raid of this unit was made in spring of 1945, when rumour had it that a cache of geodetic data and instrumentation was held in secret including data on parts of the USSR invaded by Germany. On chance when visiting a hospital for wounded Germany soldiers this rumour was confirmed which led to the discovery on April 17 th of a huge cache (Bottoms, 1992) in the village of Saalfeld in Thuringia. Interestingly Saalfeld is close (only ~50Km south west) to the town of Jena in the Jena Valley home of Zeiss Optik, the legendary photogrammetry-equipment company that manufactures just the equipment that HOUGHTEAM were hunting, perhaps the team were exploring this area with this knowledge. The cache, found in a remote warehouse on the outskirts of Saalfeld turned out to include the entire geodetic archives of the German Army! (Mindling and Bolton, 2008) In true world war two stories of adventure, the discovery of these documents didn’t finish this story, instead the reader noting the location of Saalfeld and the time of discovery little time was left for grabbing the materials (the advancing Red Army was within days of occupying the town), of which there were 90 tons (Mindling and Bolton, 2008), this equated to around 75 truckloads of geodetic data, maps and instruments that needed transport to Bamburg in the American Occupation Zone. In realising the difficult logistical task ahead for the HOUGHTEAM the Soviets had already began moving in to their zone of occupation. According to the story in Life Magazine (12 th May 1958)... “Hough hurriedly borrowed trucks from a U.S artillery unit and the last of them loaded with data was just clearing one side of the village, rushing for the U.S zone, when the Soviets moved in with their tanks on the other side”. The materials were lifted completely by May 28 th destined for Bamberg and onto Washington for evaluation and archiving. Russian troops arrived in the city the next day. The horde of information was huge including... “triangulation surveys running from Moscow to Vladivostok carried out by Germans in the 1900’s planning of the Trans-Siberian Railway […] first order surveys done by the German army deep within the Soviet Union on the Eastern Front” [as well as] the inaccessible regions of the Communist Bloc countries” (Mindling and Bolton, 2008). The importance of this cache, the realisation that the Soviets were also looking for this cache and its closeness to being compromised by the occupying Soviet forces is suggested by a short quote at a meeting of geodesists in Toronto a few years later where leading Russian delegates mentioned that ...“We have heard a lot about you, Mr. Hough". The data gathered by the HOUGHTEAM throughout the Second World War, data from Spain into Russia formed the beginning of a framework for European wide geodetic datum and framework for ballistic missile target localisation.   Bottoms, D., 1992. Reference paper 79. World War II Cartographic and Architectural Bank of the National Archives Washington, D.C.Mindling, G., and Bolton, R., 2008. U.S. Air Force Tactical Missiles, 1949-1969, The Pioneers. Lulu.com Hough, F., (1948) The adjustment of the Central European triangulation network. Bulletin géodésique 7(1) pp64-93 Mindling, G., and Bolton, R., 2008. U.S. Air Force Tactical Missiles, 1949-1969, The Pioneers. Lulu.com ... View more

Introduction Considering the de facto use of the European datum of 1950 (ED50) throughout the oil industry operating in Northern Europe and the North Sea, I thought it would be interesting to explore this datum’s history and how it came to be the first European continent-wide datum. During the research for this project I uncovered a fasinating story of military intelligence during the Second World War. But first we must set the scene and go back to... European Geodesy at the Turn of the 20th Century “The first-order triangulation of Europe [was completed] over the last 200 years” (Hough, 1948) Prior to World War Two (WW2), Europe was divided into a jumble of independent national and sub-national geodetic datums with their own centre point, triangulation networks and ellipsoids only sometimes connecting to their neighbour’s triangulation effort along the borders. Central Europe during the late 19 th to early 20 th Century is a prime example of this situation. Within the German Confederation and other German States their existed nearly as many datum’s as there were political entities (e.g. Hannover (Gauss, 1821); Bavaria (Soldner, 1808-1828), Prussia (Schreiber, 1975), Württemberg etc). Each of these states contained a survey office directing surveying activities. One of the attempts to connect various datums was during the First German Reich. The Reiehsdreieeksnetz began in Prussia through the Preußische Landesaufnahme (Prussian State Survey) along the Baltic coast as far as Berlin and Lübesk. This triangulation was continued under orders for the survey of Hannover by King George IV (the Hannover triangulation is known as Hannoversche triangle chain). These networks had their origin normally at a major observatory such as Greenwich in London, Pulkovo near St. Petersburg and the Pantheon in Paris. Additionally these datums referenced a variety of ellipsoids making transformation calculations difficult. However a common more fundamental problem summarised by Hough (1948), on the original triangulation of Germany, was that... “…no attempt [was made] to minimize the effect of the deflection of the vertical at the initial station” Hough (1948) ...and therefore errors in position were found at the place of joining to other triangulation networks before any transformation had even been started. The direction of the vertical is defined by a local plumbline, where a survey instrument is set up to measure the horizontal plane that is exactly perpendicular to the vertical. The ellipsoid normal through the same point is perpendicular to the local tangent to the ellipse. However due to variations of gravity, the two are not necessarily coincident. The difference is called deflection-of-the-vertical. Other technical issues existed for trying to connect existing triangulations. The connection between the New Triangulation of France (NTF) Datum and the Belgian Datum of 1927 is an example where the connecting of triangulation networks was insufficiently calculated. A calculation was conducted to find the difference in longitudinal values between Brussels and Greenwich. However this was result was not  incorporated in the joining of the triangulation networks and hence left large errors for the connection of the networks. Germany - An example of “first order triangulation” Since the formation of the First German Reich after unification in 1871, efforts had been made to standardise triangulation across the country beginning to solve some of the issues mentioned above. However, state military survey organisations within the German army produced uncoordinated products throughout the period up to the end of WW1, perhaps indicating disloyalty within the newly unified country. This lack of coordinatation and communication between survey organisations led to some poor quality mapping products being produced during the First World War (see Cruickshank, 2006 for more details). After the First World War and the Treaty of Versailles in 1919 a reduction in military staff led to the demilitarisation of survey groups and the establishment of Reichsamt für Landesaufnahme (Reich Office for State Survey) who led an overhaul of Germany's mulitiple triangulations. A “Neutriangulation” of Bavaria, Baden, Württenberg, Silesia, Pomerania, Mecklenburg and Schleswig-Holstein took place in 1925. This “Neutriangulation” can been noted as a geodetic manifestation in the balance of power from the German Provinces. As political tensions rose during the 1920 – 1930’s, driven in part by the dire economic situation throughout Germany and global depression, extremes in the political arena took hold eventually leading to the events that resulted in the rise of Nazism. Adolf Hitler and the Nazi party took hold of the country via emergency decree on 27 th February 1933 after the Reichstag fire. Development of a Military Survey After the seizing of power by the Nazi’s Germany no longer cooperated according to the Treaty of Versailles, restoring pre-war military institutions and a 9 th Division to the General Staff of the Army, known as the Military Survey (Reichsamt Kriegskarten und Vermessungswesen, see details about the organisation in Cruickshank, 2005). In 1936 Lt. Colonel Hemmerich was appointed Department Chief. Under Hemmerich’s leadership the division dealt with the collection, evaluation, cataloguing and co-ordination of foreign maps and geodetic data, which were collated and reported in the ‘Planhefte’. These became major publications of the German Military Survey. Figure 1 Lt. Colonel Hemmerich (image from http://disturbedgeographer.com) The development of the military survey coincided with early attempts by the Minister of the Interior to create a A Neuordnung des Vermessungswesens (New Order of Survey and Mapping) and by 1936 Survey Commissars were established throughout the regions of the now Third Reich. These commissars were also the local political leaders of individual states. “In 1936 the German main triangulation network was readjusted. Since considerable portions were introduced into the readjustment without any modification and since others had not yet been observed completely, the readjustment could be carried out in parts only.” Hough 1948 An attempt by the German's to create an early equivalent of the European Datum was started in preparation for, and developed throughout,  the Second World War. This was due to the failings of the pre-First World War military survey activity that resulted in poor location plots and the use of old data (see Cruickshank, 2006 for a detailed discussion). During the inter-war period lessons were drawn from the experience of the First World War,  in particular about the importance of collecting up-to-date foreign maps and geodetic data. With war imminent in August 1939, the Military Survey was mobilized and made ready to be attached to the individual commanding authorities within the Germany Army. These geodetic units followed the German army into field of operations that by 1942 occupied the vast majority of Europe and Northern Africa. Figure 2 Maximum Extent of Nazi Germany during World War 2 (image taken from wikipedia) From this military position work began on the establishment of a single unified geodetic framework for the whole of continental Europe (including Northern Africa). Hemmerich’s division uniquely had control of nearly every geodetic department in Europe and thus controlled the expansion of a wealth of knowledge and equipment that would allow the Germans to accurately survey Europe. It is this work, carried out by Hemmerich’s division during the Second World War, that sowed the seeds for the creation of the European Datum. Hemmerich lost his commanding post on 05 th April 1945 where he was resigned to the Führerreserve and later arrested and imprisoned by Allied forces until 04 June 1947. Next time we shall have a look at the development of the European Datum from the side of the allies and explore the story of the military intelligence division code named the HOUGHTEAM. [1]This discrepancy was one of the major factors that prompted the recomputation of all geodetic control in Western Europe after the First World War. The Bonne Grid “New Convention” is also referred to as the “Orange Report Net Grid” and was used through WWII until 1950. References Cruickshank, J. L., 2005. “The Reichsamt fur Landesaufnahme and the Ordnance Survey (Part 1)”. Sheetlines, 72, pp.9-22 Cruickshank, J. L., 2006. “Kaiser Bill thought he knew where you lived”. Sheetlines, 77, pp.5-20 Hough, F., (1948) The adjustment of European first-order triangulation. Bulletin géodésique 7(1) pp35-41 ... View more

Whilst not a blog written out on this site I thought this link was worth sharing. It discusses geodetic integrity and provides some nice insights into geodesy in the Oil and Gas Industry...positional integrity is so important in natural resource exploration and production it forms an essential element of the expensive process of drilling and producing Earth's natural resource. Managing geodetic risks in E&P - Exprodat Blog - "Geodetic integrity plays a small but vital part in the success of every E&P venture. It’s basically like Vitamin C: you don’t need much of it, but you can’t live without it. A deficiency in geodetic controls will slowly lead to guaranteed damage: “geo-scurvy”." The following blog lays out some examples of where positional accuracy has not been good enough outside of the Lake Peigneur Example. Managing geodetic risks in E&P - Exprodat Blog - ... View more

What is an antipode? Any point on the surface of a sphere, in this case the Earth, that lies diametrically opposite from a given point on the same surface, so that a line drawn between the two points through the center of the sphere forms a true diameter (e.g. through the Poles of a Sphere). The Antipodes islands of New Zealand, in the South Pacific, are named after this phenomenon because of there "closeness" to the antipodes of London. The image below shows the relative distribution of landmasses on opposite sides of the Earth. How can you calculate the antipodal point for any point on the Earth's surface? The method using decimal degrees: Take the latitude and convert it to the opposite hemisphere. This is done by multiplying by minus 1 (e.g. -x * -1 = x). The longitude is calculated by taking the maximum possible longitudinal value and subtracting the input longitude value. The if statements allow for "which way round the Earth" the calculation is conducted this is important because the values are bounded to +180 and -180. For example a longitude of -10 has an antipodal location of ((-180) - (-10))*-1 = 170. # Original latitude and longitude values in Decimal Degrees Latitude =  33.918861 Longitude = 18.4233 # Convert latitude to opposite hemisphere (e.g. −x* −1 = x) AntiLatitide = Latitude *-1 print "Antipodal Latitude: " + str(AntiLatitide) # Convert Longitude to opposite hemisphere (e.g. (180 - x)*-1 = y) # Note this binds the maximum values to be -180 and 180 degrees if Longitude > 0:     AntiLongitude = (180 - Longitude)*-1 elif Longitude < 0:     AntiLongitude = (-180 - Longitude)*-1 print "Antipodal Longitude: " + str(AntiLongitude) A result...the Antipodal point of London Combining the above code with the XY to Line tool allows me to construct a geodesic line joining the two points thus producing this result! A free map calculating the antipodal point of any location: http://www.freemaptools.com/tunnel-to-other-side-of-the-earth.html ... View more

A quick history of Geodesy...created by NASA/Goddard Space Flight Center Have  a look at the NOAA Education site for more details! NOAA National Ocean Service Education: Geodesy ... View more

Here's a map and method to find out what's on the opposite side of the world at a particular location. What is an antipode? Any point on the surface of a sphere, in this case the Earth, that lies diametrically opposite from a given point on the same surface, so that a line drawn between the two points through the center of the sphere forms a true diameter (e.g. line through the Poles of a Sphere). The Antipodes islands of New Zealand, in the South Pacific, are named after this geodetic feature because of there near opposite location to London. Calculating the antipodal point for any point on the Earth's surface can be summarized in the following Python code: The method using decimal degrees: Take the latitude and convert it to the opposite hemisphere. This is done by multiplying by minus 1 (e.g. -x * -1 = x). The longitude is calculated by taking the maximum possible longitudinal value and subtracting the input longitude value. The if statements allow for "which way round the Earth" the calculation is conducted this is important because the values are bounded to +180 and -180. For example a longitude of -10 has an antipodal location of ((-180) - (-10))*-1 = 170. # Original latitude and longitude values in Decimal Degrees Latitude =  33.918861 Longitude = 18.4233 # Convert latitude to opposite hemisphere (e.g. −x* −1 = x) AntiLatitide = Latitude *-1 print "Antipodal Latitude: " + str(AntiLatitide) # Convert Longitude to opposite hemisphere (e.g. (180 - x)*-1 = y) # Note this binds the maximum values to be -180 and 180 degrees if Longitude > 0:     AntiLongitude = (180 - Longitude)*-1 elif Longitude < 0:     AntiLongitude = (-180 - Longitude)*-1 print "Antipodal Longitude: " + str(AntiLongitude) A result...the Antipodal point of London Combining the above code with the XY to Line tool allows me to construct a geodesic line joining the two points thus producing this result! A free map calculating the antipodal point of any location: http://www.freemaptools.com/tunnel-to-other-side-of-the-earth.htm ... View more

An easier place to search for coordinate systems... If you need a quick and easy to use resource for coordinate systems search try: EPSG.io. This is an open source web-service providing a database based on the official EPSG database that is maintained by OGP Geomatics Committee. You can quickly search for an area, name and type like any other web-search engines. For Example searching "United Kingdom" and click on the British National Grid result produces the following page: See below for a British National Grid example: OSGB 1936 / British National Grid - United Kingdom Ordnance Survey - EPSG:27700 Some of the Key Features: Easy full text search for the complete database of coordinate systems from EPSG Short URLs that reference the EPSG code e.g. http://epsg.io/27700 Area of use for any CRS referenced on an embedded map Export definitions in various formats Check it out...it's free ... View more

How to calculate a distance over a surface A point-to-point distance taken from a map does not provide a true measurement of the distance between those points; the intervening topography has to be taken into account...Calculating True Distance Over a Surface - Blogs -‌ http://www.exprodat.com/Blogs/blog_Plotting-Dip-and-Strike-Readings.htm Making Elevation Profiles in 3D Analyst An elevation profile charts the elevation along a straight or irregular line...Making Elevation Profiles in 3D Analyst - Blogs - ... View more